Nonlinear rate-dependent spectral constitutive equation for viscoelastic solids with residual stresses

Based on a state variable theory proposed by Onat some discriminating creep tests of stainless steel have been designed and carried out at elevated temperature conditions. Quantitative correlations of the results are sought with predictions from a physical theory for recovery creep proposed by Lagneborg. The findings are utilized to interpret the behavior of creeping members when subjected to a rapid increase in the rate of straining. Different approaches toward generalization of physical one-dimensional creep laws to multiaxial stress states are discussed. A tentative constitutive equation applicable to the solution of general boundary value problems is proposed.

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A rate-dependent constitutive equation for 5052 aluminum diaphragms

Materials & Design (1980-2015) ◽

10.1016/j.matdes.2014.03.003 ◽

2014 ◽

Vol 60 ◽

pp. 13-20 ◽

Cited By ~ 8

Author(s):

S.A. Hosseini Kordkheili ◽

M.M. Ashrafian ◽

H. Toozandehjani

Keyword(s):

Constitutive Equation ◽

Rate Dependent

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Strain Rate Dependent Constitutive Equation of Rubber and Simulation of Deformation Behavior of Carbon-Black-Filled Rubber

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A ◽

10.1299/kikaia.73.558 ◽

2007 ◽

Vol 73 (729) ◽

pp. 558-566 ◽

Cited By ~ 3

Author(s):

Keisuke AZUMA ◽

Masato NAITO ◽

Yoshihiro TOMITA

Keyword(s):

Constitutive Equation ◽

Carbon Black ◽

Strain Rate ◽

Deformation Behavior ◽

Rate Dependent ◽

Filled Rubber

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FEM-implementation of practical rate-dependent inelastic constitutive equation

The Proceedings of Conference of Tokai Branch ◽

10.1299/jsmetokai.2002.51.373 ◽

2002 ◽

Vol 2002.51 (0) ◽

pp. 373-374

Author(s):

Tomofumi ISHIKAWA ◽

Mineo KOBAYASHI ◽

Nobutada OHNO ◽

Hiroyuki TAKAHASHI ◽

Minoru MUKAI ◽

...

Keyword(s):

Constitutive Equation ◽

Rate Dependent

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Power-Formula Viscoplasticity, Its Modification and Some Applications

Journal of Engineering Materials and Technology ◽

10.1115/1.3225734 ◽

1984 ◽

Vol 106 (4) ◽

pp. 383-387 ◽

Cited By ~ 3

Author(s):

Yu Chen

Keyword(s):

Constitutive Equation ◽

Strain Rate ◽

Boundary Value Problems ◽

Physical Phenomenon ◽

Boundary Value ◽

The Body ◽

Dislocation Dynamics ◽

Basic Relation ◽

Mathematical Form ◽

Rate Dependent

A power viscoplastic constitutive equation was first proposed by Bodner and Partom in 1972. This specific formula has its origin in the physical phenomenon of dislocation dynamics and due to the simplicity of its mathematical form, it is a useful constitutive equation in solving boundary value problems. In this paper a brief review of the basic relation is given, followed by discussion of some relatively less known features of this formula. The body of the paper deals with the modification of the equation to explore its potential in several directions. The first modification consists of making the “threshold stress” strain rate dependent. The second modification aims of modeling strain rate history dependency. Due to space the formulation of the boundary value problems of uniaxial testing and its implementation through finite element programs will not be reported here. Results demonstrating the effect of strain rate and strain-rate history are presented. They are in good qualitative agreement with available experimental data.

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Simulating Distortion and Residual Stresses in Carburized Thin Strips

Journal of Engineering Materials and Technology ◽

10.1115/1.1543973 ◽

2003 ◽

Vol 125 (2) ◽

pp. 116-124 ◽

Cited By ~ 21

Author(s):

V. C. Prantil ◽

M. L. Callabresi ◽

J. F. Lathrop ◽

G. S. Ramaswamy ◽

M. T. Lusk

Keyword(s):

Residual Stresses ◽

Mechanical Response ◽

Material Model ◽

Carbon Steels ◽

Low Carbon ◽

Rate Dependent ◽

Heat Treated ◽

Out Of Plane ◽

Gear Steels ◽

The Individual

This paper illustrates the application of a new multiphase material model for simulating distortion and residual stresses in carburized and quenched gear steels. Simulation is focused on thin, metallic strips that are heat treated to introduce a through-thickness carbon gradient. Because the material properties are strongly dependent on the carbon content, quenching causes significant transverse out-of-plane distortion. The material model accounts for a multiphase alloy structure where inelasticity in the individual phases is temperature and rate dependent. The model is fit to an extensive matrix of experimental data for low carbon steels (0.2–0.8 percent) whose transformation kinetics and mechanical response are similar to 4023 and 4620 alloys used in experiments. While residual stress data are limited, reasonable agreement with X-ray diffraction measurements was obtained. Comparisons of transverse deflections predicted numerically showed excellent agreement with those measured experimentally for all five thicknesses reported. Accurate transformation and lattice carburization strains are critical to correctly predict the sense and magnitude of these transverse distortions and in-plane residual stresses.

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