PSI - Issue 7

Robert Goldstein et al. / Procedia Structural Integrity 7 (2017) 222–228 / Structural Integrity Procedia 00 (2017) 000–000

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R.Goldstein, M. Perelmuter

Fig. 5. Distributions of the normal traction over bridged zone, relative bonds compliance c 0 variation.

Fig. 6. Time variation of the stress intensity factor module, relative bonds compliance c 0 variation.

of the stress state analysis as compliance variation along the bridged zone over time, see (3) and (8). According to bonds density variation, compliance is also rather slowly changed the most part of time before the crack formation and considerably increased on the last steps, see Fig. 4 where the compliance variation along the bridged zone for several steps of time, including next to the last is shown. Note, that at the last step the density of bonds is rather small at ∆ = 0 . 1 d and the value of the compliance at the nucleated flaw center is c / c 0 ≈ 70. Bonds destruction at the crack bridged zone is followed by the compliance increasing and the bonds stress decreas ing (stress relaxation). In Fig. 5 the distributions of the normal traction over bridged zone if the crack is nucleated (for di ff erent values of initial bonds compliance c 0 ) is presented. If initial compliance is increased then bonds become softer and bonds destruction is more intensive. As the result, a high stress relaxation is observed in these cases. The time variation of the stress intensity factor (SIF) module (see (12)) for di ff erent values of the bonds elastic module E B is shown in Fig. 6, t 0 = 1 s . If relative bonds sti ff ness E B / E 2 is increased then strengthening e ff ect of bonds is also increased. In the bond breakage process over time, their strengthening e ff ect decreases, and the stress intensity factor increases. The largest increase in the SIF module occurs at the last steps of the defect formation. The values of the SIF module are normalized by the value the SIF modulus due to the action of the external load for the same crack without bonds. The dependencies of the initial defect formation time ( t 0 = 1 s ) on the initial size of the crack bridged zone are given in Fig. 7 for various values of the initial bonds compliance and the external loading σ 0 = 10 MPa . For each value of the bridged zone relative length, the size of the bond-free region is set to be equal to ∆ = 0 . 1 d and was considered as one step of increase in the defect length. The variation in the initial bond compliance from c 0 = 0 . 1 to c 0 = 0 . 3 (which can be also treated as a decrease in the elasticity modulus of one of the materials) leads to an increase in the durability by more than an order of magnitude. Note that the di ff erence in the values of the time of the initial defect formation is minimal for d = , because the stress variation along the crack filled with bonds varies weakly for di ff erent relative bond compliance. The trend of the curves in Fig. 7 corresponds to the dependencies in Fig. 8, where the dependencies of traction vector at the edge of the bridged zone vs its relative size are shown; the initial defect formation time is smaller for the crack bridged zone with larger stresses.

4. Summary

The method of estimation of bonds degradation in the weakened region on the interface between materials is proposed. The theory of thermal fluctuation fracture and the interfacial crack bridged zone model are combined in numerical algorithm. The results of computations allow to estimate the increasing the SIF module due to bonds degra dation over time and the time of crack nucleation. These results might be helpful for durability analysis of adhesion joints. Since the computational parameters strongly depend on the initial data (which is caused by the exponential de-