Strain-rate effects in rheological models of inelastic response (original) (raw)
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Study of plastic/viscoplastic models with various inelastic mechanisms
International Journal of Plasticity, 1995
This paper describes a general framework for the development of plastic or viscoplastic constitutive equations. As the applications are focused on cyclic loadings, only small strains are considered, with an additive decomposition of the total strain into a thermo-elastic part, and several inelastic parts, the evolution of which is determined by several plastic or viscoplastic criteria. Quadratic or linear (crystallographic) criteria could be used, so that the approach is able to describe the contribution of several physical levels, or deformation mechanism, to the inelastic behavior. The present work is restricted to the case of quadratic criteria, and specially to the study of tlhe various interactions which can be introduced between the mechanisms. The most important case is the coupling between kinematic hardening variables which allows to describe: (1) either noraaal rate sensitivity or inverse rate sensitivity; (2) plasticity-creep interaction; (3) ratcheting for high mean stress but either adaptation or plastic shakedown for lower mean stress.
Rate-dependent inelastic constitutive equation: the extension of elastoplasticity
International Journal of Plasticity, 2005
A rate-dependent inelastic constitutive equation is formulated by extending the elastoplastic constitutive equation so as to retain the latter's mathematical structure and thus reduce to the latter equation at an infinitesimal rate of deformation. That structure differs substantially from that of the over-stress model, the best-known rate-dependent inelastic constitutive model. The proposed constitutive model is a type of superposition model, which is premised on the additive decomposition of the inelastic strain rate into the plastic and creep strain rates. The plastic strain rate is formulated so as to become suppressed as the rate of deformation increases but is induced even at the infinite rate of deformation. This is the distinguishing features of this model from the existing superposition models. The present model can describe realistically the rate-dependent inelastic deformation for a wide range of strain rates. On the other hand, the over-stress model cannot predict appropriately the difference of mechanical response due to the rate of deformation, especially being inapplicable to the description of deformation at high rate of deformation as known from the unrealistic prediction of the infinite strength at an infinite rate of deformation. The proposed model is applied to various metals, and its adequacy is verified through comparisons with various test data under a wide variety of strain rates and temperatures.
Generalized Rate-Dependent Inelastic Constitutive Equation. The Extension of Elastoplasticity
Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
A rate-dependent inelastic constitutive equation is formulated by extending the elastoplastic constitutive equation so as to retain the latter's mathematical structure and thus reduce to the latter equation at an infinitesimal rate of deformation. That structure differs substantially from that of the over-stress model, the best-known rate-dependent inelastic constitutive model. The proposed constitutive model is a type of superposition model, which is premised on the additive decomposition of the inelastic strain rate into the plastic and creep strain rates. The plastic strain rate is formulated so as to become suppressed as the rate of deformation increases but is induced even at the infinite rate of deformation. This is the distinguishing features of this model from the existing superposition models. The present model can describe realistically the rate-dependent inelastic deformation for a wide range of strain rates. On the other hand, the over-stress model cannot predict appropriately the difference of mechanical response due to the rate of deformation, especially being inapplicable to the description of deformation at high rate of deformation as known from the unrealistic prediction of the infinite strength at an infinite rate of deformation. The proposed model is applied to various metals, and its adequacy is verified through comparisons with various test data under a wide variety of strain rates and temperatures.
Rate equations for viscoplastic materials subjected to finite strains
International Journal of Plasticity, 1988
The constitutive equations for plasticity proposed by VoYL~m 11984] and VOrtADJ1S KIOUSlS [1987l are modified here in order to introduce rate sensitivity in the plastic region. Some of the basic concepts of the theory of viscoplasticity outlined by NAGHDi & MURCH [1963], ~^ a Womo [ 1966l, and E~Ro a YEar [1981] are used in this work in order to obtain the proposed viscoplastic constitutive model for finite strain deformation analysis.
A class of viscoelastoplastic constitutive models based on the maximum dissipation principle
Mechanics of Materials, 2000
A class of viscoelastoplastic constitutive models is derived from the maximum inelastic dissipation principle, in the framework of in®nitesimal deformations, and in analogy to the elastoviscoplastic case examined in Simo and Honein (cf. Simo, J.C., Honein, T., 1990. J. Appl. Mech. 57, 488±497). Here the existence of the equilibrium response functional with respect to which the overstress is measured, and the existence of an instantaneous elastic response (Haupt, P., 1993. are assumed. A broad set of overstress functions turns out to characterize the class of models derived herein. Both the¯ow rule for the viscoplastic deformation and the rate form of the constitutive equation for the class of models cited above are obtained, and the behavior of this equation under very slow strain rates and very high viscosity is investigated. A numerical simulation is also given by selecting two overstress functions available in the literature (Haupt, P., Lion, A., 1993. Continuum Mech. Thermodyn. 7, 73±90;. In: Rie, K.T. (Ed.), Low-Cycle Fatigue and Elasto-Plastic Behavior of Materials. Elsevier, New York, pp. 137±148). Loading conditions of repeated strain rate variation, monotonic strain rate with relaxation and cyclic loading at dierent strain rates are examined, and qualitative agreement is shown with the experimental observations done in Krempl and Kallianpur and Haupt and Lion (cf. Krempl, E., Kallianpur, V.
Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials.
Frattura ed Integrità Strutturale
The behavior of thermoplastics depends on several factors, mainly time and temperature. The present work is focused on an analysis of the time sensitivity of the viscoelastic and viscoplastic parameters of a rheological model. The material considered in this study is a polyamide 6. The analogical model is represented by the Kelvin-Voigt viscoelastic mechanism mounted in series with a viscoplastic branch of Bingham. After a mathematical formulation of the equations governing the model, tensile tests at different strain rates are conducted. The model parameters are then identified by inverse analysis. The technique of genetic algorithms has been favored. A nonlinear dependence of these parameters on the rate of strain has been observed. The dependence function has been established by a nonlinear regression technique. The comparison of the experimental results with those obtained by the model reveals a satisfactory agreement, hence the validation of the approach adopted.
The consequence of different loading rates in elasto/viscoplasticity
Procedia Engineering, 2011
In the present paper computational applications are illustrated with reference to elasto/viscoplastic problems. The influence of different loading programs on the inelastic behaviour of rate-sensitive elasto/viscoplastic materials is illustrated with specific numerical examples. An associated formulation of the evolutive laws is adopted. Different loading procedures are taken into account by considering different values of the loading rates and of the intrinsic properties of the material. A suitable integration scheme is applied and a numerical example is considered by analysing different loading programs. Numerical computations and results are reported which illustrate the ratedependency of the constitutive model in use. Consequently the significance of the loading program is emphasized with reference to the non-linear response of rate-dependent elasto/viscoplastic materials.
The role of strain rate in the dynamic response of materials
We start with the response of ductile materials. To understand the response of these materials to fast dynamic loadings, we introduce two approaches to dynamic viscoplasticity. These are the flowstress approach and the overstress approach, and strain rate has different roles with these two approaches. At very high loading rates the flowstress approach implies very high strength, which is hard to explain by microscale considerations, while the overstress approach does not.We then demonstrate the advantage of using the overstress approach by applying the two approaches to the elastic precursor decay problem. Next use the overstress approach to treat the following problems: 1) the 4 th power law response in steady flow of ductile materials; 2) high rate stress upturn (HRSU) of ductile materials; and 3) HRSU of brittle materials. With these examples we demonstrate the advantage of using the overstress approach over the flowstress approach. It follows that HRSU means High (strain) Rate Stress Upturn and not High Rate Strength Upturn, as would follow from using the flowstress approach.