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.

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.

Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity With Damage- Application to Eutectic Sn/Pb Solder Alloy

2007 ◽  
Vol 23 (4) ◽  
pp. 433-444 ◽  
Author(s):  
C. F. Lee ◽  
Y. C. Chen
Keyword(s):  
Internal State ◽  
Low Cycle Fatigue ◽  
Cyclic Stress ◽  
Irreversible Thermodynamics ◽  
Damage Parameter ◽  
Fatigue Tests ◽  
Future Research ◽  
Mathematical Form ◽  
State Variables ◽  
Endochronic Theory

AbstractIn this paper, an endochronic theory of cyclic viscoplasticy with damage is established based on the irreversible thermodynamics of continuous media with internal state variables containing an isotropic damage parameter. The constitutive equations derived have the same mathematical form as those of convectional endochronic theory without damage, except the effective stress with damage is used. This result coincides with the Lemaitre's statements of stain equivalence principle.Using the experimental cyclic stress-strain curves of 63Sn/37Pb solder bars, corrected from the uniaxially constant displacement amplitude cyclic tests under MTS Tytron microtester, the computational results of cyclic stess-strain curves with several degrees of damage can reproduce the experimental data quite well. Based on compressive buckling appeared in the vicinity of the compressive end parts of the hysteresis loop, the critical values of damage are determined between 0.3 and 0.4.The evolution equation of damage proposed in terms of the intrinsic damage time scale and its results in the modified Coffin-Manson LCF law can be extended in the future research for a statistical theory of life distribution under low cycle fatigue tests.

scholarly journals An extension of Gronwall inequality in the theory of bodies with voids

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1161-1167
Author(s):  
Marin Marin ◽  
Praveen Ailawalia ◽  
Ioan Tuns
Keyword(s):  
Boundary Value Problem ◽  
Internal State ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Internal Variables ◽  
State Variables ◽  
Gronwall’S Inequality ◽  
Initial Boundary Value

Abstract In this paper, we obtain a generalization of the Gronwall’s inequality to cover the study of porous elastic media considering their internal state variables. Based on some estimations obtained in three auxiliary results, we use this form of the Gronwall’s inequality to prove the uniqueness of solution for the mixed initial-boundary value problem considered in this context. Thus, we can conclude that even if we take into account the internal variables, this fact does not affect the uniqueness result regarding the solution of the mixed initial-boundary value problem in this context.

scholarly journals Influence of Different Annealing Atmospheres on the Mechanical Properties of Freestanding MCrAlY Bond Coats Investigated by Micro-Tensile Creep Tests

Metals ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 692 ◽  
Author(s):  
Sven Giese ◽  
Steffen Neumeier ◽  
Jan Bergholz ◽  
Dmitry Naumenko ◽  
Willem J. Quadakkers ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Creep Strength ◽  
Bond Coat ◽  
Oxide Dispersion Strengthened ◽  
Tensile Creep ◽  
Creep Tests ◽  
Bond Coats ◽  
Nial Phase ◽  
Lower Strain ◽  
Plasma Sprayed

The mechanical properties of low-pressure plasma sprayed (LPPS) MCrAlY (M = Ni, Co) bond coats, Amdry 386, Amdry 9954 and oxide dispersion strengthened (ODS) Amdry 9954 (named Amdry 9954 + ODS) were investigated after annealing in three atmospheres: Ar–O2, Ar–H2O, and Ar–H2–H2O. Freestanding bond coats were investigated to avoid any influence from the substrate. Miniaturized cylindrical tensile specimens were produced by a special grinding process and then tested in a thermomechanical analyzer (TMA) within a temperature range of 900–950 °C. Grain size and phase fraction of all bond coats were investigated by EBSD before testing and no difference in microstructure was revealed due to annealing in various atmospheres. The influence of annealing in different atmospheres on the creep strength was not very pronounced for the Co-based bond coats Amdry 9954 and Amdry 9954 + ODS in the tested conditions. The ODS bond coats revealed significantly higher creep strength but a lower strain to failure than the ODS-free Amdry 9954. The Ni-based bond coat Amdry 386 showed higher creep strength than Amdry 9954 due to the higher fraction of the β-NiAl phase. Additionally, its creep properties at 900 °C were much more affected by annealing in different atmospheres. The bond coat Amdry 386 annealed in an Ar–H2O atmosphere showed a significantly lower creep rate than the bond coat annealed in Ar–O2 and Ar–H2–H2O atmospheres.

Elastoviscoplastic Models with Relaxed Configurations and Internal State Variables

1990 ◽  
Vol 43 (7) ◽  
pp. 131-151 ◽  
Author(s):  
Sanda Cleja T¸igoiu ◽  
Eugen Soo´s
Keyword(s):  
Experimental Data ◽  
Structural Analysis ◽  
Internal State ◽  
State Variables ◽  
Internal State Variables ◽  
Local Current

We present the microstructural basis, the initial macroscopical formulations, and a possible axiomatic reconstruction of the elastoviscoplastic model for metals based on the use of the local, current, relaxed configurations. Structural analysis and experimental data show that using these configurations offers advantages for the formulation of the material laws when the deformations are small or moderately large. Our review aims to be a concise, historical, and critical exposition of the main stages, contributions and results, which led, during the late sixties and the beginning of seventies, to the formulation of the fundamental ideas lying at the basis of the model. We delineate the role played by Lee, Liu, Teodosiu, Sidoroff, Mandel, and Kratochvil in the first formulation of the theory between 1966 and 1972, as well as the contributions of Dafalias and Loret to the development of the model between 1983 and 1985. Finally, we discuss some results obtained between 1985 and 1988 with models based on local current relaxed configurations.

scholarly journals Study on creep performance of launch canister under long-term storage

2019 ◽  
Vol 43 (2) ◽  
pp. 199-208 ◽  
Author(s):  
Cun-Gui Yu ◽  
Tong-Sheng Sun ◽  
Guang-Yuan Xiao
Keyword(s):  
Residual Deformation ◽  
Bottom Layer ◽  
Tensile Creep ◽  
Creep Model ◽  
Model Parameters ◽  
Creep Tests ◽  
Software Environment ◽  
Long Term Storage ◽  
Term Storage

In this paper, the creep performance of a multi-barrel rocket launch canister under long-term stacking storage is studied. Based on the Bailey–Norton model, a creep model for the frame material of a launch canister was established. Constant stress tensile creep tests under different stress levels at room temperature were carried out on the frame materials of the launch canister and the creep model parameters were obtained by test data fitting. The three-dimensional finite element model of the launch canister was established in the ABAQUS software environment and the creep deformation of the launch canister after long-term stacking storage was studied. The results indicated that the bottom layer of the launch canister frame presented an extended residual deformation when the stacking storage solution with the original support pad was used. Therefore, a position adjustment program of the support pad was put forward. The residual deformation of the launch canister frame after long-term storage could be significantly reduced, thus the performance requirements for the launch canister are guaranteed.

Modeling and Simulation of Microstructure Evolution in Extruded Aluminum Profiles

2009 ◽  
Vol 424 ◽  
pp. 43-50
Author(s):  
Farhad Parvizian ◽  
T. Kayser ◽  
Bob Svendsen
Keyword(s):  
Plastic Deformation ◽  
Aluminum Alloys ◽  
Modeling And Simulation ◽  
Microstructure Evolution ◽  
Internal State ◽  
Extrusion Process ◽  
State Variables ◽  
Cooling Process ◽  
Microstructure Parameters ◽  
Simulation Results

The purpose of this work is to predict the microstructure evolution of aluminum alloys during hot metal forming processes using the Finite Element Method (FEM). Here, the focus will be on the extrusion process of aluminum alloys. Several micromechanical mechanisms such as diffusion, recovery, recrystallization and grain growth are involved in various subsequent stages of the extrusion and the cooling process afterward. The evolution of microstructure parameters is motivated by plastic deformation and temperature. A number of thermomechanical aspects such as plastic deformation, heat transfer between the material and the container, heat generated by friction, and cooling process after the extrusion are involved in the extrusion process and result in changes in temperature and microstructure parameters subsequently. Therefore a thermomechanically coupled modeling and simulation which includes all of these aspects is required for an accurate prediction of the microstructure evolution. A brief explanation of the isotropic thermoelastic viscoplastic material model including some of the simulation results of this model, which is implemented as a user material (UMAT) in the FEM software ABAQUS, will be given. The microstructure variables are thereby modeled as internal state variables. The simulation results are finally compared with some experimental results.

Sign in / Sign up

Export Citation Format

Share Document