Issue 33

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 33 (2015) 33-41; DOI: 10.3221/IGF-ESIS.33.05

In all cases the numerical values of the SED calculated from the FE analyses have been compared with those analytically obtained by using the expressions for the SED based on the elastic peak stresses, Eq. (6), in order to verify the range of applicability of the proposed method.

Figure 4 : Calibration of the PSM approach for a crack (2α = 0°) under mixed mode (I+II) loading ( ϕ = 60°). Normalized SIF related to (a) mode I and (b) mode II. Being available the exact values of the SIFs, the mean value of the SED has been evaluated also according to Eq. (3). In particular the maximum difference between the SED parameter evaluated analytically (Eq. (3)) and numerically (by FEM) results to be about 5%, which means that the influence of higher order terms, as the T-stress, can be neglected in these cases, at least from an engineering point of view. The ratio between the SED based on the elastic peak stresses (Eq. 6, PSM W ) and the SED calculated from the FE analyses ( FEM W ) has been reported in Fig. 5, with reference to an inclination ϕ of the crack equal to 0°, 30° and 60°. From Fig. 5, it can be observed that the ratio FEM PSM W W / converges to unity, within a scatter band of ±10% for all different mode mixities taken into consideration. This occurs for a ratio a/d greater than a value equal to 3 for the case MM = 0 ( ϕ = 0°), 8.50 for MM = 0.37 ( ϕ = 30°) and 16 for MM = 0.63 ( ϕ = 60°). In particular the minimum a/d ratio to assure the validity of the proposed method increases as the mode II loading becomes dominant, that is increasing the mode mixity ratio (MM) defined by Eq. (7). This confirms the behavior observed in the previous paragraph and in [10], with reference to K * FE and K ** FE .

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