scholarly journals Unified Creep Plasticity Damage (UCPD) Model for Solder

2011 ◽  
Author(s):  
Michael Neilsen ◽  
Paul Vianco
Keyword(s):  
Finite Elements ◽  
Crack Initiation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Acceleration Factor ◽  
Element Analysis ◽  
Damage Evolution Equation ◽  
Thermal Mechanical Fatigue ◽  
Size Dependent ◽  
Element Size

A unified creep plasticity damage (UCPD) model for Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model’s damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, two significant developments were needed to model crack initiation and growth in solder joints. First, an ability to accelerate the simulations such that the effects of hundreds or thousands of thermal cycles could be modeled in a reasonable amount of time was needed. This was accomplished by applying a user prescribed acceleration factor to the damage evolution; then, damage generated by an acceleration factor of cycles could be captured by the numerical simulation of a single thermal cycle. Second, an ability to capture the geometric effects of crack initiation and growth was needed. This was accomplished by replacing material in finite elements that had met the cracking failure criterion with very flexible elastic material. This diffuse crack modeling approach with local finite elements is known to generate mesh dependent solutions. However, introduction of an element size dependent term into the damage evolution equation was found to be effective in controlling mesh dependency. Finally, experimentally observed cracks in a typical solder joint subjected to thermal mechanical fatigue are compared with model predictions.

A Capability to Model Crack Initiation and Growth in Solder Joints

2009 ◽  
Author(s):  
Mike Neilsen ◽  
Paul Vianco ◽  
Alice Kilgo ◽  
Elizabeth Holm
Keyword(s):  
Finite Elements ◽  
Crack Initiation ◽  
Solder Joints ◽  
Acceleration Factor ◽  
Element Analysis ◽  
Damage Evolution Equation ◽  
Thermal Mechanical Fatigue ◽  
Modeling Approach ◽  
Geometric Effects ◽  
Model Crack

A new capability to model both crack initiation and growth in eutectic Sn-Pb solder joints was developed and implemented into finite element analysis codes. Two significant developments were needed to create this new capability. First, an ability to accelerate the simulations such that the effects of hundreds or thousands of thermal cycles could be modeled in a reasonable amount of time was needed. This was accomplished by applying a user prescribed acceleration factor to specific terms in the solder model’s damage evolution equation; then, the damage generated by an acceleration factor of cycles could be captured by the numerical simulation of a single thermal cycle. Second, an ability to capture the geometric effects of crack initiation and growth was needed. This was accomplished by replacing material in finite elements that had met the cracking failure criterion with very flexible elastic material. This diffuse crack modeling approach with local finite elements is known to generate mesh-dependent solutions. However, mesh refinement studies revealed that for thermal mechanical fatigue simulations, the mesh dependency is small and has a small effect on predictions for cycles to generate an electrical open. The new crack modeling approach will be described. Finally, crack predictions are compared with experimental observations.

Damage Analysis of Concrete Subjected to Freeze-Thaw Cycles and Chloride Ion Erosion

2011 ◽  
Vol 488-489 ◽  
pp. 464-467
Author(s):  
Ji Ze Mao ◽  
Zhi Yuan Zhang ◽  
Zong Min Liu ◽  
Chao Sun
Keyword(s):  
Constitutive Equation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Chloride Ion ◽  
Offshore Structures ◽  
Damage Evolution Equation ◽  
Freeze Thaw ◽  
Concrete Materials ◽  
Ion Erosion

With the development of damage mechanics, many researchers have used it to analyze the constitutive equation of concrete. Since the special environment in the cold marine regions, the offshore structures are common to subject to the comprehensive effects of freeze-thaw action and chloride erosion. This might cause concrete materials degradation and reduce the mechanical performance of concrete seriously. In this paper, based on the analysis and mechanical experiments of concrete materials under the comprehensive effects of freeze-thaw action and chloride ion erosion, the damage evolution equation of concrete elastic modulus along with the freeze-thaw cycles and chloride ion contents was established. The effects of chloride ion were investigated during the process of concrete degradation. According to the damage evolution equation, a new constitutive equation of concrete under freeze-thaw action and chloride erosion was established. And then, by means of the element simulation analysis of concrete beams when subjected to the comprehensive actions, the feasibility and applicability of the equation was examined and discussed. In this equation, both the freeze-thaw action and chloride ion erosion were considered together. It will be more suitable for analyzing the durability of concrete structures in the real cold marine regions. It will also provide some references for concrete constitutive theory.

Study On the Damage Evolution Equation of Rockburst

2008 ◽  
Vol 33-37 ◽  
pp. 663-668
Author(s):  
Quan Sheng Liu ◽  
Bin Liu ◽  
Wei Gao
Keyword(s):  
Energy Dissipation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Minimum Energy ◽  
Strength Criterion ◽  
Internal Variable ◽  
Total Strength ◽  
Damage Evolution Equation ◽  
Traditional Research ◽  
Minimum Energy Dissipation

This paper introduces the principle of minimum energy dissipation and its general procedures to establish development equation of internal variable. With the accepted viewpoint that the damage is only mechanics of energy dissipation during the rockburst and utilizing the total strength criterion based on released strain energy, the general damage evolution equation is deduced. Compared with the traditional research method of damage evolution equation, this method has universal and objective characteristics.

scholarly journals Unified Creep Plasticity Damage (UCPD) Model for SAC396 Solder

2013 ◽  
Author(s):  
Michael Neilsen ◽  
Paul Vianco
Keyword(s):  
Finite Element ◽  
Solder Joints ◽  
Element Analysis ◽  
Damage Evolution Equation ◽  
Thermal Mechanical Fatigue ◽  
Model Predictions ◽  
Solder Fatigue ◽  
Solder Joint Fatigue ◽  
The Relationship ◽  
Model Crack

A unified creep plasticity damage (UCPD) model for Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model’s damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, developments needed to model crack initiation and growth in solder joints will be described. Finally, experimentally observed cracks in typical solder joints subjected to thermal mechanical fatigue are compared with model predictions. Finite element based modeling is particularly suited for predicting solder joint fatigue of advanced electronics packaging, e.g. package-on-package (PoP), because it allows for evaluation of a variety of package materials and geometries.

Damage Evolution Equation of AZ31B Magnesium Alloy during Superplastic Deformation

2009 ◽  
Vol 610-613 ◽  
pp. 831-837
Author(s):  
Mei Juan Song ◽  
Ling Yun Wang ◽  
Rao Chuan Liu ◽  
Zhi Xiang Wang
Keyword(s):  
Quantitative Analysis ◽  
Evolution Equation ◽  
Superplastic Deformation ◽  
Damage Evolution ◽  
Volume Fraction ◽  
Tensile Tests ◽  
Critical Value ◽  
Cavity Volume ◽  
Characteristic Parameters ◽  
Damage Evolution Equation

After superplastic tensile tests and quantitative analysis of cavity volume fraction, the damage evolution equation based on the law of the micro-damage evolution and statistical mechanics was derived out. The characteristic parameters of damage evolvement and critical value of damage variables are achieved from the experiments.

Damage-coupled FLD of Sheet Metals for Warm Forming and Nonproportional Loading

2011 ◽  
Vol 20 (8) ◽  
pp. 1243-1262 ◽  
Author(s):  
M. Jie ◽  
C. L. Chow ◽  
X. Wu
Keyword(s):  
Evolution Equation ◽  
Damage Evolution ◽  
Strain Softening ◽  
Forming Limit ◽  
Sheet Metals ◽  
Nonproportional Loading ◽  
Damage Evolution Equation ◽  
Localized Necking ◽  
Loading Paths ◽  
Necking Criterion

A method of forming limit prediction for sheet metals at high temperatures and under nonproportional loading is presented. The method takes into account the strain-softening behaviors of the material at elevated temperatures. A localized necking criterion based on an isotropic damage-coupled acoustic tensor is developed and employed to determine the forming limits of strain-softening materials. The damage evolution equation is developed within the thermo-mechanical framework. A closed-form expression of the forming limit strains is derived by coupling the damage evolution equation into the localized necking criterion. A computer program, incorporating the incremental theory of plasticity, the damage evolution equation and the localized necking criterion, is developed to compute the forming limit strains under several nonproportional loading paths. A series of the uniaxial tensile tests is performed to measure the relevant mechanical properties of AA6061 at the elevated temperature of 450°C. The material damage variables are determined from the measured elastic modulii from a series of loading and unloading paths. The damage evolution equation of AA6061 at 450°C is formulated based on the test data. The computed limit strains are compared with the test results under various loading paths and a good agreement is observed. It is found that the critical damage value is independent on the stress states and loading paths. It may be concluded that the application of the material damage as a reliable criterion of localized necking including the nonproportional loading cases.

A Nonlinear Viscoelastic and Micromechanical Damage Constitutive Model for Solid Propellant

2013 ◽  
Vol 750-752 ◽  
pp. 2196-2199
Author(s):  
Zhi Xu Gu ◽  
Jian Zheng ◽  
Wei Peng ◽  
Xi Nan Tang ◽  
Jun Hui Yin
Keyword(s):  
Constitutive Model ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Solid Propellant ◽  
Damage Evolution Equation ◽  
Nonlinear Viscoelastic ◽  
Tension Tests ◽  
Composite Solid Propellant ◽  
Damage Process ◽  
Viscoelastic Constitutive Model

This paper studies the damage process induced by dewetting microcracks in composite solid propellant. A nonlinear viscoelastic constitutive model for composite soild propellant is presented. The damage variable D is derived from the microcrack system and is function of microcrack size density. The damage evolution equation is determinded by the extending of microcrack. Form the proposed model of microrack evolution process, an explicit form of damage evolution equation which is a function of stress field is given. The cracking event N and the new crack surface area damage ΔA formed by microcrack extension are defined. Material constants are determinded by acoustic emission tests. The rationality of our model has been confirmed by tension tests.

Stress Sensitivity of Damage Evolution Equation and Mesh-Dependence in Local Approach.

1995 ◽  
Vol 44 (507) ◽  
pp. 1417-1422 ◽  
Author(s):  
Yan LIU ◽  
Sumio MURAKAMI ◽  
Tetsuya YAMADA ◽  
Yasushi KANAGAWA
Keyword(s):  
Evolution Equation ◽  
Damage Evolution ◽  
Stress Sensitivity ◽  
Local Approach ◽  
Damage Evolution Equation
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