Issue 41

P. Lopez-Crespo et alii, Frattura ed Integrità Strutturale, 41 (2017) 203-210; DOI: 10.3221/IGF-ESIS.41.28 206                                    3 2 2 2 2 1 2 3  2 cos 2 1 cos 3 1 sin sin 2 3 1 sin       2 2 2 A B r r B r (2) where E is the Young’s modulus, ε yy are the strains in the crack opening (vertical) direction, A n and B m are unknown coefficients or number of terms in the series expansion, r and θ are the polar coordinates of the different points around the crack tip and υ is the Poisson’s ratio. The singular term, A 0 can be related to the SIF as:   0 2 I K A (3) Substitution of all experimental data points in Eq. (2) yields an over-deterministic system of equations that can be solved for the unknown coefficients and thereby computing the SIF (K exp ). P ARAMETRIC STUDY he evaluation of the key parameters involved in the estimation of the SIF, K exp , is done through comparison with the theoretical SIF, K theo [20]. To this end, the error between both values can be determined as:       % 100 exp theo theo K K error K (4) Key parameters influencing the K estimation with the current scheme were identified previously [26,27]. These include the number of terms used in Williams’ expansion, the size and shape of the area of interest (AOI) used for the fitting, the influence of the plastic zone and the number of experimental data points considered. Number of terms, size and shape of the area of interest The size of the AOI is studied through the outer radius of the AOI, R out , defined in Fig. 2. The combined influence of number of terms and size of AOI is shown in Fig. 3. Figure 3 : Effect of number of terms and size of the AOI (R out ) on the error in estimating the SIF. Fig. 3 shows that the error decreases to a minimum for each value of number of terms studied. The minimum error as a function of R out observed is summarised in Tab. 2. Number of terms 1 2 3 4 5 6 R out (µm) 350 450 850 950 950 950 Table 2 : Combination of number of terms and outer radius, R out , that give a minimum error in Fig. 3 T