Temperature Dependent Constitutive Model Research Articles

A constitutive model for fcc crystals with application to polycrystalline OFHC copper

Based on the results of a series of experiments on commercially pure OFHC copper (an fcc polycrystal), a physically based, rate- and temperature-dependent constitutive model is proposed for fcc single crystals. Using this constitutive model and the Taylor averaging method, numerical calculations are performed to simulate the experimental results for polycrystalline OFHC copper. The model calculation is based on a new efficient algorithm which has been successfully used to simulate the flow stress of polycrystalline tantalum over broad ranges of temperature, strain rate, and strain (Nemat-Nasser, S., Okinaka, T., Ni, L., 1998. J. Mech. Phys. Solids 46, 1009). The model effectively simulates a large body of experimental data, over a broad range of strain rates (0.001–8000 s −1), and temperatures (77–1096 K), with strains close to 100%. Few adjustable constitutive parameters of the model are fixed at the outset for a given material. All other involved constitutive parameters are estimated based on the crystal structure and the physics of the plastic flow.

A physically-based constitutive model for bcc crystals with application to polycrystalline tantalum

Based on the results of an extensive series of systematic experiments on commercially pure tantalum (bcc crystals), a physically-based, rate- and temperature-dependent constitutive model is proposed for bcc single crystals and is applied to simulate the experimental results, using the Taylor averaging method. The model calculation is based on a new efficient algorithm for the numerical solution of the finite deformation of bcc single crystals, involving up to 48 potentially active slip systems. The accuracy and efficiency of the proposed algorithm are checked through comparison with the results of the conventional explicit Euler time-integration scheme, using a very large number of timesteps. The model effectively simulates a large body of experimental data, over a broad range of strain rates (10 −3 − 4 × 10 4/s), and temperatures (77 to 1300 K), with strains exceeding 100%, using very few adjustable parameters whose values are fixed at the outset for a given material. All other involved constitutive parameters are estimated based on the crystal structure and the physics of plastic flow.

Thermo-elasto-viscoplasticity of isotropic porous metals

A rate and temperature dependent elastic-plastic model for isotropic, moderately porous metallic materials is formulated. This model is intended for material rate-sensitivities in the entire range spanning from highly rate-dependent behavior at high homologous temperatures to nearly rate-insensitive behavior at low homologous temperatures. The predictive capabilities of the constitutive model are verified by comparing results from finite element calculations against results from physical experiments. Specifically, example calculations are presented for: (a) isothermal hot compression of a tapered disk made from an initially porous material. This calculation illustrates the effect of secondary tensile stresses on hot workability of metals, (b) Tension tests, under isothermal conditions at low homologous temperatures, on axisymmetric notched bars made from initially porous materials. This calculation illustrates the effects of nonuniform multiaxial tensile stress states on void growth. Predictions from the computational procedures for both examples agree well with experimental results. The new state variable rate and temperature dependent constitutive model for microporous materials and the associated computational procedures form a basis for the simulation and design of deformation processing operations. This new capability should be useful for the prediction of formation of defects during both cold-working when the material rate sensitivity is low, as well as hot-working when the material is highly rate sensitive. The computational capability should also be useful in simulating the late stages of densification of powder metallurgical products in complex forming operations.

A constitutive model for cold deformation of aluminium at large strains and high strain rates

Abstract A temperature-dependent constitutive model for viscoplastic deformation of aluminium based on a single, scalar internal variable is presented. The model is designed particularly for the strains, strain rates, and temperatures important for cold forging. Special attention is paid to the underlying physical processes that determine the flow stress in the metal. The kinetic constitutive equation is based on thermal activation of dislocations over an average potential barrier from various kinds of obstacles. Strain hardening is modelled through the internal variable which represents the increasing height of these barriers. The model is generalized to three dimensions, and it has been implemented in the finite-element code ABAQUS. Simulations of simple forging operations are presented.

A constitutive model for isotropic, porous, elastic-viscoplastic metals

A complete rate and temperature dependent constitutive model for the high temperature deformation of isotropic, moderately porous metallic materials is formulated. The essential new feature of the constitutive model is a new potential function for the viscoplastic stretching. This viscoplastic potential contains one undetermined scalar valued function of the material strain rate sensitivity and the volume fraction of voids. The form of this function is determined by fitting certain predictions from the model to results obtained from full finite element periodic unit cell calculations of initially spherical holes in a viscoplastic medium. Finite element calculations are carried out for two sets of material constants, one representing the highly rate dependent behaviour of a real material (Fe-2%Si) under hot-working conditions, and the other representing the rate independent limit of a perfectly plastic material. The fit of the new potential to the finite element calculations for a large range of void volume fractions and stress triaxialties is shown to be very good. It is also shown that the predictions from the potential proposed in this paper are in better agreement with the numerical unit cell calculations than the predictions from other existing models in the literature. The constitutive model presented here should find use in modeling hot workability of metals, and also in modeling the late stages of densification of metallic powders by hot isostatic pressing.

Issues In The Numerical Simulation Of Strain-Rate And Pressure Sensitive CementitiousGranular Materials

Because cementitious, granular, pressure-sensitive materials constitute a wide range of construction materials like, concrete, soils and rocks, a project of investigation has been undertaken for the purpose of identifying the micromechanical mechanisms leading to the development and propagation of damage in these materials. One of the major goals of the investigation has been the development and the Finite Elements implementation of a triaxial, strain-rate sensitive, history and temperature dependent constitutive model. The model is under continuing development as additional material test results become available. In its present form it has been implemented in CAPA-3D, a massively parallel, nonlinear, static/dynamic Finite Elements system for the solution of very large-scale 3-D solid models.