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

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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.

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Abbreviations

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

T p :

Peak temperature the node has experienced during thermal cycles

T m :

Maximum temperature the model has experienced during thermal cycles

T r :

Room temperature

T mel :

Melting temperature

T e, 1 :

First critical temperature in three-segment equivalent residual stress model

T e, 2 :

Second critical temperature in three-segment equivalent residual stress model

T 1, 1 :

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

T 1, 2 :

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

θ :

The angle to heat surface

a :

The coefficient of thermal expansion

ε radiation :

Radiation coefficient

h convection :

Convection coefficient

ε * :

Inherent strain

ε P :

Plastic strain

ε T :

Thermal plastic strain

ε X :

Phase transformation strain

σ Y :

Yield stress

σ res :

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

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Funding

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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Authors and Affiliations

  1. Department of Structural Engineering, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Li Sun, Jianying He, Jim Stian Olsen & Zhiliang Zhang

  2. SINTEF Industry, 7456, Trondheim, Norway

    Xiaobo Ren

  3. Materials and Mechanical Engineering, Centre for Advanced Steels Research, University of Oulu, 90570, Oulu, Finland

    Sakari Pallaspuro

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  1. Li Sun
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  2. Xiaobo Ren
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Correspondence to Zhiliang Zhang.

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Sun, L., Ren, X., He, J. et al. A new method to estimate the residual stresses in additive manufacturing characterized by point heat source. Int J Adv Manuf Technol 105, 2415–2429 (2019). https://doi.org/10.1007/s00170-019-04443-1

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