in this paper, we give a generalization of the integral dependence from rings to modules. we study the stability of the integral closure with respect to various module theoretic constructions. moreover, we introduce the notion of integral extension of a module and prove the lying over, going up and going down theorems for modules.

The theory for the constant rate of crack closure was investigated. The aim of this theory is to explain why the rate of crack closure is constant during the wetting stage of healing. Assuming that a surface crack in a material is treated by compression or with solvent, its crack closes up at a constant rate and its shape is independent of time. This approach was based on the Gibbs energy of an...

An analytical solution is presented for the thermoelastic problem of a half-plane with several cracks under thermo mechanical loading using distributed dislocation technique. The uncoupled quasi-static linear thermoelasticity theory is adopted in which the change in temperature, if any, due to deformations is neglected. The stress field in a half-plane containing thermoelastic dislocation is ob...

Experimentally determined T ε and CTOA resistance curves were used to simulate numerically, stable crack growth and the ensuing crack linkup in 0.8 mm thick 2024-T3 aluminum tension specimen with multiple site damage (MSD) subjected to monotonically/cyclically increasing loading. The T ε integral correctly predicted the crack growth and linkup history as well as the onset of rapid fracture in M...

The Green's function and the boundary element method for analysing fracture behaviour of cracks in piezoelectric half-plane are presented in this paper. By combining Stroh formalism and the concept of perturbation, a general thermoelectroelastic solution for half-plane solid subjected to point heat source and/or temperature discontinuity has been derived. Using the proposed solution and the pot...

The present paper is concerned with the application of a “plasticity-induced” crack closure model to study fatigue crack growth under various load histories. The model was based on the Dugdale model but modified to leave plastically deformed material in the wake of the advancing crack. The model was used to correlate crack growth rates under constant-amplitude loading and then used to predict c...

The standard experimental procedures for determining the interlaminar fracture toughness are designed delamination propagation in unidirectional specimens. However, aerospace structural components, usually occurs between plies at different orientations resulting damage mechanisms which can increase value of as propagates. Generally, numerical analyses employ measured onset, leading to conservat...

In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.

Stationary cracks along and near interfaces between two time-dependent materials are simulated using the finite element method (FEM) to examine crack tip fields and candidate driving force parameters for crack growth. Plane strain conditions are assumed. In some cases, a thin transition layer is included between the two materials. This transition layer features a functionally graded blend of pr...