Problem 9 Materials often have small cracks i on their surface (A). When the material is under stress in}, the crack would tend to enlarge in order to reduce strain energy UV = -Kar2 dzw where a is the stress, d is the depth of the crack, w is the width of the crack, and Kis a constant. same" However, the crack creates more surface area, and thus costs ml Surface energy . AU' = +2ydw I" w I . where y is the surface energy of the solid. : d : The total energy AUT associated with formation and growth of a crack is thus MIT = MI" 4- AU' Find the critical depth d of the crack for it to grow. If you could add surface active agents that change the surface energy of the solid in order to inhibit crack growth, should the surfactant increase or decrease the surface energy? 10