PSI - Issue 42

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

264 6

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

In previous expressions (9), q F and q R represent the frontal and rear power density, respectively; Q W is the welding heat input estimated from the input current (I) and voltage (V) parameters (QW=  VI, with  the thermal efficiency found to be equal to 0.33); f f (= 0.6) and f r (= 1.4) denotes the fractions of heat present in the front and rear parts of the heat source, while a, b, c f and c r are Gaussian parameters of the Goldak’s heat source (1984), as described in Fig. 3 that were chosen in a way that it produces a proper molten weld pool (Chen et al., 2018). All Goldak’s heat source parameters adopted in the FE analyses have been summarized in Table 4.

y

z

v

x

c f

a

c r

b

adiabatic conditions

Fig. 3. Schematic of Goldak’s heat source shape and parameters

Table 4. Goldak’s heat source parameters used in the simulations . Welding pass Q (=VI) [W] a [mm] b [mm]

c f [mm]

c r [mm]

v [mm/sec]

1 2 3

3.5

2.2 1.8 2.5

4.5 4.0 3.0

9.0 9.0 3.0

1.66 1.93 2.22

7 8

2175

In the frame of CWM, the temperature history obtained at each node of the model is used as input load for the mechanical computation (uncoupled thermo-mechanical analysis). In this simplification, the heat generation due to plastic deformation is neglected, being much lower than the heat induced by the arc heat source. The equilibrium equations to be solved are:

ì í ï îï

σ ij + ρ b i = 0 σ ij = σ ji

(10)

where  ij and b i are the stress tensor and body forces, respectively. Moreover, the problem solving requires the formulation of the constitutive equations for the thermal elastic-plastic material as:

ì í ï îï

d σ éë ùû = D ep éë ùû d ε éë ùû − D th éë ùû dt D ep éë ùû = D e éë ùû + D p éë ùû

(11)