Thermal stress wave and spallation induced by an electron beam

Thermal stress wave and spallation in aluminium alloy exposed to a high fluency and low energy electron beams are studied theoretically. A simple model for the study of energy deposition of electrons in materials is presented on the basis of some empirical formulae. Under the stress wave induced by energy deposition, microcracks and/or microvoids may appear in target materials, and in this case, the inelastic volume deformation should not vanish. The viscoplastic model proposed by Bodner and Partom with corresponding Gurson's yield function requires modification for this situation. The new constitutive model contains a scalar field variable description of the material damage which is taken as the void volume fraction of the polycrystalline material. Incorporation of the damage parameter permits description of rate-dependent, compressible, inelastic deformation and ductile fracture. The melting phenomenon has been observed in the experiment, therefore one needs to take into account the melting process in the intermediate energy deposition range. A three-phase equation of state used in the paper provides a more detailed and thermodynamical description of metals, particularly, in the melting region. The computational results based on the suggested model are compared with the experimental test for aluminium alloy, which is subjected to a pulsed electron beam with high fluency and low energy. (C) 1997 Elsevier Science Ltd.

Shock slip-relations for thermal and chemical nonequilibrium flows

This paper appears to be the first where the multi-temperature shock slip-relations for the thermal and chemical nonequilibrium flows are derived. The derivation is based on analysis of the influences of thermal nonequilibrium and viscous effects on the mass, momentum and energy flux balance relations at the shock wave. When the relaxation times for all internal energy modes tend to sere, the multi-temperature shock slip-relations are converted into single-temperature ones for thermal equilibrium hows. The present results can be applied to flows over vehicles of different geometries with or without angles of attack. In addition, the present single-temperature shock slip-relations are compared with those in the literature, and Some defects and limitations in the latter are clarified.

The effect of thermal-activation on dislocation processes at an atomistic crack-tip

The effects of thermal activation on the dislocation emission from an atomistic crack tip are discussed, Molecular dynamics simulations at different constant temperatures are carried out to investigate the thermal effects. The simulated results show that the processes of the partial dislocation generation and emission are temperature dependent. As the temperature increases, the incipient duration of the partial dislocation nucleation becomes longer, the critical stress intensity factor for partial dislocation emission is reduced and, at the same loading level, more dislocations are emitted. The dislocation velocity moving away from the crack tip and the separations of partial dislocations are apparently not temperature dependent. The simulated results also show that, as the temperature increases, the stress distribution along the crack increases slightly. Therefore stress softening at the crack tip induced by thermal activation does not exist in the present simulation. A simple model is proposed to evaluate the relation of the critical stress intensity factor versus temperature. The obtained relation is in good agreement with our molecular dynamics results.

Influence of inertial and thermal effects on the dynamic growth of voids in porous ductile materials

The influence of inertial, thermal and rate - sensitive effects on the void growth at high strain rate in a thermal - viscoplastic solid is investigated by means of a theoretical model presented in the present paper. Numerical analysis of the model suggests that inertial, thermal and rate - sensitive effects are three major factors which greatly influence the behavior of void growth in the high strain rate case. Comparison of the mathematical model proposed in the present work and Johnson's model shows that if the temperature - dependence is considered, material viscosity eta can take the experimentally measured values.

Effects of contact resistance on thermal-conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties ot these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.

Thermal-conductivity of periodic composite media with spherical inclusions

The thermal conductivity of periodic composite media with spherical inclusions embedded in a homogeneous matrix is discussed. Using Green's function, we show that the Rayleigh identity can be generalized to deal with the thermal properties of these systems. A technique for calculating effective thermal conductivities is proposed. Systems with cubic symmetries (including simple cubic, body centered cubic and face centered cubic symmetry) are investigated in detail, and useful formulae for evaluating effective thermal conductivities are derived.

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.

Local stresses and strains in axially cracked cylindrical shells

A perturbation solution is obtained for the local stress-strain fields in an axially cracked cylindrical shell. The tenth-order differential equations are used that take into account the transverse shear deformation. The perturbation of a curvature parameter, λ, is employed, where . The stress intensity factors for finite size cylindrical shells subjected to bending and internal pressure are evaluated. Sufficient accuracy can be obtained without using fine mesh sizes in regions near the crack tip. Also analyzed are the influence of cylinder diameter and shearing stiffness on bulging.

Mechanical and thermal structure of a cylindrical plume in the earth's mantle

A mantle plume is understood as a hot, narrow, upwelling flow in the earth's mantle and accompanied by an efficient transfer of mass and energy from deep to upper layer of the earth. The cylindrical plume in earth's mantle plays an important role in explaining the origin of the surface hot spots and linear island chains. From the basic hydrodynamical equations, the detailed mechanical and thermal structure of a cylindrical plume of Newtouian fluids with temperature and pressure-dependent viscosity are given in the present paper. For two sets of rheological parameters the radial profiles of upward velocity, temperature and viscosity in the plume and radiuses of the plume at various depths have been calculated.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.