Material Parameters In Constitutive Equations Research Articles

Material Parameters in Constitutive Equation for Plastic Deformation at a High Strain Rate Estimated by High-Velocity Microparticle Collisions

Material Parameters in Constitutive Equation for Plastic Deformation at a High Strain Rate Estimated by High-Velocity Microparticle Collisions

Gradient theory for crack problems in quasicrystals

Constitutive equations in gradient theory of quasicrystals are written for phonon and phason stresses, and the higher-order stress tensor. They are expressed by the phonon and phason strains and the gradient of phonon strains. The higher-order elastic parameters are proportional to the conventional elastic stiffness coefficients by the internal length material parameter. Material parameters in constitutive equations correspond to the decagonal quasicrystals. The principle of virtual work is applied to derive governing equations and corresponding boundary conditions. The finite element method (FEM) is developed to solve general 2D boundary value problems in problems described by governing equations for strain-gradient theory of quasicrystals. The path-independent J-integral is also derived for fracture mechanics analysis of such solids. Numerical examples are presented to demonstrate the veracity of the formulations.

Identification of Kinematic Hardening Material Parameters for Martensitic Steel Sheets

The identification of the material models which are used in the finite element analysis for the forming operation and springback are very important in terms of accurate predictions. The aim of this paper is to characterize both the anisotropy and the hardening of the ultra-high strength steel such as martensitic steel (MS steel) in order to identify material parameters of constitutive equation, which able to reproduce the mechanical behavior. Uniaxial tensile tests were carried out for characterizing the anisotropic plastic behavior of the MS steel. Cyclic tests under tension-compression load were also carried out for characterizing the Bauschinger effect during reverse deformation. Yoshida-Uemori hardening model associated with orthotropic yield criterion Hill’s 1948 is used to represent the in-plane mechanical behavior of the martensitic steel. The resented results show a very good agreement between model predictions and experiments: flow stresses during loading and reverse loading are well reproduced.

A novel constitutive model for hot deformation behaviors of Ti–6Al–4V alloy based on probabilistic method

The flow behaviors of Ti–6Al–4V alloy are studied by isothermal compressive experiments at the deformation temperature from 850 to 950 °C and strain rate from 0.001 to 1 s−1. To analyze the uncertainties induced by material itself and testing procedure, repetitive compressive tests are conducted under each experimental condition. It is found that the uncertainties of flow behaviors are too great to be ignored. The innovation of the study is that the probability theory is introduced to model flow behaviors. 312 (=531,441) sets of flow curves are created by the resampling method, in which 10,000 sets are used to determine the material parameters of constitutive equations. Therefore, the probability densities of material parameters can be easily obtained. It is found that the probability density functions of the most material parameters are similar to the normal distribution. The values of material parameters with the maximum probability density are selected for the established constitutive model. The advantage of the established constitutive model is that it can describe the most probable flow characteristics of Ti–6Al–4V alloy.

Three-Dimensional Viscoelastic Simulation for Injection/Compression Molding Based on Arbitrary Lagrangian Eulerian Description

Different from conventional injection molding (CIM), injection/compression molding (ICM) evolves boundary variation in gapwise direction. In order to describe melt flow characteristics in ICM correctly, a new material derivative based on arbitrary Lagrangian Eulerian (ALE) description was introduced to modify the material derivatives in the governing and constitutive equations. To avoid large amount of calculation and weak stability of integral numerical method, an iterative approach employing twofold iterations was proposed to decouple the interdependence between velocity, stress, and temperature. The initial values of material parameters in constitutive equations were obtained or fitted by rheological experiments. The ICM experiments for an iso-thick and a var-thick rectangular panel were carried out to validate the proposed method and find the special characteristics of ICM. In addition, the photoelastic tests on a quarter of spherical part processed by ICM were conducted to identify the relationship between residual flow-induced stress distributions and flow fields. Both simulations and experiments show that the pressure profile displays a plateau during compression, temperature decreases with time according to exponential law, large flow-induced stress originates in thick transitional region, flow start, and flow end areas, and gravity has significant effect on meltfront for thick part ICM. The good agreement between experiments and simulations indicates that the current method can properly describe the flow characteristics of ICM.

Modeling Friction Stir Welding Process of Aluminum Alloys

The friction stir welding (FSW) process of aluminum alloys has been modeled using a two-dimensional Eulerian formulation. Velocity field and temperature distribution are strongly coupled and solved together using a standard finite element scheme. A scalar state variable for hardening is also integrated using a streamline integration method along streamlines. A viscoplastic constitutive equation to consider plastic flow and strength variations was implemented for the process modeling. Precipitates inside AA6061 alloys are sensitive to elevated temperatures and affect strength evolution with temperature. The overall effects of the precipitate variations with temperature on strength were reflected using temperature-dependent material parameters. The material parameters of constitutive equations were obtained from isothermal compression tests of various temperatures and strain rates. The effects of FSW process conditions on heating and hardening were investigated mainly near the tool pin. The microhardness distribution of the weld zone was compared with the prediction of strength. In addition, crystallographic texture evolutions were also predicted and compared with the experimental results.

Strain Rate Gradient Model with Couple Stress for Micro Scale Rigid-Viscosity-Plastic Deformation

In order to describe scale effects in rigid-viscosity-plastic deformation at micro scale, a strain rate gradient model with couple stress is proposed. In the constitutive equation, couple stress, strain rate gradient are introduced on the assumption that the potential energy depends upon the scalar invariants of the strain rate tensor and strain rate gradient tensor, at the same times, the influences of length scale of body, grain size and temperature are also considered. A FEM-based program based on this strain rate gradient model is used to simulate the process of high temperature gas pressure forming, and the value of length scale 2 l is evaluated by simulation pilot calculation. It is indicated that rigid-viscosity-plastic deformation can be more accurately simulated by the present strain gradient rate model as long as the material parameters in constitutive equation are selected suitably.

The application of Hart's state variable description of inelastic deformation to Carrara marble at T < 450°C

An attempt has been made to determine if the material parameters in constitutive equations for inelastic deformation which fully accommodate the deformation history dependence of inelastic properties can be evaluated with sufficient accuracy at elevated confining pressures for such equations to be of interest in characterizing geological materials. Accordingly, a large number of constant displacement rate and load relaxation experiments (or variants thereof) have been conducted on Carrara marble at 200 MPa confining pressure in the temperature range 120 to 400°C, and the results have been interpreted in terms of Hart's state variable description of inelastic deformation. The observed mechanical behavior conforms to Hart's description, with a changeover at about 250°C from deformation rate controlled by dislocation glide controlled processes (as represented by concave upward () load relaxation curves), to rate control by strongly thermally activated processes (as represented by concave downward relaxation curves). All relaxation curves generated at a given temperature may be superposed by a translation in fixed direction in the () plane. This defines a master relaxation curve which represents what any individual relaxation curve would look like if it could be determined over a sufficiently wide range of strain rates. For Concave downward relaxation curves the master curve extends over 9 orders of magnitude of strain rate and, in consequence, substantially eases the problem of extrapolating the laboratory data to geological strain rates. The success of Hart's description in accounting for the mechanical behavior means that it is possible to avoid the steady state approximation both in the experimental evaluation of inelastic flow laws and in the application of those flow laws in geophysical modeling problems. Moreover, it provides a simple method of quantifying the mechanical state of a material and thereby is of potential significance for the problem of correlating microstructural observations with mechanical properties.

Analysis of viscoplasticity in 6061-T6 aluminum

Results from a previous analysis of experimental data on 6061-T6 aluminum have been used to determine values for material parameters in constitutive equations for viscoplasticity and hardening. In contrast to previous work, the present model includes the continued hardening observed in Hopkinson bar tension experiments and predicts the wave structure measured in plate impact experiments reasonably well. An interesting conclusion of the present work is that the structure of the unsteady portions of weak shocks measured in plate impact experiments can provide a sensitive measure of hardening near the onset of plasticity.