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# 2. J integral of interfacial fracture

A flexure specimen (shown in Figure 2) is designed to measure fracture toughness of bi- material interfaces.

(a) Using J integral to show that the energy release rate for interfacial fracture is given

by:

where P is the load per unit thickness, E is the Young's modulus, and n = h/H. Ignore any mismatch in elastic constants of the two materials.

(b) A prerequisite for using such a specimen for brittle materials is that interfacial fracture initiation should precede the damage of the specimen due to bending at the middle section of the bottom beam (point A). Assuming the damage stress is .. show that this condition is just met when the following equation is true.

where G is the critical energy release rate for fracture. Plot the dimensionless quantity EG/ ho as a function of n for the range 0

(c) Given that h = 1 mm, H = 2 mm, Ge=5 J/m2, and E=300 GPa, calculate the lower bound of tensile strength of the bottom beam necessary to measure the interfacial fracture energy

Fig: 1

Fig: 2