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Showing papers on "Viscoplasticity published in 1986"


Journal ArticleDOI
TL;DR: In this article, an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations was carried out, where attention was confined to infinitesimal deformations.
Abstract: An accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate-independent and rate-dependent behaviour, with plastic hardening or softening, associated or non-associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.

800 citations


Journal ArticleDOI
TL;DR: In this article, a review of papers published during the last 10 or 15 years to describe the crack behavior in structures by means of continuum damage mechanics is presented, focusing on a classification of the different methods used and on the different behaviors taken into account: elasticity, plasticity, viscoplasticity; brittle damage, fatigue damage, ductile and creep damages.

363 citations


Journal ArticleDOI
TL;DR: In this paper, an elastic-viscoplastic model of a material with internal imperfections is proposed, which describes the work-hardening viscoplastic response of solid and takes also account of the interactions of microvoids.

144 citations


Journal ArticleDOI
TL;DR: In this article, a self-consistent averaging scheme is proposed for estimating the overall, finite deformation response of polycrystalline aggregates consisting of single crystals which undergo plastic flow by rate-dependent crystallographic slip, accompanied by elastic lattice distortion.
Abstract: Based on Hill’s method, a self-consistent averaging scheme is proposed for estimating the overall, finite deformation response of polycrystalline aggregates consisting of single crystals which undergo plastic flow by rate-dependent crystallographic slip, accompanied by elastic lattice distortion. First, constitutive relations for such single crystals are developed assuming that the slip-rate and the associated resolved shear stress are governed by: (1) a power-law relation, and (2) a viscoplastic relation. Then, Hill’s idea that the constraint imposed on a single crystal by the remaining aggregates may be represented by embedding the single crystal in a homogeneous, infinitely extended matrix having the instantaneous overall moduli, is used to formulate a completely self-consistent averaging procedure, valid for rate-dependent materials at finite strains and rotations. This method includes both the Hill and the Krӧner‒Budiansky‒Wu (K. B. W.) methods as limiting cases; when rate-effects are negligible, it reduces to Hill’s self-consistent method as formulated by Iwakuma and Nemat-Nasser for finite deformations, while it reduces to a generalized finite deformation version of the K. B. W. method for strongly rate-dependent materials. Illustrative numerical examples are presented for a plane uniaxial deformation, using a two-dimensional poly crystalline model. These examples clearly show that the rate-dependent crystallographic slip on the level of single crystals produces a more stable overall behaviour of poly crystals. This supports similar results arrived at by other investigators for single crystals and for polycrystals, by using the Taylor averaging scheme. It is shown that, while Taylor’s averaging scheme gives accurate estimates of the incremental quantities at large strains, the total overall quantities differ considerably from the ones obtained by the self-consistent method.

140 citations


Journal ArticleDOI
TL;DR: In this paper, two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate-dependent inelastic behavior of structural metals in the absence of recovery and aging.

140 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of strain hardening, strain rate sensitivity, thermal softening, heat conduction and the imposed strain rate on the shear localization process in plane strain compression are examined.

135 citations


Journal ArticleDOI
TL;DR: In this paper, the authors study simple models of collision between two continental plates patterned after the geometry of the India-Asia collision, but which may be applicable to more general situations.
Abstract: Summary. We study simple models of collision between two continental plates patterned after the geometry of the India-Asia collision, but which may be applicable to more general situations. The collision is modelled by the indentation of a viscoplastic plate (Asia) by a rigid punch (India). Although deformation is three-dimensional in nature, a plate thickness of the order of 100 km permits a 2-D approach for wavelengths longer than a few hundred kilometres. We assume an Airy compensation at the crustmantle boundary throughout the deformation. We can then reduce the problem to a 2-D one within the context of thin plate theory. This model makes it possible to study crustal thickening during collisions. The opposition between buoyancy forces, which tend to flatten the topography, and viscous resistance, appears clearly and we show the existence of a relaxation mechanism associated with the volumetric part of the deformation. The asymptotic behaviour of the model is of the incompressible plane strain type and thus crustal thickening tends to a maximum value. When this limit is reached no more thickening is possible and distensive phenomena can be induced. Buoyancy effects can be described by a nondimensional parameter, the Argand number Ar, which is the ratio between the relaxation time and the characteristic time of the viscous flow. A finite element approximation, based on a material description of the finite deformation, is used to investigate the evolution of the indentation process. The role of pre-existing heterogeneity (stiff inclusion) is also considered. Lateral boundary conditions on the plate are chosen to approximate the boundary interactions that are believed to apply for the Asian plate, i.e.

96 citations


Journal ArticleDOI
TL;DR: In this paper, the hollow-sphere model with temperature-dependent viscoplastic material response was used to investigate thermal effects in shock compaction of metal powders, and the results showed that the dynamic compaction may be qualitatively different depending on whether viscoplastics or inertial effects dominate the pore collapse process.
Abstract: The hollow‐sphere model, with temperature‐dependent viscoplastic material response, is used to investigate thermal effects in shock compaction of metal powders Model calculations show very good agreement with experimental shock rise times only if the temperature dependence is considered The results also suggest that the dynamic compaction may be qualitatively different depending on whether viscoplastic or inertial effects dominate the pore collapse process

66 citations


Journal ArticleDOI
TL;DR: In this paper, the authors computed the viscoplastic stresses and dislocation densities in silicon ribbon for axially changing thermal profile by using an iterative finite difference method, which is interpreted as showing that there is a maximum width of silicon ribbon that can be grown when viscasticity and dislocations are considered.
Abstract: The thermal viscoplastic stresses and the dislocation densities in silicon ribbon are computed for an axially changing thermal profile by using an iterative finite difference method. A material constitutive equation (Haasen–Sumino model) which involves an internal variable (mobile dislocation density) is used. The results are interpreted as showing that there is a maximum width of silicon ribbon that can be grown when viscoplasticity and dislocations are considered. This maximum width limitation does not exist if the material behavior is elastic.

51 citations


Journal ArticleDOI
TL;DR: In this article, a procedure for including isotropic and directional damage as load-history dependent softening variables in a set of elastic-viscoplastic constitutive equations is described.

49 citations


Journal ArticleDOI
TL;DR: In this article, the case of creep crack growth is studied in detail, through the use of viscoplastic constitutive equations including creep damage effect, and the approach is applied to the creep of initially cracked CT specimen.

Journal ArticleDOI
Aris Phillips1
TL;DR: The authors discuss des travaux experimentaux bases on trois concepts: theorie de surface-deux de la plasticite, concept de methode de determination de la limite d'elasticite, courbe contrainte-deformation en equilibre ou quasistatique.

Journal ArticleDOI
TL;DR: In this paper, the authors describe the present possibilities of structure computer code EVPCYCL, made at ONERA to treat cyclic viscoplastic problems and present results of cyclic computations on a biaxial fatigue disc made in INCO 718 alloy and on axisymmetric notched specimens made in 316 stainless steel.

01 Jan 1986
TL;DR: In this paper, a metal forming model for analyzing large strain bulk operations such as forging, rolling, and drawing is presented. But the model is based on a damage model in which the porosity serves as an internal variable.
Abstract: A metal forming model is outlined for analyzing large strain bulk operations such as forging, rolling, and drawing. Plastic deformations are assumed to be viscoplastic in that the strain rate dependent flow stress depends on the strain hardening through an internal variable that evolves with the deformations. Volumetric deformations are linked to the growth of voids (porosity) using a damage model in which the porosity serves as an internal variable. Several applications are presented that demonstrate by comparison to experimental data that the model can simulate effectively the response of a workpiece under realistic forming conditions.

Journal ArticleDOI
TL;DR: In this paper, a model that represents inelastic behavior as coupled plastic and creep response was developed for a nickel base alloy, Hastelloy X, subjected to thermomechanical cycles in which both the mechanical strain and temperature are simultaneously changing.

Journal ArticleDOI
TL;DR: In this article, a damage parameter is introduced which is the total energy release due to microcracking when dilatancy takes place, expressed with the irreversible part of the volumetric stress power.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the theory of elastic-viscoplastic work hardening material proposed by Bodner and Partom for small deformations may be generalized for large deformations by reformulating the equations using Lagrangian quantities.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a material model consisting of a viscoelastic Burgers element and an additional viscoplastic element, which includes Bingham viscosity and a viscplastic Kelvin element.


Journal ArticleDOI
TL;DR: In this article, an application of augmented Lagrangian techniques to numerical solution of quasistatic flow problems in incompressible viscoplasticity, focusing on cases where the internal viscoplast dissipation potential is not a differentiable function of the material deformation rate, is described.
Abstract: : This report describes an application of Augmented Lagrangian techniques to the numerical solution of quasistatic flow problems in incompressible viscoplasticity, focusing on cases where the internal viscoplastic dissipation potential is not a differentiable function of the material deformation rate. The stresses of elastic origin are neglected, and the variational formulation of these problems is approximated via mixed finite elements of order 1. Convergence results are proved or recalled, both for the finite element approximation and for the augmented lagrangian algorithm. A detailed study of the local minimization problems which occur in the augmented lagrangian decomposition of the above problems is also presented, together with several numerical results. These results were obtained using the MODULEF finite element code on a VAX 780 at the Mathematics Research Center and cover successively the case of Norton, of Bingham and of Tresca type materials. (Author)

Book ChapterDOI
01 Jan 1986
TL;DR: In this paper, the hardening rules for metals in the range of small strains are discussed, where the evolution rules depend on a previous deformation history and can be formulated by either the structural approach or the representative variable approach.
Abstract: In this chapter the hardening rules for metals in the range of small strains are discussed The simple hardening rules, such as isotropic, kinematic or mixed hardening models, involve one scalar and/or one tensor state variable whose evolution rule is expressed in terms of the plastic strain rate The composite hardening rules involve more state variables and multiple loading surfaces for which evolution rules depend on a previous deformation history Such composite rules can be formulated by using either the structural approach or the representative variable approach Whereas the structural approach requires numerous state variables and material parameters, the representative variable approach offers a much simpler material description The creep hardening rules for viscoplastic deformation processes are discussed at the end of the chapter


Journal ArticleDOI
TL;DR: In this paper, coupled thermoviscoplasticiry equations for a thick-walled cylinder subjected to thermomechanical loading at the inner surface are presented and implemented in a finite-element program.
Abstract: The coupled thermoviscoplasticiry equations for a thick-walled cylinder subjected to thermomechanical loading at the inner surface are presented and implemented in a finite-element program. The numerical solution for a steel cylinder subjected to a single traction and temperature pulse shows considerable temperature rise due to mechanical energy dissipation. The results also suggest a criterion for the yield stress in order to avoid failure due to excessive viscoplastic deformation at the inner surface.

Journal ArticleDOI
TL;DR: In this paper, an implicit-explicit integration method for analyzing the quasi-static deformations of solids, in the elastic-viscoplastic range, including damage and temperature effects, is presented.

Journal ArticleDOI
TL;DR: In this paper, the velocity profiles and the stresses are not restricted by the usual assumptions of plane-strain or axially symmetric behaviour, however, the shear stresses, induced by wall friction, are small in comparison with the effective stress.

01 Oct 1986
TL;DR: In this article, a time dependent constitutive theory with stress dependence on J sub 2 and J sub 3 is presented, that reduces to a known J sub2 theory as a special case.
Abstract: Many viscoplastic constitutive models for high temperature structural alloys are based exclusively on uniaxial test data. Generalization to multiaxial states of stress is made by assuming the stress dependence to be on the second principal invariant (J sub 2) of the deviatoric stress, frequently called the effective stress. If such a J sub 2 theory, based on uniaxial testing, is called upon to predict behavior under conditions other than uniaxial, e.g., pure shear, and it does so poorly, nothing is left to adjust in the theory. For a fully isotropic material whose inelastic deformation behavior is relatively independent of hydrostatic stress, the most general stress dependence is on the two (non-zero) principal invariants of the deviatoric stress, J sub 2 and J sub 3. These invariants constitute what is known as an integrity basis for the material. A time dependent constitutive theory with stress dependence on J sub 2 and J sub 3 is presented, that reduces to a known J sub 2 theory as a special case.

Journal ArticleDOI
TL;DR: In this article, complex constitutive equations including nonlinear kinematic as well as isotropic hardening rules are introduced in the framework of the finite element method to analyse the behaviour of structures in quasi-static elasto-viscoplasticity under cyclic loadings.
Abstract: Complex constitutive equations including non‐linear kinematic as well as isotropic hardening rules are introduced in the framework of the finite element method to analyse the behaviour of structures in quasi‐static elasto‐viscoplasticity under cyclic loadings. An implicit time marching process is developed together with a substructuring technique and the corresponding numerical details are underlined. Practical examples are treated to demonstrate the capabilities of the proposed finite element code.

Book ChapterDOI
01 Jan 1986
TL;DR: In this paper, the authors outline a program suggesting new possibilities for describing the inelastic behavior of materials at the macro scale by properly considering the dominant features of the corresponding micro scale.
Abstract: We outline a program suggesting new possibilities for describing the inelastic behavior of materials at the macro scale by properly considering the dominant features of the corresponding micro scale We show, in particular, that many phenomenological theories of inelasticity ranging from classical plasticity and viscoplasticity to recent internal variable models can be recovered from the structure of single slip Single slip is assumed to occur by means of gliding dislocations which, in addition to their interaction with the lattice and themselves, can also be generated and annihilated The transition from the micro scale to the macro scale is realized through a maximization procedure motivated by an argument of microscopic irreversibility Even though the hypothesized microscopic configuration is highly idealistic, it is shown that the implied macroscopic situation is extremely rich It provides a framework for calculating the phenomenological coefficients of various plasticity theories and leads, among other things, to finite size shear band widths and a physically motivated analysis of large plastic deformations


Book ChapterDOI
01 Jan 1986
TL;DR: A review of elastic-viscoplastic constitutive equations that incorporate isotropic and directional hardening and additional hardening due to nonproportional loading is given in this paper.
Abstract: A review is presented of a set of elastic-viscoplastic constitutive equations that incorporate isotropic and directional hardening and additional hardening due to nonproportional loading. These equations employ the isotropic form of the flow law in the presence of directional hardening and a physical argument is given to justify this use. An alternative form of the flow law is also suggested that could account for deviations of the directions of stress and plastic strain rate. Generalization of the theory to large deformations has been carried out using Lagrangian quantities and thermodynamic restrictions. Examples of simple tension and simple shear show that the large strain theory produces physically plausible results.