Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension .a=W D 0:5/ and three-point bend .a=W D 0:1 and 0:5/ specimens under plane stress condition. The crack growth is controlled by the experimental J -integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack-tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress.

Effect of constraint on ductile crack growth and ductile-brittle fracture transition of a carbon steel

Ductile-brittle fracture transition was investigated using compact tension (CT) specimens from -70oC to 40oC for a carbon steel. Large deformation finite element analysis has been carried out to simulate the stable crack growth in the compact tension (CT, a/W=0.6), three point-point bend (SE(B), a/W=0.1) and centre-cracked tension (M(T), a/W=0.5) specimens. Experimental crack tip opening displacement (CTOD) resistance curve was employed as the crack growth criterion. Ductile tearing is sensitive to constraint and tearing modulus increases with reduced constraint level. The finite element analysis shows that path-dependence of J-integral occurs from the very beginning of crack growth and ductile crack growth elevates the opening stress on the remaining ligament. Cleavage may occur after some ductile crack growth due to the increase of opening stress. For both stationary and growing cracks, the magnitude of opening stress increases with increasing in-plane constraint. The ductile-brittle transition takes place when the opening stress ahead of the crack tip reaches the local cleavage stress as the in-plane constraint of the specimen increases.

Universal crack closure integral for SIF estimation

Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin's original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

Fatigue crack propagation analysis of plaque rupture

Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

Biaxial-load effects on isopachics for a crack at the interface of dissimilar media

The plane problem of two dissimilar materials, bonded together and containing a crack along their common interface, which were subjected to a biaxial load at infinity, is examined by giving a closed-form expression for the first stress invariant of the normal stresses, which is equally valid everywhere, near to, and far from, the crack-tip region. This exact expression for the first-stress invariant is compared by constructing the respective isopachic-fringe patterns, to the approximate expression with non-singular terms, due to the biaxiality factor, for the same quantity. Significant differences between respective isopachic-patterns were found and their dependence on the elastic properties of both materials and the applied loads was demonstrated. The relative errors between the computedK I - andK II -components by using the approximate expression for the first stress-invariant and the accurate one, derived from closed-form solution along either isopachic-fringes or along circles and radii from the crack-tip have been given, indicating in some cases large discrepancies between exact and approximate solutions.

New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems

A posteriori error estimation and adaptive refinement technique for fracture analysis of 2-D/3-D crack problems is the state-of-the-art. The objective of the present paper is to propose a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region and to use this along with the stress based error estimator available in the literature for the region away from the crack tip. The proposed a posteriori error estimator is called the K-S error estimator. Further, an adaptive mesh refinement (h-) strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance of the proposed a posteriori error estimator and the h-adaptive refinement strategy have been demonstrated by employing the 4-noded, 8-noded and 9-noded plane stress finite elements. The proposed error estimator together with the h-adaptive refinement strategy will facilitate automation of fracture analysis process to provide reliable solutions.

Observation of crack closure using a crack mouth opening displacement gauge

A crack mouth opening displacement (CMOD) gauge has been designed to estimate the crack length as well as the crack opening stress level in an automated fatigue crack propagation test programme. The CMOD gauge accurately predicts crack tip opening levels in K-controlled tests with constant K, K increasing or K decreasing. In all three K-controlled tests with a single 100% overload cycle, the CMOD gauge does not measure the crack tip opening stress level over a large range of crack lengths after the application of the overload. The CMOD gauge measures the stress level at which the overload plastic zone site opens. Caution should thus be exercised in using the crack opening stress level, estimated by the CMOD gauge, to explain fatigue crack propagation under arbitrary load sequences from the viewpoint of crack closure phenomena.

Micromechanics Of Fatigue Crack-Growth At Low Stress Intensities In A High-Strength Steel

An attempt to systematically investigate the effects of microstructural parameters in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels has been made for a high strength low alloy steel to observe in general, widely different trends in the dependence of both the total threshold stress intensity range, DELTA-K(th) and the intrinsic or effective threshold stress intensity range, DELTA-K(eff-th) on the prior austenitic grain size (PAGS). While a low strain hardening microstructure obtained by tempering at high temperatures exhibited strong dependence of DELTA-K(th) on the PAGS by virtue of strong interactions of crack tip slip with the grain boundary, a high strength, high strain hardening microstructure as a result of tempering at low temperature exhibited a weak dependence. The lack of a systematic variation of the near-threshold parameters with respect to grain size in temper embrittled structures appears to be related to the wide variations in the amount of intergranular fracture near threshold. Crack closure, to some extent provides a basis on which the increases in DELTA-K(th) at larger grain sizes can be rationalised. This study, in addition, provides a wide perspective on the relative roles of slip behaviour embrittlement and environment that result in the different trends observed in the grain size dependence of near-threshold fatigue parameters, based on which the inconsistency in the results reported in the literature can be clearly understood. Assessment of fracture modes through extensive fractography revealed that prior austenitic grain boundaries are effective barriers to cyclic crack growth compared to martensitic packet boundaries, especially at low stress intensities. Fracture morphologies comprising of low energy flat transgranular fracture can occur close to threshold depending on the combinations of strain hardening behaviour, yield strength and embrittlement effects. A detailed consideration is given to the discussion of cyclic stress strain behaviour, embrittlement and environmental effects and the implications of these phenomena on the crack growth behaviour near threshold.

Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK th , and the intrinsic threshold stress intensity range, ΔK eff, th , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK th and ΔK eff, th on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK th and ΔK eff, th on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔKth and ΔKeff, th with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure.

A general procedure for modified crack closure integral in 3D problems with cracks

In linear elastic fracture mechanics (LEFM), Irwin's crack closure integral (CCI) is one of the signficant concepts for the estimation of strain energy release rates (SERR) G, in individual as well as mixed-mode configurations. For effective utilization of this concept in conjunction with the finite element method (FEM), Rybicki and Kanninen [Engng Fracture Mech. 9, 931 938 (1977)] have proposed simple and direct estimations of the CCI in terms of nodal forces and displacements in the elements forming the crack tip from a single finite element analysis instead of the conventional two configuration analyses. These modified CCI (MCCI) expressions are basically element dependent. A systematic derivation of these expressions using element stress and displacement distributions is required. In the present work, a general procedure is given for the derivation of MCCI expressions in 3D problems with cracks. Further, a concept of sub-area integration is proposed which facilitates evaluation of SERR at a large number of points along the crack front without refining the finite element mesh. Numerical data are presented for two standard problems, a thick centre-cracked tension specimen and a semi-elliptical surface crack in a thick slab. Estimates for the stress intensity factor based on MCCI expressions corresponding to eight-noded brick elements are obtained and compared with available results in the literature.

Modified Crack Closure Integral (MCCI) For 3-D Problems Using 20-Noded Brick Elements

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

Modified crack closure integral (MCCI) for 3-d problems using 20 noded brick elememnts

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Re-examination of crack opening model of interface fracture

The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts, such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. To avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singularity at an interface crack. International Journal of Fracture 1980;16(2):111-9) assumed a finite crack opening angle (COA) such that the singularity lambda became real equal to 1/2. This paper extends the COA model by considering real singularities not necessarily equal to 1/2. When COA is 0 degrees: the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields. (C) 1999 Elsevier Science Ltd. All rights reserved.

The effect of T-stress on plane strain dynamic crack growth in elastic-plastic materials

In this paper, the effects of T -stress on steady, dynamic crack growth in an elastic-plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J (2) flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T -stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T -stress for both ductile and cleavage mode of crack growth.