Fracture Mechanics Two strips of metal are glued together as

Fracture Mechanics

Two strips of metal are glued together as shown in Fig. 14-12. A patch of glue was omitted over the central section. The joint is pulled apart by equal and opposite central forces as shown. At what load will the glued joint start to fail? You may assume beam theory for the metal strips, which have E = 210 GPa. The fracture toughness of the glue m 300 J/m^3, that is R = 300 J/m^3 also.

Solution

Joint will fail when strain energy is equal to fracture toughness

Strain Energy   =   0.5 * (stress)^2 * Volume / E

                       = 0.5 * ( P / Area)^2 * 0.12 * 0.01 * 0.001 / 210 * 10^9

                       = 0.5 * (P / 0.12 * 0.01)^2 * 0.12 * 0.01 * 0.001 / 210 * 10^9

                       = 1.984127 P^2 E-12 J

Fracture toughness of glue = 300 * (2*0.03*0.01) = 0.18

P = ( 0.18 / (1.984127 * E-12) )^0.5

P = 301.1976 kN