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Residual stress prediction in selective laser melting

A critical review of simulation strategies
  • Leonardo Bertini
  • Francesco Bucchi
  • Francesco Frendo
  • Mattia Moda
  • Bernardo Disma MonelliEmail author
ORIGINAL ARTICLE
  • 65 Downloads

Abstract

This review focuses on the analysis of numerical models aimed at predicting the residual stress-strain field produced by the selective laser melting process. Our first intent is to favor an intuitive understanding of the underlying physics and then to provide an overview of the available simulation strategies specifying their field of application. In fact, given the complexity and the multi-scale nature of the process, various tailored models are needed for the assessment and prediction of defects and manufacturing issues arising during the building phase. Regarding the estimation of residual stresses, the available models were reviewed and classified on the basis of the dimensional scale of the simulated phenomena. Meso-scale models perform the detailed simulation of the scanning process, but the high computational cost currently prevents their application on the whole build volume (the current limit on the scanning volume is approximately 100 mm3 with dynamic mesh coarsening techniques). Macro-scale models have been developed to overcome this limit by introducing deep simplifications of the thermo-structural problem. From our review, it appears that meso-scale modeling has reached a significant maturity, while a widely adopted strategy for macro-scale simulations has not emerged yet.

Keywords

Additive manufacturing Powder bed fusion Multi-scale modeling Finite element simulation Residual stress Distortion 

Nomenclature

Δ

Difference operator

Vector differential operator

~

Same order of magnitude

I

Identity matrix

σ

Stefan–Boltzmann constant

Nu

Nusselt number

Fo

Fourier number

r

Position vector

t

Time

P

Beam power

v

Scanning speed

a

Laser energy absorptivity

T

Temperature

λ

Thermal conductivity

\(\mathbf {q}^{\prime \prime }\)

Heat flux density

\(q^{\prime \prime \prime }\)

Heat generation per unit volume

h

Heat transfer coefficient

L

Characteristic length

ρ

Density

µ

Dynamic viscosity

cp

Specific heat at constant pressure

ε

Emissivity of the grey body

ΔHf

Enthalpy of fusion per unit volume

ΔHv

Enthalpy of vaporization

Tsol

Solidus

Tliq

Liquidus

Tboil

Boiling point

ν

Poisson’s ratio

EDv

Volume energy density

α

Thermal diffusivity

s

Layer thickness

dt

Distance between adjacent tracks

d

Generalized beam diameter

n

Surface normal unit-vector

V

Volume

S

Surface

β

Coefficient of thermal expansion

γ

Surface tension

g

Standard acceleration due to gravity

Bi

Biot number

Ma

Marangoni number

Gr

Grashof number

σij

Cauchy stress tensor

εij

Green-Lagrangian strain tensor

u

Displacement field

\( \ddot{\mathbf{u}} \)

Acceleration field

[CT]

Thermal specific heat matrix

[KT]

Thermal conductivity matrix

[Cu]

Structural damping matrix

[Ku]

Structural stiffness matrix

[CTu]

Thermoelastic damping matrix

[KuT]

Thermoelastic stiffness matrix

{T}

Nodal temperature vector

{u}

Nodal displacement vector

{Fq}

Thermal body force vector

{Fg}

Thermal gradient force vector

{Fu}

Structural nodal loads vector

{FT}

Thermal nodal loads vector

δp

Optical penetration depth

\(q_{\text {I}}^{\prime \prime }\)

Irradiance

||·||

Euclidean norm

e

Euler’s number

τ

Precision of a normal distribution

H

Enthalpy per unit volume

D

Average diameter of powder particles

C

Compliance elastic tensor

Sy

Yield stress

t

Cauchy traction vector

Notes

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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Industrial EngineeringUniversity of PisaPisaItaly

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