Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 223-230; DOI: 10.3221/IGF-ESIS.42.24 225 For Terfenol-D, the constitutive relations can be written as: 11 11 31 11 12 13 22 22 31 12 11 13 33 33 33 13 13 33 23 23 15 44 31 31 15 44 12 12 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 H H H H H H H H H H H H d s s s d s s s d s s s d s d s s                                                                           1 2 3 0 0 0 0 0 H H H                               (6) 11 22 1 15 11 1 33 2 15 11 2 23 3 31 31 33 33 3 31 12 0 0 0 0 0 0 0 0 0 0     0 0 0 0   0 0 0 0 0 T T T B d H B d H B d d d H                                                                         (7) where:   23 32 31 13  12 21 23 32  31 13 12 21 11 1111 2222 12 1122 13 1133 2233 33 3333 44 2323 3131 66 1212 11 12  ,   ,   ,    ,    ,    ,    ,   4 4 ,   4 2  H H H H H H H H H H H H H H H H H s s s s s s s s s s s s s s s s s                                 15 131 223 31 311 332 33 333 2 2 ,    ,   d d d d d d d d         Averaged Strain Energy Density (SED) approach According to Lazzarin and Zambardi [10], the brittle failure of a component occurs when the total strain energy, W , averaged in a specific control volume located at a notch or crack tip, reaches the critical value W c . In agreement with Beltrami [17], named σ t the ultimate tensile strength under elastic stress field conditions and E the Young's modulus of the material, the critical value of the total strain energy can be determined by the following: 2 2 t c W E   (8) The control volume takes different shapes based on the kind of notch. If the notch is represented by a crack, its opening angle is equal to zero and the control volume is a circumference of radius R c , centered on the crack tip. Being this the case, the radius R c can be evaluated once known the fracture toughness, K IC , the tensile stress and the Poisson's ratio, ν , of the material, by means of the following expression proposed by Yosibash et al. [18]: 2 (1 )(5 8 ) 4 IC c t K R              (9) The SED averaged in the control volume can be computed directly by means of a finite element analysis . Finite element model In order to compute the averaged strain energy density, W , analyses were performed by means of ANSYS R14.5 finite element code, both in plane strain and plane stress conditions depending on the specimens' width. For the purpose, solid models were used to determine which was the most appropriate condition. As shown by Tiersten [19], the basic equations for magnetostrictive materials are mathematically equivalent to those of the piezoelectric materials, so four nodes PLANE13 and eight node SOLID5 coupled-field solid elements from ANSYS'