Constitutive Modeling of Multiaxial Deformation and Induced Anisotropy in Superplastic Materials

2000 ◽  
Author(s):  
Marwan K. Khraisheh
Keyword(s):  
Constitutive Modeling ◽  
Continuum Theory ◽  
Yield Function ◽  
Yield Potential ◽  
Induced Anisotropy ◽  
Dynamic Yield ◽  
Fixed End ◽  
Unit Vectors

Abstract The multiaxial deformation of superplastic materials is modeled within a continuum theory of viscoplasticity using a generalized anisotropic dynamic yield function. The anisotropic dynamic yield function is capable of describing the evolution of the initial anisotropic state of the yield potential through the evolution of unit vectors defining the direction of anisotropy. The evolution of the direction of anisotropy is represented by a constitutive spin such that initially it is identical to the Eulerian spin and as deformation continues, it tends towards an orthotropic spin. Experiments on the model Pb-Sn alloy were conducted and used to calibrate and verify the constructed model. It is shown that the model in conjunction with the anisotropic dynamic yield function is capable of predicting the actual trend of the induced axial stresses recorded in fixed-end torsion experiments.

An Investigation of Yield Potentials In Superplastic Deformation

1999 ◽  
Vol 122 (1) ◽  
pp. 93-97 ◽  
Author(s):  
Marwan K. Khraisheh
Keyword(s):  
Effective Strain ◽  
Yield Function ◽  
Yield Potential ◽  
Anisotropic Yield Function ◽  
Superplastic Alloy ◽  
Degree Of Anisotropy ◽  
Anisotropic Function ◽  
Experimental Yield ◽  
Dynamic Yield ◽  
Von Mises

Recent results (Khraisheh et al., 1995 and 1997) have indicated that superplastic materials exhibit a strong degree of anisotropy and that the plastic flow cannot be described by the isotropic von Mises flow rules. In this study, the yield potential for the model Pb-Sn superplastic alloy is constructed experimentally for different effective strain rates using combined tension/torsion tests. A generalized anisotropic “dynamic” yield function is also proposed to represent the experimentally constructed yield potentials. The anisotropic function is not only capable of describing the initial anisotropic state of the yield potential, it can also describe its evolution through the evolution of unit vectors defining the direction of anisotropy. The anisotropic yield function includes a set of material constants which determine the degree of deviation of the yield potential from the isotropic von Mises yield surface. It is shown that the anisotropic yield function successfully represents the experimental yield potentials, especially in the superplastic region. [S0094-4289(00)01401-8]

A Yield Criterion for Porous Ductile Media at High Strain Rate

1997 ◽  
Vol 64 (3) ◽  
pp. 503-509 ◽  
Author(s):  
Ze-Ping Wang ◽  
Qing Jiang
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Yield Surface ◽  
High Strain ◽  
Yield Criterion ◽  
Matrix Material ◽  
Yield Function ◽  
Inertial Effects ◽  
The Matrix ◽  
Dynamic Yield

An approximate yield criterion for porous ductile media at high strain rate is developed adopting energy principles. A new concept that the macroscopic stresses are composed of two parts, representing dynamic and quasi-static components, is proposed. It is found that the dynamic part of the macroscopic stresses controls the movement of the dynamic yield surface in stress space, while the quasi-static part determines the shape of the dynamic yield surface. The matrix material is idealized as rigid-perfectly plastic and obeying the von Mises yield. An approximate velocity field for the matrix is employed to derive the dynamic yield function. Numerical results show that the dynamic yield function is dependent not only on the rate of deformation but also on the distribution of initial micro-damage, which are different from that of the quasi-static condition. It is indicated that inertial effects play a very important role in the dynamic behavior of the yield function. However, it is also shown that when the rate of deformation is low (≤103/sec), inertial effects become vanishingly small, and the dynamic yield function in this case reduces to the Gurson model.

scholarly journals Constitutive modeling of cyclic viscoplasticity considering induced anisotropy.

1990 ◽  
Vol 56 (532) ◽  
pp. 2457-2463
Author(s):  
Hiromasa ISHIKAWA ◽  
Katsuhiko SASAKI ◽  
Kiyohide SUZUKI
Keyword(s):  
Constitutive Modeling ◽  
Induced Anisotropy

Yield Function for Solder Elastoviscoplastic Modeling

2004 ◽  
Vol 127 (2) ◽  
pp. 147-156 ◽  
Author(s):  
M. Dube ◽  
T. Kundu
Keyword(s):  
Constitutive Modeling ◽  
Yield Function ◽  
Materials Processing ◽  
Accelerated Tests ◽  
Mechanics Of Materials ◽  
Disturbed State Concept ◽  
Wide Range ◽  
University Of Arizona ◽  
Material Behaviors ◽  
Field Reliability

Field reliability extrapolations from accelerated tests necessitate simulation of a variety of material behaviors under general loading conditions. The Hierarchical Incremental Single Surface (HiSS) yield function (Desai, C. S., 2001, Mechanics of Materials and Interfaces: The Disturbed State Concept, CRC Press, Boca Raton, FL.) has been applied extensively to a wide range of materials, from solders and silicon to ceramics and geotechnical materials, for simulating continuous-yield elastoplastic and elastoviscoplastic behavior. This work presents a continuous-yield function that avoids problems with HiSS for thermal and tensile loading. Validations are presented for eutectic Pb∕Sn data of Wang et al. (Wang, Z., Desai, C.S., and Kundu, T., 2001, “Disturbed State Constitutive Modeling and Testing of Joining Materials in Electronic Packaging,” report to NSF for Materials Processing and Manufacturing Division Grant 9812686, University of Arizona, Tucson, AZ). Limitations on the range of validity of the elastoplastic and the Perzyna elastoviscoplastic formulations are discussed.

A Thermoplastic Constitutive Modeling and Geotechnical Centrifuge Simulation of Partially Saturated Soil Under Buried Explosive Loading

2013 ◽  
Author(s):  
Asghar Yarahmadi ◽  
Rebecca Brannon ◽  
Carlos Bonifasi Lista
Keyword(s):  
Constitutive Modeling ◽  
Thermal Effects ◽  
Saturated Soil ◽  
High Rate ◽  
Internal Variables ◽  
Induced Anisotropy ◽  
Geotechnical Centrifuge ◽  
Partially Saturated ◽  
Partially Saturated Soil ◽  
Buried Explosive

In high-rate failure models for geological and rock-like materials, heating due to inelastic deformation is often neglected or accommodated incompletely through the use of an isentropic elastic response. However, for realistic prediction of geomaterials response to high-rate large deformations with significant released energy (such as buried explosive), dissipation caused by the initial mechanical work of the blast wave results in a non-negligible entropy generation that must be accounted for in constitutive modeling. In this study, thermal effects in the vicinity of a buried explosive in partially saturated soil are investigated using the Jones-Wilkins-Lee (JWL++) detonation model of High Explosive (HE) material, along with coupled multiphysics balance equations in an open-source massively parallel computational framework (Uintah) via Material Point Method (MPM) and Implicit, Continuous fluid, Eulerian (ICE) for compressible multi-material formulation of fluid-structure interactions (including highly pressurized explosive gaseous products). The temperature is allowed to evolve according to thermo-plasticity equations (derived from dissipation inequalities and basic conservation/thermodynamics laws) and thereafter, the state of internal variables (porosity, entropy, yield stress, etc) and stress in the partially saturated soil are determined for the obtained temperature. In order to account for material hardening from pore collapse, a yield surface based on Gurson’s upper bound theory evolves with stress, temperature, and internal state variables in plastic phase. Comparisons of soil response to blast loading are provided to quantify the importance of thermal effects. Furthermore, geomaterials develop anisotropy in their response to deformation caused by prompt high-pressure shock waves. Thermodynamic admissibility implies that the fourth-order tangent stiffness tensor of geomaterials must develop a recoverable deformation-induced anisotropy (RDIA) even if the material is initially isotropic. This effect is significant for materials, like geomaterials, that have strongly pressure-sensitive strength. The degree of RDIA and the required additional terms in the form of deformation-induced anisotropy based on thermodynamics requirements in a high-temperature phenomenon are summarized for the region near the buried explosive source in partially saturated soil.

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