Deformation induced anisotropy and memorized back stress in constitutive model

1998 ◽  
Vol 14 (7) ◽  
pp. 627-646 ◽  
Author(s):  
H. Ishikawa ◽  
K. Sasaki
Keyword(s):  
Constitutive Model ◽  
Back Stress ◽  
Induced Anisotropy

A Visco-Plastic Constitutive Model for 60/40 Tin-Lead Solder Used in IC Package Joints

1992 ◽  
Vol 114 (3) ◽  
pp. 331-337 ◽  
Author(s):  
E. P. Busso ◽  
M. Kitano ◽  
T. Kumazawa
Keyword(s):  
Steady State ◽  
Constitutive Model ◽  
Bauschinger Effect ◽  
Back Stress ◽  
Steady State Creep ◽  
Stress Dependence ◽  
State Variable ◽  
Hardening Behavior ◽  
Measured Stress ◽  
Ic Package

A new unified visco-plastic constitutive model for the 60 Sn-40 Pb alloy used in solder joints of surface-mount IC packages and semiconductor devices is proposed. The model accounts for the measured stress-dependence of the activation energy and for the strong Bauschinger effect exhibited by the solder. The latter is represented by a back stress state variable which, in turn, evolves according to a hardening-recovery equation. Based on the observed hardening behavior, it is assumed that the isotropic resistance to plastic flow does not evolve within the deformation range covered in this study (ε< 3 percent). The deformation phenomena associated with the solder’s monotonic and steady-state cyclic responses are accurately predicted for −55°C≦T≦150°C and 8 x 10−2 s−1 ≦ ε ≦ 8 x 10−5 s−1. The model also predicts well the overall trend of steady-state creep behavior. The constitutive model is formulated within a continuum mechanics framework and is therefore well suited for implementation into finite element or other structural codes.

A Micromechanically Based Constitutive Model for the Inelastic and Swelling Behaviors in Double Network Hydrogels

2015 ◽  
Vol 83 (2) ◽  
Author(s):  
Yin Liu ◽  
Hongwu Zhang ◽  
Yonggang Zheng
Keyword(s):  
Constitutive Model ◽  
Strain Energy ◽  
Polymer Chains ◽  
Loading Path ◽  
Induced Anisotropy ◽  
Double Network ◽  
Strain Energy Density Function ◽  
Damage Process ◽  
Single Polymer Chain ◽  
Swelling Behaviors

This paper presents a micromechanically based constitutive model within the framework of the continuum mechanics to characterize the inelastic elastomeric and swelling behaviors of double network (DN) hydrogels, such as the stress-softening, necking instability, hardening, and stretch-induced anisotropy. The strain-energy density function of the material is decomposed into two independent contributions from the tight and brittle first network and the soft and loose second network, each of which is obtained by integrating the strain energy of one-dimensional (1D) polymer chains in each direction of a unit sphere. The damage process is derived from the irreversible breakages of sacrificial chains in the first network and characterized by the directional stretch-dependent evolution laws for the equivalent modulus and the locking stretch in the non-Gauss statistical model of a single polymer chain. The constitutive model with the optimized-material evolution law predicts stress–stretch curves in a good agreement with the experimental results during loading, unloading, and reloading paths for both ionic and covalent DN hydrogels. The deformation-induced anisotropy is investigated and demonstrated by the constitutive model for the free swelling of damaged specimen. The constitutive model is embedded into the finite-element (FE) procedure and proved to be efficient to model the necking and neck propagation in the plane-strain uniaxial elongation. Based on the procedure, the effects of imperfection and boundary conditions on the loading path and the material evolution during different stages of deformation are investigated.

Behavior of Lead-Free Solder Under Thermomechanical Loading

2004 ◽  
Vol 126 (3) ◽  
pp. 367-373 ◽  
Author(s):  
Y. Wei ◽  
C. L. Chow ◽  
K. J. Lau ◽  
P. Vianco ◽  
H. E. Fang
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Damage Mechanics ◽  
Base Alloy ◽  
Back Stress ◽  
General Purpose ◽  
Lead Free ◽  
Element Analysis ◽  
Different Temperatures ◽  
Free Solder

This paper presents an investigation of lead-free Sn-Ag base alloy, 95.5Sn-3.9Ag-0.6Cu, both experimentally and analytically. Experimentally, the deformation behavior of the material was measured for different temperatures (25°C and 1000°C) over a range of strain rates (10−5 to 10−3/s) under isothermal and thermomechanical conditions. Development of a unified viscoplastic constitutive model followed, taking into account the effects of the measured strain rate and temperature changes. The temperature rate effects are considered in the evolution equation of back stress. In order to include material degradation in the solder, the theory of damage mechanics is applied by introducing two damage variables in the viscoplastic constitutive model. Finally, the constitutive model is coded into a general-purpose finite element computer program (ABAQUS) through its user-defined material subroutine (UMAT). The damage-coupled finite element analysis (FEA) is then employed to monitor the condition of failure of a notched component. The predicted and measured maximum loads have been compared and found to be satisfactory. In addition, the calculated damage distribution contours enable the identification of potential failure site for failure analysis.

The Numerical Simulation of Multi-Stage Sheet Metal Forming Based on Modified Yoshida-Uemori Hardening Model

2016 ◽  
Vol 725 ◽  
pp. 554-559
Author(s):  
Jiang Chen ◽  
Wen Liang Chen
Keyword(s):  
Numerical Simulation ◽  
Constitutive Model ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Boundary Surface ◽  
Back Stress ◽  
Experimental Result ◽  
Multi Stage ◽  
Tension And Compression

Bauschinger effect is significant for metal forming, particularly for aluminum. A material constitutive model especially for multi-stage sheet metal forming is presented in this paper, which is improved based on Yoshida-Uemori(Y-U) model assumes that there exists different coefficient on equivalent back stress and boundary surface between stages. The prediction of this model is validated through real tension and compression test. Compared to other hardening rules, it can be shown that a more accurate result can be predicted by this model. This model is also successfully applied to be used in the numerical simulation of a multi-stage manufacturing process of an A-pillar, the experimental result demonstrates the advantage of this model in springback analysis in multi-stage simulation over other constitutive model.

A constitutive model for gravelly soils considering shear-induced volumetric deformation

2010 ◽  
Vol 47 (6) ◽  
pp. 662-673 ◽  
Author(s):  
Bin-Lin Chu ◽  
Yeun-Wen Jou ◽  
Meng-Chia Weng
Keyword(s):  
Hydrostatic Pressure ◽  
Constitutive Model ◽  
Triaxial Compression ◽  
Compression Tests ◽  
Induced Anisotropy ◽  
Volumetric Deformation ◽  
Proposed Model ◽  
Gravelly Soils ◽  
Deformational Behavior ◽  
Stress Induced Anisotropy

This study elucidates the deformational behavior of gravelly soils by analyzing how hydrostatic pressure and pure shearing affect deformational behavior. A series of drained, triaxial compression tests have been performed using large specimens made of gravelly soils, where the grain-size distribution curve was based on the field condition. The volumetric and shear deformations of gravelly soils have been determined by performing experiments with controlled stress paths — hydrostatic pressure was applied first followed by pure shearing. A simple and innovative constitutive model is also proposed. The proposed model is characterized by the following features of gravelly soils: (i) significant shear-induced volumetric deformation prior to failure, (ii) modulus stiffening under hydrostatic loading and degradation under shearing, and (iii) stress-induced anisotropy. In the proposed model, deformational moduli K and G vary according to the stress state. The stiffening and degradation of these moduli result in diverse deformational behavior of gravelly soils. In addition, an anisotropic factor, β, is introduced to represent stress-induced anisotropy. Moreover, the proposed model only requires eight material parameters; each of which can be obtained easily from experiments.

From Micro- to Macro-Plasticity: The Scale Invariance Approach

1995 ◽  
Vol 117 (4) ◽  
pp. 352-355 ◽  
Author(s):  
E. C. Aifantis
Keyword(s):  
Scale Invariance ◽  
Grain Orientation ◽  
Constitutive Relations ◽  
Back Stress ◽  
Plastic Behavior ◽  
Induced Anisotropy ◽  
Anisotropic Plasticity ◽  
Phenomenological Coefficients ◽  
Kinetics Of ◽  
Kinematics And Kinetics

An account of recent contributions to the theory of plasticity advanced by the author and his co-workers is provided with emphasis on deformation-induced anisotropy and texture formation. For the description of these effects, the so-called scale invariance approach is adopted which allows information and constitutive relations pertaining to single slip to be cast in the form of macroscopic constitutive equations. Various phenomenological plasticity models are derived this way with the extra dividend of deducing explicit expressions for the phenomenological coefficients. The method is particularly suited for large deformation anisotropic plasticity, as it reveals the inherent coupling between the evolution of back stress and the plastic spin. Extended models of macroscopic plastic behavior accounting for vertex and texture phenomena can also be obtained by slightly generalizing the kinematics and kinetics of the microscopic configuration to include rate, non-Schmid, secondary slip and grain orientation effects.

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