13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- of the Fraunhofer biaxial cruciform specimens was determined to be 85.7 N/mm. 3.4. J-A2 Method Applied to Fraunhofer Test Data Loads were applied to the 3PB and C(T) FEA models until the Jc values presented in Table 1 were achieved. The stress (obtained from FEA output) perpendicular (i.e., θ = 0°) to the crack front at a node ahead of the crack tip, along with radial position, r, of the node and Jc, can be substituted into Equation 4 to solve the quadratic equation for A2 at each node. Again, according to the RKR model, fracture typically initiates within the range 1 < r/(J/σ0) < 5. Thus, A2 was calculated at each node within this range and the average was tabulated. For this study, the average was actually taken approximately for the range 2 < r/(J/σ0) < 5 i.e., the first few nodes adjacent to the crack tip were neglected for the average A2 calculation. The A2 results are also summarized in Table 2 in the form of (Jc, A2) pairs. Table 1. (Jc, A2) pairs for the 3PB and C(T) specimens Jc is in N/mm, A2 is unitless -85°C 3PB shallow (a/W = 0.18) (54.2, -0.392) 1T-C(T) (a/W = 0.5) (13.1, -0.260) Next, using the (Jc, A2) pair for the 3PB specimen, and substituting the published value of σc = 1830 MPa [15, 16], Equation 6 can be used to solve for the fracture initiation location rc, which is 0.104 mm for both specimens, a value which is in agreement with other published results. A study conducted by Wang et al. [17] focused on the determination of the fracture initiation location and they determined that, for temperatures in this range, rc lies within the range of 0.1 mm to 0.25 mm. Additional evidence of an appropriate range of rc values was found in [18], in which dozens of data points for the similar A508 material yielded 0.05 mm < rc < 0.25 mm. Substituting rc and σc into Equation 5, the Material Failure Curve can be plotted. The FEA models are processed with incremental loads to determine a range of J values above and below Jc such that the Crack Driving Force curves for each specimen can be determined. The Material Failure Curve and Crack Driving Force curves are then plotted on the same J vs. |A2| plot. As the loading increases, the applied J increases from zero. And, therefore, referring to Figure 2, points on the plot above and left of the Material Failure Curve indicate fracture has occurred. Crack Driving Force curves, as shown in Figure 3, are indicative of each specimen’s constraint and can be used to determine if the desirable “loss of constraint” occurs, i.e., fracture toughness increases due to geometry and/or loading conditions. The J vs. |A2| plot for the specimens is shown in Fig. 5. The triangles are actual data points obtained from the Fraunhofer study.
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