Measurement of fracture toughness of bimaterial interfaces and a stress-based approach to their fracture

On the Reference Length and Mode Mixity for a Bimaterial Interface

“…For smaller variations, the average of the two values was assumed as the fracture load of the sample, sum marized in Table 3. The scatter in the experimental data is com parable to that available in the literature [8,11,[13][14][15][16]19]. How ever, the scatter could be reduced by implementing precracks and utilize a mounting fixture to assure proper alignment of the speci mens, as discussed above.…”

“…In spite of the limitations, linear fracture mechanics (including the oscillatory solution) is commonly used to determine the mode mixity of tested bimaterial systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][24][25][26][27][28], either analyti cally [2,25] or through finite element simulation [26][27][28]30]. Thus, we will, regardless of the drawbacks of the oscillatory so lution, use this approach due to its simplicity, by recasting Eq.…”

“…A mode mixity based on a material-scale reference length l [23] is adopted by some authors [2,7,10,12,15,16,23], even though there is no consensus on how to select l [2]. Since the fracture resistance of the interface is controlled by the shear and normal stresses in the fracture process zone, l could be based on a rel evant microstructure dimension, such as grain size or the plastic zone [2,9,23,24].…”

“…Alternatively, the selection of l is commonly based on a suitable choice outside the plastic zone [7,9,11] or by judgment [12][13][14][15][16]. The mode mixity associated with interfacial toughness of the aluminum-epoxy system (which has properties similar to aluminum-vinyl ester system used in this study) has been based on various reference lengths, such as l =1 mm [12], l = 100 fm [11,15,18], and l =crack length [13]. Since the selec tion of such reference length is arbitrary, the mode mixity does not necessarily represent the conditions in the fracture process zone.…”

“…Thus, r int is governed by the mode mixity, which relates the relative proportions of the sliding and the opening modes ahead of the crack tip [1,2]. The interfacial fracture is commonly characterized by a toughness curve, expressing the in terfacial fracture toughness as a function of mode mixity, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The toughness curve is a property of the bimaterial inter face and should be invariant of the specimen type or specimen geometry [1,2,[7][8][9].…”