PSI - Issue 56

Hanane YAAGOUBI et al. / Procedia Structural Integrity 56 (2024) 33–40

34

Structural Integrity Procedia (2023) 000 – 000

2

presented. II. Mechanical Modelling

Solving a thermal problem in the selective laser sintering of polyamide 12 has already been done in our previous articles Yaagoubi.all (2019,2020,2021,2022) , the objective in this study is to solve a mechanical problem amounts to determining the displacement field responding to equilibrium equations and the law of behavior while taking into account the different boundary conditions ,these conditions can be a constraint or an imposed displacement, The equilibrium equations of static coupled with the divergence theorem allow us to obtain Roberto.all (2021): Nomenclature SLS Selective laser sintering PA12 polyamide 12 ε e Elastic strains

ε p Inelastic strains E Young's modulus v Poisson rate FE Finite Element AM Additive Manufacturing ( ) + = 0

(1)

With: -

σ: symmetric second -order tensor of Cauchy constraints - f: vector of internal volume forces. The boundary conditions as for them, depend on the modelled case. By considering that the strains are infinitesimal, it is possible to use the assumption of additive partition to describe the constitutive laws. Thus, the tensor of the deformations follows the following equation, Roberto.all (2021) : ε = ε e + ε vp + ε p + ε th + ε pt (2) With ε e , ε vp , ε p , the elastic and inelastic strains respectively, and ε th the strain caused by volume changes due to temperature and phase changes. This can be defined using the following formula, Paolucci F.all (2020): ε th = ∆ (3) Where β is the coefficient of thermal expansion of polyamide .

Table 1. Model parameters using in COMSOL software (yaagoubi.all (2021))

Material property E Young's modulus

Value

2. 10 9 Pa

Poisson rate v

0.3

1030 kg/ m 3 1090 J/kg/K 0.28 W / m k

Density ρ

Heat capacity Cp

Thermal conductivity Ke

Power of laser P

1.8 W 130C°

Temperature Prehating T 0 Convection coefficient h

15 j/sm²k 1.2 10- 4 m

Laser radius