Constitutive equation and model validation for a 31 vol.% B4Cp/6061Al composite during hot compression

doi:10.1016/j.jmst.2018.02.001

Abstract

Abstract:

An accurate constitutive equation is essential to understanding the flow behavior of B₄C/Al composites during the hot deformation. However, the constitutive equations developed previously in literature are generally for low strain rate deformation. In the present work, we modified the general constitutive equation and take the high strain rate correction into account. The constitutive equation for a 31 vol.% B₄Cp/6061Al composite was constructed based on the flow stresses measured during isothermal hot compression at temperatures ranging from 375 to 525 °C and strain rates from 0.01 to 10 s^-1. The experimental flow stresses were corrected by considering temperature-dependent Arrhenius factor. The modified equation was then verified by using DEFORM-3D finite element analysis to simulate the experimental hot compression process. The results show that the modified equation successfully predicts flow stress, load-displacement, and the temperature rise. This helps to optimize the hot deformation process, and to obtain desirable properties, such as reduced porosity and homogenous particle distribution in B₄C/Al composites.

Key words: Composites, B₄C/Al, Constitutive equation, Hot compression, Finite element simulation

L. Zhou, C. Cui, Q.Z. Wang, C. Li, B.L. Xiao, Z.Y. Ma. Constitutive equation and model validation for a 31 vol.% B₄Cp/6061Al composite during hot compression[J]. J. Mater. Sci. Technol., 2018, 34(10): 1730-1738.

Figures/Tables 22

Fig. 1. Optical micrograph of the 31 vol.% B4Cp/6061Al composite.

Fig. 2. Schematic of the position of a hot compression specimen in the hot-rolled plate.

Fig. 3. Experimental procedure of hot compression.

Fig. 4. True stress-true strain curves of the 31 vol.% B4Cp/6061Al composite at (a) 0.1 s-1 for different temperatures and (b) 425 °C for different strain rates.

Fig. 5. Measured temperature changes of hot compressed specimens with true strain at 400 °C for different strain rates.

Fig. 6. Relationship between ln σ and 1/T at strain rate of 1 s-1.

Fig. 7. Experimental flow stresses and corrected stresses of 12 strain points at a strain rate of 1 s-1.

Fig. 8. ∫σdε and C at different temperatures.

Fig. 9. Relationship between σ and 1/T at strain rate of 10 s-1.

Fig. 10. Experimental flow stresses and corrected stresses of 12 strain points at a strain rate of 10 s-1.

Table 1 Flow stresses at a strain of 0.3 under different deformation conditions (MPa).

Strain rate (s^-1)	Temperature (°C)
Strain rate (s^-1)	375	400	425	450	475	500	525
0.01	87.73	75.84	62.31	50.38	37.94	31.46	25.39
0.1	107.83	94.38	81.36	71.30	58.72	49.60	41.79
1	129.50	115.31	105.33	91.50	80.01	71.34	65.95
10	152.83	138.42	126.74	116.09	104.97	93.37	83.13

Fig. 11. Evaluation of (a) n1 by fitting ln σ vs lnε˙, and (b) β by fitting σ vs lnε˙.

Fig. 12. Evaluation of (a) n by fitting ln[sinh(ασ)] vs lnε˙ , and (b) Q by fitting ln[sinh(ασ)] vs 1000/T.

Fig. 13. Fitting of ln Z vs ln[sinh(ασ)] for calculating ln A.

Table 2 Calculated material constants of the Arrhenius constitutive equation for the 31 vol.% B4Cp/6061Al composite.

Constant	Q (kJ/mol)	lnA	n	α (MPa^-1)
Value	177.79	27.8	5.21	0.0117

Fig. 14. Comparison between the calculated and experimental flow stress curves at (a) a strain rate of 0.1 s-1 for different temperatures and (b) 425 °C for different strain rates.

Fig. 15. Three-dimensional finite element model.

Fig. 16. Stress (σz) distribution by FEM, calculated at a temperature of 375 °C and a strain rate of 0.1 s-1, of (a) the whole model and (b) the vertical section along the compression direction.

Fig. 17. Comparison between experimental flow stress and stress (σz) calculated by FEM.

Fig. 18. Comparison between experimental and simulated force-displacement curves during hot compression, at (a) a strain rate of 0.1 s-1, and (b) a temperature of 425 °C.

Fig. 19. Distribution of temperature at a strain rate of 10 s-1 and a temperature of 375 °C, of (a) the whole model and (b) the vertical section along the compression direction.

Fig 20. Comparison of the temperature rise ΔT at a strain rate of 10 s-1, between the theoretical calculation and FEM simulation.

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Constitutive equation and model validation for a 31 vol.% B₄Cp/6061Al composite during hot compression

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