Refining constitutive relation by integration of finite element simulations and Gleeble experiments

doi:10.1016/j.jmst.2018.12.026

Abstract

Abstract:

Thermo-mechanical coupled finite element calculations were carried out to simulate the Gleeble compression of the samples of a titanium alloy (Ti60), and the results are analyzed and compared with the actual compression tests conducted on a Gleeble 3800 thermo-mechanical simulator. The changes in temperature, stress and strain distribution in the samples and the source of error on the constitutive relations from Gleeble hot compression test were analyzed in detail. Both simulations and experiments showed that the temperature distribution in the specimen is not uniform during hot compression, resulting in significant deformation inhomogeneity and non-ignorable error in the flow stress strain relation, invalidating the uniform strain assumption commonly assumed when extracting the constitutive relation from Gleeble tests. Based on the finite element simulations with iterative corrections, we propose a scheme to refine the constitutive relations from Gleeble tests.

Key words: Titanium alloy, Constitutive relation, Finite element, Compression, Temperature distribution

D.J. Yu, D.S. Xu, H. Wang, Z.B. Zhao, G.Z. Wei, R. Yang. Refining constitutive relation by integration of finite element simulations and Gleeble experiments[J]. J. Mater. Sci. Technol., 2019, 35(6): 1039-1043.

Figures/Tables 7

Table 1 Heat exchange related parameters employed in the FEM simulation.

Blackness coefficient of sample & anvils	Heat transfer coefficient between sample and air (W/m²K)	Interfacial heat transfer coefficient between sample and insulating coat (W/m²K)	Interfacial heat transfer coefficient between sample and anvils (kW/m²K)
0.75	0.002	0.02	6

Fig. 1. The stress strain curves of Ti60 under compression at different temperatures under strain rate of 1 s-1.

Fig. 2. Simulated temperature distribution (a) and experimental microstructure at the corresponding positions in (a) after Gleeble annealing at 1000°C for 10 min (b, c, d). Only one quarter of the cross section is shown in (a) to save space.

Fig. 3. Volume fractions of different phases in Ti60 as a function of temperature, obtained from thermodynamic calculation using Pandat [18].

Fig. 4. Comparison of the distribution of (a) microstructure, (b) temperature (in °C), (c) shear and (d) normal strain in the compressed Gleeble sample. The compression is done at 1000°C under strain rate of 1s-1, and to nominal strain of 0.5. Only one quarter of the cross section is shown to save some space.

Fig. 5. The stress strain curves of Ti60 under compression at 1000°C and strain rate of 1 s-1. Curve A is the direct Gleeble result, and B from FEM simulation with curve A as input. The Curve C is the corrected and D is the second FEM result with curve C as input.

Table 2 Parameters obtained in the constitutive relation after one-time correction. Q is the corrected deformation activation energy, m the modified strain rate sensitivity index, and n, o, p are modified hardening indexes, A is the modified structure factor. B, C, D and E are fitting parameters in Eq. (1).

Strain	A	m	Q	n	o	p	B	C	D	E
0-0.01	0	0.04	-12437	0	0	0	0	0	0	26.765.6
0.01-0.04	-0.0744384	0.04	-12,437	-1.267	-0.534	-3.434	62.81	-28.2	-0	-0.0736
0.04-1.00	1.41026	0.04	-12437	7.0457	2.681	2.6241	1.924	-66	64.8	0
1.00-1.40	-7.36E-02	0.04	-12437	-59.93	-2.099	-59.55	-0.092	-0	-1	0

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