Griffith s theory of brittle fracture

Methods for mechanical testing of materials are briefly introduced along with various strengthening mechanisms. The number and siu-face area of the slip systems in metals and in ceramics are shown to be responsible for the ductility (or the lack of it) and for ductile-to-brittle transitions. Griffith s theory of brittle fracture is used to introduce fracture mechanics and to develop the concept of fracture toughness. The viscoelastic behavior of polymers is briefly discussed. 

Irwin proposed the concept of quasi-elastic fracture, which allows us to extend the limits of applicability of Griffith s theory [11], Irwin s criterion is valid not only for brittle materials, but also for elastic-plastic materials with significant plastic deformation developing until the moment of actual destruction of a material. 

The well-known Griffith s theory constitutes the principle of fracture mechanics. In fracture mechanics, the fracture of a brittle material is caused by the increase of tension-stress at the edges of micro-cracks (disfigurements) in the material. The breaking strength of a catalyst follows the Griffith equation. 

Modem fracture mechanics was pioneered by A.A. Griffith who showed that brittle materials could fail catastrophically by cracks that become self-propagating even at stresses much lower than their tensile strength. Griffith s theory was expanded to include ductile materials and has led to the definition of a material property called fracture toughness that allows the prediction of critical crack lengths. 

The classic Griffith-Orowan theory describes the relationship between the strength and toughness of brittle materials such as ceramics (Griffith, 1920 Orowan, 1949). In the simple basic equation of the theory, the stress to fracture Of is related to Young s elastic modulus E, the fracture energy y, and the critical crack length c, by ... 

Fracture mechanics for brittle materials is basically derived from the theory presented by Griffith (1920). Initially it was proposed for an elliptical crack in an infinite elastic and homogeneous medium subjected to distant tensile forces and the conditions for crack propagation were formulated for that case. Later, the brittle fracture mechanics were developed for various situations in real structural elements, with non-negligible plastic deformations and with several complications necessary to account for heterogeneity of materials, time effects, etc. In that approach the crack s appearance and propagation is considered as a basic effect of loading and as phenomena directly related to final failure. 

The development of the fracture mechanics approach to metals lead to Kaplan s (1961) proposal to apply fracture mechanics to concretes, using also relations applied in other fields of materials science. The Griffith s approach to cracks in perfectly brittle and homogeneous materials was extensively followed in numerous studies of cracking processes in cementitious materials, (cf. Section 10.1.1). Then the question arose whether the cracks themselves, and which of them, were governed by the Griffith s approach. Later, however, it became clear that the situation in these materials is much more complex and requires a more diversified approach. The answer for the above question is therefore also more complex the Griffith s approach is applicable to those materials, but with several restrictions and complementary assumptions. Various related questions are the subject of further developments of new theories and proposals (cf. Section 10.1). 

The analysis was first carried out by Griffith in a treatment of the brittle fracture of metals. Actually, the considerations are of general nature and can also be applied to polymers, after introducing some physically important but formally simple modifications. Griffith s approach is based on linear elasticity theory and its utility for polymers may look questionable at first, as those are neither elastic nor linear under the conditions near to failure. However, as we will see, the theory is indeed applicable and provides also here a satisfactory description of crack growth. 

This equation for lap joint failure is surprising in a number of ways. It is equivalent to Griffith s brittle fracture theory for glass [4], Moreover, it fits the puzzling historic results for lap joint failure which showed that the overlap length was not important for long joints, and the strength increased with sheet thickness d and stiffness E. Additionally, it is now clear why chemical environment can weaken the Joint because the failure depends on work of adhesion W, which decreases markedly with surface contamination. 

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