Improved distortion prediction in additive manufacturing using an experimental-based stress relaxation model

doi:10.1016/j.jmst.2020.04.056

Abstract

Abstract:

In additive manufacturing (AM), numerous thermal cycles make stress relaxation a significant factor in affecting the material mechanical response. However, the traditional material constitutive model cannot describe repeated annealing behavior. Here, we propose an improved constitutive model based on a serial of stress relaxation experiments, which can descript the temperature and time-dependent stress relaxation behavior during AM. By using the proposed relaxation model, the prediction accuracy is significantly improved due to the recovery of inelastic strain during multilayer deposition. The results are validated by both in-situ and final distortion measurements. The influence mechanism of the relaxation behavior on material mechanical response is explained by the three-bar model in thermo-elastic-plastic theory. The relaxation behavior during the whole AM process is clarified. The stress behavior is found to have a limited effect when merely depositing several layers; nevertheless, it becomes a prominent impact when depositing multiple layers. The proposed model can enhance modeling accuracy both in AM and in multilayer welding.

Key words: Additive manufacturing, Welding, Thermo-mechanical modeling, Distortion prediction, Stress relaxation

Ruishan Xie, Qingyu Shi, Gaoqiang Chen. Improved distortion prediction in additive manufacturing using an experimental-based stress relaxation model[J]. J. Mater. Sci. Technol., 2020, 59: 83-91.

Figures/Tables 17

Fig. 1. Schematic of the thermal cycles during welding (a), and additive manufacturing (b).

Fig. 2. Schematic of the stress relaxation experiment: (a) the dimensions of samples, and (b) the evolution history of temperature-stress-strain during the experiment.

Fig. 3. Stress relaxation data and the fitted curves of Ti-6Al-4 V at different temperatures.

Fig. 4. (a) Ln(ε)-ln(σ) curves to obtain the values of n and A.

Table 1 Values of A and n at different temperatures.

Temperature (℃)	A	n
600	5.37 × 10^-27	6.47
700	2.13 × 10^-29	8.22
800	7.31 × 10^-23	7.16

Table 2 Temperature-dependent material parameters [25].

Temperature, T (℃)	Expansion coefficient, α(μm/(mK))	Elastic modulus, E(×10GPa)	Yield strength, σ_Y(×10²MPa)
20	8.64	10.4	7.68
93	8.82	10.0	7.35
205	9.09	9.42	6.85
250	9.20	9.18	6.65
315	9.33	8.84	6.35
425	9.55	8.26	5.86
500	9.70	7.86	5.52
540	9.70	7.65	5.34
650	9.70	7.07	4.85
760	9.70	6.49	4.35
800	9.70	4.81	3.27
900	9.70	0.6	0.57
1600	9.70	0.6	0.57

Fig. 5. Mesh of domain (a) and the moving heat source (b).

Fig. 6. (a) Experimental set-up of in situ measurement during AM, and (b) locations of the measurement points at the substrate.

Fig. 7. (a) Experimental set-up to measure the final distortion of the substrate. (b) Schematic diagram of the measurement area, and (c) locations of the measurement points at the substrate.

Fig. 8. Comparison of temperature history of two points in the substrate.

Fig. 9. Comparison of in-situ displacement of point A during manufacturing process between the experimental results and the simulation results.

Fig. 10. Final distortion distribution of the bottom of substrate (a) simulation-without relaxation model, (b) simulation-with relaxation model, (c) experiment, and (d) comparison of the final distortion along the center line.

Fig. 11. (a) Displacement history of point A (as indicated in Fig. 9) when deposing the first three layers. The longitudinal stress distribution of the substrate at selected time: (b) t = 1 s, (c) t = 6 s, (d) t = 8 s, (e) t = 9 s and (f) t = 16 s. (g) enlarged image of the selected area in Fig. 11(e).

Fig. 12. (a) Typical three-bar model. (b) Temperature history during deposition. (c) Stress evolution. (d) Inelastic strain evolution.

Fig. 13. Evolution histories of temperature (a), stress (b) and inelastic strain (c) during the first four deposition.

Fig. 14. Evolution of temperature (a) and relaxation strain (b) during the whole AM process.

Fig. 15. Temperature field when depositing (a) the 2nd layer, (b) the 20th layer and (c) the 30th layer.

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