Showing papers on "Viscoplasticity published in 1982"

Numerical modeling of intraplate deformation: Simple mechanical models of continental collision

Abstract: We study a model of continental collision in which one of the continents acts as a rigid die indenting the other plate which flows as an incompressible viscoplastic medium. We consider two extreme cases of plane deformation: (1) plane strain which corresponds to an infinitely thick lithospheric plate, and (2) plane stress corresponding to a very thin plate. Deformation of the lithosphere, a thick plate, should be intermediate between those extremes. We found that the flow in the plane strain case is quite similar to that obtained by slip line, theory. The plane stress results are quite different, since in this case most of the plate shortening is taken up by the thickening of the lithosphere. We also explored the role of boundary conditions on the flow, in particular, the role of the side walls containing the flow of the lithosphere. In the case of a free lateral boundary the main feature is a flow of matter toward this free wall and a S-like pattern for the horizontal stress field. For a rigid wall, on the other hand, the plane strain and the plane stress results are quite different. In the first case, there is a large return flow on the sides of the punch, the material being extruded along the only free surface available. In the plane stress case, the return flow disappears, and the material displaced by the penetration of the die tends to thicken the plate. The role of a nonlinear constitutive relation is studied for power law creep. As the power of the flow limit increases, the flow retains its general features, but the deformation localizes creating sharper contrasts between high and low strain rate areas; in plane stress, the effect of nonlinearity is to increase the contrasts in vertical motion. Available data for Asia are discussed in the light of the new results.

Theory of viscoplastic shells for dynamic response

Abstract: : Viscoplastic shell model is formulated which utilizes the shell membrane strains and curvatures as the kinematic variable and the shell stress resultants as the dynamic variables. The viscoplastic shell model combines the concept of Perzyna's viscoplastic constitutive equations with Bieniek's shell stress resultant formulation. The model is incorporated into the EPSA code for the analysis of shells in an acoustic medium subjected to dynamic loading which produce large elasto-viscoplastic deformations in the shell. Several examples are presented to exhibit the effect of material rate dependence upon structural response.

A statistical theory of polycrystalline plasticity

Abstract: The plasticity and viscoplasticity of polycrystalline materials are studied analytically in terms of lattice dislocations, with the principal effects attributed to non-extended obstacles. Non-equilibrium statistical mecha­nics is used to describe the evolution of the dislocation structures during loading and unloading processes. A plausible variation in the probability density function for mobile dislocations for such processes is suggested. The proposed material model is in good qualitative agreement with several observed phenomena that previously could not be quantified on the basis of the dislocation theory. Numerical examples illustrate the effect of the rate of loading, the variations in the recovery effect as it relates to the extent of load reversal, and a means for treating materials that exhibit a yield plateau. In the limit, the proposed model yields results for inviscid plasticity.

Finite-Element Formulation for the Analysis of Plastic Deformation of Rate-Sensitive Materials in Metal Forming.

Abstract: : The finite-element formulation for the analysis of metalworking problems for rigid-viscoplastic materials, including the effect of temperature, has been established. Of particular significance is an accomplishment of the coupled analysis of deformation and heat transfer. The formulations were applied to the problems of solid cylinder compression and ring compression. Then, the forming processes of shell nosing at room temperature, as well as at elevated temperatures, were analyzed. The results demonstrate that it is now possible to analyze accurately not only cold forming processes, but also processes in warm and hot forming regimes, by the finite-element method, including the effects of strain, strain-rate, and temperature on material properties. Most recent achievement is an introduction of a new approach to the problem of preform design in shell nosing as a unique application of the finite-element method. The concept involved in the approach is to trace backward the loading path from a given final configuration. The method was applied to preform design in shell nosing. (Author)

On the non‐linear ‘squeezing’ effects around circular tunnels

Abstract: An analysis is presented of the non-linear creep effects around a deep circular tunnel driver in "squeezing" ground. The time-dependent behaviour of the geotechnical medium is described by means or a simple viscoplastic rheological model capable of approximating primary, secondary and Tertiary creep behaviours. It is shown that Tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the "evolutive" procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered. (Author/TRRL)

Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical transmission lines

Abstract: For the subject media the constitutive laws remaining invariant under the dilatation and spiral groups are determined. Then exact invariant solutions are constructed for a classical (linear) material, for a quadratic constitutive law and for a linear viscoelastic material. Lastly, a viscoplastic material is studied in the light of group analysis and the machinery to determine the solution (numerically) for a variety of viscoplastic problems is established.

The Role of Servocontrolled Testing in the Development of the Theory of Viscoplasticity Based on Total Strain and Overstress

Abstract: The rate-dependent properties of AISI Type 304 stainless steel and of the high-strength Ti-7Al-2Cb-1Ta alloy obtained with tension specimens using a servocontrolled testing machine at room temperature are discussed. Testsinvolve strain rates between 10 - 8 and 10 - 2 s - 1 , strain rate changes, relaxation periods, stress rates between 10 - 1 and 10 2 MPa s - 1 , and creep periods. The viscoplasticity model based on total strain and overstress is introduced and shown to qualitatively reproduce the properties observed under strain control. The theory is then examined for its qualitative prediction under stress control, and it is found that the average creep rate need not increase with an increase in stress owing to the overstress (effective stress) dependence of the creep rate. Numerical experiments illustrate this property, which is then confirmed by real experiments. The theory has two material functions representing work hardening and rate dependence. A method of determining the function representing rate dependence from strain rate change tests is discussed. For Type 304 stainless steel this function is represented by two equivalent expressions which can be used from static (10 - 8 s - 1 ) to dynamic strain rates (10 3 s - 1 ). A rate sensitivity factor M (akin to the m-factor used in materials science) is introduced. It is shown to vary with overstress or strain rate.

Elasto-viscoplastic and elasto-plastic large deformation analysis of thin plates and shells

Abstract: To account for plastic deformation in plate and shell structures an elasto-viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time-dependent elasto-viscoplastic situations and by allowing steady-state conditions to be reached, elasto-plastic problems can also be considered. For the large displacement elasto-viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization. The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources where available.

Comparison of the unloading and reversed loading behavior of three viscoplastic constitutive theories

Abstract: The predictions of three constitutive theories of viscoplasticity are compared in uniaxial homogeneous reversed loading. Previously each theory has been fitted to the same set of tensile data (E.P. Cernocky, Technical Report, University of Colorado, 1981), and here both analytical and numerical methods are used to highlight similarities and differences in the predictions of the theories. None of the theories use yield surfaces, and unloading is shown to be both inelastic and rate-dependent. Suitable combinations of strain- (stress-) rates are shown to produce unloading which appears elastic. Relaxation is examined in the unloading region, and the responses of the theories are shown to be qualitatively different. A bias is shown to exist between each theory's prediction in stress- and strain- control. A new cyclic test is demonstrated which highlights differences in the history-dependence modeled by the theories, and they are shown to have different memories for the same prior plastic deformations.

Multiaxial Creep of 2618 Aluminum Under Proportional Loading Steps

Abstract: : Creep data of 2618-T61 aluminum alloy under multistep multiaxial proportional loadings at 200 degrees C (392 degrees F) are reported. Two viscoplastic flow rules were developed using constant stress creep and strain recovery data. One was based on the accumulated strain (strain hardening), and the other on a tensorial state variable (kinematic hardening). Data were represented by two models: a nonrecoverable viscoplastic model and a viscous-viscoelastic model in which the time-dependent strain was resolved into resolved into recoverable (viscoelastic) and nonrecoverable components. The modified superposition principles was used to predict the viscoelastic strain component under variable stress states for both models. The experiments showed that the viscous-viscoelastic model with either strain-hardening or kinematic hardening gave very good predictions of the material responses. Strain hardening was best in some step-down stress states. The viscoelastic component accounted for not only the recovery strain but also the transient creep strain upon reloadings and step-up loadings.

Homogeneous Flow in Metallic Glasses

Abstract: Creep of an iron based glassy alloy (FeBSiC) is studied: both aspects (viscoelastic and viscoplastic) of deformation, the relation between strain rate and stress, and the effect of structural relaxation are precised. A model of homogeneous deformation of metallic glasses near Tg, able to take all the experimental features into account, is proposed. Following such a model, the plastic deformation would be principally dependent on recovery processes associated to structural relaxation. Le fluage d'un alliage vitreux FeBSiC a ete etudie: le caractere a la fois viscoelastique et viscoplastique de la deformation, la relation entre vitesse de deformation et contrainte appliquee et, enfin, l'effet de la relaxation structurale ont ete precises. Apres avoir discute certains hypotheses physiques, un modele de deformation homogene pouvant rendre compte du comportement des verres metalliques vers Tg, est propose. Selon ce modele, la deformation plastique, serait essentiellement commandee par des processus de restauration associes a la relaxation structurale.

Rock dilatancy in uniaxial tests

Abstract: Rock Dilatancy in Uniaxial Tests A procedure to find an elastic/viscoplastic constitutive equation able to describe rock dilatancy in uniaxial unconfined creep tests is given starting from experimental data. The influence of the loading rate on the rock dilatancy can also be described with this model. It is shown that a creep of the volume takes place during tests and that this volume creep has the following property: the volume strain is oscillating before ariving at its final stable value. This property is described by the proposed mathematical model using a variable viscosity coefficient which may change sign. According to the model the volume creep takes place during loading only.

Implicit time integration of elasto-viscoplastic solids subject to the Mohr-Coulomb yield criterion

Abstract: For selected situations in geotechnical engineering, the use of implicit time integration techniques for elasto-viscoplastic analysis is advantageous, or even unavoidable. In this paper the necessary expressions are derived for the implicit analysis of a material governed by the Mohr-Coulomb yield criterion. In particular, detailed expressions are provided for the viscoplastic, strain rate derivative matrix Hn in a form suitable for numerical computation. Use of this algorithm is illustrated by the solution of a numerical example.

The Application of a Theory for Elastic Fluids in Suspension Rheology

Abstract: A theory for elastic fluids is developed using a tensor analogous to the Cauchy deformation measure to characterize the microstructure. The resulting mechanical theory is equivalent to that formally proposed by Hand. A free energy function is introduced and the constitutive functions are required to satisfy a dissipation inequality in any possible motion. Sufficient conditions for satisfying this inequality are obtained for constitutive functions that are linear in the rate of deformation. Several molecular theories of suspensions that are of this form appear to be inconsistent with some of these conditions. A particular theory that satisfies the dissipation inequality is analyzed in steady shear and elongational flows. This five‐constant model describes a shear‐thinning fluid with a nonvanishing extinction angle at high shear rates. Yield phenomena exhibited by some suspensions can be incorporated easily here through the material parameters.

Analyses of ductile flow and fracture in two dimensions

Abstract: Previous work on analysis of viscoplastic flow and spall fracture by ductile void growth has been extended to configurations to two‐dimensional plane strain and axisymmetric deformation. Current work includes reduction of the general theory to a form applicale to these cases, and incorporation of the resulting equations into a Lagrangian finite‐difference code suitable for analyzing nonlinear wave propagation. Results of applying this code to study of symmetric axial impact of aluminum bars are presented.

Stress wave propagation in an elastic/viscoplastic half-space containing a spherical cavity

Abstract: The governing equations of the dynamic problems in an elastic/viscoplastic three-dimensional medium containing spherical cavities are formulated by means of bipolar coordinates introducing a generalized strain rate tensor. As numerical examples, the stress wave propagation in an elastic/viscoplastic half-space containing a spherical cavity is analyzed by the method of direct integration of the basic equations of the problem, when an axisymmetric dynamic load is applied to the plane boundary by impact of a projectile with the boundary. Stress distributions on the boundary of the spherical cavity and the plastic wave front in the semi-infinite body are shown for successive times. It is also illustrated that, when a dynamic load is applied on a small area in the plane boundary, the tensile stress arises at the upper portions of the cavity.