Strain Rate Dependent Ductility and Strain Hardening in Q&P Steels

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

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

Journal of Engineering Materials and Technology ◽

10.1115/1.3225028 ◽

1982 ◽

Vol 104 (1) ◽

pp. 12-17 ◽

Cited By ~ 301

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.

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Flow Curve Modelling of an Austenitic Stainless Steel at High Temperatures Starting from the One-Parameter Model of Strain Hardening

Materials Science Forum ◽

10.4028/www.scientific.net/msf.706-709.1361 ◽

2012 ◽

Vol 706-709 ◽

pp. 1361-1366 ◽

Cited By ~ 3

Author(s):

Giuliano Angella

Keyword(s):

Stainless Steel ◽

Flow Stress ◽

Austenitic Stainless Steel ◽

Strain Rate ◽

Strain Hardening ◽

Flow Curve ◽

Flow Curves ◽

Rate Dependent ◽

The One ◽

Voce Equation

The flow curves of an austenitic stainless steel deformed at temperatures 700-1000°C with strain rates 10-5-10-2s-1were modelled with the Voce equation. The parameters needed to draw the Voce equation, are the saturation stressσVthat defines the height of the flow curve, the critical strainεCthat defines the velocity to achieveσV, and the stressσo, namely the back-extrapolated flow stress to zero strain. A modified strain hardening analysis based on the one-parameter model was used to analyze the strain hardening rate dσ/dεvs. the flow stressσin order to obtainσVandεC. The modified approach was based on the assumption that the dislocation multiplication component of strain hardening was temperature and strain rate dependent through the thermal activation termsof flow stress. A parameters’ proportional toswas obtained from the strain hardening analysis and a relationship betweens’ and temperature and strain rate was found. Relationships betweenσV,σo,εCands’ were finally established and at this stage the Voce equation could reproduce the experimental flow curves at any imposed deformation conditions of temperature and strain rate.

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Investigation of Density- and Strain Rate-dependent Strain Hardening-softening-coupled material Behavior of Polyurethane Foams using Elasto-viscoplastic Constitutive Model

Korean Journal of Metals and Materials ◽

10.3365/kjmm.2020.58.5.357 ◽

2020 ◽

Vol 58 (5) ◽

pp. 357-367

Author(s):

Tae-Rim Kim ◽

Chi-Seung Lee

Keyword(s):

Constitutive Model ◽

Strain Rate ◽

Strain Hardening ◽

Material Behavior ◽

Implicit Time ◽

Stress Strain ◽

Integration Algorithm ◽

Material Response ◽

Material Parameters ◽

Rate Dependent

Polyurethane foam (PUF) is one of the most well-known cellular materials and is widely employed in various industrial and biomedical fields thanks to its many advantages. These include mechanical and material characteristics such as low density and thermal conductivity, and high specific elastic modulus and strength. Despite of these advantages, the PUF has extremely complex material nonlinearity, with changes in density and strain rate, which is a major obstacle to material design and the application of PUF-based structures. PUF has elasto-viscoplastic behavior including three stages of material features, linear elasticity, softening/plateau with stress drop and densification. These phenomena depend strongly on strain rate and density. Therefore, in this study, a phenomenological constitutive model, namely, an elasto-viscoplastic model, was proposed to describe the density- and strain rate-dependent material nonlinear behavior of PUF. The yield surface-independent plastic multiplier, and the hardening- and softening-associated internal state variables proposed by Frank and Brockman, and Zairi et al. were adopted in the constitutive model, respectively. The proposed constitutive model was discretized using the implicit time integration algorithm and was implemented into a user-defined subroutine of the commercial finite element analysis program, ABAQUS. At the same time, a deterministic identification method for material parameters of the constitutive model was introduced to predict the precise material response of PUF under arbitrary densities and strain rates. To do this, the three-dimensional constitutive model was contracted to a one-dimensional equation, and the explicit equation for each material parameter was derived. Then, the strain hardening- and softeningdependent material parameters were calculated using experimental results, such as the work hardening ratestress curve and the yield stress-strain rate curve. After analyzing the obtained material parameters, it was found that the material parameters were strongly dependent on the density and the strain rate. Consequently, the macroscopic material response of PUF, such as a uniaxial compressive stress-strain curve, can be predicted based on the proposed method in this study.

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