Dynamic stress intensity factor KⅢ and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials,the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated.Stress,strain and displacement around the crack tip are expressed as an analytical complex function,which can be represented in power series.Constant coefficients of series are determined by boundary conditions.Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained.Components of dynamic stress,dynamic strain and dynamic displacement around the crack tip are derived.Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials,i.e.,crack propagation velocity M and the parameter α.The faster the crack velocity is,the greater the maximums of stress components and dynamic displacement components around the crack tip are.In particular,the parameter α affects stress and dynamic displacement around the crack tip.     

Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips

The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

The collinear crack problem for an orthotropic functionally graded coating–substrate structure

A theoretical treatment of antiplane crack problem of two collinear cracks on the two sides of and perpendicular to the interface between a functionally graded orthotropic strip bonded to an orthotropic homogeneous substrate is put forward. Various internal cracks and crack terminating at the interface and crack crossing the interface configurations are investigated, respectively. The problem is formulated in terms of a singular integral equation with the crack face displacement as the unknown variable. The asymptotic stress field near the tip of a crack crossing the interface is examined, and it is shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case, the “kink” in material property at the interface does not introduce any singularity. Numerical calculations are carried out, and the influences of the orthotropy and nonhomogeneous parameters and crack interactions on the mode III stress intensity factors are investigated.     

Mixed mode fracture of a piezoelectric–piezomagnetic bi-layer structure with two un-coaxial cracks parallel to the interface and each in a layer

The purpose of the present work is to study the mixed mode fracture of a piezoelectric–piezomagnetic composite with two un-coaxial cracks parallel to the interface and each in a layer. Methods of generalized dislocation simulation, Green’s function, Cauchy singular integral equation and Lobatto–Chebyshev collocation are combined together to get the numerical results of mechanical strain energy release rate (MSERR). Three kinds of effects are revealed by parametric studies, i.e., the free-surface effect, the shielding effect and the interference effect, and they are used to interpret the characteristics of COD and MSERR curves. In addition, the effects of shear loading, magnetic loading and electric loading on MSERR are also disclosed, respectively, by varying the corresponding loading factor.     

Turbulence structure in the immediate vicinity of the shear-free air–water interface induced by a deeply submerged jet

 A PIV based technique is developed to perform flow measurements in the vicinity of the air–water interface of a submerged confined jet. Both the interface movement and the velocity field immediately beneath it are measured simultaneously. A detailed turbulence structure in the surface influence region is thus obtained. Flow parameters evaluated without and w.r.t. the interface are quantified and compared against previous works obtained using the conventional Eulerian-based instrumentation which do not account for the interface fluctuation, and checked against analytical model characterising the turbulence close to a assumed flat air–water interface. Received: 15 March 1998/Accepted: 19 October 1998     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Crack paths in three-dimensional elastic solids. i: two-term expansion of the stress intensity factors—application to crack path stability in hydraulic fracturing

The aim of this work is to lay theoretical foundations for the prediction of crack paths within the theory of quasistatic LEFM under the most general hypotheses: arbitrary three-dimensional geometry, arbitrary loading. This objective requires to derive the expression of the stress intensity factors along the crack front after an arbitrary infinitesimal propagation. Only the first two terms of their expansion in powers of the crack extension length δ, proportional to δ⁰ = 1 and δfn1fn2, are considered in this paper. Fully general formulae for these terms are obtained by combining arguments of dimensional analysis (scale changes) and regularity properties (continuity, differentiability) of the stresses at a fixed, given point with respect to δ for δ = 0 derived from the Bueckner–Rice weight function theory. This notably allows to extend the Cotterell–Rice criterion for stable rectilinear propagation of a mode I crack under plane strain conditions to the three-dimensional case. As an application, a penny-shaped crack induced by hydraulic fracturing is considered. Conclusions concerning the influence of the orientation and depth of such a crack upon the stability of its coplanar propagation seem to be compatible with experimental evidence.     

Dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed loading

In transversely isotropic elastic solids, there is no surface wave for anti-plane deformation. However, for certain orientations of piezoelectric materials, a surface wave propagating along the free surface (interface) will occur and is called the Bleustein–Gulyaev (Maerfeld–Tournois) wave. The existence of the surface wave strongly influences the crack propagation event. The nature of anti-plane dynamic fracture in piezoelectric materials is fundamentally different from that in purely elastic solids. Piezoelectric surface wave phenomena are clearly seen to be critical to the behavior of the moving crack. In this paper, the problem of dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed dynamic anti-plane loadings on crack faces is studied. Four situations for different combination of shear wave velocity and the existence of MT surface wave are discussed to completely analyze this problem. The mixed boundary value problem is solved by transform methods together with the Wiener–Hopf and Cagniard–de Hoop techniques. The analytical results of the transient full-field solutions and the dynamic stress intensity factor for the interfacial crack propagation problem are obtained in explicit forms. The numerical results based on analytical solutions are evaluated and are discussed in detail.     

Propagation of a mode-III interfacial crack in a piezoelectric–piezomagnetic bi-material

The transient response of a semi-infinite mode-III interfacial crack propagating between piezoelectric (PE) and piezomagnetic (PM) half spaces is investigated in this paper. The integral transform method together with the Wiener–Hopf and Cagniard–de Hoop techniques is used to solve the mixed boundary value problem under consideration. The existence of generalized Maerfeld–Tournois interfacial wave is discussed and the solutions of the coupled fields are derived for four different cases of bulk shear wave velocity. The dynamic intensity factors of stress, electric displacement and magnetic induction as well as energy release rate (ERR) are obtained in explicit forms. The numerical results of the universal functions and dimensionless ERR for several different material combinations are presented and discussed in details. It is found that the Bleustein–Gulyaev (generalized Maerfeld–Tournois) waves dominate the dynamic characteristics of the interfacial crack propagation in PE–PM bi-material.     

An approach to predict human–structure interaction in the case of staircases

Archive of Applied Mechanics - This paper presents a general approach for modelling human–structure interaction in the case of vertical vibrations that is based on a model of the system and...     

Multiple crack propagation along the interface of a non-homogeneous composite subjected to anti-plane shear loading

The present work concerns with the multiple crack propagation along the interface of two bonded dissimilar strips. The crack faces are subjected to anti-plane shear traction. Galilean transformation is employed to reduce the problem to a quasi-static one. Then, using Fourier transforms and asymptotic analysis, the quasi-static problem is reduced to a pair of singular integral equations. That are solved numerically, using Gauss-Chebyshev integration formulae. The values of the dynamic stress intensity factors are obtained and compared with the previous similar works. Further, a parametric study is introduced to investigate the effect of crack growth rate, geometric and elastic characteristics of the composite on the values of dynamic stress intensity factors.     

Gas–Dynamic Structures in Supersonic Combustion of Hydrogen in a System of Plane Jets in a Supersonic Flow

Results of numerical and theoretical studies of supersonic diffusive combustion of a system of plane hydrogen jets in a supersonic air flow are described. It is shown that large–scale vortex structures appear in the mixing zone of the system of hydrogen jets and the cocurrent flow. These vortex structures affect the mechanism of turbulent exchange between the fuel and the oxidizer.     

The study of a ratio-dependent predator–prey model with stage structure in the prey

In this paper, a ratio-dependent predator–prey model with stage structure in the prey is constructed and investigated. In the first part of this paper, some sufficient conditions for the existence and stability of three equilibriums are obtained. In the second part, we consider the effect of impulsive release of predator on the original system. A sufficient condition for the global asymptotical stability of the prey-eradication periodic solution is obtained. We also get the condition, under which the prey would never be eradicated, i.e., the impulsive system is permanent. At last, we give a brief discussion.

     

Influence of conicity on the stress–strain state of a flexible orthotropic conical shell in a nonstationary magnetic field

A problem of magnetoelasticity for a flexible conical shell in a nonstationary magnetic field is solved. The effect of conicity on the stress–strain state of the shell is analyzed     

Implementation of the exploding wire technique to study blast-wave–structure interaction

The effort invested in improving our understanding of the physics of high-energy explosion events has been steadily increasing since the latter part of the twentieth century. Moreover, the dramatic increase in computer power over the last two decades has made the numerical simulation approach the dominant tool for investigating blast phenomena and their effects. However, field tests, on both large and small scales, are still in use. In the current paper, we present an experimental tool to better resolve and study the blast–structure interaction phenomenon and to help validate the numerical simulations of the same. The experimental tool uses an exploding wire technique to generate small-scale cylindrical and spherical blast waves. This approach permits safe operation, high repeatability, and the use of advanced diagnostic systems. The system was calibrated using an analytical model, an empirical model, and numerical simulation. To insure that spherical blast geometry was achieved, a set of free air blast experiments was done in which high-speed photography was used to monitor the blast structure. A scenario in which an explosion occurred in the vicinity of a structure demonstrated the system’s capabilities. Using this simple but not trivial configuration showed unequivocally the effectiveness of this tool. From this comparison, it was found that at early times of blast–structure interaction, the agreement between the two sets of results was very good, but at later times incongruences appeared. Effort has been made to interpret this observation. Furthermore, by using similitude analysis, the results obtained from the small-scale experiments can be applied to the full-scale problem. We have shown that an exploding wire system offers an inexpensive, safe, easy to operate, and effective tool for studying phenomena related to blast-wave–structure interactions.     

Simulation of local instabilities during crack propagation in the ductile–brittle transition region

The crack propagation for a cohesive zone model within an elastic-plastic material under small-scale yielding conditions is simulated numerically. The resulting crack growth resistance curves show local instabilities, so-called pop-ins even for homogeneous cohesive properties if the cohesive strength lies sufficiently close to the maximum stress of the corresponding blunting solution. The formation of secondary cracks and unloading zones in front of the actual crack tip is identified as the underlying mechanism. It is found that the shape of the cohesive law has a considerable influence on the crack arrest behavior. Furthermore, requirements to the mesh resolution are derived.     

A priori study for the modelling of velocity–interface correlations in the stratified air–water flows

This work concerns the modelling of stratified two-phase turbulent flows with interfaces. We consider an equation for an intermittency function which denotes the probability of finding an interface at a given time t and a given point . In Wacławczyk and Oberlack (2011) a model for the unclosed terms in this equation was proposed. Here, we investigate the performance of this model by a priori tests, and finally, based on the a priori data discuss its possible modification and improvements.