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Derivation of applied stress-crack opening displacement relationships for the evaluation of effective stress intensity factor range

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Abstract

Linear elastic fracture mechanics (LEFM) integrated with the interference of fracture surface asperities has been formulated. The asperities are considered to simulate the influence of the microstructures and possibly oxide debris. The applied stress/load-crack opening displacement (COD) relationships in several cases have been derived. In the original LEFM, the stress-COD relationship is represented by a straight line passing through the origin of the stress-COD plot. The insert of one asperity results in a deviation of the stress-COD response from the LEFM relationship, leading to the exhibition of an inflection point (first contact point, σop), a larger slope, and a residual COD. In the case of two asperities, the slope and the residual COD of the stress-COD relationship become further larger, and two inflection points emerge. A general stress-COD expression in the case of multiple asperities has been derived. The slope of the stress-COD equation, the residual COD, and the minimum COD all increase with increasing number of asperities for a given loading condition, resulting in a smaller ΔCOD and Δσeff. The number of the inflection points is the same as that of the asperities. To the authors' knowledge, this paper is the first to derive analytically an applied stress-COD curve with a gradual variation below σop, caused by the asperity-/roughness-, or oxide-induced crack closure.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Ryerson University, 350, Victoria Street, Toronto, Ontario, M5B 2K3, Canada

    D.L. Chen

  2. Department of Materials Science and Engineering, University of Toronto, 184, College Street, Toronto, Ontario, M5S 3E4, Canada

    Z. Wang

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  1. D.L. Chen
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  2. Z. Wang
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Correspondence to D.L. Chen.

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Chen, D., Wang, Z. Derivation of applied stress-crack opening displacement relationships for the evaluation of effective stress intensity factor range. International Journal of Fracture 125, 371–386 (2004). https://doi.org/10.1023/B:FRAC.0000022243.38144.ce

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  • DOI: https://doi.org/10.1023/B:FRAC.0000022243.38144.ce

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