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By David E. Malach

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It thus is not right to regard an additional deformation  r , as is done, due to the non-linearity and clamping effect of the cantilevers βh, formed by the crack. The clamping effect change is of lower order at aninfinitesimal crack extension. 2). 1). The part above the crack (stiffness I 2  b 1    h /12 ) carries a moment M3 and 3 3 3 3 normal force N and the part below the crack (stiffness I1  b h /12 ) carries a moment M1 , normal force N and a shear force V. and at the end of the crack a negative moment of about: M 2  M1 .

20) for the circular crack tip, 2 2 28 T. A. C. M. van der Put showing a difference by a factor 4, depending on the form of the crack tip and thus depending on the value of the tangential tensile stress along the crack-tip boundary. 5 and 2 but is too far away from the elliptic value 2 which applies generally. Also the theoretical elastic elliptic crack opening displacement of  c  (2 c) / E is far above the Dugdale value. The Dugdale model thus is a 2 model according to the equilibrium method, based on a chosen, allowable equilibrium system, providing however a too low and thus rejectable lower bound with respect to the theoretical description of Section 2.

F '( x0 )  f ''( x0 )  ....... 1! 2! giving: n    x x  x0 1 1/ n 1/ n 1 f ( x)   f1 (1)   f1 (1) .   f1 (1). 8) when:  f1 (1)  1/ n  1 1/ n 1  f1 (1)   f ' (1) or: n  f1' (1) / f1 (1), n where: f1' (1)    f1  x / x0  /   x / x0   x / x  0 1 and f1 (1)  f ( x0 ) Thus:  x f ( x)  f ( x0 ). 9) It is seen from this derivation of the power law, using only the first 2 expandedterms, that the equation only applies in a limited range of x around x0 . Using this approach on the damage equation: a  2C  sinh( )  C exp( ) gives: Fracture Mechanics of Wood and Wood-like Reinforced Polymers 31  0   a  C.

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