Large deformation field near a crack tip in rubber-like material

This paper deals with strain field near a crack tip in a rubber-like material under plane strain condition. The constitutive relation adopted here is valid for both small and large strain. The asymptotic equations are derived for a shrinking sector and expanding sector. The closed mathematic solution is obtained for the latter while a numerical solution is found for the former. By connecting deformation of the two sectors, the crack tip field character is found.     

Analysis of the Interface Crack for Rubber-like Materials

The interface crack between two dissimilar rubber materials under mixed load is asymptotically analyzed in this paper. It is shown that the crack tip field is composed of one expanding sector and two shrinking sectors. For the case considered, the interface is located in the expanding sector. Analytical solutions are obtained for both the expanding sector and the shrinking sectors. The structures of the crack tip field obtained in this paper is compared with those in previous works for different constitutive equations.     

A transverse crack tip field in bimaterial

The asymptotic field near an interface crack tip is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed.     

Large strain field near a notch-tip under tension

This paper considers the plane strain notch-tip filed in a rubber-like material under tension. Based on a new constitutive relation, the asymptotic equations of the near tip field are derived and solved. It is shown that the notch tip field is composed of two narrowing sectors and an expanding sector. The dominant stress and strain near the notch tip are found to be in a state of uniaxial tension.     

Logarithm strain singularity at tip of mode I growing crack in elasticand perfectly-plastic material

Reanalyzed in detail is the stress and strain distribution near the tip of a Mode I steadily growing crack in an elastic and perfectly-plastic material. The crack tip region is divided into five angular sectors, one of which is singular in character and represents a rapid transition zone that becomes a line of strain discontinuity in the limit as crack tip is approached. It is shown for an incompressible material (ν=0.5) under plane strain that the local strain in all the angular sectors possesses the same logarithm singularity, i.e., In r where r is the radial distance measured from the crack tip. This result also prevails for the compressible material ( v < 0.5) and resolves a long standing controversy concerning the strain singularity in the sector just ahead of the crack tip.     

橡胶楔体与刚性缺口接触大变形分析

利用Ｋｕｏｗｌｅｓ与Ｓｔｅｒｎｂｅｒｇ提出的非线性弹性大变形应变能函数,对橡胶楔体与刚性缺口接触问题进行大变形渐近分析,推导了楔体尖端场的渐近方程,得到楔体尖端附近的应力应变场及应力的奇异性指数与橡胶楔体角度、刚性缺口角度及材料常数有关的表达式;楔尖附近同一半径上应力分量为常数,同时,利用非线性有限元理论编制了大变形有限元程序,考虑楔体尖端与缺口接触边界条件,计算得到了与分析解一致的结论,当缺口角     

Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

承受弯曲板断裂问题的特征根

把Rekner型平板裂纹尖端位移场展开式推广到任意切口、任意边界的多材料问题．证明了Reissner型平板断裂问题的特征根等价于相类似的反平面切口问题和平面切口问题两部分的特征根迭加．     

A finite element study of the near crack tip deformation of a ductile material under mixed mode loading

In ductile fracture, voids near a crack tip play an important role. From this point of view, a large deformation finite element analysis has been made to study the deformation, stress and strain, and void ratio near the crack tip under mixed mode plane strain loading conditions, employing Gurson's constitutive equation which has taken into account the effects of void nucleation and growth. The results show that: (i) one corner of the crack tip sharpens while the other corner blunts, (ii) the stress and strain distributions except for the near crack tip region, can be superimposed by normalizing distance from the crack tip by a crack tip deformation length, i.e., a steady-state solution under a mixed mode condition has been obtained, (iii) the field near a crack tip can be divided into four characteristic fields (K field, HRR field, blunted crack tip field, and damaged region), and (iv) the strain and void volume fraction become concentrated in the sharpened part of a crack tip with increasing Mode II component.     

Cracking characteristics of mixed mode dislocations near a lip-like mode crack

This work is concerned with the cracking characteristics of mixed mode dislocations near a lip-like mode crack, stress intensity and strain energy density factor are obtained by using conformal mapping, singularity analysis and Cauchy integrals. Shielding effect generated by screw dislocation near a lip-like mode crack decreases with the increment of the distance between screw dislocation and crack tip. Larger distance between two faces of the crack leads to the shielding effect waning. The strain energy density factor of mode III decreases with the increment of the distance between dislocation and crack tip. Larger distance between two faces of lip-like mode crack also leads to the strain energy density factor waning and encourages crack initiation; the shielding effects generated by edge dislocation near the crack decrease with the increment of the distance between edge dislocation and crack tip.     

The singular elastostatic field due to a crack in rubberlike materials

Within the framework of finite-strain elastostatics an asymptotic analysis is carried out in order to calculate the singular field near the crack tip in a slab under conditions of plane deformation. A class of Ogden-Ball hyperelastic rubberlike materials and general loading conditions ensuring vanishing tractions on the crack faces near the crack tip are considered. It is shown that the singular deformation field near the crack tip can be specified by applying a rigid body rotation with a subsequent parallel translation to a so-called canonical field. The adjective canonical is adopted here to denote the field with symmetrically opening crack faces, just resembling the displacement field of the symmetric mode in linear elastic fracture mechanics. No analogy with the antisymmetric mode is possible, and the crack equilibrium criterion requires only one stress intensity factor to be determined.     

Investigation of the Dynamic Behavior of a Griffith Crack in a Piezoelectric Material Strip Subjected to the Harmonic Elastic Anti-plane Shear Waves by Use of the Non-local Theory

In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material strip subjected to the harmonic anti-plane shear waves is investigated by use of the non-local theory for impermeable crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near at the crack tip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the thickness of the strip, the circular frequency of incident wave and the lattice parameter.     

Crack tip behavior of flexible bio-materials

An elastic constitutive model is proposed to describe the mechanical property of bio-materials that possesses strain limits. Analytical solution for the Mode I crack tip behavior is obtained. The tensile strain limit can be reached by approaching the crack tip in any direction while the compression strain limit can only be reached in two sectors of the crack tip domain.     

Exact solutions for piezoelectric screw dislocations near two asymmetrical edge cracks emanating from an elliptical hole

The interaction between piezoelectric screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under combined mechanical and electric load at infinity is dealt with. The closed-form solutions are derived for complex potentials and generalized stress fields. In the limiting cases, some well-known results can be obtained from the present solutions. Moreover, some new exact solutions are shown. The stress intensity factor and the energy release rate at the right tip due to a screw dislocation near the right interfacial crack are also calculated. The results show that the shielding effect of dislocation on crack expanding decreases with the increase in dislocation azimuth angle and the distance between the dislocation and the crack tip, and the repulsion acting on the dislocation from the other half plane demotes crack propagation. The increasing of the length of the other crack promotes crack growth, but the increasing of the minor semi-axis demotes it.     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

三点弯曲试样动态应力强度因子计算研究

利用Hopkinson压杆对三点弯曲试样进行冲击加载,采集了垂直裂纹面距裂尖2mm和与裂纹面成60°距裂尖5mm处的应变信号。根据裂尖附近测试的应变信号计算试样的动态应力强度因子,并与有限元计算结果进行比较,结果表明由于裂尖有一段疲劳裂纹区,通过裂尖附近应变信号来计算动态应力强度因子时,如果裂尖位置确定不准及粘贴应变片位置不够准确对计算结果将带来很大影响。因此利用应变片法计算动态应力强度因子时,为了获得更准确的计算结果,在实验后应对试件裂纹面进行分析测量,重新确定裂尖位置,必要时需对应变片至裂尖距离进行修正后再计算动态应力强度因子值。     

单边裂纹通电瞬间裂尖处应力场的复变函数解

本文应用复变函数中的Schwarz-Christoffel变换方法，在具单边裂纹的导电薄板通电瞬间温度场复变函数解的基础上，推导出用复变函数表示的应力场的表达式，并且给出算例，通过理论计算得知；当对具有单边裂纹的导电薄板通入适当密度的电流时，裂尖处温度急剧升高并熔化便裂尖变钝。同时，在裂尖周围形成了有利于遏制裂纹扩展的压应力场，有效地防止了裂纹沿其主方向和其它方向延伸。从理论上证明了电磁热效应在裂尖处产生高温形成焊口的同时，压应力场的形成是遏制裂纹扩展的主要因素之一。理论计算结果与实验结果比较吻合，为这一止裂方法的应用打下了理论基础。     

STRESS-STRAIN FIELD NEAR THE CRACK-TIP OF AN INCOMPRESS RUBBER-LIKE MATERIAL

ＳＴＲＥＳＳ－ＳＴＲＡＩＮＦＩＥＬＤＮＥＡＲＴＨＥＣＲＡＣＫ－ＴＩＰＯＦＡＮＩＮＣＯＭＰＲＥＳＳ　ＲＵＢＢＥＲ－ＬＩＫＥ　ＭＡＴＥＲＩＡＬＷａｎｇＺｈｅｎｑｉｎｇ（王振清）ＳｈｉＳｈｏｕｘｉａ（史守峡）（ＨａｒｂｉｎＥｎｇｉｎｅｅｒｉｎｇＵｎｉｖｅｒ...     

Asymptotic Analysis of the Nonlinear Boussinesq Problem for a Kind of Incompressible Rubber Material (Compression Case)

A half rubber space compressed by a concentrated force normal to the surface is asymptotically analyzed based on large strain elastic theory. The material domain near the singular point is divided into an expanding domain and a shrinking domain. The asymptotic equations are derived and solved individually for both domains. The solutions to expanding and shrinking domains are further assembled together so that there is only one free parameter left which can indicate the amplitude of the singular stress and strain field. Finally, the amplitude parameter of the field is determined by the given concentrated force. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study on fracture behavior of ferroelectric ceramics under combined electromechanical loading by using a moiré interferometry technique

This paper discusses an in situ observation of fracture behavior around a crack tip in ferroelectric ceramics under combined electromechanical loading by use of a moiré interferometry technique. The deformation field induced by the electric field and the stress concentration near the crack tip in three-points bending experiments was measured. By analysis of the moiré images it is found that under a constant mechanical load, the electric field almost has no effect on the crack extension in the case that the directions of the poling, electric field and crack extension are perpendicular to each other. When the poling direction is parallel to the crack extension direction and perpendicular to the electric field, the strain decreases faster than that calculated by FEM with and without electrical loading as one goes away from the crack tip. In addition, as the electric field intensity increases, the strain near the crack tip increases, and the strain concentration becomes more significant. The project supported by the National Natural Science Foundation of China (10132010, 10025209, 10232023)