Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 223-230; DOI: 10.3221/IGF-ESIS.42.24 224 present in the Tb 0.3 Dy 0.7 Fe 1.9 alloy, commercially known as Terfenol-D. Thus, among all the giant magnetostrictive materials, the (Tb 0.3 Dy 0.7 Fe 1.9 ) alloy has broadly gained interest in the last years. However, despite of the great attention that this alloy has gained in the industrial applications and though it is susceptible to in-service fracture due to its brittleness [2], very few works are available concerning the assessment of the influence of manufacturing induced defect and cracks on magnetostricitve material performances, notwithstanding the widely reported harmful effects of notches [3–5]. Moreover, the fracture behavior of these materials are highly affected by the presence of magnetic fields, since the fracture resistance uder mode I is inversely related to the intensity of the field Narita et al. [6]. Regarding the determination of the fracture behavior of different materials, it is widely reported that brittle and high-cycle fatigue failures of components weakened by different notches geometries occur when the strain energy density (SED) averaged in a control volume surrounding a crack or notch tip reaches a critical value [7-15]. Colussi et al. [16] showed that this criterion could be extended also to giant magnetostrictive materials, under mode I loading condition, employing a control volume having radius 0.07 mm. In this work, three point bending tests on Terfenol-D have been carried out, assessing the failure load at different loading rates both in presence and absence of an applied magnetic field. Then, coupled-field finite element analysis have been performed in order to evaluate the effect of the loading rate and of the magnetic field, allowing the development of a relationship between the critical radius R c of the control volume and the loading rate. A NALYSIS Basic equations of the material he basic equations for magnetostrictive materials are outlined as follows. Considering a Cartesian coordinate system, O-x 1 x 2 x 3 , the equilibrium equations are given by: σ ji,j = 0; ε ijk H k,j = 0; (1) B i,i = 0 where σ ji , H i and B i are respectively the components of the stress tensor, the intensity vector of the magnetic field and the magnetic induction vector, whereas ε ijk is the Levi-Civita symbol. A comma followed by an index denotes partial differentiation with respect to the spatial coordinate x ୧ and the Einstein’s summation convention for repeated tensor indices is applied. The constitutive laws are given as: H ij ijkl kl kij k T i ikl kl ik k s d H B d H         (2) where ij  are the components of the strain tensor and H ijkl s , ikl d , T ik  are respectively the magnetic field elastic compliance, the magnetoelastic constants and the magnetic permittivity. Valid symmetry conditions are: H H H H ijkl jikl ijlk klij kij kji T T ij ji s s s s d d        (3) The relation between the strain tensor and the displacement vector u i is:   , , 1 2 ij j i i j u u    (4) The magnetic field intensity, named φ the potential, is written as: , i i H   (5) T