Showing papers on "Viscoplasticity published in 1989"

Dynamic Shear Band Development in Plane Strain

Abstract: : Plane strain compression of a rectangular block is used as a model problem to investigate the dynamics of shear band development from an internal inhomogeneity. The material is characterized as a von Mises elastic-viscoplastic solid, with a hardness function that exhibits a local maximum. Regardless of whether the material is hardening or softening, plastic strain development involves the evolution of finger-like contours emanating from the inhomogeneity at 45 degrees to the compression axis. Once a given strain contour crosses the specimen, it fans out about its initial direction of propagation. For a softening solid, this fanning out ceases for some strain level greater than the strain at the hardness maximum and further straining takes place in an ever narrowing band. Many of the qualitative features of shear band development under dynamic loading conditions are the same as under quasi-static loading conditions, but a significant retardation of shear band development due to inertial effects is found.

Viscoplastic modeling of texture development in quartzite

Abstract: Polycrystal plasticity theory has been successfully used to simulate development of preferred orientation in rocks. In particular, G. Lister and coworkers have done a comprehensive study, applying the Taylor theory to quartzite. In these calculations it was assumed that deformation is homogeneous; that is, all grains deform at the same rate, that critical resolved shear stresses (CRSS) of slip systems remain constant, and that deformation is rigid-plastic; that is, dislocations move only when the CRSS has been reached and then with indeterminate velocity. We have been investigating the influence of work hardening and of strain rate dependence on texture development. In particular, modification of the viscoplastic Taylor theory suggests that textures are greatly dependent on the rate sensitivity of flow stress when this stress exponent is small, such as in quartz where it is near 3. The influence of work hardening is less critical in the case of quartz. Results from Taylor simulations are also compared with those from a self-consistent theory. The latter sacrifices local strain continuity for better stress equilibrium. In the self-consistent scheme, grains which are favorably oriented for slip are allowed to deform at a faster rate. Texture patterns obtained with the two theories are moderately different. In self-consistent deformation a C axis maximum in the intermediate strain direction (Y) is generated which is absent in Taylor deformation but is a common feature of many natural quartz fabrics. Grains associated with this maximum are most strongly deformed. Deformation modeling with more realistic boundary conditions adds complexities but appears to be necessary in the case of anisotropic and rate sensitive rocks.

Adiabatic Shear Banding in Plane Strain Problems

Abstract: Two different loadings, namely, the top and bottom surfaces subjected to a prescribed, tangential velocity, and these two surfaces subjected to a preassigned normal velocity, are considered. In each case a material defect, flaw, or inhomogeneity is modeled by introducing a temperature bump at the center of the specimen. The solution of the initial boundary value problem by the Galerkin-Adams method reveals that the deformation eventually localizes into a narrow band aligned along the direction of the maximum shearing strain

Constitutive Equations and a Time Integration Procedure for Isotropic Hyperelastic-Viscoplastic Solids

Abstract: From a physical point of view, it is desirable that the elasticity, in a set of elastic-plastic constitutive equations for metallic materials, be modeled as a hyperelastic relation, and the plasticity as rate dependent. However, it has been common practice in most of the current analytical and numerical work in elasto-plasticity to use a hypoelastic relation to model the elastic response of a material, and to approximate the plasticity (at low homologous temperatures) as rate-independent. We have formulated a set of simple constitutive equations for isotropic materials which have the desirable attributes listed above. Also, we have formulated, implemented, and evaluated the performance of a fully implicit time integration procedure for our constitutive equations.

Mechanical behaviors of 60/40 tin-lead solder lap joints

Abstract: Creep-fatigue interactions have been shown to play a critical role in the failure of surface mount solder joints. Monotonic, fatigue, and creep-fatigue data for 60/40 tin-lead solder lap joints at room temperature are presented. Monotonic tests performed include rapid-strain shear, creep, and stress relaxation tests. Fundamental data for the strain range partitioning (SRP) approach to creep-fatigue life-prediction are presented. SRP is found to model adequately the solder creep-fatigue response for the range of frequencies (0.007 to 0.5 Hz) and waveforms tested. Instantaneous plastic strains and viscoplastic strains are found to be equally damaging, in any combination, for isothermal room-temperature creep-fatigue. Fatigue lives obtained for 0.5-Hz tests performed under load control correlate with the lives to 50% load drop obtained for tests performed under strain control. >

A Statistical Formulation of Viscoplastic Behavior in Heterogeneous Polycrystals

Abstract: A formulation for viscoplastic behavior of heterogeneous polycrystals is presented based upon the familiar constructs of statistical continuum theory. The non-local interaction law is derived which relates properties of the local velocity field to correlation functions of the local microstructure. It is demonstrated that correlation functions, based upon the two-point orientation coherence function, are required in a theory which considers first-order deviations from Taylor's 1938 uniform strain (rate) assumption. The evolution of the coherence function with deformation is also briefly considered.

A time integration procedure for plastic deformation in elastic-viscoplastic metals

Abstract: A simple unconditionally stable numerical procedure for time integration of the flow rule for large plastic deformation of an elastic-viscoplastic metal is developed. Specific attention is focused on a unified set of constitutive equations which represents a generalization (for large deformation and thermomechanical response) of the Bodner-Partom model [6, 7]. An analytical solution is obtained for large deformation simple shear at constant shear rate. Numerical examples of simple shear, a corner test exhibiting the transition from uniaxial compression to shear, and simple tension are considered which demonstrate the stability and accuracy of the procedure. It is shown that the same procedure can be used for a rate insensitive metal characterized by a yield function as well as for a rate sensitive metal characterized by an overstress model. Finally, an appendix is provided which records the basic equations associated with the small deformation theory.

Deformation modeling and constitutive modeling for anisotropic superalloys

Abstract: A study of deformation mechanisms in the single crystal superalloy PWA 1480 was conducted. Monotonic and cyclic tests were conducted from 20 to 1093 C. Both (001) and near-(123) crystals were tested, at strain rates of 0.5 and 50 percent/minute. The deformation behavior could be grouped into two temperature regimes: low temperatures, below 760 C; and high temperatures, above 820 to 950 C depending on the strain rate. At low temperatures, the mechanical behavior was very anisotropic. An orientation dependent CRSS, a tension-compression asymmetry, and anisotropic strain hardening were all observed. The material was deformed by planar octahedral slip. The anisotropic properties were correlated with the ease of cube cross-slip, as well as the number of active slip systems. At high temperatures, the material was isotropic, and deformed by homogeneous gamma by-pass. It was found that the temperature dependence of the formation of superlattice-intrinsic stacking faults was responsible for the local minimum in the CRSS of this alloy at 400 C. It was proposed that the cube cross-slip process must be reversible. This was used to explain the reversible tension-compression asymmetry, and was used to study models of cross-slip. As a result, the cross-slip model proposed by Paidar, Pope and Vitek was found to be consistent with the proposed slip reversibility. The results were related to anisotropic viscoplastic constitutive models. The model proposed by Walter and Jordan was found to be capable of modeling all aspects of the material anisotropy. Temperature and strain rate boundaries for the model were proposed, and guidelines for numerical experiments were proposed.

Similarity and bifurcation in unstable visoplastic shear

Abstract: The linear stability of perturbed simple shear in a ductile plastic material which can strain-soften is analyzed on a finite time interval. An asymptotic study is made of the influence of two small dimensionless coefficients, which are shown to be connected by a similarity parameter. The first coefficient is a dimensionless group of parameters which can be interpreted as the ratio of the momentum flux to the plastic flow stress, while the second coefficient gives the scale of the viscous damping. A criterion is derived for the minimum strain rate where the early-time behavior changes from oscillatory to exponential.

Refinements in a viscoplastic model

Abstract: A thermodynamically admissible theory of viscoplasticity with two internal variables (a back stress and a drag strength) is presented. Six material functions characterize a specific viscoplastic model. In the pursuit of compromise between accuracy and simplicity, a model is developed that is a hybrid of two existing viscoplastic models. A limited number of applications of the model to Al, Cu, and Ni are presented. A novel implicit integration method is also discussed. Applications are made to obtain solutions using this viscoplastic model.

Modal analysis of vibrating viscoplastic composite beams on multiple supports

Abstract: A vibration analysis for viscoplastic, shear deformable composite beams is presented, where non-linear strains consistently are treated as an additional loading of the linear elastic structure due to fictitious sources of eigenstresses. Therefore, linear solution methods such as mode superposition and Green's functions become applicable, and a fast, computer-oriented solution strategy is developed. The non-linear structural response is found as the sum of the corresponding linear elastic response and the solution due to the additional loading by the inelastic strains, where the sources of eigenstresses are calculated from the material's law in a time-stepping procedure. The method is demonstrated using a composite sandwich beam with thin surface layers on multiple supports, which are excited independently. Elastoplastic material behaviour of endochronic type as well as a viscoplastic material's law are considered simultaneously.

A Transversely Isotropic Thermoelastic Theory

Abstract: A continuum theory is presented for representing the thermoelastic behavior of composites that can be idealized as transversely isotropic. This theory is consistent with anisotropic viscoplastic theories being developed presently at NASA Lewis Research Center. A multiaxial statement of the theory is presented, as well as plane stress and plane strain reductions. Experimental determination of the required material parameters and their theoretical constraints are discussed. Simple homogeneously stressed elements are examined to illustrate the effect of fiber orientation on the resulting strain distribution. Finally, the multiaxial stress-strain relations are expressed in matrix form to simplify and accelerate implementation of the theory into structural analysis codes.

A finite element method for an incremental viscoplasticity theory based on overstress

Abstract: A one-step time integration method is developed for Krempl's viscoplasticity theory based on overstress. Differential growth laws for the tensorial and scalar state variables are included in the constitutive model. This time integration method leads to explicit symmetric tangent operators which are suitable for finite element implementation. An adaptive time-steppping scheme has been developed for the incremental finite element procedure

A stability analysis of the uniaxial viscoplasticity theory based on overstress

Abstract: In the development of a viscoplasticity theory without a yield surface and without a loading and unloading condition, the properties of a uniaxial constitutive model consisting of two coupled nonlinear differential equations are examined. The critical points of the system of differential equations are evaluated for monotonic loading, creep and relaxation conditions and are shown to be stable. The conditions necessary for the elimination of stable but oscillatory solutions are given. Also given are the asymptotic solutions valid near the critical points. The analytical predictions are confirmed by numerical results.