Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Catastrophic rupture of heterogeneous brittle materials under impact loading

The catastrophic failure of heterogeneous brittle materials under impact loading is not fully understood. To describe the catastrophic failure behavior of heterogeneous brittle materials under impact loading, an elasto-statistical-brittle (ESB) model is proposed in this paper. The ESB model characterizes the disordered inhomogeneity of material at mesoscopic scale with the statistical description of the shear strength of mesoscopic units. If the applied shear stress reaches the strength, the mesoscopic unit fails, which causes degradation in the shear modulus of the material. With a simplified ESB model, the failure wave in brittle material under uni-axial compression is analyzed. It is shown that the failure wave is a wave of strain or particle velocity resulted from the catastrophic fracture in an elastically stressed brittle media when the impact velocity reaches a critical value. In addition, the failure wave causes an increase in the rear surface velocity, which agrees well with experimental observations. The critical condition to generate failure wave and the speed of failure wave are also obtained.

Numerical simulation of thermal loading produced by shaped high power laser onto engine parts

Recently a new method for simulating the thermal loading on pistons of diesel engines was reported. The spatially shaped high power laser is employed as the heat source, and some preliminary experimental and numerical work was carried out. In this paper, a further effort was made to extend this simulation method to some other important engine parts such as cylinder heads. The incident Gaussian beam was transformed into concentric multi-circular patterns of specific intensity distributions, with the aid of diffractive optical elements (DOEs). By incorporating the appropriate repetitive laser pulses, the designed transient temperature fields and thermal loadings in the engine parts could be simulated. Thermal-structural numerical models for pistons and cylinder heads were built to predict the transient temperature and thermal stress. The models were also employed to find the optimal intensity distributions of the transformed laser beam that could produce the target transient temperature fields. Comparison of experimental and numerical results demonstrated that this systematic approach is effective in simulating the thermal loading on the engine parts. (C) 2009 Elsevier Ltd. All rights reserved.