A Steady Creep Theory of High Lead Pb/Sn Solder with Creep-Parameters Maps

2005 ◽  
Vol 21 (4) ◽  
pp. 217-225 ◽  
Author(s):  
C. F. Lee ◽  
J. J. Wang ◽  
W. K. Chung
Keyword(s):  
Internal State ◽  
Irreversible Thermodynamics ◽  
Steady Creep ◽  
Creep Tests ◽  
Finite Elements Analysis ◽  
Creep Theory ◽  
Deformation Kinetics ◽  
State Variable ◽  
Β Phase ◽  
High Lead

AbstractIn this paper, Valanis' steady creep theory with four creep parameters was derived from a liaison of the theory of deformation kinetics with internal isotropy and the theory of irreversible thermodynamics of continuous media with only one internal state variable.According to the theory, steady creep rates under simple shear and simple tensile conditions are related and allow one to construct creep-parameters maps of high lead Pb/Sn solders (from 90% to 100% Pb). When testing temperatures are higher than solder's solvus temperature, microstructural transformation from lamellae α + β phase to solid solution α phase in the bulk specimens are considered in the construction of maps. Applications of maps in the 97.5Pb/2.5Sn solder joints creep tests need minor modifications due to dispersive precipitation of tin particles in lead matrix. As a result, the maps may provide estimated steady creep rates for the usage of finite elements analysis in the microsystem or electronic packaging analysis.

Deformation Kinetics of Steady Creep in Sn/Pb Solder Alloys With Applications

2004 ◽  
Vol 20 (2) ◽  
pp. 85-93 ◽  
Author(s):  
C. F. Lee ◽  
M. K. Chang ◽  
W. K. Chung
Keyword(s):  
Constitutive Equation ◽  
Internal State ◽  
Tensile Creep ◽  
Future Research ◽  
State Variables ◽  
Steady Creep ◽  
Solder Alloys ◽  
Creep Tests ◽  
Shear Creep ◽  
Deformation Kinetics

AbstractIn this paper, a constitutive equation of steady creep rates:is derived based on a liaison of the theory of irreversible thermodynamics of continuous media with internal state variables (ISV); and the deformation kinetics. In steady creep, only one ISV is used, whose evolution equation is derived by the concepts of deformation kinetics, in which micromotions are generated by a group of atoms climbing over a tilted potential barrier of the highest height ε0.Applications of the constitutive equation in the cases of some Sn/Pb solder alloys-63Sn/37Pb, 60Sn/40Pb and 97.5Pb/2.5Sn under shear creep tests; and 98Pb/2Sn under tensile creep tests, show that the theoretical results can describe the experimental data quite well. These results pave the way for future research in the comparisons of creep resistance among solders with various Sn/Pb compositions and in the generalization of three-dimensional constitutive equation.

High-temperature Deformation Kinetics of Gold at 473K to 773K

2008 ◽  
Vol 1137 ◽  
Author(s):  
Vineet Bhakhri ◽  
Robert J. Klassen
Keyword(s):  
High Temperature ◽  
Cell Structure ◽  
Dislocation Cell ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Indentation Creep ◽  
Creep Tests ◽  
Dislocation Glide ◽  
Deformation Kinetics ◽  
Temperature Constant

AbstractHigh-temperature constant-force indentation creep tests of 200 seconds duration were performed on an annealed gold specimen at 473K to 773K, to investigate the dependence of the micro-/nano-indentation deformation kinetics upon indentation stress, temperature and time. The indent stress displayed a clear indentation size effect at 473 K. An analysis of the measured indentation creep rate, and its dependence upon temperature and stress, indicate that the strength of the deformation rate limiting obstacles increases with temperature. This is consistent with the expected temperature dependent evolution of the dislocation cell structure whose boundaries become the primary obstacles to dislocation glide.

Constitutive Modeling of Beta Titanium Alloy Ti-10V-4.5Fe-1.5Al during Hot Deformation Process

2012 ◽  
Vol 510 ◽  
pp. 729-733
Author(s):  
Feng Bo Han ◽  
Jin Shan Li ◽  
Hong Chao Kou ◽  
Bin Tang ◽  
Min Jie Lai ◽  
...  
Keyword(s):  
Titanium Alloy ◽  
High Temperature ◽  
Dislocation Density ◽  
Internal State ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Model Parameters ◽  
Internal State Variable ◽  
Dislocation Interaction ◽  
State Variable

A constitutive model using dislocation density rate as an internal state variable has been proposed for hot working of β titanium alloy in this paper. The β phase was only taken into consideration during high temperature deformation. The solution strengthening and dislocation interaction were included in the constitutive equations. The strength coefficient was determined by equivalent vanadium content, Veq, which was calculated according to the alloy constituent. A Kocks-Mecking model was adopted to describe the variation of dislocation density. The constitutive relationship of a β titanium alloy Ti-10V-4.5Fe-1.5Al for high temperature deformation was established using the internal-state-variable based model. Model parameters were determined by the genetic algorithm based objective optimization method. The predicted results agree fairly well with the experimental value.

scholarly journals Formulation of a macroscale corrosion damage internal state variable model

2014 ◽  
Vol 51 (6) ◽  
pp. 1235-1245 ◽  
Author(s):  
Christopher A. Walton ◽  
M.F. Horstemeyer ◽  
Holly J. Martin ◽  
D.K. Francis
Keyword(s):  
Internal State ◽  
Corrosion Damage ◽  
Internal State Variable ◽  
Variable Model ◽  
State Variable ◽  
State Variable Model

A State Variable Interpretation of Some Rate-Dependent Inelastic Properties of Steel

1978 ◽  
Vol 100 (4) ◽  
pp. 395-401 ◽  
Author(s):  
B. Larsson ◽  
B. Stora˚kers
Keyword(s):  
Stainless Steel ◽  
Elevated Temperature ◽  
Constitutive Equation ◽  
Physical Theory ◽  
Creep Tests ◽  
Variable Theory ◽  
One Dimensional ◽  
State Variable ◽  
Rate Dependent ◽  
Stress States

Based on a state variable theory proposed by Onat some discriminating creep tests of stainless steel have been designed and carried out at elevated temperature conditions. Quantitative correlations of the results are sought with predictions from a physical theory for recovery creep proposed by Lagneborg. The findings are utilized to interpret the behavior of creeping members when subjected to a rapid increase in the rate of straining. Different approaches toward generalization of physical one-dimensional creep laws to multiaxial stress states are discussed. A tentative constitutive equation applicable to the solution of general boundary value problems is proposed.

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