A macro scale constitutive model for TRIP steel
H.J.M. Geijselaers†∗, E.S. Perdahcıo ˘glu‡, A.H. van den Boogaard†
†Universiteit Twente
Enschede, the Netherlands
‡M2i Materials innovation institute
Delft, the Netherlands
Keywords: TRIP, martensitic transformation, mean-field homogenization, constitutive model. ABSTRACT
The existence of different phases in the micro structure of TRIP steels is a consequence of its chemical composition and the heat treatment during production. Two main constituents are ferrite and austenite. The austenite phase (γ) can transform into stable martensite (α’) during deformation. One of the at-tractive features of these steels is the fact that with slight changes in the heat treatment and/or chemical composition, a material with significantly different mechanical properties can be obtained [1].
The aim of this study is to build a model that can be used to predict the final mechanical properties based on knowledge about the constituent phases. The model is based on the Mean-Field homogenization technique for computing the stress-strain distribution into different phases [2].
The martensitic transformation is modeled as a stress-driven process [3, 4]. The transformation depends on the stress resolved in the austenite phase and is determined as a function of the mechanical driving force supplied to the material [5, 6]. The martensitic transformation involves a diffusionless change of crystal structure. This is analyzed starting from the postulate of an invariant plane (habit plane) as interface between the martensite and the parent austenite [7]. The result is a set of 24 habit plane normalsn and corresponding shear vectors m. When a stress σ acts, while the transformation evolves, it supplies mechanical driving forceU for the transformation.
U = σγ : (m ⊗ n) = σγ: 12(m ⊗ n + n ⊗ m) (1) Hereσγis the Cauchy stress in the austenite phase. In a polycrystalline material there are always some grains optimally oriented with respect to the local stress to maximize the mechanical driving forces. When this maximum exceeds a critical valueΔGcrthe transformation will start [3].
Umax=σ
γjλj > ΔGcr (2)
where λj are the eigenvalues of the transformation deformation tensor in (1) and σγj are the eigen-values of the local austenite stress tensor, both sorted in ascending order. The eigen-values of λ are material parameters, which are based on measured data. The amount of martensite formed is a function ofUmax:
fα = fα0+ fγ0F (Umax− ΔGcr) (3)
wherefα andfγ0are the initial fractions of martensite and retained austenite. An analytical expression forF (Umax− ΔGcr) is obtained.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 200 400 600 800 1000 1200
total equivalent strain
total equivalent stress (MPa) model
experiment 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 250 500 750 1000 1250 1500
total equivalent strain
phase stress (MPa)
model experiment
fcc
bcc
Figure 1: a) Overall stress as a function of overall strain, b) Stress partitioning over the phases. The transformation plasticitydtpis calculated as [8]:
dtp= ˙fα 1 3δ1 + 3 2T sγ σvMγ (4) whereδ is the volume change, sγ andσγvM are the austenite deviatoric and Von Mises stress,T is the amount of shape change and can be calculated analytically.
In figure 1 results from the model are compared to measurements from [9].
References
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[4] H.J.M. Geijselaers, E.S. Perdahcıo˘glu, Mechanically induced martensitic transformation as a stress driven process. Scripta Materialia 60 (2009), 29–31.
[5] J.R. Patel, M. Cohen, Criterion for the action of applied stress in the martensitic transformation. Acta Metallurgica 1 (1953), 531–538.
[6] F.D. Fischer, G. Reisner, A criterion for the martensitic transformation of a micro region in an elastic-plastic material. Acta Metallurgica 46 (1998), 2095–2102.
[7] M.S. Wechsler, D.S. Lieberman, T.A. Read, On the theory of the formation of martensite. AIME Transactions Journal of Metals 197 (1953), 1503–1515.
[8] C.L. Magee, Transformation kinetics, microplasticity and aging of martensite in Fe-31Ni. Ph.D. thesis, Carnegie Institute of Technology, (1966).
[9] P.J. Jacques, Q. Furn´emont, F. Lani, T. Pardoen, F. Delannay, Multiscale mechanics of TRIP-assisted multiphase steels: I. Characterization & testing. Acta Materialia 55 (2007), 3681-3693.
