Engineering Failure Analysis 13 (2006) 18–31

www.elsevier.com/locate/engfailanal

Failure investigation and design improvements of Al 7075piston for hydraulic actuators

A. Cerrini, S. Beretta *

Dipartimento di Ingegneria Meccanica, Politecnico di Milano, Via La Masa 34, 20158/20156 Milano, Italy

Received 10 December 2004; accepted 11 December 2004

Available online 31 March 2005

Abstract

Failure analysis was applied to a hydraulic actuator piston made of aluminium alloy 7075 T6 which failed at a rel-

atively low number of cycles. Cracks were seen to nucleate from some defects naturally present in the material, and their

propagation lead to component failure before 100,000 cycles. Experimental tests were carried out to characterize the

material by means of the cyclic curve and the fatigue threshold DKth. The resultant failure analysis showed the problem

in terms of crack propagation thus justifying a fracture mechanics approach to the component failure. Finally, some

design recommendations were suggested to increase the fatigue life of the component.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Fatigue life; Crack propagation; Microflaws; Anisotropy

1. Introduction

A common cause of failure seen in aluminium alloy hydraulic actuator pistons was the fracture of the

component in the fillet zones, after a few numbers of cycle at load ratio R = 0. The dimensions and the

geometry of the piston are given in Fig. 1, where the critical zones are also underlined. The piston is screwed

on the steel shaft of the actuator, and failures occur at the fillet after the last engaged thread and at the seal

groove fillet. The nucleation and propagation of cracks can be seen in these areas. The piston was extracted

from a cold drawn bar made of the aluminium alloy 7075 T6. The alloy�s material tensile properties areachieved using the heat treatment properties [1]. The resultant microstructure of 7075 T6 alloy is not homo-

geneous, and microcracks initiate where microstructure is relatively weak [1].

1350-6307/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engfailanal.2004.12.026

* Corresponding author. Tel.: +39 2 2399 8246; fax: +39 2 2399 8202.

E-mail address: stefano.beretta@polimi.it (S. Beretta).

Nomenclature

n 0, H 0 Ramberg–Osgood coefficientsKt elastic stress concentrator factor

Kr stress concentration factor

Ke strain concentration factor

DKth fatigue threshold

DKI stress intensity factor range for mode I

DKII stress intensity factor range for mode II

DKeq equivalent stress intensity factor (MTS criterion)

R load ratioC,m Paris coefficients

mIp, mIiq weight functions for an edge crack

bi weight function coefficients

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 19

Piston failure occurred on a prototype hydraulic cylinder which was subjected to fatigue tests with a pul-

sating pressure of 400 bar (40 MPa): failures at both aforementioned locations occurred before 100,000

cycles.

The failure investigations which are presented in this paper were carried out primarily considering the

possibility of nucleation at notches, and then considering the presence of small flaws in the critical regions.

The analysis has been based on material properties (cyclic curves and fatigue thresholds) which have been

obtained in different directions in order investigate the presence of a possible anisotropy due to the drawing

process.

Fig. 1. Piston dimensions.

20 A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31

1.1. Failures

In Fig. 2(a) the end thread fillet crack path is shown. The first segment at 45� to the loading direction is

about 4 mm long, after which the crack deviates and grows for 3.8 mm along the drawing direction. Then

the crack returns to the angled direction until component failure. Fig. 2(b) details the first segment of thecrack at 45� with respect to the drawing and loading direction. Fig. 3 shows the fracture which occurred at

the fillet of the seal groove. The crack nucleates at the fillet and propagates along the fibres stretched in the

drawing direction. Furthermore, Fig. 4 clearly reveals the inhomogeneities of the material; defects even of

the order of 100 lm can be seen, which, by finding a weakness in the material microstructure, could begin to

propagate and lead to piston failure.

Fig. 2. Failure at the thread end fillet: (a) crack path; (b) detail of crack in the initial phase.

Fig. 3. Failure at the seal groove.

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 21

Fig. 4. Small flaws revealed by polished sections.

22 A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31

1.2. Methods

First of all an analysis of the fracture surfaces was done in order to visually analyze the path followed by

the cracks. Then, an experimental investigation of the material characteristics was conducted to produce thecyclic curve, fatigue limit, mode I fatigue threshold and Paris curve. Attention was focused on a possible

anisotropy effect on the fatigue limit and fatigue threshold due to the drawing process. A FE analysis of

the component was carried out to determine the stress intensity factors at the crack (using the ABAQUS

SIF calculation and the weight function method) and thus the life of the component in terms of fatigue cy-

cles at R = 0. Using the results obtained from the experimental tests and FE analysis, a design solution to

improve the fatigue life was presented.

2. Experimental details

Tests were run to characterise the component material and determine its cyclic curve, mode I fatigue

threshold, and to ascertain how the drawing process could cause anisotropy in material properties. All

of the tests were carried out on specimens extracted in three different characteristic directions with respect

to the drawing direction: longitudinal, transversal and at 45� with respect to the drawing direction.

Table 1

Mechanical properties of Al 7075 T6

E (MPa) Rp0.2 (MPa) Rm (MPa)

66000 325 465

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 23

2.1. Tensile test

A preliminary tensile test was carried out to determine the monotonic properties of the material. Table 1

shows the material mechanical properties for specimens cut in the longitudinal direction.

2.2. Cyclic curve

The geometry and the dimensions of the specimens tested are indicated in Fig. 5(a), in Fig. 5(b) the direc-

tions of specimen extraction are shown.

The cyclic test was run at R = �1 with deformation control set at 0.2% – 0.3% – 0.4% – 0.5% – 0.6% –

0.7% – 0.8% ascending and descending until the specimen failure. The cyclic curves were obtained by inter-

polating the extreme values of the stabilized cycles at the different imposed deformations by means of the

Ramberg–Osgood equations:

Table

Cyclic

Specim

Longit

Transv

45�

e ¼ eae þ eap ¼rEþ r

H 0

� �1=n0

: ð1Þ

Table 2 reports the cyclic properties and Fig. 6 shows the cyclic curves obtained for the specimens in the

three specified directions. Comparing the curves, it can be noted how at a relatively high deformation per-

centage (0.5–0.8%), the cyclic curve for the specimen loaded parallel to the drawing direction is different

from the other two curves, and in particular it shows higher values along the drawing direction.

2.3. Fatigue threshold and Paris’ curve

The geometry and the dimensions of the SEB specimen tested in order to ascertain the mode I fatigue

threshold DKth and the Paris curve for the three different directions described are shown in Fig. 7(a) and

(b). Fatigue tests were performed by means of a high frequency electro-resonance machine. The crack

length was monitored using a Crack gauge that cracked along with the specimen crack. This caused the

Fig. 5. Experiments for cyclic curve determination: (a) specimen dimension; (b) specimen extraction directions.

2

properties of Al 7075 T6

en extraction direction H 0 n 0 Rp0.05,cycl (MPa) Rp0.2,cycl (MPa)

udinal 630 0.044 460 480

ersal 630 0.096 305 350

530 0.068 310 350

-600-500-400-300-200-100

0100200300400500600

-0.01 -0.005 0 0.005 0.01

σM

Pa

-600

-400

-200

0

200

400

-0.01 -0.005 0 0.005 0.01

ε

ε

σ [M

pa]

-500

-400

-300

-200

-100

0

100

200

300

400

-0.01 -0.005 0 0.005 0.01

ε

σ [M

pa]

(a)

(b)

(c)

Fig. 6. Cyclic curves: (a) longitudinal specimens; (b) transversal specimens; (c) specimens at 45�.

24 A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31

DC potential to drop between the two ends of the gauge, thus allowing measurement of the crack length

with FRACTOMAT.

To obtain DKth, tests were carried out at a constant value of R = 0.05 with a decreasing DK. Two spec-

imens were tested in each direction. Fig. 8(a) reports the results obtained for three specimens with differentfibre orientations. The values of the fatigue threshold obtained in these tests can be considered the same for

specimens with different orientations with respect to the drawing direction. This shows that material anisot-

ropy, which has been observed at fracture toughness [2,3], is not significant for near-threshold fatigue crack

propagation.

In order to estimate the life of the component in terms of fatigue cycles, the Paris diagram is needed. This

was obtained at R = 0.05 under a constant applied load for the specimen with the fibres transversally ori-

ented with respect to the drawing direction. Fig. 8(b) shows the Paris diagram. It can be seen that the linear

part is limited to the DK range 6 6 DK 6 12. Unstable propagation occurs from DK = 20 MPapm, a value

close to the fracture toughness of 7075 alloys [4].

Fig. 7. Crack propagation experiments: (a) SEB specimen dimensions; (b) specimen extraction directions.

0.01

0.1

1

10

100

1 10

∆K [MPam1/2]

da/

dN

[n

m/L

w]

Trasv

Long

45˚

0.001

0.01

0.1

11

10

100

1000

10 100

∆K [MPam1/2]

da/

dN

[n

m/L

w]

(a)

(b)

Fig. 8. Crack propagation results: (a) DK-decreasing threshold data; (b) da/dN diagram for longitudinal direction.

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 25

26 A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31

3. Failure analysis

The finite element code ABAQUS was used to determine the stress distribution of the piston-shaft sys-

tem at the threaded attachment point with focus on the stress distribution near the fillets at the end of the

threads and the seal groove. This is where the cracks which caused component failure were seen. The modelused in analysis was built as axisymmetric (Fig. 9). The element used to create the mesh was the QUAD4

quadratic element, and the mesh was refined in areas where the stress gradient was predicted to be higher,

hence near the fillets. The contact area between the piston and the shaft in the threaded region between the

two deformable surfaces corresponding to thread flanks was defined as a �hard contact�.

3.1. Thread end fillet Neuber analysis

In defining Kt as the elastic stress concentration factor of the section, it can be correlated to the stressconcentration factor and the strain concentration factor, which are valid in the case of localised plastic

deformation at the fillet (r > ryield) [5]:

Kr ¼r

rnom

Ke ¼e

enom; ð2Þ

K t ¼ffiffiffiffiffiffiffiffiffiffiffiKrKe

p: ð3Þ

Substituting Eq. (2) in Eq. (3) and rearranging:

re ¼ ðK trnomÞ2

E: ð4Þ

The stress and strain at the notch is given by the intersection of the above equation with the cyclic curve of

the material:

Fig. 9. FE analysis: (a) model of the piston; (b) detail of the engaged threads.

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 27

rrEþ r

H 0

� �1=n0� �

¼ ðK trnomÞ2

E: ð5Þ

For the present case, the stress concentration factor Kt can be obtained from the finite element analysis

(Fig. 10(a)):

K t ¼ 5:88:

The results are given in Fig. 10(b). The intersection of the Neuber curve with the cyclic curve shows that

the local strain at the notch root is in the elastic range of the cyclic response of the material. The conclusionthat can be drawn is that, without any doubt, the failure studied here was not caused by crack nucleation.

3.2. Fracture mechanics analysis

In order to analyse the problem in terms of fracture mechanics and driven by the fact that the material is

not homogeneous, a crack of 100 lm at the fillet locations was modelled. This is about the maximum defect

size observed in the material. Using ABAQUS, the stress intensity factors were calculated. In order to

correctly catch the 1/2 singularity at the crack tip, the mesh around the crack tip was highly refined; the

Fig. 10. Notch strain analysis at the thread fillet: (a) stress concentration (Kt = 5.88); (b) Neuber analysis.

28 A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31

smallest element had a length of 4 lm. The element size was increased when moving away from the singu-

larity. In order to allow the pre and post processor to visualize the mesh, and the computer to analyze with

a reasonable number of elements and within relatively short time, a submodel of the crack zone was created

(Fig. 11). The global model from which the sub model was extracted, ‘‘drives’’ the analysis of the sub model

by means the contour driving nodes common to the global model and sub model. It does this by imposingthe nodal displacements obtained for the driving nodes in the global model onto the identical nodes in the

sub model.

3.2.1. Thread end fillet

The calculation of the variations in the stress intensity factors DKI and DKII for a 100 lm crack in the

fillet zone inclined at 45� with respect to the loading direction (and then the drawing direction) and with

R = 0, lead to the following results:

Fig

DKI ¼ 5:53 MPaffiffiffiffim

p;

DKII ¼ 0:03 MPaffiffiffiffim

p:

The propagation angle was determined using the maximum tensile stress criterion [6,7]. The crack practi-

cally grows following the mode I criterion; the crack growth angle is, in fact, about �0.6� with respect to themain crack direction. The comparison of the value of DKI with the fatigue limit threshold of the material

(DKth = 3 MPapm) can surely explain the early failure of the piston at the thread fillet.

An estimation of the component fatigue life in terms of number of cycles can be obtained by interpolat-

ing and numerically integrating the curve in Fig. 8(b),which represents the stable crack propagation before

the unstable brittle fracture of the component. By means of the weight function (WF) method suggested by

Bertini and Beghini [8], the variation of DKI for a crack perpendicular to the surface described by the thread

end fillet was calculated as a function of crack length. The WF technique permits calculation of the stress

intensity factors for a crack perpendicular to the surface by integrating numerically the WF expressionsmultiplied by the normal and the tangential stresses along the crack (r and s).

KIðaÞ ¼1ffiffiffiffiffiffiffiffi2pa

pZ a

0

mIpðx; aÞrðxÞdx;

KIIðaÞ ¼1ffiffiffiffiffiffiffiffi2pa

pZ a

0

mIIqðx; aÞsðxÞdx:ð6Þ

. 11. SIF at the tip of a flaw located at the root of thread end fillet: (a) FE crack detail; (b) submodel for a 100 lm crack.

Table 3

SIF calculations for cracks at the thread fillet

Crack length KI (MPapm) KII (MPa

pm)

100 lm ABAQUS 5.53 0.029

WF 5.89 0.031

4 mm ABAQUS 11 �0.515

WF 12 0.059

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 29

For a crack perpendicular to the surface:

mIpðx; aÞ ¼ mIIqðx; aÞ ¼X5

i¼1

bIð1� xÞði�3=2Þ: ð7Þ

The results obtained in terms of DKI and DKII correlated well with the FE results (Table 3).

To estimate the number of cycle to failure, the curve in Fig. 8(b) was interpolated:

logdadN

� �¼ aðlogDKÞ3 þ bðlogDKÞ2 þ cðlogDKÞ þ d: ð8Þ

Eq. (8) was then numerically integrated from a crack of 100 lm, which is the size of defects present in the

material, to 4 mm (Fig. 12). The value of stress intensity factor range DKI for a 4 mm crack is 12 MPapm.

This corresponds to the region where the crack growth data deviates from the Paris line and tends to unsta-

ble growth controlled by the fracture toughness KIC = 20 MPapm [4]. The calculated propagation life for

crack growth to a length of 4 mm is about 50,000 cycles.

3.2.2. Seal groove fillet

A similar analysis was conducted for the crack which can be really observed at the fillet of the seal

groove. Using FE analysis, DKI and DKII were calculated for a 100 lm crack with the loading direction

defined as parallel to the drawing fibres. The results obtained for the stress intensity factors are as follows:

DKI ¼ 3:44 MPaffiffiffiffim

p;

DKII ¼ 1:90 MPaffiffiffiffim

p:

In this case the value of DKII cannot be ignored. In order to find a value which could be compared with the

fatigue threshold, DKeq was calculated using the MTS criterion:

DKeq ¼ 4:6 MPaffiffiffiffim

p:

4 mm

3.8 mm

0.001

0.01

0.1

11

10

100

1000

1 1 10

∆K [MPam ]1/2

da/

dN

[n

m/L

w]

100µm 100

45˚

Fig. 12. Analysis of crack propagation at the thread fillet.

30 A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31

The comparison between DKeq and the fatigue threshold DKth permits the conclusion that the crack nucle-

ated from a pre-existing flaw and started to grow under the applied pressure cycles.

4. Design improvements

Considering that the material is not homogeneous and that some defects such as cracks are naturally

present in the material due to the forming process, it becomes necessary to reduce the value of DKI (for

the end thread fillet) and DKeq (for the seal groove fillet) near the fatigue threshold DKth in order to increase

component life. To achieve this purpose, it is suggested to increase the size of the thread end fillet from 1 to

3 mm, and the seal groove fillet from 0.4 to 0.7 mm. The new values of the stress intensity factors were cal-

culated using the WF method, having just before verified the agreement of the results obtained using FE

analysis. In particular, for the lower thread end fillet crack, the WF for a crack perpendicular to the surfaceproposed by Bertini and Beghini [8] was used For the seal groove crack, which was seen to propagate along

the loading direction inclined with respect to the fillet, the WF for an inclined surface crack as suggested by

Rooke [9] was implemented.

Fig. 13. Design improvements: (a) old and new solution for the thread end fillet and (b) old and new solution for seal groove fillet.

Table 4

SIF for design improvements

DKI (MPapm) DKII (MPa

pm) DKeq (MPa

pm)

Thread end fillet r = 1 mm 5.53 0.029 Old design

r = 3 mm 2.5 �0.016 New design

Seal groove fillet r = 0.4 mm 3.44 1.90 4.6 Old design

r = 0.75 mm 2.35 1.77 3.6 New design

A. Cerrini, S. Beretta / Engineering Failure Analysis 13 (2006) 18–31 31

The new value of DKI calculated for the 100 lm lower crack is:

DKI ¼ 2:5 MPa;

which is lower than the fatigue threshold DKth limit for the crack propagation. Fig. 13(a) compares the new

solution (r = 3 mm) with the old solution (r = 1 mm), and also shows the maximum tensile stress values.

The new value of DKeq calculated for the 100 lm seal crack is:

DKeq ¼ 3:6 MPa:

Fig. 13(b) details the differences between r = 1.4 and r = 0.75 in terms of the maximum tensile stress and

SIF�s. Table 4 summarizes the results obtained from modifying the fillets in terms of DKI, DKII and DKeq.

5. Conclusions

The failure of the aluminium hydraulic actuator pistons after a low number of cycles was caused by the

propagation of cracks originating from defects naturally present in the material. Two zones were recog-nized as critical zones: the thread end fillet and the seal groove fillet. Defects which began to grow in these

locations lead to component failure before 100,000 cycles. The analysis, carried out using fracture mechan-

ics, justified the low fatigue life of the piston. To reduce the values of DKI and DKeq and thus increase the

component life, it was suggested to increase the fillet size, thus bringing DKI and DKeq nearer the fatigue

threshold experimentally found for DKI.

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[4] Lampman SR. Fatigue data book: light structural alloys. ASM International; 1996.

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