非晶态高聚物裂尖银纹损伤场

在非晶态高聚物裂端塑性区引入银纹损伤，提出了一个修正的Dugdale模型，并由它确定塑性区的大小，算例表明，银纹损伤导致了塑性区深度的增加。此外，在Dugdale模型下研究了稳态扩展的端塑性区，在裂纹缓慢扩展、小范围银纹化以及材料为线粘弹性等假定下，由能量原理得到了控制裂纹生长的一个非线性微分一积分方程，从中看到银纹损伤的影响十分显著。     

聚乙烯Ⅰ-Ⅱ复合型疲劳裂纹扩展实验研究

本文采用中密度聚乙烯(MDPE)单边斜切口板状试样,完成了多种条件下的Ⅰ-Ⅱ复合型疲劳裂纹扩展试验。通过对裂尖和裂尖银纹区演化的全程显微测量,获取了各试样疲劳裂纹扩展过程的一致性特征,其过程分为初始银纹区萌生、银纹区转向、裂纹宏观扩展三个阶段。通过计算发现最大周向拉应力准则能精确预测第一阶段初始银纹区的萌生角度。试验表明第二阶段中银纹区发生转向,且第三阶段中裂纹始终沿垂直于外载荷方向的路径扩展,该现象通过银纹机理结合对裂尖奇异场的分析得到了解释,并从断面分析中得到印证。对比不同加载角下试样的裂纹扩展过程,发现裂纹萌生时间随加载角增大显著增长,但裂纹扩展特征一致。     

平面应变脆性损伤裂纹场分析

根据Ｂｕｉ的脆性损伤理论，本文研究Ｉ型拉伸裂纹的平面应变过程区及其力学场。计及裂尖材料的有限变形，细致的有限元分析给出了小范围屈服条件下两种典型的损伤区形貌。     

扩展裂纹尖端的塑性热耗散与温度场

材料的不可逆变形功以热的形式耗散，形成温度场，本文考虑Ⅰ型裂纹尖端过程区塑性变形功的热耗散，视裂尖塑性过程区为内热源，通过合理地构造一个热源密度函数，结合裂尖塑性区的近似模型，给出了裂纹定常扩展过程中的裂尖温度场。     

热辐射应力图像分析确定裂纹尖端塑性区

本文借助于热辐应力图像分析技术记录了铝质紧养伤拉伸试件的热辐射应力图像。根据裂尖周围温度变化曲线的分布规律确定其特征区的,从而得以裂尖塑性区的开头曲线,并与理论值比较,符合良好。对裂纹扩展面进行ＳＥＭ分析,得出该试件的断裂特性,对于进行细观损伤研究有重要的意义。     

评估材料断裂韧的损伤等效法

以实际结构或实验试件与ＨＲＲ裂尖场的一特征点的损伤相当为原则，建立了ＨＲＲ场的裂尖控制参数与实际试件或结构裂尖控制参数之间的关系。据此可消除不同试件因约束不同而导致的断裂韧性的变化；亦可用来评估实际结构及试件的断裂失效。     

评估材料断裂韧性的损伤等效法

以实际结构充实验试件与ＨＲＲ裂尖场的一特征点的损伤相当为原则，建立了ＨＲＲ场的裂尖控制参数与实际试件在结构裂尖控制参数之间的关系．据此可消除不同试件因约束不同而导致的断裂韧性的变化；亦可用来评估实际结构及试件的断裂失效。     

金属韧性断裂的细观研究

对三点弯曲试件裂尖及断裂过程分别用 Prandtl-Reuss本构、Gurson本构方程作了大变形弹塑性有限元分析 ,并比较了二者的结果。对裂尖应力分布 ,应变分布和裂尖处空穴演化作了初步研究。计算模拟结果表明裂尖空穴化区域是一个很小量级的区域 ,采用 Gurson本构方程来研究裂尖“过程区”比采用 Prandtl-Reuss本构方程分析“过程区”来的合理 ,更接近材料实际断裂过程。     

单向拉伸界面裂纹的条形损伤－塑性区域模型

本文提出单向拉伸情况下两相介质界面裂纹的条形损伤－塑性区域模型。假设在塑性区端点的应力有界，且使弱相介质达到屈服，损伤区的尺寸和δ＝成正比的条件；可确定损伤区与塑性区的长度及其上的法向和切向接合力，ＣＴＯＤ值等。由此导出的裂尖应力场无ｒ￣（－１／２＋ｊｅ）的强奇异振荡，位移场无ｒ￣（１／２＋ｉｅ）的振荡项。     

单向拉伸界面裂纹的条形损伤－塑性区域模型

本文提出单向拉伸情况下两相介质界面裂纹的条形损伤－塑性区域模型。假设在塑性区端点的应力有界，且使弱相介质达到屈服，损伤区的尺寸和δ＝成正比的条件；可确定损伤区与塑性区的长度及其上的法向和切向接合力，ＣＴＯＤ值等。由此导出的裂尖应力场无ｒ￣（－１／２＋ｊｅ）的强奇异振荡，位移场无ｒ￣（１／２＋ｉｅ）的振荡项。     

A phenomenological model of fatigue crack growth in perfectly plastic infinite plates under completely reversed uniaxial loading

The fatigue failure of a thin infinite center-cracked plate under completely reversed uniaxial loading is considered. A two-stage fatigue crack model including the incubation and crack propagation stages is constructed. The stress distribution in the vicinity of the crack tip is described using the concept of a conventional elastic crack. The crack-tip plastic zone is simulated by a Dugdale thin plastic zone, and the condition for the movement of the failure front is given by criteria of damage mechanics. It is shown that the fatigue crack growth rate in perfectly plastic materials with a plastic zone of constant length is a power-law function of the stress intensity factor range. This relationship is quadratic when the length of the plastic zone is not constant Published in Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 116–127, December 2005.     

Geometry dependence of crack growth resistance curve for a ligament toughened brittle material

Many brittle materials exhibit a time-independent behaviour, whereby the crack tip stress intensity (K) increases during crack growth (R). This increase is associated with the development of a ligament zone behind the crack tip, the restraining stresses due to the crack-bridging elements within this zone being responsible for the stress intensity increase. Theoretical analyses, based on the assumption of a constant restraining stress within the ligament zone, show that, for a prescribed crack-solid geometry configuration, although the K - R curve shape is independent of the loading conditions up to the full development of a ligament zone, the K and R values associated with this full development are critically dependent on the loading conditions. Particular attention is focused on the difference between bend and tensile loading of a finite width solid containing an edge crack.     

An I-integral method for crack-tip intensity factor variation due to domain switching in ferroelectric single-crystals

In the present study, an I-integral method is established for solving the crack-tip intensity factors of ferroelectric single-crystals. The I-integral combined with the phase field model is successfully used to investigate crack-tip intensity factor variations due to domain switching in ferroelectricity subjected to electromechanical loadings, which exhibits several advantages over previous methods based on small-scale switching. First, the shape of the switching zone around a crack tip is predicted by the time-dependent Ginzburg–Landau equation, which does not require preset energy-based switching criterion. Second, the I-integral can directly solve the crack-tip intensity factors and decouple the crack-tip intensity factors of different modes based on superimposing an auxiliary state onto an actual state. Third, the I-integral is area-independent, namely, the I-integral is not affected by the integral area size, the polarization distributions, or domain walls. This makes the I-integral applicable to large-scale domain switching. To this end, the electro-elastic field intensity factors of an impermeable crack in PbTiO₃ ferroelectric single crystals are evaluated under electrical, mechanical, and combined loading. The intensity factors obtained by the I-integral agree well with those obtained by the extrapolation technique. From numerical results, the following conclusions can be drawn with respect to fracture behavior of ferroelectrics under large-scale switching. Under displacement controlled mechanical loading, the stress intensity factors (SIFs) decrease monotonically due to the domain switching process, which means a crack tip shielding or effective switching-induced toughening occurs. If an external electric field is applied, the electric displacement intensity factor (EDIF) increases in all cases, i.e., the formed domain patterns enhance the electric crack tip loading. The energy release rate, expressed by the crack-tip J-integral, is reduced by the domain switching in all examples, which underlines the switching-induced-toughening effect. In contrast, under stress controlled load, the SIF evolves due to large-scale switching to a stable value, which is higher than the non-switching initial value, i.e., fracture is promoted in this case.     

Effects of surface diffusion and resolved shear stress intensity factor on environmentally assisted cracking

Hydrogen induced crack-tip plastic deformation has been known as the primary mechanism of hydrogen assisted cracking and stress corrosion cracking. It has been systematically shown that the same mechanism of environmentally assisted crack-tip dislocation emission causes hydrogen assisted cracking, stress corrosion cracking, and liquid metal embrittlement cracking.An embrittling chemical species has to reach a crack tip in order to accelerate crack growth. Very close to a sharp crack tip, surface diffusion is shown to be the dominant transport process of embrittling species for stage-II crack growth. The role of surface diffusion in stage II crack growth is analyzed. The constant cracking velocity is proportional to the surface diffusion coefficient of an embrittling species and inversely proportional to a length parameter, , which is related to the transport process upstream.Dislocation emission at a crack tip is driven by crack-tip resolved shear stress. Crack-tip resolved shear stress field is characterized by resolved shear stress intensity factor, K_RSS·K_RSS is defined, the procedure for its calculation outlined, and its applications to crack-tip dislocation emission and environmentally assisted cracking discussed.     

Cohesive-zone laws for void growth — I. Experimental field projection of crack-tip crazing in glassy polymers

A hybrid framework for inverse analysis of crack-tip cohesive-zone model is developed in this two-part paper to measure cohesive-zone laws of void growth in polymers by combining analytical, experimental, and numerical approaches. This paper focuses on experimental measurements of the cohesive-zone laws for two nonlinear fracture processes in glassy polymers, namely multiple crazing in crack-growth toughening of rubber-toughened high-impact polystyrene (HIPS) and crazing of steady-state crack growth in polymethylmethacrylate (PMMA) under a methanol environment. To this end, electronic speckle pattern interferometry (ESPI) is first applied to measure the crack-tip displacement fields surrounding the fracture process zones in these polymers. These fields are subsequently equilibrium smoothed and used in the extraction of the cohesive-zone laws via an analytical solution method of the inverse problem, the planar field projection method (P-FPM) [Hong, S., Kim, K.-S., 2003. Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method. Journal of the Mechanics and Physics of Solids 51, 1267-1286]. Results show that the proposed framework of the P-FPM could provide a systematic way of finding the shape of the cohesive-zone laws governed by the different micro-mechanisms in the fracture processes. In HIPS, inter-particle multiple crazing develops and the craze zone broadens ahead of a crack-tip under mechanical loading. The corresponding cohesive-zone relationship of the multiple-craze zone is found to be highly convex, which indicates effectiveness of rubber particle toughening. It is also observed that the effective peak traction, 7 MPa, in the crack-tip cohesive zone of HIPS (30% rubber content) is lower than the uniaxial yield stress of 9 MPa, presumably due to stress multi-axiality effects. In contrast, in PMMA, methanol localizes the crack-tip craze, weakening the craze traction for craze-void initiation to about 9 MPa and the fibril pull-out stress to less than 6 MPa. This reduction in cohesive traction, coupled with a strongly concave traction-separation cohesive-zone relationship, signifies environmental embrittlement of PMMA. These experimentally determined cohesive-zone laws are compared with detailed numerical analyses of effective microscale-void growth ahead of a crack tip in Part II.     

Crack propagation in an elastic solid subjected to general loading—III. Stress wave loading

The stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to stress wave loading is determined. A plane stress pulse strikes the crack at time t = 0, the wavefront being parallel to the plane of the crack. At some arbitrary later time t = τ, the crack begins to extend at a non-uniform rate. It is found that the stress intensity factor is a universal function of instantaneous crack-tip velocity times the stress intensity factor for an equivalent stationary crack. An energy rate balance fracture criterion is applied to obtain an equation of motion for the crack tip. The delay time between the arrival of the incident pulse and the onset of fracture is also calculated for this fracture criterion.     

Fatigue fracture model for thin isotropic plates with cracks in axial loading

Conclusion We have constructed a model of the growth of a fatigue crack in a thin, isotropic plate, taking the two-stage evolution of the fracture process into account. The model is based on concepts of the mechanics of a continuous defective state and on a schematic representation of the neighborhood of the tip of a fatigue crack as a plastic zone moving together with the crack. The model takes into account the influence of the cumulative defective state (damage level) along the crack propagation front on the speed of propagation.We have formulated solutions for the cases when the length of the plastic zone is constant and when it varies during the growth of fatigue cracks. We have established the fact that the plastic zone at the crack tip tends to disrupt the stability of the motion immediately at the time of inception or opening of the crack. The speed of crack propagation decreases as the plastic zone grows in size.We have shown that the problem of estimating the kinetics of fatigue cracks in thin plates can be reduced to calculating the growth rate as a function of the peak-to-peak amplitude of the stress intensity factor while preserving the structure of the governing equations of the model. We have also shown that the concept of a plastic zone of constant length induces a power-law dependence of the crack rate on K, the power exponent varying from 2 to 10–12. The Dugdale model gives a square-law dependence of the crack rate on K, which for the most part is applicable to plastic materials.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 7, pp. 53–63, July, 1994.     

Contact Zone Approach for a Moving Interface Crack in a Piezoelectric Bimaterial under Thermoelectromechanical Loading

An interface crack of a finite length moving with a constant subsonic speed v along an interface of two semi-infinite piezoelectric spaces is considered. It is assumed that the bimaterial compound is loaded by a remote mixed mode mechanical loading and a thermoelectrical field and that a frictionless contact zone arises at the leading crack tip. Electrically permeable and electrically insulated cases of the open part of the crack are involved into the consideration. By introducing a moving coordinate system at the crack tip the problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved exactly. For both cases of the electrical conditions the transcendental equations are obtained for the determination of the real contact zone length, and moreover, the associated closed form asymptotic formulas are found for small values of this parameter. Variations of the contact zone length and the stress intensity factor with respect to the crack speed and the loading have been investigated both for electrically permeable and electrically insulated cases.     

Effects of pre-stress on crack-tip fields in elastic,incompressible solids

A closed-form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre-stressed configuration of a nonlinear elastic, incompressible material. In particular, a biaxial pre-stress is assumed with stress axes parallel and orthogonal to the crack faces. Two boundary conditions are considered on the crack faces, namely a constant pressure or a constant dead loading, both preserving an homogeneous ground state. Starting from this configuration, small superimposed Mode I or Mode II deformations are solved, in the framework of Biot's incremental theory of elasticity. In this way a definition of an incremental stress intensity factor is introduced, slightly different for pressure or dead loading conditions on crack faces. Specific examples are finally developed for various hyperelastic materials, including the J₂-deformation theory of plasticity. The presence of pre-stress is shown to strongly influence the angular variation of the asymptotic crack-tip fields, even if the nominal stress rate displays a square root singularity as in the infinitesimal theory. Relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence.     

Crack shielding and material deterioration in damaged materials: an antiplane shear fracture problem

Summary A simple damage evolution model is proposed for a quasibrittle material in the framework of continuum damage mechanics. The model is used to obtain a closed form solution for a mode-III stationary crack under small scale damage conditions. It is found that the crack tip stress intensity factor is reduced, i.e., the crack is shielded by the damage. However, this shielding effect is completely offset by the material deterioration caused by the damage. It also holds for steady state crack growth. When the most effective shielding is reached for the stationary crack, the zone dominated by the stress intensity factor shrinks to the crack tip. The results for the antiplane shear problem should shed some light on the in- plane fracture problem. Received 4 August 1997; accepted for publication 7 October 1997