13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- used to determine the load applied to the specimen up to the point of fracture. 3.2. Fracture time (tf) Determination To determine fracture time a small uncalibrated strain gauge was mounted on the specimen close to the crack tip, Fig. 2. The location of the strain gauge is important, as it must be placed within the elastic region but outside the damage zone to yield accurate results [6]. Upon loading, stress within the specimen builds up and the gauge experiences a voltage change. As the crack passes the gauge an unloading wave is generated and a drop of the measured voltage indicates this. The time from the initial voltage rise to the drop off represents the fracture time. Due to the finite size of strain gauges it is difficult to place them exactly at the crack tip. In order to more accurately determine the fracture time a hybrid experimental/numerical approach is undertaken here. Modeling of the fracture specimen using the finite volume method (FVM) was done in OpenFOAM [13,14]. Strain gauge locations on the experimental samples were accurately measured and this data was adopted for the modeling work. Time up to unloading was found to agree well between the two methods. By combining experimental and numerical data increased accuracy of fracture time determination can be ensured. Figure 2. Strain gauge for fracture time detection 3.3. Temporal Stress Intensity Factor Determination 3.3.1. Applied load method Dynamic fracture toughness (K1d) can be determined as the critical stress intensity factor value at the crack tip at the instant of crack initiation. For Mode I fracture it is approximated as: KId =KI (tf ), (3) A closed form solution to predict the SIF from the measured load is applied here [15]. KI (t) = 3SP(t) 4BW3 2 α (1− α) 3 2(1+3α) (1.72+0.23α+1.04α2 −0.39α3), (4) where P(t) is the applied load to the sample and α is the ratio of crack length to width of the specimen (a/W). It has been demonstrated that this equation is valid for different crack to width ratios [8]. 3.3.2. Crack tip strain Another method for determining the SIF evolution experimentally is shown in Eq. (5). This method
RkJQdWJsaXNoZXIy MjM0NDE=