Fracture criterion

Fracture Toughness. The fracture criterion was defined by a critical value of the crack tip stress intensity, known as the fracture toughness. Ceramics often fail ia pure tension, designated mode I, and Kj replaces ia equation 6. Thus die appHed tensile stress at which fracture... 

Fig. 23.9. Brittle fracture the largest crack propagates when the fast-fracture criterion is satisfied.

T. D. Burchell, A. P. G. Rose and M. O. Tucker. The influence of grain size distribution on a fracture criterion for graphites. In Proc. 17th Biennial Conf on Carbon, Lexington KY, USA. Pub. American Carbon Society, 1985, pp.346 347. 

The presented explanation for the existence of the fracture envelope will be used in formulating a fracture criterion for polymer fibres. Let us suppose a hypothetical polymer fibre with chains having a single orientation angle in the unloaded state. The shape of the fracture envelope is now calculated by taking into account the shear deformation of the chains only. For this case the work per unit volume up to fracture is given by... 

The strength of a fibre is not only a function of the test length, but also of the testing time and the temperature. It is shown that the introduction of a fracture criterion, which states that the total shear deformation in a creep experiment is bounded to a maximum value, explains the well-known Coleman relation as well as the relation between creep fracture stress and creep fracture strain. Moreover, it explains why highly oriented fibres have a longer lifetime than less oriented fibres of the same polymer, assuming that all other parameters stay the same. 

The first fracture criterion was defined by Griffith, supposing that fracture occurs when sufficient energy is released (from the stress field) by growth of the... 

Another fracture criterion has been introduced by Irwin, based on the stress intensity existing at a point of polar coordinates, r and 9 from the tip of a sharp crack of length 2a in a body uniformly stressed by an applied stress, a0. For regions close to the crack tip, the components of the stress tensor at the considered point take the form ... 

Irwin postulated that the condition, Kj > K c, represented a fracture criterion. K c is a critical value for crack growth in the materials it is frequently termed the fracture toughness. The units for Kjc are MPam1/2. 

Pietruszczak, S., Inglis, D., and Pande, G.N. 1999. A fabric-dependent fracture criterion for bone. J. Biomech. 32, 1071-1079. 

Another important result from the atomistic simulations was that the stress-strain response of a region of material around an interface that debonded could be represented by an elastic fracture analysis at the next higher size scale if the interface was assumed to be larger than 40 A. Hence, an elastic fracture criterion was used in the microscale finite element analysis, which focused on void-crack... 

The above refers primarily to linear elastic fracture mechanics (LEFM) studies related to the onset of brittle fracture as well as fatigue. The states of the sciences of ductile and dynamic fracture, which only became of serious concern in the early 1960s and 1970s, respectively, have not reached a similar level of maturity despite the immense research efforts expended on these topics in recent years. Yet to be resolved in the former is a viable ductile fracture criterion in view of the recently uncovered uncertainties regarding the /-integral as a crack tip parameter.5,6 As for the latter, a reliable dynamic crack propagation criterion is yet to be established, as will become apparent in subsequent sections of this chapter. 

In a disordered solid, as modelled by the percolation model (discussed in Section 1.2) with intact bond concentration p on a lattice, there occur various vacancy clusters (voids), or pre-existing cracks, of different sizes and shapes. The typical crack size in such a percolating solid being of the size of the correlation length (see Section 1.2.1) the application of the Griffith fracture criterion gives (Chakrabarti 1988, Ray and Chakrabarti 1985a,b) from equation (3.4)... 

In the light of these results previously formulated fracture criteria need to be revised. A critical displacement at the crack tip seems not to be a unique criterion, and a fracture criterion formulated in K,-terms alone e.g. 

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