J.C. Moosbrugger

A rate-dependent bounding surface model with a generalized image point for cyclic nonproportional viscoplasticity

Abstract A phenomenologically based time- and rate-dependent bounding surface model is introduced which can be classified among the unified creep-plasticity theories. The model is motivated chiefly by experimental behaviors over a wide range of strain rates with particular emphasis on the behavior of metals under nonproportional loading where bounding surface theories have found success in modeling rate-independent behavior. In addition, a micromechanical interpretation is given for two kinematic hardening variables which lead to the rate-dependent bounding surface interpretation. The definition of the image point for the directional indices of kinematic hardening is left unspecified to maintain generality. The distinction between instantaneous rate sensitivity and rate sensitivity of material hardening is discussed and a framework for partitioning material rate sensitivity is presented. The relationship of the model to previously proposed formulations is discussed. Asymptotic and parametric behaviors of the model are examined with reference to experimentally observed behavior. A rate-independent idealization of the theory is obtained as a limiting, special case of the more general rate-dependent bounding surface framework.

Continuum slip viscoplasticity with the Haasen constitutive model: Application to CdTe single crystal inelasticity

Small strain constitutive equations are developed for the thermomechanical behavior of semiconductor single crystals, including dislocation density as an evolving parameter. The model of Haasen, Alexander and coworkers is modified (extended) to include evolution of coefficients in the definition of internal stress. These account for an evolving dislocation substructure. The resulting model is applied in a continuum slip framework to allow multiple slip orientations. Slip system interaction rules are adapted to include slip system interaction for multiple slip conditions and to suppress secondary slip and dislocation density generation for single slip orientations. The approach is discussed relative to other models for viscoplasticity of single crystals and is examined in the context of thermodynamics with internal state variables. The framework is used to correlate experimental data from compression tests of single crystals of the compound semiconductor CdTe from room temperature to near the melting point. Sensitivity of the model to uncertainties such as initial dislocation density is explored.

Cyclic plasticity of nickel at low plastic strain amplitude : hysteresis loop shape analysis

Abstract The cyclic plasticity of nickel was studied by accomplishing room temperature fully-reversed fatigue experiments at constant plastic strain amplitudes of 1.0×10−4 and 2.5×10−4 on single crystal and polycrystal nickel with 290 μm grain size. The cyclic plasticity behavior within a hysteresis loop was analyzed by measuring shape characteristics of the loop. Parameters that were evaluated include the loop shape parameter, friction stress, back stress, and second derivative of stress with respect to total strain. Results indicate that these parameters correlate well with the development of dislocation substructures. In addition, at low plastic strain amplitude, polycrystal and single crystal hysteresis loops exhibit a distinct constriction. The constriction is more pronounced in single crystals cycled at the lower plastic strain amplitude.

Some developments in the characterization of material hardening and rate sensitivity for cyclic viscoplasticity models

Abstract Kinematic hardening rules with multiple kinematic hardening subvariables and an additive decomposition have been used successfully in viscoplasticity models. In this paper, a general framework for such rules is introduced. A method for determining total rate sensitivity, combined with a technique for measuring overstress using biaxial tests is introduced to compute backstress histories, and backstress rate histories. Using these results, special cases of the general kinematic hardening rule are evaluated for the case of room temperature cyclic behavior of Type 304 stainless steel. It is shown that the appropriate number of kinematic hardening subvariables may be determined, as well as the proper means for accounting for cyclic, isotropic hardening in a model. Model parameters are determined for two special cases and numerical results are compared to experimental results for strain-controlled proportional and nonproportional cycles. The results are discussed with reference to recent studies.

Anisotropic Nonlinear Kinematic Hardening Rule Parameters From Reversed Proportional Axial-Torsional Cycling

A procedure for determining parameters for anisotropic forms of nonlinear kinematic hardening rules for cyclic plasticity or viscoplasticity models is described. An earlier reported methodology for determining parameters for isotropic forms of uncoupled, superposed Armstrong-Frederick type kinematic hardening rules is extended. For this exercise, the anisotropy of the kinematic hardening rules is restricted to transverse isotropy or orthotropy. A limited number of parameters for such kinematic hardening rules can be determined using reversed proportional tension-torsion cycling of thin-walled tubular specimens. This is demonstrated using tests on type 304 stainless-steel specimens and results are compared to results based on the assumption of isotropic forms of the kinematic hardening, rules.

Nonlinear kinematic hardening rule parameters — relationship to substructure evolution in polycrystalline nickel

Abstract General cyclic plasticity results and detailed analyses of experimental data from constant plastic strain amplitude, completely reversed, tension–compression tests on polycrystalline nickel with two grain sizes are reported. These analyses focus on kinematic hardening behavior and are based on Armstrong–Frederick-type kinematic hardening rules and Masing-type assumptions. Juxtaposition of these analyses with observations of specimen surface relief and substructure evolution using TEM provides a context for discussion of mechanisms and modeling of nonlinear kinematic hardening and its relationship to heterogeneous microstructure in metals.

Experimental parameter estimation for nonproportional cyclic viscoplasticity: Nonlinear kinematic hardening rules for two waspaloy microstructures at 650°C

Abstract An earlier reported approach for estimating backstress from uninterrupted, biaxial strain-controlled, nonproportional tests is applied to two different heat treatments of Waspaloy at 650°C. These results are then used to compute backstress histories from cyclic proportional tests. Information regarding the appropriate number of nonlinear kinematic hardening rules for use in viscoplasticity models as well as estimates of the values of the parameters in the kinematic hardening rules are obtained from direct analysis of the experimental data. Complete sets of isothermal model parameters are presented for both heat treatments, and model results are compared with experimental results for several nonproportional, cyclic, strain-controlled test histories. It is shown that the nonlinear kinematic hardening rules determined using the presented methods allow a faithful description of the subtle differences in stress space response paths for the two different heat treatments. Isotropic hardening for the two heat treatments under the experimental conditions is also discussed.

Nonlinear Kinematic hardening rule parameters-Direct determination from completely reversed proportional cycling

A methodology for the determination of parameters for superposed, uncoupled, A-F type nonlinear kinematic hardening rules is presented for reversed cyclic plasticity or viscoplasticity. The important aspects of the procedure are presented for general reversed proportional cycling and then special cases of axial-torsional and uniaxial loadings are considered along with several experimental examples. The approach yields a quantitative estimate of the saturation state of stress for these types of models, directly from experimental responses to reversed proportional cycling. Iterations are not required to obtain parameter estimates, except for the numerical solution to a set of nonlinear algebraic equations when more than two A-F type rules are superposed to model backstress evolution.

A Biomechanical Model of Human Ankle Angle Changes Arising From Short Peri-Threshold Anterior Translations of Platform on Which a Subject Stands

This study modeled ankle angle changes during small forward perturbations of a standing platform. A two-dimensional biomechanical inverted pendulum model was developed that uses sway frequencies derived from quiet standing observations on a subjects anterior posterior center of pressure (APCoP) to track ankle angle changes during a 16 mm anterior displacement perturbation of a platform on which a subject stood. This model used the total torque generated at the ankle joint as one of the inputs, and calculated it assuming a PID controller. This feedback system generated a simulated ankle torque based on the angular position of the center of mass (CoM) with respect to vertical line passing through the ankle joint. This study also assumed that the internal components of the net torque were only a controller torque and a sway-pattern-generating torque. The final inputs to the model were the platform acceleration and anthropometric terms. This model of postural sway dynamics predicted sway angle and the trajectory of the center of mass. Knowing these relationships can advance an understanding of the ankle strategy employed in balance control.

Non-linear structural modeling for life predictions: Physical mechanisms and continuum theories

Abstract A review of several viscoplastic theories that incorporate isotropic hardening, directional hardening and additional effects due to non-proportional loading is presented. The equations reviewed are generalizations of the internal stress concept and use two internal state variables, namely the drag stress and the back stress variables. Theories that incorporate additional internal variables to model physical phenomena such as strain ageing have also been reviewed. Most of these constitutive equations employ isotropic evolutionary equations for the drag stress and nonlinear hardening rules for the back stress variable. The physical arguments to justify this procedure are given. The similarities between a wide number of formulations of flow and evolutionary equations, as well as the essential differences between them, are presented. Finally, it is shown how a careful examination of experimental behaviors, in conjunction with micromechanical considerations based on the physics of deformation, leads to the formulation of a more general unified framework.