PSI - Issue 28

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

2324

5

a ) b ) Fig. 4. The rates of deformation energy absorption by bonds vs the relative crack bridged length, t = d / : a ) - total, see (12); b ) - for shear deformations, G x bond ( d , ).

by the deformation energy release rate for a crack of equal length in the absence of bonds G tip (0 , ) and on the graphs the following notations are used

G x , y bond ( d , ) G tip (0 , )

G tip ( d , ) G tip (0 , ) ,

G bond ( d , ) G tip (0 , ) ,

¯ G x , y

¯ G bond =

¯ G tip =

(13)

bond =

The results presented below were obtained for the following mechanical properties of materials subregions: elastic moduli E 1 = 135 GPa (metal), E 2 = 25 GPa (polymer), Poisson’s ratios of materials ν 1 = ν 2 = 0 . 35, the elastic modulus of bonds was assumed to be equal to the elastic modulus of one of the materials ( E b = E 2 ). For given values of materials mechanical properties (see (3) ) β < 0 and | β | = 0 . 0509313. The bond compliances in the normal and tangential directions were assumed to be equal and constant along the crack bridged zone. The bonds traction, the crack opening in the bridged zone and the energy characteristics of the bridged crack were computed by the method of singular integro-di ff erential equations, see details in Goldstein and Perelmuter (1999); Perelmuter (2007). The dependencies of the deformation energy release rate (3) on the relative length of the crack bridged zone at various values of the relative bonds compliance c 0 are shown in Fig. 3. The rate of release of elastic deformation energy decreases with decreasing in the relative bonds compliance. At small values of the relative bonds compliance a zone of low change in the elastic energy release rate can be identified. As in bonds absence, the deformation energy release rate can be divided into components proportional to K 2 I and K 2 II , see Sun and Jih (1987); Toya (1992). The e ff ect of the materials properties and bonds characteristics on the deformation energy release rate and its components can be traced from the results of the analysis of the SIF given in Goldstein and Perelmuter (1999); Perelmuter (2007). Fig. 4 shows the results of calculations the rate of deformation energy absorption by bonds G bond ( d , ) under uniaxial tension. This energy characteristic of bridged crack reaches its maximum value at a certain size of the crack bridged zone. With the above properties materials, the following relationships are met: G bond ( d , ) ≈ G y bond ( d , ) and G x bond ( d , ) G y bond ( d , ). The position of the maximum with increasing bond compliance shifts to the center of the crack ( d / = 1, crack filled with bonds), and its magnitude decreases. The dependencies of the rate of deformation energy absorption by bonds for di ff erent ratio of the elastic moduli of materials are shown in Fig. 5. Calculations were performed for equal Poisson’s ratios of materials ( ν 1 = ν 2 = 0, for these values of Poisson’s rations the phenomenon is more pronounced). The changing in the relative sti ff ness of the materials E 1 / E 2 was carried out according to the method used in Goldstein and Perelmuter (1999). Increasing in the relative sti ff ness of the materials leads to an increase in the contribution of shear deformation, the component of the rate of deformation energy absorption by bonds G x bond ( d , ) increases, and G y bond ( d , ) decreases at an almost constant total value of the energy parameter G bond ( d , ) = G x bond ( d , ) + G y bond ( d , ), see Fig. 5.