13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- The present paper is aimed at to determine the residual fracture toughness of wedge splitting specimens subjected to high temperatures and prove the validation of double-K fracture model to the post-fire concrete. The wedge-splitting experiments of totally ten temperatures varying from 20ºC to 600ºC and the specimens size 230×200×200 mm with initial-notch depth ratios 0.4 are implemented. Both analytical and weight function methods are used to calculate the residual fracture toughness parameters. Comparison between the two methods and to experimental results is carried out respectively. From the calculated values of double-K fracture parameters using experimental results the nondimensional parameter, brittleness of concrete may be conceived. Hence, the paper is structured to present the following: (i) details of softening traction-separation law of post-fire concrete, (ii) determination of double-K fracture parameters using existing analytical method, (iii) implementation of weight function method, and (v) experimental validation and comparison of results. 2. Softening traction-separation law of post-fire concrete The softening traction-separation law is a prior to determine the double-K fracture parameters, at room temperature, many expressions have been proposed based on direct tensile tests [22-26]. Based on numerical studies, simplified bilinear expressions for the softening traction-separation law (illustrated in Fig.1) were suggested by Petersson in 1981[22], Hilsdorft and Brameshuber in 1991 [25], and Phillips and Zhang in 1993 [26]. The area under the softening curve was defined as the fracture energy GF by Hillerborg et al in 1976 [1]. Therefore, one could get the following equation: ) ( 2 1 0 G f w ws t s F σ + = (1) As a consequence, a general form of the simplified bilinear expression of the softening traction-separation law is given as follows: ⎪⎩ ⎪ ⎨ ⎧ ≥ = ≤ ≤ − − = ≤ ≤ = − − 0 0 0 0 0 0 ) ) ( ( 0 ) ( ww σ w w / w w www σ σ w w w/w σ f f σ s s s s s t t (2) w sσ s w0 w ft σ Fig. 1. The bilinear softening traction-separation law Different values of the break point (σs, ws) and the crack width w0 at stress-free point were used for the expression proposed by different researchers. In present work, the bilinear softening function of concrete proposed by Petersson is used for post-fire specimens: ⎪⎩ ⎪ ⎨ ⎧ = = = t F t F s t s f w G f w G f / 3.6 / 0.8 /3 0 σ (3) 3. Analytical determination of cohesive fracture toughness
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