Higher-order analysis of near-tip fields around an interfacial crack between two dissimilar power law hardening materials

By means of an asymptotic expansion method of a regular series, an exact higher-order analysis has been carried out for the near-tip fields of an interfacial crack between two different elastic-plastic materials. The condition of plane strain is invoked. Two group of solutions have been obtained for the crack surface conditions: (1) traction free and (2) frictionless contact, respectively. It is found that along the interface ahead of crack tip the stress fields are co-order continuous while the displacement fields are cross-order continuous. The zone of dominance of the asymptotic solutions has been estimated. The project supported by the National Natural Science Foundation of China     

Mode I and mode II crack tip asymptotic fields with strain gradient effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material lengthl, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient. The project supported by the National Natural Science Foundation of China (19704100), National Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-20), CAS K.C. Wong Post-doctoral Research Award Fund and Post-doctoral Science Fund of China     

Semi-weight function method on computation of stress intensity factors in dissimilar materials

Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue-lambda. Integral expression of fracture parameters, KⅠ and KⅡ, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.     

Hole-drilling method using grating rosette and Moiré interferometry

The hole-drilling method is one of the most wellknown methods for measuring residual stresses. To identify unknown plane stresses in a specimen, a circular hole is first drilled in the infinite plate under plane stress, then the strains resulting from the hole drilling is measured. The strains may be acquired from interpreting the Moire signature around the hole. In crossed grating Moire interferometry, the horizontal and vertical displacement fields （u and v） can be obtained to determinate two strain fields and one shearing strain field. In this paper, by means of Moire interferometry and three directions grating （grating rosette） developed by the authors, three displacement fields （u, v and s） are obtained to acquire three strain fields. As a practical application, the hole-drilling method is adopted to measure the relief strains for aluminum and fiber reinforced composite. It is a step by step method; in each step a single laminate or equivalent depth is drilled to find some relationships between the drilling depth and the residual strains relieved in the fiber reinforced composite materials.     

Higher order asymptotic fields at the tip of a sharp V-notch in a power-hardening material

The higher order asymptotic fields at the tip of a sharp V-notch in a power-hardening material for plane strain problem of Mode I are derived. The order hierarchy in powers ofr for various hardening exponentsn and notch angles β is obtained. The angular distributions of stress for several cases are plotted. The self-similarity behavior between the higher order terms is noticed. It is found that the terms with higher order can be neglected for the V-notch angle β>45°. Project supported by the National Natural Science Foundation of China (Nos. 10132010 and 10072033).     

THE ELASTIC FIELD INDUCED BY A HEMISPHERICAL INCLUSION IN THE HALF—SPACE

The elastic field induced by a hemispherical inclusion with uniform eigeustralns in asemi-infinite elastic medium is solved by using the Green‘s function method and series expansion tech-nique. The exact solutions axe presented for the displacement and stress fields which can be expressedby complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. Thepresent method can be used to determine the corresponding elastic fields when the shape of the inclusionis a spherical crown or a spherical segment. Finally, numerical results axe given for the displacementand stress fields along the axis of symmetry (x3-axis).     

A generalized self-consistent Mori-Tanaka model for predicting the effective moduli of the coated inclusion based composite materials

The weak point of the generalized self-consistent method (GSCM) is that its solution for the effective shear moduli involves determining the complicated displacement and strain fields in constitutents. Furthermore, the effective moduli estimated by GSCM cannot be expressed in an explicit form. Instead of following the procedure of GSCM, in this paper a generalized self-consistent Mori-Tanaka method (GSCMTM) is developed by means of Hill's interface condition and the assumption that the strain in the inclusion is uniform. A comparison with the existing theoretical and experimental results shows that the present GSCMTM is sufficiently accurate to predict the effective moduli of the coated inclusion-based composite materials. Moreover, it is interesting to find that the application of Hill's interface condition in volumetric domain is equivalent to the Mori-Tanaka average field approximation. This project was supported by the National Natural Science Foundation of China and China Postdoctoral Science Foundation.     

A SOLUTION PROCEDURE FOR LOWER BOUND LIMIT AND SHAKEDOWN ANALYSIS BY SGBEM

The symmetric Galerkin boundary element method (SGBEM) instead of the finite element method is used to perform lower bound limit and shakedown analysis of structures. The self-equilibrium stress fields are constructed by a linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains and obtained through elastic-plastic incremental analysis. The complex method is used to solve nonlinear programming and determine the maximal load amplifier. The limit analysis is treated as a special case of shakedown analysis in which only the proportional loading is considered. The numerical results show that SGBEM is efficient and accurate for solving limit and shakedown analysis problems. Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent Doctorial Dissertation of China (No. 200025) and the Basic Research Foundation of Tsinghua University.     

Perfectly plastic caustics for the opening mode of fracture

Exact expressions for the caustics generated by the reflection of light surrounding crack tips in perfectly plastic materials under plane stress loading conditions and tensile tractions at infinity (mode I) are derived. Two individual cases are examined involving two different yield criteria. The first case uses an approximation of the Mises yield condition, where in the principal stress plane two intersecting parabolas replace the standard ellipse. The second case uses the Tresca yield condition where the mode I caustic is obtained as a limit of an elliptical hole in a perfectly plastic material. In both cases, kinematically admissible velocity fields are employed to obtain strain fields from which the theoretical caustics are predicted.     

A unified multiaxial fatigue damage parameter

According to the critical plane principle, a unified multiaxial fatigue damage parameter is presented based on the varying behaviour of the strains of the critical plane. Both the parameters of the maximum shear strain amplitude and normal strain excursion between adjacent turning points of the maximum shear strain on the critical plane are considered in the multiaxial fatigue damage parameter presented. An equivalent strain amplitude is made with both parameters of the maximum shear strain amplitude and normal strain excursion by means of von Mises criterion. Thus a new multiaxial fatigue damage parameter proposed in this paper may be used under either proportional or nonproportional loading, and may also be reduced to a uniaxial form. It is used to predict multiaxial fatigue life and good agreement is demonstrated by experimental data. The project is supported by the National Doctoral Foundation of China and National Natural Science Foundation of China.     

Quadrilateral isoparametric finite elements for plane elastic Cosserat bodies＊

4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.The project supported by the National Natural Science Foundation of China (10225212, 50178016, 10421002) and the Program for Changjiang Scholars and Innovative Research Team in University of China The English text was polished by Keren Wang.     

Crack tip field andJ-integral with strain gradient effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventionalJ ₂ deformation theory. No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory. Two typical crack problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-IK-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory. The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, theJ-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases. The project supported by the National Natural Science Foundation of China (19704100 and 10202023) and the Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-20)     

An orthotropic piezoelectric ellipsoid in a centrifugal field

A rotating ellipsoid composed of an orthotropic piezoelectric material (2mm) are considered, and the stress and electric displacement fields in this rotating ellipsoid are obtained exactly and completely. The solutions of the same problem for transversely isotropic piezoelectric material (6 mm) are also given by degenerating above results. At last, numerical examples for four kinds of media are illustrated in figures for comparison. Supported by the National Natural Science Foundation of China (No. 19872060).     

Two dimensional stress intensity factor computations by multi-domain boundary element method for crack closure with friction

A multi-domain boundary element method is used to compute the stress intensity factor of plane stress/plane strain crack problems with friction. The analysis is performed by using traction-singular quarter-point boundary elements on each side of the crack tips. The increment iteration is given. The technique is applied to some specific examples in order to show that the results will be with good accuracy.The Project 13 supported by National Natural Science Foundation of China.     

A constitutive relation for pseudo-elastic behaviour in shape memory alloys

A constitutive relation to describe pseudo-elastic deformation in shape memory alloys is presented in this paper. It is capable of describing deformation behaviour of polycrystalline materials under triaxial stress state as well as of monocrystalline materials under one-dimensional condition. Total strain rate is supposed to be composed of elastic strain rate and transformation strain rate. Deformation behaviour of Cu−Zn−Sn alloy and Ti−ni alloy is simulated by use of the proposed constitutive relation. it is shown that simulated results are in a good agreement with experimental data. The project supported by National Natural Science Foundation of China.     

梯度增强Cosserat连续体的广义Hill定理

基于经典Cauchy连续体的Hill定理,在平均场理论的框架下导出了梯度增强Cosserat连续体细、宏观均匀化方法的广义Hill定理。在梯度增强Cosserat连续体中,不仅宏观样条点上的应变和应力张量,而且它们的梯度均作用于与该样条点相关联的细观表征元（RVE）。依据此广义Hill定理,对梯度增强Cosserat连...     

MULTIPLE SCATTERING AND DYNAMIC STRESS ANALYSIS OF ELASTIC WAVES IN A FIBER—REINFORCED COMPOSITE WITH INTERFACES

Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber-reinforced composite are studied. The analytical expressions of elastic waves in different regions are presented. The mode coefficients of elastic waves are determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi-interfaces. By using the addition theorem of Hankel functions, the formula of scattered wave fields in different local coordinates are transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors (DSCFs). The influences of the distance between two inclusions, material properties and structural size on the DSCFs near the interfaces are analyzed. As examples, the numerical results of DSCFs near the interfaces for two kinds of fiber-reinforced composites are presented and discussed. The project supported by the National Natural Science Foundation of China (19972018)     

Application of the quadrilateral area coordinate method： a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-processing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. The project is supported by the National Natural Science Foundation of China (10502028), the Special Foundation for the Authors of the Nationwide (China) Excellent Doctoral Dissertation (200242), and the Science Research Foundation of China Agricultural University (2004016).     

金属切屑塑性流动的稳定性

对金属正交切削过程中切屑形成机制和材料塑性流动行为进行实验研究和理论分析. 通过对4 种常用金属材料正交切削过程的实验研究和切屑形貌的微观观察,确定了连续切屑转变成锯齿切屑的临界速度. 结果表明该临界速度与材料性能相关. 在实验观察基础上,提出描述材料正交切削过程的二维分析模型. 该模型假设切屑形成区为包括主剪切区和次剪切区的一个平行四边形. 载荷有主剪切区中的剪应力和次剪切区中的正压力;通过量纲分析得到描述材料正交切削过程的无量纲主控参数和无量纲形式的基本控制方程;应用线性稳定性分析方法建立平面应变状态下评价材料塑性流动稳定性的普遍准则;求得切屑形成区内材料塑性变形的速度和应力近似解. 讨论切屑形成、形貌转变以及相关的塑性失稳机制. 分析结果表明, 表征材料惯性与阻尼之比的无量纲参数— 雷诺数可以作为主控参数描述金属切削过程以及切屑材料塑性流动的稳定性.