Parameter Evaluation for a Unified Constitutive Model

1993 ◽  
Vol 115 (2) ◽  
pp. 157-162 ◽  
Author(s):  
P. E. Senseny ◽  
N. S. Brodsky ◽  
K. L. DeVries
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Least Squares ◽  
Constitutive Equations ◽  
Laboratory Data ◽  
Constant Strain Rate ◽  
Nonlinear Least Squares ◽  
Evolutionary Equation ◽  
Internal Variables ◽  
Isotropic Hardening

Parameters for the unified constitutive model MATMOD [1] were evaluated for rock salt (NaCl) by using nonlinear least squares to fit the model to isothermal laboratory data. MATMOD incorporates two internal variables that represent the effects of both kinematic and isotropic hardening. The constitutive equations contain nine parameters that must be evaluated to model isothermal deformation. Laboratory data from stress relaxation, constant strain rate, and long-term creep tests were used. The latter two test types included staged tests in which the strain rate or stress was changed step-wise during the test. The test conditions were precisely controlled by a computer and the constitutive equations were integrated to simulate the laboratory conditions closely. The MATMOD parameters were then evaluated by fitting the integrated equations to the laboratory data using nonlinear least squares. The model fits the data well, but the fit may be improved by changing the evolutionary equation for the internal variable that accounts for isotropic hardening.

A State Variable Modeling of Plasticity and Necking Under Uniaxial Tension

1992 ◽  
Vol 114 (4) ◽  
pp. 378-383 ◽  
Author(s):  
G. Ferron ◽  
H. Karmaoui Idrissi ◽  
A. Zeghloul
Keyword(s):  
Strain Rate ◽  
Uniaxial Tension ◽  
Plastic Flow ◽  
Constitutive Equations ◽  
Growth Process ◽  
Constant Strain Rate ◽  
Uniaxial Tensile ◽  
Long Wavelength ◽  
State Variable ◽  
Diffusion Controlled

Constitutive equations based on a state variable modeling of the thermo-viscoplastic behavior of metals are discussed, and incorporated in an exact, long-wavelength analysis of the neck-growth process in uniaxial tension. The general formalism is specialized to the case of f.c.c. metals in the range of intragranular, diffusion controlled plastic flow. The model is shown to provide a consistent account of aluminum behavior both under constant strain-rate and creep. Calculated uniaxial tensile ductilities and rupture lives in creep are also compared with experiments.

A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

Tensile Stress-Strain Curves Modeling of Four Kinds of Solders with Temperature and Rate Dependence

2005 ◽  
Vol 297-300 ◽  
pp. 905-911 ◽  
Author(s):  
Xu Chen ◽  
Li Zhang ◽  
Masao Sakane ◽  
Haruo Nose
Keyword(s):  
Tensile Stress ◽  
Constitutive Model ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Strain Rate Range ◽  
Rate Dependence ◽  
Strain Rates ◽  
Stress Strain ◽  
Rate Range

A series of tensile tests at constant strain rate were conducted on tin-lead based solders with different Sn content under wide ranges of temperatures and strain rates. It was shown that the stress-strain relationships had strong temperature- and strain rate- dependence. The parameters of Anand model for four solders were determined. The four solders were 60Sn-40Pb, 40Sn-60Pb, 10Sn-90Pb and 5Sn-95Pb. Anand constitutive model was employed to simulate the stress-strain behaviors of the solders for the temperature range from 313K to 398K and the strain rate range from 0.001%sP -1 P to 2%sP -1 P. The results showed that Anand model can adequately predict the rate- and temperature- related constitutive behaviors at all test temperatures and strain rates.

A variable-order viscoelastic constitutive model under constant strain rate

2020 ◽  
Author(s):  
Yao Wang ◽  
Dagang Sun ◽  
Zhanlong Li ◽  
Yuan Qin ◽  
Bao Sun
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Fractional Order ◽  
Viscoelastic Material ◽  
Constitutive Models ◽  
Constant Strain Rate ◽  
Variable Order ◽  
Hyper Elastic ◽  
Material Coefficient ◽  
Viscoelastic Coefficient

The traditional viscoelastic constitutive models encounter the problems of massive parameters and ambiguous physical meanings. A new concept of variable-order viscoelastic constitutive (called VOVC) model is put forward based on the constant fractional-order constitutive model and the viscoelastic theory. The determination methods of the two parameters in the VOVC model, including the material coefficient and the viscoelastic coefficient, are discussed both in the tensile and the resilient processes. The comparisons are made between the VOVC model and the traditional constitutive models i.e. the constant fractional-order Kelvin-Voigt (CFKV) model, the Zhu-wang-tang nonlinear thermo-viscoelastic constitutive (ZWT) model and the Ogden nonlinear hyper-elastic (Ogden) model. The results show that the VOVC model with the constant material coefficient and the variable viscoelastic coefficient predicts the whole evolution of the constitutive behavior of the viscoelastic material under the constant strain rate more precisely. The constant material coefficient in the VOVC model means the stiffness of the viscoelastic material. The variable viscoelastic coefficient in the model means the distribution of the elasticity and viscosity. The VOVC model contains a simpler structure, fewer parameters, clearer physical meanings and higher precision.

Theoretical Deduction of Constitutive Equations with Variational Parameters during Superplastic Tension

2014 ◽  
Vol 941-944 ◽  
pp. 1509-1512
Author(s):  
Zhi Ping Guan ◽  
Xiao Fang Guan ◽  
Yu Quan Song
Keyword(s):  
Strain Rate ◽  
Test Data ◽  
Constitutive Equations ◽  
Constant Strain Rate ◽  
Rate Sensitivity ◽  
State Equation ◽  
Sensitivity Index ◽  
Tensile Tester ◽  
Strain Rate Sensitivity Index ◽  
Superplastic Tension

In this article, firstly, the strain hardening index and the strain rate sensitivity index were deducted from the general state equation and the mechanical meaning of the two indexes were correspondingly depicted, and then constitutive equations, where both/either of the two indexes appear as constants, were theoretically deducted from the same state equation. Secondly, constitutive equations where both/either of the two indexes present as variables were put forward by numerical simulation. Next, constitutive equations were built, where mechanical variables are replaced by test data obtained on an electronic universal tensile tester with the capacity to carry out a true constant strain rate path. Finally, based on the test data of Zn-5%Al during superplastic tension, it is proved that the theoretical results in this article are valid.

Constitutive Equations for the Rate-Dependent Deformation of Metals at Elevated Temperatures

1982 ◽  
Vol 104 (1) ◽  
pp. 12-17 ◽  
Author(s):  
L. Anand
Keyword(s):  
Dynamic Recrystallization ◽  
Strain Rate ◽  
Strain Hardening ◽  
Constitutive Equations ◽  
Elevated Temperatures ◽  
Internal Variable ◽  
Internal Variables ◽  
Homologous Temperature ◽  
Static Recovery ◽  
Rate Dependent

Approximate constitutive equations are proposed for use in the analysis of the rate-dependent deformation of metals at temperatures in excess of a homologous temperature of 0.5. The constitutive equations are formulated within the scope of some recent theories of elastoviscoplasticity with internal variables, but employ only a single scalar internal variable representing an isotropic resistance to plastic flow offered by the internal microstructural state of the material. The special constitutive euqations incorporate strain hardening of the Voce type, and account for the effects of the prior histories of strain rate and temperature undergone by the material. These equations, however, do not represent the important effects of static recovery or of static and dynamic recrystallization.

Stress prediction analysis during hot working of 100MnCrW4 steel

2021 ◽  
Vol 16 (1) ◽  
pp. 25-31
Author(s):  
Maroš Eckert ◽  
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Constitutive Model ◽  
Strain Rate ◽  
Predictive Model ◽  
Correlation Coefficient ◽  
Constitutive Equations ◽  
Experimental Measurements ◽  
Material Parameters ◽  
Stress Prediction

This paper deals with the analysis and the possibility of using a constitutive model based on the Arrhenius equationfor tool steel 100MnCrW4. Experimental measurements were performed on a DIL 805 dilatometer in the range of strain rate 0.001 s-1 for 10 s -1 and temperature from 800 to 1200 °C. Using constitutive equations, material parameters and activation energy were derived, which can be subsequently applied to other models selated to hot behavior of deformation. The experimental data were compared to the ones obtained by the predictive model with the correlation coefficient R = 0.97885 and the parameter MAPE = 17.28 % which means a very good level of prediction.

Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation

1993 ◽  
Vol 60 (4) ◽  
pp. 813-821 ◽  
Author(s):  
J.-L. Chaboche
Keyword(s):  
Constitutive Equations ◽  
Evolution Equations ◽  
Internal Variables ◽  
Isotropic Hardening ◽  
State Variables ◽  
Inelastic Analysis ◽  
Hardening Process ◽  
Classical Models ◽  
Energy Dissipated ◽  
Consistent Formulation

Cyclic viscoplastic constitutive equations are increasingly used for the inelastic analysis of structures under severe thermomechanical conditions. The purpose of the paper is to show how the classical models can be modified in order to follow the general principles of thermodynamics with internal variables. Using the restrictive framework of standard generalized materials, the state variables associated to various kinds of kinematic and isotropic hardening are selected. The evolution equations for these internal variables are then formulated in a slightly less restrictive form. For each hardening process, the separation of the total plastic work into energy dissipated as heat and energy stored in the material is discussed in detail.

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