Dynamic Constitutive Relation Research Articles

Nonunique Dynamic Equilibrium Constitutive Relation of Metal Powder Depending on its Microstructure

It was observed in an earlier work by Morimoto et al. [Inst. Phys. Conf. Ser. No. 70, Oxford 1984, p. 427] that the dynamic compact of an aluminium powder medium had greater flakiness and contiguity ratio than the static compact of the same density. This observed difference in micro structure is used to explain their result that the dynamic pressure of the medium is higher than the static pressure for a given density: the degree of rotation of particles during compaction is assumed to decrease for higher strain rates, because of the shorter time available, causing an increase in plastic particle deformation in the compaction direction, and increased resistance to the compaction. The normal Hugoniot equation derived, in which the mean strain rate averaged over a single steady wavefront is introduced, indicates that a rise of the normal Hugoniot with an increase in the strain rate results macroscopically from the increase in the propagation velocity of the wavefront. The multiwave Hugoniot equation is found to depend on the strain rate history of a given material. In compactions of a metal powder medium by punch impact, the wavefronts passing through the medium are approximately steady if the punch mass is sufficiently larger than the medium mass. But both the number of wavefronts arising during the compaction and the amplitudes of the strain waves, and hence the strain rate histories, vary with compaction conditions such as punch mass and initial punch velocity. This implies that a dynamic equilibrium constitutive relation for the medium will depend on the compaction conditions, and therefore cannot be determined uniquely for any two compactions.

An advanced dynamic three-dimensional finite element method to simulate deformation-damage process of laminates under impact

An advanced dynamic three-dimensional finite element method based on both the dynamic damage constitutive relation in incremental form and the damage parameter model is given in this paper, which can be used to simulate the deformation-damage-failure process of laminates under impact. The interaction algorithm has further been developed, and the dynamic equation has also been derived.

An experimental and numerical analysis for high strain rate compressional behavior of 6061-O aluminum alloy

The split Hopkinson pressure bar apparatus is used in studying the high strain rate compressional behavior of 6061-O aluminum alloy. Circular disks of approximately 6 mm in thickness and 10 mm in diameter are tested at average strain rates of 10 3 to 3 × 10 3 sec −1. Transient wave forms are measured using a four-channel signal conditioner, strain gages, and a digital oscilloscope. In order to obtain the dynamic stress-strain relationship, uniaxial elastic stress wave theory is utilized in analyzing the measured signals. Quasi-static tests are performed using an MTS machine, with samples being tested at a strain rate of 3 × 10 −4 sec −1. In addition, the MARC finite element code is used in simulating the transient response of the input bar, output bar, and specimen following impact by the striker bar at a specified velocity. Experimental results reveal that the dynamic yield stress of 6061-O aluminum alloy increases under high strain rate loading conditions. When the dynamic yield stress is considered in the simulations, code simulated wave forms agree well with the measured test results; verifying the fact that the dynamic constitutive relationship obtained by simple one-dimensional stress wave theory adequately describes the high strain rate behavior of 6061-O aluminum alloy.

銅の動的塑性構成関係に関する実験的研究

This paper presents some experimental results carried out to investigate dynamic constitutive relationship of material from a view point of dynamic plasticity. Three kinds of experiments were executed on annealed pure copper; the jump test in which the strain rate is suddenly changed from quasi-static to dynamic, the dynamic test in which dynamic load is applied to the specimen and the dynamic reloading test in which a dynamic load is applied to the specimen previously strain-hardened to some extent. The experimental procedure is based on the torsional stress bar method, where the dynamic stress and the corresponding strain are measured at one point of the specimen in purely dynamic manner. It has been revealed that in the jump test the over-stress is uniquely related to the instantaneous plastic strain rate all through the dynamic deformation process. On the other hand, in the dynamic and dynamic reloading tests the behavior was different from the jump test such that in the initial stage of increasing strain rate the over-stress lies above the curve determined from the jump test but tend to coincide in the decreasing stage.These results are interpreted from microscopic viewpoint of dislocation motion and it is concluded that the mechanism of the rate sensitivity is same in all the cases, but the mobile dislocation density is different at the start of the dynamic plastic deformation in each test.

A failure criterion for beams under impulsive loading

An energy criterion is suggested in this paper for predicting the inelastic failure modes of beams subjected to large dynamic loadings. The experimental results of Menkes and Opat on the failure of impulsively loaded beams may be interpreted to show that the length of a plastic hinge varies with the ratio of the plastic shear work to the total plastic work dissipated at a hard point or other region of intense localized plastic strain. The variation of this parameter is obtained from a theoretical analysis for the impulsive loading of a rigid, perfectly plastic clamped beam with plastic yielding governed by an interaction yield surface which combines the influences of bending, shear and membrane tension. The Cowper-Symonds dynamic constitutive relation is used to study the influence of material strain rate sensitivity.