PSI - Issue 42

4

P. Ferro et al. / Structural Integrity Procedia 00 (2022) 000 – 000

P. Ferro et al. / Procedia Structural Integrity 42 (2022) 259–269

262

where E is the Young’s modulus,  is the Poisson’s coefficient, d 0 (1.0771016 Å) is the is the stress-free lattice spacing, m is the gradient of the d vs. sin2ψ curve and ψ is the angle between the normal of the sample and the normal of the diffracting plane (bisecting the incident and diffracted beams).

Fig. 2. Goniometer head with a detector (a) and Bruker D8-Discover TM diffractometer used for the measurements (tube, Mn K  )

Table 3 summarizes the main parameters used for XRD measurements.

Table 3. Parameters used for XRD measurements. Parameter Value Type of Tube Mn-K-Alpha Voltage [KV] 20 Current in tube [mA] 4 Bragg’s Angle (°) 155 Wavelength [Å] 2.103

2.2. Numerical Model A thermo-mechanical numerical model was developed using Sysweld® numerical code with the aim at estimating RSs. The temperature history at each node is obtained by solving the heat flow balance equation:

æ è ç

ö ø ÷ + q(x, y, z, t ) = ρ c

¶ R y ¶ y

¶ R x ¶ x

¶ R z ¶ z

¶ T(x, y, z, t ) ¶ t

−

+

+

(3)

where the rate of heat flow per unit area is denoted by R x , R y and R z ; the current temperature is T(x,y,z,t), the rate of internal heat generation is q(x,y,z,t), c is the specific heat,  is the alloy density, and t is the time. Eq. (3) can be revised by bringing Fourier‘s heat flow as