By Ting T.C.T.

ISBN-10: 0195074475

ISBN-13: 9780195074475

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67) (c) Motion of the Front of Fracture. At the moment t[ the surface layer Yo =ho fractures. 17. Let the thickness of the fractured layer be 20 at the moment t; it is obvious that ho = h + 0. 68) where the generalized moment of inertia I rn =~h2+11 2+)l is a function of 't, and y is reckoned from the new position of the neutral axis, while y = Yo + ho - h. 64) we have (n + I)AMn {[2h(t)-h('t)]n/rn~= 1 . o I~('t) But at this moment of time y = h (t). 17 (n + I)AM nl[2h(t)-h(1:)]n/m~= 1 . o 1::'(1:) Assume, for simplicity, that m =n; differentiating the equation with respect to t, we obtain 2!!!!...

We can assume (see [9]) that the index m does not depend on temperature, and B =B(9)=Bo e J3S where 13 and Bo are constants. 74) 13 2C I cry =Kexp(--9); K=2(-B )Il. 75) 0 Determining C I from the condition of equilibrium, we find K=p[fh exp( -~9)dx]-I . M. Kachanov where 8 1,8 2 are the temperatures of the boundaries x = h, x = - h, respectively. 20 At the first stage of fracture (prior to the formation of the fracture front), the stress O'y does not depend on time. 77) where 1( = a. - 13n / m.

Note, in conclusion, that various cross-sections of beams and various cycles can be considered in an analogous way. 7 Fracture of a Rotating Shaft in Bending Consider the fracture of a slowly rotating circular shaft (radius a) in pure bending. If the rotation is slow the stress redistribution can be neglected and the stresses can be assumed to be the same as in the state of steady creep. For sufficiently great number of cycles, damage can be treated as axially symmetric. A ring-shaped zone of full fracture r>c forms at t>t/.

### Anisotropic elasticity by Ting T.C.T.

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