Crack extension criterion

Buczck, M.B. and Herakovich, C.T. (1985). A normal stress criterion for crack extension direction in orthotropic composite materials. J. Composite Mater. 19, 544-553. 

A criterion for matrix crack extension, based on Ktip, is needed. For this purpose, to be consistent with the energy criterion (Eqn. (24)), the critical stress intensity factor is taken to be... 

The above elastic crack curving criterion requires that r0material constant which specifies the characteristic crack tip region in which the off-axis microcracks enlarge and connect to the main crack tip, as shown schematically in Fig. 3.3. The angular deviation of the crack from its original direction of self-similar crack extension is given in Ref. 21. 

Again, the above crack kinking and branching criteria are limited to isotropic homogeneous material, which for all practical purposes will include particulate/whisker-filled ceramic matrix composites. No equivalent criterion exists for orthotropic/inhomogeneous material. Limited experimental results show that self-similar crack extension is a rare phenomenon in fracture of fiber-reinforced ceramic matrix composites and thus the kinking and branching criterion, if developed, must necessarily be a three-dimensional one. 

COD results can be used directly to evaluate and compare materials or to calculate defect sizes for particular structures. Two criteria are typically selected for COD evaluation. The first is the type of load-displacement record developed in the test. There are usually four types. These are shown in Fig. 2 in order of increasing resistance to crack extension. The second criterion is the magnitude of the critical COD, which occurs at maximum load or unstable crack extension. The value of 0.10 mm minimum COD is often cited as a criterion for acceptability, similar to 20-J CVN impact energy. 

This alternative will be developed further in Section 8.5. If the failure criterion df//dc=0 is applied to Eq. (8.8), the critical stress for crack extension (the fracture stress tTj.) is obtained, i.e.. 

Griffith set up an energy balance equation, comparing the amount of elastic energy released by crack extension with the amount of surface energy needed to generate the newly exposed crack surface. The Griffith criterion for britde fracture is expressed as... 

This theory combines the influence on strength of both groups of voids considered independently the first one characterized by its total volume P, but does not contain long cracks, and the second one without appreciable volume but characterized by length c of a crack. The criterion for crack extension according to Kendall et al. (1983) is ... 

Strictly, (4.6.1) should be an inequality stating that the left-hand side is greater than or equal to the right, in which case conditions (4.6.16- 18) become inequalities. These conditions have the same form as the Griffith criterion for crack extension for an elastic body with which is an instantaneous inverse modulus, replacing the elastic inverse modulus. If a unique Poisson s ratio exists, then... 

The similarity between elastic and extending viscoelastic cracks carries over to the criteria for crack extension. In Sect. 4.6, the implications of an energy balance criterion for the growth of a crack in a viscoelastic body are explored. The condition obtained depends only on the initial values of the relaxation functions and takes the same form as that derived by Griffith for an elastic body. There follows, in Sect. 4.7, a demonstration valid in viscoelasticity, that the above condition may be expressed in terms of critical values of the stress intensity factors, which in turn are expressed in terms of distributions of cohesive forces at the crack ends. In this way, Barenblatt s elastic fracture criterion has been extended to viscoelasticity. 

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

Landes and has since received wide attention. As yet, there are no published papers describing the direct measurement of. rubber-tou ened plastics or other particulate composites. Williams and co-workers have attempted to estimate Jjc for HIPS and ABS indirectly, from the work done at the crack tip in SEN specimens sulqected to tenaon or bending As the fracture surfaces were extensively whitened, these estimates were probably hi the 7/ criterion should strictly be applied to the point of crack initiation rather tiian to later stages of ductile tearing. 

The fracture criterion of LFEM based on the is invalid when extensive plastic deformation occurs ahead of the crack tip. For ductile polymers and their blends, the... 

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