PSI - Issue 64

Hamid Dahaghin et al. / Procedia Structural Integrity 64 (2024) 1192–1199 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1194

3

deposited WAAM was 5 mm in width and 2 mm in height. The models consisted of two parts: the steel plate and the deposited WAAM. The simulation began with the reference pre-cracked steel plate, including the notch and pre-crack. Subsequently, double-sided WAAM deposition was added to the steel plate. To enhance computational efficiency, only half of the sample was simulated, utilizing symmetry. The FE model and mesh pattern were optimized to accurately capture stress concentrations around critical areas such as the hole, crack tip, and WAAM edge, as depicted in Fig. 2. DC3D8 elements were used for both parts to simulate thermal loading. The WAAM deposition was also modeled using the element birth technique (Michaleris & DeBiccari, 1997).

Precrack= 1

R=2.5

Crack tip

7.5

Deposited WAAM thickness= 8 mm

Plate thickness= 10

Symmetric BC about Z axis

Fig 2. The FE model of half of the steel plate with central notch repaired with deposited WAAM (all the dimensions are in mm)

The Goldak double ellipsoidal heat source, shown in Fig. 3, was applied using the DFLUX subroutine to impose heat. The heat flux distribution is described by Eq (1). Goldak parameters and deposition process parameters for Eq (1) are listed in Table 1. In Eq (1), a represents the width of the heat source; b r and b f denote the lengths of the frontal and rear ellipsoids, respectively; c indicates the depth of the heat source; f r and f r are the distribution factors for the front and rear of the heat source; and Q is the energy input.

2 2 2 r f x y z a b c 2 2 2 ,

6 3

, r f f Q

3( − + +

)

, r f q x y z ( , , )

e

=

(1)

, r f ab c  

Z

q = Heat flux

X

a

b f

b r

Y

c

Fig. 3. Double ellipsoid heat source configuration along with power distribution function (Goldak et al., 1984)

Table 1. Heat source parameters a(mm) b r (mm)

Traveling speed (mm/s)

Q(W) 1732

b f (mm)

c(mm)

f r

f f

2.5

6

2

3

1.4

0.6

10

3. Numerical results Temperature-dependent thermal and mechanical properties of the material were adopted from (Michaleris & DeBiccari, 1997). Thermal boundary conditions, including convection and radiation, were applied to the surfaces. The radiation and convection coefficients were set to 0.2 and 5.7 W/m2k, respectively, based on (Ding et al., 2011).