Abstract
A crack propagation criterion was proposed for model I crack in concrete by using the initial fracture toughness KICini as an inherent material property. Based on this criterion, crack begins to propagate when the difference, between the stress intensity factors caused by the applied load KIP and that by the cohesive stress KIσ, exceeds KICini. Finite element analyses was then carried out to calculate the complete load vs. crack mouth opening displacement (P-CMOD) curve, the critical crack propagation length ΔaC and the unstable fracture toughness KICun for notched beams under three-point bending. It was found that numerical results showed a good agreement with the experimental ones. Based on this crack propagation criterion, crack extension resistance, in terms of stress intensity factor, KR being able to consider the variation of fracture process zone (FPZ) was employed for describing crack propagation in concrete. KR is composed of KICini and KIσ, which is actually equal to the driving action of crack extension. It was concluded that given the elastic modulus E, the uniaxial tensile strength ft, the fracture energy GF and KICini, the complete fracture process in concrete and the KR-curve of concrete can be calculated based on the numerical method. Finally, discussion was made on the effects of fracture process zone, GF and specimens geometries on KR-curve.
Highlights
Crack extension resistance curve (R-curve) has been used as the fracture criterion for decades
It can be seen that the P-CMOD curves obtained from numerical simulation agree well with those from experiment suggesting that the proposed numerical method, together with the crack propagation criterion, in this paper can be used for simulating the complete fracture process in concrete
About the definition of KR-curve, Xu and Reinhardt [13] and Reinhardt and Xu [14] claimed that Eq (9) gave the stress intensity factors for different Da, but not KR-curve considering crack propagation in concrete, because material parameters relevant to concrete properties were not included in this equation
Summary
Crack extension resistance curve (R-curve) has been used as the fracture criterion for decades. In order to describe the increase of fracture toughness during crack propagation, a new approach was proposed by Xu and Reinhardt [13] and Reinhardt and Xu [14] to evaluate the crack extension resistance in terms of considering the cohesive stress acting on the fracture process zone (FPZ) In this method, KR is obtained by combining the crack initiation fracture toughness is an property, with which represents the contribution of the along the fictitious crack zone. Using the method proposed by Xu and Reinhardt [13] and Reinhardt and Xu [14] but considering the variation of FPZ during crack propagation, Xu et al [25] calculated the KR-curve based on P-CMOD curve obtained from experiment Their results revealed that the KR-curve is size independent. The effect of variation of FPZ length and fracture energy on KR-curve, as well as size effect of KR-curve, was discussed
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