PSI - Issue 15

Mikhail Perelmuter / Procedia Structural Integrity 15 (2019) 60–66

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M.N. Perelmuter / Structural Integrity Procedia 00 (2019) 000–000

Fig. 5. Crack opening during self-healing process, totally filling of a crack with a healing material.

Fig. 6. Bonds restoration e ff ect. The relative MSIF versus time, di ff erent bridged zones sizes.

are shown in Fig. 3. During the first part of the healing time the MSIF decreases due to bonds restoration approximately linearly and after t / t m ≈ 0 . 3 variation of the MSIF is rather small. This means that the condition of a crack healing (13) can be relaxed. Time variations of the average relative bonds density along a crack during bonds restoration are shown in Fig. 4 where we can determine that at the instant t / t m ≈ 0 . 3 the average bonds density is ¯ N ( t ) ≈ 0 . 5 n 0 and this value can be used as the healing criterion. During the self-healing process the initial crack opening without bonds considerably decreases. For example, this decreasing is about u / u 0 ≈ 0 . 05 at the crack center, condition (13) for N cr = 0 . 95 n 0 is fulfilled after 215 time-steps, see Fig. 5. The next part of calculations was performed for final relative bond compliance c 0 = 0 . 1 and di ff erent lengths of crack parts filled with healing agent (bridged zones). If only the crack quarter length is involved in the self-healing process then the materials interface strengthening (decreasing of the MSIF) is reasonable in compared with the cases d / = 0 . 5 and d / = 0 . 75, see Fig. 6. The normal stresses variations along the bridged zones are shown in Fig. 7. It can be noticed that the area under the graph for d / = 0 . 5 at the final state is approximately equal to the area under the graph for d / = 0 . 75 and this parameter determines the MSIF value, see Goldstein and Perelmuter (1999). Time variations of the stress vector modulus for di ff erent values of crack bridged zone length are shown in Fig. 8. It is interesting to note that the rate of the stress vector increasing is bigger in the case of small healing zone. The model for evaluation of cracks self-healing time has been proposed. The kinetic theory of bonds restoration and the crack bridged zone model are combined in the numerical algorithm and implemented in the computer code. The results of computations allow to estimate the MSIF decreasing due to bonds restoration over time. Since the computational parameters strongly depend on the initial data (which is caused by the exponential dependence in formula (9)), the comparative analysis of di ff erent self-healing methodology under appropriate loading conditions is of greatest practical interest in this model. This model can be used for analysis of self-healing processes in di ff erent types of materials with various physico chemical nature of these processes. The nature of a self-healing process will define the main model parameters (see (9)-(11): the dimensionless factor α for the characteristic time, the energy of bonds healing U h , the dependence of bonds healing time on the position inside of a crack ψ ( x , t ), the bonds density after a crack self-healing n 0 and the rigidity of a single bond k s ( x ). The most part of these parameters can be only determined experimentally for a specific healing process and some of them, perhaps, can be found based on physical modelling of the self-healing process. Note, the model should be experimentally verified for every set of the model parameters. 5. Closing