SPECIAL ISSUE - ORIGINAL ARTICLE

Determination of J-integral and stress intensity factor usingthe commercial FE software ABAQUS in austenitic stainlesssteel (AISI 304) plates

G. Venkatachalam & R. Harichandran & S. Rajakumar &

C. Dharmaraja & C. Pandivelan

Received: 26 February 2008 /Accepted: 18 September 2008# Springer-Verlag London Limited 2008

Abstract This paper presents J-integral and stress intensityfactor solutions for several crack configurations in plates.The edge crack is considered for the analysis. The tensileload is applied and the crack propagation is studied. Thefinite element method is used to model the plate and mode Istress intensity factors are evaluated. For solving the FEmodel, commercial FE software ABAQUS is used. Severalcases including different thickness and crack lengths arepresented for not only linear elastic analysis but also forelastic-plastic analysis. The 3-D model is taken for theanalysis and eight-noded brick element is used for FE mesh.

Keywords J-integral . Stress intensity factor .

Finite element method

1 Introduction

Fracture mechanics has reached the level of sophistication aswell as wide industrial acceptance such that many actual andpotential brittle failure problems can be dealt through this

discipline. The stress intensity factor (SIF) characterizes thestresses, strains, and displacements near the crack tip. If theplastic zone near the crack tip is large, then the SIF no longercharacterizes the crack tip conditions. So calculation of SIFis limited to linear elastic fracture mechanics. When theplastic zone is large or non-linear material behavior becomessignificant, one should discard SIF and crack tip parameters(either J-integral or CTOD) that takes larger plastic zonenear the crack tip and non-linear material behavior intoaccount. Here, an attempt is made to find out J-integral.The T-stress is increasingly being recognized as animportant additional stress field characterizing parameterin the analyses of cracked bodies. The elastic T-stressrepresents the stress-acting parallel to the crack plane. It isknown that the sign and magnitude of T-stress cansubstantially alter the level of crack tip stress triaxiality.

2 Literature review

Rice [1] applied the deformation plasticity to the analysis ofa crack in a non-linear material. He showed that the non-energy release rate J could be written as a path-independentline integral. Rice and Rosengren [2] showed that Juniquely characterizes crack tip stresses and strains innon-linear materials. Kobayashi et al. [3] used finiteelement analysis to determine numerically Rice’s J-integralvalues in centrally notched plates of 43.40 steel. Forincreasing level of loading, the rate of increase in J-integraldecreases and J-integral remains almost constant at whenthe load is at yield point under such crack extension.Courtin et al. [4] applied the crack opening displacementextrapolation method and the J-integral approach in 2D and3D ABAQUS finite element models. The results obtainedby them are in good agreement with those found in the

Int J Adv Manuf TechnolDOI 10.1007/s00170-008-1872-z

G. Venkatachalam : C. Dharmaraja :C. PandivelanSchool of Mechanical & Building Sciences, VIT University,Vellore 632014, India

R. Harichandran (*)Department of Mechanical Engineering,National Engineering College,Kovilpatti 628503, Indiae-mail: hari_chandra1984@yahoo.com

S. RajakumarDepartment of Mechanical Engineering,SCAD College of Engineering,Cheranmahadevi, Tirunelveli, India

Fig. 1 Edge-crack model

Fig. 2 Close view of crack

Fig. 3 FE mesh of model

-35

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-5

00.5 0.6 0.7 0.8 0.9

a (mm)

J (J

/Sq.

m)

Elastic Elastic-Plastic

Fig. 4 a vs. J

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0

200

400

600

800

1000

12000.5 0.6 0.7 0.8 0.9

a (mm)

K1c

(MPa

/√m

m)

Fig. 5 a vs. K1c

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0

50

1000.5 0.6 0.7 0.8 0.9

a (mm)

T S

tres

s (M

Pa)

Fig. 6 a vs. T-stress

Int J Adv Manuf Technol

0

500

1000

1500

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3 5 6 7

t (mm)

K1

c (

MP

a/m

m)

4

Fig. 8 t vs. K1c

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6003 6

t (mm)

T S

tres

s (M

Pa)

74 5

Fig. 9 t vs. T-stress

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0100 150 200 250 300 325 350

Load (N)

J (J

/Sq.

M)

elastic elastic - plastic

elastic RI elastic-palstic RI

Fig. 10 F vs. J

0

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800100 150 200 250 300 350

Load (N)

K1c

(M

Pa/

√mm

)

Fig. 11 F vs. K1c

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t (mm)

J (J

/Sq.

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Elastic Elastic-Plastic

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Fig. 7 t vs. J

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Load (N)

T S

tress (

MP

a)

Fig. 12 F vs. T-stress

Int J Adv Manuf Technol

literature. Nevertheless, since the knowledge of the fieldnear the crack tip is not required in the energetic method, theJ-integral calculations seem to be a good technique to dealwith the fatigue growth of general cracks. Rajaram et al.[5] presented an approach to obtain fracture mechanicssingularity strength (J, K1, etc.) along a 3D crack-frontusing tetrahedral elements. Hocine et al. [6] determined theenergy parameter J for rubber-like materials. Owen andFawkes [7] developed many numerical methods using finiteelement analysis to obtain SIF values.

3 Finite element analysis

The edge-crack model shown in Fig. 1 is taken for theanalysis. The Fig. 2 shows the close view of crack. The tensileload distributed in nature is applied at the top of the plate andthe bottom face is constrained. The material taken for ouranalysis is Austenitic stainless steel (AISI 304). Figure 3shows the finite element mesh of the model. The eight-nodelinear brick elements (C3D8 in ABAQUS) with three degreesof freedom at each node are considered. An attempt is alsomade with reduced integration. Reduced integration uses alower-order integration to form the element stiffness. Itreduces running time, especially in three dimensions. Thereare 375 nodes and 224 elements are used in the model.

4 Results and discussions

This paper is basically dealing three kind of analysis. Thevariations of J-integral, T-stress and SIF with respect to cracklength (a), thickness of model (t) and load (F) conditions arestudied. In all the cases, one parameter is varied and othertwo parameters are kept constant. For a constant load andthickness, the increase in the value of J-integral for bothelastic and elastic-plastic is same up to the elastic limit whichis shown in the Fig. 4. After elastic limit, there is noappreciable increase in the value of J-integral for the elasticanalysis. Figure 5 shows that the increase in t for elastic hasno influence on the value of J-integral whereas it is linear inthe case of elastic-plastic. The variation of J with load is alsostudied (Fig. 6). Here, the values of J are compared withreduced integration. Until the elastic limit, there is novariation for all cases; but when the load goes beyond theelastic limit, decrease in the value of J for elastic-plastic ismore than that of elastic. In elastic analysis, elements withreduced integration have no influence where as in elastic-plastic, it matters. Figure 7 shows that the SIF decreasesinitially when a increases; but there is no significant decreasein SIF for further increase in a. SIF linearly increases withrespect to t and F (Figs. 8 and 9). The T-stress distribution ishighly turbulent for both different crack lengths and different

thickness which are shown in Figs. 10 and 11. But the sameis linear when a and t are kept constant (Fig. 12).

Constant F and t

a vs. J (Fig. 4).a vs. K1c (Fig. 5).a vs. T-stress (Fig. 6).

Constant F and a

t vs. J (Fig. 7).t vs. K1c (Fig. 8).t vs. T-stress (Fig. 9).

Constant a and t

F vs. J (Fig. 10).F vs. K1c (Fig. 11).F vs. T-stress (Fig. 12).

5 Conclusion

Finite element model is created to find the fractureproperties of Austenite stainless steel (AISI 304). The FEanalysis was carried out by FEA commercial softwareABAQUS. Fracture properties of edge-crack plate withtensile load are studied. SIF and T-stress are found out forelastic limit where as J-integral is found out for both elasticand elastic-plastic models. It is found that there is aconsiderable change in the value of J-integral in when theload crosses elastic limit.

References

1. Rice JR (1968) A path independent integral and the approximateanalysis of strain concentration by notches and cracks. J Appl Mech35:379–386

2. Rice JR, Rosengren GF (1968) Plane strain deformation near a cracktip in a power law hardening material. J Mech Phys Solids 16:1–12

3. Kobayashi AS, Chiu ST, Beeuwkes R (1973) A numerical andexperimental investigation on the use of J-integral. J Appl Mech15:293–305

4. Courtina S, Gardina C, Bezinea G, Ben Hadj Hamoudab H (2005)Advantages of the J-integral approach for calculating stressintensity factors when using the commercial finite element softwareABAQUS. Eng Fract Mech 72:2174–2185

5. Rajaram H, Socrate S, Parks DM (2000) Application of domainintegral methods using tetrahedral elements to the determination ofstress intensity factors. Eng Fract Mech 66(5):455–482

6. Ait Hocine N, Nait Abdelaziz M, Ghfiri H, Mesmacque G (1996)Evaluation of the energy parameter J on rubber-like materials:comparison between experimental and numerical results. Eng FractMech 55(6):919–933

7. Owen DRJ, Fawkes AJ (1983) Engineering fracture mechanics:numerical methods and applications. Pineridge, Swansea, UK

Int J Adv Manuf Technol