Design of automotive structural components using high ...

Missouri University of Science and Technology Missouri University of Science and Technology

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Center for Cold-Formed Steel Structures Library Wei-Wen Yu Center for Cold-Formed Steel Structures

01 Jan 1989

Design of automotive structural components using high strength Design of automotive structural components using high strength

sheet steels the effect of strain rate on mechanical properties of sheet steels the effect of strain rate on mechanical properties of

sheet steels sheet steels

Maher Kassar

Wei-wen Yu Missouri University of Science and Technology, [email protected]

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Civil Engineering Study 89-2Structural Series

Eleventh Progress Report

DESIGN OF AUTOMOTIVE STRUCTURAL COMPONENTSUSING HIGH STRENGTH SHEET STEELS

THE EFFECT OF STRAIN RATE ON MECHANICAL PROPERTIES OF SHEET STEELS

by

Maher KassarResearch Assistant

Wei-Wen YuProject Director

A Research Project Sponsored by the American Iron and Steel Institute

January 1989

Department of Civil EngineeringUniversity of Missouri-Rolla

Rolla, Missouri

ii

TABLE OF CONTENTS

Page

LIST OF TABLES iv

LIST OF FIGURES vii

I. INTRODUCTION.............................................. 1

II. REVIEW OF LITERATURE..................................... 3

A. MECHANICAL PROPERTIES OF SHEET STEELS....... 3

1. Engineering Stress-Strain Curves , 3

2. True Stress-Strain Curves................ 7

B. STRAIN RATE 9

1. Strain-Rate Dynamic Testing. . . . . . . . . . . . . . . . . . . . . . . . 9

2. Effect of Strain Rate on Mechanical Properties..... 11

a. Structural Steels and High Strength Steels...... 11

b. Stainless Steels................................ 18

c. Aluminum........................................ 19

~. Strain-Rate History Effect........ 20

III. EXPERIMENTAL PROGRAM 24

A. MATERIALS 24

B. UNIAXIAL TESTS 24

1. ASTM Specifications..................... . . . . . . . . . . . 25

2. Specimens........................................... 25

3. Equipment.......................................... 26

4. Procedure.......................................... 28

TABLE OF CONTENTS (Cont.)

C. RESULTS

1. Stress-Strain Curves .

2. Mechanical Properties .

a. Yield Strength or Yield Point .

b. Ultimate Tensile Strength .

c. Ductility .

D. DISCUSSION .

1. Mechanical Properties .

a. Yield Strength or Yield Point .

b. Ultimate Tensile Strength .

2. Strain-Rate Sensitivity .

IV. CONCLUSIONS .

ACKNOWLEDGMENTS .

REFERENCES .

iii

Page

30

30

31

32

33

33

33

33

34

34

35

37

39

40

iv

LIST OF TABLES

Table

2.1

2.2

Dynamic Aspects of Mechanical Testing30 .

Experimental Techniques for High Strain Rate Testing32

Page

45

46

2.3 Values of Strain Rate Sensitivity Exponent, m, and

Constant C of Yield Strength of the Tested Materials40 46

2.4 Standard Strain Rate Sensitivity and New Strain Rate

40Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.5 Strain Rate Sensitivity for Different Microstructures

Determined by Strain Rate Jump Tests at 6.7 x 10-5

-1 -4 -1 10-3-1sec , 6.7 x 10 sec , and 6.7 x sec (Ref. 46) ... 47

3.1

3.2

Chemical Compositions of the Sheet Steels Used .

Classification of the MTS Extensometer .

48

48

3.3 MTS Transducer Ranges and the Corresponding Load,

Strain, or Displacement Values.. 49

3.4 Ramp Time 1 and the Corresponding Strain Rate . 49

3.5 Tested Mechanical Properties of 100XF Sheet Steel,

Virgin Material.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


Virgin Material '.' . . . . . . . . . 51


2% Cold Stretched, Non-Aged Material...................... 52

3.8 Tested Mechanical Properties of SOXF Sheet Steel,

8% Cold Stretched, Non-Aged Material.................. .... 52

v

LIST OF TABLES (cont.)

Table Page


2% Cold Stretched, Aged Material............... 53


8% Cold Stretched, Aged Material............. .... .... ..... 53


Virgin Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54


2% Cold Stretched, Non-Aged Material............... 55


8% Cold Stretched, Non-Aged Material.... 55


2% Cold Stretched, Aged Material..................... ..... 56


8% Cold Stretched, Aged Material , 56

3.16 Average Tested Mechanical Properties of 100XF Sheet Steel,

Longitudinal Tension, Virgin Material.. 57


Transverse Tension, Virgin Material. . . . . . . . . . . . .. . . . . . . . . . 57


Longitudinal Tension...................................... 58


Transverse Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

vi

LIST OF TABLES (Cont.)

Table Page


Longitudinal Tension.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60


Transverse Tension.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.22 Ratios of Dynamic to Static Mechanical Properties for

Three Sheet Steels Based on Tables 3.16 to 3.21.......... 62

3.23 Values of Strain Rate Sensitivity m for Three Sheet

Steels Based on the Changes of the Yield Stresses at

Different Strain Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

vii

LIST OF FIGURES

Figure Page

2.1 24Stress-Strain Curves of Carbon Steel Sheets . 64

2.2 Determination of Yield Point for Gradual-Yielding

24Steel , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

662.4

2.3 Effects of Strain Hardening and Strain Aging on Stress-

Strain Characteristics24..................... 65

Influence of Bauschinger Effect28 .

2.5 Comparison of Engineering and True Stress-Strain

25Curves " . . . . . . . . . . . . . . . . . . . . . 66

2.6 Effect of Strain Rate on Stress-Strain Curve

34for Structural Steel....................... 67

2.7 True Yield Stresses at Various Strains Versus Strain

37Rate for a Low-Carbon Steel at Room Temperature 67


o 37 'Rate for a Low-Carbon Steel at 200 C...... 68


o 37Rate for a Low-Carbon Steel at 400 C...... 68


o 37Rate for a Low-Carbon Steel at 600 C...... 69

o. 0

2.11 Effect of Strain Rate at -50, 75, and 600 F on the

39Yield and Tensile Strengths of USS COR-TEN Steel 70000

2.12 Effect of Strain Rate at -50, 75, and 600 F on the

Yield and Tensile Strengths of USS TRI-TEN Steel39 ..... 71

viii

LIST OF FIGURES (Cont.)

Figure Page

2.13 Effect of Strain Rate on Mechanical Properties of a

40HSLA Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

2.14 Strain-Rate Changes During Tensile Test, Four Strain

-1 -2 -3 -4-1Rate Shown Are 10 , 10 ,10 ,and 10 sec

(Ref. 41).............................................. 72

2.15 Effect of Crosshead Speed on Yield Behavior and Tensile

42Strength

2.16 Stress-Strain Curves for SA-106 Carbon Steel Pipe43

73

73

2.17 The Variation of the Strain Rate Sensitivity (m-value)

With Strain Rate44. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.18 Stress-Strain Curves for High Strength Steel at Varying

Strain Rate45 •.................................... _. . . . . 74

2.19 Dynamic Stress-Strain Curves for AISI Type ,304

Stainless Steel47 ...................................... 75

2.20 Dynamic Stress-Strain Diagram of AISI Type 304L

Stainless Steel47 ...................................... 75

2.21 Dynamic Stress-Strain Diagram -of AISI Type 347

Stainless Steel47 ...................................... 76

2.22 The Ambient-Temperature Yield Stress of Anneald Type

21-6-9 Stainless Steel As a Function of Strain Rate48 .. 76

2.23 Analysis of the Uniaxial Stress, Strain, and Strain Rate

Data for Aluminum 1060-049 ..... 77

ix


Figure Page

2.24 Dynamic Yeild Stress (Minus the Static Yeild Stress)

50Versus Strain Rate for Steel......................... 78

2.25 Dynamic Yeild Stress (Minus the Static Yeild Stress)

Versus Strain Rate for Aluminum50 ...................... 78

2.26 Strain and Strain-Rate Dependence of the Flow Stress of

High-Purity Aluminum51 . . . . . . . . . . .. . . . . .... .... .. .. .. . . . 79

2.27 Strain and Strain-Rate Dependence of the Flow Stress

of Aluminum 1060-051 ................................... 79

2.28 Strain and Strain-Rate Dependence of the Flow Stress

51of Aluminum 1100-0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

2.29 Compression Tests on Aluminums 7075-T6 and 6061-T653 ... 80

2.30 Strain-Rate Sensitivity of Aluminum Alloys31........... 80

2.31 Cyclic Static-Dynamic-Static Loading for Aluminum52 .... 81

2.32 Cyclic Dynamic-Static-Dynamic Loading for Aluminum52 81

2.33 Cyclic Dynamic Loading for Aluminum52 . 82

2.34 Effect of Alteration of Strain Rate Upon Flow Stress

( Static-Dynamic )55................................... 83

2.35 Effect of Alteration of Strain Rate Upon Flow Stress

( Dynamic-Static )55................................... 83

2.36 Results of Constant and Incremental Strain-Rate Tests on

571020 Hot Rolled Steel (HRS) . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.37 Results of Constant and Incremental Strain-Rate Tests on

571080 Cold Rolled Steel (eRS) 84

x


Figure Page

2.38 Tensile True Stress-True Strain Curves at Ambient

Temperature for Monotonic Loading to Fracture at a

-1 -1Strain Rate of O.OO~ sec (Curve A) and 500 sec

(Curve B), and for Quasi Static Prestraining Followed

54by Dynamic Reloading to Fracture 85

3.1 11Location of Tension and Compression Coupons 86

3.2 Nominal Dimensions of Tension Coupons Used for 100XF,

1150XF, and 35XF 87

3.3 Material Test System (MTS) 880 Used for Tension Tests.. 88

3.4 MTS 880 Test Controller and Function Generator , 89

3.5 Data Acquisition System.......................... . . . . . . . 90

3.6 Data General Graphic Display Terminal............. ..... 91

3.7 Data General MV-10000 Mini Computer............. 92

3.8a Test Setup Showing the Attachment of Extensometer...... 93

3.8b Test Setup Showing the Attachment of Extensometer...... 94

3.9 IBM PS/2 Model 30 Personal Computer with IBM Color

Plotter and NEC Pinwriter P5XL Printer......... 95

3.10 MTS 880 Automated Test System and Software Overview.... 96

3.11 MTS 880 Test Controller Servo Control Loop............. 97

3.12 Typical Test Function Generator Ramp Waveform.......... 98

3.13 Strain-Time Curve for 100XF-LT-l,(Virgin Material)..... 99

3.14 Strain-Time Curve for 100XF-LT-3,(Virgin Material)..... 100

xi


3.18

3.17

3.15

3.16

Figure

Strain-Time Curve for 35XF-LT-7,(Virgin Material) .

Stress-Strain Curves for 100XF-LT-1. 100XF-LT-4.

and 100XF-LT-6.(Virgin Material) .

Stress-Strain Curves for 100XF-TT-2. 100XF-TT-4.

and 100XF-TT-S.(Virgin Material) ,

Stress-Strain Curves for 50XF-LT-1, SOXF-LT-4.

and 50XF-LT-9,(Virgin Material) .

3.19 Stress-Strain Curves for SOXF-TT-1, SOXF-TT-6.

Page

101

102

103

104

and 50XF-TT-9, (Virgin Material)... . . . . . . . . . . . . . . . . . . . . . 105

3.20 Stress-Strain Curves for SOXF-LT-1, SOXF-LT-4. and

SOXF-LT-S, (2% Cold-Stretched,Non-Aged Material)........ 106

3.21 Stress-Strain Curves for SOXF-TT-1 and SOXF-TT-3.

(2% Cold-Stretched. Non-Aged Material)". . . . . . . . . . . . . . . . . . 107

3.22 Stress-Strain Curves for 50XF-LT-1, 50XF-LT-4, and

SOXF-LT-6.(8% Cold-Stretched,Non-Aged Material)........ 108

3.23 Stress-Strain Curves for 50XF-TT-1 and 50XF-TT-3,

(8% Cold-Stretched. Non-Aged Material)............ 109

3.24 Stress-Strain Curves for 50XF-LT-1. SOXF-LT-3.and

50XF-LT-6. (2% Cold-Stretched. Aged Material).......... 110

3.25 Stress-Strain Curves for 50XF-TT-1 and 50XF-TT-3.

(2% Cold-Stretched, Aged Material)...... 111

3.26 Stress-Strain Curves for 50XF-LT-l. 50XF-LT-3, and

SOXF·LT-6, (8% Cold-Stretched, Aged Material).... 112

xii

LIST OF FIGURES (Cant.)

Figure Page


(8% Cold-Stretched, Aged Material)............ 113

3.28 Stress-Strain Curves for 35XF-LT-l, 35XF-LT-4,

and 35XF-LT-9,(Virgin Material)............... 114

3.29 Stress-Strain Curves for 35XF-TT-1, 35XF-TT-4,

and 35XF-TT-5,(Virgin Material)........................ 115


35XF-LT-5,(2% Cold-Stretched,Non-Aged Material)........ 116


(2% Cold-Stretched,Non-Aged Material)........... 117


35XF-LT-5,(8% Cold-Stretched,Non-Aged Material)........ 118


(8% Cold-Stretched,Non-Aged Material)........ 119


35XF-LT-6, (2% Cold~Stretched, Aged Material).. 120


(2% Cold-Stretched, Aged Material) ~........ 121


35XF-LT-6, (8% Cold-Stretched, Aged Material).......... 122


(8% Cold-Stretched, Aged Material)..................... 123

xiii


Figure Page

3.38 Effect of Strain Rate on the Yield Strength of 100XF

Steel in Longitudinal and Transverse Directions....... ... 124

3.39 Effect of Strain Rate on the Yield and Ultimate Strengths

of 50XF-LT Steel, (Virgin Material)...................... 125


of 50XF-LT Steel, (2% Cold-Stretched, Non-Aged Material).




of 50XF-LT Steel, (2% Cold-Stretched, Aged Material) .....


of 50XF-LT Steel, (8% Cold-Stretched, Aged Material) ... :.


126

127

128

129

of 50XF-TT Steel, (Virgin Material)..... 130


of 50XF-TT Steel, (2% Cold-Stretched, Non-Aged Material).




of 50XF-TT Steel, (2% Cold-Stretched, Aged Material) .....


131

132

133

of 50XF-TT Steel, (8% Cold-Stretched, Aged Material)..... 134

xiv


Figure Page


of 35XF-LT Steel, (Virgin Material).................... 135




of 35XF-LTSteel, (8% Cold-Stretched, Non-Aged Material).






136

137

138

139

of 35XF-TT Steel, (Virgin Material).............. 140






of 35XF-TT Steel, (2% Cold-Stretched, Aged Material) .....


141

142

143

of 35XF-TT Steel, (8% Cold-Stretched, Aged Material)..... 144

3.59 Stress-Strain Curves for 50XF-LT Steel at Strain Rate of

0.0001 in. lin. Isec , . . . . . . . . . 145

xv


Figure Page


0.01 in./in./sec....................................... 146


1.0 in./in./sec........................................ 147

1

I. INTRODUCTION

During recent years, automotive manufacturers have produced lighter

vehicles for the purpose of achieving fuel economy. To accomplish the

construction of such automobiles, high strength sheet steels with various

yield strengths up to 190 ksi have been used for auto parts and structural

1-9components

In order to provide some technical assistance for the design of such

high strength steels, the first edition of the "Guide for Preliminary

Design of Sheet Steel Automotive Structural Components" was issued by

American Iron and Steel Institute (AISI) in February 1981. 10 The use of

the Guide was discussed by Errera at the SAE International Congress and

Exposition held in Detroit, Michigan in February 19825

. In view of the

fact that the design information contained in this document can be used

only for sheet steels with yield strengths of up to 80 ksi, a research

project has been conducted at the University of Missouri-Rolla (UMR) since

1982 to study the structural strength of automotive components using high

strength sheet steels. In the first phase of the UMR program, typical

mechanical properties and representative stress-strain curves were es-

tablished by a series of static tests for different grades of sheet steels

with yield strengths ranging from 49 to 164 ksi. The second phase of the

UMR project was directed toward the web crippling strength of beam webs

and the strength of members consisting of flat and curved elements. The

11-20research findings were presented in ten progress reports In addi-

tion, the effective design widths of high strength cold-formed steel

. t d21members were also invest1ga e Some of the research results were used

2

in the first edition of the AISI Automotive Steel Design Manual published

in 198659 . This Manual brings together material properties, product

design, and manufacturing information to make the most effective use of

sheet steels with yield strengths of up to 140 ksi. The contents and use

of the Design Manual were discussed by Cowie and Lutz at the 1987 SAE

International Congress and Exposition22 - 23

Because the previous UMR studies were limited only to the tests

subject to static loads and it is well known that the yield strength,

tensile strength, and the stress-strain relationship of sheet steels are

affected by the rate of strain used for the tests, additional research

work was conducted at the University of Missouri-Rolla in 1988. This

study primarily involved the experimental determination of the dynamic

material properties of three selected sheet steels with nominal yield

strengths ranging from 35 to 100 ksi.under different strain rates. The

-4strain rates ranged from 10 to 1.0 in./in./sec. All tests were per-

formed at UMR Engineering Research Laboratory by using the new MrS 880

Test System. The test data developed from this work will be used for the

evaluation of future member tests on the design of automotive components.

This study began with a review of the available literature on

stress-strain curves of sheet steels and the effects of the strain rate

and strain rate history on the mechanical properties of sheet steels. The

literature survey is presented in Section II. Section III presents the

detailed information obtained from 124 tension tests. This Section also

discusses the strain rate effects on the mechanical properties of the

sheet steels tested. Finally, the research findings are summarized in

Section IV.

3

I I. REVIEW .OF LITERATURE

A. MECHANICAL PROPERTIES OF SHEET STEELS

1. Engineering Stress -Strain Curves. The stress -strain curve is

the relationship between the stress and the corresponding strain. For

engineering stress-strain curves, the stress, f, is measured by the

load, P , divided by the original, unreduced area, A ,a of the spec-

imen, i. e.

f = P / Ao(2.1)

The engineering strain, e, is the difference between the original,

unreduced gage length, t ,and the deformed length, t ,. divided by thea

original length, i.e.

For high strength sheet steels, the two basic types of engineering

curve is based on theThe classification of the f-e

stress-strain (f-e) curves are gradual and sharp yielding as shown in

Figure 2. 124

yielding behavior of the steel. As a general rule, hot-rolled sheet steels

tend to be sharp yielding (Figure 2.1(a)) while those sheet steels that

are cold-rolled or cold reduced in thickness are gradual yielding (Figure

2.1(b)).

Sharp yielding steels typically exhibit an upper and lower yield

point (points A and B in Figure 2.1(a), respectively). Because the upper

yield point is much more sensitive to strain rate, specimen alignment,

and shape of the tested cross-section than the lower yield point, the

lower yield point is customarily used to represent the yield stress of

b · t t statl.·c loadl.·ng25 ,26.sharp yielding sheet steels su Jec 0

4

In view of the fact that gradual yielding steels do not have such

an obvious yield point, their yield strength is defined by either an

offset method or the strain-under-load method as described in ASTM

Standard A370. The offset method consists of drawing a straight line

parallel to the initial linear portion of the f-e curve at a given strain

offset. For this study, an offset of 0.2 percent strain was chosen. Using

this method, the intersection of the straight line and the f-e curve de

fines the yield strength as shown in Figure 2.2(a)24. The strain-under-

load method defines the yield point as the stress corresponding to some

fixed value of strain. The strain usually chosen is 0.5 percent as shown

in Figure 2.2(b)24.

The slope of the linear portion of the f-e diagram is known as the

modulus of elasticity, E. The point beyond which the f-e curve becomes

nonlinear is called the proportional limit (point A in Figure 2.1(b)).

For sheet steels, whether they are gradual or sharp yielding, the pro-

portional limit may be determined by the 0.01 percent offset method in

exactly the same manner that the yield stress was defined for gradual

yielding sheet steels, except that the offset is now only 0.01 percent.

Once the specimen is strained beyond the yield point, the load car-

rying capacity of the steel continues to increase slightly in spite of

the fact that the cross-sectional area of the specimen is continually

decreasing. Since engineering stress is calculated based on the original

area, there must be some other phenomenon occuring that causes the ·in-

crease in load carrying capacity. This phenomenon is commonly referred

to as work hardening or strain hardening and may be explained by dislo-

t · h 25ca ~on t eory . The rate of strain hardening is high at the onset of

5

yielding. However, as the strain is increased, the amount of strain

hardening decreases to the point where it can no longer offset the con-

tinuous reduction of specimen area. At that point the maximum possible

stress or ultimate strength, F , is reached in the steel. Furtheru

elongation of the tensile specimen results in localized straining of a

small portion of the gage length known as necking27 The necked region

continues to decrease in area at a faster pace than the strain hardening

can keep up with which results in a decrease in the total load that the

specimen can withstand. This unloading results in all areas of the spec-

imen, other than the necked region, being unloaded back into the elastic

range while the stress in the necked area continues to increase until

25fracture .

A material property that is dependent on the strain that a material

can withstand up until fracture-is ductility. Ductility is commonly de-

fined by two methods. They are

a)

b)

total elongation (percent) = 100*( t f - to)/to' and

reduction in area (percent) = 100*(Ao-Af )/Ao

(2.3)

(2.4)

In the above equations, the f subscripts denote the values at fracture

Although standard values are usually used for to andAo ' it is important

to realize that either method of measuring ductility will give varying

25results if non-standard values of to and Ao are used .

Another important material property yet to be discussed is the ca

pability of a material to absorb energy without fracture. Energy absorp

tion is especially important in the design of structures such as

28automobile components, highway guard rails, and machinery guards For

a particular material the energy absorption is given by the area under

6

the stress-strain curve from zero loading to fracture. Therefore the

amount of absorption depends not only on the yield and ultimate strength

but on the total elongation of the material as well.

Figure 2.324

illustrates the effect on the stress-strain curve of

stressing a given sheet steel beyond the yield stress and then removing

the load before failure. As shown by curve 2 of Figure 2.3, if the load

is removed at point C along the stress-strain curve, then the unloading

path follows a line very nearly the slope of the elastic portion of the

stress-strain diagram. The elastic strain, E , recovered upon unloadinge

from point C is equal to the stress at C, f ,divided by the modulusc

of elasticity, E, or E = f IE . The permanent set or plastic strain,e c

Ep

, is represented by the line AD. Curve 3 represents the stress-strain

curve if reloading occurs immediately and Curve 4 if reloading occurs

after strain aging. It can be seen that, if the material is immediately

reloaded (Curve 3), strain hardening produces an increase in apparent

yield strength and a decrease in ductility as compared to the virgin ma-

terial. If reloading occurs after a period of time, a phenomenon known

as strain aging occurs (Curve 4) which results in an even higher value

of yield stress and tensile strength; however, the ductility decreases

even more.

If the reloading from point D is opposite the original loading (e.g.

compression instead of tension) as shown in Figure 2.428

, the new value

of the yield point G might be lower than the original yield point B. Also,

if this load is reversed so that the load is now in the original direc-

tion, the yield point H may be lower than the original yield point B. This

7

effect was observed by Johann Bauschinger, of Germany, in 1886 and is

commonly referred to as Bauschinger Effect 28.

2. True Stress-Strain Curves. The exact or true stress, 0, in a

tensile test is equal to the load, P, divided by the actual area, A, as

follows:

o = P / A (2.5)

By comparing the shape of the true and engi-

As the load increases and thus the cross-sectional area decreases, the

corresponding true stress will be greater than the engineering stress

computed for the same loading. Since there is no appreciable change in

area in the elastic range, the true and engineering stresses are practi-

cally identical. However, as the stress reaches the inelastic range, the

strain increases and thus the area decreases much more for a given stress

increase than in elastic range. Therefore, the difference between true

and engineering stresses become apparent in the inelastic range as can

be seen in Figure 2.525

neering stress-strain diagrams in the inelastic range, it can be seen that

the difference between the two curves continually increases with

increassing strain. It is also interesting to note that the true stress

steadily increases up to fracture. This type of continuous increase of

the o-e curve seems much more logical than the engineering curve because

it is difficult to imagine the stress actually decreasing in a material

that is tested from zero load to fracture.

The true stress and strain may be related to the engineering stress

and strain by assuming constancy of volume of the specimen. In other

words, the initial volume,

volume, At. Thus

At, should be equal to the instantaneous00

A i = A io 0

A = A iIi = A Ciol ( io (l+E))000

A = A 1(l+E)o

Therefore the true stress, cr, may be given as

8

(2.6)

(2.7)

cr = PIA = P (1+E)1 A = f(l+E)o . (2.8)

The true or natural strain, E', can be determined from the differ-

ential increment of strain, dE', as

dE' = dtlt

where t is the actual length to which di is added.

elongation becomes

(2.9)

The total unit

i

e' =j dill =io

In(ili ) = In( 1+E )o

(2.10)

Equations 2.8 and 2.10 obviously may be used in converting from en

gineering stress and strain to true stress and strain26

. After necking,

the above equations are not valid. Since the length changes within the

gage length are now localized in the necked region, the engineering

strain, which assumes a uniform strain over the gage length, cannot be

used to calculate the true stress and natural strain. An alternate method

for computing the true stress in the necked region is described by Hosford

and Caddel on page 53 of Ref. 25.

From inspecting the above equations for stress and strain, it can

be seen that for very small strains, such as those occuring in the elastic

range, the engineering and true stresses and strains will be practically

the same. Therefore, for properties such as yield stress and modulus of

elasticity, the engineering values should be sufficiently accurate. How-

9

ever, for studies using stress-strain data in the plastic range, "the true

stress and strain are more meanl."ngful than . .. engl.neerl.ng stress and

strain25."

B. STRAIN RATE

Strain rate (e')is the rate of change of strain (e) with respect

to time (t)

e = de / dt (2.11)

where e can be either the engineering or the true strain. For a constant

strain rate experiment, the, strain rate is simply the total strain divided

by the duration of the test29 :

e' = e / t

The unit of strain rate is the inverse of time sec-1

(2.12)

For the design of economical and safer cars, understanding of the

effects of impact loading, controlled crush and energy absorption on

automobile components is essential. Since these design considrations in-

volve dynamic loading, the effects of strain rates on the mechanical

properties of the sheet steels must be known in order for the engineer

to design a safe and efficient vehicle and moreover to reduce the need

for conducting expensive full-scale dynamic testing1

1. Strain Rate Dynamic Testing. Some considerations in strain rate

dynamic testing have been summarized by Lindholm'30 as shown in Table

30 -6 -5 -12.1 . At strain rates of the order of 10 to 10 sec the creep be-

havior of a material is the primary consideration, usually at elevated

temperature for metals, for which the creep-type laws are used to describe

the mechanica1 behavior31

. At a higher strain rate, in the range of

10-4 to 10-3 sec-1, ,the uniaxial tension, compression, or quasistatic

10

stress-strain curve obtained from constant strain-rate-test is used to

describe the material behavior. Although the quasistatic stress-strain

curve is often treated as an inherent property of a material, it is a

valid description of the material only at the strain rate at which the

test was conducted. When higher strain rates are encountered, the stress-

strain relationships may change, and alternate testing techniques have

to be employed. Constant strain-rate tests can be performed with spe-

cialized testing apparatus at strain rates up to approximately 104

-1 -1 2 -1sec The range of strain rates from 10 to 10 sec is generally re-

ferred to as the intermediate or medium strain-rate condition. It is

within this condition that strain- rate effects first become a consider-

ation in most metals, although the magnitude of such effects may be quite

31small or even nonexistent in some cases Strain rates of 103 sec-lor

higher are generally treated as the range of high strain-rate response,

although there are no precise definitions as to strain-rate conditions

and care must be taken in evaluating the test data to note the actual

strain rates rather than the terminology. It is within the high strain-

rate condition that inertia and wave-propagation effects first become

important in interpreting experimental data. At these high rates, care

must be taken to distinguish between average values of stress and strain

and local values that may be the result of one or more high-intensity

h t · I At the stra1'n rate of 105

stress wave propagation throug a ma er1a .

sec-1 or higher, it is generally dealing with shock waves propagating

through materials that are in a state of uniaxial strain. At these very

high rates and the associated very short time scale involved,

31thermodynamic considerations become important 'Table 2.232 shows the

11

experimental techniques that are used for various strain rate conditions

in compression, tension, and shear testing. Unfortunately, there are no

standardized procedures for high strain rate tests. Many different ma-

chines, specimen configurations, and measuring devices have been used.

This makes a comparison of the test results of different investigators

difficult and often makes it impossible to compare the properties of a

group of materials since the behavior of a material is quite often in-

fluenced by the experimental conditions. It is important that the true

behavior be studied by different methods to isolate any excessive influ

ence of the technique and to verify the validity of the data33 .

2. Effect of Strain Rate on Mechanical Properties. The effect of

strain rate on mechanical properties varies for each material. These

general trends are well known, but because the magnitude of the change •

in properties with strain rate is so varied for each material, no general

quantitative theory exists that satisfactorily predicts the mechanical

b h 'd 31e avior of materials over a WI e range

For most materials, mechanical properties tend to increase at higher

strain rates. The following sections discuss the effect of strain rate

on mechanical properties of structural and high strength sheet steels,

stainless steels, and aluminum.

a. Structural Steels and High Strength Steels. The effect of the

strain rate on the mechanical behavior of mild steel has long been a

Subject of interest to researchers since the beginning of this century.

Figure 2.634 shows stress-strain curves obtained from structural steels

tested at various strain rates. Clearly, the yield strength of the mate-

12

rial increases as the strain rate increases. This is the most consistently

observed effect of strain rate on material properties.

Historically, Ludwik was the first to study the effect of the speed

of streching upon the stress at which a metal yields35 . He found a loga

rithmic relation between the stress at which a metal yields and the strain

rate as early as 1909.

In 1925, Korber and Storp compared impact tests with ordinary static

tests for various metals35 . These tests showed a considerable increase

in the yield stress in the more rapid tests.

The effect of changing the speed of deformation on various metals

were studied by Prandtl and his associates in 193235 . Their results were

in agreement with the relation found by Ludwik.

In 1937, Winlock and Leiter investigated the effect of the strain

rate upon the yielding of deep-drawing sheet stee136

. Their results showed

that the yield stress and the corresponding elongation were considerably

affected by the strain rate. The ultimate strength was also influenced

but to a smaller extent than the yield strength.

In the 1940s, Manjoine37 studied the relationships between strain

rate, temperature, and the material properties of mild steels. Figure

2.737 illustrates the true yield stresses at various strains for a low-

carbon steel at room temperature. It can be seen that between strain rates

of 10-6 sec-1 and 10-3 sec- 1 yield stress increases only by 10%. Above

the strain rate of 1.0 sec-I, however, the same increase of strain rate

doubles the yield stress. For the data shown in Figure 2.7, at every level

of strain the flow stress increases with increasing strain rate. However,,

a decrease in strain~hardening rate is exhibited at higher strain rate.

13

The results of the combined effects of strain rate and temperature at 200,

400, and 600 C are shown in Figures 2.8 to 2.1037 , respectively. At the

highest temperature of 600 C, yield strength increases with increasing

strain-rate, but strain hardening increases (rather than decreases) with

increasing strain rate. At intermediate temperatures shown in Figures

2.8 and 2.9, however, regions of negative strain rate sensitivity are

visible; that is, under certain conditions of strain, strain rate, and

temperature, the flow stresses of carbon steels decrease with an increase

in strain rate. This is in contrast with the usual strain rate effect38

.

I 1963 U · d S SIC . 39 d dn ,n1te tates tee orporat10n con ucte numerous tests

on high-strength, low-alloy steels (COR-TEN and TRI-TEN) for the purpose

of studying the effects of the strain rate and temperature on the tensile

properties of these steels. The tests were conducted at strain rates of

3 x 10-5 in./in./sec, 5 x 10-3 in./in./sec., and 1.0 in./in./sec at tem-

perature of -50 F, 75 F (room temperature), and 600 F. The results ob-

tained from this investigation indicated that as the strain rate was

increased at -50 F and at 75 F, the tensile strength and the 0.2 percent

offset yield strength increased as shown in Figures 2.11 and 2.1239

.

However , as the strain rate increased at 600 F, the tensile strength

decreased. The ductility of the COR-TEN steel, as measured by percent

elongation and reduction of area, did not appear to be strain-rate sen-

sitive at -50 F and room temperature, but at 600 F, the-reduction of area

for the fastest rate was higher than that for the slowest rate.The percent

elongation of the TRI-TEN steel appeared to be somewhat strain-rate de

pendent, decreasing slightly as the strain rate increased.

14

In 1974, Chatfield and Rote40 completed a comprehensive report con-

cerning the influence of strain rate on the mechanical properties of high

strength, low alloy (HSLA) steels. In this study six different HSLA

steels were tested with yield strengths ranging from 40 to 80 ksi. They

also tested three different aluminum alloys for comparison with the HSLA

steels. Approximate strain rates used were 0.008, 0.8, 8.0 and 80.

in. lin. Isec. All tests were performed at room temperature. Figure

shows the relationship between yield and tensile strengths,

uniform elongation and strain rate for a typical HSLA steel.

As can be seen from Figure 2.13, the yield and tensile strengths both

increase substantially with increasing strain rate while the uniform

elongation, which is the strain at the onset of the necking, decreases

slightly. This indicates that the total elongation is relatively inde-

pendent of strain rate. It is, therefore, expected that the absorbed en-

ergy of the HSLA steel also increases with increasing strain rates. Such

an increase in absorbed energy is obviously desirable for the automotive

components.

Based on the research findings presented in Refs. 2S and 40, the true

stress in metals may be determined by the strain rate as follows:

C e·m0=

where

a = true stress

e· = true strain rate

(2.13)

m

c

= strain rate sensitivity exponent

= material constant

15

In Equation (2.13), it is possible to determine the value of "m" from

tensile tests by changing the stra1'n t dd I d bra e su en y an y measuring the

instantaneous change in stress. This technique is illustrated in Figure

412.14 . By applying Equation (2.13) to two different strain rates and

eliminating C, 41we have

m = In( 0"2 /0"1) / In( e' 2 / e' 1 ) (2.14)

According to Hosford and Caddel25 , the magnitude of "m" for most metals

is usually between 0 and 0.03. The value of C depends on the strain rate,

temperature and the type of material25 . For a given material, the values

of C and m can be determined empirically. For example, the resulting

magnitudes of C and m obtained from Chatfield and Rote's tests are listed

in Table 2.34°. It is interesting to note from Table 2.3 that the m values

range from 0.018 to 0.056, which are slightly exceeding the range of m

values given by Hosford. As expected, the values of InC (and thus C) in-

crease as the yield strength increases. However, the m values show a

steady decrease with the increasing yield strength. An analysis of the

40results given in Table 4 of Chatfield and Rote's report seems to in-

dicate that the increase in C is offset by the decrease in m values, such

that the total increase in yield strength for a given strain rate remains

approximately the same regardless of the material strength.

Another useful relationship between the true stress and strain rate

'. - 2515 g1ven by Hosford as:

0"2 = 01 x ( e· Z/e· 1)m

where oland 0z are the true stresses corresponding

(Z.15)

to strain rate e' 1

and . , 1 Th efore if 0"1' E' 1 and m are known. then O"zE 2' respect1ve y. er ,

can be found for any desired value of e' Z'

16

If the strain rate sensitivity of a material is known as a design

parameter, the engineer may use this property to his advantage and thus

a more economical design may be obtained. For example, an automotive en-

gineer may take advantage of the increased yield point (if available)

caused by the high strain rate associated with impact when he design a

part to . th t d' t 1 d . . h f' 40Wl S an lmpac oa lng Wlt out permanent de ormatlon .

In 1982, Watanabe42 studied the yield behavior of low-carbon sheet

steels at room temperature under the strain rates of 10-4 to 10- 1 sec-1

using an Instron type machine. The results showed another break point of

the dependence of the yield stress on the strain rate of 3 x 10-3

sec-1

, which is different from Manjoine's strain rate of 10-1

sec-1

as shown

in Figure 2.15 42 . This means that the dependence of yield stress, yield

point elongation, and tensile strength on the strain rate in the range

of high strain rate above 3 x 10-3 sec- 1 is larger than that at lower

strain rates. Figure 2.15 also shows that the yield stress is more sen-

sitive to strain rate as compared with the tensile strength.

Also in 1982, Peterson, Schwabe, and Fertis43

conducted experiments

to measure the effect of strain rate on the tensile properties of SA-I06

carbon steel pipe. It was observed that the increase in the strain rate

from 4xl0 -4 to 4 sec-1 raised the yield strength by approximately 30

percent as illustrated in Figure 2.16.

d W44 f und that the strain rate sensitivity

In 1983, Sachdev an agoner 0

1 This investigationm is strongly dependent on the strain rate for stee .

included four types of steels: an interstitial free (IF) steel, a hot

rolled, plain carbon steel (HR), and two high strength steels one with a

LA) and the other with a ferriteferrite-pearlite mi~rostructure (BS

17

(2.16)

martensite (DP) microstructure. A new equation was developed to correlate

the strain-rate sensitivity and the strain rate as follows 44 :

m = b e' a

In the above equation, a and b are constants to be determined from tests.

Figure 2.1744

shows the strain-rate sensitivity index, m, for the steels

tested as a function of strain rate. The curves represent the best fits

for Equation (2.16) for the steels tested under the selected strain rate

Note that for each steel thealong with the m-values.

range. The best fit coefficients obtained from these curves are given in

Table 2.444

strain-rate sensitivity is well-characterized by the new equation.

In 1984, Meyer45 conducted tension tests on high strength sheet

steels at strain rates between 5x10-4 sec- 1 and 5xl03 sec-I. Figure 2.18

shows the stress-strain curves of the tested steel at different strain

rates. It is observed from this figure that both yield and ultimate

tensile strengths are increased with the increasing strain rate. However.-4 -1

the ductility decreased when the strain rate increased from 5xl0 sec

t 2 3 -1o xl0 sec .3

At higher strain rates above 2xl0-1

sec the material

becomes more ductile again.

Recently, Nagorka46 conducted an experimental investigation to ob-

serve the effect of microstructure and strain rate on the stage III strain

hardening and ductility of dual-phase steels. Five types of steels in-

I ld rolled normalized. martensitic.c uded in this investigation were co - ,

Table 2.546 lists the valuestempered martensitic and ferrite-carbide.,

steels studied. The m valuesof the strain rate sensitivity for the five

-5 -1in ates (6.7 x 10 sec

Were calculated for low to intermediate stra r-4

h t in rates (6.7 x 10to 6.7 x 10-4 sec-I) and intermediate to hig s ra

18

-1 -3-1sec to 6.7 x 10 sec ). Based on the m values given in this table,

Nagorka concluded that the strain rate sensitivities of various micro-

structures are the same for any given strain rate and increase with in-

creasing strain rate. These observations indicate that m is insensitive

to changes in microstructures. Also, it was concluded from this study

that the uniform elongation increases slightly with increasing strain

rate for most of the microstructures tested, whereas post-uniform

elongation increases significantly with increasing strain rate.

Another very important mechanical property is the modulus of

elasticity, E. Norris et al. state in Ref. 34 that, based on a limited

number of tests on ordinary structural carbon steel, the modulus of

Stainless Steels.b.

elasticity is unaffected by strain rates.

Albertini and Montagnani47 have conducted

tests on three austenitic stainless steels CAISI Types 304, 304L and

347) . The results of these tests are presented in Figures 2.19 to

2.2147 , which indicate an increase in yield and ultimate strengths for

all materials when the strain rate increases. However, decreases in the

total elongations are exhibited.

In 1984, Hopkinson split-bar tests were performed on Type 21-6-9

austenitic stainless steels from ambient temperature to 1023 K by Kassner

and Breithaupt48 2 4 -1These high-strain-rate tests C 10 to 10 sec ) were

compared with lower-strain-rate tests C 10-4

sec-1

). The results as

shown in Figure 2.2248 indicate that the strain-rate sensitivity of this

type of stainless steel is not strongly dependent on the strain rate. The

value of m was determined to be 0.03846 by measuring the slope of the

indicated best-fit line.

19

c. Aluminum. Structural aluminums were found to be less strain rate

sensitive than steels. Figure 2.2349 shows the data obtained for 1060-0

l' B t . -3 -1 3-1a um1num. e ween stra1n rates of 10 sec and 10 sec , the stress

at 2% plastic strain increases by less than 20%. Another contrast to the

behavior of steel as demonstrated in Fig. 2.23 is that strain hardening

increases with increasing strain rate. Reference 50 summarizes several

data sets relating to the yield stress dependence on strain rate in steel

and aluminum (Figures 2.24 and 2.2550 ). The comparison shows that for

aluminum, the effect on yield stress is less significant and occurs only

at extremely high strain rates. Note the difference in vertical scales

in Figs. 2.24 and 2.25.

A large amount of the available data has been reviewed by Lindholm

and Bessy51 The materials tested include several commercial aluminum

alloys. The data cover strain rates from 10-5 to about 103

sec-I. The

strain rate sensitivity was found to be constant over a large range of

strain rates. Figures 2.26 to 2.2851 show the effect of plastic strain

rate on the flow stress at a constant true strain and a constant tem-

perature. In some cases, rate independent behavior is observed at low

strain rates. In general, the value of m was found to increase with in-

creasing strain rate. From these figures, it can be seen that the flow

stress may be related to the strain and strain rate over the wide range

. 52of strain rates by the following equat10n

° = 0o(e) + 01 (e) log e

Wher~a~ is the stress-strain relation at unit strain rate.

~ and Maiden53 have conducted two compression tests on

·(2.17)

two types

?

of aluminums, 6061-T6. and 707S-T6. The range of the strain rates was from

20

-1 -1 530.03 sec to 560 sec Figure 2.29 shows the stress strain data of

7075-T6 at various strain rates. It is apparent from the results of these

tests that both aluminums are not senSl.'tl.'ve to th h 'he c ange l.n t e strain

rate.

Figure 2.3031

shows a method of comparing the previous investigation

data in terms of a rate-sensitivity parameter versus the static flow

stress. The parameter is the increase in flow stress from a static test

to a dynamic test at a given strain divided by the static flow stress and

the log of the difference in strain rates. It represents the percentage

increase in stress per unit of log strain rate. It is shown from this

figure that the degree of rate sensitivity is increased as material

strength is decreased, or as purity increases.

3. Strain-Rate History Effect. In addition to the effect of

strain rate on the mechanical properties of materials, the history of

loading can affect the flow stresses at a given strain and strain rate.

A number of investigators have examined the loading history to de-

termine its contribution to the mechanical behavior character-

istics. A technique that has achieved popularity over the last decade

is the jump test or more properly the incremental strain-rate test,

for which a specimen is subjected to a slow rate of loading followed by

a very high loading31rate .

Incremental as well 'as interrupted ( prestrained) tests are most

useful tools for the study of strain-rate history effects in metal,

especially if the change in strain-rate covers several orders of mag-

nitude, say from quasi-static to dynamic or vice versa, in order to

submit the

21

material in question to the most critical and demanding

d 't' 54con 1 10ns .

The early experiments involved with dynamic strain rates and in-

tended for a study of strain-rate history are those of Lindholm52 . Fig-

ures 2.31 to 522.33 show Lindholm's results for cyclic loading of

aluminum. It is evident that the stress in dynamic tests following a

static pre-loading is not equal to the stress found at the same strain

in all dynamic loading ( as shown by the dotted line) . This difference

is due to strain rate history. In addition, Lindholm wondered if the

result was influenced by the dwell-time at zero load. To investigate

this question he loaded a specimen dynamically to 8 percent strain,

unloaded, and then reloaded dynamically. The result, as shown in Fig.

2,33, shows a history effect for a dwell-time of three minutes, while

for a dwell-time of 450 micro seconds none can be seen.

Sirakashi and Usui55 tested three materials over a large range of

temperatures. J~ps in strain rate were made-3 -1

from 10 sec to four

different dynamic strain rates. Figures 2.34 and 2.3555

show the effect

of alteration of strain rate upon the flow stress on the way of straining,

In Fig. 2.34, point A is reached with a constant strain rate of 10-3

o1 3 -1

sec - . The strain rate is then changed to 10 sec . Two dotted curves

in the figure are stress strain curves with a constant strain rate. It

may be seen in the figure that the flow stress does not reach the value

at point A2

, which lies on the dotted curves with constant strain

rate of 103 sec-I, in spite of the alteration of strain rate. The same

situation may be seen in Fig. 2.35, where the strain rate is changed from

3 -110 sec to-3 -1

10 sec at point B . These results clearly show thato

22

the history of strain rate is another factor which has an effect upon

the flow stress. In other words, the flow stress will be different de-

pending upon the strain rate history, which the material has experienced,

even if strain, strain rate and temperature are all the same at the mo-

ment considered. The effect of strain rate history may be attributed to

the "memory", of strain rate which has been stored in the material,

probably as a change in structure.

The most extensive series of jump tests is probably that of Eleiche

and Campbell conducted in 197656 . These investigators tested copper,

titanium and mild steel. The tests were performed over a range of tem-

peratures and to strains up to 60% in shear. They concluded that

copper is sensitive to strain rate history, while titanium and steel are

less sensitive to history,

strain rate .

but more sensitive to direct effects of

Jump tests to higher strain rates using 1020 hot rolled steel and

1080 called rolled steel were performed by Wilson et al57

in 1979. See

Figures 2.36 and 2.3757 Both steels, 1020 hot rolled steel, and 1080

called rolled steel show a strong strain rate sensitivity and insensi-

tivity to strain rate history.

A recent experimental study of the strain rate history effect on

the tensile strength of AISI type 316 stainless steel using interrupted

testing was conducted by Eleiche, Albertini, d M.54 .

an ontagnan1 1n 1985.

True stress -true strain curves resulting from their interrupted

testing accompanied by a strain rate change from 0.004-1

to 500 sec

at various values of strain are presented in Fig. 2.3854

. Also plotted

are curves showing. the variation of the temperature rise in each

23

specimen during the corresponding dynamic deformation. The investigated

prestrain range was from 0.0047 in.jin to 0.3048 in.jin. It can be seen

from this figure that a well-defined yield point whose level is much /?higher than that reached in the quasi-static prestraining. For

small prestrains, this yield stress level is very close to the flow

stress level reached at the same strain in a test conducted entirely

at the dynamic rate (curve B in Fig. 2.38). The conclusion of this.f I'

study was that even~'~1ainless steel is known to be strain-rate y

sensitive, it has been shown that it is insensitive to strain-rate

history, within the range of strain rate covered in the tests and

at ambient temperature.

24

III. EXPERIMENTAL PROGRAM

A. MATERIALS

Currently, numerous grades of high strength sheet steels are com-

mercially available for automotive structural components 1. Two types of

sheet steels (3SXF and SOXF) were selected by members of the Task Force

on Automotive Structural Design of the AISI Automotive Applications

Committee for the purpose of studying the effect of strain rate on the

mechanical properties of high strength sheet steels and the structural

strength of cold-formed steel members subjected to dynamic loads. The

chemical compositions for these two sheet steels are listed in Table 3.1.

Also included in this table is the chemical composition of 100XF sheet

steel, which was used in the first phase of the study of automotive

structural components using high strength sheet steels. The 100XF sheet

steel was also used in the study of the effect of strain rate on the me-

chanical properties.

B. UNIAXIAL TESTS

All these three virgin materials listed in Table 3.1 were uniaxially

tested in tension in the longitudinal (parallel to the direction of

rolling) and transverse (perpendicular to the direction of rolling) di

rections under three different strain rates of 10-4 , 10-2 , and 1.0

in./in./sec. Two of the three materials (SOXF and 3SXF) were also tested

in tension in both directions to determine the combined effects of cold

stretching and strain rate. The amounts of uniform cold-stretching used

for the tests were 0.02 in./in.(20 mils) and 0.08 in./in.(80 mils). In

order to determine the combined. effects of strain rate and aging, half

25

of the coupons (non-aged coupons) were tested in an average of two days

after cold stretching operation. The remaining . half of the cold-

stretched coupons (aged coupons) were tested to failure under different

strain rates at least 30 days after cold stretching operation.

1. ASTM Specifications. All tension tests followed the procedures

outlined in the ASTM Specifications listed below:

E8-69

E83-67

E111-82

Tension Testing of Metalic Materials

Standard Method of Verification and Classification

of Extensometers

Standard Test Method for Young's Modulus, Tangent

Modulus and Chord Modulus

2. Specimens. The tensile specimens tested in the longitudinal and

transverse directions were prepared by the Machine Shop of the Department

of Civil Engineering at the University of Missouri-Rolla. The test

specimens were cut from the quarter points of the steel sheets as shown

in Figure 3.1. The sketch in Figure 3.2 shows the tensile specimen di-

mensions for the three materials (35XF, 50XF, and 100XF). A total of 124

coupons were tested in this phase of study. They are summarized in the

following 22 different cases:

Cold-StretchedCondition

Virgin Materials

Type ofMaterial

Number of CouponsUsed

Longitudinal Tension( LT )

Transverse Tension( IT )

100XF-LT 7 -e- -- ?-50XF-LT 9 ,35XF-LT 9

100XF-IT 650XF-IT 935XF-IT 6

26

Cold-Stretched Type of Number of CouponsCondition Material Used

2% Cold-StretchedNon-Aged Materials

Longitudinal Tension 50XF-LT 6( LT ) 35XF-LT 6

Transverse Tension 50XF-TT 2( TT ) 35XF-TT 4




2% Cold-StretchedAged Materials






3. Equipment. All the specimens were tested in a 110 kips MrS 880

Test System located in the UMR Engineering Research Laboratory. Figure

3.3 shows the Test System along with the remaining equipment used for

the tension tests under controlled strain rates. Other equipment used

for the tests includes the MrS controller (Fig. 3.4), the data acquisition

27

system (Fig. 3.5), Data General graphic monitor (Fig.3.6), Data General

MV-IOOOO mini computer to store and manipulate the data (Fig. 3.7), MTS

Model No. 732.25b-20 extensometer (Figs. 3.8a and 3.8b), and IBM PS/2

Model 30 personal computer with IBM color plotter and NEe Pinwriter P5XL

printer (Fig. 3.9).

An MTS extensometer with a 2-in. gage length was used to measure the

strains from zero load to failure. The classification of this extensometer

according to ASTM Designation E-83 was found to be dependent on the

extensometer range used in the tests. Table 3.2 contains the classi

fications of the four extensometer ranges according to the MTS transducer

calibration data.

The load was measured by an MTS System Model 380041-06 load cell and

associated conditioning, which was calibrated prior to testing according

to the procedure of the National Bureau of Standard.

Figure 3.10 shows the MTS 880 automated test system which consists

of four components: the load frame, the control console, the CAMAC (Com

puter Automated Measurement and Control) data acquisition, and Data Gen

eral MV -10000 computer. The testing machine is of a servohydraulic

closed-loop type. Figure 3.11 shows the simplified block diagram of the

servo control loop. The moving piston is driven by a double-action hy

draulic cylinder; so that it can operate under tension and compression.

The fluid pressure in the chamber is controlled by a servovalve. This

servovalve responds to the difference between the measured signal and

the desired signal. The signal is amplified to drive the valve so as to

remove the error. There are three main modes of operating the machine,

commonly referred to as stroke, strain, and load. Under the stroke mode,

28

the movement of the piston is the controlling variable. Under the load

mode, it is the load acting on the specimen. Under the strain mode, it

is the strain, as read from the extensometer. For each of these three

modes, different time functions can be established by the function gen-

erator to match the application needed. Tensile tests under a constant

strain rate can be made by setting a ramp function under the strain mode.

The slope of this ramp is the desired strain rate. Each of these modes

has four different ranges of operation i.e., 100%, 50%, 20%, and 10%.

Table 3.3 summarizes the transducer ranges and the corresponding load,

strain, or displacement values. The test results can be processed by the

Data General mini computer and displayed graphically as desired. The

data acquisition used in this system conforms to the CAMAC standards.

The main data acquisition module used in this system is a Kinetic Systems

Model 4022 Transient Recorder. The unit has 32 simultaneous sampling input

channels at a resolution of 12 bits. The unit is capable of acquiring sets

of data at the maximum rate of 25,000 sets of readings per second. The

recorder has a storage capacity of 1,000,000 samples. The simultaneous

sampling feature of the system eliminates the timing skew between data

points. After the data has been acquired, it is downloaded into the com-

puter for analysis. The transient recorder includes a direct readout for

" l" 't'present va ue mon.1. or.1.ng,

real-time as the test runs.

which allows the data to be displayed in

4. Procedure. Prior to testing, the dimensions of the tensile

specimens were measured to the nearest 0.001 in., cleaned with acetone,and

the gage length (2 in.) was marked in ink. The grips of the machine were

alligned by operating the machine under stroke mode. The specimen was

29

then placed in the grips such that the longitudinal axis of the specimen

coincided with the center line of the grips. The load mode was selected

to place the specimen in the grips before running the test. Next, the

extensometer was attached to the specimen such that the extensometer knife

edges lined up with the gage marks as illustrated in Figure 3.8. The

function generator was then programmed to produce the desired ramp. The

ramp function has two time values needed to be selected i.e., ramp time

1 CRT1) and ramp time 2 CRT2). See Fig. 3.12. Table 3.4 shows ramp

different

time 1 and the corresponding strain-rate value. Ramp time 2 was chosen

to give enough time to remove the extensometer and the specimen from the

load frame. Transfer from load mode to strain mode was made before the

test was started. For almost all the tests, load range 4, strain range

1, and stroke range 1 were selected. As the test proceeded, the stress

strain graph was plotted simultaneously on the graphic display terminal.

The stress and strain data were stored by the Data General computer for

later plotting and determination of mechanical properties.

A constant strain-rate is very difficult to maintain with the con

ventional testing machine especially at the high strain rate. The strain

rate was controlled electronically by the new MrS 880 Test System, which

allowed the exact strain rates to be performed without any difficulty.

Figures 3.13 to 3.15 show the strain versus time curves for

strain rates.

The cold-stretching coupons were loaded to the desired 2% strain or

8% strain by using strain as a control mode with the strain rate of 0.1

in./in./sec. The span in the MrS system controller was used to stop the

test when the desired strain is reached.

30

C. RESULTS

1. Stess-Strain Curves. The stress-strain curves were plotted by

using the Data General graphics software named Trendview with the

stress-strain data recalled from the computer storage. Because the

stresses were computed by dividing the loads by the original cross-

sectional areas of the specimens, they should be regarded as the engi-

neering stress-strain curves. Figures 3.16 through 3.37 present the

stress-strain curves for the following 22 different cases, which were

studied under different

in. / in. /sec. ).

strain rates (0.0001, 0.01, and 1.0

Cold-Stretched Type of FigureCondition Material Number

Virgin Materials

Longitudinal Tension 100XF-LT 3.16( LT ) 50XF-LT 3.18

35XF-LT 3.28

Transverse Tension 100XF-IT 3.17( IT ) 50XF-IT 3.19

35XF-IT 3.29


Longitudinal Tension 50XF-LT 3.20( LT ) 35XF-LT 3.30

Transverse Tension 50XF-IT 3.21( IT ) 35XF-IT 3.31

Cold-StretchedCondition



Transverse Tension( TT )







Type ofMaterial

50XF-LT35XF-LT

50XF-TT35XF-TT

50XF-LT35XF-LT

50XF-TT35XF-TT

50XF-LT35XF-LT

50XF-TT35XF-TT

FigureNumber

3.223.32

3.233.33

3.243.34

3.253.35

3.263.36

3.273.37

31

For the purpose of comparison, each figure includes two or three stress-

strain curves representing the test data obtained from the same material

for different strain rates. In order to study the effect of aging on the

mechanical properties of 50XF-LT steel, Figures 3.59 to 3.61 compare three

stress-strain curves for 50XF-LT steel with different amount of cold

stretching tested under a constant strain rate.

2. Mechanical Properties. The procedures used for determining the

mechanical properties of sheet steels are discussed in the subsequent

sections (Sections III.C.2.a through III.C.2.c). The mechanical proper-

ties so determined are the yield point F , the tensile strength F , andy u

32

elongation in 2-in. gage length. These tested mechanical properties are

presented in Tables 3.5 through 3.15 for each individual test. Tables 3.16

through 3.21 present the average values of the mechanical properties for

each material tested in either longitudinal tension (LT) or transverse

tension (TT), but with different amount of cold stretching (i.e., virgin

material, 2%, or 8%) under different strain rates (0.0001, 0.01, or 1.0

in. jin. jsec.).

a. Yield Strength or Yield Point. F . The method commonly used toy

determine the yield point of sheet steels depends on whether the stress-

strain curve is of the gradual or sharp-yielding type. For the types of

sheet steels tested in this phase of study, the stress-strain curves of

the 100XF and 50XF sheet steels are the sharp-yielding type, while the

stress-strain curves of the 35XF steel are the gradual-yielding type.

Because the 50XF sheet steel exhibited a considerable amount of strain

hardening, the stress-strain curves became the gradual-yielding type af-

ter the material was cold-stretched to a selected strain of either 2% or

8%.

The yield point of the sharp-yielding steel was determined as the

stress where the stress-strain curve becomes horizontal. Typical sharp

yielding stress-strain curves are shown in Figure 3.16 for the 100XF steel

in the longitudinal direction. For this case, the lower yield point is

given in Table 3.5. The same method was used to determine the yield

points included in Table 3.6 for the 50XF sheet steel.

For the gradual-yielding type stress-strain curves as shown in Fig-

ure 3.28, the yield point of 35XF steel was determined by the intersection

of the stress-strain. curve and the straight line drawn parallel to the

33

elastic portion of the stress-strain curve at an offset of 0.002 in. lin.

A Fortran 77 code was written to determine the yield points presented in

Tables 3.7 through 3.15 for the gradual-yielding type curves using the

Least Square Method.

b. Ultimate Tensile Strength, F . The ultimate tensile strength wasu

determined from each of the tension tests as the maximum stress that the

given tensile coupon could withstand before fracture. This value was

calculated by the computer for each test and is presented in Tables 3.5

through 3.15.

c. Ductility. Ductility is a very important property of high

strength sheet steels not only for the structural behavior of the member,

but also for the fabrication of the desired structural shape. In this

study, ductility was determined by the total elongation in a 2-in. gage

length. For this method, the maximum strain recorded by the computer be-

fore fracture was taken as the ductility. The maximum elongation was also

verified by placing the fractured ends of the specimen together and

measuring the distance between the gage marks.

D. DISCUSSION

The test results presented in Section III.C are discussed in this

section with an emphasis on the effects of strain rate on the mechanical

properties of sheet steels. The materials used in this experimental pro-

gram included virgin steels and steels with different amount of cold

stretching. They were tested in both longitudinal tension and transverse

tension.

1. Mechanical Properties. The test results indicate that all me-

chanical properties are affected by the strain rate and the amount of cold

stretching.

34

Table 3.22 compares the dynamic mechanical properties de-

termined at the strain rate of 1.0 in./in./sec. and the static properties

determined at the strain rate of 0.0001 in. / in. /sec. The effects of

strain rate on yield stress and tensile strength are discussed in the

following sections.

a. Yield Strength or Yield Point, F. In Table 3.22, the dynamicy

yield strength, (F )d' and the static yield strength, (F ) , are comparedy y s

by using a ratio of (Fy)d/(Fy)s. In the above expressions, (Fy)d is the

yield strength determined for the strain rate of 1.0 in./in./sec. while

(Fy) s is the yield strength determined for the strain rate of 0.0001

in./in./sec. It can be seen that for all cases, the yield strength of

sheet steel increases with the strain rate. The increases in yield

strength for the three steels studied in this investigation are: 4% for

100XF steel, 4% to 15% for SOXF steel, ·and 12% to 29% for 3SXF steel when

the strain rate increased from 0.0001 to 1.0 in./in./sec. It is observed

from this table that the increases in yield strength for the virgin ma-

terials are independent of the test direction (LT or TT). The effect of

the strain rate on yield strength decreases as the static yield stress

and/or the amount of cold stretching increases. Previous studyS8 indi-

cated that the increase in yield strength due to cold work is caused

mainly by strain hardening and strain aging. However, in the present in-

vestigation no significant increase in yield strength was observed due

to the strain aging effect. In addition, Figs. 3.24 to 3.27 show that the

strain aging has little or no effect on the type of stress-strain curve.

b. Ultimate Tensile Strength, F . Similar to the effect of strainu

rate on yield strength, the ultimate tensile strengths of sheet steels

increased with the strain rate.

35

The increases in ultimate tensile

strengths for the three materials studied in this investigation are: 4%

for 100XF steel, 7% to 11% for 50XF steel, and 13% to 18% for 35XF steel

when the strain rate increased from 0.0001 to 1.0 in./in./sec. It is

noted from Table 3.22 that the amounts of increase in ultimate tensile

strength due to the increase in strain rate are approximately the same

for both longitudinal tension and transverse tension.

2. Strain Rate Sensitivity. In the literature review the strain

rate sensitivity was discussed in Section II.B.2. For two given values

of the flow stress of a material at two different strain rates, the

strain rate sensitivty exponent m may be calculated as

m = InC 02 / 01 ) / InC e· 2 / e· 1 )

Figures 3.38 through 3.58 copmare the average values of the yield and

ultimate tensile strengths at different strain rates for different cases.

The data plotted in these figures are in terms of flow stress vs. strain

rate on a logarithmic scale. The slopes of the straight lines shown in

these figures represent the material strain rate sensitivity values,

which were calculated on the basis of the above equation and are listed

in Table 3.23 for different cases. The value of m1 was calculated for

the yield strengths corresponding to the strain rates of 0.0001

in./in./sec. and 0.01 in./in./sec., while the value of m2 was calculated

for the yield strengths corresponding to the strain rates of 0.01

in./in./sec. and 1.0 in./in./sec. Whenever only two strain rates were used

in the tests, the value of m3 was calculated for the yield strengths

corresponding to the strain rates of 0.0001 in./in./sec. and 1.0

in./in./sec. From Table 3.23, it can be seen that, in general, the value

36

of m increases as the strain rate increases. The strain rate sensitivity

decreases progressively as the static yield strength level or the amount

of cold stretching increases.

37

IV. CONCLUSIONS

In the past, high strength sheet steels with various yield strengths

up to 190 ksi have been used for auto parts and structural components for

the purpose of achieving fuel economy. In order to provide some technical

assistance for the design of automotive structural components using high

strength sheet steels, American Iron and Steel Institute published the

first edition of the "Guide for Preliminary Design of Sheet Steel Auto

motive Structural Components" in .1981 and the first edition of the "Au

tomotive Steel Design Manual" in 1986. . The latter brings together

material properties, product design, and manufacturing information to

make the most effective use of sheet steels with yield strengths of up

to 140 ksi.

In view of the fact that the available design equations were devel

oped on the basis of previous tests subject to static loads and that the

yield strength, tensile strength, and the strees-strain relationship of

sheet steels are affected by the strain rate used for the tests, addi

tional research work was conducted at the University of Missouri-Rolla

since May 1988. The objective of the work is to study the effect of strain

rate on the mechanical properties of the selected sheet steels and the

structural strengths of the cold-formed steel members when they are sub

jected to dynamic loads. The major task is to develop the needed back

ground information for improvement of the existing design procedures.

During the period from May 1988 through December 1988, progress has

been made on a study of the effect of strain rate on mechanical properties

of sheet steels. This initial work included a review of literature and

38

testing of 124 tension specimens. The literature survey is presented in

Section II. Section III contains the detailed information on the exper

imental investigation, which inculdes materials, test specimens, equip

ment, test procedure, test results and the discussion of test data.

Future research work will include the testing of compression coupons

and a study of the structural strengths of cold-formed steel stub columns

and beams subject to dynamic loads. Additional evaluation of the test data

on tensile coupons will be presented in the Twelfth Progress Report.

39

ACKNOWLEDGMENTS

The research work reported herein was conducted in the Department

of Civil Engineering at the University of Missouri-Rolla under the spon

sorship of the American' Iron and Steel Institute.

The financial assistance granted by the Institute and the technical

guidance provided by members of the Task Force on Automotive Structural

Design and the AISI Automotive Applications Committee and the AISI staff

are gratefully acknowledged. These members are: Messrs. S. J. Errera

(Chairman), J. Borchelt, R. Cary, F. L. Cheng, A. M. Davies, J. D.

Grozier, C. Haddad, A. L. Johnson, C. M. Kim, J. P. Leach, K. H. Lin, J.

N. Macadam, H. Mahmood, D. Malen, J. McDermott, P. R. Mould, J. G.

Schroth, P. G. Schurter, T. N. Seel, F. V. Slocum, R. Stevenson, and M.

T. Vecchio. An expression of thanks is also due to Mr. D. L. Douty for

his help.

All materials used in the experimental study were donated by Inland

Steel Company and LTV Steel Company.

Appreciation is expressed to Messrs. K. Haas, A. D. Johnston, J.

Tucker, and R. Hoselhorst, staff of the Department of Civil Engineering,

for their technical support. The advice provided by Dr. J. E. Minor,

Chairman of the UMR Department of Civil Engineering, is greatly appreci

ated.

"Design of AutomotiveSheet Steels", First83-1, University of

40

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21. Pan, L. C., "Effective Design Widths of High Strength Cold-FormedSteel Members," Ph.D. Thesis, University of Missouri-Rolla, 1987.

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27. Malvern, L.E., Introduction to the Mechanics of a Continuous Medium, Prentice Hall; Inc., 1969, 327-333.

42

28. Juvinall, R.C., Stress. Strain and Strength, McGraw-Hill Book Company, New York, (1967), 96-100.

29. Follansbee, P. S., '.'High Strain Rate Compression Testing", MetalsHandbook, American Society for Metals, Ninth Edition, Volume 8, 1985.

30. Lindholm, U. S., "Techniques in Metal Research", Vol. 5, Part 1,Wiley-Interscience, New York , 1971.

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32. Staker, M.R., "High Strain Rate Testing," Metals Handbook, AmericanSociety for Metals, Ninth Edition, Volume 8, 1985.

33. Kumar, S., "Introduction," Mechanical Behavior of Materials UnderDynamic Loads, U.S. Lindholm (Ed.), Springer-Verlag, New York, 1968.

34. Norris, C.H., Hansen, R.J., Holley, M.J. Jr., Biggs, J.M., Namyet,S. , and· Minami, J. K. , ~S~t~rol:u~c~t:.::u~r;.,!:a~I!:.-~D~e::.:s~J.~·gn~_;!:.;fo~ro!:-~D.:Lyn~a~m!.:!:i..:.c:.-.....!L~o~a~d~s

McGraw-Hill Book Company, 1959.

35. Davis, E.A., "The Effect of the Speed of Streching and the Rate ofLoading on the Yeilding of Mild Steel," Journal of Applied Mechanics, ASHE Transactions, Vol. 60,1938.

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39. Holt, J.M., "The Effect of Strain Rate on the Tensile Properties ofUSS COR-TEN and USS TRI-TEN High-Strength Low-Alloy Steels", UnitedStates Steel Corporation, Applied Research Center, Project Number37.12-100(2), Pittsburgh, PA., 1962.

40. Chatfield, D.A. and Rote, R.R., "Strain Rate Effects on the Propertiesof High Strength, Low Alloy Steels," SAE Tech. Paper Ser. 740177,February 25-March 1, 1974.

41. Meyers, M.A., and Chawla, K.K., Mechanical Metallurgy: Principles andApplications, Prentice-Hall, Englewood Cliffs, N.J., 1984.

42. Watanabe, T., "Effect of Strain Rate on Yield Behavior of Cold-RolledSheet Steel," Transactions of the Iron and Steel Institute of Japan, Vol. 22, 1982.

43

43. Peterson, D., Schwabe, J.E., and Fertis, D.G., "Strain Rate Effectsin SA-106 Carbon Steel Pipe," Journal of Pressure Vessel Technology, ASME Transactions, Vol. 104, February, 1982.

44. Sachdev, A.K., and W'agonar, R.H., "Uniaxial Strain Hardening at LargeStrain in Several Sheet Steels," Novel Techniques in Metal Deformation Testing , The Metallurgical Society of AlHE, 1983.

45. Meyer, L. W., "Dynamic Tens ion Studies of Strength and Formabi lityCharacteristic of a High Alloyed Steel With Respect to Thermal Activation," Mechanical Properties at High Rate of Strain , Instituteof Physics, London, No. 70, 1984.

46. Nagorka, M.S., "The Effect of Microstructure and Strain Rate on theStage III Strain Hardening and Ductility of Dual-Phase Steels," Material Science and Engineering, 94, 1987, 183-193.

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48. Kassner, M.E., and Breithaupt, R.D., "The Yield Stress of Type 21-6-9Stainless Steel Over a Wide Range of Strain Rate ( 10-5-104-s- 1 )andTemperature," Mechanical Properties at High Rates of Strain, Institute of Physics, London, No.70, 1984.

49. Jones, A.H., Maiden, C.J., Green, S.J., and Chin, H., "Prediction ofElastic-Plastic Wave Profiles in Aluminum 1060-0 under UniaxialStrain Loading," Mechanical Behavior of Materials under Dynamic Loads, U. S. Lindholm (Ed ..), Springer-Verlag, New York, 1968, 96-133. .

50. Kanninen, M.F., Mukherjee, A.K., Rosenfield, A.R., and Hahn, G.T.,"The Speed of Ductile-Crack Propagation and the Dynamics of Flow inMetals, Mechanical Behavior of Materials under Dynamic Loads , U.S.Lindholm (Ed.), Springer-Verlag, New York, 1968, 96-133.

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53. Maiden, C.J., and Green, S.~" "Compressive _~train Ret: Te~ts on S~xSelected Materials at Stra1n Rates From 10 to 10 1n./1n./sec. ,Transaction of the ASHE , Sep. 1966.

54. Eleiche, A.M., Albertini, C. and Montagnani, M., "The Influenceof Strain-Rate History on the Ambient Tensile Strength of AISI Type316 Stainless Steel," Nuclear Engineering and Design, 1985.

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45

Table 2.1 Dynamic Aspects of Mechanical Testing30

10& 100 1()'.2 10.... 10'" 10~ Characteristic time (sec)

Isothermal .

Inertia forces neglected lnenia forces imponant

Usual methodof loading

DynamicconSIderations

In testing

10. Strain rate (sec-II

Shock-wavepropagation

Ugtlt-gal gunor

explosivedriven

plate imp;,ct

11)4

~~ High-velocity~ plate impact~,,

Adiabatic

Barimpact

.

IMechanical I

or Iexplosive IImpact I,

IPneumatic I

ormechanical I

machines III.

I Mechanical: . :I resonance in Elastlc-I- specimen I plastic _ve I• and I propagation I• machine I' IH I IU

100

~ ~, .'~ Intermechate ~

~ Strain-rate :, ., ', ,, ,II

•1I

•••

:

auasistatic

Hydraulic orscrew machine

Constant strainrate test

~,,,,,,,,,IIIIIII

Creep

Strain vs. timeor creep rate

recorded

Constant loador

stress machine

10 8

,o

Plane stress

Increasing stress levels -Plane strain

46

Table 2.2 Experimental Techniques for

High Strain Rate Testing32

Mode

Compression

Tension

Shear

Applicable StrainRate, sec- 1

s; 0.10.1 to 1000.1 to 500200 to 104

104 to 105

S; 0.10.1 to 100100 to 104

104

~ 105

s; 0.10.1 to 10010 to 1000100 to 104

103 to 104

104 to 107

Table 2.3

Testing Technique

Conventional load framesSpecial servohydraulic framesCam plasometer and drop testHopkinson pressure barTaylor impact test

Conventional load framesSpecial servohydraulic framesHopkinson pressure barExpanding ringFlyer plate

Conventional shear testSpecial servohydraulic framesTorsional impactHopkinson (Kolsky) barDouble-notch shear and punchPressure-shear plate impact

Values of Strain Rate· Sensitivity Exponent, m, and Constant

C of Yield Strength of the Tested Materials40

Material m In C

HRAK-AR 0.045 10.72223

JIRAK - Ann+TR 0.056 10.58935

HSLA-40 0.045 10.74515

HSLA-4S-1 0.035 10.94544

HSLA-4S-2 0.024 10.83534

HSLA-50 0.026 10.98135

HSLA-80-1 0.020 11. 36871

HSLA-80-2 0.018 11. 40914

Table 2.4

Standard Strain Rate Sensitivity

and New Strain Rate Parameters40

Material m b a

IF 0.011 0.039 0.150HR 0.008 0.029 0.134HSLA 0.004 0.010 0.102DP 0.003 0.013 0.149

Table 2.5

Strain Rate Sensitivity for Different Microstructures

Determined by Strain. Rate Jump Tests at 6.7 x 10-5 sec-I,

-4 -1 -3-16.7 x 10, sec ,and 6.7 x 10 sec (Ref. 46)

47

Microstructures

Cold-rolledNormalizedMartensiticTempered martensiticFerrite-carbide

mlow to intermediate

strain rate

0.0020.0020.0030.0030.003

mintermediate to high

strain rate

0.0040.0040.0050.0060.005

Table 3.1

Chemical Compositions of the Sheet Steels Used

48

AISI Thick. C Mn P S Si V Cu Al Cb ZrDesigna. in.

035XF 0.085 .070 .40 .007 .017 .08050XF 0.077 .081 .96 .017 .003 .27 .04100XF 0.062 .070 .43 .006 .023 .11 .056 .064 .08

Table 3.2

Classification of the MTS Extensometer

Range Maximum Strain Maximum Error ASTM ClassificationIn·/In. In·/In.

100% 0.50 0.00065 Between Classes B-2 and C50 % 0.25 0.00030 Between Classes B-2 andC

20 % 0.10 0.00011 Between Classes B-1 and B- 210 % 0.05 0.00002 Between Classes A and B- 1

Table 3.3

MTS Transduc~r Ranges and the Corresponding Load,

Strain, or Displacement Values

49

Transducer

Load

Strain

Stroke

Range Value

100 % 100.0 Kips50 % 50.0 Kips20 % 20.0 Kips10 % 10.0 Kips

100 % 0.50 In./ln.50 % 0.25 In./ln.20 % 0.10 In. /In.10 % 0.05 In./ln.

100 % 10.0 In.50 % 5.00 In.20 % 2.00 In.10 % 1. 00 In.

Table 3.4

Ramp Time 1 and the Corresponding Strain Rate

Ramp Time 1sec.

5000500

505

0.5

Strain Ratein./in./sec.

0.00010.0010.010.11.0

50

Table 3.5

Tested Mechanical Properties of 100XF Sheet Steel

Virgin Material

Test Strain Rate F Fu Elongation in 2-in.No. in. / in. /sec. (k~i) (ksi) Gage Length (percent)

LT-1 0.0001 122.44 122.44 9.4LT-2 0.0001 126.07 126.07 9.7LT-3 0.01 123.98 123.98 10.3LT-4 0.01 125.91 125.91 10.3LT-5 0.01 127.52 127.52 9.8LT-6 1.0 129.06 129.06LT-7 1.0 128.75 128.75

TT-l 0.0001 138.20 138.20 4.9TT-2 0.0001 137.34 137.34 4.9TT-3 0.01 140.11 140.11 6.1TT-4 0.01 139.05 139.05 4.4TT-S 1.0 144.11 144.11 8.0TT-6 1.0 143.03 143.03 5.1

51

Table 3.6


Virgin Material

Test Strain Rate F Fu Elongation in 2-in.No. in./in./sec. (k~i) (ksi) Gage Length (percent)

LT-l 0.0001 49.80 73.87 29.9LT-2 0.0001 49.39 72.54 32.0LT-3 0.0001 49.32 72.51 31.0LT-4 0.01 51. 89 75.44 27.2LT-5 0.01 50.83 74.07 27.4LT-6 0.01 52.09 75.11 26.4LT-7 1.0 54.71 79.18 26.2LT-8 1.0 54.99 79.64 25.4LT-9 1.0 54.29 77.36 25.7

TT-l 0.0001 50.38 73.73 26.8TT-2 0.0001 51.13 73.39 28.3TT-3 0.0001 50.25 73.21 24.8TT-4 0.01 54.22 75.26 25.9TT-5 0.01 52.77 74.80 26.7

TT-6 0.01 52.64 74.16 27.0

TT-7 1.0 56.21 79.86 28.3

TT-8 1.0 54.31 79.85 27.9

TT-9 1.0 56.13 80.03 27.1

Table 3.7


2% Cold Stretched, Non-Aged Material

Test Strain Rate F Fu Elongation in 2-in.No. in. / in. /sec. (k~i) (ksi) Gage Length (percent)

LT-1 0.0001 56.37 72.62 26.5LT-2 0.0001 56.44 73.41 27.5LT-3 0.01 58.46 74.81 25.4LT-4 0.01 58.88 74.20 25.7LT-5 1.0 63.19 80.58 26.1LT-6 1.0 62.16 80.06 27.9

'IT-I 0.0001 59.29 74.90 23.1'IT-2 1.0 68.48 81. 29 24.6

Table 3.8



Test Strain Rate F FuElongation in 2-in.

No. in./in./sec. (k~i) (ksi) Gage Length (percent)

LT-1 0.0001 71. 22 73.73 24.6

LT-2 0.0001 71.86 73.99 23.8

LT-3 0.01 73.87 76.21 21. 6

LT-4 0.01 75.06 76.81 20.3

LT-5 1.0 77.00 80.77 21.6

LT-6 1.0 78.18 81.55 19.8

'IT-I 0.0001 72.59 74.90 20.0

'IT-2 0.0001 74.71 76.86 23.6

TT-3 1.0 77.90 82.07 19.4

TT-4 1.0 77.78 81. 94 17.5

52

53

Table 3.9


2% Cold Stretched, Aged Material


LT-l 0.0001 58.78 74.84 30.3LT-2 0.0001 59.68 75.31 27.7LT-3 0.01 60.49 76.05 26.4LT-4 0.01 60.55 76.27 26.7LT-5 1.0 63.45 81. 39LT-6 1.0 62.97 81.16 28.8'

TT-1 0.0001 60.33 74.96 26.5TT-2 0.0001 60.20 75.13 28.9TT-3 1.0 65.43 83.62 22.1TT-4 1.0 64.15 82.57 22.1

Table 3.10




No. in./in./sec. (k~i) (ksi) Gage Length (percent)

LT-1 0.0001 73.33 74.41 20.1

LT-2 0.0001 72.94 73.21 20.0

LT-3 0.01 72.51 74.49 22.4

LT-4 73.80 75.92 20.50.01

LT-5 1.0 75.60 77 .19

LT-6 1.0 75.93 80.69

TT-1 75.06 75.41 17.10.0001 21.5

TT-2 0.0001 73.54 74.4919.1

TT-3 1.0 78.11 81.8216.4

TT-4 1.0 77.26 81.47

54

Table 3.11


Virgin Material


LT-1 0.0001 32.42 49.22 39.7LT-2 0.0001 32.57 49.19 40.2LT-3 0.0001 33.63 49.64 36.7LT-4 0.01 36.42 51. 68 38.1LT-5 0.01 36.65 52.02 36.0LT-6 0.01 36.12 51.59 36.5LT-7 1.0 42.53 56.82 41.6LT-8 1.0 41. 87 56.48 40.2LT-9 1.0 42.70 56.60 40.9

TT-1 0.0001 33.53 49.41 34.9TT--2 0.0001 33.49 49.19 37.5TT-3 0.01 36.21 50.98 39.0TT-4 0.01 36.57 51.10 35.3TT-5 1.0 43.00 55.70 36.9

TT-6 1.0 43.47 56.15 34.1

Table 3.12



Test Strain Rate F Fu Elongation in 2-in.No. in. /in./sec. (k~i) (ksi) Gage Length (percent).

LT-1 0.0001 39.20 49.08 36.2LT-2 0.0001 39.89 49.86 39.3LT-3 0.01 42.62 52.11 31.4LT-4 0.01 42.29 52.44 33.5LT-5 1.0 47.44 57.05 39.8LT-6 1.0 47.20 57.05 38.7

TT-1 0.0001 38.06 47.73 32.7TT-2 0.0001 38.14 48.18 34.5TT-3 1.0 46.36 55.81 32.1TT-4 1.0 46.45 56.04 37.5

Table 3.13




No. in. / in. /sec. (k§i) (ksi) Gage Length (percent)

LT-l 0.0001 46.05 49.41 29.9

LT-2 0.0001 46.57 49.08 29.730.0

LT-3 0.01 48.54 52.0029.5

LT-4 0.01 49.75 52.6731.5

LT-S 1.0 53.23 57.7238.5

LT-6 1.0 52.57 56.71

Tr-l 44.77 47.84 29.00.0001 22.1

Tr-z 0.0001 46.14 47.7328.5

Tr-3 1.0 52.35 56.2626.9

Tr-4 1.0 52.59 56.49

55

56

Table 3.14




LT-l 0.0001 40.02 49.32 31.8LT-2 0.0001 39.89 50.10 35.7LT-3 0.01 41.80 51. 77 37.3LT-4 0.01 41.25 51.16 36.1LT-5 1.0 47.52 56.91 35.9LT-6 1.0 47.28 56.80 40.9

TT-l 0.0001 38.89 48.73 29.8TT-2 0.0001 39.27 48.90 31. 8TT-3 1.0 45.02 55.78 34.3TT-4 1.0 45.23 55.34 32.6

Table 3.15



Elongation in 2-in.Test Strain Rate F FuNo. in. / in. /sec. (k~i) (ksi) Gage Length (percent)

LT-1 45.69 48.19 34.80.0001 30.7

LT-2 0.0001 46.61 49.1130.6

LT-3 0.01 48.85 51. 7430.7

LT-4 0.01 49.70 52.3432.0

LT-5 1.0 53.82 57.5231.1

LT-6 1.0 53.53 57.55

47.60 25.3IT-I 0.0001 45.25 28.7IT-2 0.0001 45.64 47.65

2.8.5IT-3 1.0 50.83 55.48 2.8.111'-4 1.0 51.25 56.01

Table 3.16

Average Tested Mechanical Properties of 100XF Sheet Steel

Longitudinal Tension, Virgin Material

Strain Rate F . Fu Elongationin. lin. Isec. (k~i) (ksi) (percent)

0.0001 124.25 124.25 9.50.01 125.80 125.80 10.21.0 128.91 128.91

Table 3.17

Average Tested Mechanical Properti~s of 100XF Sheet Steel

Transverse Tension, Virgin Material

Strain Rate F FuElongation

in·/in./sec. (k~i) (ksi) (percent)

0.0001 137.77 137.77 4.9

0.01 139.58 139.58 5.3

1.0 143.57 143.57 6.6

57

58

Table 3.18


Longitudinal Tension

Amount of Cold Strain Rate F Fu ElongationStretching in. lin. Isec. (k~i) (ksi) (percent)

Virgin 0.0001 49.50 72.97 31. 0Virgin 0.01 51.60 74.87 27.0Virgin 1.0 54.66 78.73 25.8

2%, Non-Aged 0.0001 56.40 73.01 27.02%, Non-Aged 0.01 58.67 74.50 25.52%, Non-Aged 1.0 62.67 80.32 27.0


2%, Aged 0.0001 59.23 75.07 29.02%, Aged 0.01 60.52 76.16 26.52%, Aged 1.0 63.21 81.27 28.8

8%, Aged 0.0001 73.13 73.81 20.08%, Aged 0.01 73.15 75.20 21.58%, Aged 1.0 75.71 78.94

Table 3.19


Transverse Tension

Amount of Cold Strain Rate F Fu ElongationStretching in./in./sec. (k~i) (ksi) (percent)

Virgin 0.0001 50.59 73.44 26.7Virgin 0.01 53.21 74.74 26.5Virgin 1.0 55.55 79.91 27.8

2%, Non-Aged 0.0001 59.29 74.90 23.12%, Non-Aged 1.0 68.48 81. 29 24.6

B%, Non-Aged 0.0001 73.65 75.88 21.88%, Non-Aged 1.0 77.84 82.00 18.5

2%, Aged 0.0001 60.27 75.05 27.72%, Aged 1.0 64.79 83.09 22.1

B%, Aged 0.0001 74.30 74.95 19.3B%, Aged 1.0 77 .69 81.65 17.7

59

60

Table 3.20


Longitudinal Tension

Amount of Cold Strain Rate F Fu ElongationStretching in. lin. Isec. (k§i) (ksi) (percent)

Virgin 0.0001 32.87 49.35 38.9Virgin 0.01 36.40 51. 76 36.8Virgin 1.0 42.37 56.63 40.9



2%, Aged 0.0001 39.95 49.71 33.82%, Aged 0.01 41.53 51.47 36.72%, Aged 1.0 47.40 56.85 38.4

8%, Aged 0.0001 46.15 48.65 32.7

8%, Aged 0.01 49.27 52.04 30.7

8%, Aged 1.0 53.67 57.53 31.5

Table 3.21


Transverse Tension

Amount of Cold Strain Rate F Fu ElongationStretching in./in./sec. (k§i) (ksi) (percent)

Virgin 0.0001 33.51 49.30 36.2Virgin 0.01 36.39 51.04 37.1Virgin 1.0 43.23 55.93 35.5

2%, Non-Aged 0.0001 38.10 47.95 33.62%, Non-Aged 1.0 46.41 55.93 34.8

8%, Non-Aged 0.0001 45.45 47.79 25.68%, Non-Aged 1.0 52.47 56.37 27.7

2%, Aged 0.0001 39.08 48.81 30.82%, Aged 1.0 45.13 55.56 33.5

8%, Aged 0.0001 45.45 47.63 27.08%, Aged 1.0 51.04 55.75 28.3

61

Table 3.22

Ratios of Dynamic to Static Mechanical Properties for

Three Sheet Steels Based on Tables 3.16 to 3.21

Type of (Fy)d/(Fy)s (Fu)d/(Fu)s (Elong·)d/(Elong·)sSheet Steel

100XF-LT-Virgin 1. 04 1.04100XF-TT-Virgin 1. 04 1.04 1.3

50XF-LT-Virgin 1.10 1. 08 0.850XF-LT-2%, Non-Aged 1.11 1.10 1.050XF-LT-8%, Non-Aged 1.08 1.10 0.8550XF-LT-2%, Aged 1. 07 1. 08 0.9950XF-LT-8%. Aged 1. 04 1. 07

50XF-TT-Virgin 1.10 1.09 1. 0450XF-TT-2%, Non-Aged 1.15 1. 09 1.0650XF-TT-8%. Non-Aged 1. 06 1. 08 0.8550XF-TT-2%. Aged 1. 07 1.11 0.8050XF-TT-8%, Aged 1. 05 1. 09 0.92

35XF-LT-Virgin 1.29 1.15 1. 05

35XF-LT-2%. Non-Aged 1. 20 1.15 1. 04

35XF-LT-8%, Non-Aged 1.14 1.16 1.18

35XF-LT-2%, Aged 1.19 1.14 1. 14

35XF-LT-8%. Aged 1.16 1.18 0.96

35XF-TT-Virgin 1. 29 1.13 0.98

35XF-TT-2%. Non-Aged 1. 22 1. 17 1. 04

35XF-TT-8%, Non-Aged 1.15 1.18 1. 08

35XF-TT-2%, Aged 1. 15 1.14 1. 09

35XF-TT-8%, Aged 1.12 1. 17 1. 05

62

Notes

= dynamic yield stress for the strainrate of 1.0 in./in./sec .

(Fy)s = static yield stress for the ~rain

rate of 0.0001 in./in./sec .

(Fu)d = dynamic ultimate stress for the strain


(Fu)s = static ultimate stress for the strain


63

Table 3.23

Values of Strain Rate Sensitivity m for Three Sheet

Steels Based on the Changes of the Yield Stresses at

Different Strain Rates

Type ofSheet Steel

100XF-LT-Virgin100XF-TT-Virgin

50XF-LT-Virgin50XF-LT-2%, Non-Aged50XF-LT-8%, Non-Aged50XF-LT-2%, Aged50XF-LT-8%, Aged

50XF-TT-Virgin50XF-TT-2%, Non-Aged50XF-TT-8%, Non-Aged50XF-TT-2%, Aged50XF-TT-8%, Aged

35XF-LT-Virgin35XF-LT-2%, Non-Aged35XF-LT-8%, Non-Aged35XF-LT-2%, Aged35XF-LT-8%, Aged

35XF-TT-Virgin35XF-TT-2%, Non-Aged35XF-TT-8%, Non-Aged35XF-TT-2%, Aged35XF-TT-8%, Aged

Notes:

0.003 0.0050.003 0.006

0.009 0.0130.009 0.0140.009 0.0090.005 0.0090.000 0.008

0.011 0.009

0.022 0.0330.015 0.0230.013 0.0160.008 0.0290.014 0.018

0.018 0.037

0.0040.004

0.0110.0110.0090.0070.004

0.0100.0160.0060.0080.005

0.0270.0190.0140.0190.016

0.0280.0210.0150.0160.013

strain rate sensitivity based on the changes of yield stressbetween strain rates of 0.0001 in./in./sec. and 0.01 in./in./sec.

strain rate sensitivity based on the changes of yield stressbetween strain rates of 0.01 in./in./sec. and 1.0 in./in./sec.

strain rate sensitivity based on the changes of yield stressbetween strain rates of 0.0001 in./in./sec . and 1.0 in./in./sec.

f rELASTIC RANGE

INELASTICRANGE STRAIN HARDENING

D

64

A 8

(0) SHARP-YIELDING STEEL

~/ .-- -----\Whlc--. \

~c~ 1-~~...---.------~~.".._---'-~. '.

(

2

E= fiE.

(b) GRADUAL-YIELDING STEEL

c

Fig. 2.1 Stress-Strain Curves of Carbon Steel Sheets24

65

(fJ(fJ

wa::I(fJ

LOFFSET STRAIN,€

(a) OFFSET METHOD

j I TOTAl ELONGATION STRAIN, (I- OR EXTENSION

(b) STRAIN-UNDER-LOAD METHOD

Fig. 2.2 Determination of Yield Point for Gradual-Yielding Stee124

STRAINAGING

STRAINHARDENING

Fig. 2.3 Effects of Strain Hardening and Strain Aging on Stress. . 24

Strain Character1st1cs

66

f

c

---JI-+=---~~----C

Fig. 2.4 Influence of Bauschinger Effect28

,

---,'

"_---...c...~ENGINEERING

U'IU'IlAJa::tel)

STRAIN

Fig. 2.5 Comparison of Engineering and True Stress-StrainCurves 25

67

.enen

'"a::ten

70

RATE OF STRllNI in/in. I

sec..,

~~I -,0.00001 in/in

V sec

"'"I in./in. V""iiC:u /

~.. :11J.WI J

~

....

10

0o • 12 zo

STRAIN (PER CENT)

Fig. 2.6 Effect of Strain Rate on Stress-Strain Curvefor Structural Steel34

• 100

• .. -CL 80 •~ --. 500 .-• •• 60 •• «l1 .... -- •• •• 31) 40 ::J~ 4% ..

t-.. 2lI1 Yeeld point100

20

10-· 10-· 10-2 1 IOZS . t -1tra.n ra e, S

Fig. 2. 7,~rue"~Stresses at Various Strains Versus StrainRate for a Low-Carbon Steel at Room Temperature37 ·x

68

10 -•.III

20

10 10' loJ

2DO t;:::S=:$=;~~I-r--r-...,lao Yeeld point

10-'10-.,0-'10.2,0-' 1

Serain rate. 1-1

Fig. 2.8 True ~~Stresses at Various Strains Versus StrainRate'~~~Low-Carbon Steel at ZOO·C 37

JGO ,............,.--r--r--,.~.--=11oa

~ ., J,.;.....:t.:.:.:.:.+~.....-t--t--t"-1 !~ . .: SID !~ • &: «10 ~~s;..i:iH ~

C a.c~ MI t-

.. : l-;,~~~!l~f:J~J ~10•• 10.'10-'10.1 1 10 10' 10'

• -1Stra.n rate. I

Fig. 2.9 True~ Stresses at Various Strains Versus Strain ><Rate for a Low-Carbon Steel at 400·C 37

69

•

10 10' 10'

100

•CL~..•! 300 1--..04~ ....-+--t--••::t~

Fig. 2.10 True ~~ Stresses at Various Strains Versus StrainRate '{,6~: Low-Carbon Steel at 600·C 37

10-'10-210-310-410-5

'I ' 11111111 I '.UIIJII 'I!

I IYIELD STRENGTH (0.2 'I. OFFSET)I

-50F -A , \I

75 F 0~..I II

IIJ600F0

(

v

, _' ITTr"r· '-TTENSILE STRENGTH

I"

-50 F..)J

7'51FCfl,~60

0f

)

II)

4

60

3

&0

70

80

6,

7

80

90

100

.U)enw~cn

tit..

STRAIN RATE, In./ln./sec

• 0 •Fig. 2.11 Effect of Strain Rate at -50. 75. and 600 F on theYield and Tensile Strengths of USS COR-TEN Steel39

~

o

10-110-210-310-4 .10-0

, , , 'I'"' , --.- TENSILE STRENG.TH...

1 -SOF

0

~5F

0oQ

600F,,.

~

J I 11111111 I 11111111 I I I I AYIELD STRENGTH (0.2 % OFFSET) -SOF0 I

1 I ~

75 F-0

.....600F

0

lt1

9

7

10

7

8

: 60.enen~ 81...en

STRAIN RATE, In.!In./"c

Fig. 2.12 Effect of Strain Rate at -50: 75: and 600·F on theYield and Tensile Strengths of USS TRI-TEN Steel 39

-..J....

72

100 25

50~__~~ L...-__...L.__-J ..I-__...J 0

-3.0 -Z.O -1.0 0 1.0 Z.O 3.0

LOG STRAIN RATE, Sec-I

90 ZO

... ~~

0 -(J') Z(J') 0W 15a:: ...... c(

(J') C)

~..J

10 W

~a::0La.

60 5Z::::>

Fig. 2.13 Effect of Strain Rate on MechanicalProperties of a HSLA Steel40

IIlISI 01 SfEELI_!lED

01 02

ENGINEERING $TRAIN

Fig. 2.14 Strain-Rate Changes During Tensile Test, Four Strain RatesShown Are 10-1, 10-2, 10-3, and 10.4 sec· 1(4l)

-N.

.,. E

.. E••L. ..- -til

e 'ens'" streftVCh30 -.Uppe,'~'~ l-.~

Olo-er ,iftd point ,.....- .......-J-. - -

lcf 1dCrossheod speed

73

Fig. 2.15 Effect of Crosshead Speed on YieldBehavior and Tensile Strength42

.,.-------------------,

•

.. ., t' :..~ I·t

CAl ,0 ... ~ ,,~ ,-,

Fig. 2.16 Stress-Strain Curves for SA-106 Carbon Steel Pipe43

74

;/I estimated expt'l error

o6,ofJ experimental data

- new rate law

O'------'----~----'-------J

10-5 10-4 10.3 10.2

Strain Rate, (s·11

0.024

Q) 0.016:I

o>

Fig. 2.17 The Variation of the Strain Rate Sensitivity (m-value)With Strain Rate44

1250.....--~--r---....----,

7

500

250

ste(l( X45 CrS,9 3t(lmp(lrotur(l RT

• -4a) Ep ,= 5·10 1/5

• 2b) Ep, =1 10 1/5

• 2c) EPi =5 10 Us• 3

d) Ep1 =2 10 1/5• 3eo) Ep ,=5 10 Us

10 20 E 30 .,.

Fig. 2.18 Stress-Strain Curves for High Strength Steel at VaryingStrain Rate 5

ao~........~...

o

ClI'W Strain rote

: fJSC""'• 171• 808

75

Fig. 2.19 Dynamic Stress-ftrain Curves for AISI Type 304Stainless Steel 7

Jl...~...

f... Tfj:• 140• S02

o~---rr--....,tor---"ft---~N-"--""-

Fig. 2.20 Dynamic Stress-Strain Diagra. of AISI Type 304LStainless Steel47

Strain rate

r]SC"1129827

76

O~--'"iIO:'---~20r----""30=----:"~O----::SO~

(0) EngineeillJ struin <%)

Fig. 2.21 Dynamic Stress-Strain Diagram of AISI Type 347Stainless Steel47

3.0 .--..,...--.--r--..,.-T-.....,..-r---r--'T-~...,1000

500

Fig. 2.22 The Ambient-Temperature Yield Stress of Annea1d Type 21-6-9Stainless Steel As a Function of Strain Rate48

77

10 uti W

50 S~~--1---¥::+-I4O~.....1--......_.-._.-.._......-lL-.;;;J

10-1 10-2 10-' 1

110 r--,.-.,.-.....,-..,...-r---

100

Plastic .train rate••- ,

Fig. 2.23 Analysis of the Uniaxial Stress, Strain, and Strain RateData for Aluminum 1060-0

49

78

II Mo••nd DuffyII National Physical laboratoryII Minshall" Campbell and Harding

- TtwftoPolft -uJ description

--t-----+---~~+_---___J100

oo~e--~~=-~~~::....----L-L---J 0

.,;..e;;'a..>~•;;..::scE....e;;'a'0.>'"E•c~ -lIlI.'=" ---"L.:- ..J. ...L. ..L ---=:l - 100

lli-· 10-' 10' 10" Icf

:. 14lll1r----....,:-----,.-----,-----r.,------""~ ~~~ ~

o RoMnfI4lld and Hahn

• Krafftv Winloclt.. Manjoineo Taylor

• Chalupni.• Johnson. at .,.6HatCli"ll

Sir,,", rate. S - •

Fig. 2.24 Dynamic Yield Stress (Minus the Static Yield Stress)Versus Strain Rate for SteelSO

.~;;... ;;;..::scE....e

20 ;;'tl..>-u

E•c:>-o10"10'

Slraift r.... s - •

10'

I I I

AIlIIniI_.. 16061·T6IBulchet and Karnes- IPu,. AI, Karnes and Ripperg.- IAJuminum'lindholm

0 IAI single cryst.'s' Ferguson Kumar .nd Corn-m IPure AI, Yoshida and NagacoDeduced from crack velocity data

! ..i

..I ..

I 0

•Q.

~4lllI.-..!;;-'4iiii•;,ce 2111••!;;:!l•>-.~

!c~

Fig. 2.2S Dynamic Yield Stress (Minus theS' oStatic Yield Stress)

. R "I: Al .Versus Stra1n ate Lor um1num

•

•

•-. ••••I: . :j =:1· ::

...~.:--=....----:..~_~._....J.'-- ...&.:--......:--.....J.....__._'lFig. 2.26 Strain and Strain-Rate Dependence of the

Flow Stress of High-Purity Aluminum51

.,.----......--,.--...--..,...-.....- ....a

.~.r_~.T.__.~.~--'--.'-_ ....._........-...J....._-.....Fig. 2.27 Strain and Strain-Rate Dependence of the

Flow Stress of Aluminum 1060-051

..r---..,...-_-.....,.-......,..--...---r--,

••••~------;: .

_a __ .--==:::-. _:::: .I ~ ..-!"I:--~: -1 - ~....

1 ....

',II"t'~_"""""--."=4---',--.~-~~r---:~r~~---_...

Fig. 2.28 Strain and Strain-Rate Dependence of theFlow Stress of Aluminum 1100-051

79

80

10

• 40.0" ..

• 910.0" ..

SPECIMEN: .37 S inOIA x .500 in LONG

•.009 in/in/sec

50

•.~.., o~

~4"

~.,,;I.8· COMPRESSION TESTS ON

I ALUMINUM 6061-T640 I

8

130 '

I ..13

a 2.0

20,

COMPRESSION TESTS ONALUMINUM 7075·16

100~ ..,."'-.'....,.

80 ....,r- -

~ t SPECIMEN: .375 in OIA x.... c

c 60 "........ t .500 in LONG ::2~

I 0 0.03 in/in/sec0

0 • 00 I

00 • 4.0 • -

40 ""j -'"

'" 0 D 18.0 · • '"'" I

........ DCII:

CII: • 560~

~ I • · • '"'" 0

20 '.

•°0:-+~2:--.~3-4~-!5l-+6-O:7~~8--::!9

STRAIN ~ (in/in)

o0:-+--:!2~3~~4~5l-6+--::!7:--8±--:!:9~10STRAIN ~ (in/in)

Fig. 2.29 Compression Tests on Aluminums 7075-T6 and 6061-T653

4 KARN£S/RIPP£RGER (1966)

o GREEN ET AL. (1970)

o HOLT ET AL. (1967)

9 LINOHOLMI YEAKLEY (1965)

<> LINOHOLM I BESSEY (1969)

6"4 STRAIN

01060-0

1060-001100-0

9';-'"00-0

~'-O

06061'~ ~7075-02024-0~ __

07l78-0~'-T6 2024-T3

OL--,.L.0--2J.O--30~--:4J.:O~--:50=-.&.-:6O;;.·:::~"'~0~=;80~~~;-=~o STATIC FLOW STRESS v, (KSII

010...---------------------------,

~008....- ..:CI'.2

~• 0.06

,gol)

)-

~ 004;:iiiz...,:: 002~a:

Fig. 2.30 Strain-Rate Sensitivity of Aluminum Alloys31

81

0.12 0.'6 0.20 024 0 ze O.R

1IlUl STlta* C.,ltll

008

------"'" ---"."" .... -- ._-

~~ ....if-",,' --

"/

; V I

! "el'r" .- StaTe

,

Zo,ooo

,.,000

oo

_16,001);;~....! 12,000..!lc~ 8.QOO

Fig. 2.31 Cyclic Static-Dynamic-Static Loading for A1uminum52

02OJZ 0J6 0.20,... snu- c•.,.,

0.08

----;..::-I.-

...... -.... ;. ... /" -

" .... 11- -v·....~ ....---

j ~/[(

l/~ .'ate --I

I .. oz• 0."

••000

20.000

Fig. 2.32 Cyclic Dynamic-Static-Dynamic Loading for Aluminum52

82

1---........ :.:::--~ .-r ;

1 0.'" ~ --

~\ ~--- -!/ --,....,. .. -. .

f ,,;'

,r~ - -I I

oo 004 oae OJI 0.16 010 OZ4 oze 0.32

lllUI !lTltAI. '.'IN'

Z4.QOO

4.000

-'-.000..~

::r IZ.QOO:;

Fig. 2.33 Cyclic Dynamic Loading for Aluminum52

80.-----,r-----,..---r----

'040t---Ill'41..-

°O~-~:---~~--:-:---:f.0.2 0.4 0.6 OSLOo,I. slr~n~ IE

Fig. 2.34 Effect of Alteration of Strain Rate Upon Flow Stress( Static-Dynamic )55

8O_---.---..,..--~-"?'f

20

83

0.2 010 OSLog.straift. I

O.P.

Fig. 2.35 Effect of Alteration of Strain Rate Upon Flow Stress( Dynamic-Static )55

'Cji 60

=

84

Strain 10/.)

Fig. 2.36 Results of Constant and Incremental Strain-Rate Tests on1020 Hot Rolled Steel (HRS)57

20

L......--'---'._*......---::..'::-....--::~-' 0o 10 20 30 1.0

Strain (%).

Fig. 2.37 Results of Constant and Incremental Strain-Rate Tests on1080 Cold Rolled Steel (CRS)57

1250Str8lft Rale (I") : AISI 316 H Test Temperature: 20 °C.- flrestrain

Q. • 0.0047 A , 0.004~ + 0.0162 e ' 500

"":'000 I 0.0917l: • 0.1665.,;.. • 0.2300! • 0.3048u; 750Ql::l

~

-80 sao~...~

i40 250It

ci.E•... 0 0

0.36 0.48 0.600 0.12 0.24True Strain,ft

Fig. 2.38 Tensile True Stress-True Strain Curves at Ambient Temperaturefor Monotonic Loading to Fracture at a Strain Rate of 0.004sec-1 (Curve A) and 500 sec- l (Curve B). and for Quasi 54Static Prestraining Followed by Dynamic Reloading to Fracture

85

I T Ie I I T C II T C I

T'T T T

T T 1,

T T --

T T ROLLING DIRECTION T TI T ! C I I T ! C I

I I T C I

· ..

·r- -r-

~r r ,.. r r r

h .... .... 0 !;.., .... .... .... ---..... , - .

LEGEND

LT - LONGITUDINAL TENSION,LC - LONGITUDINAL COMPRESSIONTT - TRANSVERSE TENSION

TC - TRANSVERSE COMPRESSION

•

W/4 W/4 W/4 W/4

W: WIDTH OF STEEL SHEET

2"

12"

Fig. 3.! Location of Tension and Compression Coupons!!000\

1-1/2" 1/2" OIA. HOLE

----$-----1- 12"

1-1/2"

"\\0

Fig. 3.2 Nominal Dimensions of Tension Coupons Used for IOOXF. 50XF.

and 35XF 11

00'-J

Fig. 3.3 Material Test System (MrS) 880 Used for Tension Tests

0000

Fig. 3.4 MTS 880 Test Controller and Function Generator

89

Fig. 3.5 Data Acquisition System

90

Fig. 3.8a Test Setup Showing the Attachment of Extensometer

93

Fig. 3.8b Test Setup Showing the Attachment of Extensometer

94

Fig. 3.9 IBM PS/2 Model 30 Personal Computer with IBM ColorPlotter and NEC Pinwriter P5XL Printer

\.0Ln

DATA GENERALMV/10000COMPUTER

CAMAC --.TI..._1/1111111 'H•• MAl'HIC8

TMHDYIIIW MAPHIC.

SOFTWARE

SYSTEM AND SOFTWARE OVERVIEW

CAMACDATA

ACQUISITIONtc=l -mAIN I_1/11111 .td H'

MTSCONTROLCONSOLE

ACTUATOR

~ICATION ~TW~

U8ItI' ....ITTIIN P'1IA

" IIPllCIl"IC TII.T

P'lIAT_ " -=-CAMC MODUL• .-nol...

l"_" eClOf:

avaTItN 1~1fT

CIoMAC JNTIEN'''" .-.ouT1...

P'lIAT_ " COOtl

.VaTltMJ~

_1111111. , ••

ClMUoC INTII,.,."" .-nol...

.V.TItM~

_ 1/lIIII'H

fWIlDW.... INTI""""

CAMAC CRATE

U CHIoNNlIL_oe TO DlalTM. CDNYIltTIA

............111'UNCT10N _TlIA

CCIHT-. JNTVPACIIl TO NTa

- -Ir:~ :CX;:I;- - - jo __1- _

CANAC CClHTItDU.IA

IIII

'0C'\

Fig. 3.10 MrS 880 Automated Test System and Software Overview

S,rvonl"Control Sign.1

Actuator

448.'"VaIv' Driver

448.22AC Conditioner

IXdcr 31

Displacement - I P'1Xdcr

DC Error

Displacemenl

....8.21f ore, IDC Conditioner I~ I

i IXdcr 11

....8.21~ SUlin IDC Conditioner

IXdc,21

f"dblckSllect

Analog Switch

Actl"Control

Modi

Fledback Sllect

Comm.ndS,Iact

448.17 Micro SuplrvlsedS,rvoffHdbec:k

CommandS,Iact

, I ~ I An.lot Switch

448.85Ta.. Controllerr----,ISit Point \1,.4IIIISpan 1I

Xdcr 3

448.85Tlit Controller,----------,

Xdcr 1 Actlv' IModi I--L I

Xdcr 2 :ctiv;l!Modi--Lo O......-..-+I...~...I

tIIIIL ..;,J

Protram Input fromComputer Command 'Glneratlon D,vlci

Input ProtramCommand fromProtrammer 2

Input ProgramCommand fromProgrammer 1

Fig. 3.11 MrS 880 Test Controller Servo Control Loop\0"-oJ

Strain , Percent

RT1 RT2

Time , Seconds

RT1

98

Fig. 3.12 Typical 'Test Function Generator Ramp Waveform

\0\0

1000900800700

Strain Rate = 0.0001 in./in./sec.

400 500 600Time, Seconds

300200100o

2

4

o te== I i I I I Iii iii I Iii I I i I I

8,

ercent

P 6

S 14 --I

tr 12a•

I 10n

Fig. 3.13 Strain-Time Curve for 100XF-LT-l.(Virgin Material)

I-"oo

2018161410 12Seconds

8

Time


64

S 20

t 18

r 16a· 14I

n 12

p 10

e 8

r 6ce- 4n 2t

00 2

Fig. 3.14 Strain-Time Curve for 100XF-LT-3,(Virgin Material)

30 · i

~

o~

0.40.350.3


0.25, Seconds

0.2TIme

0.150.1Oi I I I I I I I I I I I I I t

0.05

Str 25

a•I 20n

p 15

er 10ce 5nt

Fig. 3.15 Strain-Time curve for 50XF-LT-7, (Virgin Material)

III

---T--r--T I I I I I I I

......oN

.... 0.0001 in.jin.jsec.- 0.01 in.jin.jsec.-- 1.0 in.jin.jsec.

161412I I I I I ~

100XF-LT-4

6 8 10

Strain , Percent4

lOOXF-LT-6

100XF-LT-l :

2

••• 0 •••••• 0 •••• •••• •••• • 0 •••••••••• 0 •

.. .............. - -- - - -- -- - - - - - - - --

o

160150140

S 130t 120r 110e 100

90s 80s 70

60K 50S 40I 30

20100

Fig. 3.16 Stress-Strain Curves for 100XF-LT-l, 100XF-LT-4,and 100XF-LT-6,(Virgin Material)

160150140 ~ ~._---------------S 130 . q"." ............... ~ -- 0,\ lOOXF-TI-5

t 120r 110 ::l ,

. 100XF-TI-4

e 100

s 90 .... 0.0001 in.jin.jsec.80

,,

s 70- 0.01 in/in/sec.

60 -- 1.0 in.jin.jsec.K 50

:100XF-TI-2

S 40I 30

20100

0 2 4 6 8 10 12 14 16Strain, Percent ~

0w

Fig. 3.17 Stress-Strain Curves for 100XF-TI-2, 100XF-TI-4,and lOOXF-TI-5,(Virgin Material)

~

o~

.... 0.0001 in.jin.jsec.- 0.01 in.jin.jsec.-- 1.0 in.jin.jsec.

50XF-LT-9

: 50XF-LT-l

50XF-LT-4

------------------~. . :..:...:....: .

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain , Percent

100

90

S 80t

70re 60s ......... ,

50s

40

K 30SI 20

10

0o 2

Fig. 3.18 Stress-Strain Curves for 50XF-LT-l. 50XF-LT-4.and 50XF-LT-9.(Virgin Material)

.... 0.0001 in/in/sec.- 0.01 in/in/sec.-- 1.0 in/in/sec.

50XF-TI'-9

------------- ..............., -' ,. 50XF-TI'-6 ...,..

" .,.~ 50XF-TT-l

II I

,.1II .,"I""

40

K 30S

1

20

,,,,,II I

10

. I I •• I •iii Iiii Ii I I i II iiio I I - •.--.-r.-,-.,. -- I

i100 I

90

S 80

t 70re 60

s 50s

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain J Percent ....oV1

Fig. 3.19 Stress-Strain Curves for 50XF-TI'-1. 50XF-TI'-6.and 50XF-TI'-9.(Virgin Material)

.,., 0.0001 in/in/sec.- 0.01 in/in/sec.-- 1.0 in/in/sec.

••••••• 00

•

50XF-LT-l

..".----------- -__ 550XF-LT-4 -- - _ OXF-LT-5....

"' "' \". \

", \

'~

\t,r,I'.,:1:I:,:,:,:I:,:,:\ :,:,:,',,',

\: .,:I'·

....

100

90

80"l ...

/

70 -3;'

//

//

I

60 .::tl /,'

50

40

30

20

10

0

KSI

Stres·s

o 2 4 6 8 10 12 14 16 18' 20 22 24 26 28 30 32 34 36 38 40

Strain , Percent ....o()\

Fig. 3.20 Stress-Strain Curves for 50XF-LT-l. 50XF-LT-4. and50XF-LT-5.(2% Cold-Stretched.Non-Aged Material)

.... 0.0001 in.jin.jsec.- 1.0 in.jin';sec.

\

.

..

50XF-TT-l

50XF-IT-3---------.................. - ..

• I

0-; I11I111111 r 111111111111111111111" I I" I ,

100

90

S 80t

70re 60s

50s

40

K 30SI 20

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain f PercentFig. 3.21 Stress-Strain Curves for 50XF-TT-l and 50XF-TT-3,

(2% Cold-Stretched,Non-Aged Material)

.....o'-l

100

90

s 80] 50XF-LT-6~ .... ---------

t- .... _-

r 70

e 60ss

50

40KS,

~ .\\\,,,,~\ : 50XF-LT-I,I,,,,,,,,

\

50XF-LT-4

.... 0.0001 in/in/sec.- 0.01 in/in/sec.-- 1.0 in.jin.jsec.

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain , PercentFig. 3.22 Stress-Strain Curves for 50XF-LT-I, 50XF-LT-4, and

50XF-LT-6, (8% Cold-Stretched,Non-Aged Material)

~

o00

100

90

S 80t

70re 60s

50s40

K 30S, 20

10

00

50XF-TT-3

._ 0 -·········.0. _0.50XF-TT-l

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain , PercentFig. 3.23 Stress-Strain Curves for 50XF-TT-I and 50XF-TT-3,

(8% Cold-Stretched,Non-Aged Material)

.... 0.0001 in.fin.fsec.- 1.0 in.fin.fsec.

~

o\0

.... 0.0001 in/in/sec.~ 0.01 in./in.fsec. .-. - 1.0 in.fin.fs~c.

. ".... ,.'.'.

\ "., ..\ .., .., .., :, :, :, :

I :I :I :. 50XF-LT-lI .II,II

50XF-LT-3 \ ,,II •,II

SOXF-LT-6

..........................----------------,-,--- ,--

, I I I r'-', I I ( , I I , I ( I ( , , I , r",.-' , I , I 1 I I I , r I I ..'

100

90

S 80t

70re 60s

50s

40

K 30S, 20

10

0o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain I Percent........o

Fig. 3.24 Stress-Strain Curves for 50XF-LT-l, 50XF-LT-3, andSOXF-LT-6, (2% Cold-Stretched, Aged Material)

50XF'-Tf-3

--------

100

90

S 80 i

t70r

e 60s

50s

40

K 30S, 20

10

0

.. " _ ..

50XF-Tf-l ""

,..... .. 0.0001 in.fin.fsec.- 1.0 in.fin/sec.

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain I PercentFig. 3.25 Stress-Strain Curves for 50XF-Tf-l and 50XF-Tf-3,

(2\ Cold-Stretched, Aged Material)

......

......

......

.... 0.0001 in/in/sec.- 0.01 in/in.fsec.-- 1.0 in/in/sec.

50XF-LT-3

...•

.

.

..

.SOXF-LT-l:

50XF-LT-6__ .."...... - A~""'''''",,,,,,, ""\.,J ...... " ... ¥fI

_.~""......I..

100 :rl ----------------------.I

90

70

60

50

40

K 30S

I W I

i , iii'

10

iii i • • i i •• f • • • •

i i fI Ii.I I I I Io IIIIIIII

S 80tress

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40Strain , Percent ~

~

N

Fig. 3.26 Stress-Strain Curves for SOXF-LT-l. SOXF-LT-3. andSOXF-LT-6. (8~ Cold-Stretched. Aged Material)

.... 0,0001 in.jin.jsec,'- 1.0 in/in/sec.

···

50XF-IT-3

~ : ]~~~~rr~'2"~~re 60:t

S 50s

40K'S 30

I 20

100 , I

90

o Iliitiiiliiiiiiiiiiiiiiiiiiiiiiiil'I'iiil

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain , PercentFig. ).27 Stress-Strain Curves for 50XF-TT-2 and 50XF-TT-3,

(8~ Cold-Stretched, Aged Material)

........w

70 i I

... "0.0001 in.jin.jsec.- 0.01 in.jin.jsec.-- 1.0 in.jin.jsec.

35XF-LT-l

-------------------,- - - - - 35XF-LT-4 "", 35XF-LT-9

,\

\\

, \. \

" \" i" I: ,: i: I: I: I: I: I: I: I: I: I: I: I" I,

I

................................................................

."

."

o t I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I 1 1 1 I I I I' 1 I I I ITT

60St 50re 40s

s 30

K 20S

I 10

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42" 44 46 48 50

Strain , Percent .........~

Fig, 3.28 Stress-Strain Curves for 35XF-LT-l. 35XF-LT-4.and 35XF-LT-9.(Virgin Material)

70 -- I

6035XF-TT-5S ~ __ ----_____

~-~- ~-~~-- ,... - - - 35XF-TT-4 "' ...

t 50 /~~ .................................. '\r " -,.... ..... \/ .. , \

e if...·· 35XF-TI-l .... \

.... 0.0001 in.jin.jsec.40 . . ,

in.jin.jsec.s .... . ,

- 0.01:\ 's 30 ~ : ,in.jin.jsec.

: I -- 1.0I,: ,

K 20 : ,: ,: ,S : ,: ,, : ,: ,10 : ,

-I I 1 I 1 I 1 I I I 1 , I I I I 1 I I I I i I I I I I i I I , i , I , i I I , i , I , I ,

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50Strain , Percent ~

~

V1

Fig, 3.29 Stress-Strain Curves for 35XF-TT-l. 35XF-TT-4.and 35XF-TT-5.(Virgin Material)

70 1 I

..0'

.... 0.0001 in.fin.fsec.- 0.01 in.fin.fsec.-- 1.0 in.jin.jsec.

.......

35XF-LT-2

35XF-LT-4

3SXF-LT-S

---------------------,-- ,--- ,-- ,\

" \\

"". \'. \'. \

'. I: I: I: I: I: I: I: I: ,: ,: ,: ,:," ,: ,:,

....... - .oo- ·· OO" ..

.'

o til r IIII II II II II II IIII II II II II II II II II IIII II' r r ••• f

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50Strain , Percent

60

10

St 50r

e 40ss 30

K 20S\

Fig. 3.30 Stress-Strain Curves for 3SXF-LT-2. 3SXF-LT-4. and3SXF-LT-S.(2\ Cold-Stretched.Non-Aged Material)

70 I I

.. .. 0.0001 in/in/sec.-- 1.0 in/in/sec.

35XF-Tf-4

35XF-Tf-l

'.

.. , ~ ..'

o " 1 1 I I I I I 1 I I I 1 I 1 I I I 1 I 1 I T I I I 1 I 1 I 1 I 1 I I I ,-,-1 I 1 I ,-rrr"-T

60St 50re 40ss 30

K 20S

I to

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Strain , Percent ~

~.....

Fig. 3.31 Stress-Strain Curves for 35XF-TT-l and 35XF-TT-4,(2X Cold-Stretched,Non-Aged Material)

70 I I

.... 0.0001 in.fin.fsec.- 0.01 in.jin.jsec.-- 1.0 in.fin.jsec.

35XF~LT-3

35XF-LT-l

35XF-LT-5--------------"---- ,-- ,\

\\\\\,,,,,

I,IIII,II,,,

.. " " ..

o I 1 r I , I , I I I I , 1 , I , I , I , I I I I 1 , I , I , I , , I , I , I , I ,r' · · , · · · · I

60St 50re 40ss 30

K 20S,

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Strain , Percent........00

Fla· 3.32 StrU&s-Strain Curves for JSXF-LT-l. 35XF-LT-3. and35XF-I.'T-S.(8\ Cold-Stretched.Non-Aaed "ateria})

70 • I

.... 0.0001 in.jin.jsec.- 1.0 in.jin.jsec.

35XF-IT-3

35XF-IT-l...............................................

o 'I i , , iii , Ii' , , iii , iii ii' i , iii •• , • ii' , i , •• , ••• I , , , , l

60St 50re 40ss 30

K 20S

. \ 10

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Strain t PercentFig. 3.33 Stress-Strain Curves for 35XF-TT-I and 35XF-TT-3.

(8% Cold-Stretched.Non-Aged Material)

~

~

\0

.... 0.0001 in.fin.fsec.- 0.01 in.fin/sec.-- 1.0 in./in./sec.·

·······•

35XF-LT-2

•,If ••• -·············· •••••••••••••••••• ,. ••••••••.... .....

35XF-LT-6-- ........ --_ ....... ----~~ --~-

~~' ---~--35XF-LT-3 - - .... - .... ....

..........

\\\\\II,,,,,,

IIIIIIII,I,

o liiiiiiiili"'iliii"i"i'i'i"iiiii'l"""'i •• ,,1

llJ I I

60St 50re 40ss 30

K 20S, to

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 JO 32 34 36 38 40 42 44 46 48 50Strain • Percent

Fla. 3.34 Stre•• -Strain Curve. for 3SXF-LT-2. 3SXF-LT-l. and35XF-IX-6. (2' Cold-Stretched. A.ed Haterial)

....No

70 I I

.... 0.0001 in/in/sec.- 1.0 in.fin.fsec.

\

.- ..

35XF-TI-3

35XF-TT-l

.".. '

o l'iii'iliiiiiiiJI'ii.iiiiiifiiiiiiiii'iii;iiiiil'J~

60S j

t 50 ~

r ~I"e 40ss 30

K20S

I 10

o 2 4 6 8 10 12 14 16 18 20 22 24 26.28 30 32 34 36 38 40 42 44 46 48 50

Strain , PercentFig. 3.35 Stress-Strain Curves for 35XF-TT-l and 35XF-TT-3,

(2% Cold-Stretched, Aged Material)

......N......

70 I i

.... 0.0001 in.fin.fsec.- 0.01 in.fin.fsec.-- 1.0 in.~n.fsec.,I

I1II,I.l,l,I,I,

35XF-LT-6

35XF-LT-2

35XF-LT-4~~-----~~~-~~~~-~~--

........", , -, .....

o I'i.ii.li.i) ••••• ili.iiiii •• ii •• i •• ilii.iiiil.li •• '

60

10

St 50re 40ss 30

K 20S,

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50Strain , Percent

Fig. 3.36 Stress-Strain Curves for 35XF-LT-2, 35XF-LT-4, and35XF-LT-6, (8% Cold-Stretched, Aged Material)

......NN

70 I I

35XF-TI-360

S.

t 50r

e 40s

s 30

K 20S

I 10

.... .

35XF-TI-l• ~ •••• I ••••••••••••••••••••••

.... 0.0001 in.jin./sec.- 1.0' in.jin.jsec.

o Iii' iii iii ii' iii iii iii iii iii f , Iii iii iii iii iii iii iii

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50Strain , Percent

Fig. 3.31 Stress-Strain Curves for 35XF-TT-l and 35XF-TT-3.(8% Cold-Stretched. Aged Material)

....NU>

Fig. 3.38 Effect of Strain Rate on the Yield Strength of IOOXFSteel in Longitudinal and Transverse Directions, (Virgin Material)

.....N~

* Yield Strength, LTe- Yield Strength. IT

101

t •••••••••• ~ •••• ............. ( ..

0.001 0.01 0.1

Strain Rate, in./in./sec.0.0001

···

···

·· .· .· .· .· .·· .· .· .· .· .· .. . .

.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. : '" ! : ~ : ... .... .. .. .... .. .. ... .· .· .· .

· ............. "' " :, .. , .

· .· ---

120 I I i I I I I I I I Iii I I I I I I I I I, i i

0.00001

Stre 140

ss,

k 130

s.I

90 I I

......NlJl

"* Yield Strength-e- Ultimate Strength

1010.001 0.01 0.1

Strain Rate, in./in./sec.

................................ , ..

.. .. .. .. ............................................................. f , , , ..

Fig. 3.39 Effect of Strain Rate on the Yield and Ultimate Strengthsof SOXF-LT Steel, (Virgin Material)

................ f ! ! ~ , I ..

........ __ I "'-., , ro : ! , ~ ~ ... .. .. .... .. .. .... .. .. .... .. .. ... .. .. .... .. .. .... .. .. .... .. .. .... .. .. .... .. .. .... .. .. .... .. .. ..

40--1 I Iii I II~ I II~ I II~ I II~ I III0.00001 0.0001

S 80tr

e 70ss, 60

ks 50.I

90 T1---:---:--------:---~--------.I

'* Yield Strength-e- Ultimate strength

. . ... , , , ..

............... ~ \ \ ( ; .

. . .. . .. .

: : ~ ; .

........ w ..· .· .· .: r.

St 80ress 70,

ks 60•,

N0\

1010.001 0.01 0.1

Strain Rate. in./in.1sec.0.0001

Fia. 3.40 Effect of StrAin Rate on the Yield and Ultj.ate Stren~ths

of SOXF-l,T Stee It (21. Cold-Stretcbed.Non-Aaed Haterial)

50-\ I Iii I Iii I Iii I Iii I Iii I III

0.00001

90 i •• •• I

....N......

"* Yield Strength-e Ultimate Strength

101

- 1 • I .

.

·

·

·

0.001 0.01 0.1


······

Fig. 3.41 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50Xf-l~ Steel, (8~ Cold-StrBtched.Non-Aged Material)

· .· . . .•······· .. ·······,············ .. ···,············· .. ··1··· : , .

................ ~ \ ~ ~ : .· .' .· . . . .· . . . ..' .· .'· ..'· . . . .· .'. .· ..'· ..'· . . . .· ..'· . . . .· .' .· . . . .· .' .

60 I : . : : :0.0000; ,., · ... · ,.; · ,.: · ..; , ·-.--l

Stre 80

ss,

k 70

s•,

90 TI --~----:-----::------------,.-------.I

'* Yield Strength-e Ultimate strength

·····

" , .········ ·. .. , ..

············ .. ·-·f··············· lll c················!······· .... ······ .. r······.,··· .. ··.··!···············,.. .. . ..· .. .. .. .... . .. .. ...... ...... .. .. . .... . .. .. .... .. . .. ..· ~ .. .. ..· .... .... .. . .. .· . .· . .· . .

.

.

~: :.................~ •••••• 'ee •••• ,.: • •••••• •• •• 0' •••••••. e •• :' ••••••••••••••• : .

. . .. . .............................. , •••• , ••••••••••• 4i ••••••• ~ ••••• , .

~ .. .. ... . ., ..· . .· . .· . .· .· .

St 80ress 70,

ks 60•,

Fig. 3.42 Effect of Strain Rate on the Yield and Illtimate Strpngthsof SOXf-(~' Sleel. (2~ Cold-Stretched, Aged Heterle})

t-oN00

1010.001 0.01 0.1


50-1 I Iii I Iii I Iii I Iii I Iii I lit

0.00001 .

90 i • • i

.....N\0

"* Yield Strengthe- Ultimate Strength

1010.001 0.01 0.1


Fig. 3.43 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50XF-LT Steel. (81 Cold-Stretched, Aged Material)

···

·· .. .. . .·· .

·· .· .· .··.. . . .

···· .... ,·········i················!················i·· .. ,··· .. ······· .. i,···············i.·· .. ············

.. . . .................. ! , : ~ ! ~ .

.. .. .. .. .· .. . , ..· .. . .. .... .. .. .. .... .. . . .t .. • • •

.. . .. . .... . .. . ..· .. .. . ... .. . .... . .. ... . .. ... .. . ..· . . ... . . ... .. . .... . .. ... .. . .· . . .· .. .. .... . .. .· . . .

60., I "~ I II~ , III I II~ , II) I III

0.00001

Stre 80

ss,

k 70

s•I

'* Yield Strength-e Ultimate Strength

.

.

····

.. ................................................................................................................. " .... . . . .· . . ..· . . .· . .. ... .: . : *. .· * -:-~ :~ : :'.. .. . ..· . . .• .. .. • • • .. • .. • • .. • .. .. .. , t '; , .

·.. .. . . .................. , , ••••••••••••••••••••••••••••••••• t. •••••••••••• " ••• , ••••••••••••••••

II •• ..· . . .. ... . . . .... . . .. ... . . .. .· .. . . .... .. . .. ... .. .. .. .. . .. .

.

90 I : : : . : I· . .. . .... . .· .. . . .· . . . .· . . " .~ . . .· . . . .· . ... . .. ...................................................................... ,~..........•..... " .

. . . . . ... . . . .· . .. . .· . .· . .· . ., .· .

ks 50•l

St 80

res 70

st 60

Fig. 3.44 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50XF-TT Steel, (Virgin Material)

....wo

1010.001 0.01 0.1


40 -I I I I j I I I i I I I i I I Ii-II I I I I I I

0.00001

90 I I

....w....

'* Yield Strengthe- Ultimate Strength

101

.. II , •••• II .

···•

0.001 0.01 0.1


.

.

0.0001

Fig. 3.45 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50XF-rr Steel. (21 Cold-Stretcbed.Non-Aaed Haterial)

... .. . .· . . .. .···········,····!················!········· "·····I .. ·· ! ! ... .. .. ... .· . . ... . . ..· . .. .• • flo •· .· .· .· .· .· .

· .· . .................. II flo '" ••••••••••••••• II •••••••••••••••••. . .. . .· .

.. . . ........ , .. ' , , .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .· . .50-1 I Iii I Iii I Iii I Iii I Iii I III

0.00001

St 80ress 70,

k 60s•I

. I,•90 1 ; :

Fig. 3.46 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50Xf-rr Steel, (8X Cold-Stretched,Non-Ased Material)

....WN

'* Yield strength-e Ultimate Strength

101

... I i ..· .· .· .··

···

·······

0.001 0.01 0.1

Strain Rate, in./in.1sec.0.000\

·· . .···.···,········1 .. ···············1···············4, .· . .· .· .· .· .· ~··

··•·. ... .. . .. .........................................................................................., ... .. .. .. .... .. .. .. ... .. . , ..... .. .. .. ...... .... 't ..• to .. .. .... . .. .. .... .. .. .. .... .. .. .. ... .. .. .. .... .. .. .. ... " .. ... .. .. .... .. . .... .. . .... .. . ... .. .. ...... .. . .. . .. . .

60 -\ : : : : : II I II I I II I III I ill i I II I I I

0.00001

k 70

s•,

,

Stre 80

ss


··

·

·····

.

.

·······

·····

·····•

··

·.. .. .. ..••• •••••••••••• iiiiJIIIIiiiI , ••••••••••••••••

··.. .................. ··1···· .~., !, _ !- ! , -f- .... .. .. .. .... .. .. .. ... " .. .. ..· .. .. .. .... .. .. .. ..· .. .. . .... .. . . ..· . .· . .· . .· . ...

.• • " "' It " ..· . .· .· .· .· .

I90I· ~

A

•··St 80ress 70,

ks 60•I

Fig. 3.41 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50XF-1T Steel, (2~ Cold-Stretched, Aled Haterial)

...UJUJ

1010.001 0.01 0.1

Strain Rate, in./in./sec.O.ooOt

50, , "I I 'i Ii' 'I iii I , "I Iii I

0.00001

*" Yield Strengthe- Ultimate Strength

;.................... , I" ..

··••·

···.

•·· . . .····,,··· .. ·······I················I··· .. ···.. ·····.,·i··· , ..· . ... ... ... ... ... ... .··

90 ~ ! I I·····

Stre 80

ss•k 70

s•,

Fig. 3.48 Effect of Strain Rate on the Yield and Ultimate Strengthsof 50Xf-Tr Steel, (81 Cold-Stretched, Aged Haterial)

0.0001 0.001 0.01 0.1

Strain Rate, in./in./sec.1 10

....w~

60i·· I

~

V)

VI

"* Yield Strength-e Ultimate strength

101

·- f ..

·

··

..

.

·

··

.

.

. .. .. ........ , , ,................•................

0.0001

.

.

······

0.001 0.01 0.1

Strain Rate. in./in./sec.Fig. 3.49 Effect of Strain Rate on the Yield and Ultimate Strengths

of 35XF-LT Steel. (Virgin Material)

.. .. .. .... .. .. ............................................ tit OlIo I> .... .. .. ..· .· . .· . .· . .· .· .

30' 1 i I Iii iii 'i iii t. iii iii i-l

0.00001

•

k 40

s•l

Str 50ess

"* Yield S~ength

-e Ultimate Strength

····

·····

········ . . .

'-lL~.•• ' • ••••• t·· ...•....•.•••. ~ .••........•.... ~ ! ..............•.· .. .. .· . .. ... .. . .· . .. ..· . . ... . .. .. . .. . .· .· .··

•··•·

·•···········

k 40

s•,

60

,

Stre 50

ss

Fig. 3.50 Effect of Strain R~t~ on the Yi~ld ftnd Ultimate Strengthsof 35Xf-I.T Steel. (2~ Cold-Stretched,Non-Aaed "aterial)

.....W0\

1010.001 0.01 0.1


30;-- I " i , I I i I I I ii, I i I I I i I I I I

0.00001

60

Fig.3.S1 Effect of ;ll.lolill Nill., on the Yiplrl And Ultimate StrenRthRof 35XF-I.T Slee I (8X Cold-Stretc.bed.Non-Aged Haterta!)

....IN

"

'* Yield Strength-e Ultimate Strength

101

·-*·

·····

··· ·· ·· ···· ······ ·· ··· ·· ··· ··

·· .1l······,···~········· .. ··I·················

···

.

.

·..·

····..

0.001 0.01 0.1Strain Rate, in./in./sec.

0.0001

··········

····

.. . .. .. ........................................ " , , ... .. . . .... .. .. . ..· . . .. .· . .. .. .... . .. .. ..• • .. It .... .. .. ... . .... . .·····•

'tn-l ~ . I Iii I Iii I iii I III\IU I iii i Iii

0.00001

t

k40

s•,

Stre 50

ss

··.

* Yield Strengthe Ultimate Strength

··

.

.

······· - ..~

. :· . .....•.. ·t·· .. · ; ... .. II .... .. .. .... . .. ..· .. .. ..· . .· . .· . .· . .· .· .· .· .· .

.

.: ~:_--.-,~~

.........' ~ ; ! : : ... .. .. .... . .. .· . .· . .· . .· . .· . .· . .· .· .· .· .·

k 40

s•I

t

Stre 50

ss

Fia, 3,S2 Effect of Strain Rate on the Yield and Ultiaate Strenathsof 3SXF-I.T Steel. (2\ Cold-Stret.ched. Aled Katerial)

-~OD

1010.001 0.01 0.1

Strain Rate. in. lin. / sec.0.0001

30-\ 1111 I Iii I Iii I Iii I Iii I III

0.0000\


····

··· .t •••••••• , ~ ••••••••••••••••

·· ·· ···· ··· ·· ···

· .· .· .· .· .· .· .· .· .. . ... .. .. ..· .. .. .. .... .. .. .. .· .. .. .. .... .. .. .... ... .. .. .... .. .. .... .. .. .. ..· .· ... .. .. .. .... .. .. .. .... .. .. .. .... .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. , , " .... . .. .. ... .. .. .. .... .. .. .. .... .. .. .. .... .. .. .. .... .. .. ..· .· .·

I..60 I : : 1

· . .· . .· . .· . .· .·····

k 40

s•,

t

Stre 50

ss

Fla. 3,53 Effect of StrAin Rale on thfl Yield and Ultt.ate Strengthsof 35XF-IX Steel. (81 Cold-Stretched. Aaed "atertal)

....W\D

1010.001 0.01 0.1Strain Rate, in./in./sec.

0.0001

11\, I iii iii iii , i • i. i • iiiJU i. • I

0.00001

....~o

*' Yield Strengthe- Ultimate Strength

10

·····

········

·······

,,,·

· ..' .· . . .· . . .· . . .· .'· .····

0.001 0.01 0.1 1

Strain Rate, in./in./sec.Effect of Strain Rate on the Yield and Ultiaate Strenathsof 3SXF-TT Steel, (Virain "aterial)

····

·······

0.0001

Fia. 3.54

·· .· .· . .· .· . .· . .· . .· . .· . ................. ~ ~ , : .· . .· . .· . .···

···· . .· . .· .· ... .· .................. . , , "· .··· ····

30; , "I , 'ii , 'ii , 'ii I Iii, "I

0.0000\

k 40

s•,

60

•

Stre 50

ss

* Yield Strengthe- Ultimate strength

···

···· . ...11 .• · ....•.. ·, ....•........... 1••••.••••••••••• , .· . .· . .· . .· . .· . .· . .: : ,;•···

·····

.. .. . .· , .• • It. •II • • •· . .· ... .· . .· .· -· .· -· .· .

······

·····

········

..

····

···

····

········. •• . . . .. . . . . . . . t· .··

····.•.•.. , .•••••... I· .•. II II II ••

···

· I.60 -, i i ~

..

t

k40

s•,

Str 50ess

Fla- ).~~ Effect of Strain Rate on the Yield and Ulti.ate StrenRthsof J5XF·TT Sleel, (2X Cold-Stretched.Non-A.ed "aterial)

...~...

1010.001 0.01 0.1


30; I Iii I Iii I Iii I Iii I Iii 11,10.00001

....~N

*" Yield Strengthe- Ultimate Strength

101

~. ..

·····

······

0.001 0.01 0.1

Strain Rate, .in./in./sec.0.000\

····

Fig. 3.56 Effect of Strain Rato on the Yield and Ulti.ate Strengthsof 3SXF-TT Steel (8\ Cold-Sttetched.Non-A.ed "aterial)

.. .. .. .. ..••••••••••• •••• • •• • •••• • •••••••••••••••••••••••••• 1 ... .. .. .. ...... ...... .. .. .. .... .. .. .. .... .. .. .. ..... ..... .. .. .. .... .. .. .. .... ........ .. .. .. ..· . ...· .· .· .· .· .· .· .· .· ..

·· .........................~.· .· .· .

300.00001

60 I . : -. : ~ I

· .· .······

·

Stre 50

ss•

k 40

s•,

Fla· 3.57 Effect of Strain Mlttf' nn the Vi .. lrl "oti Ultimllte Stn~oglhs

of J5XF-Tr Sl~"J. (2' Cold-Stretched. AK~d "aterlal)

.....$:'W

'* Yield Strengthe Ultimate strength

10

·····

···

0.001 0.01 0.1 1


·~·i················i·····IIII .... 4·····i············ .. ···i········.· .. ·· ..

0.0001

·····

········

I I • I I'U\ ; I I I I I I I I I I I I • I I •Il1U I II

0.00001

I

'k 40

·s•,

Stre 50

ss

*' Yield Strengthe Ultimate Strength

·······- , ..

··············

·······

······

····.f

····

···f··

..•............. i ...~.........•....· .· .· ..L :

· ,. .· . .60 ....1 . . . . .· . . . .· . . . .· . . .· . .· .·•·········

•

Str

50ess

Fig. 3.58 Effect of Strain Rate on the Yield and Ultimate Strengthsof 35XF-TT Steel. (8\ Cold-Stretched, Aged Haterial)

....l:l:-

101

.

.

0.001 0.01 0.1


·. . ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. '" .... .. .. .. .... .. .. .. .... .. .. .. .... .. .. .. .... .. . .. .... .. .. .. ..· . .· . .· . .· . . ·

····4 .. .

30 i I I ~ iiiIii iii iii I Iii I I I 1

0.00001

k 40

s•\

.... 50XFLT-1, VIrgin- 50XFLT-2, 2%,Aged- - 50XflT-1, 8%,Aged

·················....······.

......········

•••• :-::-:I"'t ..~ ••••••••••••••• i'.... , , ,,\\\IIIIIII,I,,,,,,,,,,

....'.......'..

•....,

I100 ~

90

S 80

t 70re 60

s 50s

40

K 30S

,,20 111

1

1'1'..1

' I , I I I\1) I I I I I I I

I I I I II , I , II I I0,.,."o 1 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Strain t Percent'ta· 3.59 Stress-Strain Curve. for SOXELT Ste.l at Strain Rate of

0.0001 in.fin./sec. ~

~Vt

,... 50XflT-4, ~r9in

- 50XFLT-3, 2%, Aged-- 50XflT-3, 8%, Aged

,,,,,,·,··,,,.,,.

•,

,,

···.

---:::::::-:""'~:"'::-': .. """........ ....".' ".' " ,

" ,.' \

" \: \

: I' , ,,' ,,,,I,,,,,,,,,,

\\•

100 J I

70

60

50

40

K 30

S 20

, Ii II IIiiI i I

\0 I I I I I I I I I I I I ,I 1 I I I1 tit,0;-111111

90

5 80tress

o 2. 4 6 8 \0 \2 \4 16 18 20 22 24 26 28 30 32 34 36 38 40Strain t Percent

ria· 3.60 Str•••-Strain Curv•• fol' SOULT Ste.l at Strain Rate of0.01 in./in./.ec. ....

~0\

..... SOXflT-9. Virgin

- SOXflT-5. 2%, Aged

-- 50XAJ-6. 8%. Aged

-"'-""¥"'V_ .........•......•.........................• t-...'...',t."...••.

"•"-.......

1:r'----------I

80

10

60

50

40

30

, 20

\0

o I Ii ••• • • I I i I • lilill • iii• Iii Iii i I iii .ill,1

o 2. 4 6 8 \0 \2 \~ 16 18 20 22 14 26 28 30 32 34 36 J8 40Strain I Percent

Fla. 3.61 Str•••·S~t.ln Curvaa for SOXiLT St••l .t Strain Rate of1.0 tn./tn./••e. ,...

~......,

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