Analytical Calculation Method for Unstable Toughness of Double-K Fracture Model

WANG Zhan-ke; GAO Hong-bo; HAN Xiao-yan; MA Peng

doi:10.11988/ckyyb.20171144

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Journal of Changjiang River Scientific Research Institute ›› 2019, Vol. 36 ›› Issue (6) : 106-109. DOI: 10.11988/ckyyb.20171144

HYDRAULIC STRUCTURE AND MATERIAL

Analytical Calculation Method for Unstable Toughness of Double-K Fracture Model

WANG Zhan-ke^1,2, GAO Hong-bo¹, HAN Xiao-yan¹, MA Peng¹

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Abstract

An analytical method which merely needs the axial compressive strength f_c of concrete to calculate the unstable toughness K^un_Ic of double-K fracture model is proposed in this paper. Massive experimental data indicate that the ratio of critical crack propagation length Δa_c to ligament length (h-a₀) tends to be a constant. According to this regularity and on the basis of the bilinear constitutive relationship of the fictitious crack model, the maximum load P_max of three-point bending notched beam is calculated under equilibrium condition. Then the calculated result of P_max is substituted to the formula and the unstable toughness K^un_Ic of double-K fracture model is calculated. The calculated results of P_max and K^un_Ic are compared with those of test values to verify the accuracy of the method. Results conclude that the calculated results of P_max and K^un_Ic agree well with test values for relatively big size concrete specimens with maximum aggregate size not greater than 40 mm. The maximum load P_max and the unstable toughness K^un_Ic can be predicted by the proposed analytical method.

Key words

concrete / maximum load / unstable toughness / fracture mechanics / analytical calculation / bilinear constitutive relationship / double-K fracture model

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WANG Zhan-ke, GAO Hong-bo, HAN Xiao-yan, MA Peng. Analytical Calculation Method for Unstable Toughness of Double-K Fracture Model[J]. Journal of Changjiang River Scientific Research Institute. 2019, 36(6): 106-109 https://doi.org/10.11988/ckyyb.20171144

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