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There have been indications that the flow stress level in the plastically flowing part of a long rod penetrator may have a significant influence on the penetration efficiency. We refer to this phenomenon as the projectile-flow effect. We performed a series of AUTODYN runs to investigate the projectile-flow effect. We show that when the projectile material hardens/softens as it flows, its penetration can be reduced/enhanced significantly. We also show that the projectile-flow effect is less pronounced at high velocities, and is enhanced for high L/D penetrators. It seems that the L/D effect at high L/D may be explained by the projectile-flow effect.

It has been known for some time that, for a given target, a flat cross section projectile would penetrate deeper than a circular cross section projectile, other factors being equal. This invoked the idea that a cruciform cross section projectile would have an advantage over the circular cross section projectile. We used AUTODYN2D to simulate penetration of steel and tungsten alloy projectiles into steel targets for axial and planar symmetries. The purpose was to see to what extent the planar projectiles have an advantage over circular projectiles. We found that: planar projectiles penetrate more than circular projectiles at low velocities (1.5 km/s); planar projectiles lose their advantage with increasing velocity; much larger target dimensions are needed for full confinement of planar projectiles; and craters created by planar projectiles are much wider and their width is not constant.

Elastic-viscoplastic constitutive equations based on two internal state variables are utilized to determine material response for uniaxial cyclic loading conditions. These equations are capable of representing the principal features of cyclic loading behavior including softening upon stress reversal, cyclic hardening or softening, tendency towards a stable limit cycle, cyclic relaxation, and cyclic creep. Calculations were performed for various stress and strain controlled conditions using material constants intended to represent commercially pure titanium and aluminum and OFHC copper. Capabilities and limitations of the analytical formulations are discussed in relation to computed results and corresponding test data. (Author)

The constitutive equations that have been developed by the authors to represent elastic-viscoplastic, strain-hardening materials have been modified to apply to changes in the direction of stressing. This modification involves altering the strain-hardening parameters with a change in the sign of the stress and also adding a linear viscosity term to the plastic deformation rate. These modifications are shown to have a physical basis and enable the constitutive equations to predict the general features of cyclic stress-strain behavior at various extensions rates and strain amplitudes including the tendency toward a limit cycle. An unusual feature of cyclic loading tests on some metals is a local concavity of the stress-strain curve which is predicable by these equations. Cyclic stress-strain curves were calculated for titanium for various conditions and compared to corresponding experimental results., Also pub. as ISSN-0072-9310.

Numerical calculations were performed for two examples of the response of elastic-plastic beams subjected to dynamic loads. These were a simply supported, axially restrained beam under suddenly applied uniform pressure, and an axially restrained, clamped beam with a central mass that is impacted by a projectile. Large elastic-plastic deflections were considered, and the method of finite differences was used. Two different constitutive equations were assumed: the elastic-perfectly plastic relation, and a special elastic-viscoplastic strain hardening model. Analysis of the results included examining the interaction between the bending moment and the axial force, the variation of the axial force, bending moment and deflection with time, and the propagation velocities of the various phenomena during motion. Experiments were carried out in which a rifle projectile hit a central mass which had been fastened to a clamped beam. Comparison between the theoretical and experimental dynamic deflections shows good agreement for relatively short response times. (Author)

A representation of anelastic material behavior, i.e. materials that exhibit energy losses and rate dependent moduli for geometrically reversible deformations, is proposed for multiaxial stress states and large deformations (finite strains). The constitutive equations are relations between the deformation rate and the stress components. An 'anelastic stress' is considered to be part of the total applied stress and to be responsible for the phenomena of energy losses, rate dependent moduli, and delayed elasticity (creep and recovery). In this incremental formulation, 'memory' and 'history' effects are incorporated into the current deformation state and the state variable, the elastic stress, which makes the method suitable for computer solution of structural problems involving arbitrary loading histories. The present analysis is limited to isothermal conditions but the procedure can be generalized to consider thermal effects., Also pub. as ISSN-0067-0340.

A set of constitutive equations has been formulated to represent elastic-viscoplastic strain hardening material behavior for large deformations and arbitrary loading histories. An essential feature of the formulation is that the total deformation rate is considered to be separable into elastic and inelastic components which are functions of state variables at all stages of loading and unloading. The theory, therefore, is independent of a yield criterion or loading and unloading conditions. The deformation rate components are determinable from the current state which permits an incremental formulation of problems. Strain hardening is considered in the equations by introducing plastic work as the representative state variable. The problem of uniaxial straining has been examined for a number of histories that included straining at various rates, rapid changes of strain rate, unloading and reloading, and stress relaxation. The calculations were based on material constants chosen to represent commercially pure titanium. The results are in good agreement with corresponding experiments on titanium specimens. (Author)

A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading. The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading. The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of dislocation dynamics. A numerical scheme for calculating deformations is developed and applied to a thick walled spherical shell under internal pressure. Various numerical examples are presented. (Author)