Application of the FEM to elastoplastic wave propagation in metals

E. El‐Magd; W. Abdel‐Ghany; M. Homayun

doi:10.1108/eb023609

Elastoplastic Wave Propagation in a Rate-Sensitive Finite Rod Having a Thermal Gradient

Journal of Applied Mechanics ◽

10.1115/1.3408508 ◽

1970 ◽

Vol 37 (2) ◽

pp. 315-323 ◽

Cited By ~ 3

Author(s):

P. H. Francis

Keyword(s):

Wave Propagation ◽

Thermal State ◽

Nonlinear Problems ◽

Temperature Fields ◽

Computational Technique ◽

Viscoplastic Material ◽

Strong Discontinuities ◽

Elastoplastic Wave ◽

Propagation Of Waves ◽

Increasing Temperature

In this paper, the problem of one-dimensional wave propagation in a bar of a thermally sensitive viscoplastic material is considered. A constitutive equation is developed which explicitly accounts for the thermal state in both the elastic and inelastic components of the strain rate. A computational technique is proposed for solving the governing hyperbolic system of equations. This technique is a synthesis of the finite-difference method and the method of characteristics, and utilizes the most attractive features of both for solving nonlinear problems involving the propagation of strong discontinuities. Some results are shown for the propagation of waves through both decreasing and increasing temperature fields.

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Mathematical modelling of elastoplasticity at high stress

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2012.0269 ◽

2012 ◽

Vol 468 (2148) ◽

pp. 3842-3863 ◽

Cited By ~ 5

Author(s):

P. D. Howell ◽

H. Ockendon ◽

J.R. Ockendon

Keyword(s):

Mathematical Model ◽

Wave Propagation ◽

Elastic Wave ◽

Wave Speed ◽

High Stress ◽

Plastic Wave ◽

Simple Mathematical Model ◽

One Dimensional ◽

Plastic Compression ◽

Elastoplastic Wave

This study describes a simple mathematical model for one-dimensional elastoplastic wave propagation in a metal in the regime where the applied stress greatly exceeds the yield stress. Attention is focused on the increasing ductility that occurs in the over-driven limit when the plastic wave speed approaches the elastic wave speed. Our model predicts that a plastic compression wave is unable to travel faster than the elastic wave speed, and instead splits into a compressive elastoplastic shock followed by a plastic expansion wave.

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Electron Microscopy of Shock Loaded Polycrystalline Beryllium

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100052547 ◽

1974 ◽

Vol 32 ◽

pp. 506-507 ◽

Cited By ~ 1

Author(s):

J. M. Galbraith ◽

L. E. Murr ◽

A. L. Stevens

Keyword(s):

Electron Microscopy ◽

Wave Propagation ◽

Structural Change ◽

Single Crystal ◽

Diffraction Pattern ◽

Shock Loading ◽

Slip Systems ◽

Compression Tests ◽

X Ray Diffraction ◽

X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

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