裂尖曲率对裂纹前缘塑性区的影响

考虑尖端为圆弧形的钝头裂纹模型，在外围取线弹性无裂纹体的解，应用线场分析方法。形成一套估计钝头裂纹前缘塑性区尺寸的方法。对含径向裂纹和圆弧形裂尖的圆盘受均匀张力作用情况，给出了塑性区的裂纹前缘尺寸与裂纹尖端曲率的关系。得到的结论是，塑性区的裂纹前缘尺寸与裂纹尖端曲率有关；对于给定的塑性区的裂纹前缘尺寸，载荷反比于外缘尺寸的平方。前一结论说明了塑性区的裂前尺寸作为裂纹失稳扩展判断的局限性；后一结论说明了裂纹体强度失效的尺寸效应规律：抗断强度与总体线尺寸的平方成反比。     

静止裂纹顶端塑性区内应力场

本文对不可压缩的理想塑性材料裂纹顶端塑性区内的应力场进行了数学分析,证明了当塑性区包围着裂纹顶端而应力函数可用分离变匱型的级数展开且该级数展开的首项与第一类渐近解相同时,第一类渐近解即是塑性区内应力场的精确解。本文又提出了第二类渐近解,说明应力场的渐近解不是唯一的。     

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.     

Formation of a plastic zone in an anisotropic body under loads acting along a crack

The effects of tension and compression along a crack on the plastic zone in a finite anisotropic body under plane strain are studied. The formation pattern for the plastic zone with increasing load is established by numerically solving a boundary-value problem for each of the cases. In particular, a new plastic zone is revealed. It occurs at the crack face under a compressive load of certain magnitude. How this plastic zone interacts with that at the crack tip is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 3–19, May 2007.     

Analytic solutions to crack tip plastic zone under various loading conditions

Based on stress field equations and Hill yield criterion, the crack tip plastic zone is determined for orthotropic materials and isotropic materials under small-scale yielding condition. An analytical solution to calculating the crack tip plastic zone in plane stress states is presented. The shape and size of the plastic zone are analyzed under different loading conditions. The obtained results show that the crack tip plastic zones present “butterfly-like” shapes, and the elastic–plastic boundary is smooth. The size of the plastic zone for orthotropic composites is less at the crack tip for various loading conditions, compared with the case of isotropic materials. Crack inclination angle and loading conditions affect greatly the size and shape of crack tip plastic zone. The mode I crack has a crucial effect on the plastic zone for mixed mode case in plane stress state. The plastic zone for pure mode I crack and pure mode II crack have a symmetrical distribution to the initial crack plane.     

自适应分析在确定裂纹尖端塑性区中的应用

在分析裂纹扩展及材料强度时对塑性区的估算是很重要的,本文提出采用自适应有限元分析来确定裂纹尖端塑性区的方法,计算结果表明这种方法通过网格自动加密能够有效地跟踪出弹塑性的交界面。     

A Ring-Shaped Plastic Zone at an Elliptic Crack under Triaxial Axisymmetric Loading

The paper addresses a three-dimensional problem for an elliptic crack with a ring plastic zone under uni- and triaxial loading at infinity. The normal stresses in the plastic zone are found from the conditions that the stresses are constrained and the plane strain is local and from the yield criterion for the given material. The size of the elliptic ring is calculated by Rice's variational formula. It is shown that the constraint ratio for plastic strains under triaxial loading may be greater than that under loads close to hydrostatic tension. The contour of the plastic zone is confocal to the initial crack     

Influence of tension along a crack on the plastic zone in an anisotropic body

The influence of longitudinal loading on the size and shape of the plastic zone near a crack in an anisotropic body is analyzed. A generalized plane stress state is considered. A relevant boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, a new plastic zone above the crack, and an additional plastic zone on the lateral surface, which merge to form a single plastic zone     

Elastoplasticity of crack loaded by two pairs of isolated shear forces in finite width plate

The failure behavior of an elastic-perfectly plastic body with a crack loaded by two pairs of concentrated shear forces is discussed. The analytical solutions of an eccentric crack in a finite plate loaded by two pairs of point shear forces are obtained. It includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line and the law of the plastic zone along the crack line with external loads. The solutions of this paper are sufficiently precise near the crack line in elastic-perfectly plastic materials. Subsequently, the present results are compared with solutions based on the minimum strain energy density theory and elastic-plastic solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.     

Model of Plastic Deformation at the Front of a Circular Crack Under Nonaxisymmetric Loading

The constrained plastic deformation at the front of a circular mode I crack under nonaxisymmetric loading in the crack plane is studied. It is shown that the normal stresses in the plastic zone depend on the polar angle and external stresses. The constraint is maximum at those points on the crack front along tangents to which the maximum external tensile stresses act     

Strip yield zones around ring-shaped crack in transversely isotropic thick layer

A ring-shaped crack under uniform load in an infinitely long elastic–perfectly plastic thick layer is considered. The problem is formulated for a transversely isotropic material by using integral transform technique. Due to the geometry of the configuration, Hankel integral transform technique was chosen and the problem was reduced to a singular integral equation which is solved numerically by using Gaussian Quadrature Formulae and the values were evaluated at discrete points. The plastic zone widths were obtained by using the plastic strip model after stress intensity factors were obtained. Numerical results are plotted for various ring-shaped crack sizes and transversely isotropic materials. It was found that the width of the plastic zone at the inner edge of the crack was greater than the outer one.     

考虑应力松驰复合型裂纹顶端塑性区分析

Ｓｈｉｈ［１］应用奇异单元，获得了不考虑应力松驰小范围屈服条件下复合型裂纹尖端塑性区形状。Ｚ．Ｚ．Ｚｕ等［２］采用Ｒｉｃｅ［５］给出的裂纹尖端应力关系式，利用有限元分析获得了不考虑应力松驰下复合型裂纹尖端塑性区，本文基于静力学中内力与外力平衡条件，用线弹性的全场解代替局部解，给出了考虑应力松驰下复合型裂纹尖端塑性区边界方程，获得了考虑应力松驰下的任意方向的塑性区尺寸及塑性区形状     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Elastic–plastic near field solution of an eccentric crack under shear in a finite width plate

The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite width plate, and the analytical solution is obtained in this paper. The solution includes: the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line, variations of the length of the plastic zone along the crack line with an external loads, and the bearing capacity of a finite plate with a centric crack loaded by shear stress in the far field. The results obtained in this paper are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions have been taken. Subsequently, the present results are compared with the traditional line elastic fracture mechanical solutions and elastoplastic near field solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.     

Formation of the plastic zone in an anisotropic body with a crack

The influence of the length of a mode I crack on the plastic zone in an anisotropic body under hard loading is studied. The case of a generalized plane stress state is examined. A boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, the additional plastic zone on the lateral face of the body, and the merged plastic zone Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 36–52, September 2008.     

Study of the plastic zone near a crack in an anisotropic body

The plastic zone at a crack tip in a finite anisotropic body is studied. A boundary-value problem is formulated in terms of the components of the covariant displacement vector for small strains. Particular attention is given to the case of plain strain. In this case, a numerical solution is found for a long rectangular body with a central crack under tension. As a result, conditions for the occurrence and development of a plastic zone at the crack tip are established. A plastic zone on the lateral surface of the body is discovered. How both zones extend and coalesce is elucidated. The effect of anisotropy on the occurrence of a plastic zone is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 29–44, July 2006.     

Refined Dugdale plastic zones of an external circular crack

The refined Dugdale-type plastic zones ahead of an external circular crack, subjected to a uniform displacement at infinity, are evaluated both analytically and numerically. The analytical method utilizes potential theory in classical linear elasticity with emphasis on the contrast from the internal crack problem. A closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition. The analytical solution is also used to benchmark the results obtained from the numerical method, which show good agreement. Through an iterative scheme, the numerical technique is able to estimate the size of crack tip plasticity zone, which is governed by the non-linear von Mises criterion. The relationships between the applied displacement and the length of the plastic zone are compared for the different yielding conditions. Computational modeling has demonstrated that the plastic constraint effect based on the true yield condition can significantly influence the load-bearing capacity. It is also discovered from the comparative study that the stress components predicted by the three different yield conditions may differ notably; however, the stress triaxiality in the ligament region has only small deviations. The proposed study may find applications in predicting the plastic flow in a circumferentially notched round bars under tension.     

过载作用下聚乙烯疲劳裂纹扩展行为研究

论文针对中密度聚乙烯材料(MDPE)，采用平板试样进行了I型疲劳裂纹扩展和单次过载下裂纹扩展试验．发现与金属材料类似，单次拉伸过载对聚乙烯(PE)的疲劳裂纹扩展有明显的迟滞作用，降低了裂纹扩展速率．试验还通过变载荷刻线法获取疲劳裂纹扩展前缘的实际形貌和变化规律，对常规变载荷刻线方法进行了调整和验证，其修正方法对高分子材料的疲劳裂纹扩展前缘刻线具有较好的效果．通过观察发现含楔形塑性区的裂尖钝化是裂纹迟滞的主要原因．过载引入的塑性区内残余应力对裂纹迟滞也起了重要作用．论文利用Dugdale模型计算了塑性区尺寸，使用基于残余应力的Wheeler模型对过载迟滞进行了很好的拟合．     

Effect of crack-tip shape on the near-tip field in glassy polymer

The physical nature of a crack tip is not absolutely sharp but blunt with finite curvature. In this paper, the effects of crack-tip shape on the stress and deformation fields ahead of blunted cracks in glassy polymers are numerically investigated under Mode I loading and small scale yielding conditions. An elastic–viscoplastic constitutive model accounting for the strain softening upon yield and then the subsequently strain hardening is adopted and two typical glassy polymers, one with strain hardening and the other with strain softening–rehardening are considered in analysis. It is shown that the profile of crack tip has obvious effect on the near-tip plastic field. The size of near-tip plastic zone reduces with the increase of curvature radius of crack tip, while the plastic strain rate and the stresses near crack tip enhance obviously for two typical polymers. Also, the plastic energy dissipation behavior near cracks with different curvatures is discussed for both materials.     

Study on the coalescence mechanism of splitting failure of crack-weakened rock subjected to compressive loads

It is of important significance to study the coalescence mechanism of splitting failure of crack-weakened rock masses under compressive loads. In this paper, a simplified mechanism of crack propagation, in which the crack grows along the direction of maximum principal compressive stress, is proposed. Thus, only mode I is taken into account in the formulation and solution. On the basis of the near crack line analysis method, the elastic–plastic stress field near the crack line is analyzed, and the law that the length of the plastic zone along the crack line is varied with an external loads have been established by the matching condition of the elastic- plastic fields on the boundary, the coalescence stress and the strength properties of rock masses have been determined. The solution is a function of the geometry of the crack array. The results show that the crack coalescence depends on the crack interface friction coefficient, the sliding crack spacing, orientation of the cracks, and the crack half-length. The conclusions are of important significance for rock mass engineering.