On a micromechanical fracture model for cracked reinforced composites

The fracture process of reinforced composite materials is examined. In the outer region of the crack tip anisotropic continuum mechanics is employed, while for the crack tip region a heterogeneous micromechanical model is proposed. A solution is obtained using combined boundary layer — non-linear finite elements.     

裂尖大应变细观断裂研究

本文用反映空穴形核成长的Gurson本构方程来描述裂尖区域材料在大应变情形下的力学特性，并进一步考虑了空穴演变对材料杨氏模量的影响。文中用上述本构方程分别结合弹塑性大应变有限元方法对平面应变I型裂纹问题作了计算，分析了裂尖应力分布、裂尖形状变化和裂尖空穴演变过程，并与用Prandtl-Reuss本构方程教育处的结果作了比较。     

基于扩展有限元法的裂尖场精度研究

扩展有限元方法基于单元分解的基本思想,通过引入位移加强函数来表征裂纹的不连续性和裂尖的奇异性。在裂尖加强单元与常规单元之间有一层混合单元,当对裂尖特定区域进行加强时,混合单元个数相应增加,混合单元个数与计算精度存在一定联系。本文提出一种正方形裂尖加强区域的选择方式,可得到较单个加强和圆形加强精度更高、更稳定的计算结果。对于不同长度的裂纹,表征裂尖场奇异性所需的裂尖加强范围存在较大差异,以正方形裂尖加强方式进行计算,得到了不同裂纹长度下最优的加强尺寸。     

Analyses on micro-fracture of crack tip under large deformation conditions

In the present paper, Gurson's constitutive equation, which takes into account the development of voids, is used to study the behaviour of the material in the region near crack tip. Furthermore, the effect of void development on Young's modulus, which was not considered by Gurson, is taken into consideration. The analyses on void development, on stress distribution near crack tip, and on the variance of COD for the plane strain mode I problem are carried out with the large elastic-plastic deformation finite element method. The results are compared with those estimated from the Prandtl-Reuss constitutive equation.     

Special approach for the determination of fracture mechanical parameters at an interface crack tip

An interface crack of finite length is considered between two semi-infinite planes with an artificial contact zone at one of the two crack tips. A transcendental equation and certain simple asymptotic formulas are established for the real contact zone (in the Comninou-Dundurs sense) in terms of the stress intensity factors (SIFs) of the considered model. In these terms analytical expressions are also provided for the energy release rate and for the SIF of the classical interface crack model with an oscillating singularity at the crack tip. The appropriate length of the artifical contact zone is shown to be attainable on the basis of the analysis of the stresses at the crack tip. The use of the proposed model is suggested for integrity assessment of inhomogeneous structural elements of composites containing interface cracks. Received 26 March 1997; accepted for publication 12 September 1997     

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     

Stress and energy density fields near a blunted crack front in power hardening material

Using Jaumann and Dienes rates of Euler stress in elastic-plastic constitutive equations of finite deformation, plane strain finite element analysis for a compact tension specimen with a blunted crack front is made. The Euler stress, Kirchhoff stress and volume strain energy density near a blunted crack tip are computed. Constitutive relations with different deformation rates affect the the near crack tip solution in a region within an order of magnitude of the crack opening displacement. The results differed from the corresponding solution of deformation plasticity (or nonlinear elasticity) with increasing deformation. They are smaller in a local region of about 2 to 10 times of the crack opening distance.The volume energy density near the crack tip is computed, the stationary values of which determine the locations of extensive yielding and possible sites of crack initiation. It remained nearly constant with increasing deformation. Such a character tends to support the volume energy density criterion as a means for quantifying the ductile fracture behavior of metals.     

孔洞对平面裂纹应力强度因子影响分析的广义参数Williams单元

本文采用圆形奇异区广义参数Williams单元（W单元）建立了中心裂纹与圆孔共存的平面应力模型,奇异区外围利用ABAQUS有限元软件自动网格离散技术与FORTRAN95编程前处理相结合,克服了自主编程中网格离散的局限性．算例分析了圆孔位置和几何参数对I-II混合型裂纹尖端应力强度因子(SIFs)的影响,并与扩展有限元法(XFEM)计算结果进行比较．结果表明：靠近圆孔一侧的裂尖SIFs大于远离圆孔一侧的裂尖SIFs;控制圆孔左边缘到裂纹中心的距离,则两侧裂尖SIFs随圆孔半径的增大而增大;圆孔中心与裂纹中心水平距离越远,圆孔对裂纹扩展的影响越小．同时,基于圆形奇异区的W单元直接计算得到的裂尖SIFs与扩展有限元法得到的解吻合较好,证明了W单元对奇异区离散形状不敏感,且具有高效率和高精度．     

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.     

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

Analyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J-integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.     

Mechanics and fracture of crack tip deformable bi-material interface

Novel interface deformable bi-layer beam theory is developed to account for local effects at crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable sub-layers with consideration of crack tip deformation. Unlike the sub-layer model in the literature in which the crack tip deformations under the interface peel and shear stresses are ignored and thus a “rigid” joint is used, the present study introduces two interface compliances to account for the effect of interface stresses on the crack tip deformation which is referred to as the elastic foundation effect; thus a flexible condition along the interface is considered. Closed-form solutions of resultant forces, deformations, and interface stresses are obtained for each sub-layer in the bi-layer beam, of which the local effects at the crack tip are demonstrated. In this study, an elastic deformable crack tip model is presented for the first time which can improve the split beam solution. The present model is in excellent agreements with analytical 2-D continuum solutions and finite element analyses. The resulting crack tip rotation is then used to calculate the energy release rate (ERR) and stress intensity factor (SIF) of interface fracture in bi-layer materials. Explicit closed-form solutions for ERR and SIF are obtained for which both the transverse shear and crack tip deformation effects are accounted. Compared to the full continuum elasticity analysis, such as finite element analysis, the present solutions are much explicit, more applicable, while comparable in accuracy. Further, the concept of deformable crack tip model can be applied to other bi-layer beam analyses (e.g., delamination buckling and vibration, etc.).     

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.     

NiTi形状记忆合金裂纹尖端热力耦合行为研究

本文对NiTi形状记忆合金I型裂纹尖端热力耦合行为进行了数值仿真分析和实验验证。建立了包含相变和热力耦合的本构模型,通过有限元计算得到了裂纹尖端附近的纵向应变、马氏体体积分数和温度场分布,依据马氏体相变情况对裂纹尖端有效应力强度因子进行了修正,揭示了加载速率对形状记忆合金裂纹尖端有效应力强度影子的影响规律。参数研究表明,随着加载频率的增加,裂纹尖端附近温度逐渐升高,马氏体相变区域逐渐缩小,有效应力强度因子呈下降趋势,形状记忆合金表现出增韧效应,有助于减缓裂纹扩展。本研究结果对于揭示热力耦合作用下超弹性形状记忆合金疲劳裂纹扩展规律具有重要参考意义。     

复合型裂纹断裂的新准则

以Ⅰ-Ⅱ复合型裂纹为研究对象,对裂纹尖端的塑性区分布规律进行了理论分析。引入两组评价裂纹尖端应力场对裂纹扩展影响的参数,考虑裂纹尖端存在的局部塑性变形,并采纳如下两个假设,(1)裂纹沿最短路径穿过塑性区向弹性区扩展,(2)当在扩展方向上的弹塑性边界极半径r大于其临界极半径rC时,裂纹开始扩展。在此基础上,导出了新的复合型裂纹断裂准则,并与现有部分断裂准则及实验结果进行了对比。结果表明：新建立的复合裂纹断裂准则与实验结果吻合程度非常高。最后,阐明了以单一KIC或KIIC建立的复合裂纹扩展准则的局限性以及考虑裂纹尖端当前应力场的必要性。     

Thermo-electro-structural coupled analyses of crack arrest by Joule heating

Using the finite element method, thermo-electro-structural coupled analyses of the cracked conducting plate under high electric current have been solved. The crack contact condition and temperature-dependent material properties are considered in this analysis. The crack tip temperature, electric current density factor, stress intensity factor and strain energy density factor are obtained for discussions. Due to high electric current density and Joule heating at the crack tip, a circular melting area may exist around the tip. After cooling, a circular void or hole may occur at the crack tip and the crack arrest is achieved. The crack tip temperature decreases when the crack contact area increases. The proper tensile load is necessary for making the crack open enough and causing high current density at the crack tip and associated crack arrest. On the other hand, the crack tip temperature increases with time by the increasing external current and Joule heating. The values of mode-I stress intensity factor and strain energy density factor decrease with time due to the thermal deformation around the crack tip. Because of the temperature-dependent resistivity, the variation of the electric current density factor is complicated. In addition, it is not easy to create a crack-arrest condition when the crack length relative to the plate width is too small.     

Crack problem for superconducting strip with finite thickness

The inclined crack problems are considered for a thin strip and a strip with finite thickness in a perpendicular magnetic field. The critical current density is assumed to be a constant. The crack orientation is varied and the effect of crack on the magnetic field distribution is neglected. Based on the analytical results and variational inequality, the field and current distributions are computed for both thin strip and strip with finite thickness cases, respectively. Then, the stress intensity factors at the crack tip are determined using the finite element method for magnetic field loads. The numerical results are presented for different inclined crack angles, magnetization processes and geometry parameters of the strip. The results show that the fracture behavior of the strip with finite thickness is more complicated than that of the thin strip. With the numerical results, we can predict the largest possibility of cracking as the strip is in an external field.     

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.     

梁在纯弯曲力矩作用下的动态塑性断裂

本文采用刚塑性分析方法,研究了带裂纹有限长韧性材料梁在纯弯曲力矩作用下的动态塑性断裂过程,本文考虑了由于断裂引起的附加轴向力对断裂过程的影响,并在分析中考虑了应变率对断裂过程的影响。文章给出了断裂过程中断裂截面上弯曲力矩和轴向力随时间的变化规律,以及裂纹长度,裂纹扩展速度和加速度随时间的变化规律。     

Dynamic fracture of idealized fiber-reinforced materials

Dynamic plane stress of sheets composed of two orthogonal families of inextensible fibers, with infinitesimal elastic shearing stress response, is considered. The fibers through the tip of a propagating tear or crack carry finite forces. Fracture criteria that can be expressed in terms of these tip forces are discussed. In a particular example it is shown that the maximum energy release rate criterion leads to a circular crack trajectory, while the so-called critical force and critical stress criteria imply that the crack is L-shaped, like cracks or tears in real fibrous materials.     

A crack perpendicular to the bimaterial interface in finite solid

The dislocation simulation method is used in this paper to derive the basic equations for a crack perpendicular to the bimaterial interface in a finite solid. The complete solutions to the problem, including the T stress and the stress intensity factors are obtained. The stress field characteristics are investigated in detail. It is found that when the crack is within a weaker material, the stress intensity factor is smaller than that in a homogeneous material and it decreases when the distance between the crack tip and interface decreases. When the crack is within a stiffer material, the stress intensity factor is larger than that in a homogeneous material and it increases when the distance between the crack tip and interface decreases. In both cases, the stress intensity factor will increase when the ratio of the size of a sample to the crack length decreases. A comparison of stress intensity factors between a finite problem and an infinite problem has been given also. The stress distribution ahead of the crack tip, which is near the interface, is shown in details and the T stress effect is considered.