Cracks deflection

One possible mechanism is the modulus interaction, already discussed in another context in the chapter on metals (section 6.4.3). If the particles have a larger Young s modulus than the matrix, the matrix is partly unloaded in the vicinity of the particles, and the stress available to propagate the crack is reduced. The crack is deflected away from the particle (see figure 7.2). If Young s modulus of the particles is smaller than that of the matrix, the stress is raised in the vicinity of the particles, and the crack is attracted by the particle. If the crack cannot penetrate the particle, the crack must proceed along its boundary. In all these cases, the crack path becomes longer. 

Another way to deflect cracks are residual stresses caused by the particles. Compressive stresses reduce the force opening the crack tip and thus repel cracks. Such residual stresses can stem from differences in the coefficient of thermal expansion of the particles or from phase transformations on cooling from the sintering temperature. 

There have been many attempts to increase the toughness of ceramics because they are inherently brittle. All these attempts are an effort to increase the value given in Equation 15.56. The basic approaches are crack deflection, crack bridging, and transformation toughening. These approaches are discussed further here. 

Taking an average 9 value of 45°, the Ki, value of polycrystalline material should be greater by 1.25 over that of a single crystal. If we apply this value to alumina, the polycrystalline alumina should have a value of 3.45 Mpa.m /. This says that crack deflection does not account for all of the increase. So, let us consider the next mechanism. 

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Crack Reflection. Crack deflection can result when particles transform ahead of a propagating crack. The crack can be deflected by the locali2ed residual stress field which develops as a result of phase transformation. The force is effectively reduced on the deflected portion of the propagating crack resulting in toughening of the part. 

A partial answer to the first question has been provided by a theoretical treatment (1,2) that examines the conditions under which a matrix crack will deflect along the iaterface betweea the matrix and the reinforcement. This fracture—mechanics analysis links the condition for crack deflection to both the relative fracture resistance of the iaterface and the bridge and to the relative elastic mismatch between the reinforcement and the matrix. The calculations iadicate that, for any elastic mismatch, iaterface failure will occur whea the fracture resistance of the bridge is at least four times greater than that of the iaterface. For specific degrees of elastic mismatch, this coaditioa can be a conservative lower estimate. This condition provides a guide for iaterfacial desiga of ceramic matrix composites. 

The toughness induced in ceramic matrices reinforced with the various types of reinforcements, that is, particles, platelets, whiskers, or fibers, derives from two phenomena crack deflection and crack-tip shielding. These phenomena usually operate in synergism in composite systems to give the resultant toughness and noncatastrophic mode of failure. 

Crack Deflection Contribution to Toughening. Crack deflection is a phenomenon that leads both to toughening and to the formation of bridges that shield the crack tip from the appHed stress. Little is known of the bridge formation process, but its effect, that is, crack-tip shielding, is considered in the following section. 

Figure 7 shows these results schematically for both twist and tilt crack deflections. Thus, for the stress intensity factor required to drive a crack at a tilt or twist angle, the appHed driving force must be increased over and above that required to propagate the crack under pure mode 1 loading conditions. Twist deflection out of plane is a more effective toughening mechanism than a simple tilt deflection out of plane. 

Fig. 6. (a) Crack deflection and propagation through a tilt angle K 0) = Kj ... 

Deflection rarely operates as the sole toughening mechanism in a system, although its contribution in some systems may be significant. Crack deflection, however, is a major aspect of bridge formation processes that leads to toughening via bridging ligaments. 

Fig. 14—Schematics of shear stress in (a) single constituent thick coating and in (b) multilayer coating. The shear stress in each layer of multilayer is less than that in the single constituent thick coating due to the layer slide at the interface of the multilayer coating. In addition, crack deflection in the multilayer coating was illustrated schematically.

The implication of Eq. (6.21) is that the criterion is dependent mainly on the ratio of the energies for longitudinal splitting and transverse cracking, and is relatively insensitive to crack length and the elastic modulus. It is also noted from experimental study that crack speed has a pronounced effect on the toughness ratio, Rl/Ri, and thus the crack deflection phenomenon. 

Gupta, V., Argon, A.S. and Suo, Z. (1991). Crack deflection at an interface between two orthotropic media. Trans. ASMEJ. Appt. Mech. 91-WA/APM-42, 1-9. 

He, M.Y. and Hutchinson, J.W. (1989). Crack deflection at an interface between dissimilar elastic materials. Int. J. Solids Structures 25, 1053-1067. 

Fig. 8.1. Toughening mechanisms in rubber-modified polymers (1) shear band formation near rubber particles (2) fracture of rubber particles after cavitation (3) stretching, (4) debonding and (5) tearing of rubber particles (6) transparticle fracture (7) debonding of hard particles (8) crack deflection by hard particles (9) voided/cavitated rubber particles (10) crazing (II) plastic zone at craze tip (12) diffuse shear yielding (13) shear band/craze interaction. After Garg and Mai (1988a).

The toughness and mechanical performance of a filament wound composite component is enhanced by crack deflection mechanisms and/or molecular flow occurring in the... 

Two cracks on extension of diagonals originating from neighbouring comers or one crack deflected from the direction of diagonal... 

The influence of the shell thickness has also been reported (Sue et al., 1996a). By varying the shell thickness from 15% to 35% of the total thickness, the dispersion of CSR particles changed from a random to a well-dispersed but locally clustered distribution. The latter produced a higher toughening effect, probably due to the promotion of a crack-deflection mechanism, in addition to the other toughening mechanisms. 

Sue et al. (1997) reported results for the same LC epoxy monomer cured with various hardeners. KIe values could be increased up to 1.89 MPa m1/2. Observations of fracture surfaces indicated that crack bridging, crack branching, and crack deflection were the main toughening mechanisms. 

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