13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- where φel is denoted as maximum elastic angular deformation of the hinge and βi is dimensionless factors defined in Eq. (10). Figure 3. WST specimen geometry with the blue area indicating the groove and the red area indicating 4.5mm notch. The computation of inverse analysis is based on three steps that are repeated until convergence criteria are obtained. The first step involves computation of elastic modulus, E. Therefore, only data corresponding to the elastic loading are considered. Determination of elastic modulus is very fast and reliable since the part of working diagram is governed by E. Once elastic modulus is found, the tensile strength ft and the first decreasing branch of softening curve a1 are searched. Furthermore, N-1 searchings are performed in order to find ai and bi, where i ≥ 2. The process of inverse analysis can be written as: ( ) 1 1 1 , , 1 , , , 1 , , , 1 while convergence is not achived min min for i 2 min check convergence el t K j obs j hinge E j K j obs j hinge f a j K j obs j hinge a b j P P P P P P = = = − − ≥ − ∑ ∑ ∑ (19) Where K is total number of recorded load-crack opening pairs in the experiment, Kel is number of recorded load-crack opening pairs corresponding to elastic part of loading, Pj,obs denotes splitting force in j-th recorded load-crack opening pair, Pj,hinge is optimized splitting force in j-th computed load-crack opening pair. The each measurement can be influenced by errors, and it is impossible to fit the model exactly to the measurements, which means that the choice of the suitable robust form ||Pobs Phinge|| plays important role. The iterative process minimizes the difference between observed loads applied in the experiments, Pobs, and the load predicted by CHM, Phinge according to the error normalization function as:
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