Part I: (50 points)

From lecture notes and copies of Ref.s [4] and [5], derive an intermediate equation (equation (2) of Ref[5]) that can be used to derive equation (3) in section 3.0 of Web lecture for a crack perpendicular to an interface seperating two dissimilar isotropic materials. Equation (3) in the class notes in Section 3 is the same as equation (16) in Ref [5].

Derive equation (2) in Ref [5]:

(2)

Using boundary conditions equation (2) in Ref [5] can be simplified to equation (16) in Ref [5] or equation (3) in Section 3 of the lecture notes.

(3)

More information about this derivation is given Ref [5] which is a technical report from the California Institute of Technology (CIT) which will be handed out in class.

Part II: (50 points)

Find a publication on cracks at or near interfaces between dissimilar materials (isotropic or anisotropic) and discuss how the micro-model (analytic and/or numeric) was used to predict the mechanical behavior.