Elastic Fracture Mechanics Behavior of Graphite

3 Linear Elastic Fracture Mechanics Behavior of Graphite 

Linear elastic fracture mechanics (LEFM) is based on a mathematical description of the near crack tip stress field developed by Irwin [23]. Consider a crack in an infinite plate with crack length 2a and a remotely applied tensile stress acting perpendicular to the crack plane (mode I). Irwin expressed the near crack tip stress field as a series solution  

is the mode I stress intensity factor which serves as a scalar multiplier of the crack tip stress field. 

The variation of the stress oy as a function of r at 0 = 0 is illustrated in Fig. 1. For large values of r in eq. 2, oy approaches zero, whereas in reality it can only fall to the remotely applied stress (o ). As r approaches zero at the crack tip, oy approaches infinity, while it should not exceed 0. Hence, it is clear that eq. 2 is valid only for a limited region around the crack tip and is more accurate for low values of a . 

Rather than bearing an infinite stress at the crack tip, yielding occurs resulting in a volume of inelastically deformed material along the crack front called the process zone, as shown in Fig. 2. The size of the inelastic zone, r jnm, under a monotonic tensile stress, o inm, can be approximated by substituting o = oin into eq. 2 for the horizontal plane, 0 = 0 

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