Influence of Initial Stresses on Stress Intensity Factors at Crack Tips in a Composite Strip

The influence of initial tension or compression along cracks on the stress intensity factor (SIF) at crack tips under the action of additional normal forces on crack edges is studied for infinite bodies. A strip made of a composite material is considered. The strip ends are simply supported, and the strip contains a crack whose edges are parallel to its face planes. The strip is first stretched or compressed along crack edges, and then additional uniformly distributed normal forces are applied to the crack edges. The influence of the initial tension (compression) on the SIF caused by the additional normal forces is studied. The corresponding boundary-value problems are modelled with the use of the three-dimensional linearized theory of elasticity. All the investigations are carried out numerically by employing the finite-element method. The values of SIF are calculated by the energy release method.     

Forced vibration of an initially stressed thick rectangular plate made of an orthotropic material with a cylindrical hole

The forced vibration of an initially statically stressed rectangular plate made of an orthotropic material is studied. The plate is simply supported along all its edges and contains an internal across-the-width cylindrical hole of rectangular cross section with rounded corners. The initial stresses are created by uniformly distributed normal forces applied to opposite end faces of the plate. Because of the hole, these stresses are not uniform in the plate and significantly affect the stress field caused by additional time-harmonic dynamical forces acting on the upper face of the plate. Hence, for solving the boundary-value problem considered, the superposition principle is unsuitable. Therefore, our investigations are carried out within the framework of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The corresponding boundary- value problems on determining the initial and additional, dynamical stress states are solved by using the three-dimensional finite-element method. Numerical results on stress concentrations around the cylindrical hole and the fundamental frequencies, and on the influence of the initial stresses on the frequencies are presented.     

Interaction between two neighboring circular holes in a prestretched simply supported orthotropic strip under bending

In this work, the influence of initial stretching of a simply supported plate-strip containing two circular holes on the stress concentration around the holes caused by bending of the strip is examined using the finite-element method. The mathematical formulation of the corresponding boundary-value problem is presented within the frame work of the three-dimensional linearized theory of elasticity (TDLTE) under a plane strain state. The material of the plate-strip is linearly elastic, homogeneous, and orthotropic. The numerical results obtained in investigating the influence of the initial stretching and the location of holes on the stress concentration are presented. In particular, it is established that the initial stretching significantly decreases the stress concentration at some characteristic points on the contour of the holes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 827–838, November–December, 2008.     

功能梯度材料有限宽板的反平面断裂问题研究

研究了功能梯度材料有限宽板中与板边平行的III型裂纹问题．假设材料的剪切模量沿板宽度方向呈指数规律变化,利用Fourier变换将问题描述为奇异积分方程,并进一步将未知的位错密度函数表示为Chebyshev多项式的级数式,从而将奇异积分方程化为线性代数方程组进行配点数值求解．基于数值结果,讨论了材料非均匀性参数、板和裂纹的几何参数等对应力强度因子（SIF）的影响．研究表明,SIF随裂纹长度的增大而增大,随裂纹所在区域材料刚度的增大而减小;板越窄,SIF对非均匀性参数的变化越敏感,且变化规律也越复杂．随着非均匀性参数的增大,SIF既可能增大也可能减小还可能基本保持不变,这主要取决于板的相对宽度和裂纹的相对位置．当裂纹位于板的中央或当板较宽时,SIF对非均匀性参数的变化都不太敏感．     

Energy release rate in a prestressed sandwich plate-strip containing interface cracks

Within the framework of a piecewise homogeneous body model, by utilizing the three-dimensional linearized theory of elasticity, the problem of opening of interface cracks in an initially stressed sandwich plate-strip is studied. To solve the corresponding boundary-contact problem, the FEM is employed. Numerical results for the influence of the initial stresses on the energy release rate (ERR) at various values of problem parameters are presented and discussed. In particular, it is established that the ERR in creases (de creases) with growing initial tension (compression) of the plate-strip.     

一维六方准晶双材料中圆孔边共线界面裂纹的反平面问题

研究了一维六方准晶双材料中圆孔边不对称共线界面裂纹的反平面问题。利用Stroh公式和复变函数方法得到了声子场和相位子场耦合作用下的复势函数,给出了裂纹尖端应力强度因子和能量释放率的解析表达式。通过数值算例,讨论了圆孔半径和裂纹长度对应力强度因子的影响,以及耦合系数、声子场应力和相位子场应力对能量释放率的影响。结果表明:当圆孔半径不变时,应力强度因子随右裂纹长度的增大趋向稳定值。当相位子场应力取一定值时,能量释放率达到最小值,说明特定的相位子场应力可以抑制裂纹的扩展。     

The stress field problem for a pre-stressed plate-strip with finite length under the action of arbitrary time-harmonic forces

In the framework of the three-dimensional linearized theory of elastodynamics the finite element modeling of the stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation under the action of inclined linearly located time-harmonic forces is developed. The numerical results involving the normal stress acting on the interface plane of the plate-strip and the rigid foundation are presented. Moreover, the dependencies between this stress, the frequency of the arbitrary inclined linearly located external force and the initial stretching of the plate-strip are analyzed.     

Buckling delamination of a sandwich plate-strip with piezoelectric face and elastic core layers

In this study, the buckling delamination problem of a sandwich plate-strip with a piezoelectric face and elastic core layers is studied. It is assumed that the plate-strip is simply supported and grounded along its two parallel ends and is subjected to uniformly-distributed compressive forces on these ends. Moreover, we suppose that the plate-strip has two interface inner cracks between the face and the core layers and it is also supposed that before the plate-strip is loaded (i.e. in the natural state), the surfaces of these cracks have insignificant initial imperfections. Due to compressive forces acting along the cracks we investigate the evolution of the initial imperfections of the cracks’ surfaces. Hence, the values of the critical buckling delamination force of the considered plate-strip are determined from the criteria, according to which, the considered initial imperfections of the cracks’ surfaces grow indefinitely by the compressive forces. Mathematical modeling of the considered problem is formulated within the scope of the exact nonlinear equations of electro-elasticity in the framework of the piecewise homogeneous body model, the solution of which is found numerically by employing the finite elements method. Numerical results showing the influences of the geometrical and material parameters as well as the coupling of the electrical and mechanical fields on the values of the critical force are presented and analyzed.     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

Stability of transversely isotropic annular plates with low shear resistance

The stability differential equations of a cylindrically orthotropic circular plate are obtained on the assumption of an axisymmetric buckling mode with allowance for transverse shears. These equations are solved for the case of a transversely isotropic material when the inner and outer edges of the plate are identically loaded by uniformly distributed radial forces. The transcendental equations for the critical load parameter are constructed for various edge conditions. The dependence of this parameter on the boundary conditions and the relative thickness of the plate, Poisson's ratio, and the ratio of the Young's and shear moduli of the material are investigated. Certain conclusions are reached concerning the design of reinforced-plastic plates.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 872–880, September–October, 1969.     

Stress Analysis for a Thick Rectangular Plate of a Composite Material with a Spatially Periodically Curved Structure under Forced Vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially periodically curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz'. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of curving parameters on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three- dimensional FEM modeling.     

The Mathematical Study of an Edge Crack in Two Different Specified Models under Time-Harmonic Wave Disturbance

Mechanics of Composite Materials - This paper devotes to determining a stress intensity factor (SIF) at the tip of an edge crack in two models considered. Problem-1 is an orthotropic strip of a...     

Dynamic response of planar interface crack between viscoelastic bodies

IntroductionThe dynamic stress intensity factor (SIF) plays an important role in dynamic fracture underboth harmonic and transient loads. It predicts whether or not the fracture toughness of thematerial will be exceeded and catastrophic crack propagation will follow. The dynamic SIFof interfaCe cracks between two dissimilar elastic materials has been studied widely. Kundull]studied the dynamic SIF of interface crack under transient loading with the method based onBetti's reciprocal theore…     

Three-Dimensional Stress Analysis for a Thick Plate of a Composite Material with a Spatially Locally Curved Structure

The stress distribution in a thick rectangular plate of a multilayered composite with a spatially locally curved structure is investigated with the use of three-dimensional exact equations of elasticity theory. The investigations are carried out within the framework of the continuum approach proposed by Akbarov and Guz'. It is supposed that the plate edges are clamped and uniformly distributed normal forces are applied to its upper face. The corresponding boundary-value problem is solved by employing the three-dimensional FEM modeling. Numerical results for the normal stresses acting in the thickness direction of the plate are given. The influence of the spatial local curving on the distribution of these stresses is analyzed.     

On the peculiarities of a crack growth path in anisotropic solid

One of the possibilities to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. In this connection the influence of the elastic moduli of an anisotropic material on the possibilities of crack rotation are studied. In particular a linear elastic problem for a straight Mode I crack, located on a symmetry axis of an orthotropic plane is considered. The strength properties of the material are supposed to be isotropic. For studying a direction of a crack growth path several crack models are considered. It is shown that a thin elongated elliptical hole as a crack model leads to more plausible results concerning crack rotation conditions than an ideal cut model. The maximal tensile stresses are taken as a crack growth criterion. It is shown that for some class of orthotropic materials a crack deviates from the straight path just after it starts to grow even in the conditions of uniaxial normal tension. The problem of the stability of a straight crack path under Mode I loading is also considered. This problem is reduced to the problem of the fracture direction determination for thin elongated elliptical cavity slightly inclined to the initial direction. In the frame of the proposed approach the conditions of instability are obtained. It is shown that for some class of orthotropic materials a straight crack path is unstable in the conditions of uniaxial normal tension. This class of materials is wider than one for which a crack deviates from the straight crack path just after its start. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anti-plane analysis of an orthotropic strip weakened by several moving cracks

In this paper several finite cracks with constant length (Yoffe-type crack) propagating in an orthotropic strip were studied. The distributed dislocation technique is used to carry out stress analysis in an orthotropic strip containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in an orthotropic strip by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by moving cracks. Finally several examples are solved and the numerical results for the stress intensity factor are obtained. The influences of the geometric parameters, the thickness of the orthotropic strip, the crack size and speed have significant effects on the stress intensity factors of crack tips which are displayed graphically.     

Delamination buckling of a rectangular orthotropic composite plate containing a band crack

The delamination buckling problem for a rectangular plate made of an orthotropic composite material is studied. The plate contains a band crack whose faces have an initial infinitesimal imperfection. The subsequent development of this imperfection due to an external compressive load acting along the crack is studied through the use of the three-dimensional geometrically nonlinear field equations of elasticity theory for anisotropic bodies. A criterion of initial imperfection is used in determining the critical forces. The corresponding boundary-value problems are solved by employing the boundary-form perturbation technique and the FEM. Numerical results for the critical force are presented.     

非均匀圆柱型正交各向异性圆板的弯曲问题

本文研究了非均匀圆柱型正交各向异性圆板的弯曲问题,求得了折算刚度随半径按指数函数规律变化的非均匀圆柱型正交各向异性圆板在横向均布载荷作用下的通解,并给出了周边固定夹支条件下的精确解。     

Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Two-dimensional Green's function of orthotropic three-phase material under a normal line force with application in the design of composite

Green's function of orthotropic three-phase material is an important and basic problem in the study of mechanics of materials. It is also the foundation of further theoretical researches and engineering applications. Most of adhesive structures in engineering can be well simulated by the mechanical model of orthotropic three-phase material, such as composite laminate, integrated circuit (IC) packaging, micro-electro-mechanical systems (MEMS) and biomedical materials, etc. In order to understand the mechanical properties of the adhesive structure, a two-dimensional Green's function of orthotropic three-phase material loaded with a normal line force is presented. Based on the Green's function proposed in this paper, the stress field of adhesive structure under arbitrary normal loadings can be obtained with superposition method. Besides, this Green's function is convenient to be used in further studies, because it is expressed explicitly in form of elementary functions. Numerical examples are proposed to study the mechanical properties of the adhesive structure in five difference aspects: (1) the distribution rule of stress fields of the adhesive structure; (2) the influence from fiber orientation of composite to the stress fields of the adhesive structure; (3) the influence from elastic modulus of adhesive layer to the stress transfer of the adhesive structure; (4) the influence from the thickness of adhesive layer to the stress transfer of the adhesive structure; (5) the reasonability of spring interface model.