Plastic Constitutive Relations Research Articles

Effect of Wall Roughness on Laminar Flow of Bingham Plastic Fluids through Microtubes

Miniaturization of traditional devices is in high demand formicro-electro-mechanical systems~MEMS!. Examples includebut are not limited to optics, communication and information sys-tems, fluidics, biotechnology, medicine, automotive, and aero-space. An area of interest in several engineering fields is the con-trol of fluid flow within microchannels and microtubes. Theapplications include, but are not limited to, fields such as vibrationcontrol of structures and systems using small devices, reactors formodification and separation of biological cells, energy systems asa mobile power supply, heat exchangers for micro and macro de-vices, and propulsion engines @1–3#.In recent years, there has been growing attention given to theliquid flow in microchannels in parallel with the development ofminiaturized devices and systems. The understanding of flowcharacteristics, such as velocity distribution and pressure loss isnecessary in design and process control of microfluidic devices.Peng, Peterson, and Wang @4# experimentally studied the flowcharacteristics of water flowing through rectangular microchan-nels having hydraulic diameters of 0.133 to 0.367 mm and heightto width ratios of 0.333 to 1. Their results indicated that the lami-nar flow transition occurred for the range of the Re number be-tween 200 and 700. They also claimed that friction behavior forboth laminar and turbulent flow depart from classical thermofluidcorrelations, and the friction factor is proportional to Re

Effect of Strain Gradient on Formation of Shear Band under Kinematic Hardening Rule

In the present work, the formation of shear band under simple shear loading is investigated using the rate-independent elastic-plastic constitutive relations. A small initial perturbation representing material imperfection is introduced into the work piece to develop the post-localization behaviors. Since kinematic hardening rule assumed under a finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure using the plastic spin concept. Moreover, the strain gradient terms are incorporated into the yield function to obtain a non-local plastic constitutive relation and its results are compared with a conventional plasticity model. It is noted that the shear band formation is accompanied by decrease in the magnitude of spatial increment within the regime of localization. Moreover, the strain gradient affects the shear localization behavior significantly such that the intensity of shear band increases as the strain gradient coefficient increases when the J2 flow theory is employed. The effect of strain gradient on the deformation localization is, however, almost negligible for a material deformed accord with the J2 deformation theory.

Damage model for metal–matrix composite under high intensity loading

A damage model for a composite structure under high intensity dynamic loading is presented. The model is based on a thermodynamic micromechanic approach, which is formulated using the conservation laws and the energy balance equations (the first and second laws of thermodynamics). A homogenization or averaging technique is implemented in the development to simplify the representation of the non-homogeneous material. The metal–matrix composite's inelastic response is modeled using elastic–plastic constitutive relations considering finite plastic strain and damage effect. The damage model is validated with experimental data available in the literatures, and it shows fairly good agreement. A parametric study demonstrating the characteristics of the damage model is also presented.

A numerical model of deformation and fluid-flow in an evolving thrust wedge

To investigate deformation and fluid-flow in an actively deforming tectonic wedge, we model the evolution of a large, two-dimensional (100 km long, 5 km thick), mechanically and hydrologically homogeneous and isotropic pile of sedimentary strata that is deformed to become a thrust wedge. We compare both ‘dry’ and ‘wet’ cases, in order to illustrate: (1) the relative importance of fluids on wedge evolution, and (2) the effect of brittle deformation on fluid-flow. We use an elastic–plastic constitutive relation, including a Mohr–Coulomb failure criterion and a non-associated flow rule, and coupled fluid flow, with bulk rock properties that approximate typical foreland sedimentary strata. Simulations are made both with and without dilation. The model is fully dynamic, but inertial forces remain small. Results show that deformation within the wedge is accommodated by reverse-slip movement on shear bands, which migrate in both directions through the wedge as both fore- and back-thrusts. The model has features predicted by the critical-taper theory: (1) overall wedge geometry; (2) crudely self-similar growth during evolution; (3) more intense deformation toward the rear of the wedge. The models show strong overall in-sequence faulting behavior with major thrusts isolating relatively undeformed packages, which are moved in a piggyback manner upon the active thrusts. Intermittent out-of-sequence faulting does however occur, in order to maintain the wedge taper. Fluid-flow in the deforming wedge is dominated by topography, but is also strongly affected by dilational plastic deformation. In all simulations, there is focused fluid flow within fault zones. When mechanical time-stepping is shut off (uncoupled), flow systems evolve to steady-state where inflow equals outflow. By subtracting the two ‘states’ we isolate the mechanical fluid response from the total coupled system response. The mechanical fluid response is manifest as contours of head and pressure difference and focusing of fluid-flow in areas of active deformation. In non-dilational simulations, these zones are quite localized and are a result of the contrasting stresses in and adjacent to a brittle shear zone. In simulations with dilation, the zones of head and pressure difference are broad and regional in extent. They are ten times greater in magnitude than in non-dilation simulations, and they track a rock-damage front that moves through the wedge.

A 3-D Finite Deformation Anisotropic Visco-Plasticity Model for Fiber Composites

A 3-D finite deformation anisotropic visco-plasticity model is presented for fiber composites in total Lagrangian co-ordinates. The plastic potential function is given by a quadratic function in stresses in the local co-ordinates system of the lamina. The model is used to derive the anisotropic plastic constitutive relation of a woven composite made of S-2 glass fibers embedded in polyester resinwith approximately 60% by weight of fibers. The coefficients of the constitutive model are experimentally determined through off-axis tension tests and out-of-plane shear tests. Off-axis tension tests are carried out by varying the angle between the fiber orientation and loading direction. The measured stress-strain curves are used to derive a master effective stress–effective plastic strain curve, which is described by two power laws. Amodified Arcan fixture is used to carry out pure shear tests to determine the out-of-plane shear coefficient. Compression tests are carried out to establish the material compressive response in the plane of the lamina and along the fiber direction. The anisotropic plasticity model is integrated into the in-house finite element code FEAP98. Numerical analyses are carried out for the off-axis tension tests and compression tests. These analyses show that the model reasonably predicts the constitutive response of wovenGRPcomposites in confirmation with the experimental data. The model further incorporates strain rate and temperature dependence on the anisotropic plastic flow constitutive law. Ballistic penetration simulations are carried out using the integrated code. The velocity at the back surface of the composite target, obtained by analyses, is compared with the data measured experimentally using interferometry. Insight into the failure process is obtained through analysis of different energy dissipation mechanisms.

Inelastic constitutive properties and shear localization in Tennessee marble

AbstractThe inelastic response of Tennessee marble is modelled by an elastic plastic constitutive relation that includes pressure dependence of yield, strain‐softening and inelastic volume strain (dilatancy). Data from 12 axisymmetric compression tests at confining pressures from 0 to 100 MPa are used to determine the dependence of the yield function and plastic potential, which are different, on the first and second stress invariants and the accumulated inelastic shear strain. Because the data requires that the strain at peak stress depends on the mean stress, the locus of peak stresses is neither a yield surface nor a failure envelope, as is often assumed. Based on the constitutive model and Rudnicki and Rice criterion, localization is not predicted to occur in axisymmetric compression although faulting is observed in the tests. The discrepancy is likely due to the overly stiff response of a smooth yield surface model to abrupt changes in the pattern of straining. The constitutive model determined from the axisymmetric compression data describes well the variation of the in‐plane stress observed in a plane strain experiment. The out‐of‐plane stress is not modelled well, apparently because the inelastic normal strain in this direction is overpredicted. In plane strain, localization is predicted to occur close to peak stress, in good agreement with the experiment. Observation of localization on the rising portion of the stress–strain curve in plane strain does not, however, indicate prepeak localization. Because of the rapid increase of mean stress in plane strain, the stress–strain curve can be rising while the shear stress versus shear strain curve at constant mean stress is falling (negative hardening modulus). Copyright © 2001 John Wiley & Sons, Ltd.

Analysis of the elastic–plastic problem involving finite plastic strain using the boundary element method

This paper presents a formulation of the static problem of metallic solids undergoing both material and geometrical non-linearities. The plastic constitutive relations are based on the von Mises yield criterion with associated flow rule and isotropic hardening. The plastic strains can be large. The numerical approach is based on the boundary element method (BEM) but, since it is not possible to take all the integrals to the boundary, both domain and boundary discretization are needed. A material description is adopted together with an updated Lagrangian approach. The generalized midpoint algorithm is used for the computation of the large scale plastic strains. The displacement gradients are obtained, in order to avoid singularities, from polynomial differentiation of the displacement field in each domain element from the nodal values. The resulting method is incremental and iterations are needed in each increment. The two-dimensional plane strain case has been implemented and one example is presented, to show the applicability of the method proposed.

THE VERIFICATION OF PLASTIC CONSTITUTIVE RELATION AND ITS APPLICATION TO FEM ANALYSIS OF PLASTIC FRACTURE OF STEEL MEMBERS

過大な塑性変形による鋼構造部材の延性破壊はその後の脆性破壊の引き金になっている可能性も指摘されている. したがって, 鋼構造物の終局挙動を有限要素法により解析するためには延性破壊も考慮できるようにすることが望ましい. しかしながら今のところ破壊を含む適切な数理モデルの構築をはじめ数値解析による検討ができる基盤が整っていないのが現状である. そこでここではこれらの問題を解決するひとつの段階として, 適切な応力ひずみモデルの検定を行い, グルソン型モデルが鋼材の軟化挙動を一定の信頼性をもって適切に表していることを新たに考案した実験法で直接的に確認した.

Analysis of Deformation of Shape Memory Alloy Composite Based on Shear-Lag Model.

Incremental constitutive relation of shape memory alloy composite, in which shape memory alloy short-fibers are dispersed in a matrix, has been developed based on the shear-lag model. In the model, the shape memory alloy is described by one-dimensional constitutive relation proposed by Brinson and the matrix is described by the conventional elastic plastic constitutive relation. Using the proposed constitutive relation, the deformation of NiTi short-fiber dispersed nylon 66 composite is analyzed under thermo-mechanical loading. The shape memory alloy composite exhibits the unique performance such as pseudoelasticity, shape memory effect, contraction by heating, formation of compressive residual stress in matrix, and so on. The constitutive relation is useful in the investigation to explore the potentiality of the shape memory alloy composites.

PLASTIC DAMAGE ANALYSIS FOR THE PROCESS ZONE OF A FATIGUE CRACK

The process zone of a mode I fatigue crack is described asymptotically with damage coupled plastic constitutive relations. A parametric study is conducted to obtain the orders and angular distribution modes of stress, strain and damage fields, as well as the profiles of the related process zones. The fatigue crack growth rate is also formulated theoretically.

Effect of stress on transformation and prediction of residual stresses

The effect of stress on transformation is studied through a series of dilation experiments. The results obtained are used to modify models of transformation kinetics, transformation plasticity, and elastoplastic constitutive relations so as to predict residual stresses after quenching. Results of the simulation show that the modified models are fit to predict residual stresses after quenching, which agree well with experimental results if both transformation plasticity and stress induced transformation are taken into account.

Inertia-sensitive impact energy-absorbing structures part I: Effects of inertia and elasticity

By assuming an elastic-perfectly plastic constitutive relation for the material and employing a model which consists of four compressible elastic-plastic bars connected by four elastic-plastic “hinges” of finite length, the dynamic behaviour of an inertia-sensitive impact energy-absorbing structure (previously called a Type II structure) under impact is analysed in detail. By taking account of the complicated deformation history involving loading, unloading and reversed loading, the large deformation process is traced completely and the variation of the “impact force” with time or with the vertical displacement is determined. In particular, the peak load is determined on the basis of elastic-plastic material behaviour and the consideration of inertia effects. The analysis presented indicates that the dynamic behaviour of the structure considered significantly differs from the quasi-static behaviour of the same structure even when the effect of strain-rate on the material properties is excluded. Therefore, inertia would appear to be the dominant effect in this sort of impact problems.

Nonlinear analysis and elastic-plastic behavior of anisotropic structures

An elastic-plastic analysis of anisotropic work-hardening materials based on a quadratic approximation of the Tsai-Wu criterion is presented. General expressions for the anisotropic parameters in the yield condition are derived for initial and subsequent yielding. Particularly, the plastic constitutive relations are expressed by means of both the flow theory as well as the deformation theory extended to anisotropic plasticity. The numerical algorithms are based upon the notion of a return mapping procedure and a consistent tangent operator valid for anisotropic elastic-plastic materials including work-hardening effects is developed. The solution equations are evaluated by consistent linearization of a nonlinear variational principle and a Newton-Raphson scheme is adopted for the iterative solution of the nonlinear problems. Numerical examples exhibit the reliable performance of the proposed algorithm in some practical calculations. The effects of anisotropy and the differences between flow and deformation theories in the obtained solutions are discussed and compared with available numerical results.

Large-scale crystal plasticity computations of microstructural failure modes

A computational scheme is introduced for the integration of rate-dependent multiple-slip crystal plasticity constitutive relations. Fundamental issues of accuracy, stability, and stiffness that are intrinsically related to the evolution of microstructural failure modes in metallic crystals are addressed. An adaptive finite-element methodology is introduced to classify these characteristics. A nonlinear initial value system is derived to update the plastic deformation-rate tensor. An explicit method is used in non-stiff domains, where accuracy is required. If a time-step reduction is due to stability, a harbinger of numerical stiffness, the algorithm is automatically switched to an A-stable method. A stiffness ratio is defined to measure the eigenvalue dispersion of the system. The adaptability of the proposed algorithm for the solution of a class of inelastic constitutive relations is illustrated by investigating the influence of high angle grain boundary orientations on failure in face-centered cubic (f.c.c.) bicrystals. The effects of grain boundary misorientation, dislocation densities, strain hardening, and geometrical softening on failure evolution are investigated. This study underscores the importance of understanding the origin of numerical instabilities, such that these instabilities are not mistaken for inherent material instabilities.

Ductile failure analyses on massively parallel computers

Full three-dimensional analyses of ductile failure are carried out for tensile test specimens under dynamic loading, using a data parallel implementation of a ductile porous material model in a transient 3D finite element program. The elastic-viscoplastic material model accounts for ductile failure by the nucleation, growth and coalescence of micro-voids. Most of the results are obtained using 20 node isoparametric brick elements and reduced (2×2×2) quadrature. The capabilities of the model are checked by a number of simulations for one layer of elements subject to overall plane strain conditions, compared to plane strain predictions. Comparisons are made with results using other orders of interpolation and other quadrature rules. It is shown that the high order 3D elements give a good representation of shear localization. For a uniaxial tensile test specimen with a square cross-section, full three-dimensional computations are carried out with meshes consisting of many brick elements in each coordinate direction, and these analyses are used to study the final failure mode in the neck region. The scalability of the parallel implementation is verified and the performance with the porous plastic constitutive relation is compared with that obtained using a standard isotropic hardening model.

Use of crystal plasticity in metal forming simulations

Some recent work on the implementation of crystal plasticity constitutive relations in the simulation of metal deformation processes is discussed. The rate-dependent crystal plasticity theory employed is first briefly presented. We then consider some special cases of fcc metals with certain “ideal textures”, for which closed-form analytical solutions are given for rolling and biaxial sheet stretching modes. Finally, the incorporation of the crystal plasticity constitutive relations into the finite element analysis of large-strain boundary-value problems is illustrated. The example treated is the behaviour of axially constrained and freely elongating solid circular bars subject to finite strain torsion.

Finite Deformation Constitutive Relations for Elastic-Plastic Fibrous Metal Matrix Composites

This paper presents a finite strain formulation of a plasticity theory of fibrous composite materials. An additive decomposition is adopted to describe the kinematics of large deformations; a lattice is defined by the current fiber direction. Elastic and plastic constitutive relations are developed from the proposition that distortions take place relative to the fiber direction. A numerical method is proposed for integrating the constitutive equations. Finally, an illustrative example of the formulation indicates that when axial loads along the fiber direction are comparable to the instantaneous shear stiffness, the finite deformation formulation is needed even with small strains.

On the Development of Constitutive Relations for Metallic Powders

This article describes the development of elastic and plastic constitutive relations as functions of relative density for partially consolidated —100 mesh aluminum powder. First, measurements of yield stress as a function of stress state and relative density are described. Measurements of the plastic strain increments associated with yielding in unconstrained compression tests and elastic properties, both as functions of relative density, are also described. The experimental results are combined with the associated flow rule to show that the yield surface is asymmetric with respect to hydrostatic tension and compression. Second, it is shown that the yield stress results can be represented by a two-part (capped Drucker-Prager) yield surface. The consoli-dation yield surface moves along the hydrostatic stress axis during densification, while the shear yield surface approaches the Mises yield surface. For the Al powder used in the present inves-tigation, superposition of shear stress on a hydrostatic stress state aids the densification process. However, the hydrostatic stress requirement was found to be reduced by only about 20 pct for relative densities below 0. 98.

Dynamic damage evolution in brittle solids

For brittle solids containing preexisting microflaws, a two-dimensional model is developed to simulate dynamic damage evolution in uniaxial compression. Frictional, and rate-dependent and rate-independent plastic constitutive relations are considered to describe the deformation of preexisting microflaws. The inelastic deformation of microflaws is assumed to produce tensile microcracks in the matrix. These microcracks emanate from microflaws and grow in the direction of compression. Numerical calculations employing the dynamic damage evolution model are carried out to illustrate the resulting overall response of the solid. The propagation of a compressive stress pulse in a semi-infinite bar is studied to demonstrate the stress-pulse attenuation due to compression-induced microcracking, and frictional deformation and inelastic flow of preexisting flaws, including the rate effects.

A kinematic model for plastic limit analysis of solids by the boundary integral method

A mixed boundary integral formulation for plastic limit analysis by linear programming is presented. The interpolation criteria are so defined as to preserve duality in the description of equilibrium and compatibility and reciprocity in the plastic constitutive relations. The governing systems appears in the form of a symmetric linear complementarity problem. The associated linear programs are derived and identified with the static kinematic theorems of plastic limit analysis as applied to the discretized structure.