Fracture mechanics applied to engineering problems-strain energy density fracture criterion

The paper studies the adhesive strength of aluminum alloy specimens bonded with the use of an epoxy adhesive, under the tensile-shear stress state, depending on the testing temperature. Tension of modified Arcan specimens with load angles of 0, 22.5, 45, 67.5, and 90° with respect to the plane of adhesion is chosen as the experimental method. Experiments were performed at temperatures of −50, +23, and +50 °С. The analysis of the obtained results yields a linear fracture criterion and a fracture locus for the adhesive failure strain energy density, which takes into account the ratio of the elastic properties of the adhesive to those of the substrate. The region bounded by the fracture loci of adhesive strength and ultimate strain energy density determines the conditions for the safe loading of the bonded assembly in terms of the energy and force criteria of adhesive failure. The proposed fracture loci can be used, preferably simultaneously, to estimate the in-service strength and reliability of adhesively bonded assemblies.

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The Mode III Crack Problem in Microstructured Solids Governed by Dipolar Gradient Elasticity: Static and Dynamic Analysis

Journal of Applied Mechanics ◽

10.1115/1.1574061 ◽

2003 ◽

Vol 70 (4) ◽

pp. 517-530 ◽

Cited By ~ 104

Author(s):

H. G. Georgiadis

Keyword(s):

Energy Density ◽

Fracture Mechanics ◽

Density Function ◽

Strain Energy Density ◽

Strain Energy ◽

Crack Problem ◽

Strain Gradient Theory ◽

Gradient Theory ◽

Mode Iii ◽

Strain Energy Density Function

This study aims at determining the elastic stress and displacement fields around a crack in a microstructured body under a remotely applied loading of the antiplane shear (mode III) type. The material microstructure is modeled through the Mindlin-Green-Rivlin dipolar gradient theory (or strain-gradient theory of grade two). A simple but yet rigorous version of this generalized continuum theory is taken here by considering an isotropic linear expression of the elastic strain-energy density in antiplane shearing that involves only two material constants (the shear modulus and the so-called gradient coefficient). In particular, the strain-energy density function, besides its dependence upon the standard strain terms, depends also on strain gradients. This expression derives from form II of Mindlin’s theory, a form that is appropriate for a gradient formulation with no couple-stress effects (in this case the strain-energy density function does not contain any rotation gradients). Here, both the formulation of the problem and the solution method are exact and lead to results for the near-tip field showing significant departure from the predictions of the classical fracture mechanics. In view of these results, it seems that the conventional fracture mechanics is inadequate to analyze crack problems in microstructured materials. Indeed, the present results suggest that the stress distribution ahead of the tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur. Also, in the vicinity of the crack tip, the crack-face displacement closes more smoothly as compared to the classical results. The latter can be explained physically since materials with microstructure behave in a more rigid way (having increased stiffness) as compared to materials without microstructure (i.e., materials governed by classical continuum mechanics). The new formulation of the crack problem required also new extended definitions for the J-integral and the energy release rate. It is shown that these quantities can be determined through the use of distribution (generalized function) theory. The boundary value problem was attacked by both the asymptotic Williams technique and the exact Wiener-Hopf technique. Both static and time-harmonic dynamic analyses are provided.

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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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