Showing papers in "Journal of The Mechanics and Physics of Solids in 1985"
TL;DR: In this article, a general expression for the near-tip stress intensity factor in terms of the remote intensity factor was derived for the overall release-rate of a growing crack in elastic/rate-dependent plastic solids.
Abstract: At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10 3 s −1 to 10 5 s −1 . At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.
189 citations
TL;DR: In this paper, the kinematical shakedown theorem is used to investigate this mode of deformation for rolling and sliding point contacts, in which a Hertz pressure and frictional traction act on an elliptical area which repeatedly traverses the surface of a half-space.
Abstract: I n the plane-strain conditions of a long cylinder in rolling line contact with an elastic-perfectly-plastic half-space an exact shakedown limit has been established previously by use of both the statical (lower bound) and kinematical (upper bound) shakedown theorems. At loads above this limit incremental strain growth or “ratchetting” takes place by a mechanism in which surface layers are plastically sheared relative to the subsurface material. In this paper the kinematical shakedown theorem is used to investigate this mode of deformation for rolling and sliding point contacts, in which a Hertz pressure and frictional traction act on an elliptical area which repeatedly traverses the surface of a half-space. Although a similar mechanism of incremental collapse is possible, the behaviour is found to be different from that in two-dimensional line contact in three significant ways: (i) To develop a mechanism for incremental growth the plastic shear zone must spread to the surface at the sides of the contact so that a complete segment of material immediately beneath the loaded area is free to displace relative to the remainder of the half-space, (ii) Residual shear stresses orthogonal to the surface are developed in the subsurface layers, (iii) A range of loads is found in which a closed cycle of alternating plasticity takes place without incremental growth, a condition often referred to as “plastic shakedown”. Optimal upper bounds to both the elastic and plastic shakedown limits have been found for varying coefficients of traction and shapes of the loaded ellipse. The analysis also gives estimates of the residual orthogonal shear stresses which are induced.
175 citations
TL;DR: A series of plastic strain controlled cyclic tests was performed by applying combined axial force and torque to thin-walled tubular specimens of Type 316 stainless steel at room temperature as discussed by the authors.
Abstract: The title problem was discussed to facilitate the formulation of constitutive models of cyclic plasticity under general states of loading. A series of plastic strain controlled cyclic tests was performed by applying combined axial force and torque to thin-walled tubular specimens of Type 316 stainless steel at room temperature. These tests consist of cyclic loading along uniaxial, torsional, cruciform, stellate in eight directions, square and circular plastic strain paths with a constant amplitude of equivalent plastic strain. The results of these tests showed that the strain-hardening depends markedly on the shape of the plastic strain path, and that the strain-hardening (measured by equivalent stress amplitudes) in the saturated state is significant in the order of circular, square, stellate, cruciform and proportional paths. It was also observed that these saturated values were independent of the less significant plastic strain cycles experienced in the past. Finally, the characteristic features of strain-hardening mechanisms under non-proportional loadings were discussed in some detail on the basis of the present results.
131 citations
TL;DR: In this article, a generalization of the Differential Effective Medium Approximation (DEM) was proposed to the estimation of the effective permittivity of a two phase dielectric composite, and a canonical ordinary differential equation was derived which describes the change in material properties as a function of the volume concentration of the added phases in the composite.
Abstract: A generalization of the Differential Effective Medium approximation (DEM) is discussed. The new scheme is applied to the estimation of the effective permittivity of a two phase dielectric composite. Ordinary DEM corresponds to a realizable microgeometry in which the composite is built up incrementally through a process of homogenization, with one phase always in dilute suspension and the other phase associated with the percolating backbone. The generalization of DEM assumes a third phase which acts as a backbone. The other two phases are progressively added to the backbone such that each addition is in an effectively homogeneous medium. A canonical ordinary differential equation is derived which describes the change in material properties as a function of the volume concentration φ of the added phases in the composite. As φ→ 1, the Effective Medium Approximation (EMA) is obtained. For φ
130 citations
TL;DR: In this paper, the authors investigated the effect of frictional locking of the crack faces under the load and found that the range of SIF at the trailing tip ΔKT was about 30% greater than that of the leading tip ΔKL.
Abstract: The direction of propagation of rolling contact fatigue cracks is observed to depend upon the direction of motion of the load. In this paper approximate calculations are described of the variation of Mode II stress intensity factors at each tip of a subsurface crack, which lies parallel to the surface of an elastic half-space, due to a load moving over the surface. In particular the effect of frictional locking of the crack faces under the load is investigated. In consequence of frictional locking the range of SIF at the trailing tip ΔKT is found to be about 30% greater than that of the leading tip ΔKL, which is consistent with observations that subsurface cracks propagate predominantly in the direction of motion of the load over the surface. The effects on kt and klof crack length, crack face friction, traction forces at the surface and residual shear stresses are also investigated.
125 citations
TL;DR: In this article, the authors considered fracture energy and fracture dynamics and extended Mott analysis to explicitly account for energy dissipation during the fracture process, and showed that communication between growing fractures is relatively slow.
Abstract: The present study considers concepts relating fracture energy and fracture dynamics. Analyses of Mott are expanded to explicitly account for energy dissipation during the fracture process. Expressions are obtained for the nominal fragment size, fracture time, and dynamic fracture strain. It is shown that communication between growing fractures is relatively slow. Numerical analysis is used to examine the interaction of ductile fractures and the conditions that may lead to arrest or completion of growing fractures.
118 citations
TL;DR: In this article, large deformation finite element analysis has been used to study the near crack tip growth of long cylindrical holes aligned parallel to the plane of a mode I plane strain crack.
Abstract: Large deformation finite element analysis has been used to study the near crack tip growth of long cylindrical holes aligned parallel to the plane of a mode I plane strain crack. The near crack tip stress and deformation fields are analyzed. The results show that the holes are pulled towards the crack tip and change their shape to approximately elliptical with the major axis radial to the crack. They also grow faster directly ahead of the crack than at an angle to the crack plane. Several crack-hole coalescence criteria are discussed and estimates for the conditions for fracture initiation are given and compared with experimental results. The range of estimates now available from finite element calculations coincides quite well with the range of experimental data for materials containing inclusions which are only loosely bonded to the matrix.
109 citations
TL;DR: In this paper, a plasticity theory is introduced which starts with a dilatancy rule and a function of plastic strain rates which represents the energy dissipated during plastic deformation.
Abstract: A plasticity theory is introduced which starts with a dilatancy rule and a function of plastic strain rates which represents the energy dissipated during plastic deformation. Yield surfaces and flow rules are then derived using energy conservation and the theory of envelopes. This method allows valid plasticity theories to be derived for frictional materials, but gives results for non-frictional materials which are identical to those of the classical theories. A dissipation function which includes deformation by granule rearrangement and granule distortion is presented and used to obtain a range of yield surfaces and flow rules, which are similar to those used in the critical state theory of soil mechanics. The microstructural features which may control the governing parameters of the dissipation functions are discussed.
92 citations
TL;DR: In this article, the authors used symmetry arguments to derive the dimensionality and extent of the space necessary for representing the yield surface under various conditions of anisotropy in polycrystal materials.
Abstract: T he plastic anisotropy of a material is characterized in part by its yield surface. It is shown that conventional descriptions, based on extensions of the von Mises hypothesis for isotropic materials, are experimentally and theoretically inadequate in many instances. Symmetry arguments are used to derive the dimensionality and extent of the space necessary for representing the yield surface under various conditions of anisotropy. A useful concept is introduced: “closed” subspaces, in which sections and projections of the yield surface are identical and in which, therefore, normality is complete. Yield surfaces of heavily rolled or sheared sheets are derived from a computer simulation of polycrystal plasticity. It is found that even mild textures give rise to significant departures from “oval” yield surfaces: they develop sharp ridges and extensive flats. The anisotropy coefficients for in-plane tension of rolled sheets have been calculated. For torsion testing under fixed and free end conditions, respectively, the axial force and the length change have been calculated, as well as the change in the ratio of wall thickness to diameter.
79 citations
TL;DR: In this paper, the entire load deformation history of a cylindrical tensile bar is computed using the finite element method in conjunction with hill's (1958, 1959) variational principle.
Abstract: N ecking and neck propagation as observed in polymers which “cold draw” is analyzed numerically for a circular cylindrical tensile specimen. The entire load-deformation history of the bar is computed using the finite element method in conjunction with hill's (1958, 1959) variational principle. Rate-independent elastic-plastic material behaviour is assumed. Results are given for the overall load-elongation response of the bar, as well as for the evolution of the specimen profile and the stress and strain distributions in the bar at various stages of the deformation process. The implications of our results on conventional methods used to analyze tension data for polymers are also discussed.
67 citations
TL;DR: In this paper, the influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied, and the relationship between the applied crack driving force, represented by a remote stress intensity factor and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion.
Abstract: The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J 2 flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.
TL;DR: In this paper, the authors analyzed cracks in ductile single crystals for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields.
Abstract: Cracks in ductile single crystals are analyzed here for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by Rice (1967, 1984) and Freund (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.
TL;DR: For polycrystalline metals undergoing creep at high temperatures, the nucleation, growth and coalescence of grain boundary cavities are investigated in this paper, with main focus on the influence of grain boundaries sliding.
Abstract: For polycrystalline metals undergoing creep at high temperatures the nucleation, growth and coalescence of grain boundary cavities is investigated, with main focus on the influence of grain boundary sliding. Both the local stress state and the average rate of opening of a cavitating facet can be rather strongly affected by sliding on the grain boundaries emanating from the edges of this facet. A number of numerical solutions of axisymmetric model problems are used to study the combined influence of sliding and cavitation. The time to creep rupture by cavity coalescence is significantly reduced by grain boundary sliding, as is seen by comparison with analyses that disregard sliding. The numerical results are compared with predictions of a set of constitutive relations for creep in polycrystals with grain boundary cavitation.
TL;DR: In this paper, a variational formulation for wave propagation through dry or fluid-saturated porous elastic media is derived using a Lagrangian (rather than Eulerian) reference frame locked to the solid constituent.
Abstract: Nonlinear equations for wave propagation through dry or fluid-saturated porous elastic media are derived using a variational formulation. The method presented is very similar to the approach of Bedford and Drumheller, including microinertia terms for local density fluctuations of fluid and solid. One major difference is the choice of a Lagrangian (rather than Eulerian) reference frame locked to the solid constituent. This choice of reference frame is preferable for porous solids and also allows direct comparison to Biot's theories of nonlinear and semilinear rheology of porous solids.
TL;DR: In this article, a laser interferometer system is used to monitor the normal and transverse components of motion of a point at the rear surface of a target plate, and the experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material.
Abstract: T he pressure-shear plate impact technique is used to study material behavior at high rates of deformation. In this technique, plastic waves of combined pressure and shear stresses are produced by impact of parallel plates skewed relative to their direction of approach. Commercially pure alpha-titanium and 6061-T6 aluminum are tested under a variety of pressure and shear tractions by using different combinations of impact velocities and angles of inclination. A laser interferometer system is used to monitor simultaneously the normal and transverse components of motion of a point at the rear surface of the target plate. The experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material. Both isotropic and kinematic strain hardening models are used in the computations. The results indicate that unlike the normal velocity profiles, the transverse velocity profiles are sensitive to the dynamic plastic response and, thus, can be used to study material behavior at high strain rates. For the materials tested the results suggest that the flow stress required for plastic straining increases markedly with increasing strain rate at strain rates above 104s−1. Hydrostatic pressure of the order that exists in the tests (up to 2 GPa) does not affect the plastic flow in 6061-T6 aluminum and appears to have at most a minor effect on the deformation of the titanium.
TL;DR: The Kramers-Kronig relations as mentioned in this paper has been shown to provide the dynamic response of a random fibrous composite for the full frequency interval, 0 < ω < ∞.
Abstract: The Kramers-Kronig relations method is shown to provide the dynamic response of a random fibrous composite for the full frequency interval, 0 < ω < ∞. The method yields a conceptually simple way of deriving the dynamic response of random composites if the approximation of an effective homogeneous medium is adopted.
It is shown that some of the widely accepted theories may violate the causality and/or linearity of the effective medium. Extensive numerical data are given as well as comparison with other theories and experiments.
TL;DR: In this paper, a Gaussian probability distribution for internal stress and strain fields in disordered elastic solids such as multiphase materials or polycrystals is derived subject to constraints representing the basic equations of elasticity and experimental data.
Abstract: Internal stress and strain fields in disordered elastic solids such as multiphase materials or polycrystals are considered. In order to derive a probability distribution for those random internal fields, the information theory entropy is maximized subject to constraints representing the basic equations of elasticity and certain experimental data. Thus one can find the probability distribution which agrees with all known facts but makes no assertions about the internal fields which cannot be supported by the available information. This approach is in accordance with the formal exact solution of the statistical problem if one has complete microstructural information. In case of incomplete microstructural data, useful approximate solutions can easily be obtained. In particular, the following set of data is sufficiently detailed for the prediction of internal field fluctuations: the average strain, the one-point probability density of the random elastic constants, and the effective (overall) elastic constants. Especially the information supplied by the effective elastic constants plays a major role since it reflects the microstructural topology of the heterogeneous material. One obtains Gaussian probability distributions for stress and strain, which are applied to calculate mean values and fluctuations of stresses in a cemented metal carbide and a zinc polycrystal.
TL;DR: In this paper, the authors investigated the plastic bifurcation of an initially flat circular plate held frictionlessly between a blankholder and a die and deformed by a spherically shaped punch.
Abstract: THE PROBLEM investigated here is the plastic bifurcation of an initially flat circular plate held frictionlessly between a blankholder and a die and deformed by a spherically shaped punch. In view of the large deviations of the prebifurcation solution from proportional loading, a recently developed phenomenological corner theory has been employed and an appropriate bifurcation criterion has been developed. The effects of geometry and material properties on the onset of the (nonaxisymmetric) plastic instability have been investigated using a numerical solution of the resulting equations based on the finite element method.
TL;DR: In this article, a general formulation of the analysis of the channel die compression test for single crystals, to second order in the applied compressive load increment, is presented, with a strong recommendation for a new series of channel die experiments.
Abstract: In this paper we present a general formulation of the analysis of the channel die compression test for single crystals, to second order in the applied compressive load increment. Specific first- and second-order analyses of f.c.c. crystals in orientation [110] [001] [110] are carried out for the same four hardening rules considered in Sue and Havner (1984). These are Taylor hardening, a 2-parameter empirical rule, the “simple theory” (Havner and Shalby, 1977), and a modification of the simple theory introduced by Peirce, Asaro and Needleman (1982). In particular, we address the analysis of lattice rotation about the loading axis for each of these theories. Such rotation was a prominent feature of the deformation of a copper crystal in this orientation in experiments by Wonsiewicz and Chin (1970). We establish that all theories permit this rotation consistent with the first- and second-order channel die constraints. Regarding the issue of lattice stability, a fundamental difference between the present orientation and those analyzed in Sue and Havner (1984) is uncovered and discussed. We close with a strong recommendation for a new series of channel die experiments.
TL;DR: In this paper, a theoretical analysis of the acoustoelastic effect of sound wave propagation in a stressed heterogeneous weakly anisotropic elastic medium composed of grains is presented.
Abstract: A theoretical analysis of the acoustoelastic effect is presented. It is based upon the theory of sound wave propagation in a stressed heterogeneous weakly anisotropic elastic medium composed of grains. The effect of residual stress is included, and shown to be different from that of applied stress. The statistics of grain orientation and of grain correlation are taken into account. The acoustoelastic coefficients and the effects of dispersion, attenuation and symmetry of the medium are determined.
TL;DR: In this article, the second-order rate boundary value problem with quasistatic accelerations as unknowns is formulated for a time-independent elastic-plastic material, obeying the normality flow rule with a smooth yield surface.
Abstract: Second-order rate constitutive equations are formulated for a time-independent elastic-plastic material, obeying the normality flow rule with a smooth yield surface. Under specified regularity restrictions imposed on the involved fields, the regular second-order rate boundary value problem with quasistatic accelerations as unknowns is posed. It is shown that every solution of this generally non-linear rate problem is governed by a variational principle and that the corresponding functional reaches a strict absolute minimum, provided the solution satisfies a sufficient uniqueness condition. With the same incrementally linear comparison solid, Hill's exclusion condition rules out not only a first- but also a second-order bifurcation. The criticality of the exclusion condition is discussed and conditions are indicated under which a second-order bifurcation becomes possible, while the first-order rate problem is still uniquely solvable.
TL;DR: In this paper, the other three overall elastic moduli in the simplified stress-strain relations of Walpole (1985) are placed between upper and lower, Voigt and Reuss, bounds and some exact calculations are given for particular fibre textures.
Abstract: The crystals and the aggregate have the same bulk modulus. The other three overall elastic moduli in the simplified stress-strain relations of Walpole (1985) are placed between upper and lower, Voigt and Reuss, bounds and some exact calculations are given for particular fibre textures.
TL;DR: A cubic crystal is elastically isotropic to the extent that its linear compressibility is independent of direction as mentioned in this paper, and an anisotropic aggregate of cubic crystals exhibits the same property to the same magnitude in an overall sense.
Abstract: A cubic crystal is elastically isotropic to the extent that its linear compressibility is independent of direction An anisotropic aggregate of cubic crystals exhibits the same property to the same magnitude in an overall sense and its stress-strain relation is therefore simplified
TL;DR: In this paper, the authors constructed constitutive relations of differential-type from typical qualitative response for fluid-saturated sands under cyclic shear loads in both free draining and undrained conditions.
Abstract: Fluid-saturated sands exhibit irreversible compaction and shear hysteresis under cyclic shear loads in both free draining and undrained conditions. Constitutive relations of differential-type are constructed heuristically from typical qualitative response. An influence of pore pressure on compaction is incorporated, and the generation of pore pressure under cyclic shearing is investigated. Parameter variations in the shear relations allow a variety of hysteresis loop behaviours to be described.
TL;DR: In this article, the authors take a phenomenological (topological) look at the Shanley model and trace the possible loading sequences of a perfect system in closed form, and compare the asymptotic predictions of a standard perturbation procedure and a new scheme developed in accordance with the underlying topology.
Abstract: The paper takes a phenomenological (topological) look at the Shanley model. Allowable loading sequences of a perfect system are first traced in closed form. By employing the smoothly-varying properties of an associated elastic potential function, comparisons are then made between the asymptotic predictions of a standard perturbation procedure, and a new scheme developed in accordance with the underlying topology. The new scheme is found to converge rapidly to the exact equilibrium paths, indicating compatibility in a global as well as a localized sense.
TL;DR: In this paper, a compaction theory for saturated sand, of differential type, is applied to shear wave propagation through a layer induced by cyclic horizontal acceleration of its base.
Abstract: A compaction theory for saturated sand, of differential type, is applied to shear wave propagation through a layer induced by cyclic horizontal acceleration of its base. The compaction relation incorporates dependence on the pore fluid pressure, and in turn the pore pressure is related to the compaction through the elastic compression relations. An assumption of undrained flow, which will yield the maximum pore pressures, allows straightforward numerical solution of the simplified dynamic equations. A variety of results are computed for comparison with alternative predictions.
TL;DR: In this paper, an alternative derivation to that given by Mehrabadi and Cowin (1978) is presented for a pair of kinematic equations governing a certain class of flows in the plastic deformation of dilatant granular materials.
Abstract: An alternative derivation to that given by Mehrabadi and Cowin (1978) is presented here for a pair of kinematic equations governing a certain class of flows in the plastic deformation of dilatant granular materials. This class has been described by Spencer (1981) as double shearing flows. In their derivation Mehrabadi and Cowin (1978), prior to presenting the equations relative to rectangular Cartesian coordinates, obtained an intermediate pair of equations relative to a non-orthogonal network of characteristic coordinates. The essential difference between the original and present derivation is that here, the flow rule, expressed relative to rotating, rectangular Cartesian coordinates, is transformed directly to obtain the kinematic equations relative to fixed rectangular Cartesian coordinate axes, without the need to obtain the characteristic equations.
TL;DR: In this article, a mathematical model is proposed, developed from physical considerations, which is based upon the continuum, plane strain, rigid-plastic theory for double-shearing flows of compressible granular materials.
Abstract: The mechanical behaviour of the broken rock material occupying the waste region of a long-wall mineworking is investigated. A mathematical model is proposed, developed from physical considerations, which is based upon the continuum, plane strain, rigid-plastic theory for double-shearing flows of compressible granular materials. The model comprises the stress equilibrium equations, the Coulomb yield criterion, kinematic equations due to Mehrabadi and Cowin (1978) and the continuity equation, together with the waste region geometry and the boundary conditions imposed upon the field variables. Statical indeterminancy is a property of the formulation and this results in a connection between the stress and velocity fields through the boundary conditions. A strategy is presented for the iterative construction of the stress and velocity fields and approximations to solutions of the equations of the model are obtained numerically.
TL;DR: In this article, a new class of boundary-value problems in mathematical elasticity is proposed, wherein the medium flows steadily relative to a non-embedded surface over which tractions or velocities are prescribed.
Abstract: A new class of boundary-value problems in mathematical elasticity is proposed, wherein the medium flows steadily relative to a non-embedded surface over which tractions or velocities are prescribed. Such flows are seen in metal forming operations where purely elastic streams enter and leave the working zone. The deformations are assumed here to be plane and isochoric. A general solution is formulated in terms of two complex potentials. Residual stress is accounted for in detail and a uniqueness theorem is proved. Some simple flows are examined, but it remains to develop a systematic procedure for matching the general solution to arbitrary boundary data.
TL;DR: In this article, the results of experiments on fiber-reinforced metal beams which have been subjected to dynamic transverse loading were described, and the deformations were monitored by a number of different experimental techniques and the final plastic transverse deflection of the tip as well as the position of the plastic wave front were compared with the theoretical predictions of Spencer, Jones and their co-workers.
Abstract: The paper describes the results of experiments on fiber-reinforced metal beams which have been subjected to dynamic transverse loading. The beams were fabricated by embedding sets of parallel steel wires in a matrix of lead-tin alloy, and were clamped at one end. The transverse dynamic loading was applied to the tip of the beam so that the problem was one of the transverse deformation of a composite cantilever. Two separate techniques were employed to load the specimens, one being to hit the end with a fast moving hammer in a “Hyge” Shock Testing Machine; the other was to detonate an explosive charge in contact with a small projectile close to the tip. The deformations were monitored by a number of different experimental techniques and the final plastic transverse deflection of the tip as well as the final position of the plastic wave front were compared with the theoretical predictions of Spencer, Jones and their co-workers. The agreement was found to be very satisfactory. In making these comparisons strain rate effects in the lead-tin matrix metal had to be allowed for and this was done with the help of a separate set of tests.