Using the illustration and principles of fracture mechanics, it is possible to show that the critical stress oc required for crack propagation in a brittle material is described by the expression: 12 2 Eys ? 2 0:-() where E is the modulus of elasticity, Ys is the specific surface energy, and a is one-half the length of an internal crack. (a) According to the illustration and Gibbs energy analysis, when the crack has a depth of b, how much total energy will be released due to the crack formation? Is the released energy the toughness or resilience of the material? How much total energy is needed to maintain the newly formed crack surface? Express the answers as a function of a, b, E, Ys, 0 (b) Suppose a relatively large plate of a glass is subjected to a tensile stress of 40 MPa. If the specific surface energy and modules of elasticity for this glass are 0.3 J/m and 69 GPa, respectively. Determine the maximum length of a surface flaw without producing the fracture. a (e) Calculate the critical stress of a typical glass pane when one crack is present: a = 25 mm. The modulus of glass is E = 70000 MPa, and the specific surface energy, Ys = 3.5 J/m