Approximate Analysis for the Formation of Adiabatic Shear Bands

Abstract

Parametric solutions are given for the formation of adiabatic shear bands in the context of the one-dimensional, nonlinear theory where inertia and elasticity are ignored. When heat condition is also ignored, the exact solution reduces completely to a sequence of quadratures. For a perfectly plastic material with heat conduction, an implicit parametic solution is also constructed. This is similar to the previous one in many ways, but now it involves two quadratures; a single nonautonomous, first-order ODE; and two functions that obey heat equations. This solution appears to be very accurate (compared to the full-finite element solution) until the time of stress collapse. Results indicate that for weak rate hardening of the power-law type, intense localization depends strongly on the initial characteristics. Within the context of rigid/perfect plasticity, a scaling law for the critical strain is given, and a figure of merit is defined that ranks materials according to their tendency to form adiabatic shear bands. (JG)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA218751

Entities

People

  • Thomas W. Wright

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Equations
  • Equations Of Motion
  • Figure Of Merit
  • Hardening
  • Jet Propulsion
  • Materials
  • Materials Science
  • Mathematics
  • Mechanical Engineering
  • Mechanics
  • Military Research
  • Scaling Laws
  • Shear Bands
  • Softening
  • Strain Rate
  • Temperature Gradients
  • Thermal Conductivity

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.
  • Mechanical Engineering/Mechanics of Materials.