Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

Three-dimensional plasticity with kinematic and isotropic hardening

2020 ◽  
pp. 421-428
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Plastic Strain ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Small Strain ◽  
Back Stress ◽  
Isotropic Hardening ◽  
Evolution Law ◽  
Hardening Model ◽  
Rate Dependent ◽  
Viscoplastic Models

This chapter provides an introduction to combined isotropic-kinematic hardening plasticity models in the three-dimensional small strain setting. The additive decomposition of the strain is introduced along with the concepts of plastic strain, equivalent tensile plastic strain, and back stress for three-dimensional problems. Plastic flow is discussed and defined, and a complete model of plasticity is formulated with Kuhn-Tucker loading/unloading conditions. The kinematic hardening model is based upon the Armstrong-Fredrick evolution law. Both rate-independent and rate-dependent (viscoplastic) models are discussed.

Experimental Study of Internal Variable Evolution in SS304L, at Multiple Rates and Temperatures

1999 ◽  
Vol 121 (2) ◽  
pp. 162-171 ◽  
Author(s):  
E. J. Harley ◽  
M. P. Miller ◽  
D. J. Bammann
Keyword(s):  
Yield Strength ◽  
Kinematic Hardening ◽  
Internal Variable ◽  
Isotropic Hardening ◽  
304L Stainless Steel ◽  
Strain Rates ◽  
Inelastic Behavior ◽  
Model Framework ◽  
Wide Range ◽  
Strength Asymmetry

Most metals exhibit a deformation-induced uniaxial yield strength asymmetry. Interpreted within the context of macroscale viscoplastic models, it is conventional to describe this yield strength asymmetry with an isotropic hardening variable, κ, and a kinematic hardening variable, α. The focus of this work was to conduct a series of reverse yield experiments to directly measure the evolution of α and κ in 304L stainless steel (SS304L) over large ranges of temperatures and strain rates. We found that the material exhibited inelastic behavior immediately on changing the straining direction. We discussed the ramifications of this behavior on our goal to directly measure α and κ within the context of an isotropic/kinematic hardening model framework. We also explored the capability of the model to simulate the behavior of SS304L under different loading conditions across a wide range of temperatures and strain rates.

Analysis of large-strain shear in rate-dependent face-centred cubic polycrystals: correlation of micro- and macromechanics

1989 ◽  
Vol 328 (1600) ◽  
pp. 443-500 ◽  
Keyword(s):  
Strain Rate ◽  
Finite Strain ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Texture Evolution ◽  
Rate Sensitivity ◽  
Rate Dependent ◽  
Crystallographic Slip ◽  
Physically Based ◽  
Constitutive Response

Micro- and macroscopic aspects of large-strain deformation are examined through analyses of shear by using physical and phenomenological models. Past experiments and analyses are first reviewed to reveal current issues and put the present work in perspective. These issues are addressed by a complete set of simulations of large-strain shear with a finite-strain, rate-dependent polycrystal model. The model is based on a rigorous constitutive theory for crystallographic slip that accounts for the development of crystallographic texture and the effects of texture on constitutive response. The influences of strain hardening, latent hardening, strain-rate sensitivity, boundary constraints, and initial textures on texture evolution and constitutive response are studied. Coupled stress and strain effects such as axial elongation during unconstrained shear and the development of normal stresses during constrained shear are related to material properties, boundary constraint and texture. The formation of ideal textures and their role in determining polycrystalline behaviour is discussed in quantitative terms. Large-strain shear is also studied by using several phenomenological constitutive theories including J 2 -flow theory, J 2 -corner theory, and two versions of finite-strain kinematic hardening theory. The behaviours predicted by these phenomenological theories and the physically based polycrystal model are directly compared. A noteworthy outcome is the close correspondence found between the predictions of J 2 -corner theory and those of the micromechanically based physical model.

Large Strain, High Strain Rate Testing of Copper

1980 ◽  
Vol 102 (4) ◽  
pp. 376-381 ◽  
Author(s):  
U. S. Lindholm ◽  
A. Nagy ◽  
G. R. Johnson ◽  
J. M. Hoegfeldt
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Large Strain ◽  
Shear Banding ◽  
Testing Machine ◽  
Shear Instability ◽  
Large Strains ◽  
Rate Dependent ◽  
Torsional Testing ◽  
Strain Hardening Behavior

This paper describes the development of a high-speed torsional testing machine and results obtained on the strain-rate dependent strength of copper at large shear strains. Test techniques and data obtained are intended to be useful in applications such as ballistics and machining. For copper, the results indicate positive strain hardening behavior to very large strains under low rate, isothermal conditions and the transition to adiabatic thermal softening, shear instability and localization (shear banding) at high rates.

scholarly journals Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1166
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Plane Strain ◽  
Kinematic Hardening ◽  
Tensile Force ◽  
Plastic Region ◽  
Equivalent Plastic Strain ◽  
Isotropic Hardening ◽  
Finite Plane ◽  
Present Solution ◽  
Bending Under Tension ◽  
Elastic Unloading

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

Pertinence of the Grain Size on the Mechanical Strength of Polycrystalline Metals

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
N. A. Zontsika ◽  
A. Abdul-Latif ◽  
S. Ramtani
Keyword(s):  
Grain Size ◽  
Mechanical Strength ◽  
Kinematic Hardening ◽  
Uniaxial Stress ◽  
Isotropic Hardening ◽  
Ultrafine Grained ◽  
Consistent Model ◽  
Micromechanical Approach ◽  
Interaction Law ◽  
Small Deformations

Motivated by the already developed micromechanical approach (Abdul-Latif et al., 2002, “Elasto-Inelastic Self-Consistent Model for Polycrystals,” ASME J. Appl. Mech., 69(3), pp. 309–316.), a new extension is proposed for describing the mechanical strength of ultrafine-grained (ufg) materials whose grain sizes, d, lie in the approximate range of 100 nm < d < 1000 nm as well as for the nanocrystalline (nc) materials characterized by d≤100 nm. In fact, the dislocation kinematics approach is considered for characterizing these materials where grain boundary is taken into account by a thermal diffusion concept. The used model deals with a soft nonincremental inclusion/matrix interaction law. The overall kinematic hardening effect is described naturally by the interaction law. Within the framework of small deformations hypothesis, the elastic part, assumed to be uniform and isotropic, is evaluated at the granular level. The heterogeneous inelastic part of deformation is locally determined. In addition, the intragranular isotropic hardening is modeled based on the interaction between the activated slip systems within the same grain. Affected by the grain size, the mechanical behavior of the ufg as well as the nc materials is fairly well described. This development is validated through several uniaxial stress–strain experimental results of copper and nickel.

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