Modelling ductile fracture behaviour from deformation parameters in HSLA steels

$: Modelling ductile fracture behaviour from deformation parameters in HSLA steels$
doi: 10.1111/j.1460-2695.2004.00805.x

Modelling ductile fracture behaviour from deformation parametersin HSLA steels

S. SIVAPRASAD1, S. TARAFDER1, V. R. RANGANATH1 and K. K. RAY2

1National Metallurgical Laboratory, Jamshedpur 831 007, India, 2Department of Metallurgical and Materials Engineering, Indian Institute ofTechnology, Kharagpur 721 302, India

Received in final form 2 January 2004

A B S T R A C T In this work, an attempt is made to model the ductile fracture behaviour of two Cu-strengthened high strength low alloy (HSLA) steels through the understanding of theirdeformation behaviour. The variations in deformation behaviour are imparted by priordeformation of steels to various predetermined strains. The variations in parameters suchas yield strength and true uniform elongation with prior deformation is studied and wasfound to be analogous to that of initiation fracture toughness determined by independentmethod. A unique method is used to measure the crack tip deformation characterized bystretch zone depth that also depicted a similar trend. Fracture toughness values derivedfrom the stretch zone depth measurements were found to vary in the same fashion as theexperimental values. A semiempirical relationship for obtaining ductile fracture toughnessfrom basic deformation parameters is derived and model is demonstrated to estimateinitiation ductile fracture toughness accurately.

Keywords deformation effect; ductile fracture toughness; HSLA steels; semiempiricalmodel; stretch zone depth.

N O M E N C L A T U R E a, �a = crack length, crack extensionC = constant in the CTOD–ε relationship

C1, C2 = coefficients in the J –�a relationCOD, CTOD = crack opening displacement, crack tip opening displacement

E = Young’s modulusEPFM = elastic plastic fracture mechanicsHSLA = high strength low alloy

J, Ji, JSZD = an energy based ductile fracture toughness characterizing parameter,initiation fracture toughness, initiation fracture toughness determinedfrom stretch zone depth measurement

k = coefficient in the Hollomon’s stress–strain relationLEFM = linear elastic fracture mechanics

L-T = longitudinal transversem = constant in the J –δ relationn = strain-hardening exponent

SZD = stretch zone depthSZW = stretch zone width

t = projection of stretch zone widthTPB = three point bend

W = specimen widthw = stretch zone width

Correspondence: S. Sivaprasad. E-mail: [email protected]

c© 2004 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 27, 897–909 897

898 S. S IVAPRASAD et al.

α = angle of rotation of SEM stage during stretch zone dimension measurementδ = notation used for CTOD

ε, εu, εf = true strain, true uniform strain, true fracture strainσ y, σ o = yield stress, flow stress

I N T R O D U C T I O N

Fracture response of ductile materials depends upon themicrostructural constituents, the manner in which theydeform upon application of load and the state of stress.In general, for a given stress state, softer microstructuralphases such as austenite and ferrite are known to sus-tain more deformation than their harder counterparts likemartensite or bainite. Hence, the softer microstructuralphases are expected to be tougher than the harder phases.However, it is not only the microstructures per se thatdictates the deformation behaviour of materials. The al-loying elements that are added to the material for variouspurposes play a key role in determining their mechani-cal response. The residue of these elements in the bulkof the material in the form of inclusions or precipitatesactually control the deformation behaviour with the asso-ciated stress state and hence the fracture toughness. Howthese second phase particles participate in the deforma-tion behaviour of materials have been extensively stud-ied and modeled by various researchers,1–7 of which themodel proposed by Gurson and Tvergaard8,9 is presentlywell accepted. Although comparison and review of vari-ous such models are not within the scope of this work, astudy on these models clearly demonstrates that deforma-tion parameters such as yield strength, flow stress, fracturestrain, Young’s modulus of the material and microstruc-tural parameters such as inter particle spacing, the evolu-tion characteristics of voids on second phase particles andaverage void radius on coalescence etc. control the extentof plasticity in the material. Hence, it should be possibleto predict the fracture process by use of these parameters.Considering the interrelation between the micromecha-nisms of deformation and fracture, Saxena and Cretegny10

have proposed a model based on Rice and Tracy11 voidmodel to predict the ductile fracture phenomena.

Though it is evident from the work of Saxena andCretegny that the deformation parameters listed aboveare important for understanding the micromechanisms ofdeformation behaviour and hence the fracture process ofmaterial, determination of all these parameters and utiliz-ing them to characterize mechanical response of materialare often difficult. For instance, the interparticle spacingand average void radius at coalescence depend upon thesize, shape and spatial distribution of particles, and theprobability of finding the nearest particle or smallest voidin a three dimensional space that would eventually con-tribute to fracture phenomena is tedious to determine.

Moreover, such determinations also depend on the reso-lution of the instrument used for measurements. A simplemodel is, therefore, required that employs easily and un-ambiguously measurable deformation parameters to pre-dict the ductile fracture behaviour of materials.

The objective of the present investigation is to develop amodel to predict ductile fracture behaviour that uses de-formation parameters that are directly measurable fromsimple experiments. The proposed model uses deforma-tion parameters such as yield strength that controls theonset of plasticity in a material, strain-hardening expo-nent or true uniform elongation that controls the extentthrough which the plastic strains are spread uniformly andthe true fracture strain. The utility of this model in pre-dicting the fracture toughness is examined on two vari-eties of Cu-strengthened HSLA steels. The robustness ofthe model is tested through varying the deformation re-sponse of the two steels brought about by prestraining tovarious predetermined levels. The efficiency of the modelis judged through comparison with experimental determi-nation of fracture toughness of the variously prestrainedsteel.

A direct manifestation of deformation during the pro-cess of ductile fracture is the blunting of the crack tipprior to the onset of crack extension through ductile tear-ing. As a matter of fact, the blunted geometry of the cracktip preserves a snapshot of the local deformation statusat the moment of ductile fracture initiation. Hence, itshould be possible to correlate this deformation signa-ture to the fracture toughness of the material in a moredirect manner. An attempt has, therefore, been made inthe present investigation to characterize the geometry ofthe blunted crack tip in order to quantify the extent oflocal deformation that accompanies ductile fracture. Fur-ther, this has been employed to determine the crack initi-ation toughness from the fracture resistance curves of theHSLA steels prestrained to various extents and the val-ues obtained compared to experimental fracture tough-ness values.

E X P E R I M E N TA L

Material

The materials used in this investigation are two varietiesof low-carbon, copper-strengthened HSLA steels con-forming to the properties of HSLA-80 and HSLA-100.The steels were received from Naval Research Laboratory,

c© 2004 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 27, 897–909

MODELL ING DUCTILE FRACTURE BEHAVIOUR FROM DEFORMATION PARAMETERS 899

Table 1 Chemical composition of HSLA steels in wt%

Steel C Mn P S N Si Cr Mo Al Nb Ni Cu

HSLA-80 0.05 1.00 0.009 0.001 0.01 0.34 0.61 0.51 0.025 0.037 1.77 1.23HSLA-100 0.06 0.84 0.011 0.003 0.008 0.25 0.74 0.58 0.023 0.03 3.47 1.54

Table 2 Heat treatments of the HSLA steels

Steel Heat treatment

HSLA-80 Austenitized at 1172 K (899 ◦C)/45 min, waterquenched + tempered at 944 K (671 ◦C)/62 minAustenitized at 1177 K (904 ◦C)/70 min, water

HSLA-100 quenched + tempered at 911 K (638 ◦C)/70 min

Washington DC, in the form of rolled plates of 20 mmthick HSLA-80 and 25 mm thick HSLA-100 with theirrolling direction marked. The chemical composition ofthe steels and the heat-treatment condition in which theyare received are given in Tables 1 and 2, respectively. Themechanical properties of the two steels in the as receivedcondition are given in Table 3. The microstructures of thetwo steels are shown in Fig. 1.

Prestraining

As mentioned earlier, the change in the deformation re-sponse of the material is investigated through impositionof various levels of deformation prior to testing. Easy wayto look at it could have been to note down the changesin the yield strength or ultimate tensile strength from asingle tension test curve at the desired strain. But, as themechanical response of the material depends on the priorload history, such estimations may not portray the true de-formation behaviour after prestraining. Therefore, indi-vidual tensile tests were carried out after prestraining. Forthis purpose round tensile specimens of 5 mm gauge di-ameter with their loading axis parallel to the rolling direc-tion were prepared from the plates of the steels received.These specimens were subjected to tensile deformation ina servo-hydraulic test machine. An extensometer with 25mm gauge length was used for strain measurements. Spec-imens were deformed until a predetermined total strainlevel was achieved. At the attainment of this strain, speci-mens were unloaded to zero load. Prior deformations of 1,2, 3, 4 and 5%, total strain were imposed through this pro-cess. Tensile tests were performed on these predeformedspecimens as well as on specimens in the undeformed con-dition. For both prior deformation and tensile testing, auniform displacement rate of 0.003 mm s−1 is maintained.

In order to understand the variation in fracture behaviourdue to deformation, ductile fracture behaviour of the twoHSLA steels in prior deformed state is investigated. Forthis purpose, flats blanks of 5 mm × 10 mm cross-sectionwere cut with their shorter dimension along the platethickness. These blanks were then prior deformed adopt-ing procedures similar to described for tensile specimens.It may be noted that due to the high strength of the HSLAsteels under investigation and the available machine ca-pacity, the specimen size had to be restricted to 5 mm ×10 mm cross-section.

Fracture toughness testing

Three point bend (TPB) specimens in the L-T orienta-tion were prepared from the unstrained and predeformedblanks. Ductile fracture toughness of the two HSLA steelswas evaluated employing J-integral parameter. The pro-cedure used for J-integral fracture toughness testing anddata analysis has been described in detail in an earlier in-vestigation.12 In brief, after precracking all specimens toa/W = 0.5 (where a is the notch depth and W is the spec-imen width), J tests were carried out by single specimenunloading compliance method. A crack opening displace-ment (COD) gauge was attached to the external knife edgemounted onto the specimen and this was used for mea-suring crack mouth opening displacement. A compliancerelation for externally affixed knife edge13 was used forcrack length calculation. All tests were carried out un-der displacement control at a rate of 0.003 mm s−1 witha 20 s relaxation hold before unloading. Tests were con-tinued until well beyond the maximum load bearing ca-pacity of the specimen reached. A commercial softwarewas used for total test control and data acquisition. Theacquired data were then processed off-line to obtain in-stantaneous J and �a (crack extension) at each unload-ing. After completion of each test, specimens were fatiguepostcracked to delineate the stable tearing region, brokeopened and the monotonic crack extension is physicallyverified using a travelling microscope. It is observed thatthe crack length calculated from the compliance techniqueis within ±5% of the actual physical crack extension mea-sured on the specimen surface. A typical J − �a curveis shown in Fig. 2. It was found that for the HSLA-80steel, the slope of the blunting line of the J − R curve is



Table 3 Mechanical properties of the HSLA steels

Uniforma Hardness CharpySteel σYS (MPa) σUTS(MPa) % elong elong. (%) %RA nb VHN energy (J) YS/UTS

HSLA-80 650 715 24.2 10.5 75.8 0.12 250 218 0.91HSLA-100 840 884 21.6 8.1 73.5 0.08 300 192 0.95

aOver 25 mm gauge length in 5 mm diameter specimen.bObtained from σ = kεn, σ = true stress, ε = true strain, in plastic range.

Fig. 1 Microstructures of (a) HSLA-80 and (b) HSLA-100 steels.

considerably higher than the theoretical value of 2σ o (σ o

being the flow stress of the material) in the blunting lineequation J = 2σ o�a. The theoretical blunting slope of2 basically comes from the assumption that the crack tipassumes a semicircular profile upon blunting. However,examination of the transverse sections of the crack tipafter electroless nickel coating revealed that at all pre-strain levels the crack tip in HSLA-80 steels were far fromsemicircular shape. Such deviations from semicircularityhave been reported14–17 to be the characteristics of hightoughness materials and describe the use of the theoreti-cal blunting slope is too simplistic as no unique bluntingequation exists for such materials. In the present investiga-

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Power law: J = C1(∆a) C2

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Power law: J = C1(∆a) C2Power law: J = C1(∆a) C2Power law: J = C1(∆a) C2

Fig. 2 A typical J – �a curve showing the blunting line, and stabletearing region.

tion, an experimental blunting line was, therefore, drawnto the initial linear region of the J − R data by best fitmethod and a slope of ∼8σ o was calculated for HSLA-80steel. For HSLA-100 steel, however, a blunting slope of∼2σ o was found to be adequate in defining the experi-mental data. A power law curve of the form J = C1 (�a)C2

is constructed for the data falling within the window �a =0.15 mm and 1.5 mm. Deviating from the ASTM standard(E 813), in this work, the initiation fracture toughness, Ji,is determined at the intersection of this best fit line withthe power law curve on the J − �a plot so that com-parison with the fracture toughness determined throughstretch zone dimension is easier. This entire data analysiswas carried out using an in-house developed software.

The value of JQ at 0.2 mm crack extension was also es-timated for the two HSLA steels in unprestrained con-dition. The values were noted to be 680 kJ m−2 forHSLA-80 steel and 580 kJ m−2 for HSLA-100 steel. Thesefracture toughness values were slightly higher than theestimated18,19 JIC for these steels. However, consideringthe predominantly plain stress condition in which the



tests were carried out, such high fracture toughness isexpected.

Measurement of crack tip deformation parameter

Cracks in ductile materials first blunt prior to the onset ofductile tearing. The extent of crack tip blunting dependson the deformation behaviour of the material and the stateof stress ahead of the crack tip. This blunting process oftenleaves a signature on the fracture surface of the specimenbetween the fatigue precrack end and the onset of ductiletearing. This region is called the stretch zone. This zonehas direct reference to the toughness of the material sinceit is a measure of crack tip opening prior to tearing. Inhighly ductile materials this zone would have two compo-nents, a horizontal component called stretch zone width(SZW) and due to high plastic relief of the material, a ver-tical region called stretch zone depth (SZD). Both theseparameters are correlatable with the fracture toughness ofmaterial and have been extensively used by several inves-tigators20–26 as a measure of ductile fracture toughness. Infact, the JSME standard uses a blunting line based on SZWmeasurements to derive the fracture toughness of ductilematerials and an investigation by Hideo Kobayshi27 onvarious grades of steels claims the SZW-based bluntingline recommended by JSME standard is useful in case ofmaterials where the intersection of the theoretical blunt-ing line and the R-curve does not exist.

The measurement of SZW is direct and well documentedin the JSME S001. As per this procedure, a three-pointaverage of SZW at the midthickness of the specimen isrecommended to construct the blunting line. Scatter insuch SZW measurements has been statistically analysed bya round robin program organized by the European Groupof Fracture.28 It is brought out clearly that the subjectivityin defining the stretch zone boundary can give rise to highscatter and proposes such measurements to be carried outpersonally with good working experience in SEM in orderto have minimum error.

However, there is also a general opinion that SZD is abetter parameter than SZW for ductile fracture charac-terization.29–31 Determination of SZD is tedious and nostandard procedure is available as in the case of SZW. Theauthors have proposed a simple methodology for SZDmeasurements on the fracture surface elsewhere.32 Thismethod is employed in this investigation for SZD mea-surements.

As per this method, the fractured surface of the specimenis examined in the SEM in the 0◦ tilt position. The stretchzone geometry is recorded at sufficiently high magnifi-cation so that some prominent features on the fracturesurface can be noted for reference. Care was taken toensure that a good contrast was obtained so that stretch

zone limits could be demarcated unambiguously. Now, thespecimen is tilted through an angle 45◦ without makingany lateral shift. This is ensured by the reference featuresnoted earlier. Stretch zone geometry in this tilted angle isrecorded. From these untilted and tilted configurations, ageometric relationship can be obtained as shown in Fig. 3and an expression can be derived for SZD in terms of SZWand its projection as given below

SZD = h = t cos α + t sin α tan α − wtan α

. (1)

If the tilt angle α = 45◦, then the expression reduces to

SZD = h =√

2t − w, (2)

where h is the SZD to be measured; w is the SZW recordedin the untilted view and t is its projection recorded in thetilted view.

The stretch zone boundaries recorded in the 0◦ and 45◦

tilt conditions were traced and approximately 30 measure-ments were made for each test on both halves of the spec-imens as against the three point measurement suggestedin the JSME standard. The correspondence of measure-ments made in 0◦ and 45◦ tilt conditions is maintainedwith the help of the reference features. Such large num-ber of measurements was made so that the variation in thestretch zone dimension across the specimen thickness canbe seen and sufficient data for statistical analysis can beobtained. The average of these measurements was takenas representative w and t and the value of h (i.e. SZD) iscalculated using Eq. (2). A single person made all thesemeasurements so that the error in the measurement pro-cedure is minimized. The scatter in the w and t measure-ments were statistically analysed and were found to bewithin ±30 µ.32 A typical stretch zone feature in the un-tilted and tilted configurations depicting the measurementprocedure is shown in Fig. 4.

Determination of fracture toughness from crack tipdeformation parameter

The manifestation of crack tip deformation parameter,SZD, measured from the fracture surface is used to es-timate the initiation fracture toughness of the materialsunder investigation. For this purpose, two methods wereadopted. In the first method, a plot of J-CTOD datais used. The CTOD values were determined at any in-stance of crack extension following ASTM standard33 us-ing the same set of experimental data generated from Jexperiments. As stretch zone depth is equivalent to halfof CTOD, a perpendicular line was drawn at CTOD =2 SZD. Intersection of this line with the J-CTOD curveis taken as Ji. In the second method, CTOD-�a curvewas taken. A line at CTOD = 2 SZD was drawn and the



αααααααα

t

(b) Tilted view

start of

ductile tearing

(a) Normal view

SZW, w

SZD

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precrack

O A

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D B

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α


t

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D B

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hα

α


Fig. 3 Geometric interrelation between the untilted and tilted configurations of stretch zone dimensions.

�a corresponding to the intersection of this line with theCTOD-�a curve was noted. The fracture toughness valuecorresponding to this �a on the J − �a plot was takenas the initiation fracture toughness. It may be noted thatboth the methods are same but have different approach.

R E S U LT S A N D D I S C U S S I O N

Microstructure

The microstructure of HSLA-80 in the as received con-dition is predominantly ferritic with acicularity at localregions. This microstructure is typical of this variety ofsteels as reported by Wilson,34 Jessemann and Murphy.35

In the case of HSLA-100, the microstructure is essen-tially tempered bainite. For a similar grade of steel Wilsonet al.36 have also identified tempered bainite structure.

Variation of yield strength with prior deformation

The variation in the yield strength of the two HSLAsteels due to prior deformation is depicted in Fig. 5. In

order to clearly understand the relative changes in theyield strength due to prior deformation, the data are nor-malized with respect to yield strength at 0% predefor-mation. It may be noted from Fig. 5 that for HSLA-80steel, the yield strength remains almost unaffected up toabout 2% prior deformation beyond which it increasedproportionally. By contrast, for the HSLA-100 steel, theyield strength increased monotonically with prior defor-mation. The initial retention of yield strength up to about2% prior deformation by the HSLA-80 steel can be at-tributed to its yielding behaviour as shown in Fig. 6. It maybe noted that the HSLA-80 steel showed an appreciableyield point elongation up to about 2% strain. A ferriticstructure as in HSLA-80 is reported to exhibit such yieldpropagation owing to the initial shortage of mobile dislo-cations.37 As this provides a mechanism to prevent harden-ing upon prior deformation, the yield strength maintainsa near constancy up to 2% prestrain in HSLA-80 steel.The inflections in the curve in Fig. 5, therefore, indicatechanges in the hardening rate. In contrast, the HSLA-100 steel with bainitic structure in which majority of the



Fig. 4 A typical stretch zone feature recorded at 0◦ and 45◦ tilt conditions. Figures at (c) and (d) shows the marked boundaries withreference points for multiple measurements.

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Fig. 5 Variation of yield strengths of the two HSLA steels withprior deformation.

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Fig. 6 A magnified view of the yielding behaviour of HSLA steels.The HSLA-80 shows a distinct yield point phenomena with a longLuder’s stretch.



dislocations are believed to be mobile,38 does not exhibita yield propagation effect. Hence, its yield strength pro-portionally increased with deformation. It may be notedthat the ultimate tensile strength of both the steels alsoexhibited a similar nature of variation upon prior defor-mation.

Variation of deformation capability withprior deformation

The capacity of a material to deform plastically is nor-mally measured by its strain-hardening exponent, n. Thisn may be derived from various constitutive equations.39

The simplest and the most popular of all of them is theHollomon relation σ = kεn. In this work, an attempt wasmade to obtain n for the two HSLA steels by fitting var-ious constitutive equations employing a number of datafitting techniques. Details of this exercise is reported else-where.40 It was found that it is difficult to ascribe a singlevalue of n for the entire range of plastic deformation forboth the HSLA steels. This behaviour is typical of manysteels that exhibit multiple stages of hardening.41 In theabsence of a mathematically-derived exponent to repre-sent the strain-hardening behaviour, an alternative is touse the true uniform strain, εu, obtained from experimen-tal stress–strain curves. It may be noted that for Hollomontype of hardening, εu is numerically equivalent to n.

In this investigation, the true uniform elongation, εu,at the onset of necking was considered to illustrate theplastic-deformation characteristics of the HSLA steels. Inorder to represent the homogenous plastic deformationof the material in all prior-deformed conditions, the elas-tic strains and the strains arising out of inhomogeneousdeformation such as yield propagation are not consideredin the measurement of εu. The variation of εu with priordeformation for the two HSLA steels is shown in Fig. 7.It can be noted from this figure that εu for both the steelsremains unaltered up to a level of 2% prior deformationand subsequently decreases for further prior deformation.This indicates the fact that in both the steels prior defor-mation less than 2% does not affect the measured uniformstrain.

Variation of ductile fracture toughness withprior deformation

The variation of ductile fracture toughness, Ji, with priordeformation in the two varieties of HSLA steels is de-picted in Fig. 8. It is evident that for both the steels,the Ji did not deteriorate, but perhaps increased slightlyup to 2% prior deformation, beyond which it decreasedabruptly. A similar fracture toughness variation is reportedfor annealed 4340 steel.42,43 This initial retention of frac-

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Fig. 7 Variation of true uniform strain, εu with prior deformationfor the two HSLA steels.

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Fig. 8 Nature of variation of initiation fracture toughness, Ji, withprior deformation in two HSLA steels.

ture toughness is significant from the viewpoint of struc-tural fabrication with these steels, as it indicates the extentof cold deformation that can be imposed during shap-ing of steel plates without fearing any loss of fracturetoughness.

Conventionally, it is anticipated that the fracture tough-ness of a material to decrease with prior deformation asthe process of prior deformation is likely to increase theyield strength, and the strength and toughness of a ma-terial are inversely related. However, the toughness of amaterial is not dictated by its strength alone, but largelydepends on its capacity to deform plastically. Therefore,



fracture toughness of a material is expected to deterioratewhen such fracture toughness controlling parameters areproportionally affected on imposition of prior deforma-tion. However, as it is seen in previous sections, the yieldstrength (of HSLA-80 steel) and the true uniform elon-gation (for both the steels), which regulate the fracturebehaviour, did not alter in a proportional manner. Theinitial retention of yield strength by the HSLA-80 andthat by true uniform elongation for both the HSLA steelscan, therefore, be directly correlated to the near constancyin fracture toughness exhibited by the two HSLA steels atsmall magnitudes of prior deformation.

Some of the published results on annealed 4340 steel42,43

cited earlier which also showed considerable yield pointelongation, a similar mechanism can be assumed to beoperative, leading to a maintenance of fracture tough-ness with prior deformation initially. However, althoughsuch mechanism of limiting strength properties with priordeformation is not observed for HSLA-100 steel, itsretention of fracture toughness is thought to be con-trolled by its strain-hardening capacity, rather than itsstrength. It may be noted that the yield strength deter-mines the onset of plasticity in a material and the strain-hardening exponent (or true uniform elongation) regu-lates the plastic strain to spread uniform throughout thematerial. Both these parameters, individually or syner-gistically controls the fracture behaviour of the mate-rial. It appears, therefore, in HSLA-80, both the yieldstrength and strain-hardening exponent controls the frac-ture toughness whereas in HSLA-100 steel, it is the strain-hardening exponent that controls its fracture behaviour.

Variation of crack tip deformation parameter withprior deformation

The variation of mean SZD values of both the HSLA steelswith prior deformation is illustrated in Fig. 9. The error inthe mean SZD values is shown as error bars in the figure.It may be seen from this figure that the nature of vari-ation of SZD with prior deformation for both the steelsdepicts a similar trend to that of Ji. During the crack tipblunting process, plasticity would engulf the crack frontand the spread of this plasticity is governed by the strain-hardening response of the material. As the variation in thespread of plastic strains with prior deformation, measuredas εu, does not change for small magnitudes of deforma-tion (as seen earlier in Fig. 7), it is expected that the vari-ation of SZD with prior deformation would be similar tothat of εu. It may be further noted that SZD is related tothe fracture toughness parameter–crack tip opening dis-placement, δ and hence it is possible to derive the initiationfracture toughness, Ji, from these measurements so thatthe observed experimental variation of fracture toughnesswith prior deformation can be verified.

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Fig. 9 Nature of variation of SZD with prior deformation in thetwo HSLA steels.

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450

experimental Ji

JSZD (by method 1)

JSZD (by method 2)

HSLA-80

J, k

J/m

2

% Prior deformation

experimental Ji

JSZD (by method 1)

JSZD (by method 2)

HSLA-80

J, k

J/m

2

% Prior deformation

Fig. 10 Variation of JSZD with prior deformation in HSLA-80steel.

The variation of fracture toughness, JSZD, derived fromthe SZD measurements with prior deformation is shownin Figs 10 and 11 for HSLA-80 and HSLA-100 steels,respectively. The errors in JSZD originating from the errorin the determination of mean SZD values are shown aserror bands in these figures. This plot also contains thevariation of experimental Ji with prior deformation forready comparison. It can be seen that the error in JSZD

values is nominal, and the scatter due to the errors doesnot alter the nature of variation of fracture toughness withprior deformation.



It is evident from Figs 10 and 11 that irrespective of themethod of measurement, the nature of variation of JSZD

with prior deformation is similar to that exhibited by Ji

for both the steels. This not only indicates the usefulnessof SZD for predicting fracture toughness variation butalso demonstrates that the variation in Ji with prior de-formation noted earlier takes into consideration the effectof prior hardening and changes in the microstructure bythe distribution of dislocations ahead of the crack tip. Itmay be noted, however, that the SZD dimensions couldnot accurately predict the magnitude of Ji. The failure ofSZD in predicting the magnitude of Ji can be attributed

0 1 2 3 4 5

50

100

150

200

250

300

350

400

experimental JiJSZD (by method 1)JSZD (by method 2)

J, k

J/m

2

% Prior deformation

HSLA-100

0 1 2 3 4 5

50

100

150

200

250

300

350

400

experim ntal JiJSZD (by method 1)JSZD (by method 2)

experim ntal JiJSZD (by method 1)JSZD (by method 2)

J, k

J/m

2

% Prior deformation

HSLA-100

Fig. 11 Variation of JSZD with prior deformation in HSLA-100steel.

Fig. 12 A typical secondary crack formationduring ductile tearing in HSLA-80 steel.

to a number of reasons. It may be noted that despite goodcontrast of stretch zones, inaccuracies in identifying thestart and end of stretch zone extents visually may be re-flected in the measurement of SZD. Minor errors are alsopossible due to the non-consideration of elastic compo-nents of stretching that are recovered posttest. By far, themost important reason can be traced to the occurrenceof secondary cracks in both steels as typically shown inFig. 12. Role of such cracks on the SZD measurementsand the fracture toughness of a material are elaboratelydiscussed in our earlier investigation.32 Nevertheless, itis apparent that the SZD measurements can be used asa tool to understand the fracture behaviour of a materialand also can be correlated to its fracture toughness. How-ever, SZD measurement may not yield accurate magni-tude of fracture toughness values for the reasons discussedabove.

Modelling of ductile fracture behaviour fromdeformation behaviour

As seen in previous sections, there exists a strong cor-relation between the manner in which the deformationparameters such as yield strength and uniform elongationvary with prior deformation and that of fracture tough-ness. Therefore, from the understanding of the nature ofvariation of deformation parameters, it should be possibleto predict the variation in the fracture toughness of a ma-terial. For brittle materials Hahn and Rosenfield44 havepostulated that fracture would initiate from the crack tipwhen the crack tip strain given by

ε = δ

2Cn2 (3)



exceeds a critical value. This critical value is generally re-lated to the true fracture strain, εf in a uniaxial tensiontest. In the above equation, δ is the crack tip opening dis-placement and C is a constant equivalent to 0.025 m.45

Employing relationship between δ and K IC, Hahn andRosenfield arrived at a relation

KIC =√

2C Eσyεfn3

2

. (4)

This relation correlates the fracture toughness with tensileproperties of material. This correlation holds good for lowtoughness materials which predominently fall under thecategory of LEFM. For high toughness materials such asthe HSLA steels in the presnt investigation, which exhibitsubstantial plastic deformation prior to crack initiation,the Eq. (4) cannot be used. A relation has, therefore, tobe established to correlate the ductile fracture toughnesssuch as J with deformation parameters. A procedure forobtaining such a relation is described below.

The crack tip opening displacement, δ of a material canbe related to the ductile fracture toughness, J through,

J = mσoδ, (5)

where m is a constant having a value between 1 to 246

and σ o is the flow stress of the material (average of yieldand ultimate stress). Substituting Eq. (3) into Eq. (5) andreplacing n with εu, it can be written as

Ji = 2Cm(εu)2εfσo (6)

for the condition of ductile fracture initiation. It may benoted that the critical crack tip strain at which a ductilecrack initiates, is taken as εf due to predominantly planestress conditions in the present investigation. Therefore,from the knowledge of the strain-hardening response of amaterial, flow stress and the fracture strain, it is possibleto characterize the ductile fracture behaviour.

Using Eq. (6), the initiation fracture toughness, Ji, valueswere calculated at different prior deformation conditionsfor the two HSLA steels. The value of m is obtained as 1.3for HSLA-80 and 1.43 for HSLA-100 steel from three setsof experimental J − δ data in each prestrain level. The val-ues of εu, εf and σ o used for such calculation were obtainedfrom the tensile tests on various deformed conditions.

A comparison of variation of fracture toughness withprior deformation predicted by the model with that ob-tained experimentally is shown in Fig. 13. It may be notedthat the model’s prediction is exactly similar to the natureof variation of fracture toughness with prior deformationobserved experimentally. Predictions of fracture tough-ness obtained through the Hahn and Rosenfield modelhave been found to be within ±30% of the experimentalvalues.45 The predictions of the present model are wellwithin this range of deviation. In fact, at low magnitudes

Fig. 13 Variation of initiation fracture toughness in HSLA steels.Both experimental and model predictions are shown.

of prior deformation, where an apparently anomalous re-tention of fracture toughness was observed, the predic-tions of the model are within ±5% of the experimentalresults. It, thus, demonstrates the possibility of develop-ing a semiempirical model to understand the fracture be-haviour of ductile materials under EPFM regime from thebasic understanding of their hardening and flow proper-ties. It may, however, be noted that an accurate estimateof experimental blunting line slope is essential for closeprediction of fracture toughness.

C O N C L U S I O N S

In this investigation, an attempt was made to correlate theductile fracture behaviour of two HSLA steels from an un-derstanding of their deformation parameters that controlthe fracture phenomena. A variation in their deformationproperties is brought about by prior deformation so thatthe corresponding variation in the fracture behaviour canbe understood. It is noted that the fracture controlling pa-rameters such as yield strength and the strain-hardeningcapacity of the material remained unaltered up to about2% prior deformation. This, in turn, kept the ductilefracture behaviour of two steels impassive for small mag-nitudes of prior deformation. A simple methodology isproposed to measure the stretch zone depth during duc-tile fracture. A similar behaviour is demonstrated by thestretch zone depth dimension measurement and the frac-ture toughness derived from such measurements for boththe steels. From the understanding of the ability of thedeformation parameters to control the ductile fracture be-haviour, a semiempirical model is developed. This modelincorporates the basic deformation parameters such as the



flow stress, true uniform elongation and the true fracturestrain to predict the ductile fracture toughness. The pre-dictions of the model were found to be exactly similarto the nature of variation of fracture toughness observedexperimentally.

Acknowledgement

This investigation has been carried out as part of the workfor Office of the Naval Research (ONR), USA under grantN00014-95-1-0015.

R E F E R E N C E S

1 Rice, J. R. and Johnson, M. A. (1970) In: Inelastic Behaviour ofSolids (Edited by M. F. Kannien, W. F. Adler, A. R. Rosenfieldand R. I. Jaffee). McGraw-Hill Book Co., New York, pp.641–672.

2 McMeeking, R. M. (1977) Finite deformation analysis ofcrack-tip opening in elastic-plastic materials and implicationsfor fracture. J. Mech. Phys. Solids. 25, 357–381.

3 McClintock, F. A. (1968) Local criteria for ductile fracture. Int.J. Fract. Mech. 4, 101–130.

4 McMeeking, R. M. (1977) Blunting of a plane strain crack tipinto a shape with vertices. J. Engng Tech. 99, 290–297.

5 McClintock, F. A. (1967) On the mechanics of fracture frominclusions. In: Ductility, ASM Seminar. ASM, Metals Park, OH,pp. 255–277.

6 Edelson, B. I. and Baldman, W. J., Jr. (1962) The effect ofsecond phases on the mechanical properties of alloys. Trans.ASME 55, 230–250.

7 Bates, R. C. (1984) Modelling of ductile fracture by microvoidcoalescence for the prediction of fracture toughness. In:Fracture: Interactions of Microstructure, Mechanisms, Mechanics(Edited by J. M. Wells, J. D. Landes). In: Proceeding of 113thAIME Annual Meeting in Los Angeles, California, TheMetallurgical Society of AIME. pp. 117–155.

8 Gurson, A. L. (1977) Continum theory of ductile rupture byvoid nucleation and growth: Part I-yield criteria and flow rulesfor porous ductile media. J. Engng Mater. Tech. 99, 2–15.

9 Tvergaard, V. (1990) Material failure by void growth tocoalescence. Adv. Appl. Mech. 27, 83–151.

10 Saxena, A. and Cretgny, L. (1998) The relationship betweenmicrostructure and J-R curve. Met. Trans A 29A, 1917–1922.

11 Rice, J. R. and Tracy, D. M. (1969) On the ductile enlargementof voids in triaxial stress fields. J. Mech. Phys. Solids 17, 201–217.

12 Sivaprasad, S., Tarafder, S., Ranganath, V. R. and Ray, K. K.(2000) Effect of prestrain on fracture toughness of HSLA steels.Mater. Sci. Engng A A284, 195–201.

13 Tarafder, M., Tarafder, S. and Ranganath, V. R. (1997) Locationindependent CCL relations for standard fracture mechanicsspecimens. Int. J. Fatigue 19, 635–640.

14 Kolednik, O. and Stuwe, H. P. (1986) An extensive analysis of aJIC test. Eng. Fract. Mech. 24, 277.

15 Putatunda, S. K. (1986) Determination of fracture toughness byCTOD-R curve method. J. Test. Eval. 14, 49–57.

16 Prantl, G. (1986) Equations for CTOD blunting lines. Int. J.Fract. 32, R7.

17 Pandey, R. K., Sundaram, P. and Kumar, A. N. (1991) A SZmethod for CTOD evaluation. Int. J. Fract. 47, R29–R32.

18 Czyryca, E. J., Link, R. E., Wong, R. J., Ayler, D. A.,Montemarano, T. W. and Gudas, J. P. (1990) Development andcertification of HSLA-100 steel for naval ship construction.Nav. Engng J., 63–82.

19 Czyryca, E. J. (1990) Devalopment of low-carbon, copperstrengthened HSLA steel plate for naval ship construction. In:R & D Report No. DTRC-SME-90/21, Ship MaterialsEngineering Dept. David Tayler Research Center, Bethesda,MD 20084-5000.

20 Yin, S. W. and Gerbrands, R. A. (1983) An investigation of theblunting line. Engng Fract. Mech. 18, 1025–1036.

21 Hopkins, P. and Jolley, G. (1983) Limitations of the crack tipblunting line used in the JIC test procedure. Engng Fract. Mech.18, 239–242.

22 Ranganath, V. R., Kumar, A. N. and Pandey, R. K. (1991)Fracture toughness characterisation of a weldment in amicroalloyed steel using resistance curves. Mater. Sci. Engng132, 153–160.

23 Amouzouvi, K. F. and Bassim, M. N. (1982) Determination offracture toughness from stretch zone width measurement inpredeformed aisi type 4340 steel. Mater. Sci. Engng 55, 257–262.

24 Pandey, R. K., Sundaram, S. and Kumar, A. N. (1992) Criticalassessment of methods for jic determination. J. Test. Eval. 20,106–113.

25 Srinivas, M., Kamat, S. V. and Ramarao, P. (1994) Afractographic technique for the estimation of initiation fracturetoughness JIC for ductile materials. J. Test. Eval. 22, 302–308.

26 Bassim, M. N., Mathews, J. R. and Hyatt, C. V. (1992)Evaluation of fracture toughness of HSLA80 steel at highloading rates using stretch zone measurements. Engng Fract.Mech. 43, 297–303.

27 Kobayashi, H., Nakamura, H. and Nakazawa, H. (1983)Evaluation of blunting line and elastic-plastic fracturetoughness. In: Elastic-Plastic Fracture: Second Symposium, VolumeII-Fracture Resistance Curves and Engineering Applications, ASTMSTP 803, American Society for Testing and Materials,Philadelphia, pp. II 420–II 438.

28 Halim, A., Dahl, W. and Hagedorn, K. E. (1988) Measurementsof stretched zone width (SZW): a round robin program ofeuropean group of fracture. Engng Fract. Mech. 31, 857–866.

29 Sreenivasan, P. R., Ray, S. K., Vaidyanathan, S. and Rodriguez,P. (1996) Measurement of stretch zone height and itsrelationship to crack tip opening displacement and initiation Jvalue in an AISI 316 stainless steel. Fatigue Fract. Engng Mater.Struct. 19, 855–868.

30 Cao, Wei-Di and Lu, Xiao-Ping (1984) The relation betweenthe geometry of deformed crack tip and crack parameters. Int. J.Fract. 25, 33–52.

31 Kasai, Y. and Uehara, N. (1981) Fracture toughness and thestretched zone of ultra-high strength steels. In: FractureMechanics of Ductile and Tough Materials and Its Applications toEnergy Related Structures. Proceeding of USA-Japan Joint Seminar,Hyama, Japan (Edited by H. W. Liu , T. Kunio, V. Weiss and H.Okamura). Martinus Nijhoff Publs, The Netherlands, pp.199–208.

32 Sivaprasad, S., Tarafder, S., Ranganath, V. R., Das, S. K. andRay, K. K. (2002) Effect of prestrain on stretch zone formationduring ductile fracture of Cu-strengthened HSLA steels. Met.Trans. A 33A, 3731–3740A.

33 ASTM E 1820–99a (1999) Standard test method formeasurement of fracture toughness. In: Annual Book of ASTMStandards 03.01. Philadelphia.



34 Wilson, J. D. (1987) High strength, weldable precipitation agedsteel. J. Met. 39, 36–38.

35 Jesseman, R. J. and Murphy, G. J. (1984) Mechanical propertiesand precipitation hardening response in ASTM A710 Grade Aand 736 alloy steel plates. J. Heat Treat. 3, 228–236.

36 Wilson, J. D., Hamburg, E. G., Colvin, D. J., Thompson, S. W.and Krauss, G. K. (1988) Properties and microstructures ofcopper precipitation aged plate steels. In: Microalloyed HSLASteels, ASM International, Ohio, pp. 259–275.

37 Hall, E. O. (1970) Yield Point Phenomena in Metals and Alloys,MacMillon, London, p. 117.

38 Bhadeshia, H. K. D. H. (1992) In: Bainite in Steels:Transformation, Microstructure and Properties, The Institute ofMetals, London, p. 295.

39 Mishra, M. N., Mishra, S. and Ramaswamy, V. (1989) Analysisof the temperature dependence of strain-hardeningbehaviour in high strength steels. Met. Trans. A 20A,2819–2829.

40 Sivaprasad, S. (2000) Fatigue and fracture behaviour of copperstrengthened HSLA steels. Ph.D. thesis, Indian Institute ofTechnology, Kharagpur, India.

41 Reed-Hill, R. E., Cribb, W. R. and Monterio, S. W. (1973)Concerning the analysis of tensile stress-strain data using logdσ /dp versus log σ diagrams. Met. Trans. A 4, 2665–2667.

42 Amouzouvi, K. F. and Bassim, M. N. (1982) Influence of coldworking on the J-integral in Steel. In: Fracture Problems andSolutions in Energy Industry. Pergamon, Oxford, pp. 179–190.

43 Amouzouvi, K. F. and Bassim, M. N. (1983) effect of the type ofprior straining on the fracture toughness of AISI 4340 steel.Mater. Sci. Engng 60, 1–5.

44 Hahn, G. T. and Rosenfield, A. R. (1968) Sources of fracturetoughness: The relation between KIC and the ordinary tensileproperties of metals. ASTM STP 432, American Society forTesting and Materials, Philadelphia, pp. 5–32.

45 Garret, G. G. and Knott, J. F. (1978) The influence ofcompositional and microstructural variations on the mechanismof static fracture in aluminium alloys. Met. Trans. A 9A,1187–1201.

46 Robinson, J. N. (1976) Experimental investigation of the effectof specimen type on the crack tip opening displacement andJ-integral fracture crieteria (for a mild steel). Int. J. Fract. 12,723–737.


Modelling ductile fracture behaviour from deformation parameters in HSLA steels

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