13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- problems cause by self-weight of the specimen. The work of Elser et al. [8] should be mentioned as well. Their work presented the fracture behaviour of polypropylene fiber-reinforced concrete. The present paper focuses on the inverse analysis of WST approach developed by Østergaard et al. [4] for bi-linear softening curve and the approach, which comes out Skocek et al. [9] work for multi-linear softening curve. So far, Østergaard’s bi-linear softening curves are mostly used to approximate the softening behaviour of concretes. It is expected that refinement of the softening curves will reflect in improved accuracy of the WST simulation. For that purpose the semi-analytical approached is used as the background for inverse analysis of the WST. The inverse analysis is capable in estimating both elastic and fracture properties from the WST. Fracture energy, Gf, was found to increasing with age, while the characteristic length, Lch, was found to decrease. 2. Modelling Loading of the specimen by wedge leads to splitting force and subsequently initiation of a crack at the bottom of the notch. Furthermore with increase of load stable crack propagation is observed. The control of the experiment may be performed by crack mouth opening displacement or by constant displacement rate of the wedge. The crack hinge model (CHM) to the WST geometry was developed by Ulfkjaer et al. [10] and later extended by Olesen [11]. The CHM simulates the area closely surrounded by propagated crack. The hinge is modelled as array of springs, which are attached to the rigid boundaries of the element. The stress transferred by the spring is assumed to be linear elastic in the pre-cracked state, whereas the cracked state is determined by the stress-crack opening relationship as shown in Eq. (1) ( ) Preckracked State ( ) ( ) Cracked State w t E w g w f σ ε ε σ σ ⎧ = = ⎨ = ⎩ (1) where E represent elastic modulus, ε denotes elastic strain, σw(w) denotes stress-crack opening relationship with crack opening w, and ft represents tensile strength. In Fig.1 the function g(w) is for the N-linear (N ≥ 2) softening curve is shown and is defined as : Figure 1. The scheme of multi-linear softening curve. ( 1) ( ) ; i i i i w g b w w w w a − = < < − (2) where wi corresponds to the intersection of i-th and i + 1th line and has the form: 1 1 where i i i i i b b w i N a a + + − = < − (3) The critical crack width (width at which g(w) = 0) is calculated by:
RkJQdWJsaXNoZXIy MjM0NDE=