# Accession Number:

## ADA218751

# Title:

## Approximate Analysis for the Formation of Adiabatic Shear Bands

# Descriptive Note:

## Memorandum rept.

# Corporate Author:

## ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

# Personal Author(s):

# Report Date:

## 1990-01-01

# Pagination or Media Count:

## 42.0

# 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 rigidperfect 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

# Descriptors:

- *SHEAR PROPERTIES
- *SOLID STATE PHYSICS
- *ADIABATIC CONDITIONS
- *PLASTIC PROPERTIES
- *HEAT RESISTANT MATERIALS
- INERTIA
- BANDS(STRIPS)
- ONE DIMENSIONAL
- THEORY
- ELASTIC PROPERTIES
- RATES
- NONLINEAR SYSTEMS
- MATHEMATICAL ANALYSIS
- SCALING FACTOR
- THERMAL CONDUCTIVITY
- FIGURE OF MERIT
- EQUATIONS
- HARDENING
- PARAMETRIC ANALYSIS
- FUNCTIONS
- STRESSES
- LOW STRENGTH
- MATERIALS

# Subject Categories:

- Plastics
- Solid State Physics