Issue 46

A. Kostina et alii, Frattura ed Integrità Strutturale, 46 (2018) 332-342; DOI: 10.3221/IGF-ESIS.46.30 334 In this work, a finite-element simulation of the thermosonic method has been carried out to determine the local heating of the bi-metallic specimen (steel sample coated by a thin layer of copper) with an edge crack. The sample is considered as a linear elastic solid while the coating is modelled as a visco-elastic media. Thermophysical and mechanical parameters of the materials are presented in Tabs. 1 and 2. Material Heat capacity, J/(kg*K) Thermal conductivity, W/(m*K) Density, kg/m3 Copper 385 401 8900 Steel 502 45.4 7870 Table 1 : Thermophysical properties of the specimen and coating. Material Young’s modulus, Pa Poisson’s ratio Thermal expansion coefficient, 1/K Shear modulus, Pa Isotropic loss factor Relaxation time, s Copper 10 11 0.35 16.7*10 -6 3.7*10 10 10 -4 5.5*10 -10 Steel 2.13*10 11 0.28 11.9*10 -6 - - - Table 2 : Mechanical properties of the specimen and coating. T HEORY ropagation of elastic waves in an isotropic media is described by the differential equation of motion, which has the following form:        2 2 t u σ f (1) where  is the density, u is the displacement vector, t is the time, σ is the Cauchy’s stress tensor, f is the volumetric force. Differential Eqn. (1) can be transformed into the algebraic in the frequency domain with the use of Fourier transform of time derivative [9]. According to the differentiation theorem, Fourier transform of the second time derivative can be expressed as     2 2 2 d F t F t dt              u u (2) where   ( )e i t F f t f dt           t is Fourier transform of a function t ( ) f ,  is the angular frequency, i is the imaginary unit. Application of Fourier transformation together with the differentiation theorem to (1) give the representation of (1) in the form: 2 i e        u σ F (3) where  is the phase. For an elastic solid the relation between stress and strain tensor components can be expressed in the form of the Hook’s law:  : el σ С ε (4) P