General forms of elastic-plastic matching equations for mode-Ⅲ cracks near crack line

Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode- Ⅲ crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method axe summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.     

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     

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.     

A weighted residual method for elastic-plastic analysis near a crack tip and the calculation of the plastic stress intensity factors

In this paper,a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample.The elastic-plastic solutions of the crack tip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field,to calculate the plastic stress intensity factors,are also developed.Therefore,a complete analysis based on the calculation both for the crack tip field and for the whole crack body field is provided.     

SINGULAR SOLUTIONS OF ANISOTROPIC PLATE WITH AN ELLIPTICAL HOLE OR A CRACK

In the present paper, closed form singular solutions for an infinite anisotropic plate with an elliptic hole or crack are derived based on the Stroh-type formalism for the general anisotropic plate. With the solutions, the hoop stresses and hoop moments around the elliptic hole as well as the stress intensity factors at the crack tip under concentrated in-plane stresses and bending moments are obtained. The singular solutions can be used for approximate analysis of an anisotropic plate weakened by a hole or a crack under concentrated forces and moments.They can also be used as fundamental solutions of boundary integral equations in BEM analysis for anisotropic plates with holes or cracks under general force and boundary conditions.     

DYNAMIC PROPAGATION PROBLEM ON DUGDALE MODEL OF MODE Ⅲ INTERFACE CRACK

By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.     

ELASTIC-PLASTIC FIELDS NEAR CRACK TIP GROWING STEP-BY-STEP IN A PERFECTLY PLASTIC SOLID

In this paper,based on the three-dimensional flow theory of plasticity,the fundametalequations for plane strain problem of elastic-perfectly plastic solids are presented.By usingthese equations the elastic-plastic fields near the crack tip growing step-by-step in an elasticincompressible-perfectly plastic solid are analysedThe first order asymptotic solutions for the stress field and velocity fields near thecrack tip are obtained.The solutions show the evolution process of elastic unloading domainand the development process of central fan domain and reveal the possibility of the presenceof the secondary plastic domain.The second order asymptotic solution for stress field is alsopresented.     

A STUDY OF CRACK CLOSURE IN ELECTRIC-FIELD-INDUCED FATIGUE IN FERROELECTRIC CERAMICS

Considering the influence of the domain switching near the tip of a crack and apply-ing the idea of multiscale singularity fields in piezoelectric fracture,we have obtained an empiricalcriterion for the crack closure.Based on the domain switching in the electric yield region,referringto Yang's results on the small scale yield model for the electrical fatigue crack,a model of thecrack closure during electric-field-induced fatigue is developed to analyze the crack growth.Interms of the model we have obtained the formula of the rate of the crack growth under cyclicelectric loading.Finally we compare the theoretical predictions with the results given by Cao andEvans experimentally.It should be pointed out that the model proposed is empirical and needsto be verified by more experimental results.     

Antiplane problem of circular ARC interfacial rigid line inclusions

The antiplane problem of circular arc rigid line inclusions under antiplane concentrated force and longitudinal shear loading was dealt with. By using RiemannSchwaz‘s symmetry principle integrated with the singularity analysis of complex functions, the general solution of the problem and the closed form solutions for some important practical problems were presented. The stress distribution in the immediate vicinity of circular arc rigid line end was examined in detail. The results show that the singular stress fields near the rigid inclusion tip possess a square-root singularity similar to that for the corresponding crack problem under antiplane shear loading, but no oscillatory character. Furthermore, the stresses are found to depend on geometrical dimension, loading conditions and materials parameters. Some practical results concluded are in agreement with the previous solutions.     

BENDING OF A CIRCULAR CYLINDER CONTAINING A CRACK

The sludy of bending of cracked circular cylinders is of more significance.The bendingof cylinders containing radical crack or cracks was discussed by refs.[1]-[4]and that ofconcentrically craked circular cylinders was studied by[5].Continuing[6]and usingcomplex variable methods in elasticity,this paper deals with the bending problems of acircular cylinder,containing an internal linear crack at any position under an acting forceperopendicular to the crack.The general forms of displacements stresses,and stress-intensity factors,expressed in terms of series,are obtained and to this bending problemswith small Ah are presented good approximate formulas for the stress-intebsity factorswhose variations with the center of the crack are analysed.Finally,the twist angle per unitlength and the center of bending for the radically cracked circular cylinder,one of whosecrack-tips is located at the origin,have been computed and the results are almost the sameas that calculated in[1].     

General forms of elastic-plastic matching equations for mode-Ⅲ cracks near crack line

Crack line analysis is an effective way to solve elastic-plastic crack problems.Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode-Ⅲ crack problems under the perfect elastic-plastic condition,matching procedures of the crack line analysis method are summarized and refined to give general forms and formulation steps of plastic field,elastic-plastic boundary,and elastic-plastic matching equations near the crack line. The research unifies mode-Ⅲ crack problems under different conditions into a problem of determining four integral constants with four matching equations.An example is given to verify correctness,conciseness,and generality of the procedure.     

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

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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．     

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.     

Finite element analysis of mode III steady crack growth in anisotropic hardening materials

In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk _ss/k_c varies appreciably with the anisotropic hardening parameterM and the hardening exponentN.     

Near crack line elastic-plastic analysis for a finite plate loaded by two pairs of antiplane point forces

I.IntroductionThenearcracklineanalysismethodhasbeengreatlyimprovedbyYill'2].In[l,21,theimprovednearcracklineanalysismethodhasbeenusedtoinvestigateamodeIllcrackinanelastic-perfectlyplasticsolid.Andthesmallscaleyieldingconditionshavebeencompletelyabandoned,andcompletelynewandprecisesolutionsoftheelastic-plasticfieldsofamodeillstationarycrackandamodelillquasi-staticallygrowingcrackwithremotealltiplaneshearinginanelastic-perfectlyplastic'materialhavebeenobtained,respectively.In[3]weanalyzedthene…     

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

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