Characteristics and Generation of Interface J integrals in Layered Elastic Materials

CHEN Chang-rong

doi:10.21656/1000-0887.370270

Volume 38 Issue 10

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CHEN Chang-rong. Characteristics and Generation of Interface J integrals in Layered Elastic Materials[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1155-1165. doi: 10.21656/1000-0887.370270

Citation:

CHEN Chang-rong. Characteristics and Generation of Interface J integrals in Layered Elastic Materials[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1155-1165. doi: 10.21656/1000-0887.370270

Citation:

CHEN Chang-rong. Characteristics and Generation of Interface J integrals in Layered Elastic Materials[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1155-1165. doi: 10.21656/1000-0887.370270

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Characteristics and Generation of Interface J integrals in Layered Elastic Materials

doi: 10.21656/1000-0887.370270

CHEN Chang-rong

School of Flight Technology, Shanghai University of Engineering Science, Shanghai 201620, P.R.China

Funds: The National Natural Science Foundation of China（51175321）

Received Date: 2016-09-05
Rev Recd Date: 2016-12-21
Publish Date: 2017-10-15

Abstract

Abstract

When a crack in a layered elastic material is perpendicular to the interface, the Jintegral along path Г surrounding the crack tip can be separated into 2 parts: J_Г=J_tip+J_int, where J_tip means the J integral generated by the crack tip, and J_int the J integral generated by the interface enclosed by Г. The J integral generated by the crack tip is path-independent, and its physical meaning is the energy release rate of crack growth; the J integral generated by the interface is pathdependent, and has no relation to the energy release rate of crack growth. Due to the existence of the interface J integral, J_Г loses the path-independent property and has no real physical meaning. To better understand the physical meaning and limitations of the J integrals in inhomogeneous materials, the generation and characteristics of the interface J-integrals in layered elastic materials were analyzed. The results show that, for a layered elastic material composed of different homogeneous materials, the interface J-integrals are generated by the jumps of the strain energy density at the interfaces, and the jumps of the residual stresses and Young’s moduli at the interfaces would result in the jump of the elastic strain energy density. Moreover, offset effects exist between interface J integrals.
- J integral,
- interface,
- layered elastic material,
- material inhomogeneity

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References(28)

References

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