Showing papers on "Viscoplasticity published in 1980"

An experimental study of uniaxial creep, cyclic creep and relaxation of aisi type 304 stainless steel at room temperature

Abstract: Following previous work ( Krempl , 1979), a servocontrolled testing machine and strain measurement at the gage length were used to study the uniaxial rate(time)-dependent behavior of AISI Type 304 stainless steel at room temperature. The test results show that the creep strain accumulated in a given period of time depends strongly on the stress-rate preceding the creep test. In constant stress-rate zero-to-tension loading the creep strain accumulated in a fixed time-period at a given stress level is always higher during loading than during unloading. Continued cycling causes an exhaustion of creep ratchetting which depends on the stress-rate. Periods of creep and relaxation introduced during completely reversed plastic cycling show that the curved portions of the hysteresis loop exhibit most of the inelasticity. In the straight portions, creep and relaxation are small and there exists a region commencing after unloading where the behavior is similar to that at the origin for virgin materials. This region does not extend to zero stress. The results are at variance with creep theory and with viscoplasticity theories which assume that the yield surface expands with the stress. They support the theory of viscoplasticity based on total strain and overstress.

Hysteretic Fracturing Endochronic Theory for Concrete

Abstract: An improved endochronic nonlinear triaxial constitutive relation for concrete is developed: (1)In addition to plastic strain increments proportional to stress tensor, fracturing strain increments proportional to strain tensor are used to model strain-softening; (2)the plastic and fracturing inelastic strain increments are characterized by different intrinsic times; (3)degradation of the elastic shear modulus is determined by the intrinsic time for the fracturing strain increments, and degradation of the bulk modulus is related to that of the shear modulus using Budianski-O'Connell's expressions for the elastic moduli of randomly microcracked material; (4)jump-kinematic hardening, in which the center of the loading surface jumps into the current stress and strain point whenever loading reverses to unloading or vice versa, is introduced. The theory also exhibits hydrostatic pressure sensitivity, inelastic dilatancy, initial shear compaction in triaxial loading, and inelastic strain due to hydrostatic pressure.

The Initiation of Explosive Charges by Rapid Shear

Abstract: : Friction and/or shear have been suggested by many people as possible sources of ignition in solid explosives. Although these two mechanisms are usually considered to be distinct, on a microscopic scale they are essentially the same. On a macroscopic scale, friction involves sliding interfaces and is described in terms of the coefficient of friction and the stress normal to the interface. The rate of heat generation at the surface is the product of the sliding velocity times the coefficient of friction times the normal stress. On a microscopic level, friction is caused by surface irregularities (asperities) which deform as the surfaces slide. The frictional heating is caused by viscoplastic work on the asperities. In this paper, I will consider the conditions required for ignition as the result of shear deformation and viscoplastic heating.

A theory of viscoplasticity based on infinitesimal total strain

Abstract: A viscoplasticity theory based upon a nonlinear viscoelastic solid, linear in the rates of the strain and stress tensors but nonlinear in the stress tensor and the infinitesimal strain tensor, is being investigated for isothermal, homogeneous motions. A general anisotropic form and a specific isotropic formulation are proposed. A yield condition is not part of the theory and the transition from linear (elastic) to nonlinear (inelastic) behavior is continuous. Only total strains are used and the constant volume hypothesis is not employed. In this paper Poisson's ratio is assumed to be constant. The proposed equation can represent: initial linear elastic behavior; initial elastic response in torsion (tension) after arbitrary prestrain (prestress) in tension (torsion); linear elastic behavior for pure hydrostatic loading; initial elastic slope upon large instantaneous changes in strain rate; stress (strain)-rate sensitivity; creep and relaxation; defined behavior in the limit of very slow and very fast loading. Stress-strain curves obtained at different loading rates will ultimately have the same “slope” and their spacing is nonlinearly related to the loading rate. The above properties of the equation are obtained by qualitative arguments based on the characteristics of the solutions of the resulting nonlinear first-order differential equations. In some instances numerical examples are given. For metals and isotropy we propose a simple equation whose coefficient functions can be determined from a tensile test [Eqs. (31), (35), (37), (38)]. Specializations suitable for materials other than metals are possible. The paper shows that this nonlinear viscoelastic model can represent essential features of metal deformation behavior and reaffirms our previous assertion that metal deformation is basically rate-dependent and can be represented by piecewise nonlinear viscoelasticity. For cyclic loading the proposed model must be modified to account for history dependence in the sense of plasticity.

A volumetric constitutive law for snow based on a neck growth model

Abstract: A volumetric constitutive law for snow is developed by considering the deformation of the ice grains and grain bonds which form the porous material. The equations of equilibrium and mass conservation are applied to both the grain body and neck regions to calculate the rate of change of grain geometry and neck geometry. The matrix material, ice, is assumed to be a nonlinear viscoplastic material. Comparison with data shows excellent agreement for a wide range of initial densities and for large volumetric deformations. Calculations are also made to evaluate grain and neck deformation during compaction. The model can be applied to porous metals and foams, although the constitutive law for the matrix material would have to be altered.

A viscoplastic material model and its application to cyclic loading

Abstract: A kinematic hardening model is generalized by introducing plastic and viscous residual “back” stresses α, β that govern the translation of the yield surface. The evolution equations for α and β are proposed and the material functions are identified for a construction steel by carrying out tension-compression tests at different strain rates. The cyclic tests with changing strain amplitudes and frequencies are next carried out and model predictions are compared with experimental results.

Direct analysis of elastic–plastic structures with ‘overlay’ materials during cyclic loading

Abstract: Several computer codes have incorporated the ‘overlay’ material models: the volume element, which is characteristic of the material, is composed of sub-elements with different kinematic hardening, perfectly plastic or even viscoplastic flow rules and different elastic properties, these sub-elements exhibiting all, however, the same total strain.1,2 In this paper it is demonstrated how the simple mathematical framework we first proposed for elastic-plastic structures with kinematic hardening material,3 and we extended to some elastic viscoplastic ones,4 can easily be applied to these particular ‘overlay’ materials. One of the interesting advantages of this approach is a straightforward analysis of structural response under cyclic loadings by applying the linear elastic analysis.

Viscoplastic and Creep Crack Growth Analysis by the Finite Element Method.

Abstract: : Creep crack growth in a nickel base alloy at elevated temperatures was analyzed through a hybrid experimental-numerical (HEN) procedure. This HEN procedure consisted of simultaneous use of creep crack growth test displacement data from center cracked plate specimens of IN-100 at 1350 F and a theoretical finite element model of the test specimen. A two-dimensional (constant strain triangular) finite element program was developed which accounts for both nonlinear viscoplactic material behavior and changing boundary conditions due to crack growth. Three viscoplastic material models -- (1) Malvern Flow Law, (2) Norton's Creep Law, and (3) Bodner-Partom Flow Law -- were incorporated into the program. These time dependent material models were numerically integrated through time by a linear Euler extrapolation technique. A variable time step algorithm was included that maximized time step size during the analysis while maintaining good accuracy. This program was used as the plane stress theoretical model for the HEN procedure to analyze sustained load creep crack growth.

On thermodynamic yield criteria

Abstract: It is shown that a thermodynamic yield criterion, previously proposed by the author for a specific model of viscoplasticity, may be derived from the Clausius-Planck inequality for a very general model of plasticity, rate-dependent or rate-independent, provided only that a flow rule (as defined in the paper) exists. Special cases of the yield criterion thus derived include the Schmid law and the von Mises criterion. Moreover, under appropriate assumptions the thermodynamic yield stress may be identified with the Frank-Read source activation stress.

An interpretation of photoviscoelastic/plastic data

Abstract: The birefringent effect of viscoelastic and viscoplastic polymeric materials is considered and shown to have separate contributions from the stress, recoverable strain and the permanent deformations. Experimental data for a number of materials are discussed and the procedure for analyzing these data described.

Periodic Solutions in Plasticity and Viscoplasticity

Abstract: For a certain class of elastic-plastic or viscoplastic workhardening materials, which are called generalized standard materials, we study the existence of a periodic solution in terms of stress or stress and strains in a periodically loaded structure. We give conditions which are sufficient for the existence of such a solution and then the method to prove the convergence of any solution of the initial boundary value problem to a periodic one. We apply those results to the examples of perfectly plastic or viscoplastic materials and kinematically workhardening ones.

Normal Dissipativity and Energy Criteria in Fracture

Abstract: An analogy is established between the mathematical description of some usual criterion of crack propagation in fracture and fatigue and the corresponding description of standard constitutive laws in plasticity and in viscoplasticity. It is shown that the well-known formalism based upon dissipation analysis to derive systematically the rate equations of the plastic strain (and of the internal parameters) in plasticity is applicable to fracture and gives an interesting direction of investigation in fracture as well as in fatigue, under the assumption of differentiability of the energy functional with respect to the crack front curve. This analogy shows in particular that the maximum energy release rate criterion for brittle fracture is equivalent to a local criterion in planar crack propagation. The rate problem is also examined in view of the crack path description.

Stationary convection of a viscoplastic liquid in a vertical layer

Abstract: A study is made of plane-parallel convective motion of a viscoplastic liquid between parallel vertical planes on which different temperatures are maintained. In contrast to [1], the yield shear stress τ0 is not a constant but is assumed to be a function of the temperature; moreover, above a certain critical temperature T* the yield shear stress vanishes, so that for T > T* the liquid is purely Newtonian. The structure of the regions of quasirigid and viscoplastic flow is studied in its dependence on the Theological parameters. The velocity profiles corresponding to the different flow regimes are found, and the boundaries between the regimes and the longitudinal heat flux are determined.

Impact of a finite elastic-viscoplastic bar

Abstract: A method for predicting the response of strain-rate sensitive structures under dynamic loading is developed. It is based on a finite difference method, the incremental theory of plasticity, and an elastic work-hardening viscoplastic material idealization. The strain-rate effect, loading and unloading conditions, and wave interactions are automatically accounted for, and adjusted if necessary, as the deformation proceeds. No iteration is required even if the field equations are nonlinear (e.g. non-linear constitutive equations, large deformation, or complicated geometry). We solve as an example the small deflection of a finite bar with a concentrated tip mass. The accuracy is comparable to that obtained by the well-known method of characteristics, a powerful tool for solving elastic-viscoplastic wave problems but which is restricted to small deflections and simple geometry. Because of the form of the constitutive relation selected (elastic work-hardening visco-plastic), several important new features of the dynamics response are brought out. These features are not revealed when simpler, computationally-convenient constitutive relations, such as rigid ideal-viscoplastic, rigid work-hardening viscoplastic and elastic ideal-viscoplastic are used.

Finite element applications of viscoplasticity with singular yield surfaces

Abstract: The side and corner flow rules for viscoplastic materials with singular yield surfaces are discussed and applied in numerical solution of several boundary-value problems. The differences in predictions of displacement and stress fields for different flow rules are demonstrated.

Thermal instability of the axial deformation of a plastic layer and estimation of the critical pressures of impact initiation of solid he (high explosive)

Abstract: One of the conceptions of the deformation rupture of plastic bodies is based on the representation of the instability of the deformation process because of spoilage of the balance between the growth rates of the stress state of the specimen and of material hardening (see e.g., [1]). It permits the satisfactory explanation of the presence of a maximal load in the majority of tests by testing the strength under comparatively slow (quasistatic) loading rates when dissipative heating of the substance because of plastic deformation can be neglected. The deformation conditions approach the adiabatic in high-speed (dynamic) tests, hence, the case can be mentioned when the temperature of the specimen under load can be raised considerably and reaches the melting point at individual sections (principally on the slip planes). If it is taken into account that heating of the materiaI is ordinarily accompanied by a substantial increase in its plasticity, then the deduction is easiIy made that a state when the carrying capacity of the specimen becomes spontaneously diminished (its rupture sets in) can be achieved under sufficiently rapid loading conditions. In contrast to the deformational type, the rupture mechanism considered can be called thermal. However, such a classification is provisional since specimen rupture ordinarily takes place in practice because of loss of deformation stability in both the mentioned mechanisms. It should be noted that the thermal strain instability considered for the plastic material recalls, in many ways, the phenomenon of the loss of thermal stability of viscous fluid pressure flow [2] or of viscoplastic medium [3]. The question posed is related to the problem of the response of solid explosives (HE) to mechanical effects. It is known [4, 5] that the strength rupture of a HE charge by impact is the reason for its initiation under definite conditions. Briefly, the following are these conditions: the stress state in the deformable specimen should satisfy the rupture condition (strength), the pressure at the time of rupture should be so great that the melting point of the HE would reach the value of the critical temperature (resulting in an explosion). The physical meaning of the initiation mechanism of a solid HE is the development of heating loci because of dissipative heat liberation on the charge rupture planes [4-6]. In this paper, we present an approximate solution of the axisymmetric problem of thermal stability of the deformation of a thin plastic layer in the gap between solid colliding surfaces. The results obtained are used for a quantitative estimate of the magnitudes of the critical pressures exciting the explosion of solid HE under impact. Let us assume that a deformable material is chemically inert and that the dissipatable heating is distributed uniformly over its volume, where the temperature of the interlayer depends only on the magnitude of its axial deformation. To determine the stress state of the interlayer, we use the results of solving the axisymmetric problem of the deformation of a thin disc of incompressible rigidly plastic material placed in the gap between shifting rough stamps. Under conditions of developed plastic flow the pattern of the stress state of the disc is almost hydrostatic [7]. For the case of inertialess motion, the magnitude of the axial stress p averaged over the area of the disc is evaluated by the formula p = ~(Fx + l),

Finite-element nonlinear transient response computer programs PLATE 1 and CIVM-PLATE 1 for the analysis of panels subjected to impulse or impact loads

Abstract: Two computer programs are described for predicting the transient large deflection elastic viscoplastic responses of thin single layer, initially flat unstiffened or integrally stiffened, Kirchhoff-Lov ductile metal panels. The PLATE 1 program pertains to structural responses produced by prescribed externally applied transient loading or prescribed initial velocity distributions. The collision imparted velocity method PLATE 1 program concerns structural responses produced by impact of an idealized nondeformable fragment. Finite elements are used to represent the structure in both programs. Strain hardening and strain rate effects of initially isotropic material are considered.