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Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams

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Abstract

In this paper, an attempt is made to determine the double-K fracture parameters K iniIc and K unIc using three-point bending notched beams. First, based on the knowledge from extensive investigations which showed that the nonlinearity of P-CMOD curve is mainly associated with crack propagation, a linear asymptotic superposition assumption is proposed. Then, the critical effective crack length a is analytically evaluated by inserting the secant compliance c into the formula of LEFM. Furthermore, an analytical result of a fictitious crack with cohesive force in an infinite strip model was obtained. The double-K fracture parameters K iniIc and K unIc as well the critical crack tip opening displacement CTODc were analytically determined. The experimental evidence showed that the double-K fracture parameters K iniIc and K unIc are size-independent and can be considered as the fracture parameters to describe cracking initiation and unstable fracture in concrete structures. The testing method required to determine K iniIc and K unIc is quite simple, without unloading and reloading procedures. So, for performing this test, a closed-loop testing system is not necessary.

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Authors and Affiliations

  1. Institute of Construction Materials, University of Stuttgart, Pfaffenwaldring 4, 70550, Stuttgart, Germany.

    Shilang Xu & H.W. Reinhardt

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  1. Shilang Xu
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  2. H.W. Reinhardt
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Xu, S., Reinhardt, H. Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams. International Journal of Fracture 98, 151–177 (1999). https://doi.org/10.1023/A:1018740728458

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