Analytical Formulation of a Rate and Temperature Dependent Stress-Strain Relation

1979 ◽  
Vol 101 (3) ◽  
pp. 254-257 ◽  
Author(s):  
A. Merzer ◽  
S. R. Bodner
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Uniaxial Stress ◽  
Plastic Strain Rate ◽  
Isotropic Hardening ◽  
Stress Strain ◽  
Rate Dependent ◽  
Strain Relation ◽  
Strain And Strain Rate ◽  
Stress Strain Relation

The equation for plastic strain rate in the Bodner-Partom viscoplastic formulation is integrated under conditions of uniaxial stress, constant plastic strain rate, and isotropic hardening to give an analytical expression for the stress as a function of plastic strain and strain rate. Temperature dependence is introduced which leads to a general relationship between stress, strain, strain rate, and temperature. The resulting equation indicates an asymptotic saturation stress whose dependence on strain rate and temperature appears to agree with experimental results. Strain hardening given by the analytical equation also seems to be consistent with experiments. A possible new definition of yield stress is a consequence of the rate dependent stress-strain relation.

Numerical Analysis on Usability of SHPB to Characterize Dynamic Stress–Strain Relation of Metal Foam

2017 ◽  
Vol 09 (05) ◽  
pp. 1750075 ◽  
Author(s):  
Beixin Xie ◽  
Liqun Tang ◽  
Yiping Liu ◽  
Zhenyu Jiang ◽  
Zejia Liu
Keyword(s):  
Strain Rate ◽  
Dynamic Stress ◽  
Metal Foam ◽  
Test Method ◽  
Specimen Thickness ◽  
Strain Rates ◽  
Stress Strain ◽  
Deformation Localization ◽  
Strain Relation ◽  
Stress Strain Relation

Split Hopkinson pressure bar (SHPB) technique is the most important test method to characterize dynamic stress–strain relations of various materials at different strain rates, and this technique requires uniform deformation of specimen during the experiment. However, some studies in recent years have found obvious deformation localization within metal foam specimens in SHPB tests, which may significantly affect the reliability of the results. Usability of SHPB to characterize dynamic stress–strain relation of metal foam becomes doubtful. In this paper, based on experimental verification, we carried out numerical simulative SHPB tests to study the problem, in which the metal foam specimens were modeled to have 3D meso structures with properties of their matrix material. Numerical simulative SHPB tests of aluminum foam specimens with varying thickness at different strain rates were performed. Deformation distribution in each local region of the specimen was examined and a concept of “effective specimen” was presented. Appropriate specimen thickness and range of testing strain rate were suggested based on quantitative analysis. Finally, we recommended a method how to revise the nominal strain and strain rate measured by traditional SHPB method to acquire the reliable dynamic stress–strain relation.

Longitudinal Impact on Viscoplastic Rods—Linear Stress-Strain Rate Law

1964 ◽  
Vol 31 (2) ◽  
pp. 199-207 ◽  
Author(s):  
T. C. T. Ting ◽  
P. S. Symonds
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Constitutive Law ◽  
Plastic Strain Rate ◽  
Longitudinal Impact ◽  
Plastic Strains ◽  
Stress Strain ◽  
Structural Metals ◽  
Rate Behavior ◽  
Strain Rate Behavior

Hohenemser and Prager [1] proposed a constitutive law for a solid of Bingham type We use a form of this law to study some cases of longitudinal impact on a bar causing large plastic strains. The results are intended to be of use in the design of impact tests on structural metals and in the interpretation of data from them, as well as helpful in guiding similar studies on materials with more complex plastic strain rate behavior.

Another Solving Equation of Elastoplastic Problem Based on Stress Strain Relation

2013 ◽  
Vol 353-356 ◽  
pp. 3350-3354
Author(s):  
You Li ◽  
Yi Peng
Keyword(s):  
Plastic Strain ◽  
Constitutive Relation ◽  
Basic Equation ◽  
Equation System ◽  
Elastoplastic Problem ◽  
Simple Application ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
New Form

Based on relationship between elastic and plastic strain, a new basic equation system of plasticity mechanics was established. In this paper, modification is made to the new basic equation system, and another form of basic equation system is presented based on stress strain constitutive relation, which also makes it possible to apply the results from elasticity mechanics directly to plasticity mechanics and decreases the solving difficulty of plastic problem. Finally, a simple application example is given, which shows that the new form of basic equation system is correct and practicable.

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