scholarly journals A double incremental variational procedure for elastoplastic composites with combined isotropic and linear kinematic hardening

2019 ◽  
Vol 158 ◽  
pp. 243-267 ◽  
Author(s):  
Antoine Lucchetta ◽  
François Auslender ◽  
Michel Bornert ◽  
Djimédo Kondo
Keyword(s):  
Kinematic Hardening ◽  
Variational Procedure

On the Macroscopic Response and Field Statistics in Particulate Composites With Elasto-Plastic Phases and Random Microstructures

2021 ◽  
Vol 88 (3) ◽  
Author(s):  
Michalis Agoras ◽  
Konstantinos Garyfallogiannis ◽  
Nikolaos Aravas
Keyword(s):  
Bauschinger Effect ◽  
Kinematic Hardening ◽  
Local Strain ◽  
Spherical Particles ◽  
Particulate Composites ◽  
Variational Procedure ◽  
Two Phase ◽  
Effective Response ◽  
Elastic Plastic ◽  
Macroscopic Response

Abstract In this article, we carry out a theoretical investigation of the macroscopic response and field statistics in two-phase particulate composites with elasto-plastic constituents and random microstructures under cyclic loading conditions. To this end, we make use of the “incremental variational homogenization” (IVH) procedure of Agoras et al. (2016, “Incremental Variational Procedure for Elasto-Viscoplastic Composites and Application to Polymer- and Metal-Matrix Composites Reinforced by Spheroidal Elastic Particles,” Int. J. Solid Struct., 97–98, pp. 668–686) and corresponding unit cell finite element simulations. Results are obtained for statistically isotropic distributions of spherical particles and for “spheroidal distributions” of spheroidal particles. It is shown analytically that the IVH estimate of Agoras et al. and that of Lahellec and Suquet (2013, “Effective Response and Field Statistics in Elasto-Plastic and Elasto-Visco-Plastic Composites Under Radial and Non-Radial Loadings,” Int. J. Plasticity, 42, pp. 1–30) are equivalent. In addition, it is illustrated by means of specific numeral comparisons that the IVH estimate is also equivalent (to within numerical accuracy) to the corresponding estimates of Idiart and Lahellec (2016, “Estimates for the Overall Linear Properties of Pointwise Heterogeneous Solids With Application to Elasto-Viscoplasticity,” J. Mech. Phys. Solids, 97, pp. 317–332) and Lucchetta et al. (2019, “A Double Incremental Variational Procedure for Elastoplastic Composites With Combined Isotropic and Linear Kinematic Hardening,” Int. J. Solid Struct., 158, pp. 243–267). Furthermore, it is shown in the context of specific exact results for composite materials with lamellar microstructures that the elastic–plastic coupling and the Bauschinger effect are the macroscopic manifestations of the incompatibility of the local elastic strains. Local strain hardening is incorporate in the IVH model. The predictions of the IVH model for the macroscopic response of particulate composites are found to be in good agreement with the corresponding numerical results, in general. For the extreme cases of rigidly reinforced composites and porous materials, however, the IVH model fails to capture the elastic–plastic coupling and the Bauschinger effect. The underlying reasons for this shortcoming are discussed and a strategy toward the improvement of the IVH model is proposed.

scholarly journals On the Plastic Strain Accumulation in Notched Bars During High-Temperature Creep Dwell

2020 ◽  
Vol 36 (2) ◽  
pp. 167-176 ◽  
Author(s):  
Daniele Barbera ◽  
Haofeng Chen
Keyword(s):  
High Temperature ◽  
Cyclic Loading ◽  
Plastic Strain ◽  
Kinematic Hardening ◽  
High Temperature Creep ◽  
Strain Accumulation ◽  
Material Models ◽  
Cyclic Loading Condition ◽  
Hardening Material ◽  
Temperature Creep

ABSTRACTStructural integrity plays an important role in any industrial activity, due to its capability of assessing complex systems against sudden and unpredicted failures. The work here presented investigates an unexpected new mechanism occurring in structures subjected to monotonic and cyclic loading at high temperature creep condition. An unexpected accumulation of plastic strain is observed to occur, within the high-temperature creep dwell. This phenomenon has been observed during several full inelastic finite element analyses. In order to understand which parameters make possible such behaviour, an extensive numerical study has been undertaken on two different notched bars. The notched bar has been selected due to its capability of representing a multiaxial stress state, which is a practical situation in real components. Two numerical examples consisting of an axisymmetric v-notch bar and a semi-circular notched bar are considered, in order to investigate different notches severity. Two material models have been considered for the plastic response, which is modelled by both Elastic-Perfectly Plastic and Armstrong-Frederick kinematic hardening material models. The high-temperature creep behaviour is introduced using the time hardening law. To study the problem several results are presented, as the effect of the material model on the plastic strain accumulation, the effect of the notch severity and the mesh element type and sensitivity. All the findings further confirm that the phenomenon observed is not an artefact but a real mechanism, which needs to be considered when assessing off-design condition. Moreover, it might be extremely dangerous if the cyclic loading condition occurs at such a high loading level.

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.

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.

scholarly journals Experimental and Numerical Study of the Effects of the Reversal Hot Rolling Conditions on the Recrystallization Behavior of Austenite Model Alloys

Metals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 26
Author(s):  
Krzysztof Muszka ◽  
Mateusz Sitko ◽  
Paulina Lisiecka-Graca ◽  
Thomas Simm ◽  
Eric Palmiere ◽  
...  
Keyword(s):  
Microstructure Evolution ◽  
Hot Rolling ◽  
Strain Path ◽  
Physical Simulation ◽  
Numerical Study ◽  
Kinematic Hardening ◽  
Process Window ◽  
Recrystallization Behavior ◽  
Full Field ◽  
Strain Reversal

The experimental and numerical study of the effects of the recrystallization behavior of austenite model alloys during hot plate rolling on reverse rolling is the main goal of the paper. The computer models that are currently applied for simulation of reverse rolling are not strain-path-sensitive, thus leading to overestimation of the processing parameters outside the accepted process window (e.g., deformation in the partial austenite recrystallization region). Therefore, in this work, a particular focus is put on the investigation of strain path effects that occur during hot rolling and their influence on the microstructure evolution and mechanical properties of microalloyed austenite. Both experimental and numerical techniques are employed in this study, taking advantage of the integrated computational material engineering concept. The combined isotropic–kinematic hardening model is used for the macroscale predictions to take into account softening effects due to strain reversal. The macroscale model is additionally enriched with the full-field microstructure evolution model within the cellular automata framework. Examples of obtained results, highlighting the role of the strain reversal on the microstructural response, are presented within the paper. The combination of the physical simulation of austenitic model alloys and computer modeling provided new insights into optimization of the processing routes of advanced high-strength steels (AHSS).

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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