Y. Benveniste

A continuum model for fiber reinforced materials with debonding

Abstract A continuum theory for a fiber-reinforced material with debonding between the constituents is presented. The debonding phenomenon is simulated by imposing the continuity of the normal displacements at the fiber-matrix interfaces while allowing free tangential slip there. The derived theory is of the lowest order and is obtained by using a first order expansion in the displacements in the fiber and matrix phases. The theory is applied to investigate the effect of debonding on the propagation of waves in a boron/epoxy fiber reinforced material. It is shown that an additional mode of propagation is obtained as compared with the usual case of perfect bonding

Steady state propagation of a mode III interface crack between dissimilar viscoelastic media

Abstract The steady state propagation of a semi-infinite crack between two dissimilar viscoelastic solids is considered. By means of the Wiener-Hopf technique, the stress intensity factor is found as a function of the crack tip velocity and the material parameters. Results for an interface crack between an elastic and a viscoelastic medium are obtained as a special case. Various limiting cases are examined as a check on the accuracy of the results. Finally, graphs are presented which examine the salient features of the stress intensity factor.

On the thermomechanics of composites with imperfectly bonded interfaces and damage

Abstract General connections are established between the mechanical and thermal responses of composite materials with debonded or imperfectly bonded interfaces, and with internal cracks or cavities. In particular, such results are found for multiphase composites or polycrystals in which normal and/or shear displacement jumps may exist at interfaces or cracks, consistent with complete debonding or with the presence of a nonlinearly elastic interphase layer. In two-phase systems with isotropic phases and sliding interfaces, we also recover exact connections between the mechanical and thermal stress or strain fields in the phases.

A mixture theory for wave propagation in a laminated medium with debonding

Abstract In this paper wave propagation in the direction of the layering of a bi-laminated medium with the presence of imperfect bonding at the interfaces is investigated. The debonding mechanism is represented by a model which allows imperfect bonding both in the normal and tangential directions. A mixture theory is formulated in which every constituent has its own motion but is allowed to interact with the others. The resulting theory is applied to transient wave propagation in the laminated composite. It is shown that debonding in the tangential direction is significant in modifying the shape and amplitude of the propagating wave.

One-dimensional finite amplitude wave propagation in a compressible elastic half-space

Abstract The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible half space is considered. The half space is subject on its surface to time dependent arbitrary normal and shear loadings. The problem is solved by employing a certain stable numerical scheme which prevents almost all the numerical oscillations which usually occur near shocks when a standard finite difference scheme is applied.

The Saint-Venant torsion of a circular bar consisting of a composite cylinder assemblage with cylindrically orthotropic constituents

We consider the Saint-Venant torsion of a cylindrical rod of a circular cross section which is filled up by an assemblage of composite circular cylinders. The constituent cylinders consist of a core and a coating both of which are cylindrically orthotropic with the volume fraction of the core being the same in every composite cylinder. The described microstructure is the composite cylinder assemblage of Hashin and Rosen [J. Appl. Mech. 29 (1964) 143] which is now subjected to torsion. The main results are (a) the warping function on the lateral surface of the host rod is zero, (b) an exact expression for the torsional rigidity of the host rod is derived which depends on the size distribution of the composite cylinders but not on their position and (c) there are two circumstances in which the torsional rigidity becomes size distribution independent: The first one is that in which the sizes of the composite cylinders are much smaller than the size of the host rod; the second one is that in which a certain specific relation holds between the properties of the composite cylinder and the volume fraction of the core. If the coating disappears and the core is cylindrically orthotropic, we get the configuration of a polycrystalline rod. Simple bounds for the torsional rigidity of the constructed composite rod are obtained.

An average theory for the dynamic behaviour of a laminated elastic-viscoplastic medium under general loading☆

Abstract An average theory which models the dynamic behaviour of a bi-laminated composite medium made of elastic-viscoplastic work hardening constituents is presented. The resulting effective theory is represented by a system of nonlinear differential equations for the average stresses, displacements and the plastic work. The theory can be applied to three-dimensional problems under general types of loading. The theory is applied for the special cases of waves propagating normal to the layering and for waves propagating in a thin composite rod.

A 2-dimensional mixture theory for biaxially fiber reinforced composites with application to dynamic crack problems

Abstract A 2-dimensional mixture theory is developed for wave propagation in a laminated medium in which every layer is made of a fiber reinforced composite material with the angle of reinforcement alternating from layer to layer. The developed theory contains as special cases the 2-dimensional mixture theory for a laminated medium made of isotropic layers, as well as the equivalent modulus theories for bi-directionally and unidirectionally fiber reinforced composites. The developed mixture theory is applied to the problem of a semi-infinite crack in the composite which is under dynamic loading. The induced fracture mode of the crack is of mixed type and contains both Mode I and Mode II types of opening. A numerical method of solution is applied to the four coupled mixture equations of motion in the average displacements and results are given for the dynamic stress fields in the composite.

Finite amplitude one-dimensional wave propagation in a thermoelastic half-space

Abstract The problem of finite wave propagation in a nonlinearly thermoelastic half-space is considered. The surface of the half-space is subjected to a time-dependent thermal and normal mechanical loading. The solution is obtained by a numerical procedure, which is shown to furnish accurate results, and linear dynamic thermoelastic problems are obtained as special cases. The accuracy of the results is checked by comparison with some known analytical solutions which can be obtained in some special cases of both the linear and the nonlinear problems. In those cases where the solution contains shocks, it is shown that the numerical results satisfy the necessary jumps conditions which need to hold across such discontinuities.

Torsion of compound cross-sections with imperfect interface

SummaryThe Saint-Venant torsion problem of compound sections with imperfect interfaces is studied. Two kinds of an imperfect interface are considered: an imperfect interface which models a thin interphase of low shear modulus and an interface which models a thin interphase of high shear modulus. At the former kind, the tractions are continuous but the warping displacement undergoes a discontinuity; at the latter kind the warping displacement is continuous but the shear traction undergoes a discontinuity. These imperfect interface conditions have been derived in a companion study [1]. The present paper is concerned with deriving benchmark solutions for the Saint-Venant torsion problem of compound sections with imperfect interfaces. Specifically, analytical solutions are given for a) a two-phase rectangular section, b) a two-phase section in the shape of a circular sector with an imperfect interface located along a circular arc, c) a two-phase circular sector with an imperfect interface along a radial line. The effect of imperfect bonding on the torsional rigidity of the compound bar is examined.