A hot tearing criterion based on solidification microstructure in cast alloys

doi:10.1016/j.jmst.2021.06.071

Abstract

Abstract:

A criterion based on solidification microstructure was proposed to precisely predict the hot tearing behavior of cast alloys, which takes into account the effects of both mechanical and nonmechanical factors. This criterion focuses on the events occurring at the grain boundary, which are determined by the thermal contraction, solidification shrinkage, grain growing and liquid feeding. This criterion responds to a series of factors that affect hot tearing, such as alloy composition, mold design, casting process and microstructure. Its credibility has been validated by studying the hot tearing behavior of Mg-Ce alloys. In conformity with the experimental results, this criterion predicted decrease in the number of rods occurring hot tearing with increasing cerium content. A simplified criterion was derived and validated by Mg-Ce (equiaxed grain) and Mg-Al (columnar grain) alloy systems, which is suitable for the case where the eutectic liquid fraction is low and the liquid feeding can be ignored. In addition, a hot tearing index for equiaxed grains was proposed, that is, $|\text{d}T/\text{d}\left( f_{s}^{1/3} \right)|$ near ${{\left( {{f}_{\text{s}}} \right)}^{1/3}}=1$, and its prediction results were consistent with the hot tearing susceptibility calculated from the experimental results.

Key words: Hot tearing, Microstructure, Magnesium alloys, Casting, Criterion

Bo Hu, Zixin Li, Dejiang Li, Tao Ying, Xiaoqin Zeng, Wenjiang Ding. A hot tearing criterion based on solidification microstructure in cast alloys[J]. J. Mater. Sci. Technol., 2022, 105: 68-80.

Figures/Tables 19

Fig. 1. Casting for evaluating the HTS of each alloy.

Fig. 2. (a) Hot spots at different locations; longitudinal cross-section of the (b) rods, (c) columnar grains and (d) equiaxed grains.

Fig. 3. (a) Transverse cross-section of grains; (b) differential control volume Ω (longitudinal cross-section) at grain boundary.

Fig. 4. (a) Solidification paths, (b) densities, (c) linear expansion coefficients and (d) liquid viscosities of Mg-Ce alloys.

Table 1. Parameters used for calculation applying this hot tearing criterion.

Parameters	c	dT/dt (K/s)	g (kg m/s²)	P₀ (Pa)	γ (N/m)
Values	4.6	15	9.8	101,300	0.09

Fig. 5. OM images of (a) Mg-0.5Ce, (b) Mg-1.0Ce, (c) Mg-1.5Ce, (d) Mg-2.0Ce, (e) Mg-3.0Ce and (f) Mg-4.0Ce.

Table 2. Grain size of each alloy.

Ce content (wt.%)	0.5	1.0	1.5	2.0	3.0	4.0
Grain size, d (μm)	964 ± 102	451 ± 53	272 ± 41	128 ± 19	386 ± 35	412 ± 46

Fig. 6. The occurrence of hot tearing in the (a) Mg-0.5Ce, (b) Mg-1.0Ce, (c) Mg-1.5Ce, (d) Mg-2.0Ce, (e) Mg-3.0Ce and (f) Mg-4.0Ce alloys predicted by this criterion.

Fig. 7. Cracks and fractures in the castings of Mg-Ce alloys.

Fig. 8. Volumetric contraction force-temperature-time curves of the (a) Mg-0.5Ce, (b) Mg-1.0Ce, (c) Mg-1.5Ce, (d) Mg-2.0Ce, (e) Mg-3.0Ce and (f) Mg-4.0Ce alloys.

Table 3. The prediction and experimental results of hot tear cracks and solid fractions.

Alloys	Rods predicted	Rods observed	f_s predicted	f_s recorded
Mg-0.5Ce	1/2/3/4	1/2/3/4	0.96/0.95/0.94/0.93	0.93
Mg-1.0Ce	1/2/3/4	1/2/3/4	0.95/0.93/0.91/0.90	0.87
Mg-1.5Ce	2/3/4	2/3/4	0.91/0.89/0.88	0.87
Mg-2.0Ce	2/3/4	2/3/4	0.89/0.87/0.85	0.83
Mg-3.0Ce	3/4	3/4	0.85/0.84	0.81
Mg-4.0Ce	No	No	No	No

Fig. 9. The ratio values of thermal contraction rate (Vc), solidification shrinkage rate (Vs), grain growing rate (Vg), and liquid feeding rate (Vf) to grain size (d) when occurring hot tearing in (a) Mg-0.5Ce, (b) Mg-1.0Ce, (c) Mg-1.5Ce, (d) Mg-2.0Ce and (e) Mg-3.0Ce alloys.

Fig. 10. The occurrence of hot tearing in (a) Mg-0.5Ce, (b) Mg-1.0Ce, (c) Mg-1.5Ce, (d) Mg-2.0Ce, (e) Mg-3.0Ce and (f) Mg-4.0Ce predicted by the simplified criterion.

Table 4. The results predicted by the comprehensive criterion and the simplified criterion (Rcc and fcc are the rod and solid fraction predicted by the comprehensive criterion, Rsc and fsc are the rod and solid fraction predicted by the simplified criterion, Fel is the eutectic liquid fraction).

Alloys	R_cc	R_sc	f_cc	f_sc	F_el
Mg-0.5Ce	1/2/3/4	1/2/3/4	0.96/0.95/0.94/0.93	0.96/0.95/0.94/0.93	2.3%
Mg-1.0Ce	1/2/3/4	1/2/3/4	0.95/0.93/0.91/0.90	0.95/0.92/0.91/0.90	4.7%
Mg-1.5Ce	2/3/4	2/3/4	0.91/0.89/0.88	0.90/0.88/0.87	7.2%
Mg-2.0Ce	2/3/4	2/3/4	0.89/0.87/0.85	0.88/0.86/0.85	9.6%
Mg-3.0Ce	3/4	2/3/4	0.85/0.84	0.85/0.82/0.80	14.5%
Mg-4.0Ce	No	3/4	No	0.79/0.77	19.4%

Fig. 11. OM images of (a) Mg-1.0Al, (b) Mg-1.5Al, (c) Mg-2.0Al and (d) Mg-3.0Al.

Fig. 12. (a) The solidification path of Mg-Al alloy system calculated by Pandat using back diffusion model with a cooling rate of 15 K/s. The occurrence of hot tearing in (b) Mg-1.0Al, (c) Mg-1.5Al, (d) Mg-2.0Al and (e) Mg-3.0Al predicted by the simplified criterion. Volumetric contraction force-temperature-time curves of the (f) Mg-1.0Al, (g) Mg-1.5Al, (h) Mg-2.0Al and (i) Mg-3.0Al.

Fig. 13. Cracks and fractures in the castings of Mg-Al alloys [15].

Table 5. The prediction and experimental results of hot tear cracks and solid fractions.

Alloys	Rods predicted	Rods observed	f_s predicted	f_s recorded
Mg-1.0Al	2/3/4	2/3/4	0.99/0.99/0.98	0.98
Mg-1.5Al	2/3/4	2/3/4	0.99/0.98/0.97	0.97
Mg-2.0Al	2/3/4	2/3/4	0.99/0.97/0.96	0.95
Mg-3.0Al	2/3/4	2/3/4	0.98/0.96/0.95	0.92

Fig. 14. (a) Temperature T vs (fs)1/3 for Mg-Ce alloys; (b) hot tearing index for Mg-Ce alloys; (c) comparison plots of hot tearing index with the hot tearing susceptibility.

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