Stress state in front of a crack perpendicular to bimaterial interface

Using a dislocation simulation approach, the basic equation for a crack perpendicular to a bimaterial interface is formulated in this paper. A novel expansion method is proposed for solving the problem. The complete solution for the problem, including the T stress ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analyzed in detail. It is found that ahead of the crack tip and near the interface the normal stress, perpendicular to the crack plane, sigma(x), is characterized by the K fields and the normal stress sigma(y) is dominated by the K field plus T stress in the region of 0 < r/b < 0.4 for b/a(0) less than or equal to 0.1, where b is the distance from the crack tip to the interface.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

Derivation Of A Nonlinear Reynolds Stress Model Using Renormalization Group Analysis And Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.

Interface Layer Effect On The Stress Distribution Of A Wafer-Bonded Bilayer Structure

The interface layer plays an important role in stress transfer in composite structures. However, many interface layer properties such as the modulus, thickness, and uniformity are difficult to determine. The model developed in this article links the influence of the interface layer on the normal stress distribution along the layer thickness with the layer surface morphology before bonding. By doing so, a new method of determining the interfacial parameter(s) is suggested. The effects of the layer thickness and the surface roughness before bonding on the normal stress distribution and its depth profile are also discussed. For ideal interface case with no interfacial shear stress, the normal stress distribution pattern can only be monotonically decreased from the interface. Due to the presence of interfacial shear stress, the normal stress distribution is much more complex, and varies dramatically with changes in the properties of the interface layer, or the dimensions of the bonding layers. The consequence of this dramatic stress field change, such as the shift of the maximum stress from the interface is also addressed. The size-dependent stress distribution in the thickness direction due to the interface layer effect is presented. When the interfacial shear stress is reduced to zero, the model presented in this article is also demonstrated to have the same normal stress distribution as obtained by the previous model, which does not consider the interface layer effect.

Influence of thermal residual stresses on the composite macroscopic behavior

The influence of the thermal residual stress on the deformation behavior of a composite has been analyzed with a new micromechanical method. The method is based on secant moduli approximation and a new homogenized effective stress to characterize the plastic state of the matrix. It is found that the generated thermal residual stresses after cooling and their influence on the subsequent deformation behavior depends significantly on the aspect ratio of the inclusions. With prolate inclusions, the presence of thermal residual stresses generate a higher compressive hardening curves of the composite, but it is reversed with oblate inclusions. For particle reinforced composite, thermal residual stresses induce a tensile hardening curve higher than the compressive one and this is in agreement with experimental observations. (C) 1998 Elsevier Science Ltd.

A micromechanical model of influence of particle fracture and particle cluster on mechanical properties of metal matrix composites

A general analytical model for a composite with an isotropic matrix and two populations of spherical inclusions is proposed. The method is based on the second order moment of stress for evaluating the homogenised effective stress in the matrix and on the secant moduli concept for the plastic deformation. With Webull's statistical law for the strength of SiCp particles, the model can quantitatively predict the influence of particle fracture on the mechanical properties of PMMCs. Application of the proposed model to the particle cluster shows that the particle cluster has neglected influence on the strain and stress curves of the composite. (C) 1998 Elsevier Science B.V.

Electrothermal stress in conductive body with collinear cracks

The temperature and stress field in a thin plate with collinear cracks interrupting an electric current field are determined. This is accomplished by using a complex function method that allows a direct means of finding the distribution of the electric current, the temperature and stress field. Temperature dependency for the heat-transfer coefficient, coefficient of linear expansion and the elastic modulus are considered. As an example, temperature distribution is calculated for an alloy (No. GH2132) plate with two collinear cracks under high temperature. Relationships between the stress, temperature, electric density and crack length are obtained. Crack trajectories emanating from existing crack are predicted by application of the strain energy density criterion which can also be used for finding the load carrying capacity of the cracked plate. (C) 2003 Elsevier Ltd. All rights reserved.

Study of the surface structure of butterfly wings using the scanning electron microscopic moire method

Scanning electron microscopic (SEM) moire method was used to study the surface structure of three kinds of butterfly wings: Papilio maackii Menetries, Euploea midamus (Linnaeus), and Stichophthalma how-qua (Westwood). Gratings composed of curves with different orientations were found on scales. The planar characteristics of gratings and some other planar features of the surface structure of these wings were revealed, respectively, in terms of virtual strain. Experimental results demonstrate that SEM moire method is a simple, nonlocal, economical, effective technique for determining which grating exists on one whole scale, measuring the dimension and the whole planar structural character of the grating on each scale, as well as characterizing the relationship between gratings on different scales of each butterfly wing. Thus, the SEM moire method is a useful tool to assist with characterizing the structure of butterfly wings and explaining their excellent properties. (c) 2007 Optical Society of America.

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

Elastodynamic stress intensity factor history for a semi-infinite crack under three-dimensional transient loading

The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.

Micromechanics of elastic solids weakened by a large number of cracks

This paper presents a micromechanics analysis of the elastic solids weakened by a large number of microcracks in a plane problem. A new cell model is proposed. Each cell is an ellipse subregion and contains a microcrack. The effective moduli and the stress intensity factors for an ellipse cell are obtained. The analytic closed formulas of concentration factor tensor for an isotropic matrix containing an anisotropic inclusion are derived. Based on a self-consistent method, the effective elastic moduli of the solids weakened by randomly oriented microcracks are obtained.

Singular behaviour near the tip of a sharp V-notch in a power law hardening material

This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

Fracture behavior of axisymmetrical bars under high triaxial stress and large strain cyclic loading

Axisymmetric notched bars with notch roots of large and small radii were tested under large strain cyclic loading. The main attention is focused on the fracture behaviour of steels having cycles to failure within the range 1-100. Our study shows that a gradual transition from a static ductile nature to one of fatigue cleavage can be observed and characterized by the Coffin-Manson formula in a generalized form. Both the triaxial tensile stress within the central region of specimens and static damage caused by the first increasing load have effects on the final failure event. A generalized cyclic strain range parameter DELTAepsilon is proposed as a measure of the numerous factors affecting behaviour. Fractographs are presented to illustrate the behaviour reported in the paper.