Part II
Fracture - Surface Dissipation
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Chapter 6
Fracture Mechanics
Fracture is the behavior of materials to fail in a brittle manner, when sub jected to loading. Fracture processes initiate from cracks and involve dis placement discontinuities; that is, over the surface of a crack the displacement is discontinuous, corresponding to the crack opening. But most importantly. when a fracture occurs, the elastic energy that is stored in the (material or structural) system is released in an almost instantaneous way: it is dissi- pated in the formation of crack surfaces. It is this realization which opens the way to the application of thermodynamics of irreversible processes to the description of fracture processes also known as fracture mechanics, and to the introduction of a critical material property: the fracture energy, or, closely related to it, the fracture toughness.
6.1
Fracture Energy and Toughness - An In-
troductory Dimensional Argument
To motivate the forthcoming developments, consider a crack of length &, infi. nitely long in the Oz-- direction, in an infinite, homogeneous, linear isotropic elastic solid (Fig. 6.1). The linear elastic solid is characterized by the shear modulus G. At y = , the solid is subjected to a shear stress ozy = T Following the orientation of the applied stress, it is readily understood that the crack plane will extend the fracture plane in x-- direction. As we will see later, such an antiplane fracture mode is referred to as Mode III fracture. We are interested in determining the critical value Tcr of the applied stress 7 which defines the onset of crack propagation; and we shall use only
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&/2
Figure 6.1: Antiplane Fracture Problem of a linear elastic isotropic infinite medium (double symmetry with regard to y z-plane at x = 0 and y z-plane at z = 0).
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