不锈钢的疲劳裂纹扩展有限元模拟-英文版(另有中文翻译).pdf

Modeling of fatigue crack growth of stainless steel 304L Feifei Fan Sergiy Kalnaus Yanyao Jiang Department of Mechanical Engineering 312 University of Nevada Reno NV 89557 USA a r t i c l ei n f o Article history Received 7 November 2007 Received in revised form 9 June 2008 Keywords Damage accumulation Fatigue crack growth Fatigue criterion a b s t r a c t An effort is made to predict the crack growth of the stainless steel 304L based on a newly developed fatigue approach The approach consists of two steps 1 elastic plastic fi nite element FE analysis of the component and 2 the application of a multiaxial fatigue cri terion for the crack initiation and growth predictions based on the outputted stress strain response from the FE analysis The FE analysis is characterized by the implementation of an advanced cyclic plasticity theory that captures the important cyclic plasticity behavior of the material under the general loading conditions The fatigue approach is based upon the notion that a material point fails when the accumulated fatigue damage reaches a cer tain value and the rule is applicable for both crack initiation and growth As a result one set of material constants is used for both crack initiation and growth predictions All the mate rial constants are generated by testing smooth specimens The approach is applied to Mode I crack growth of compact specimens subjected to constant amplitude loading with differ ent R ratios and two step high low sequence loading The results show that the approach can properly model the experimentally observed crack growth behavior including the notch effect the R ratio effect and the sequence loading effect In addition the early crack growth from a notch and the total fatigue life can be simulated with the approach and the predictions agree well with the experimental observations 2008 Elsevier Ltd All rights reserved 1 Introduction Load bearing engineering components are often sub jected to cyclic loading and failure due to fatigue is of a great concern Generally fatigue process consists of three stages initiation and early crack growth stable crack growth and fi nal fracture Traditionally the crack growth rate da dN is expressed as a function of the stress inten sity factor range DK on a log log scale The stable crack growth results under constant amplitude loading with dif ferent R ratios the minimum load over the maximum load over a loading cycle are often represented by the Paris law Paris and Erdogan 1963 and its modifi cations Walker 1970 Kujawski 2001 Different materials behave differ ently under constant amplitude fatigue loading Some materials display a R ratio effect crack growth rate curves are coincided for the same R ratio but a higher R ratio re sults in a higher crack growth rate Kumar and Garg 1988 Pippan et al 2005 Wu et al 1998 Zhao et al 2008 Other metallic materials do not reveal any R ratio effect and the curves for constant amplitude loading overlap in a log log scale Crooker and Krause 1972 Kumar and Pan dey 1990 Wang et al to appear The fatigue crack growth behavior under variable amplitude loading is another subject that has been studied for a number of years The application of an overload ten sile load of high magnitude applied over one cycle pre ceded and followed by constant amplitude loading or change in the loading amplitude so called high low se quence loading experiments can introduce profound effects on the fatigue crack growth For most metallic materials the application of the abovementioned loading schemes results in a crack growth rate retardation Based on the linear elastic fracture mechanics LEFM concept such a transient behavior is often modeled by using the stress intensity factor concept and by introducing correc tion factors to the Paris law on the stable crack growth 0167 6636 see front matter 2008 Elsevier Ltd All rights reserved doi 10 1016 j mechmat 2008 06 001 Corresponding author Tel 1 775 784 4510 fax 1 775 784 1701 E mail address yjiang unr edu Y Jiang Mechanics of Materials 40 2008 961 973 Contents lists available at ScienceDirect Mechanics of Materials journal homepage regime A model of such a type was introduced by Wheeler 1972 and can be viewed as a practical way of treating the effects of variable amplitude loading Several modifi cations on Wheeler s model have been proposed Kim et al 2004 Yuen and Taheri 2006 Zhao et al 2008 targeting the par ticular shapes of the crack growth curves for different materials subjected to variable amplitude loading These models have little or no physical basis and the results of the crack growth experiments are needed in order to ob tain a set of fi tting constants to calibrate the models Since its introduction by Elber 1970 the crack closure concept is often used to explain crack growth behavior The retardation in crack growth rate generated by a single ten sile overload was explained by using the crack closure con cept in Elber s later study Elber 1971 The concept of Kop was introduced as a stress intensity factor corresponding to the crack opening load and the effective stress intensity factor range from Kopto Kmaxwas considered as a crack driving parameter As a result the contribution to crack propagation comes from a part of the total stress intensity factor range corresponding to the part of the cycle when the crack is open Such an approach is used to explain the R ratio and variable loading effects However the crack closure method has been under criticism based upon experimental observations Lang and Marci 1999 Sada nanda et al 1999 Silva 2004 Feng et al 2005 and numerical simulations Jiang et al 2005 Mercer and Nich olas 1991 Zhao et al 2004 Crack tip blunting has been used to explain the crack advance Gu and Ritchie 1999 Tvergaard 2004 The retardation caused by an overload is attributed mainly to the compressive residual stresses ahead of the crack tip plasticity induced crack closure behind the crack tip or the combination of these two The initial acceleration in the crack growth immediately after the application of an overload was explained as a result of the tensile residual stress due to crack tip blunting Makabe et al 2004 The fi nite element analysis was used to analyze the stress dis tribution and the crack opening displacement which was related to the variable amplitude loading effects Zhang et al 1992 Ellyin and Wu 1999 Tvergaard 2006 Generally a fatigue crack is nucleated at a notch due to the stress concentration The so called notch effect on short crack behavior exists and the crack growth rate may be higher or lower than that expected based on the stable growth Extensive research has been carried out to study the crack initiation and early crack growth behavior from a notch Around a notch a transition zone exists and the fatigue crack growth rate may decelerate accelerate or non propagate after the crack initiation under constant amplitude loading In order to model the short crack growth behavior from a notch efforts were concentrated on the effective stress intensity factor near the notches Sadanandam and Vasudevan 1997 Dong et al 2003 Teh and Brennan 2005 Vena et al 2006 notch tip plas ticity Li 2003 Hammouda et al 2004 and the combina tion of crack tip cyclic plasticity and the contact of the crack surfaces Ding et al 2007a A recent effort by Jiang and co workers Ding et al 2007a b Feng et al 2005 Jiang and Feng 2004a at tempted to use a multiaxial fatigue criterion to unify the predictions of both crack initiation and crack growth The notion is that both crack initiation and the subsequent crack growth are governed by the same fatigue criterion A material point fails to form a crack once the accumula tion of the fatigue damage reaches a certain critical value The approach has been applied to 1070 steel with success The predictions of the early crack growth from notches Ding et al 2007a Jiang Ding and Feng 2007 the stable crack growth Feng et al 2005 Jiang and Feng 2004a Jiang Ding and Feng 2007 the overload effect Jiang and Feng 2004a Jiang Ding and Feng 2007 the R ratio effect Jiang and Feng 2004a Jiang Ding and Feng 2007 and the crack growth under direction changing loading Ding et al 2007b agreed well with the experi mental observations All the predictions of the crack growth were based on the material constants generated from testing the smooth specimens In the present investigation the aforementioned ap proach is used to simulate the crack growth from the notched specimens made of the AISI 304L austenitic stain less steel The notch effect on the early crack growth the R ratio effect and the infl uence of the loading sequence are modeled The stress analysis is conducted by using the fi nite element method implementing a robust cyclic plastic ity model The predicted results are compared with the results of the crack growth experiments 2 Crack growth modeling In the present investigation the fatigue approach devel oped by Jiang and co workers Jiang and Feng 2004a Jiang et al 2007 is used to model the crack growth of the stain less steel 304L The approach is based on the assumption that any material point fails if the accumulation of the fa tigue damage reaches a critical value on a material plane A fresh crack surface will form on the material plane at the material point Essentially the approach consists of two major computational steps a Elastic plastic fi nite element FE stress analysis for the determination of the stress and strain history at any material point of a component and b Application of a multiaxial fatigue criterion utilizing the stress and strain obtained from the previous step for the determination of crack initiation and crack growth The following sub sections describe the methods em ployed in the current study 2 1 Cyclic plasticity model and multiaxial fatigue criterion Earlier studies indicate that an accurate stress analysis is the most critical part for the fatigue analysis of the mate rial Jiang and Kurath 1997a b Jiang and Zhang 2008 Kalnaus and Jiang 2008 Jiang et al 2007 If the stresses and strains can be obtained with accuracy fatigue life can be reasonably predicted by using a multiaxial fatigue criterion The elastic plastic stress analysis of a notched or cracked component requires the implementation of a 962F Fan et al Mechanics of Materials 40 2008 961 973 cyclic plasticity model into FE software package The selec tion of an appropriate cyclic plasticity model is crucial for an accurate stress analysis of a component subjected to cyclic loading Cyclic plasticity deals with the non linear stress strain response of a material under repeated external loading A cyclic plasticity model developed by Ohno and Wang 1993 1994 and Jiang and Sehitoglu 1996a b is used in the present FE simulations of the stress and strain response in a notched or cracked component The model is based on the kinematic hardening rule of the Armstrong Frederick type Basic mathematical equations constituting the model are listed in Table 1 A detailed description of the plasticity model together with the procedures for the determination of material constants can be found in corresponding refer ences Jiang and Sehitoglu 1996a b The choice of the cyc lic plasticity model was based on its capability to describe the general cyclic material behavior including cyclic strain ratcheting and stress relaxation that occur in the material near the notch or crack tip The plasticity model listed in Table 1 was implemented into the general purpose FE package ABAQUS 2007 through the user defi ned subroutine UMAT A backward Euler algorithm is used in an explicit stress update algo rithm The algorithm reduces the plasticity model into a non linear equation that can be solved by Newton s meth od The corresponding consistent tangent operator is de rived for the global equilibrium iteration which ensures the quadratic convergence of the global Newton Raphson equilibrium iteration procedure Jiang et al 2002 A critical plane multiaxial fatigue criterion developed by Jiang 2000 is used for the assessment of fatigue dam age The criterion can be mathematically expressed as follows dD rmr r0 1 m 1 r rf brdep 1 b 2 sdcp 1 In Eq 1 D represents the fatigue damage on a material plane and b and m are material constants randsare the normal and shear stresses on a material plane andep andcpare the plastic strains corresponding to stressesr ands respectively r0andrfare the endurance limit and the true fracture stress of the material respectively rmr is a memory stress refl ecting the loading magnitude For constant amplitude loading rmris equal to the maximum equivalent von Mises stress in a loading cycle The use of MacCauley bracket hi ensures that whenrmr6r0the fati gue damage is zero The critical plane is defi ned as the material plane where the fatigue damage accumulation fi rst reaches a critical value D0 The Jiang multiaxial fatigue criterion has been success fully applied to the fatigue predictions of a variety of mate rials Ding et al 2007a b Feng et al 2005 Gao et al to appear Jiang Ding and Feng 2007 Jiang et al 2007 Zhao and Jiang 2008 The incremental form of the criterion Eq 1 does not require a separate cycle counting method for general loading conditions Any fatigue criterion making use of the stress strain amplitude or range requires the defi nition of a loading cycle or reversal Therefore a cycle counting method is needed to deal with the variable ampli tude loading Although the rain fl ow cycle counting meth od is widely accepted for counting the loading reversals cycles it is not well defi ned for general multiaxial loading The second feature of the criterion expressed by Eq 1 is its capability to predict the cracking behavior The Jiang fa tigue criterion is a critical plane approach which is capable of predicting different cracking behavior through the intro duction of constant b in Eq 1 The value of constant b is selected to predict a particular mode of cracking based on the smooth specimen experiments It has been shown Jiang et al 2007 Zhao and Jiang 2008 that the predic tions of the cracking behavior based on the Jiang criterion are generally more accurate than the predictions based on the other multiaxial criteria such as the Fatemi Socie mod el Fatemi and Socie 1988 the Smith Waltson Topper model Smith et al 1970 and the short crack based crite rion D ring et al 2006 Table 2 lists the material constants used in the cyclic plasticity model and the fatigue model for stainless steel Table 1 Cyclic plasticity model used in the fi nite element simulations Yield functionf eS a eS a 2k2 0 e S deviatoric stress a backstress k yield stress in shear Flow lawd ep 1 hhd S ni n n normal of yield surface h plastic modulus function e p plastic strain Hardening Rule a PM i 1 a i a i ith backstress part d a i c i r i n a i kk r i v i 1 a i a i kk dpM number of backstress parts i 1 2 3 M dp equivalent plastic strain increment c i r i v i material constants Table 2 Material constants for SS304L Cyclic plasticity constants Elasticity modulus E 200 GPa Poisson s ratiol 0 3 k 115 5 MPa c 1 1381 0 c 2 507 0 c 3 172 0 c 4 65 0 c 5 4 08 r 1 93 0 MPa r 2 130 0 MPa r 3 110 0 MPa r 4 75 0 MPa r 5 200 0 MPa v 1 v 2 v 3 v 4 v 5 8 0 Fatigue constantsr0 270 MPa m 1 5 b 0 5 rf 800 MPa D0 15000 MJ m3 F Fan et al Mechanics of Materials 40 2008 961 973963 304L The cyclic plasticity material constants were ob tained from the cyclic stress strain curve which was ob tained from the experiments on the smooth specimens under fully reversed tension compression loading A com plete description of procedure for determination of mate rial constants can be found in corresponding references Jiang and Sehitoglu 1996a b The fatigue material con stants were determined by comparing the fatigue data un der fully reversed tension compression and that under pure torsion Jiang 2000 2 2 Finite element model Round compact specimens with a thickness of 3 8 mm were used in the crack growth experiments The geometry and the dimensions of the specimen are shown in Fig 1 The crack growth experiments were conducted in ambient air The specimens were subjected to constant amplitude loading with different R ratios the minimum load over the maximum load in a loading cycle and high low se quence loading All of the experiments started without a pre crack except two specimens tested under the follow ingloadingconditions R 0 85 DP 2 0 54 kNand R 1 DP 2 5 0 kN More detailed information of the experiments and the experimental results were reported in a separate presentation Due to the small thickness plane stress condition was assumed for the round compact specimen Four node plane stress elements were used in FE mesh model The FE mesh model shown in Fig 2 was created by using the FE package HyperMesh Altair HyperMesh 2004 Due to the symmetry in geometry and loading only half of the specimen was modeled To properly consider the high stress and strain gradients in the vicinity of the notch or crack tip very fi ne mesh size was used in these regions The size of the smallest elements in the mesh model was 0 05 mm There were approximately 3058 to 5067 ele ments used in the mesh model depending on the crack size The knife edges for the attachment of the open dis placement gage in the specimen Fig 1 were not modeled because the free end of the specimen does not affect the stress and strain of the material near the crack tip or notch Referring to the coordinates system employed in Fig 2 the tensile external load P is applied in the y direction uni formly over nine nodes on the upper surface of the loading hole To mimic the actual loading condition the compres sive load is applied in the negative y direction uniformly over nine nodes on the lower surface of the loading hole The displacements in the x direction of the middle nodes on the upper edge of the loading hole are set to be zero The displacements in the y direction for all the nodes on the plane in front of the crack tip or the root of the notc