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Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks

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Abstract

The in-plane classical dislocation-based linear elastic fracture mechanics analysis is extended to the case of strain gradient elasticity. Nonsingular stress and smooth-closure crack profiles are derived. As in the classical treatment, the crack is represented by a distribution of climb edge dislocations (for Mode I) or glide edge dislocations (for mode II). These distributions are determined through the solution of corresponding integral equations based on variationally consistent boundary conditions. An incompatible framework is used and the nonsingular full-field plastic distortion tensor components are calculated. Numerical results and related graphs are provided illustrating the nonsingular behaviour of the stress/strain components and the smooth cusp-like closure of the crack faces at the crack tip. The work provides an alternative approach to celebrated “Barenblatt’s treatment” of cracks, without the introduction of a cohesive zone and related to intermolecular forces ahead of the physical crack tip. It also supplements a recent paper by the authors in which the mode III crack, represented by an array of screw dislocations, was solved within the present gradient elasticity framework.

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Acknowledgments

The authors gratefully acknowledge the support of the General Secretariat of Research and Technology (GSRT) of Greece through projects Hellenic/ERC-13 (88257-IL-GradMech-ASM) and ARISTEIA II (5152-SEDEMP).

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Authors and Affiliations

  1. Department of Civil Engineering, Aalto University, Box 12100, 00076, Aalto, Finland

    S. Mahmoud Mousavi

  2. Lab of Mechanics and Materials, Aristotle University, Thessaloniki, 54124, Hellas, Greece

    Elias C. Aifantis

  3. International Laboratory for Modern Functional Materials, ITMO University, St. Petersburg, 191002, Russia

    Elias C. Aifantis

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  1. S. Mahmoud Mousavi
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  2. Elias C. Aifantis
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Correspondence to S. Mahmoud Mousavi.

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Mousavi, S.M., Aifantis, E.C. Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks. Int J Fract 202, 93–110 (2016). https://doi.org/10.1007/s10704-016-0143-5

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