2. Mode mixity of the four-point bend specimen (10 points)

a) Show that the energy release rate for the four-point bend specimen isA

where M is the applied moment per unit thickness, h and H are the thickness of the two

layers. Assume that both layers have the same Young's modulus E.

Hint: The following two papers developed the technique.

P.G. Charalambides, J. Lund, A.G. Evans, and R.M. McMeeking. A test specimen for

determining the fracture resistance of bimaterial interfaces. Journal of Applied Mechanics.

56, 77-82 (1989).

R.H. Dauskardt, M. Lane, Q. Ma, N. Krishna. Adhesion and debonding of multi-layer thin

film structures. Engineering Fracture mechanics 61, 141-162 (1998).

b) Charalambides et al (1989) used the finite element method to determine the mode angle.

When the two layers have identical elastic constants and identical thickness, one can

determine the mode angle analytically. Show that in this special case