Issue 41

P. Lopez-Crespo et alii, Frattura ed Integrità Strutturale, 41 (2017) 203-210; DOI: 10.3221/IGF-ESIS.41.28 207 Tab. 2 can be used as a reference to optimise the data array to be used depending on how many terms in Williams’ expansion are chosen to describe the crack-tip field. Tab. 2 indicates that if one term is used in Williams’ formultion, the data array should extend to around 350 µm and for six terms the array should extend to around 950 µm. Fig. 3 also shows that by using more terms in the series expansion, the error in estimating the SIF can be reduced to around 1%. The shape of the AOI was studied through the angle between the edge of the AOI and the crack plane, α (see Fig. 2). The angle α controls the number of data points that are collected from the region behind the crack tip (negative coordinates along the crack growing direction, Fig. 2). The amount of data collected in the crack wake has been previously identified as critically affecting the SIF estimation [27]. Fig. 4 shows the evolution of the error for different α angles. For each number of terms, the optimum outer radius was used, following the results of Tab. 2. When only 1 term is used the curve in Fig. 4 is very flat such that in our case a slightly better result is obtained for  =80 than 0°. In view of this, the conclusion would be that results become more reliable for >2 terms and that the best SIF predictions (minimum error) are obtained when α = 0º when using 3 to 6 terms in Williams’ expansion. That is, the best results in terms of estimating the SIF are obtained by collecting data not only ahead of the crack tip but also from the crack wake region, in agreement with previous studies [27]. Figure 4 : Effect of α angle on the error for estimating the SIF. Plastic zone The mathematical model used to describe the crack-tip behaviour is based on Linear Elastic Fracture Mechanics. Accordingly, the tool can be used under small scale yielding (SSY) conditions. For other full-field techniques such as thermo-elasticity [3], photo-elasticity [1], digital image correlation [28] or electronic speckle patter interferometry [4], this is achieved by collecting data from outside the plastic zone. This effect is studied here by including and excluding the data from the plastic zone in the data used for estimating the SIF. The plastic zone was estimated according to Irwin model [25]:             2 1 330 2 pz y K r µm (5) where K is the theoretically applied SIF and σ y is the yield stress of the material. Fig. 5 shows the error obtained when the plastic zone is included or excluded. The best predictions are observed when the plastic zone data is used in the fitting. Fig. 5 also shows that there are large differences between including and excluding the plastic zone for 1 term. This difference decreases as the number of terms is increased. The worst prediction when the plastic zone is excluded is probably due to not having enough data for the over-deterministic system of equations. This effect is studied in more detail in the following section. Number of experimental data points The effect the number of experimental data points that are fitted into the analytical model is studied in this section. The number of data points is studied relative to the number of terms in the series (Eq. 2) through parameter φ :