Fracture mode mixity

The fracture mode mixity at the crack tip in homogeneous materials is defined as the ratio between the mode II and mode I stress intensity factors. 

Adherend Thickness Ratio- h/H Fig. 14. The global fracture mode mixity in asymmetric DCB specimens. 

As outlined in Section 1.2, mode mixity can significantly alter the locus of failure, even driving debonds away from weaker regions of the joint. To investigate the effect of fracture mode mixity on the locus of failure in adhesive bonds, quasistatic DCB and ENF tests were conducted. Specimens were made of adhesive C with acetone wipe surface preparation and they were all as-produced, therefore the T-stresses were all negative. For the ENF tests, specimens were symmetric and for the DCB tests, both symmetric and asymmetric specimens were used with three different adherend thickness ratios, i.e. h/H = 0.5, 0.75, and 1. Finite element analysis was used to quantify the mode mixity and the results are shown in Fig. 14 adherend thickness ratios of h/H = 0.5, 0.75, and 1 correspond to fracture mode mixity of = 22°, 10°, and 0° or jj = 14%, 3%, and 0%, respectively. 

The critical strain energy release rates measured in each test are shown in Fig. 15. The fracture toughness measured decreases as the mode II fracture component increased in the tests for this particular material system. This mode mixity dependence of the fracture toughness of adhesively bonded joints apparently is in contrast with the observations of other researchers for other material systems [49-54]. This contradiction can be explained through analyzing the locus of failure. As discussed in Swadener and Liechti [52] and Swadener et al. [53], the locus of failure in their studies was independent of the fracture mode mixity, and the size of the plastic deformation zone at the crack tip increased with the fracture mode mixity. This increased plastic zone was shown to be responsible for a shear-induced toughening mechanism, which consequently, caused the fracture toughness to increase with the mode II components in their studies. In this study, however, as... 

Fracture mode mixity and the directional stability of cracks... 

Fig. 20 shows the failure surfaces of three typical specimens selected from each specimen group of different adherend thickness ratio. The plastic deformation in the adherends introduced before the tests in order to alter the 7-stress was 1.3% for all the three specimens. As a result, the 7-stresses for all the three specimens are positive according the FEA results in Section 2.3.1 and Eq. 7, and their values are shown in Fig. 20. Due to the positive 7-stress level (35 MPa), the crack trajectory in specimen a, in which the fracture is mode I since the specimen is symmetric h/H = 1), is alternating, highly directionally unstable. In specimen b, the 7-stress has increased slightly to 38 MPa due to the low-level fracture mode mixity with G /G = 3% introduced by the asymmetric adherends h/H = 0.75). However, the crack trajectory is predominantly directionally stable except in limited locations where alternating cracks were observed. This effect...

The results suggest that although the fracture mode mixity will cause the T-stress in the specimen to increa.se, the crack propagation will be stabilized very rapidly as the mode mixity increases regardless of the T-stress state. On the other hand the results also indicate that directionally unstable cracks can only be observed in predominantly mode 1 fracture tests with mode mixity G /G < 3% for this particular material system. Beyond this point, the mode mixity forces the debond to propagate along the preferred interface, preventing directional instability. 

He, M. Y., Turner, M. R. and Evans, A. G. (1995), Analysis of the double cleavage drilled compression specimen for interface fracture energy measurements over a range of mode mixities, Acta Metallurgica et Materialia 43, 3453-3458. 

Jensen, H. M. (1998), Analysis of mode mixity in blister tests. International Journal of Fracture 94, 79-88. 

Another important quantity in interface fracture mechanics is mode mixity. The crack tip field of an interface crack is intrinsically mixed mode [8] due to the asymmetric elastic properties across the interface. Hence, mode mixity is required to fully characterize the loading conditions at the crack tip. Furthermore, the fracture toughness of an interface is known to depend on the mixed mode condition, typically observed to rise with increasing mixed mode. The degree of the mode mixity can be characterized using the definition of the complex interface stress intensity factor K = iK + after He and Hutchinson [5] ... 

As shown in Table 5, in the mode I test, the thicknesses of the residual adhesive layer on the failure surfaces were about 250 xm for all the specimens with different surface preparations, which indicated that the failures all occurred in the middle of the adhesive layer in the test regardless of the surface preparation method since the total thickness of the adhesive of the specimens was 0.5 mm. When the phase angle increased as in the asymmetric DCB test with h/H = 0.75, which contains 3% of mode II fracture component, a layer of epoxy film with a thickness of around SO xm was detected on the failure surfaces of all the specimens. Although the failure was still cohesive, the decrease in the film thickness on the metal side of the failure surfaces indicated that the locus of failure shifted toward the interface due to the increase in the mode mixity. On the other hand, because the failure was still cohesive, no significant effect of interface properties on the locus of failure was observed. When the mode mixity increased to 14% as in the asymmetric DCB test with h/H = 0.5, where the mode mixity strongly forced the crack toward the interface, the effect of interface properties on the locus of failure became pronounced. In the specimen with adherends prepared with acetone wipe, a 4-nm-thick epoxy film was detected on the failure surfaces in the specimen with adherends treated with base/acid etch, the film thickness was 12 nm and in the P2 etched specimen, a visible layer of film, which was estimated to be about 100 nm, was observed on the failure surfaces. This increasing trend in the measured film thickness from the failure surfaces suggested that the advanced surface preparation methods enhance adhesion and displace failure from the interface, which also confirmed the indications obtained from the XPS analyses. In the ENF test, a similar trend in the variation of film thickness was observed. 

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