Showing papers on "Viscoplasticity published in 1978"
TL;DR: In this paper, the problem of elastic spring-back is investigated and transient free surface solutions are demonstrated for stretch forming and deep drawing, which is shown to be capable of dealing with boundary friction and strain hardening.
297 citations
TL;DR: In this article, the authors compare endochronic and non-associated plastic formulations by introducing an "inelastic stiffness locus", defined as the locus of all strain increments in the strain space which give the same magnitude of inelastic strain increments.
126 citations
TL;DR: In this article, Elastic-viscoplastic constitutive equations based on a single internal state variable which is a function of plastic work are used to calculate the response of copper to a six decade change of strain rates over a range of temperatures.
Abstract: : Elastic-viscoplastic constitutive equations based on a single internal state variable which is a function of plastic work are used to calculate the response of copper to a six decade change of strain rates over a range of temperatures. Calculations were performed for the conditions of an experimental program on copper by Senseny, Duffy, and Hawley, namely, temperatures ranging from 77 to 523 K and strain rate jumps from .0002/sec to 300/sec at three strain levels. The computed results are in good agreement with the experiments and show similar strain rate and strain rate history effects. Relations are obtained for the temperature dependence of certain parameters in the equations which indicate correspondence between plastic working and temperature and between strain rate sensitivity and temperature. (Author)
58 citations
TL;DR: In this paper, an assessment of the incremental solution methods for the analysis of inelastic rate problems is presented, in which the possibilities of the initial load method are explored to improve the accuracy and stability of the traditional explicit operators by higher-order time expansions and implicit weighting schemes.
58 citations
01 Jan 1978
TL;DR: In this article, the rate-sensitive flow theory and the nonlinear theory of membrane shells were used to solve the problem of plane strain and axisymmetric punch stretching with Coulomb friction.
Abstract: Plane strain and axisymmetric punch stretching problems incorporating Coulomb friction are considered. Based on a general rate-sensitive flow theory and the nonlinear theory of membrane shells, the formulation includes work hardening and normal anisotropy. Two numerical schemes are presented. One is an extension of a previously developed finite element method (restricted to axisymmetric or plane strain problems) while the other is a nonlinear iterative method (restricted to plane strain). Experimental data on aluminum-killed steel are used to devise an explicit form for the rate dependence, and these schemes are applied to plane strain punch stretching (by a flat bottomed punch) and to hemispherical punch stretching. It is shown that a theoretical instability associated with the elastic-plastic analysis in plane strain stretching is removed by inclusion of the strain rate effect, while a better fit to experimental data on strain distribution in hemispherical punch stretching is obtained.
49 citations
TL;DR: In this article, the finite element technique is employed in the solution of elastic-viscoplastic plate bending problems, which is applicable to both thick and thin plates and by attaining steady-state conditions the process offers an alternative method of solution for static elasto-plastic situations.
20 citations
TL;DR: A numerical technique based on the method of singular surfaces has been developed for the computation of wave propagation in solids exhibiting rate-independent elastic-plastic or rate-dependent elastic-viscoplastic behavior.
14 citations
13 citations
TL;DR: In this paper, a phenomenological thermodynamic theory of viscoplasticity is presented, in which the internal variables are the plastic deformation tensor and a hardening variable.
Abstract: A phenomenological thermodynamic theory of viscoplasticity is presented in which the internal variables are the plastic deformation tensor and a hardening variable. The latter is defined in such a way that a yield criterion follows from the dissipation inequality if the free energy is an increasing function of the hardening variable. The limiting case of inviscid plasticity is explored, and the significance of the results is discussed in terms of dislocation kinematics.
10 citations
TL;DR: In this paper, the significance and calculation of dynamic plastic mode-form solutions for small deflections of structures of rigid perfectly-plastic materials subjected to load systems of fixed distribution and magnitude are discussed.
Abstract: D iscussion is given of the significance and calculation of dynamic plastic mode-form solutions for small deflections of structures of rigid perfectly-plastic materials subjected to load systems of fixed distribution and magnitude. These solutions have separated form, with velocity the product of a scalar function of time by a vector-valued function of space variables. The relation is shown on the one hand to mode-form solutions for a structure of viscoplastic material, and on the other hand to limit-load solutions for those of perfectly-plastic behavior. Numerical examples are given for circular plates of material obeying the Tresca and Mises laws.
9 citations
TL;DR: In this article, a modified four-constant Oldroyd model is used to predict the film thickness in free coating and the results indicate that a more adequate characterisation of the coating fluid might produce better agreement.
Abstract: A modified four-constant Oldroyd model is used to predict the film thickness in free coating. The parameters are evaluated from previous steady shear data. The flow is assumed to be one of combined steady shearing and elongation. Despite the use of an integral momentum balance approach the agreement between theory and experiment is not good. However, the results seem to indicate that a more adequate characterisation of the coating fluid might produce better agreement.
TL;DR: In this article, a phenomenological development of a constitutive equation for the high temperature viscoplastic flow of a metal is presented, which rests on a viscoelasticity foundation but incorporates several features of a classical metals theory.
Abstract: A phenomenological development of a constitutive equation is presented for the high temperature viscoplastic flow of a metal. The development rests on a viscoelasticity foundation but incorporates several features of a classical metals theory. The one dimension representation is developed using the creep response, strain rate response, and stress rate response of wrought Udimet 700 at 926.7°C (1700°F). The strain response to several cyclic stress histories is successfully predicted using the model. A three dimensional theory is proposed.
01 Jul 1978
TL;DR: In this article, the rate sensitivity, creep, and relaxation of viscoplasticity were investigated in a cyclic steady state environment with positive loads up to 15% strain and showed that the relaxation behavior depends only on the strain rate preceding the relaxation test and is independent of the strain magnitude.
Abstract: : The results show significant rate sensitivity, creep, and relaxation. Test histories involving loading and unloading with positive loads up to 15% strain show that the relaxation behavior in the plastic range depends only on the strain rate preceding the relaxation test and is independent of the strain magnitude. Also, the relaxation behavior is uniquely related to the stress changes corresponding to instantaneous large changes in the strain rate during tensile tests. Completely reversed strain controlled loading gradually changes the stress-change strain-rate-change behavior. Annealed specimens and specimens loaded to a cyclic steady state differ not only in their work hardening characteristic but also in their rate-dependent behavior. In the cyclic steady state different hysteresis loops are traced for different strain rates with fully reversible transitions from one hysteresis loop to the other under strain-rate changes. These results support the notion that viscoplasticity can be represented by piecewise nonlinear viscoelasticity.
01 Jul 1978
TL;DR: In this paper, a constitutive equation nonlinear in the Cauchy stress and the engineering strain but linear in the stress and strain rates is specialized to an overstress model.
Abstract: : A previously proposed uniaxial constitutive equation nonlinear in the Cauchy stress and the engineering strain but linear in the stress and strain rates is specialized to an overstress model. Two unknown coefficient functions are determined by extrapolation of room temperature relaxation data on Type 304 stainless steel. The stiff first-order nonlinear differential equations are then numerically integrated for a variety of test histories.
TL;DR: In this paper, a combined tension-torsion impact testing apparatus with special mechanics was designed which could apply a combined stress pulse with a very short rise time, about 15 μs, to a thin walled tube.
Abstract: Through a theoretical study on the general constitutive equation for an elastic/viscoplastic/plastic body, the experimental methods to examine the existence of the instantaneous plastic property and to obtain directly a practical form of the general equation are given. Combined tension-torsion impact testing apparatus with special mechanics was designed which could apply a combined stress pulse with a very short rise time, about 15 μs, to a thin walled tube. In an experiment of the incremental torsional impact to commercial pure aluminum and copper specimens, the analogous phenomena to the instantaneous plastic response were observed for both materials.
TL;DR: In this paper, Gershberg et al. determined the temperature dependence of the shear and normal-elastic moduli on woven-fiberglass specimens cut out along the base, along the weft, and at 45 °.
Abstract: The total deformation in a small neighborhood (in the vicinity) of points can be separated into the following components: elastic, plastic, viscoelastic, and viscoplastic deformations. The mathematical apparatus required to determine each of these deformations has been developed, and each of them may possess physically nonlinear and linear components. The results of tests of certain materials at room temperature are presented in Table 2. If we take the total deformation as 100%, it is apparent from the table that the specific weight of each component of the total deformation varies considerably due to the type of material, and the direction, rate, and duration of the loading. This means that in each individual case, we should establish what deformation components can be disregarded and which of them are determining components. Note that in modern engineering, the appearance of viscoelastic, plastic, and viscoplastic deformations is inevitable, and even desirable. Of all the forms of deformations, elastic deformations are undoubtedly the simplest. There are, however, a number of difficulties in determining the elastic characteristics of a material. Gershberg et al. [2], therefore, investigated certain characteristics of the pulse method of determining the technical elastic constants of fiberglass. They computed the normal modulus of elasticity from the resonant frequency of the first tone of bending oscillations of rod specimens and a ring. They determined the temperature dependence of the shear and normal-elastic moduli on woven-fiberglass specimens cut out along the base, along the weft, and at 45 ° . A quantitative description of the temperature dependence of the dynamic elastic modulus in shear and the loss factor of a rigid cellutar polymer material on the basis of the linear theory of viscoelasticity is given
TL;DR: In this article, the instantaneous and delayed behavior of a double shear perturbation superimposed on an equilibrium state of an isotropic incompressible medium with internal variables is presented Elastic media with general internal variables and true viscoplastic media with an intermediate configuration and particular internal parameters are successively considered.
TL;DR: In this paper, a variational equation equivalent to a complete system of differential equations is derived for a compressible plastic body, which is used for solving problems of the mechanics of soils and friable media and for the plastic shaping of uncompacted materials.
Abstract: Variational methods used in the theory of plastic flow are formulated on the assumption of the incompressibility of the deformable medium. In solving problems of the mechanics of soils and friable media and technological problems of the plastic shaping of uncompacted materials it is very important to take account of irreversible volumetric change. Extremum and variational theorems are proved in [1, 2] for rigid-plastic and viscoplastic expanding bodies. A variational equation equivalent to a complete system of differential equations is derived for a compressible plastic body.
01 Jun 1978
TL;DR: In this paper, the combination of plasticity and viscoelasticity is the basis for the so-called visco-elastic-plastic model developed in the 1990s.
Abstract: : A textbook style development of viscoplasticity is presented. For completeness, the report also includes a detailed review of plasticity and viscoelasticity. The combination of plasticity and viscoelasticity is the basis for the so-called viscoelastic-plastic model developed herein. Other combo- viscoplastic models are also introduced. Each constitutive model is introduced with conceptual one-dimensional stress-strain models and then generalized for multidimensional stress space. Furthermore, each model is cast in an incremental form appropriate for numerical solution techniques. Finite element algorithms are outlined for incorporating these nonlinear constitutive models into boundary value problems. In particular, tangent stiffness and initial strain methods are discussed. The viscoelastic-plastic model is compared to experimental data for plexiglas and sea-ice to illustrate the versatility of the model in replicating nonlinear creep and flow of these materials. Moreover, the identification of the model parameters are shown to be no more difficult than the identification of parameters for the classical theories of plasticity and viscoelasticity.
01 Mar 1978
TL;DR: In this paper, the response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically, where a Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed.
Abstract: The response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically. A Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed. The plate deforms with monotonically increasing deflections until the dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid viscoplastic materials. For the small deflection bending response of the plate, the governing system of equations is essentially nonlinear. Transverse shear stress is neglected in the yield condition and rotary inertia in the equations of dynamic equilibrium. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and to obtain the analytical solutions in the form of eigenvalue expansions. The effects of load concentration, of an order of magnitude change in the viscosity of the plate material, and of load duration were examined while holding the total impulse constant.
TL;DR: In this paper, a study of the delayed behavior of perturbations in isotropic elastic-viscoplastic media is extended to include usual macroscopic hardening parameters and particular evolution laws proposed in plastic theories.
01 Mar 1978
TL;DR: In this paper, the response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically, where a Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed.
Abstract: The response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically. A Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed. The plate deforms with monotonically increasing deflections until the dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid viscoplastic materials. For the small deflection bending response of the plate, the governing system of equations is essentially nonlinear. Transverse shear stress is neglected in the yield condition and rotary inertia in the equations of dynamic equilibrium. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and to obtain the analytical solutions in the form of eigenvalue expansions. The effects of load concentration, of an order of magnitude change in the viscosity of the plate material, and of load duration were examined while holding the total impulse constant.
TL;DR: In this article, an approximate solution to the non-linear differential equation governing the behavior of a viscoplastic material in tension is given, which is used to generate an accurate estimate for the upper yield point for the material.
Abstract: An approximate solution to the non-linear differential equation governing the behavior of a non-linear, viscoplastic material in tension is given. This solution is used to generate an accurate estimate for the upper yield point for the material. The results are compared to those previously obtained by other means.