Griffith theory of fracture

The importance of inherent flaws as sites of weakness for the nucleation of internal fracture seems almost intuitive. There is no need to dwell on theories of the strength of solids to recognize that material tensile strengths are orders of magnitude below theoretical limits. The Griffith theory of fracture in brittle material (Griflfith, 1920) is now a well-accepted part of linear-elastic fracture mechanics, and these concepts are readily extended to other material response laws. 

Developed chiefly in Russia, the kinetic theory of fracture at first appears to represent an entirely different account of fracture phenomena to that discussed in Section 1.2. In fact some Russian authors have claimed that the kinetic theory contradicts the Griffith theory of fracture. As we shall see, however, this is not the case. 

The Griffith theory of fracture predicts the failure envelope in the following form (Jaeger et al. 2007, Eq. 10.139) ... 

Their analysis of experimental data shows that tensile strength was the only parameter that varied as a function of particle size. Model simulation indicate that larger lumps were stronger than smaller lumps which is contradictory to Waters et al. [8], Teo and Waters [9], and Griffith [10] theory of fracture, which implies that larger particle are more likely to contain larger cracks and hence be more susceptible to breakage. 

The idea that the strength of bulk solids is controlled by flaws was advanced by Griffith in 1921 and has led to the development of a mudi more sophisticated continuum approach to fracture, known as fracture mechanics. Fracture mechanics is concerned always with the conditions for the propagation of an existing crack, and it is important to bear this in mind when comparing different theories of fracture. Griffith s ideas are well known and do not need to be elaborated here. There are some aspects of his theory which are relevant to the present discussion, however. Griffith s equation for the fracture stress of an elastic material is (for plane stress). 

Thus, one needs a theory of fracture that is based on the stability of the largest (or dominant) flaw or crack in the material. Such formalism was first introduced by A. A. Griffith in 1920 [1] and forms the basis of what is now known as linear (or linear elastic) fracture mechanics (LEFM). 

The Griffith theory of brittle fracture postulates that the fracture is due to ... 

We may thus conclude that the fracture process is determined by crack formation and crack propagation. Griffith crack theory is essentially a static conception of critical crack formation. Crack growth, however, also depends on dissipative processes. Below the critical load, crack propagation may advance very slowly. In such a case there is a dissipation of energy due to creep processes. Therefore, fracture is a time-dependent process. This aspect is neglected in the Griffith-Irwin theory of fracture. 

Many tests, for example Tensile tests and Shear tests, measure a critical stress rather than an energy of fracture. Good has pointed out that this critical stress will also depend on the fracture energy. He adapted the Griffith - Irwin theory of fracture for application in adhesive bonds. According to this theory, the fracture stress Of of material of modulus E will be given by... 

One general comment is that defects are not as strong a controlling feature of breakage in these extensible textile fibres as in many other materials. Rupture forces cannot be calculated from modulus and crack depth as in Griffiths brittle fracture, or even from the later theories of fracture mechanics. As described below, Moseley (1963) showed that severe damage could be imposed on nylon and polyester fibres with no effect on strength at room temperature. 

A quantitative explanation of the effect requires an advance in fracture mechanics. Griffiths theory explains fracture in a perfectly elastic material as dependent on crack depth. This has been extended to cover the situation where there is a small zone of plastic deformation ahead of the crack. The problem is more difficult when the pla.stic deformation is large compared to the crack size, and, as far as I know, there has been no treatment of the situation when plastic deformation covers the whole thickness of the specimen over an appreciable length. Any analysis would also require an understanding of the transition in material from crystalline yielding to looking and chain breakage and the form of the local stress-strain curve beyond that which is measured. 

On the other hand, the criterion of Griffith [61] is widely accepted for the theory of fracture. It is based on the concept that the fracture takes place when there is an increase in the energy of the surface formed by the growth of the crack and it predominates over the elastic energy due to the deformation in the vicinity of the crack. 

Griffith s Theory of Fracture. Fracture of polymers and polymer-based composites is of course a subject on which entire books have been written. General fracture mechanics has been presented fairly succinctly by Pascoe (44). Here we shall quote the most important results. 

To evaluate the influx solution experimentally for an A/B cantilever beam configuration as shown in Fig. 1, we apply Griffith s theory at the critical moment of fracture, such that the incremental change in stored elastic energy U. with change in crack length a, is Just sufficient to overcome the fracture surface energy S... 

An example of a theory is the Griffith theory. It expresses the strength of a material in terms of crack length and fracture surface energy. Brittle fracture is based on the idea that the presence of cracks determines the brittle... 

The principle behind the phenomenon of fracture of materials can be described by having recourse to Griffith s theory. Alternatively, this can be done by introducing the concept of fracture toughness. 

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