On the velocity of buckle propagation in a beam on a nonlinear elastic-foundation

The paper revisits a simple beam model used by Chater et al. (1983, Proc. IUTAM Symp. Collapse, Cambridge University Press) to examine the dynamics of propagating buckles on it. It was found that, if a buckle is initiated at a constant pressure higher than the propagation pressure of the model (P-p), the buckle accelerates and gradually reaches a constant velocity which depends upon the pressure, while if it is initiated at P-p, the buckle propagates at a velocity which depends upon the initial imperfection. The causes for the difference are also investigated.

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

Kinking of an interface crack between 2 dissimilar anisotropic elastic solids

A detailed analysis of kinking of an interface crack between two dissimilar anisotropic elastic solids is presented in this paper. The branched crack is considered as a distributed dislocation. A set of the singular integral equations for the distribution function of the dislocation density is developed. Explicit formulas of the stress intensity factors and the energy release rates for the branched crack are given for orthotropic bimaterials and misoriented orthotropic bicrystals. The role of the stress parallel to the interface, sigma0 is taken into account in these formulas. The interface crack can advance either by continued extension along the interface or by kinking out of the interface into one of the adjoining materials. This competition depends on the ratio of the energy release rates for interface cracking and for kinking out of the interface and the ratio of interface toughness to substrate toughness. Throughout the paper, the influences of the inplane stress sigma0 on the stress intensity factors and the energy release rates for the branched crack, which can significantly alter the conditions for interface cracking, are emphasized.

Higher-order analysis of crack tip fields in elastic power-law hardening materials

A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode 1. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.

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.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

Crack deflection at an interface between dissimilar elastic-materials

A crack intersecting an interface between two dissimilar materials may advance by either penetrating through the interface or deflecting into the interface. The competition between deflection and penetration can be assessed by comparison of two ratios: (i) the ratio of the energy release rates for interface cracking and crack penetration; and (ii) the ratio of interface to material fracture energies. Residual stresses caused by thermal expansion misfit can influence the energy release rates of both the deflected and penetrating crack. This paper analyses the role of residual stresses. The results reveal that expansion misfit can be profoundly important in systems with planar interfaces (such as layered materials, thin film structures, etc.), but generally can be expected to be of little significance in fiber composites. This paper corrects an earlier result for the ratio of the energy release rate for the doubly deflected crack to that for the penetrating crack in the absence of residual stress.

Slightly slanting impact on an elastic cantilever column-an experimental study

Experiments concerning slightly slanting impact between a flat-ended rigid body and a flat-ended elastic cantilever column with a rectangular cross-section have been performed. The experimental results are compared with the theoretical ones. The small angle of incidence was measured by using an optical method. The impact process was studied by using a split disc for the rigid body, with the two halves bonded together and electrically insulated from each other. The disc and the column were parts of an electric circuit. Different contact states could be distinguished according to different voltage levels. Reasonably good agreement between theory and experiment was found. Thus, the impact duration has its minimum under perfectly axial impact as predicted by the theory. Also, the predicted process of alternating line and surface contact was observed. Furthermore, the existence of a small critical angle of incidence was verified. This critical angle of incidence divides the impact processes into two categories: (1) The rigid body and the column end come into surface contact before separation. (2) They separate without surface contact. Comparison of axial strains between theory and experiment shows good agreement.

The influence of microcrack density on the elastic and fracture mechanical properties of stripa granite

Microcracks can have a strong influence on the elastic and fracture mechanical properties of rocks if they are numerous, or if they are orientated in unfavourable directions in anisotropic rocks in particular. This paper presents results from a great number of mechanical tests on Stripa granite containing various amounts of microcracks. Variations in the microcrack density were obtained by shock-heating the rock at different temperatures in the range 100–600°C for 3 h.

Elastic-plastic finite element analyses of short cracks

Stress and strain distributions and crack opening displacement characteristics of short cracks have been studied in single edge notch bend and centre cracked panel specimens using elastic–plastic finite element analyses incorporating both a non strain hardening and a power law hardening behaviour. J contour integral solutions to describe stress strain conditions at crack tips for short cracks differ from those for long cracks. The analyses show that (i) short cracks can propagate at stress levels lower than those required for long cracks and (ii) a two-parameter description of crack tip fields is necessary for crack propagation.

Elastic and statistically brittle (ESB) model, damage localization and catastrophic rupture

In this paper, an elastic and statistically brittle (ESB) model is applied to the process of damage evolution induced catastrophic rupture and the influence of localization and softening on catastrophic rupture is discussed. According to the analysis, the uncertainty of catastrophic rupture should be attributed to the unknown scale of localized zone. Based on the elastic and statistically brittle model but local mean field approximation, the relation between the scale of localized zone and catastrophic rupture is obtained and then justified with experiments. These results can not only give a deeper understanding of the mechanism governing catastrophic rupture, but also provide a possible tool to foresee the occurrence of catastrophic rupture.

Size-dependent elastic properties of Ni nanofilms by molecular dynamics simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

The surface- and size-dependent elastic moduli of nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.