### Abstract

This paper considers the problem of a mixed-mode crack embedded in an infinite graded medium in which the crack is arbitrarily oriented with respect to the material gradient. The material properties are assumed to have an exponential variation and the crack surfaces are subjected to both normal and tangential tractions which can be related to the external applied loads. Classical elasticity equations are reformulated to incorporate non-local effects by employing Eringen's non-local theory resulting in a non-singular stress field. Using Fourier transform, two integral equations are derived where the unknowns are the jumps in displacements across the crack surfaces. These jumps are expanded in a series of Jacobi polynomials and then substituted into the integral equations which are solved using the so-called Schmidt method. In contrast with classical elasticity solutions, there are no stress singularities at the crack tips in this solution owing to the incorporation of non-local effects. Therefore, the use of non-local theory permits the use of maximum stress in conjunction with a brittle fracture criterion. The principal objective of this study is to investigate the effect of various parameters such as crack length, material gradient nonhomogeneity parameter, angular orientation of the crack and lattice parameter on the non-local stress field near the crack tips.

Original language | English |
---|---|

Pages (from-to) | 387-397 |

Number of pages | 11 |

Journal | Theoretical and Applied Fracture Mechanics |

Volume | 85 |

DOIs | |

Publication status | Published - 1 Oct 2016 |

### Fingerprint

### Keywords

- Arbitrarily oriented mixed-mode crack
- Functionally Graded Material (FGM)
- Non-local theory
- Schmidt method

### ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics

### Cite this

*Theoretical and Applied Fracture Mechanics*,

*85*, 387-397. https://doi.org/10.1016/j.tafmec.2016.05.001

**Analysis of an arbitrarily oriented crack in a functionally graded plane using a non-local approach.** / Jamia, N.; El-Borgi, Sami; Fernandes, R.; Vegamoor, V.

Research output: Contribution to journal › Article

*Theoretical and Applied Fracture Mechanics*, vol. 85, pp. 387-397. https://doi.org/10.1016/j.tafmec.2016.05.001

}

TY - JOUR

T1 - Analysis of an arbitrarily oriented crack in a functionally graded plane using a non-local approach

AU - Jamia, N.

AU - El-Borgi, Sami

AU - Fernandes, R.

AU - Vegamoor, V.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - This paper considers the problem of a mixed-mode crack embedded in an infinite graded medium in which the crack is arbitrarily oriented with respect to the material gradient. The material properties are assumed to have an exponential variation and the crack surfaces are subjected to both normal and tangential tractions which can be related to the external applied loads. Classical elasticity equations are reformulated to incorporate non-local effects by employing Eringen's non-local theory resulting in a non-singular stress field. Using Fourier transform, two integral equations are derived where the unknowns are the jumps in displacements across the crack surfaces. These jumps are expanded in a series of Jacobi polynomials and then substituted into the integral equations which are solved using the so-called Schmidt method. In contrast with classical elasticity solutions, there are no stress singularities at the crack tips in this solution owing to the incorporation of non-local effects. Therefore, the use of non-local theory permits the use of maximum stress in conjunction with a brittle fracture criterion. The principal objective of this study is to investigate the effect of various parameters such as crack length, material gradient nonhomogeneity parameter, angular orientation of the crack and lattice parameter on the non-local stress field near the crack tips.

AB - This paper considers the problem of a mixed-mode crack embedded in an infinite graded medium in which the crack is arbitrarily oriented with respect to the material gradient. The material properties are assumed to have an exponential variation and the crack surfaces are subjected to both normal and tangential tractions which can be related to the external applied loads. Classical elasticity equations are reformulated to incorporate non-local effects by employing Eringen's non-local theory resulting in a non-singular stress field. Using Fourier transform, two integral equations are derived where the unknowns are the jumps in displacements across the crack surfaces. These jumps are expanded in a series of Jacobi polynomials and then substituted into the integral equations which are solved using the so-called Schmidt method. In contrast with classical elasticity solutions, there are no stress singularities at the crack tips in this solution owing to the incorporation of non-local effects. Therefore, the use of non-local theory permits the use of maximum stress in conjunction with a brittle fracture criterion. The principal objective of this study is to investigate the effect of various parameters such as crack length, material gradient nonhomogeneity parameter, angular orientation of the crack and lattice parameter on the non-local stress field near the crack tips.

KW - Arbitrarily oriented mixed-mode crack

KW - Functionally Graded Material (FGM)

KW - Non-local theory

KW - Schmidt method

UR - http://www.scopus.com/inward/record.url?scp=84966937503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966937503&partnerID=8YFLogxK

U2 - 10.1016/j.tafmec.2016.05.001

DO - 10.1016/j.tafmec.2016.05.001

M3 - Article

AN - SCOPUS:84966937503

VL - 85

SP - 387

EP - 397

JO - Theoretical and Applied Fracture Mechanics

JF - Theoretical and Applied Fracture Mechanics

SN - 0167-8442

ER -