Issue 36

V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02 24 is the relative value of this small crack interaction. The data for SIFs are given in Tab. 2. SIF k 0 =0.92 for a single crack with inclination angle β =60° can be found in [19] in Tab. 4 or in [11] in Tab. 1. The SIF k I (1) for crack 1 as influenced by a crack 2 on the distance d =2 is 1.094 and this value is less than SIF k 0 =1.12 on the value |Δ 1 |=0.026 (first column in Tab. 2) , and for the cracks on the distance d =4 the SIF k I (2) =1.071 is less than k 0 on |Δ 2 |=0.05 (second column in Tab. 2). The total interaction effect of the cracks 1 and 2 on the large crack 1 is |Δ 1 + Δ 2 |=0.076 (if superposition of these interactions is assumed). The SIF k I for crack 1 under the influence of pair interacting cracks 2 and 3 is k I (3) =1.061 (distances between the cracks are d =2) and |Δ 3 |=0.06 is for this case. |Δ 3 | is less than |Δ 1 + Δ 2 | on 0.016. That is, the solution to the problem of three edge cracks gives interaction effect on 0.016 less than the superimposed effect of two separate cracks derived from the problems of two-crack interaction. It is an example of calculations for β =90°, for β =60° calculations are similar. Tab. 2 in the last column show that the interaction between small cracks (crack 2 and 3) weaken the shielding effect on 1.5% for the cracks inclined on β =90° and on 2.17% for the cracks with β =60°. It is rather small values, but, probably, for interaction of multiple cracks the effect will be stronger. d =2 d =4 d =2 β k I (1) , Δ 1 k I (2) , Δ 2 k I (3) , Δ 3 (Δ 1 +Δ 2 )– Δ 3 k 0 f% 90° 1.094, –0.026 1.071, –0.05 1.061, –0.06 –0.016 1.12 –1.5 60° 0.88, –0.04 0.86, –0.06 0.84, –0.08 –0.02 0.92 –2.17 Table 2: SIFs k I at crack 1 interacting with small cracks and their interaction effects. C ONCLUSIONS he effects of the interaction of edge cracks on further crack formation were studied with respect to main fracture characteristics, namely, stress intensity factors, fracture angles and critical loads. Some illustrative examples show the influence of inclination angles, distances between the cracks and sizes of the cracks on this interaction. The interaction of cracks leads to mixed mode conditions near the crack tips even for symmetric geometries and loading normal to the crack lines. As an illustration, a classical edge crack (i.e. the crack normal to the boundary and under tension normal to the crack line) in the presence of other crack is under mixed mode conditions and deviates from its initial propagation direction, albeit the other crack is small (Fig. 9 a and 11 c). The crack shielding takes place (as expected for this problem) for most parameters of the problem. The maximum magnitude of the shielding effect is observed for close located cracks and for a middle crack in the case of the interaction of three cracks. The influence of two interacting cracks on the third crack can weaken the shielding effect and it was shown for SIF Mode I which is dominant in this problem. The applied method of singular integral equations (which have been solved by well-known numerical method based on the quadratic formulas for integrals) in combination of a fracture criteria (the maximum hoop stress criteria has been used) is effective method for modeling of the crack interaction at the initial stage of their propagation. A CKNOWLEDGEMENT he support of the German Research Foundation under the grant Schm 746/139-1 is greatly acknowledged. A PPENDIX n Eqs. (2) the kernels R nk ( t,x ) and S nk ( t,x ) are written as T T I