Simulation of Average Strain Energy Density (SED) in the BGA Soldering during the Drop Test

A previously developed energy based high cycle fatigue (HCF) life assessment framework is modified to predict the low cycle fatigue (LCF) life of aluminum 6061-T6. The fatigue life assessment model of this modified framework is formulated in a closed form expression by incorporating the Ramberg–Osgood constitutive relationship. The modified framework is composed of the following entities: (1) assessment of the average strain energy density and the average plastic strain range developed in aluminum 6061-T6 during a fatigue test conducting at the ideal frequency for optimum energy calculation, and (2) determination of the Ramberg–Osgood cyclic parameters for aluminum 6061-T6 from the average strain energy density and the average plastic strain range. By this framework, the applied stress range is related to the fatigue life by a power law whose parameters are functions of the fatigue toughness and the cyclic parameters. The predicted fatigue lives are found to be in a good agreement with the experimental data.

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Using the Equivalent Material Concept and the Average Strain Energy Density to Analyse the Fracture Behaviour of Structural Materials

Applied Sciences ◽

10.3390/app10051601 ◽

2020 ◽

Vol 10 (5) ◽

pp. 1601 ◽

Cited By ~ 1

Author(s):

Sergio Cicero ◽

Juan Diego Fuentes ◽

Ali Reza Torabi

Keyword(s):

Energy Density ◽

Strain Energy Density ◽

Strain Energy ◽

Equivalent Material ◽

Nonlinear Behaviour ◽

Average Strain ◽

Nonlinear Materials ◽

Linear Elastic ◽

Equivalent Material Concept ◽

Material Concept

This paper provides a complete overview of the applicability of the Equivalent Material Concept in conjunction with the Average Strain Energy Density criterion, to provide predictions of fracture loads in structural materials containing U-notches. The Average Strain Density Criterion (ASED) has a linear-elastic nature, so in principle, it does not provide satisfactory predictions of fracture loads in those materials with nonlinear behaviour. However, the Equivalent Material Concept (EMC) is able to transform a physically nonlinear material into an equivalent linear-elastic one and, therefore, the combination of the ASED criterion with the EMC (EMC–ASED criterion) should provide good predictions of fracture loads in physically nonlinear materials. The EMC–ASED criterion is here applied to different types of materials (polymers, composites and metals) with different grades of nonlinearity, showing the accuracy of the corresponding fracture load predictions and revealing qualitatively the limitations of the methodology. It is shown how the EMC–ASED criterion provides good predictions of fracture loads in nonlinear materials as long as the nonlinear behaviour is mainly limited to the tensile behaviour, and how the accuracy decreases when the nonlinear behaviour is extended to the material behaviour in the presence of defects.

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Critical Load Prediction in Notched E/Glass–Epoxy-Laminated Composites Using the Virtual Isotropic Material Concept Combined with the Average Strain Energy Density Criterion

Polymers ◽

10.3390/polym13071057 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1057

Author(s):

Marcos Sánchez ◽

Sergio Cicero ◽

Ali Reza Torabi ◽

Majid Reza Ayatollahi

Keyword(s):

Energy Density ◽

Critical Load ◽

Strain Energy Density ◽

Isotropic Material ◽

Strain Energy ◽

Laminated Composites ◽

Average Strain ◽

Fracture Test ◽

Load Prediction ◽

Material Concept

This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites. This methodology was applied to E/glass–epoxy-laminated composites containing U-notches. For this purpose, a series of fracture test data recently published in the literature on specimens with different notch tip radii, lay-up configurations, and a number of plies were employed. It was shown that the VIMC–ASED combined approach provided satisfactory predictions of the last-ply failure (LPF) loads (i.e., critical loads).

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Volume free strain energy density method for applications to blunt V-notches

Procedia Structural Integrity ◽

10.1016/j.prostr.2020.10.085 ◽

2020 ◽

Vol 28 ◽

pp. 734-742

Author(s):

Pietro Foti ◽

Seyed Mohammad Javad Razavi ◽

Liviu Marsavina ◽

Filippo Berto

Keyword(s):

Energy Density ◽

Strain Energy Density ◽

Strain Energy ◽

Density Method ◽

Free Strain

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On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

Engineering Structures ◽

10.1016/j.engstruct.2020.111716 ◽

2021 ◽

Vol 230 ◽

pp. 111716

Author(s):

Pietro Foti ◽

Seyed Mohammad Javad Razavi ◽

Majid Reza Ayatollahi ◽

Liviu Marsavina ◽

Filippo Berto

Keyword(s):

Energy Density ◽

Strain Energy Density ◽

Mixed Mode ◽

Strain Energy ◽

Density Method ◽

Free Strain

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Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-021-01475-0 ◽

2021 ◽

Vol 72 (2) ◽

Author(s):

Mircea Bîrsan

Keyword(s):

Energy Density ◽

Constitutive Model ◽

Strain Energy Density ◽

Strain Energy ◽

Shell Theory ◽

Constitutive Relations ◽

Three Dimensional ◽

Classical Shell Theory ◽

Three Dimensional Elasticity ◽

General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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