This study concerns the form of constitutive models, determination of parameters, and agreement with experimental data. Studies of plasticity and cyclic loading have generated an extensive list of constitutive models that describe deformation under cyclic loading. Models vary from empirical formulations to viscoplastic models as well as time dependent and independent models. In most cases, these models are derived, evaluated in a one dimensional setting and generalized to three dimensions using a multidimensional yield criterion. Often the constitutive models are evaluated using only a limited or restricted set of experimental data. One intention of this study is to examine the application of constitutive models to constant amplitude and random amplitude loading and to compare the results with experimental stress-strain data for the same conditions. This paper addresses some basic constitutive laws used in engineering and proposes a new law which leads to a well-posed mathematical problem and agrees well with experimental data. The scope of this study is restricted to time and temperature independent models. The constitutive laws selected for this study are: kinematic hardening, isotropic hardening, and a Chaboche law that have been described in the literature. In addition to these three laws, we introduce and evaluate one new law, the B-L law. The experimental database is constructed from a series of constant amplitude and random amplitude strain controlled cyclic loading experiments with different mean levels performed on specimens of 5086 and 5454 aluminum alloy in the H32 temper. The experimental data was gathered at a constant strain rate and constant temperature. Dispersion of experimental measurements is due to experimental methods and variations in material composition, processing, and history. Measurements of stress and strain were made with care and sensitive instruments in order to reduce the dispersion associated with experimental methods to negligible levels compared to the dispersion associated with variation of the material properties from sample to sample. Replicate measurements were made to allow a more precise determination of the parameters and their dispersion due to material variability. Determination of the constitutive law parameters is based on a criterion of minimization of the deviation of the predicted stress and measured stress from several cyclic load histories. In this investigation the authors: evaluate representative constitutive models in one dimensional states of stress, identify the constitutive model parameters from an experimental database, determine the dependence of the parameters upon the material, strain history, and mean strain level by analysis of variance procedures and determine by statistic means the significance of various factors on material behavior. The agreement of stresses computed from the selected constitutive laws with the experimental data is evaluated by a relative error measure. Constitutive law parameters for error determination are taken as the average over the entire database of optimal parameters determined for each sample. The results in terms of the relative error measure indicate that: the range of variability of material response is 10% with a mean of 5%, the range for the kinematic and isotropic laws is up to 40% with a mean of 35%, and lastly the range for the Chaboche and B-L constitutive law is up 25% with a mean of 15%. The variability of material response is measured by the difference between the stresses in two samples when identical strain histories are imposed on each sample. The range and mean are defined as the statistical characterization of the stress difference over a set of various imposed strain histories. The range and associated mean for a particular constitutive law are the statistical characterization of the difference between the predicted and measured stresses for a set of strain histories Larger discrepancies are observed when parameters o
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