Linear elastic fracture mechanics framework

The above results are derived from linear elastic fracture mechanics and are strictly valid for ideally brittle materials with the limit of the process zone size going to zero. In order to apply this simple framework of results, Irwin (1957) proposed that the process zone, r be treated as an effective increase in crack length, Sc. With this modification, the fracture toughness becomes... 

The elastic stress cannot exceed the yield stress of the material, implying a region of local gelding at the crack tip. Nevertheless, to apply the simple framework of linear elastic fracture mechanics, Irwin [/. Applied Mechanics, 24, 361 (1957)] proposed that this process zone size Tp be treated as an effective increase in crack length 6c. Fracture toughness is then given by... 

Linear elastic fracture mechanics (LEFM) describes the behaviour of sharp cracks in linear, perfectly elastic materials. Since polymers are neither linear nor elastic, the utility of the theory may, at first sight, seem doubtful. In fact, the deviations from the theoretical assumptions are such that quite minor modifications to the analysis produce a precise description of crack growth in polymers within the framework of the conventional theory. The considerable resources of the subject may thus be utilised in that testing experience on other materials may be employed, together with the available analytical work. 

Applications of linear elastic fracture mechanics (primarily) to the brittle fracture of solid polymers is discussed by Professor Williams. For those not versed in the theory of fracture mechanics, this paper should serve as an excellent introduction to the subject. The basic theory is developed and several variants are then introduced to deal with weak time dependence in solid polymers. Previously unpublished calculations on failure times and craze growth are presented. Within the framework of brittle fracture mechanics and testing this paper provides for a systematic approach to the faOure of engineering plastics. 

Within the framework of linear elastic fracture mechanics, the total energy released by crack growth (work done and elastic energy released) under plane strain conditions is given by the product of the strain energy release rate [51, 53] ... 

Interface delamination and film fracture induced by residual stress in the thin film were the focus of discussion in the preceding chapter where models were developed within the framework of linear elastic fracture mechanics. Such analyses did not account for the actual separation of the film from its substrate. However, there are delamination processes for which transverse deflection of the film away from the substrate becomes an important consideration in a variety of practical applications. Examples include ... 

It must be noted that the fracture mechanics framework described above only applies when plastic deformation of the material is limited. Substantial plastic deformation may accompany propagation of existing defects in structures fabricated from relatively low-strength materials, e.g., carbon steels. In these cases, the linear elastic stress intensity factor, K, does not accurately apply in structural design. Alternately, elastic-plastic fracture mechanics methods may apply. ... 

In its turn, within the frameworks of elastic fracture linear mechanics the value 5 is determined as follows [16] ... 

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