Nobutada Ohno

Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior

Abstract Kinematic hardening rules formulated in a hardening/dynamic recovery format are examined for simulating rachetting behavior. These rules, characterized by decomposition of the kinematic hardening variable into components, are based on the assumption that each component has a critical state for its dynamic recovery to be activated fully. Discussing their basic features, the authors show that they can predict much less accumulation of uniaxial and multiaxial ratchetting strains than the Armstrong and Frederick rule. Comparisons with multilayer and multisurface models are made also, resulting in a finding that the simple one in the present rules is similar to the multilayer model with total strain rate replaced by inelastic (or plastic) strain rate. Part II of this work deals with applications to experiments.

Kinematic hardening model suitable for ratchetting with steady-state

Abstract A new kinematic hardening model useful for simulating the steady-state in ratchetting is developed within the framework of the strain hardening and dynamic recovery format. The model is formulated to have two kinds of dynamic recovery terms, which operate at all times and only in a critical state, respectively. The model is examined on the basis of nonproportional experiments of Modified 9Cr–1Mo steel at 550°C and IN738LC at 850°C. The experiments include multiaxial, as well as uniaxial, ratchetting, multiaxial cyclic stress relaxation, and nonproportional cyclic straining along a butterfly-type strain path. It is shown that the model is successful in simulating the experiments, and that the model is featured by the capability of representing appropriately the steady-state in ratchetting under multiaxial and uniaxial cyclic loading.

Kinematic hardening rules with critical state of dynamic recovery, part II: Application to experiments of ratchetting behavior

Abstract The kinematic hardening rules formulated in Part I of this work (i.e, Models I and II) are applied to ratchetting experiments of Modified 9Cr-1Mo steel done by Tanaka et al. as well as to a nonproportional experiment of OFHC copper by Lamba and Sidebottom. It is shown the Models I and II have the capability of simulating ratchetting behavior well because they can predict much less accumulation of ratchetting strain under uniaxial and multiaxial loadings than the Armstrong and Frederick model. It is also shown that if ratchetting strain is negligible, Models I and II may give nearly the same predictions as the Armstrong and Frederick model.

Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation

In this paper, we establish a homogenization framework to analyze the microscopic symmetric bifurcation buckling of cellular solids subjected to macroscopically uniform compression. To this end, describing the principle of virtual work for infinite periodic materials in the updated Lagrangian form, we build a homogenization theory of finite deformation, which satisfies the principle of material objectivity. Then, we state a postulate that at the onset of microscopic symmetric bifurcation, microscopic velocity becomes spontaneous, yet changing the sign of such spontaneous velocity has no influence on the variation in macroscopic states. By applying this postulate to the homogenization theory, we derive the conditions to be satisfied at the onset of microscopic symmetric bifurcation. The resulting conditions are verified by analyzing numerically the in-plane biaxial buckling of an elastic hexagonal honeycomb. It is thus shown that three kinds of experimentally observed buckling modes of honeycombs i.e., uniaxial, biaxial and flower-like modes, are attained and classified as microscopic symmetric bifurcation. It is also shown that the multiplicity of bifurcation gives rise to the complex cell-patterns in the biaxial and flower-like modes.

Constitutive modeling of strain range dependent cyclic hardening

Abstract In this paper, a new approach for constitutive modeling of strain range dependent cyclic hardening is proposed by extending the kinematic hardening model based on the critical state of dynamic recovery. It is assumed that isotropic, as well as kinematic, hardening consists of several parts, and that each part of isotropic hardening evolves when the corresponding part of kinematic hardening is in the critical state of dynamic recovery. The extended model is capable of simulating the cyclic hardening behavior in which different characteristics of cyclic hardening appear depending on strain range. The model is verified by simulating the relatively large cyclic straining tests of 304 stainless steel at ambient temperature, in which cyclic hardening does not stabilize before rupture if strain range exceeds a certain value. The model is further verified by predicting the history dependence of cyclic hardening under incremental cyclic loading and the maximum plastic strain dependence of strain hardening in cyclic tension.

CONSTITUTIVE MODELING OF CYCLIC PLASTICITY WITH EMPHASIS ON RATCHETTING

Constitutive modeling of cyclic plasticity for ratchetting has advanced significantly in the last about five years. Ohno and Wang [1, 2] contributed to the modeling by formulating the kinematic hardening model based on the critical state of dynamic recovery of back stress. This paper describes the characteristics of their model and its applications to uniaxial, multiaxial and thermal ratchettings as well as to nonproportional deformation without ratchetting.

Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and nonisothermal conditions

Abstract A nonlinear kinematic hardening rule with back stress decomposed into components is transformed to a multisurface form. First it is shown under isothermal conditions that the multisurfaces generated by the transformation are nested and obey a Mroz-type translation rule. It is also shown that the multisurface form can be specialized to a piecewise linear kinematic hardening rule. The transformation is then applied to a time recovery term describing thermal softening and a temperature-rate term operating in nonisothermal inelasticity. A multisurface model is thus derived for nonisothermal, as well as isothermal, plasticity and viscoplasticity.

Ratchetting characteristics of 316FR steel at high temperature, part I: Strain-controlled ratchetting experiments and simulations

The paper is concerned with characteristics in ratchetting of 316FR steel at high temperature. In Part I, first, by discussing isothermal and nonisothermal “strain-controlled” ratchetting experiments, it is shown that 316FR steel exhibits the almost perfect closure of stress and strain hysteresis loops as well as the isotropic hardening depending on maximum plastic strain rather than accumulated plastic strain. Second, it is demonstrated that the experiments are simulated well using the nonlinear kinematic hardening model proposed in 1993 by Ohno and Wang (Int. J. Plasticity 9, 375–403) if the model is extended by taking account of the isotropic hardening depending on maximum plastic strain. On the basis of these findings, thermal ratchetting of 316FR steel cylinders subjected to the axial variation of temperature is analyzed in Part II.

Uniaxial Ratchetting of 316FR Steel at Room Temperature— Part I: Experiments

Uniaxial ratchetting characteristics of 316FR steel at room temperature are studied experimentally. Cyclic tension tests, in which maximum strain increases every cycle by prescribed amounts, are conducted systematically in addition to conventional monotonic, cyclic, and ratchetting tests. Thus hysteresis loop closure, cyclic hardening and viscoplasticity are discussed in the context of constitutive modeling for ratchetting. The cyclic tension tests reveal that very slight opening of hysteresis loops occurs, and that neither accumulated plastic strain nor maximum plastic strain induces significant isotropic hardening if strain range is relatively small. These findings are used to discuss the ratchetting tests. It is thus shown that uniaxial ratchetting of the material at room temperature is brought about by slight opening of hysteresis loops as well as by viscoplasticity, and that kinematic hardening governs almost all strain hardening in uniaxial ratchetting if stress range is not large.

A homogenization theory for time-dependentnonlinear composites with periodic internal structures

Abstract A homogenization theory for time-dependent deformation such as creep andviscoplasticity of nonlinear composites with periodic internal structures is developed. To beginwith, in the macroscopically uniform case, a rate-type macroscopic constitutive relation betweenstress and strain and an evolution equation of microscopic stress are derived by introducing twokinds of Y-periodic functions, which are determined by solving two unit cell problems.Then, the macroscopically nonuniform case is discussed in an incremental form using thetwo-scale asymptotic expansion of field variables. The resulting equations are shown to beeffective for computing incrementally the time-dependent deformation for which the history ofeither macroscopic stress or macroscopic strain is prescribed. As an application of the theory,transverse creep of metal matrix composites reinforced undirectionally with continuous fibers isanalyzed numerically to discuss the effect of fiber arrays on the anisotropy in such creep.