### Journals Information

**
Mathematics and Statistics Vol. 10(1), pp. 166 - 175 DOI: 10.13189/ms.2022.100115 Reprint (PDF) (737Kb) **

## A Griffith Crack at the Interface of an Isotropic and Orthotropic Half Space Bonded Together

**A. K. Awasthi ^{*}, Rachna , Harpreet Kaur **

Department of Mathematics, Lovely Professional University, India

**ABSTRACT**

In the past 53 years, many efforts have been contributed to develop and demonstrate the properties of reinforced composite materials. The ever-increasing use of composite materials through engineering structures needs the proper analysis of the mechanical response of these structures. In the proposed work, we have an exact form of Stress components and Displacement components to a Griffith crack at the interface of an Isotropic and Orthotropic half-space bounded together. The expression was evaluated in the vicinity of crack tips by using Fourier transform method but here these components have been evaluated with the help of Fredholm integral equations and then reduce to the coupled Fredholm integral equations. In this paper, we use the problem of Lowengrub and Sneddon and reduce it to dual integral equations. Solution of these equations through the use of the method of Srivastava and Lowengrub is reduced to coupled Fredholm integral equation. Further reduces the problem to decoupled Fredholm integral equation of 2nd kind. We get the solution of dual integral equations and the problem is reduced to coupled Fredholm integral equation. We find the solution of the Fredholm integral equation and reduce it to decoupled Fredholm integral equation of 2nd kind. The Physical interest in fracture design criterion is due to Stress and crack opening Displacement components. In the end, we can easily calculate the Stress components and Displacement components in the exact form.

**KEYWORDS**

Stress Components, Displacement Components, Fourier Transform, Fredholm Integral Equation, Coupled Fredholm Integral Equation

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] A. K. Awasthi , Rachna , Harpreet Kaur , "A Griffith Crack at the Interface of an Isotropic and Orthotropic Half Space Bonded Together," Mathematics and Statistics, Vol. 10, No. 1, pp. 166 - 175, 2022. DOI: 10.13189/ms.2022.100115.

(b). APA Format:

A. K. Awasthi , Rachna , Harpreet Kaur (2022). A Griffith Crack at the Interface of an Isotropic and Orthotropic Half Space Bonded Together. Mathematics and Statistics, 10(1), 166 - 175. DOI: 10.13189/ms.2022.100115.