缺口根部和裂纹尖端残余应力的X射线法测定

X射线法用于缺口根部和裂纹尖端等徽区的残余应力测试的先决条件是解决缩小光束直径、提高衍射束的强度和准确设置试样等技术问题.在X射线衍射仪上借助于自行设计制造的限束对光装置和侧倾对中附件,成功地测定了缺口根部半径为1mm的喷丸残余应力场和板形试样压-压周期载荷下裂纹尖端的残余拉应力场.     

The effect of residual stresses on hardness measurements

The RockwellC hardness,RC, was measured as a function of position on steel rings with different residual-stress profiles through the thickness. An experimental correlation between residual stress andRC was obtained. A relationship between the average pressurep of a spherical indenter, the yield strengthS _y and the residual stress of the material was conceived and used in fitting the experimental data. In order to model the effects of residual stresses on the measured hardness, the von Mises-Hencky (power) yield criterion was utilized, together with an adaptation for residual stresses of the expression for the stress state under a spherical indenter, given in Shaw, Hoshi and Henry. A parameter α was introduced in our calculations to account for the effect of the nonperpendicularity of the residual stresses to the pressurep of the spherical indenter. The proposed model in large measure fits experimental hardness versus residual stress data, and results are consistent with different samples. This model can be used as a basis for the measurement of residual stresses in steel or other materials.     

Axi-symmetric contact on thin compliant coatings

This paper presents a theory for the indentation of a soft thin coating by a rigid body. The coating is assumed to be bonded to a rigid substrate and to behave linearly elastically. A simplifying approximation enables the stresses within the coating, averaged through its thickness, to be determined for particular indenter profiles. The results are shown to be sensitive to the thickness and compressibility of the coating material. Unlike much previous work, the results can be expressed analytically for certain indenter profiles and have been substantiated by experiment. The theory has many useful applications, in particular for situations where the layer acts as a protective coating and for the accurate, in situ and non-destructive measurement of the elastic modulus of the coating material.     

Intensity of singular stress fields causing interfacial debonding at the end of a fiber under pullout force and transverse tension

In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pullout force. Those singular stresses have not been discussed yet in the previous studies for pullout problems although they are important for causing interfacial initial debonding. The body force method is used to formulate those problems as a system of singular integral equations where unknowns are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions. In order to compare the results with the previous solutions, tension problems of a fiber in a semi-infinite body are also considered. Then, generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated for various geometrical conditions with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed for pullout problems.     

Characteristics of the process zone at sharp notch roots

The classical Williams solution for the state of stress at the tip of a semi-infinite notch is re-visited and the two-term singular solution re-written in a form making the mode mixity and load magnitude explicit. This is used to show that, for a 270° solid angle, the majority of notch problems exhibit a process zone which is entirely or substantially mode I in character, which in turn means that the notch strength may practically be governed by a single elastic parameter. A method for finding the practical limit on the load and stress intensity ratio where this holds is described.     

受移动简谐力作用的多孔弹性半平面问题

研究了匀速移动的振动荷载作用下半无限多孔饱和固体中产生的应力和孔隙水压力．应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和固体中应力与孔隙水压力的影响,并与相应的弹性介质的解答进行了比较．结果显示多孔饱和半平面中应力和孔隙水压力随荷载的移动速度与振动频率的增加而增大,多孔饱和固体在移动荷载下的动力响应与相应的单相弹性固体的动力响应有较大的差别。     

Plate punching by a deformable indenter in the presence of discharge current

The problem of interaction of a deformable indenter with a plate and the problem of plate punching as a result of interaction between the deformable indenter and the plate in the presence of a discharge current are considered. The stresses arising in the plate and in the indenter are obtained.     

Stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension

Summary This paper deals with the stress concentration problem of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r- and z-directions in semi-infinite bodies having the same elastic constants as the ones of the matrix and inclusion. In order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in [24, 25] are used. The body-force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries even when the inclusion is very close to the free boundary. The effect of the free surface on the stress concentration factor is discussed with varying the distance from the surface, the shape ratio and the elastic modulus ratio. The present results are compared with the ones of an ellipsoidal cavity in a semi-infinite body.accepted for publication 11 November 2003     

Crack initiation at the rectangular step notch surface under combined loading

Summary  Under external forces acting on the face of a notch, cracks originate at corners, and the system is liable to fail. An analysis is presented of the stress field in the neighborhood of the notch tips, based on the integral representation of the biharmonic solution and on numerical methods. Computations were performed for constant loading or constant displacement distributed along one face of the notch. The coefficients in the principal terms of the asymptotic formulae for the circumferential and shear stresses depend on the angle and height of the notch face and on the boundary conditions. The maximal values of these coefficients determine the stress intensity factors for the opening and shear modes. The angles corresponding to the maximal values of the intensity factors indicate the directions of initiation of opening and sliding cracks. Received 30 May 2000; accepted for publication 3 April 2001     

单晶硅的纳米力学响应及其相变机制

硅在大规模集成电路、MEMS/NEMS、半导体工业中具有不可替代作用,但是目前对硅的塑性变形及其相变机制的理解远未成熟.采用大规模分子动力学模拟研究(100)面的单晶硅在球形金刚石压头纳米压入过程中的纳米力学响应、相变过程和相分布规律.结果表明:在弹性变形阶段载荷-压深曲线与Hertz接触理论预测结果相吻合.两者的分离点准确地预示了塑性变形的发生.金刚石结构的Si-I相向体心结构的BCT5相转变导致了单晶硅初始的塑性变形.初始形成的BCT5相在次表面形成了一个倒置的金字塔形结构.Si-II相的形成则稍微滞后一些.在较大的载荷下BCT5在压入面上形成一个四重对称的图案分布.相对于小压头条件下大的BCT5相区,大压头更有利于SiII相的发展.卸载后生成的高压Si-II相和BCT5相全部转变为非晶硅.研究结果确认了单晶硅纳米压入中BCT5相的存在;揭示了单晶硅塑性变形的相变机理,即Si-I转变为BCT5和Si-II相;并强调了Si-I相向BCT5相转变对于单晶硅塑性变形的重要作用.     

Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters

A fracture criterion of the type of the Neuber-Novozhilov criterion is proposed to describe the fracture in the vicinity of the tip of a V-shaped notch under tensile and shear loading. In the proposed criterion, the limits of averaging of the stresses along the notch axis depend on the presence, location, and size of the initial defects in the material. The crystal lattice parameter of the initial material is chosen for the characteristic linear size. For a V-shaped notch subjected to tension and shear, simple equations are obtained that relate the stress intensity factors for the modified singularity coefficients, the singularity coefficients themselves, and the theoretical tensile and shear strengths of a single crystal of the material taking into account the damage to the material in the vicinity of the notch tip. The equations obtained allow a passage to the limit from a notch to a crack. It is shown that the classical critical stress intensity factor used in the strength analysis of cracked solids is not a material constant.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 106–115, January–February, 2005.     

Modeling of pre-fracture zones for limited permeable crack in piezoelectric materials

A plane-strain problem for a limited permeable crack in an adhesive thin interlayer between two semi-infinite piezoelectric spaces is considered. The tensile mechanical stress and the electric displacement are applied at infinity. The interlayer is assumed to be softer than the connected materials; therefore, the zones of mechanical yielding and electric saturations can arise at the crack tips on the continuations of the crack. These zones are considered in this work. It was assumed that the length of electric saturation zones is larger than the length of mechanical yield zones. The zones of mechanical yielding are modeled by the crack continuations with normal compressive stresses applied at its faces. The electric saturation zones are modeled by segments at the crack continuations with prescribed saturated electric displacements. These electric displacements can linearly vary along the mechanical yielding zones. The problem is reduced to the Hilbert–Riemann problem of linear relationship, which is solved exactly. The equation for the determination of the yielding zones length, the expressions for the crack-opening displacement jump, electric potential jump, and J-integral is obtained in an analytical form. In case of finite size body, the finite elements method is used and the variation in the fracture mechanical parameters with respect to this size is demonstrated.     

含缺陷半无限长梁在阶跃载荷作用下的塑性动力特性及失效分析

分析了在任意位置含一缺陷的半无限长梁在自由端受阶跃载荷作用下的刚塑性动力响应,重点讨论了结构响应模式和缺陷处的能量耗散,给出了不同载荷大小和缺陷参数组合下的完全解,所得结果对确定管道结构的动态失效准则有参考价值.     

Crack nucleation from a single notch caused by stress-dependent surface reactions

The surface of a solid under stress is unstable if there is mass exchange and transportation along the surface. A notch on the surface can be a preferred site for crack nucleation. This paper studies the evolution of a surface notch under stress dependant reaction. The surface is represented by a family of curves with many degrees of freedom, and the elastic field is solved using complex conformal mapping method. In the numerical simulations, the notch either deepens immediately and forms singular tip; or becomes perfectly flat after long time; or becomes blunter first, evolving slowly for a long time, then nucleates new surface instability and finally forms sharp tip; or becomes near flat first, then forms a bump on the surface. When the activation strain is small or the reaction is near equilibrium, the notch stability is mainly determined by the competition of strain energy and surface energy, and the sign of stress has little effect. When the surface reaction is away from equilibrium and activation strain is not small, stresses with different signs give totally different surface stability behaviors, depending on whether the solid is losing mass to or gaining mass from the environment.     

Constitutive behavior of a microcracking brittle solid in cyclic compression

A constitutive formulation is presented to determine the “driving force” for Mode I fatigue crack growth in notched plates of brittle solids stressed in uniaxial cyclic compression. For the particular case of a microcracking medium, it is demonstrated that residual tensile stresses are induced ahead of the notch during unloading from the maximum far-field compressive stress. We propose that it is this region of residual tensile stresses at the notch-tip which promotes fatigue crack growth in ceramics along the notch plane in a direction normal to the compression axis. The predictions of the analysis are compared with new experimental results on compression fatigue in brittle solids. Specifically, it is shown that the numerical estimates of the near-tip tensile zone size for microcracking ceramics compare favorably with the experimentally measured distance of stable Mode I fatigue crack growth after the first compression cycle. Experimental information on the threshold stress for microcracking, transition stress for the inducement of residual tension during unloading, and the effect of mean stress on fracture, as well as direct observations of microcracks and crack growth in compression fatigue, corroborate the assumptions and implications of the analysis.     

Wedge indentation into elastic-plastic single crystals, 1: Asymptotic fields for nearly-flat wedge

Asymptotic stress and deformation fields under the contact point singularities of a nearly-flat wedge indenter and of a flat punch are derived for elastic ideally-plastic single crystals with three effective in-plane slip systems that admit a plane strain deformation state. Face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal-close packed (HCP) crystals are considered. The asymptotic fields for the flat punch are analogous to those at the tip of a stationary crack, so a potential solution is that the deformation field consists entirely of angular constant stress plastic sectors separated by rays of plastic deformation across which stresses change discontinuously. The asymptotic fields for a nearly-flat wedge indenter are analogous to those of a quasistatically growing crack tip fields in that stress discontinuities can not exist across sector boundaries. Hence, the asymptotic fields under the contact point singularities of a nearly-flat wedge indenter are significantly different than those under a flat punch. A family of solutions is derived that consists entirely of elastically deforming angular sectors separated by rays of plastic deformation across which the stress state is continuous. Such a solution can be found for FCC and BCC crystals, but it is shown that the asymptotic fields for HCP crystals must include at least one angular constant stress plastic sector. The structure of such fields is important because they play a significant role in the establishment of the overall fields under a wedge indenter in a single crystal. Numerical simulations—discussed in detail in a companion paper—of the stress and deformation fields under the contact point singularity of a wedge indenter for a FCC crystal possess the salient features of the analytical solution.     

A new boundary element approach of modeling singular stress fields of plane V-notch problems

In this paper, a new boundary element (BE) approach is proposed to determine the singular stress field in plane V-notch structures. The method is based on an asymptotic expansion of the stresses in a small region around a notch tip and application of the conventional BE in the remaining region of the structure. The evaluation of stress singularities at a notch tip is transformed into an eigenvalue problem of ordinary differential equations that is solved by the interpolating matrix method in order to obtain singularity orders (degrees) and associated eigen-functions of the V-notch. The combination of the eigen-analysis for the small region and the conventional BE analysis for the remaining part of the structure results in both the singular stress field near the notch tip and the notch stress intensity factors (SIFs).Examples are given for V-notch plates made of isotropic materials. Comparisons and parametric studies on stresses and notch SIFs are carried out for various V-notch plates. The studies show that the new approach is accurate and effective in simulating singular stress fields in V-notch/crack structures.     

Bonded Joints with Nonhomogeneous Adhesives

The problem is considered of two semi-infinite elastic plane regions bonded by a non-homogeneous adhesive along their common linear boundary and subject to constant applied stresses at infinity. The complex variable method has been employed to achieve the closed-form solution for generic interface stiffness distributions. Two particular cases of practical interest have been treated in detail as particular applications of the proposed general solution. This revised version was published online in August 2006 with corrections to the Cover Date.     

The problem of sharp notch in couple-stress elasticity

The problem of sharp notch in couple-stress elasticity is considered in this paper. The problem involves a sharp notch in a body of infinite extent. The body has microstructural properties, which are assumed to be characterized by couple-stress effects. Both symmetric and anti-symmetric loadings at remote regions are considered under plane-strain conditions. The faces of the notch are considered traction free. To determine the field around the tip of the notch, a boundary-layer approach is followed by considering an expansion of the displacements in a form of separated variables in a polar coordinate system. Our analysis is in the spirit of the Knein–Williams and Karp–Karal asymptotic techniques but it is much more involved than its corresponding analysis of standard elasticity due to the complicated boundary value problem (higher-order system of governing PDEs and additional boundary conditions as compared to the standard theory). Eventually, an eigenvalue problem is formulated and this, along with the restriction of a bounded potential energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed as limit cases of the general notch problem. Certain deviations from the standard classical elasticity results are noted.     

Analysis of crack extension in anisotropic materials based on local normal stress

The normal stress ratio theory is applied to predict crack extension behavior in center-notched unidirectional graphite-epoxy of arbitrary fiber axis orientation, subjected to arbitrary far-field planar loading. The theory is applied within analytical solutions for two infinite plate geometries: a plate with a sharp center crack, and a plate with an elliptical center flaw. A critical analytical case is identified suggesting that application of the theory within a stress solution modelling crack tip shape may increase the accuracy of crack growth direction predictions. Crack extension direction, location of crack extension, and critical stress predictions of the theory are compared to those obtained from experiments on specimens subjected to tensile, shear, and mixed-mode far-field loading. The comparison shows that, applied within each analytical solution, the normal stress ratio theory provides verifiable predictions of crack growth behavior. By modelling actual notch tip shape, the elliptical notch solution is able to provide accurate qualitative predictions of the origin of crack extension along the periphery of a cut notch tip in a way that the sharp crack analysis cannot. The sharp notch solution appears to provide slightly more accurate crack growth direction predictions, however. Also, in predicting critical applied far-field stresses, the sharp crack solution appears to exhibit a stronger ability to model subtle experimental trends.