A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals

This paper is concerned with the development of a general implicit time-stepping integrator for the flow and evolution equations in a recent representative class of generalized viscoplastic models, involving both hardening and dynamic recovery mechanisms. To this end, the computational framework is developed on the basis of the unconditionally stable, backward Euler difference scheme. Its mathematical structure is of sufficient generality to allow a systematic treatment of several internal variables of the tensorial and scalar types. The matrix forms developed are directly applicable in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). The closed-form expressions for residual vectors and the algorithmic, (consistent) material tangent stiffness array are given explicitly, with the maximum matrix sizes “optimized” to depend only on the number of independent stress components, but not the number of internal state variables involved. Several numerical simulations are given to assess the performance of the developed schemes.

An Implicit integration scheme for generalized viscoplasticity with dynamic recovery

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; ie, fully associative (GVIPS) and non-associative (NAV) models The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (ie, plane stress/strain, axisymmetric, generalized plane stress in shells) On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters) Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications

Micromechanical modeling of damage growth in titanium based metal-matrix composites

A number of robust, and computationally efficient, algorithms arepresented for the development of an overall strategy to estimate thematerial parameters characterizing a class of complex viscoplasticmaterial models (ie, rate dependent plastic flow, nonlinear kinematichardening, thermal/static recovery, isotropic and anisotropic, etc) Theentire procedure is automated through the integrated software COMPARE(an acronym for COnstitutive Material PARameter Estimator) to enable thedetermination of an `optimum' set of material parameters by minimizingthe errors between the experimental test data and the predictedresponse The key ingredients of COMPARE are: (i) primal analysisutilizing the unconditionally-stable, fully implicit, integration schemefor the models' underlying flow and evolutionary rate equations; (ii) sensitivity analysis utilizing a direct-differentiation approach (ie,explicit, `exact' expressions are derived); (iii) a gradient-basedoptimization technique of an error/cost function; and (iv) graphicaluser interface The estimation of the material parameters is cast as aminimum-error, weighted-multi-objective, nonlinear optimization problemwith constraints Comparison between the sensitivities obtained by theproposed direct scheme and those produced by conventional finitedifference techniques is presented to assess accuracy Detailedderivations are given, together with the results generated by applyingthe developed algorithms to a comprehensive set of test matrices Theseinclude constant strain-rate tension, creep, and relaxation tests, forboth isotropic as well as anisotropic behaviors

Parameter-Estimation Algorithms for Characterizing a Class of Isotropic and Anisotropic Viscoplastic Material Models

A viscoplastic constitutive theory is presented for representing the high temperature deformation behavior of metal matrix composites. The point of view taken is a continuum one where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole. It is assumed that a single preferential (fiber) direction is identifiable at each material point (continuum element) admitting the idealization of local transverse isotropy. A key ingredient is the specification of an experimental program for the complete determination of the material functions and parameters for characterizing a particular metal matrix composite. The parameters relating to the strength of anisotropy can be determined through tension/torsion tests on longitudinally and circumferentially reinforced thin walled tubes. Fundamental aspects of the theory are explored through a geometric interpretation of some basic features analogous to those of the classical theory of plasticity.

David N. Robinson

Papers

A viscoplastic constitutive theory for metal matrix composites at high temperature