Atomistic simulation of hydrogen-induced plastic zone compression during cyclic loading

To investigate the effect of hydrogen atoms on the size of the plastic deformation zone, molecular dynamics (MD) simulations were performed on a single crack model. The model uses pre-charged hydrogen to quantify the compression effect of hydrogen atoms on the plastic zone during cyclic loading. The results show that stress release at the crack tip occurs mainly in the form of plastic deformation, and the degree of compression in the plastic zone increases with increasing hydrogen concentration. A compression factor, which considers hydrogen concentration, is found with the help of the simulation results. A modified fatigue crack growth rate (FCGR) model, combined with the compression factor, was then used to predict the hydrogen-assisted fatigue crack growth rate. The proposed model shows excellent agreement with the experimental data for X100 steel, and it provides a new framework to describe hydrogen-assisted cracking.     

In situ measurement of plasticity accompanying hydrogen induced cracking in a polycrystalline AlZnMg alloy

Hydrogen induced single crack propagation is studied in an embrittled aluminum alloy. Hydrogen is introduced into the system by electrochemical reactions in an acidic aqueous medium. After hydrogen charging, tensile tests are performed in air, on notched samples, with a microtensile machine under an optical microscope. A high magnification of × 2000 is used to follow the single crack initiation and propagation. Digital Image Correlation gives the displacement field on the surface with a spatial resolution of approximately 1 μm. It enables the determination of the position of the crack tip and the local velocity at a sub-grain scale. The von Mises strain is calculated and provides a precise measure of the local plastic field that accompanies crack propagation. In addition to the primary plasticity which is emitted from the crack tip or its immediate neighborhood in the form of two intense slip bands, a secondary plastic zone that spreads over several microns ahead of the tip is sytematically found. The characteristics of the plastic zone are measured, together with the velocity and the applied stress intensity factor. In addition, different fracture mechanisms are found on the fracture surface. In particular there are transitions in the fracture mode from intergranular smooth to transgranular parallel to the grain boundary plane. The local fracture mechanisms, in the vicinity of the surface, are linked to the local velocities and plastic deformations. Surprisingly no strong velocity/plasticity correlations are found while the velocities are scattered over a wide range, which is interpreted as a strong polycrystalline effect.     

连杆准静态裂解数值模拟关键技术与启裂分析

对连杆准静态裂解进行了数值模拟分析,对裂纹区网格划分、接触与约束处理、无应力投影功能与自适应加载步长等关键技术进行了探讨;运用临界J积分和最大主应力准则作为连杆启裂的判据,分析了启裂时连杆应力场、塑性场及位移场,给出启裂点的分布状况.数值分析表明:连杆裂解的塑性区只存在于裂纹区裂尖附近,启裂点不唯一且沿连杆厚度方向散布在裂尖,但启裂率先发生在中部裂纹区的最大主应力峰值域,并向上下表面和外轮廓扩展.启裂点散布以及裂纹扩展路径不同极易造成裂纹交汇异常,并导致裂解过程中的爆口、断裂面台阶等裂解缺陷.     

A phenomenological theory of subcritical creep crack growth in a cylindrical vessel weakened by an axial part-through crack

A phenomenological theory of subcritical creep crack growth is formulated for materials with large creep exponent. The subcritical crack growth is shown to be mainly controlled by the average net section stress and the plastic deformations in the vicinity of the crack tip. Plastic zone size is evaluated by considering the effects of relaxation on the plastic stress singularity at the crack tip for a power hardening material. The theory has been applied to a cylindrical vessel weakened by an axial part-through crack. The predicted rupture behaviour compares favourably with published creep rupture tests on 9Cr 1Mo steel tubing pressurised at 550°C. The concept of flaw size stress is introduced and is used in failure mode prediction. Failure will be by breakage or leakage, depending on the relative values of flaw size stress and material yield stress.     

Plastic zone size in fatigue cracking

Fatigue tests were performed on the specimens of Type 304 stainless steel and Inconel 718. To investigate the effects of specimen thickness on crack tip deformation and fatigue crack growth rate (FCGR), specimens of different thickness were used. To validate fatigue crack propagation in terms of plastic zone size, elastic plastic fracture mechanics (EPFM) are studied in this investigation. Results show that FCGR is a function of specimen thickness, which worsens as the specimen thickness increases. It is considered that plastic zone size is an important fatigue crack propagation parameter in conjunction with applied stress level, specimen thickness and crack closure.     

Residual stress due to welding and its effect on the assessment of cracks near the weld interface

An experimental/analytical hybrid-type investigation of the effects of residual stress on crack propagation due to welding has been performed. The residual stresses in the SAW welded A533B plates and electron beam welded plates that consist of HT80 and A533B steels were detected by an acoustoelastic technique. The measured residual stress was incorporated into a finite element procedure, which simulated stable crack growth in 1T compact specimens, where the effects on far-field crack parameters and on near-field crack parameters were examined. Also investigated was the effect on fatigue crack propagation with the hypothetical residual stress of the identical distribution to that in the electron beam weld. The significance of the residual stress distribution ahead and behind the crack tip in relation to the plastic zone size was identified.     

Contact Zone Approach for an Electrically Impermeable Crack in Piezoelectric Materials Under Thermal-Mechanical Loading

A partial contact zone model is developed for the stress and electric displacement fields due to the obstruction of a uniform heat flux by an electrically impermeable crack in piezoelectric materials. Green's function method is used to reduce the problem to a set of singular integral equations that are solved in closed form. When the crack is assumed to be traction free, the crack opening displacement is found to be negative over one-half of the crack unless a sufficiently large far field tensile stress is superposed. The problem is reformulated assuming a contact zone at one crack tip. The extent of this zone, the stress and electric displacement intensity factors at each crack tip are obtained as functions of the applied mechanical stress and heat flux.     

THERMAL SHOCK PROBLEMS OF ELASTIC BODIES WITH A CRACK

This paper deals with thermal shock, problems of elastic bodies with a crack. The case considered is that of an infinitely long circular cylinder with an edge crack, and a homogeneous flat plate with an edge crack initially at uniform temperature and suddenly immersed into a medium of lower temperature. The thermal disturbance near the crack tip is assumed to be neglible in the analysis of the temperature field because thermal shocks occur very quickly. We analyze the transient thermal stress problems of elastic solids with a crack and determine the stress intensity factor at the crack tip. The nondimensional maximum transient stress intensity factor is expressed as a function of the Biot number and the nondimensional crack length. Then we propose simplified formulations of the nondimensional maximum transient stress intensity factor as a function of the Biot number and the nondimensional crack length.     

Fracture analysis of hydrogen storage composite cylinders with liner crack accounting for autofrettage effect

An understanding of fracture behavior is crucial to the safe installation and operation of high-pressure composite cylinders for hydrogen storage. This work has developed a comprehensive finite element model to investigate axial surface flaws in cylinder liners using the fracture mechanics and a global–local finite element technique. Since the autofrettage process has a strong influence on cylinder fracture behavior, it is also considered in this analysis. The simulation process is broken down into three steps in order to precisely extract fracture parameters and incorporate the autofrettage effect. In the first step, the global model performs the autofrettage simulation to study the residual stress with consideration of both material hardening and the Bauschinger effect. In the second step, the global model uses residual stress to compute displacement for the local model. Finally, in the third step, the local model extracts the values of stress intensity factor and J-integral. Comparison is conducted on the fracture parameters with various autofrettage levels and crack shapes. The vicinity of the crack front is also studied by the size and shape of the plastic zone, and the validity of stress intensity factor and J-integral dominances is examined.     

3D simulation of hydride-assisted crack propagation in zircaloy-4 using XFEM

Influence of hydride precipitated at the tip of the crack on crack propagation in zircaloy-4 is numerically investigated using the extended finite element method (XFEM). Numerical simulation is performed on compact tension specimen to understand the effects of crack and hydride lengths on crack propagation in terms of stress intensity factor and J-integral. The values of stress intensity factor and J-integral indicate that hydride induces the crack instability. The stress intensity factor decreases with the precipitation of brittle hydride phase at the crack tip, resulting in hydride-assisted crack propagation. A comparison of crack propagation behaviour with different hydride lengths is also presented. The crack remains stable in the absence of the hydride while it propagates when hydride is considered at its tip for the same applied load. The crack arrests only after reaching to the zircaloy metal matrix causing complete fracture of hydride.     

A Surface Crack in a Graded Coating Bonded to a Homogeneous Substrate under Thermal Loading

The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under steady-state heat flux is considered. The coating is graded along the thickness direction and modeled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The resulting crack problem is of mode I because the orientations of the crack axis, the material gradient and the heat-flux are all parallel. The equivalent crack surface tractions are first obtained and substituted in the plane elasticity equations which are then converted analytically into a singular integral equation. The resulting equation is solved numerically using orthogonal Jacobi polynomials to yield the Mode I stress intensity factor. The main objective of the article is to study the effect of the layer thickness and nonhomogeneity parameters on the crack tip stress intensity factor for the purpose of gaining better understanding on the behavior of graded coatings under thermal loading.     

A Surface Crack in a Graded Coating Bonded to a Homogeneous Substrate under Transient Thermal Loading

The elastodynamic problem of a surface crack in a graded coating bonded to a homogeneous substrate under transient heat flux is considered. The coating is graded along the thickness direction and modelled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The resulting crack problem is of mode I because the orientations of the crack axis, the material gradient and the heat-flux are all parallel. The equivalent crack surface tractions are first obtained and substituted in the plane elasticity equations which are then converted analytically using appropriate integral transforms into a singular integral equation. The resulting equation is solved numerically using orthogonal Jacobi polynomials to yield the Mode I stress intensity factor. The main objective of the research is to study the effect of the layer thickness and nonhomogeneity parameters on the dynamic crack tip stress intensity factor for the purpose of gaining better understanding on the behavior of graded coatings under transient thermal loading.     

TRANSIENT THERMO-VISCOELASTIC RESPONSE OF A CRACK IN A LAYERED STRUCTURE

This article examines the application of a numerical method of transient stress analysis for the study of a crack located in a viscoelatic layer bonded to an elastic substrate. The layered structure containing the defect is subjected to heat conduction and associated thermo-viscoelastic effects. The finite-element technique is used to examine the time-dependent variation in the stress intensity factor at the crack tip due to a sudden reduction in the temperature at the surface of the layered structure. Numerical results presented in the article illustrates the influence of the thermo-viscoelastic coupling on the crack behavior.     

Removal of the influence of stress triaxiality on crack tip opening displacement fracture toughness by continuum damage mechanics approach

Experimental data for AS 1405-180, AS 1204-350, HY 80 and C-Mn steels shows that the crack tip opening displacement (CTOD) elastic-plastic fracture toughness at initiation δ_c decreases with increasing crack tip stress trifaxiality. This trend is confirmed by the continuum damage analysis in this paper. The dependence of the CTOD parameter at initiation on the local constraint, i.e. the stress triaxiality, provides the motivation to seek parameters that could rank the toughness of steels. Since the local effective plastic strain can be related to the CTOD, a relationship is described between the initiation CTOD toughness and the crack tip constraint, i.e. the stress triaxiality, on the basis of a new local damage theory for ductile fracture. Furthermore, a new constraint corrected toughness parameter δ_dc (and corresponding criterion) for ductile fracture is proposed, in which both crack tip deformation and crack tip constraint intensity are taken into account. Several series of experimental data have shown that the parameter δ_dc is nearly a constant or independent of the local constraint. It is found that the toughness variation with constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper.     

Theory model combined with XFEM of threshold stress intensity factor and critical hydride length for delay hydride cracking

In order to determine the threshold stress intensity factor and critical hydride length for delayed hydride cracking in Zr-2.5Nb pressure tube alloy, the distribution of normal stress in the plastic zone of crack tip by the developed method that combines theory calculation with extended finite element method (XFEM) was improved. The fracture process of two-phase composites containing Zr-2.5Nb and hydride precipitate was simulated by XFEM. Based on that, critical hydride length $L_C$ corresponding to the theoretical model for K_1H was estimated. Meanwhile, to illustrate the validity of theoretical and numerical methods, recent theoretical models and experimental measurements were utilized to verify the results of this paper. The theoretical model of DHC was improved to estimate the critical hydride length corresponding to threshold stress intensity factor. The predicted value of critical hydride length is close to the experimental values.     

A quantitative description on fracture toughness of steels in hydrogen gas

Fracture toughness or critical stress intensity factor of many steels can be reduced by hydrogen gas. In this paper, a simple quantitative model to predict the fracture toughness of steels in gaseous hydrogen is proposed. This model is based on the assumption that fracture of a cracked body occurs when the maximum principal stress ahead of the crack tip reaches the critical cohesive stress for crack initiation. The critical stress is inversely proportional to the accumulated hydrogen concentration. The notion is that the crack will initiate at the elastic-plastic boundary ahead of the crack tip when hydrogen concentration reaches a maximum value after a long-term hydrogen diffusion assisted by the hydrostatic stress. The model describes the dependence of fracture toughness on hydrogen pressure, temperature and yield strength of steels. It can be used to quantitatively predict fracture toughness of steels in hydrogen gas, particularly in high pressure. Some experimental data reported in literature were used to validate the model, and a good agreement was obtained.     

On the mode III failure of a long submerged defect

This paper analyses the elastic-perfectly plastic failure of a long uniform submerged defect offset from the centre of a uniform block under Mode III loading by a uniform remote longitudinal shear. The analysis confirms that the shorter of the two uncracked ligaments is the first to go fully plastic or to fracture. Solutions are found for the ligament yield load, the crack tip opening displacement (CTOD) and stress intensity factor at each tip, and the mean elastic stress on the shorter ligament. The results are calculated numerically and presented graphically: analytical results are available in the limit of very small remaining ligaments.The results of the Mode III analysis provide insight into the elastic-plastic behaviour of similarly cracked plates in Mode I loading under tension, and more generally illustrate some of the interactions between ‘local’ and ‘global’ plasticity during defect assessment.     

应用有限元法研究柴油机活塞的断裂破坏

本文应用有限元法和光弹性试验对活塞顶的裂纹进行断裂力学分析。针对活塞结构复杂的特点,推荐一种能对实际零件进行断裂分析的有限元计算法,计算程序简单,计算精度较高,可给出实际零件裂纹尖端附近的应力场和应力强度因子。另外,应用光弹性试验对活塞模型进行了断裂分析,叙述了试验中应注意的事项。对一台柴油机的活塞顶断裂破坏进行了分析,给出了裂纹存在对活塞顶应力场和温度场的影响,以及裂纹尖端附近的应力强度因子。有限元计算值和光弹性试验值吻合良好,并且同实际破坏相符合。     

Evaluation of crack tip constraint using photoelasticity

The method of photoelasticity has been used extensively in the past for investigating elastic stresses in cracked specimens. However, previous studies concentrate predominantly on different methods for determining the stress intensity factors. Some of these methods make use of the higher order stress terms including the T-stress to achieve more accurate experimental results for stress intensity factors. Nevertheless, the effect of T-stress on the stress fields near the crack tip has received little attention in previous photoelastic studies. In this paper, a two-parameter formulation is used to study how the T-stress influences the isochromatic fringe patterns around the tip of a mode I crack. Theoretical and experimental results obtained in this research show that the isochromatic fringes near the crack tip rotate forward and backward for negative and positive values of T-stress, respectively. Therefore, the experimental technique of photoelasticity can be used to distinguish low constraint cracked components from high constraint ones.     

CRITICAL STRESS INTENSITY FACTORS FOR CRACKED HOLLOW PIPES UNDER TRANSIENT THERMAL LOADS

Finite element analyses of a long hollow cylinder having an axisymmetric circumferential internal edge crack, subjected to convective cooling on the inner surface are performed. The transient thermal stress intensity factor is estimated using a domain version of the J-integral method. The effect of the thickness of the cylinder, crack length, and heat transfer coefficient on the stress intensity factor history are studied. The variations of critical normalized stress intensity factor with crack length-to-thickness ratio for different parameters are presented. The results show that if a small inner surface crack begins to grow, its stress intensity factor will increase with increase in crack length, reach a maximum, and then begin to drop. Based on the results, a fracture-based design methodology for cracked hollow pipes under transient thermal loads is discussed.