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A new method to estimate the residual stresses in additive manufacturing characterized by point heat source

  • Li Sun
  • Xiaobo Ren
  • Jianying He
  • Jim Stian Olsen
  • Sakari Pallaspuro
  • Zhiliang ZhangEmail author
ORIGINAL ARTICLE
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Abstract

Residual stress in additive manufacturing (AM) is one of the key challenges in terms of structural integrity and the finish quality of printed components. Estimating the distribution of residual stresses in additively manufactured components is complex and computationally expensive with full-scale thermo-mechanical FE analysis. In this study, a point heat source is utilized to predict the thermal field and residual stress distribution during the manufacturing processes. Numerical results show that the residual stress at a single material point can be expressed as a function of its spatial position and the peak nodal temperature it has experienced during thermal cycles. The distribution of residual stress can be divided into three segments according to the peak nodal temperature. The peak nodal temperature only depends on the heat flux and the distance to the point heat source center. A semi-analytical approach to predict the peak nodal temperature and residual stresses, once the heat flux is known, is proposed. The proposed approach is further validated by a numerical case study, and a very good agreement has been achieved. Compared with traditional thermo-mechanical FE analysis of additive manufacturing, the proposed method significantly improves the computational efficiency, showing great potential for prediction of residual stresses and distortion.

Keywords

Point heat source Residual stress Peak nodal temperature Additive manufacturing 

Nomenclature

d

Distance to point heat source center

E

Young’s modulus

q

Heat flux

a

Radius of point heat source

R

Radius of axisymmetric model

H

Height of axisymmetric model

Tp

Peak temperature the node has experienced during thermal cycles

Tm

Maximum temperature the model has experienced during thermal cycles

Tr

Room temperature

Tmel

Melting temperature

Te, 1

First critical temperature in three-segment equivalent residual stress model

Te, 2

Second critical temperature in three-segment equivalent residual stress model

T1, 1

First critical temperature in three-segment maximum principal residual stress model

T1, 2

Second critical temperature in three-segment maximum principal residual stress model

θ

The angle to heat surface

a

The coefficient of thermal expansion

εradiation

Radiation coefficient

hconvection

Convection coefficient

ε*

Inherent strain

εP

Plastic strain

εT

Thermal plastic strain

εX

Phase transformation strain

σY

Yield stress

σres

Residual stress

\( {\sigma}_e^{res} \)

Von Mises equivalent residual stress

\( {\sigma}_1^{res} \)

Maximum principal residual stress

\( {\sigma}_{e,1}^{res} \)

First critical equivalent residual stress

\( {\sigma}_{e,2}^{res} \)

Second critical equivalent residual stress

\( {\sigma}_{1,1}^{res} \)

First critical maximum principal residual stress

\( {\sigma}_{1,2}^{res} \)

Second critical maximum principal residual stress

Notes

Funding information

The Chinese Scholarship Council is greatly acknowledged for financial support. The authors wish to thank the Research Council of Norway for funding through the BIA Program, Contract No. 269558/O20.

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Copyright information

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

Authors and Affiliations

  • Li Sun
    • 1
  • Xiaobo Ren
    • 2
  • Jianying He
    • 1
  • Jim Stian Olsen
    • 1
  • Sakari Pallaspuro
    • 3
  • Zhiliang Zhang
    • 1
    Email author
  1. 1.Department of Structural EngineeringNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.SINTEF IndustryTrondheimNorway
  3. 3.Materials and Mechanical Engineering, Centre for Advanced Steels ResearchUniversity of OuluOuluFinland

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