Crack surface displacement modes

Mode I opening Mode II in-plane shear Mode III out-of-plane shear Fig. 9.9 Crack surface displacement modes during crack growth. 

Cracks are usually subdivided into mode I, mode II, and mode III, based on the crack surface displacement. Mode I is the tensile mode and the most commonly encountered mode. The crack tip is subject to displacements perpendicular to the crack plane. In mode II or the sliding mode, the crack faces move relative to each other in the crack plane. Mode III is also referred to as the tearing mode, where the shear stress is acting parallel to the plane of the crack and parallel to the crack front (Figure 2.5). 

Figure 5.39 The three modes of crack surface displacement (a) opening mode (b) sliding mode and (c) tearing mode.

Figure 3.483. Illustration of the opening (mode I) and forward shearing (mode II) modes of crack surface displacements [1317],...

Plane strain fracture toughness for mode I crack surface displacement... 

In order to obtain crack-tip quantities such as the strain energy release rate g, the complex stress intensity factor K, and the mode-mixity xp, the following procedure may be adopted first, the strain energy release rate Q is directly computed via a contour integral evaluation - the J-integral method, or the VCCT second, the modulus of K, can be computed from Equation (10) and third, the crack surface displacements may be substituted in Equation (8) and with the knowledge of e, the parameter a is computed. Finally, the stress intensity factors may be expressed as ... 

The linear-slope CDCB specimens shown in Figs. 13 and 14 were used for mode-I fracture tests on FRP-wood bonded interfaces under both dry and wet conditions. A typical specimen under mode-I fracture load is shown in Fig. 15 for phenolic FRP wood interface under dry conditions, and the corresponding critical tip load versus crack opening displacement is plotted in Fig. 16. As an illustration, the fracture surfaces of epoxy FRP-wood with HMR and RF primers on wood substrates are shown in Figs. 17 and 18,... 

Superposition of K solutions is subjected to the same restrictions as those used for stresses and displacements. For example, the stress intensity factors must be associated with a single loading mode, often mode I, and the body geometry should be the same. An additional restriction is that the crack surfaces must be separated along their entire length in the final configuration. This can be a problem if one of the basic solutions involves compressive stresses that push the crack surfaces together. 

For a very thin specimen i.e., with B (Kjc/ays) ), the influence of plastic deformation at the surfaces will relieve crack-tip constraint through the entire thickness of the specimen before Kj reaches Kjc. As such, the opening mode of fracture is suppressed in favor of local deformation and a tearing mode of fracture. The behavior is reflected in the load-displacement record by a gradual change in slope and final fracture, which could still be abrupt (see Fig. 4.7b), but the conditions of plane strain would not be achieved. 

Williams (49), Ward (79), and Jancar et al. (89) proposed an approximate model of mixed mode of fracture to account for the effect of finite specimen dimensions for Kc and G, respectively. The basic idea in both theories is a substitution of the actual distribution of fracture toughness across the cross-section by a simple bimodal distribution, assuming plane strain value in the center and plane stress value at the surface area of the specimen. Size of the plastic zone IR relative to the specimen width B gives the contribution of plane stress regions and is a measure of the displacement of the state of stress at the crack tip from the plane strain conditions. Note that this approach can be used only if the mode of failure does not change with the test conditions or material composition (i.e., it attains its brittle character). 

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. 

Talking into consideration the actually observed linear dependence of logarithm of lifetime on applied load for polymer samples, the non-linear correlation of these two quantities for a covalent chemical bond, the small fraction of ruptured chains, and the identical activation energy for sample failure and plastic drawing one concludes that the failure of a sample in creep is primarily a consequence of mutual shear displacement of adjacent microfibrillar elements, i.e., a frictional mode, which leads to gradual formation of microcracks at their ends. As soon as by axial and radical coalescence of such microcracks a critical size crack is formed the sample fails catastrophically with the chajracteristic fibrillar fracture surface. The rupture of polymer chains is the consequence but not the primary cause of microfibrillar displacement and ensuing sample failure. 

I. Displacement-Traction Relationships. Displacement-traction relationships, in terms of Fourier transformed quantities, on the surface of a half-space, under plane strain conditions, are derived in Sect. 7.1 and given by (7.1.15) for steady-state uniform motion. A similar relationship between the Fourier transform of the displacement and tearing stress is given by (7.1.23) for tearing mode fracture, along the line of the crack. These have the same form as the equivalent elastic relations, with moduli replaced by complex moduli, as required by the Classical Correspondence Principle. 

Figure 11. Crack opening and displacements (magnified ten times) under mode II loading at the surface.

---