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Anti-plane fracture analysis of functionally gradient material infinite strip with finite width

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Abstract

The special case of a crack under mode III conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor (SIF) results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.

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Authors and Affiliations

  1. Division of Engineering Mechanics, Department of Mechanical Engineering, Academy of Armored Force Engineering, Beijing, 100072, P. R. China

    Li Yong-dong Doctor  (李永东) (Associate Professor), Zhang Nan  (张男) & Dai Yao  (戴耀)

  2. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, P. R. China

    Jia Bin  (贾斌)

  3. College of Civil Engineering, Harbin Engineering University, Harbin, 150001, P. R. China

    Tang Li-qiang  (唐立强)

Authors
  1. Li Yong-dong Doctor  (李永东)
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  2. Jia Bin  (贾斌)
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  3. Zhang Nan  (张男)
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  4. Dai Yao  (戴耀)
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  5. Tang Li-qiang  (唐立强)
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Corresponding author

Correspondence to Li Yong-dong Doctor  (李永东).

Additional information

Communicated by WANG Yin-bang

Project supported by the National Natural Science Foundation of China (No. 90305023)

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Li, Yd., Jia, B., Zhang, N. et al. Anti-plane fracture analysis of functionally gradient material infinite strip with finite width. Appl Math Mech 27, 773–780 (2006). https://doi.org/10.1007/s10483-006-0608-z

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  • DOI: https://doi.org/10.1007/s10483-006-0608-z

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2000 Mathematics Subject Classification

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