Critical fracture parameter

Finally, when real load-time curves of pre-cracked specimens are processed, the critical fracture parameters deduced result in good agreement with the ISO protocol [15]. 

The puqjose of generalized fracture mechanics (GFM) is to overcome some of the problems raised above. Specifically, GFM addresses (1) nonlinear and inelastic materials, (2) steady-state crack propagation, and (3) the expression of critical fracture parameters in terms of the physical properties of the material(s) involved. 

Jic is the critical value of the near-tip quasi-static fracture parameter J, i.e. the crack initiation toughness. As for ductile materials a stable crack growth can occur at J values several times the value J c, the non-dimensional tearing modulus Tr was proposed for defining the crack growth toughness [26] ... 

Equation 5.21 holds for plane-stress conditions at the crack tip, which are most likely to occur if the sheet is thin (we discuss later what thin implies in this context). For plane-stress, then, the operative fracture parameter is G which is known as the firacture energy. A related (and more useful) parameter is the plane-stress critical stress intensity factor K, (5.N.6), which is defined, in the case of a wide sheet, by... 

Fds is the area under the load-displacement curve and A is the area of the remaining v-section of the specimen after notching. Comparing Jjc data with other fracture parameters, such as Kjc, and 2ywof. is of interest. Thus, in a perfecdy linear case (as indicated earlier), the critical value of J (i.e., Jic) is about the same as Kic and for the fracture criterion and Eq. (8.59) may be rewritten as ... 

Different formulations of fracture mechanics provide different fracture parameters. Linear elastic fracture mechanics (LEFM)(D defines a stress field parameter K which reflects the overall intensity of the stress field around the crack. Failure occurs when K achieves its critical value K. The formula for K depends on the test specimen configuration, but for a central crack of half-length c in a semi-infinite sheet, for example, it is given by... 

A second fracture parameter is also provided by linear elastic theory, namely, the energy G required to create unit area of fracture surface. Again there is a critical value, of G at which the crack begins to propagate, and a configuration-dependent formula which gives G in terms of measurable quantities. For the center crack mentioned above, the formula for G is... 

Distribution function of the energy density Fracture energy parameter Critical fracture energy parameter Sheet thickness... 

This method involves critical load evaluation and crack depth measurement, and has been used in recent years to define fracture parameters in several ceramics, for example, UO2, SiC, and TiC. ° ... 

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

Composite interfaces exist in a variety of forms of differing materials. A convenient way to characterize composite interfaces embedded within the bulk material is to analyze the surfaces of the composite constituents before they are combined together, or the surfaces created by fracture. Surface layers represent only a small portion of the total volume of bulk material. The structure and composition of the local surface often differ from the bulk material, yet they can provide critical information in predicting the overall properties and performance. The basic unknown parameters in physico-chemical surface analysis are the chemical composition, depth, purity and the distribution of specific constituents and their atomic/microscopic structures, which constitute the interfaces. Many factors such as process variables, contaminants, surface treatments and exposure to environmental conditions must be considered in the analysis. 

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