Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

J-M based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading

In this work, a set of J-M^p based criteria is proposed to assess the bifurcation angle of an elastic-plastic crack in plane strain under mixed mode loading. We first establish a criterion in order to study the competition between the tensile fracture (T-type fracture) and the shear fracture (S-type fracture) in the frame of RKR conception [J. Mech. Phys. Solids 21 (1973) 395]. Based on the generalized HRR [ASTM STP 560 (1974) 187] solution and on the knowledge of the mixity parameter M^p, the RKR based criterion is transformed into a J-M^p based criterion. When the crack grows in tensile manner, the maximum circumferential stress criterion is adopted to determine the crack bifurcation angle. When the crack grows in shear manner, the traditional theory of plasticity, according to which the plastic flow develops essentially along one of the slip bands immediately ahead of the crack tip, is used to determine the crack growth direction. All these proposed criteria are given as function of the mixity parameter M^p and the hardening exponent n of the material. Finally, we carry out some numerical computations by applying the proposed criteria and then compare the obtained results with experimental data gathered in literature. It is shown that these criteria are physically reasonable and highly accurate. Another advantage is that the parameters used are easy to identify numerically and experimentally, therefore, these criteria are simple to apply in engineering structures.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Fatigue threshold and crack growth in an electron beam weld made of steel and bronze

In this research topic some experimental tests with single-edge notched beams were performed to determine the threshold load value for fatigue crack growth and to characterize fatigue crack behaviour of an electron beam weld made of steel and bronze. Subsequently, numerical analyses were done to estimate the threshold value ΔK_th and to simulate the fatigue crack growth. The calculated crack path was compared to those determined experimentally. The objective was to find out the necessary fracture properties for an analysis of an electron beam welded worm wheel and to asses the capability of usual fracture analysis software to simulate fatigue crack growth in welds.     

Virtual crack extension methods for non-linear materials

The virtual crack extension technique is a very efficient and accurate approach to fracture mechanics calculations in the numerical analysis of bodies containing cracks using the finite element method. A few variations of the technique have been described in the literature, and have been extensively used in linear elastic fracture mechanics, where good validation has frequently been available with accepted alternative solutions for standard tests. However, for non-linear materials extra complications arise in the technique, particularly in describing material response in a compatible manner. It is shown that, using few assumptions, a very competitive virtual crack extension technique based, on a direct minimization of potential energy is available for elastic non-linear elastic materials. Such materials can be closely approximated to elastic–plastic behaviour for monotonically increasing loads including mechanical, thermal and body force forms. The technique is described and demonstrated via examples to be in good agreement with alternative fracture parameter evaluations when evaluated in the same computer system, BERSAFE.     

An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete*

An embedded cohesive crack model is proposed for the analysis of the mixed mode fracture of concrete in the framework of the Finite Element Method. Different models, based on the strong discontinuity approach, have been proposed in the last decade to simulate the fracture of concrete and other quasi‐brittle materials. This paper presents a simple embedded crack model based on the cohesive crack approach. The predominant local mode I crack growth of the cohesive materials is utilized and the cohesive softening curve (stress vs. crack opening) is implemented by means of a central force traction vector. The model only requires the elastic constants and the mode I softening curve. The need for a tracking algorithm is avoided using a consistent procedure for the selection of the separated nodes. Numerical simulations of well‐known experiments are presented to show the ability of the proposed model to simulate the mixed mode fracture of concrete.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

Element free galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials

Employing an extension of the convective mesh technique, an Element Free Galerkin (EFG) based formulation for steady quasi-static crack growth in elastic-plastic materials undergoing small scale yielding is established. In accordance with the steady state condition, a parallel path constitutive law integration scheme is implemented into the formulation and a body force type term is introduced for the contribution of crack tip plasticity. A detailed numerical analysis is performed for steady quasi-static growth of a mode I crack under plane strain conditions in elastic-perfectly plastic materials. The numerical solutions to this problem confirm the existence of an elastic unloading wedge. The computed near-tip stress distributions and the crack opening displacements for this problem provide good agreements with the corresponding asymptotic solutions and demonstrate the validity of the EFG based formulation. A rough estimate of the range of validity of the asymptotic solutions is also made based on the numerical solutions. In addition, the effect of strain hardening on the steady quasi-static crack growth is investigated. Both power hardening and linear hardening models are considered.     

Automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method

In this paper, automated simulation of multiple crack fatigue propagation for two-dimensional (2D) linear elastic fracture mechanics (LEFM) problems is developed by using boundary element method (BEM). The boundary element method is the displacement discontinuity method with crack-tip elements proposed by the author. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Local discretization on the incremental crack extension is performed easily. Further the new adding elements and the existing elements on the existing boundaries are employed to construct easily the total structural mesh representation. Here, the mixed-mode stress intensity factors are calculated by using the formulas based on the displacement fields around crack tip. The maximum circumferential stress theory is used to predict crack stability and direction of propagation at each step. The well-known Paris’ equation is extended to multiple crack case under mixed-mode loadings. Also, the user does not need to provide a desired crack length increment at the beginning of each simulation. The numerical examples are included to illustrate the validation of the numerical approach for fatigue growth simulation of multiple cracks for 2D LEFM problems.     

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.     

Characteristic crack-tip distances in fracture criteria: Is crack propagation discontinuous?

The present paper describes a possible mechanism for discontinuous crack advance in which surface separation occurs initially not at the crack-tip itself but within the crack-tip plastic zone of size r_p, at the mid-point of the crack-tip characteristic distance d (identified here with the finite growth step Δa), i.e., at the region of maximum opening tensile stress, spreading towards (and also away from) the crack-tip. The crack extension occurs when the crack-tip is reached and full opening over the distance d is completed.Finite element analyses show that this mechanism causes the formation of a rippled crack face surface in elastic-plastic materials in which irreversible plastic deformations take place during each growth step, in sharp contrast with the smooth surface created in ideal elastic materials in which all deformations are fully reversible. Some pictorial evidence of void formation ahead of the crack tip and of ripples during propagation, found in the literature, is presented.Although the present analysis is from a continuum standpoint it is acknowledged that micro structural features and mechanisms can condition the fracture events taking place in the process zone.The implication to the brittle-ductile transition of the dependence of the energy release rate, G^ΔΞ, on the ratio q (=Δa/r_p) is also discussed.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

Fast multipole DBEM analysis of fatigue crack growth

A fast multipole method (FMM) based on complex Taylor series expansions is applied to the dual boundary element method (DBEM) for large-scale crack analysis in linear elastic fracture mechanics. Combining multipole expansions with local expansions, both the computational complexity and memory requirement are reduced to O(N), where N is the number of DOF. An incremental crack-extension analysis based on the maximum principal stress criterion and the Paris law is used to simulate the fatigue growth of numerous cracks in a 2D solid. Some examples are presented to validate the numerical scheme.     

Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept

An energy dissipation rate concept is employed in conjunction with the J-integral to calculate crack growth resistance of elastic-plastic fracture. Different from Rice’s J-integral, the free energy density is employed in place of the stress working density to define an energy-momentum tensor, which yields that the slightly changed J-integral is path dependent regardless of incremental plasticity and deformational plasticity. The J-integral over the remote contour is split into the plastic influence term and the J _FPZ-integral over the fracture process zone which is an appropriate estimate of the separation work of fracture. Finite element simulations are carried out to predict the plane strain mode I crack growth behavior by an embedded fracture process zone. It can be concluded that J-integral characterization is in essence a stress intensity-based fracture resistance similar to the K criterion of linear elastic fracture, and energy dissipation rate fracture resistance can be taken as an extension of the Griffith criterion to the elastic-plastic fracture.     

Numerical simulation of fatigue crack growth behavior by crack-tip blunting

In ductile metals one of basic mechanisms for fatigue crack growth is that based on crack-tip blunting under the maximum load and re-sharpening of the crack-tip under minimum load. In this paper, simulations of fatigue crack growth by crack-tip blunting using ANSYS finite element code are presented. This investigation focuses solely on simulation of fatigue crack growth due to crack-tip plasticity only. As such, any material damage and its fracture is not considered. Due to high plastic deformation the present simulations utilize a remeshing technique which allows applying a number of load cycles without terminating the simulation due to the error caused by excessive mesh distortion. The simulations were conducted using a center cracked specimen under various loading conditions including different load ranges and load ratios R = −1, 0 and 0.333. It is shown that fatigue crack growth (FCG) slows down with number of cycles towards a steady state value. The simulated FCG data for constant amplitude loading follow the Paris power law relationship and also indicate a typical R-ratio dependence. It can be noted that for all load cases with load ratios R > 0 no crack closure in the vicinity of the crack-tip wake was observed.     

Fatigue crack propagation of bainitic nodular cast iron

The effects of austempering temperature and isothermal transformation time on fatigue crack growth rate in a ductile iron with a bainitic structure have been studied. Crack growth rates in austempered samples were compared with those in materials with a ‘bullseye’ casting structure. Using scanning electron microscopy, the mechanism of the fatigue crack growth can be understood by observing the fracture surface of a fatigue specimen. X-ray diffractometry was used to determine the volume fraction of retained austenite. It can be concluded that the volume fraction of retained austenite, the fracture mode and the matrix microstructure are closely related to the fatigue crack propagation rate and the fracture mode.