Numerical investigation of a novel pattern for reducing residual stress in metal additive manufacturing

doi:10.1016/j.jmst.2020.05.080

Abstract

Abstract:

Deposition patterns can significantly affect residual stress distribution in additive manufacturing processes. In this paper, a novel pattern, the S-pattern, is proposed for the metal additive manufacturing process. The finite element method is used to study the temperature field and the stress field of a cuboid structure under the S-pattern and five other representative patterns: zig-zag, raster, alternate-line, in-out spiral, and out-in spiral. The results show that the S-pattern achieves the lowest values of both equivalent residual stress and maximum principal residual stress, and the warpage of the S-pattern is close to that of counterparts. By analyzing the temperature and stress fields under all patterns, it is found that the residual stress distribution is determined by the uniformity of temperature distribution which is correlated with the peak temperatures of corners. The equivalent residual stress and the maximum principal residual stress are inversely correlated with the average peak temperature and the minimum peak temperature of corners, respectively. These correlations between temperature and residual stress provide an effective approach to evaluate the residual stress of different patterns and guide the deposition process in practice.

Key words: Additive manufacturing (AM), Deposition pattern, Temperature distribution, Residual stress, Warpage

Li Sun, Xiaobo Ren, Jianying He, Zhiliang Zhang. Numerical investigation of a novel pattern for reducing residual stress in metal additive manufacturing[J]. J. Mater. Sci. Technol., 2021, 67: 11-22.

Figures/Tables 20

Fig. 1. Representative deposition patterns: (a) Zig-zag; (b) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) Hilbert.

Fig. 2. Finite element model.

Fig. 3. Physical properties of AA2319: (a) thermal conductivity and specific heat, (b) coefficient of thermal expansion, (c) Young’s modulus and yield strength, and (d) strain-hardening [36,38].

Table 1 Parameters of the double-ellipsoid heat source.

a_f(mm)	a_r(mm)	b (mm)	c (mm)	Q (w)	f_f	f_r
4	6	5	5	5000	0.6	1.4

Table 2 Summary of AM deposition patterns.

	Zig-zag	Raster	Alternate-line	In-out spiral	Out-in spiral	Hilbert	S
Continuous	✓	✗	✗	✓	✓	✓	✓
Less pattern elements	○	✓	✓	○	○	✗	○
weave pattern	✓	✓	✓	✗	✗	✓	✓
Adjustable pass length	✗	✗	✗	✗	✗	✓	✓
Lower residual stress	✗	✗	✓	✓	✗	✓	✓
Lower warpage	✗	✗	○	✓	○	○	○

Fig. 4. The proposed deposition pattern: S pattern (a) One layer; (b) Multi-layer.

Fig. 5. S pattern in the shape made up of squares and rectangles.

Fig. 6. The transient temperature distributions of all patterns at the end of deposition process (unit: °C, the color scale of all subfigures is from 20 °C to 643 °C (liquidus temperature)), (a) Zig-zag; (b) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) S.

Fig. 7. Equivalent residual stress distribution of different deposition patterns, (top view, unit: Pa), (a) Zig-zag; (b) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) S.

Fig. 8. Maximum principal residual stress distribution of different deposition patterns, (top view, unit: Pa), (a) Zig-zag; (b) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) S.

Fig. 9. Normalized residual stress along the diagonal direction of different patterns, (a) equivalent residual stress; (b) maximum principal residual stress.

Fig. 10. Normalized maximum residual stress along the diagonal direction of different patterns, (a) equivalent residual stress (b) maximum principal residual stress.

Fig. 11. Deformation distribution of different deposition patterns (unit: mm), (a) Zig-zag; (b) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) S.

Fig. 12. Normalized warpage of different deposition patterns.

Fig. 13. Normalized maximum warpage among different deposition patterns.

Table 3 Mean and variance of deposition vector lengths for different patterns.

Patterns	Raster	Zig-zag	Alternate-line	Out-in spiral	In-out spiral	S
Mean (mm)	12	12	12	6.545	6.545	7.15
Variance	0	0	0	9.840	9.840	7.028

Fig. 14. σe distribution of the substrate before removing the constraint (bottom view, unit: Pa), (a) Zig-zag; (b) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) S.

Fig. 15. σe distribution of the substrate after removing the constraints (bottom view, unit: Pa), (a) Zig-zag; (s) Raster; (c) Alternate-line; (d) Out-in spiral; (e) In-out spiral; (f) S.

Fig. 16. Peak temperatures of the corners of different deposition patterns.

Fig. 17. (a) Average and (b) minimum peak temperatures of different deposition patterns.

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