Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Analysis and application of ellipticity of stability equations on fluid mechanics

By using characteristic analysis of the linear and nonlinear parabolic stability equations (PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

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, K-I and K-II, 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.

A moving-coil designed micro-mechanics tester with application on MEMS

A moving-coil designed micro-mechanics tester, named as MicroUTM (universal testing machine), is in-house developed in this paper for micro-mechanics tests. The main component is a moving coil suspended in a uniform magnetic field through a set of springs. When a current passes through the coil, the electromagnetic force is proportional to the magnitude of the current, so the load can easily be measured by the current. The displacement is measured using a capacitive sensor. The load is calibrated using a Sartorius BP211D analytical balance, with a resolution/range of 0.01 mg/80 g or 0.1 mg/210 g. The displacement is calibrated using a HEIDENHAIN CT-6002 length gauge with an accuracy of +/- 0.1 mu m. The calibration results show that the load range is +/- 1 N and the displacement range is +/- 300 mu m. The noise levels of the load and displacement are 50 mu N and 150 nm, respectively. The nonlinearity of the load is only 0.2%. Several in-plane load tests of the MEMS micro-cantilever are performed using this tester. Experimental results, with excellent repeatability, demonstrate the reliability of the load measurement as well as the flexible function of this tester.

Atomistic simulations of crack nucleation and intergranular fracture in bulk nanocrystalline nickel

We report large scale molecular dynamics simulations of dynamic cyclic uniaxial tensile deformation of pure, fully dense nanocrystalline Ni, to reveal the crack initiation, and consequently intergranular fracture is the result of coalescence of nanovoids by breaking atomic bonds at grain boundaries and triple junctions. The results indicate that the brittle fracture behavior accounts for the transition from plastic deformation governed by dislocation to one that is grain-boundary dominant when the grain size reduces to the nanoscale. The grain-boundary mediated plasticity is also manifested by the new grain formation and growth induced by stress-assisted grain-boundary diffusion observed in this work. This work illustrates that grain-boundary decohesion is one of the fundamental deformation mechanisms in nanocrystalline Ni.

Bio-inspired mechanics of reversible adhesion: Orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials

Geckos and many insects have evolved elastically anisotropic adhesive tissues with hierarchical structures that allow these animals not only to adhere robustly to rough surfaces but also to detach easily upon movement. In order to improve Our understanding of the role of elastic anisotropy in reversible adhesion, here we extend the classical JKR model of adhesive contact mechanics to anisotropic materials. In particular, we consider the plane strain problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic elastic half space with the axis of symmetry oriented at an angle inclined to the surface. The cylinder is then subjected to an arbitrarily oriented pulling force. The critical force and contact width at pull-off are calculated as a function of the pulling angle. The analysis shows that elastic anisotropy leads to an orientation-dependent adhesion strength which can vary strongly with the direction of pulling. This study may suggest possible mechanisms by which reversible adhesion devices can be designed for engineering applications. (C) 2006 Elsevier Ltd. All rights reserved.

Stress intensity factors calculation in anti-plane fracture problem by orthogonal integral extraction method based on femol

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions (or between the derivatives of eigenfunctions) of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors (SIFs), so any order SIF can be extracted based on a certain known solution of displacement (an analytic result or a numerical result). Many numerical examples based on the finite element method of lines (FEMOL) show that the present method is very powerful and efficient.

Analysis of spallation based upon statistical microdamage mechanics

A relationship between the cumulative length of microcracks and the amplitude and duration of tensile impulse in spallation was established based on the application of statistical microdamage mechanics, which included a statistical formulation and dynamic laws of microdamage under loading. Since the degrees of spallation, called incipient, intermediate and complete spallation, can be characterized by the cumulative length of microcracks, a physical interpretation of an empirical criterion to spallation was presented.

On crack path stability in a layered material

Crack paths in an elastic layer on top of a substrate are considered. Crack growth is initiated from an edge crack in the layer. The plane of the initially straight crack forms an angle to the free surface. The load consists of a pair of forces applied at the crack mouth and parallel to the interface. Crack paths are calculated using a boundary element method. Crack growth is assumed to proceed along a path for which the mode II stress intensity factor vanishes. The inclination and the length of the initial crack are varied. The effect of two different substrates on the crack path evolution is demonstrated. A crack path initially leading perpendicularly to the interface is shown to be directionally unstable for a rigid substrate. Irrespective of its initial angle, the crack does not reach the interface, but reaches the free surface if the layer is infinitely long. At finite layer length the crack reaches the upper free surface if the initial crack inclination to the surface is small enough. For an inextendable flexible substrate, on the other hand, the crack reaches the interface if its initial inclination is large enough. For the flexible substrate an unstable path parallel with the sides of an infinitely long layer is identified. The results are compared with experimental results and discussed in view of characterisation of directionally unstable crack paths. The energy release rate for an inclined edge crack is determined analytically.

Fracture criteria for combined cleavage and dislocation emission

A general theory of fracture criteria for mixed dislocation emission and cleavage processes is developed based on Ohr's model. Complicated cases involving mixed-mode loading are considered. Explicit formulae are proposed for the critical condition of crack cleavage propagation after a number of dislocation emissions. The effects of crystal orientation, crack geometry and load phase angle on the apparent critical energy release rates and the total number of the emitted dislocations at the initiation of cleavage are analysed in detail. In order to evaluate the effects of nonlinear interaction between the slip displacement and the normal separation, an analysis of fracture criteria for combined dislocation emission and cleavage is presented on the basis of the Peierls framework. The calculation clearly shows that the nonlinear theory gives slightly high values of the critical apparent energy release rate G(c) for the same load phase angle. The total number N of the emitted dislocations at the onset of cleavage given by nonlinear theory is larger than that of linear theory.

A BIEM optimization method for fracture dynamics inverse problem

In the present paper, based on the theory of dynamic boundary integral equation, an optimization method for crack identification is set up in the Laplace frequency space, where the direct problem is solved by the author's new type boundary integral equations and a method for choosing the high sensitive frequency region is proposed. The results show that the method proposed is successful in using the information of boundary elastic wave and overcoming the ill-posed difficulties on solution, and helpful to improve the identification precision.

Micromechanics analyses of interface crack

A new mechanics model based on Peierls concept is presented in this paper, which can clearly characterize the intrinsic features near a tip of an interfacial crack. The stress and displacement fields are calculated under general combined tensile and shear loadings. The near tip stress fields show some oscillatory behaviors but without any singularity and the crack faces open completely without any overlapping when remote tensile loading is comparable with remote shear loading. A fracture criterion for predicting interface toughness has been also proposed, which takes into account for the shielding effects of emitted dislocations. The theoretical toughness curve gives excellent prediction, as compared with the existing experiment data.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.