Evaluation of the elastic-plastic mixity parameters on the base of different crack propagation criteria. Part 1. Preliminary analysis

In order to evaluate the mechanical behavior around small-scale yielding crack tip for both plane strain and plane stress, the asymptotic governing equations and their boundary conditions by considering fracture mechanisms are formulated. A total deformation theory of plasticity with a power-law hardening is used. The analysis of the near-tip fields is carried out for both the maximum tensile and shear stress crack growth direction criteria, as well as for the complete range of mixity parameters and various strain-hardening levels. The new scheme of mixed-mode problem solution is proposed. Realationships between elastic and plastic mixity parameters are given as functions of the crack growth direction criterion and the strain-hardening exponent.Translated from Problemy Prochnosti, No. 1, pp. 60–75, January–February, 2005     

Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.     

Local failure behavior of a dissimilar metal interface region with mechanical heterogeneity

Failure analyses and assessments for dissimilar metal welded joints are usually conducted by simplified interface regions without considering actual mechanical heterogeneity and limited crack positions. In this work, the finite element simulations based on Gurson-Tvergaard-Needleman damage mechanics model are used to investigate local failure behavior of a dissimilar metal interface region with mechanical heterogeneity and a series of initial crack positions. The results show that the fracture resistance and crack growth paths of the cracks in different locations of the interface region are significantly affected by mechanical heterogeneity. The interactions of different local mechanical (strength and work hardening properties) mismatches and intrinsic toughness around cracks determine the distributions and evolution of plastic strain, stress triaxiality and damage ahead of crack tips, which cause larger variations in fracture resistance and crack growth paths. For accurate and reliable failure analyses and assessments for the cracks in dissimilar metal interface regions with mechanical heterogeneity, it is recommended to obtain and use local fracture resistance properties related to crack locations.     

On the size of plastic zone ahead of crack tip

A method for the crack tip analysis of a tensile loaded crack (mode I) due to yielding of the material is developed. The stress/strain distribution within the plastic zone, as well as size of the plastic zone are presented. The development is based on the energy interpretation of the strain hardening exponent, and an analogy between mode III and mode I for the case of small scale yielding. Predictions of the proposed method are compared with the experimental results, and a fairly good agreement is observed. A number of proposed methods to estimate the plastic zone size for ductile materials are also discussed.     

Interfacial crack-tip constraints and <Emphasis Type="Italic">J</Emphasis>-integral for bi-materials with plastic hardening mismatch

This paper investigates interfacial crack tip stress fields and the J-integral for bi-materials with plastic hardening mismatch via detailed elastic-plastic finite element analyses. For small scale yielding, the modified boundary layer formulation with the elastic T-stress is employed. For fully plastic yielding, plane strain single-edge- cracked specimens under pure bending are considered. Interfacial crack tip stress fields are explained by modified Prandtl slip-line fields. It is found that, for bi-materials consisting of two elastic-plastic materials, increasing plastic hardening mismatch increases both crack-tip stress constraint in the lower hardening material and the J-contribution there. The implication of asymmetric J-integral in bi-materials is also discussed.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.     

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J₂ incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

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.     

Mechanical heterogeneity and validity of J-dominance in welded joints

Fracture criterion of the J-integral finds wide application in the integrity evaluation of welded components, but there exist some confused problems such as the dependence of the fracture toughness on the strength mis-matching and specimen geometry which need to be clarified. It is rough and unsuitable to attribute the variation of J-integral fracture parameter simply to the effect of mechanical heterogeneity. In the present paper, a two-dimensional finite element method is employed to analyze the distribution and variation of crack tip field of welded joints with different strength mis-matching in four kinds of specimen geometry, and then the validity of J-dominance in welded joints is investigated. It is found that the crack tip field of mis-matched joint is different from that of either the weld metal or base metal of which the joint is composed, but it is situated between those of weld metal and base metal. Under the plane strain, there is obvious difference in stress triaxiality for different strength mis-matched joints. The validity of J-dominance in welded joint can not be obtained by comparing whether the stress triaxiality meets that required by the HRR solution because of the existence of mechanical inhomogeneity. By ascertaining if the stress triaxiality of welded joint near the crack tip is dependent of specimen geometry, the conclusion can be arrived at: for plane stress the validity of J-dominance is valid, whilst for plane strain the validity of J-dominance is lost. Based on the above, attempt has been made to point out that the influence of mechanical heterogeneity on the fracture toughness of weldment arises from the variation of constraint intensity-crack tip stress triaxiality. Compared with the effect of mechanical heterogeneity on the stress triaxiality, the losing of validity of J-dominance in mis-matched joint under plane strain may play a more critical role in the variation of J-integral fracture parameter of weldment.     

含半椭圆表面裂纹焊接接头断裂参量的试验研究

本文研究了半椭圆形表面裂纹最深点三维J积分的直接测试技术,并在此基础上,通过对高匹配焊接接头表面裂纹试样断裂力学参量J积分的试验测试,探讨了接头强度匹配对焊接表面裂纹扩展驱动力的影响。试验表明本文所采用的手段对于焊接表面裂纹断裂参量的测试是适用的,且结果也充分反映出焊接接头的力学性能不均匀性的影响作用。     

DETERMINATIONS OF JIC FOR 2024-T351 ALUMINIUM ALLOY

Abstract— The J -integral is an elastic-plastic fracture mechanics parameter which can be regarded as a measure of the intensity of the crack tip stress and strain fields, irrespective of the plastic zone size. The value of J at the onset of stable crack extension, J _IC, has been suggested as a fracture criterion for both large-and small-scale yielding conditions. In this work the value of J _IC for an extruded, medium-strength aluminium alloy, 2024-T351 bar, was determined using; (i) the Hutchinson-Rice-Rosengren crack tip model and experimentally-determined crack tip strain profiles; and (ii) the ASTM standard multiple-specimen technique. Knowing the critical load for initial crack extension from the crack tip strain profile method also enabled J _IC to be computed using a finite element-hybrid contour method and a modified linear elastic fracture mechanics approach. Agreement between the J _IC values obtained by the various methods was good.     

Orientation dependence of fracture in copper bicrystals with symmetric tilt boundaries

Experimental results (Wang and Anderson (1991), Acta Metall. 39, 779–792) show that the fracture behavior of Σ9 copper bicrystals depends on the cracking direction. Near-interface transgranular fracture surfaces were observed in the case of the crack growing in the [ 14] direction, with an essentially ductile failure mode, while the case of the crack growing in the [1 ] direction showed far less toughness and had an intergranular fracture surface with cleavage tongues. Asymptotic and finite element models for stationary cracks in ideally plastic and strain hardening materials have been used to examine this cracking direction dependency from a small strain continuum mechanics point of view. The tensile stress ahead of the crack tip was found to be essentially identical for the two growth directions, with the brittle orientation resulting in only slightly higher stress values at small distances from the crack tip. However, the strain field was found to be different for the two orientations, with the overall plastic zone size being much larger in the ductile case. Also, the orientations of the zones of concentrated shearing ahead of the crack, observed in the ideally plastic model, suggest two different dislocation shearing mechanisms. In the ductile case, this zone is parallel to the slip plane, resulting in a regular shearing mechanism in which dislocations can be nucleated at the crack tip and glide on the (111) slip plane. In contrast, this zone is perpendicular to the (111) slip plane in the brittle case, resulting in a kinking shear mode in which dislocations from other external sources expand in a dipole mode to produce macroscopically concentrated shearing. Thus, apart from the dislocation nucleation considerations, continuum mechanics does not seem to be able to fully explain this difference in directional dependency of fracture in the Σ9 copper bicrystals.     

Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.     

Plastic yielding at the tip of a blunt notch during static and fatigue loading

Rice's analytical Mode III solution for the relationship between anti-plane stress and anti-plane strain was used to determine the small scale plastic yielding at the tip of a two-dimensional blunt notch. The results were applied to fatigue loading. The plastic zone size and crack opening displacement derived in the present analysis were determined as functions of applied stress, geometric factors (notch radius and length) and material properties (yield stress and the work hardening rate). The minimum stress intensity required for plastic yielding at a blunt notch tip was postulated to be the experimentally observed threshold stress intensity for fatigue crack initiation. The threshold stress intensity so determined depends not only on the notch geometry but also on material properties. There is good agreement with calculated and measured values of the threshold stress intensity for fatigue crack initiation.     

Effect of Hydrogen on Plastic Deformation near Crack-tipof A537 Steel in 3.5%NaCl Solution

A computerized digital speckle-intederometry system was set up to study in-situ the influence of cathodic hydrogen charging on the crack opening displacement and on the plastic strain distribution at corrosion fatigue crack tip for the singIe-edge notched plate specimens of structural steel in 3.5%NaCl solution with an applied potential of -1400 mV (SCE). Meanwhile, the mono-directional tension tests with smooth specimens were pedermed in both air and 3.5%NaCl solution under the hydrogen charging conditions. The fracture sudece morphology from corrosion fatigue and tension was examined by SEM. The experimental results show that the existence of hydrogen in crack tip material caused an increase of both yield strength and hardening exponent and a decrease of plastic zone size at the corrosion fatigue crack tip.     

Tensile deformation behaviour of a dissimilar metal weldment of P91 and 347H steels

Deformation of a weldment is governed by the mechanical properties of its base metals and fusion zone. In a weldment, the base metals and fusion zone exhibit changing microstructural features with various phases present along the weldment. Specifically, the heat affected zone of a base metal exhibits a heterogeneous microstructure generated during weld thermal cycles and by post-weld heat treatment. As a result, the mechanical properties in a weldment are often non-uniformly distributed. In this study, tensile tests combined with digital image correlation were performed to obtain the non-uniform distributions of the mechanical properties of a weldment composed of P91 and 347H steels. From the experimental tensile tests, it was found that the 347H base metal had significantly distinct mechanical properties compared to the other zones of the weldment. Furthermore, the 347H base metal had the lowest yield stress but the highest strain hardening exponent. Because of its lowest yield stress, the 347H base metal had the highest plastic strain accumulation at any stage of global deformation. However, the strain hardening rate of the P91 base metal enabled it to accumulate the necessary plastic strain to activate its necking first. Therefore, the failure location of the P91-347H weldment was expected to occur at the P91 base metal. A 3D finite element simulation of the tensile deformation of P91-347H weldment also suggested the same. However, from the present experimental observations, one weldment out of three was found to fail unexpectedly at the heat affected zone of the P91 base metal. The reason for this unexpected failure was determined by microscopic analysis to be the presence of a large defect.     

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.     

A plastic fracture mechanics model for characterization of multiaxial low-cycle fatigue

The near-tip stress and strain fields of small cracks in power-law hardening materials are investigated under plane-stress, general yielding, and mixed mode I and II conditions by finite element analyses. The characteristics of the near-tip strain fields suggest that the experimental observations of shallow surface cracks (Case A cracks) propagating in the maximum shear strain direction can be explained by a fracture mechanics crack growth criterion based on the maximum effective strain of the near-tip fields for small cracks under general yielding conditions. The constant effective stress contours representing the intense straining zones near the tip are also presented. The results of the J integral from finite element analyses are used to correlate to a fatigue crack growth criterion for Case A cracks. Based on the concept of the characterization of fatigue crack growth by the cyclic J integral, the trend of constant J contours on the Γ-plane for Case A cracks compares well with those of constant fatigue life and constant crack growth rate obtained from experiments.     

Geometrical relationships between side necking and plastic zone size near a crack tip in ductile metals. Part I: Modified boundary layer solutions

The plastic zone size is regarded as the measure of a material's resistance, and it also determines the fracture behaviour. Recently, stereo digital speckle photography (SDSP) has been found to be useful for measuring in-situ the side necking developed on the lateral surfaces of a specimen during a standard fracture test procedure for J_IC . Because plastic deformation occurs without any volume change, the in-plane plastic zone developed around a crack tip should be accompanied by out-of-plane deformation, that is, side necking. With the aid of the new measurement technique, side necking is expected to act as a gauge for indicating the plastic zone size. As a preliminary study, the geometrical relationships between side necking and the plastic zone size near a crack tip in ductile metals are explored by using a finite element model with modified boundary conditions. As parameters representing the geometrical similarity between side necking and the plastic zone, the shapes of each region, the distances from the crack tip to the boundaries of each region, r_p and r_s and the areas of each region, A_p and A_s are examined for their sensitivities to variables such as mode mixity, hardening exponent and so on. Among them, the areas, A_p and A_s seem to be the best for application because an excellent linearity between them is maintained in a wide range of mode mixity and load level regardless of the hardening exponent, specimen thickness and yield stress.