By R.W. Dickey
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Extra info for Bifurcation Problems in Nonlinear Elasticity
Hancock and Dr. C. Betegon. The support and encouragement of Doctors J. R. Gordon and P. Dong at Edison Welding Institute in the final preparation of this paper is appreciated. REFERENCES (1) Williams, M. L, 1957, Journal of Applied Mechanics, Vol. 24, pp. 111-114. (2) Hahn, G. , Averbach, B. L, Owen, W. T. Press, Cambridge, MA, pp. 91-116. (3) Knott, J. , 1973, Fundamentals of Fracture Mechanics, Butterworths, London. (4) Hahn, G. , 1984, Metallurgical Transactions A, Vol. 15A, pp. 947-959. , Evans, A.
4 e/W ... '. -ex. J/(acr0> .. O 6 ............. •... -. _.. -... 015 ~...... M:··· .... ······ ..... •.. ••• -..... ,,_ .......... •.... 03 -... .... , ••• -.... 0 Jt'(J/uJ = Figure 5. Three-point bend bar. Evolution of Q with 'increasing J for n 10. (a) Q is evaluated at r/(J/O'o) = 2. (b) Q is evaluated at several positions ahead of crack tip for several deformation levels. 0 '---, ,----------------. •,, , QSSY •• ~QSSY / d( J / uoL) ................... 0 0 o o "', , 66 '. 0 + ' 0 .. 6 6 o ~.
Triaxiality effects on fracture toughness can be predicted by using the J - Q field in conjunction with a fracture criterion based on the attainment of a critical stress, 0'22 = O'e, at a characteristic distance, r = r e , Ritchie et al. (36). Within the J - Q annulus, the normal stress ahead of the crack is given by  or more accurately by . Assume that re is within the J - Q annulus. 50'0, Jo = 40 kPa·m and n = 5. The relation in  captures the trend of the experimental data, that is, cleavage toughness depends sensitively on constraint.