NEAR CRACK LINE ELASTIC－PLASTIC ANALYSIS FOR A CRACK LOADED BY ANTIPLANE POINT FORCES

ＮＥＡＲ　ＣＲＡＣＫ　ＬＩＮＥ　ＥＬＡＳＴＩＣ－ＰＬＡＳＴＩＣ　ＡＮＡＬＹＳＩＳ　ＦＯＲ　Ａ　ＣＲＡＣＫ　ＬＯＡＤＥＤ　ＢＹ　ＡＮＴＩＰＬＡＮＥ　ＰＯＩＮＴ　ＦＯＲＣＥＳＷｕＣｈｅｎｇｐｉｎｇ（吴承平）；ＷａｎｇＣｈｅｎｇ（王成）（ＲｅｃｅｉｖｅｄＳ...     

Near crack line elastic–plastic analysis for a infinite plate loaded by two pairs of point tensile forces

The near crack line analysis method is used to investigate a center crack loaded by two pairs of point tensile forces in an infinite plate in an elastic–perfectly plastic solid, and the analytical solutions are obtained in this paper. These solutions include: the elastic–plastic stress field near the crack line, the law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an infinite plate with a center crack. The results of this paper are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.     

偏心裂纹板在裂纹面受一对集中拉应力作用时弹塑性解析解

利用裂纹线场方法对理想弹塑性材料偏心裂纹板在裂纹面受一对集中拉力问题进行了弹塑性分析,并且获得了理论解．这个解包括：裂纹线附近弹塑性边界上的单位法向矢量,裂纹线附近的弹塑性解析解、最大塑性区长度、裂纹线上的塑性区长度随荷载的变化规律及其承载力．该分析不受小范围屈服假设的限制,并且不附加假使条件．结果在裂纹线附近足够精确．     

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.     

Elastic-plastic analytical solutions for an eccentric crack loaded by two pairs of anti-plane point forces

IntroductionTheelastic_plasticanalysisforacrackedplatewithfinitedimensionsisoneofthemostdifficultfieldsofelastic_plasticmechanics .Thenearcracklineanalysismethod ,whichwasfirstproposedbyAchenbachetal.[1,2 ] ,hasbeenimprovedbyYiinRefs.[3,4 ].InRefs.[3,4 ],…     

THE PRECISE AND NEW ANALYSIS FOR A MODE Ⅲ GROWING CRACK IN AN ELASTIC-PERFECTLY PLASTIC SOLID

The near crack line field analysis method has been used to investigate into ModeⅢ quasistatically propagating crack in an elastic-perfectly plastic material.Thesignificance of this paper is that the usual small scale yielding theory has been brokenthrough.By obtaining the general solutions of the stresses and the displacement rate ofthe near crack line plastic region,and by matching the general solutions with theprecise elastic fields(not the usual elastic K-dominant fields)at the elastic-plasticboundary,the precise and new solutions of the stress and deformation fields,the sizeof the plastic region and the unit normal vector of the elastic-plastic boundary havebeen obtained near the crack line.The solutions of this paper are sufficiently precisenear the crack line region because the roughly qualitative assumptions of the smallscale yielding theory have not been used and no other roughly qualitative assumptionshave been taken,either.The analysis of this paper shows that the assumingly“steady-state cas     

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.     

Elastoplastic solution for an eccentric crack loaded by two pairs of point tensile forces

The strain energy density theory and the near crack line analysis method are applied to investigate an eccentric crack loaded by two pairs of tensile point forces in a finite plate. The minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. Obtained is the elastic-plastic solution near the crack line of an eccentric crack loaded by two pairs of point tensile forces under large scale yielding condition. More specifically, the near field solution contains the unit normal vector of the elastic-plastic boundary and the elastic-plastic stress field. The length of the plastic zone along the crack line is found to vary with the external load and the bearing capacity of a finite plate with an eccentric crack loaded by two pairs of tensile point forces. Compared with small scale yielding condition, the normalized load obtained is higher than those under small scale yielding condition when the length of the plastic zone is the same.     

裂纹尖端附近三维效应区的有限元分析

基于Kane-Mindlin关于弹性平板面内问题位移的运动学假设,本文首次推导了一种考虑板厚效应的平板面内问题的有限元格式。将Kane-Mindl.n假设推广到弹塑性问题,推导了相应的有限元方程.对双边及中心裂纹拉伸试件的计算结果表明,裂纹尖端附近的弹性三维效应区尺寸和板厚相当.对线性硬化弹塑性材料,当切线模量E_t和弹性模量E之比E_t/E大于0.2时,三维效应区在两倍板厚以内.     

THE EXACT SOLUTIONS OF ELASTIC－PLASTIC CRACK LINE FIELD FOR MODE ⅡPLANE STRESS CRACK

ＴＨＥＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＥＬＡＳＴＩＣ－ＰＬＡＳＴＩＣＣＲＡＣＫＬＩＮＥＦＩＥＬＤＦＯＲＭＯＤＥＩＩＰＬＡＮＥＳＴＲＥＳＳＣＲＡＣＫＹｉＺｈｉｊｉａｎ（易志坚）ＷａｎｇＳｈｉｊｉｅ（王士杰）ＷａｎｇＸｉａｎｇｊｉａｎ（王向坚）（Ｒｅｃｅ...     

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.     

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。     

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

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.     

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

ＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＮＥＡＲＣＲＡＣＫＬＩＮＥＦＩＥＬＤＳＦＯＲＭＯＤＥＩＣＲＡＣＫＵＮＤＥＲＰＬＡＮＥＳＴＲＥＳＳＣＯＮＤＩＴＩＯＮＩＮＡＮＥＬＡＳＴＩＣ－ＰＥＲＦＥＣＴＬＹＰＬＡＳＴＩＣＳＯＬＩＤＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＮＥＡ...     

Elastoplastic near field solution for mode II crack loaded by remote shear stress in an infinite plate

A suitable elastic stress field near the crack line which satisfied the far field boundary conditions and the boundary conditions of the crack surfaces has been obtained and successful analysis has been made of a near crack line field for an infinite elastic-perfectly plastic medium containing a quasi-statically propagating plane stress crack subjected to far field shear stress. It is shown that the solutions of the problem of mode II crack loaded by remote shear stress from the Westergaard method in some previous papers is used as the elastic stress field near the crack line, are inappropriate.     

Crack movement in layered composites under electric field affect

The variation principle is applied for defining a crack in the solid body. The methods proposed in [G. Sih, C. Chen, Non-self-similar crack growth in elastic–plastic finite thickness plate, Theoretical and Applied Fracture Mechanics 3 (1985) 125–139] extend to presence of electromagnetic fields in material. Crack propagation in non-homogeneous media has been considered. It is shown that electromagnetic fields in the material are essentially affecting the trajectory. The crack trajectory stability has been studied as function of fracture energy, phase portraits of the trajectory in different media have been built, and various attractor types have been revealed. Different crack morphologies from single straight and oscillating crack propagation to straight double crack propagation were theoretically founded. In compliance with the experimental data of [R. Niefanger, V.-B. Pham, G. Schneider, H.-A. Bahr, H. Balke, U. Bahr, Quasi-static straight and oscillatory crack propagation in ferroelectric ceramics due to moving electric field: experiments and theory, Acta Materialia 52 (1) (2004) 117–127], it has been demonstrated that periodic electromagnetic field results in trajectory stochastization. This can be used for switching the crack over from the mode of mainline propagation into the mode of development of the field of diffused microcracks.     

Stress functions for central straight cracked anisotropic plates

In this paper, the plane problem for an anisotropic plate with a central straight crack in any direction is solved. The stress functions are given to represent the finite stress concentrations near the crack tips by the weight integral method. It shows that there is no stress singularity at the crack tip. The model can be used to appropriate to fracture mechanics for non-metallic materials.     

随机有限元方法在断裂分析中的应用

在幂律非线性随机有限元基础上,以单边裂纹板为例给出计算含量钢继裂参数,J（J积分）,δ（裂纹张开位移）,Δ（由裂纹引起的裂纹板上下底面相对位移）,θ（由裂纹引起的裂纹板上下底在相对转角）及其对基本随机变量变化率的方法和分析算例。