20 1 Deformation and Fracture of Perfect Crystals can be derived.Thus,this combination defines the bulk modulus B(Cu +2C) which expresses the elastic response of a crystal to isotropic (hydrostatic) loading. Several other elastic moduli can be related to simple types of loading. For example,the modulus Ci can be determined by a simple lattice stretch in the [100]direction (see Figure 1.5).The Young's modulus expresses the crystal response to uniaxial loading and,therefore,it depends on the crystal orientation with respect to the loading direction.For particular orientations one can derive E(100= (C1-C2)(C11+2C2) (1.8) C11+C12 E110)= C44 2C44 1+ (C11-C12)(C11+2C12). E11)= 3C44(C11+2C12) C44+C11+2C12 The shear modulus G can be expressed as 3C44(C11-C2) 4C44+C1-C12 for{111}(②11)，{111}(110)and{110}(11）slip systems, G=(Cu-Cu2) for {110)(110)slip system and G=C44 for {110}(001)slip system. [010] 00 [100j [001] Figure 1.5 Illustration of a lattice distortion for calculation of the elastic modulus C1120 1 Deformation and Fracture of Perfect Crystals can be derived. Thus, this combination defines the bulk modulus B = 1 3 (C11 + 2C12) which expresses the elastic response of a crystal to isotropic (hydrostatic) loading. Several other elastic moduli can be related to simple types of loading. For example, the modulus C11 can be determined by a simple lattice stretch in the [100] direction (see Figure 1.5). The Young’s modulus expresses the crystal response to uniaxial loading and, therefore, it depends on the crystal orientation with respect to the loading direction. For particular orientations one can derive E100 = (C11 − C12)(C11 + 2C12) C11 + C12 , (1.8) E110 = 4C44 C11 1 + 2C44 (C11 − C12)(C11 + 2C12) −1 , E111 = 3C44(C11 + 2C12) C44 + C11 + 2C12 . The shear modulus G can be expressed as G = 3C44(C11 − C12) 4C44 + C11 − C12 for {111}¯211, {111}¯110 and {110}¯111 slip systems, G = 1 2 (C11 − C12) for {110}¯110 slip system and G = C44 for {110}001 slip system. a0 a0 a0 a [100] [010] [001] Figure 1.5 Illustration of a lattice distortion for calculation of the elastic modulus C11