PSI - Issue 28

Mikhail Perelmuter et al. / Procedia Structural Integrity 28 (2020) 2320–2327 M.N. Perelmuter / Structural Integrity Procedia 00 (2020) 000–000

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a )

b ) Fig. 7. The rates of deformation energy absorption by bonds for di ff erent relations for bonds compliance variation along the crack bridged zone, t = d / , c 0 = H / : a ) - total, see (12); b ) - for shear deformations, G x bond ( d , ), 1 − γ ( ξ ) = 1 / 1 − ξ 2 ; 2 − γ ( ξ ) = 1; 3 − γ ( ξ ) = 1 − ξ 2 rate of deformation energy absorption by bonds, and this e ff ect is more significant at small sizes of the crack bridging zone. As can be seen from Fig. 4-7, the rate of deformation energy absorbtion by bonds reaches its maximum value at a certain size the crack bridged zone. The dependence of the maximum value of rate of deformation energy absorbtion on the parameter Ψ (introduced in Goldstein and Perelmuter (1999)), which contains all the mechanical properties of the model, is shown in Fig. 8. For large values of Ψ , the relation G bond ( d , ) (0 . 8 ÷ 0 . 85) G tip (0 , ) is fulfilment. In Fig. 9 is shown the dependence on the parameter Ψ the crack bridged zone size at which the maximum value of the rate of deformation energy absorbtion by bonds is reached. If bonds compliance is rather small (hard bonds, large Ψ ) the position of the maximum then is observed near the crack tip, with a small bridged zone length ( d / < 0 . 1). As bonds compliance increases, the position of this maximum shifts to the center of the crack ( d / = 1), and its magnitude decreases (at Ψ ≤ 0 . 35 the maximum is always observed at d / = 1). From Fig. 9 can be supposed that d / ∼ Ψ − 1 / 2 . For elastic parameters of materials and bonds used in the calculation, it can be established the relation that approximate the results shown in Fig. 9 with high accuracy for 1 < Ψ < 50 d ∼ 1 2 √ Ψ (16) It is interesting to note that the position of G bond ( d , ) maximum coincides with the corresponding position of bonds traction modulus maximum, see Goldstein and Perelmuter (1999). The energy characteristics of the bridged crack used in the nonlocal two-parameter criterion of quasistatic growth of cracks were analyzed in the paper. The e ff ect of materials and bonds mechanical properties on the energy charac teristics of bridged interface cracks was considered. The non-monotonic behaviour of the rate of deformation energy absorption by bonds with increasing of the crack bridged zone length was established and analysed. It has been found that the greatest e ff ect on the changing of the energy parameters a bridged crack is exerted by variation in the relative bonds compliance. With decreasing of bonds compliance in the crack bridged zone, the position of the maximum rate of energy absorbtion by bonds is observed at a small size of the bridged zone and the Ψ = E b 2 π H k 1 + 1 µ 1 + k 2 + 1 µ 2 (15) 4. Closing