PSI - Issue 15

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

64

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

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Fig. 3. Bonds restoration e ff ect. Relative MSIF versus time, crack filled with bonds, d = .

Fig. 4. Average relative bonds density along crack during bonds restora tion, self-healing threshold is N cr = 0 . 95 n 0 .

coated stents, see Hopkins et al. (2010). It was assumed that the adhesion layer between material has self-healing ability (similar to biomaterials, Brochu et al. (2011)) and at the initial time instant (when crack surfaces are free of constraints) some healing process is activated inside a crack, bonds between the crack surfaces are built and formation of the crack bridged zone is started. The algorithm of numerical implementation of the crack self-healing model is organized by time-step scheme. At the calculation start the future healed zone size is defined (crack bridged zone). At every time instant t i = ( i − 1) ∆ t , i ≥ 1 ( ∆ t is time step) the following computations are performed: • SIDE solution to obtain the bond stresses and crack opening u x , y over the crack bridged zone (see (2)); for i = 1 the solution of SIDE is performed for the infinitely small bonds sti ff ness (big compliance which corresponds to a crack without bonds); • SIFs and its module (7) are computed on the basis of the SIDE solution; • functions τ h ( x , σ ) and Z ( x , t , σ ) are determined, for i = 1, it is assumed that Z ( x , t , σ ) = 0 and σ xy , yy ( x , 0) = 0 ; • bonds density n h ( x , t ) (10) is computed; at the initial time instant ( i = 1) is assigned n h ( x , 0) = 0; • bonds compliance c ( x , t ) (2), (12) is computed; this compliance is assigned a big value for SIDE solution at i = 1 ; The condition of computations termination is the criterion of a crack self-healing process ending (bridged zone formation) in the following form: ¯ N ( t i ) ≥ N cr (13) where ¯ N ( t i ) is the average bonds density along crack bridged zone at the time instant t i and N cr is the limit value of regenerated bonds density. The numerical calculations were performed for plane strain conditions and the following elastic constants of the joint materials and bonds (stainless steel-polymer, Hopkins et al. (2010)): E 1 = 200 GPa , E 2 = 25 GPa ; E b = E 2 , ν 1 = ν 2 = 0 . 30 . The purpose of calculations is to analyze the e ff ectiveness of self-healing processes depending on the bridged zone length and the bonds properties (the measure of e ffi ciency is the SIF level at the crack tip). Computation of the MSIF dependence on the healing time and the other model characteristics were performed for the following problem parameters: the activation energy of the healing process - U h = 100 kJ / mole , τ 0 = 10 − 10 s (see relation (9)), the final bonds density is n 0 = 10 18 m − 2 , the healed crack size is 2 = 10 − 3 m , temperature of self healing process is T = 310 K , the external tension loading is σ 0 = 10 MPa , the limit value of healed bonds density is N cr = 0 . 95 n 0 . Time of self-healing t is given below as the dimensionless parameter t / t m , where t m = A ( T ) / N st and N st = 499 is maximal number of solution time-step. In the first series of calculations we assumed that the whole crack is involved in the self-healing process, ( d = ). For this case the MSIF dependencies on the healing time for di ff erent values of the relative final bonds compliance c 0