Modelling the effect of carbon on deformation behaviour of twinning induced plasticity steels
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Abstract
In this article, a physical model describing the deformation behaviour of Twinning Induced Plasticity (TWIP) steels has been extended to include the effect of carbon content. The experimental validation and the analysis show that carbon mainly controls the maximum number of dislocations piled up at the twin boundary, resulting in the increase of backstresses (i.e. kinematic hardening) and therefore the work hardening rate. This explanation seems to be in agreement with recent TEM observations.
Keywords
Twin Boundary Stack Fault Energy Trip Steel Kinematic Hardening TWIP SteelIntroduction

compute the stacking fault energy as a function of the chemical composition,

describe the interaction between dislocation glide and deformation twinning,

predict the resulting high work hardening rate due to dynamic microstructure refinement (dynamic HallPetch effect).
In addition, it has also been shown that high manganese austenitic TWIP steels exhibit a strong Bauschinger effect (i.e. kinematic hardening) as observed by experiments by Bouaziz et al. [8] and GutierrezUrrutia et al. [9], which should be incorporated in physical models predicting work hardening behaviour [10, 11, 12]. Thus, TWIP effect can be also seen as a ‘dynamic composite’ where the volume fraction of the reinforcement (twins) increases continuously with the plastic strain [13].
The aim of the present study is to capture the effect of carbon on the work hardening rate of Fe–Mn–C TWIP steels by extending a physical model proposed previously [8]. In this purpose, the mechanical behaviours of several TWIP steels with different Mn and C contents are analysed. The Mn and C composition are selected to avoid the formation of deformation induced martensite.
Model
Results and discussion
Parameters used in the current calculation
Parameters  Physical meaning  Value 

μ  Shear modulus  65 GPa 
b  Burgers vector  2.5 × 10^{−10} m 
M  Taylor factor  3.06 
α  Mean dislocation strength  0.4 
k  Forest hardening  0.025 
f  Dynamic recovery  2.8 
λ  Mean spacing between slip bands  1266b 
F _{0}  Maximum volume fraction of Twins  0.2 
e  Twin mean thickness  30 nm 
ε _{init}  The critical strain at which twinning begins  0.03 
β  –  3 
m _{0}  –  2 
It is noted that Fe–30Mn alloy (in Fig. 3c) does not have any twins during deformation as shown by TEM (Fig. 1b). In the current model prediction, the twin volume fraction is therefore set to zero for Fe–30Mn alloy. It is worth noting that the model can predict well the stress–strain behaviour by using the same k (forest hardening) and f (dynamic recovery) value for all alloys in Fig. 3, which suggests that the chemical composition has very little effect on the forest hardening and dynamic recovery.
However, the Mn content seems to have very little effect on n _{0}, which is similar to the effect of C and Mn on the friction stress as reported in the literature [14]. It is also interesting to illustrate that n _{0} seems to increase with σ _{0} (Fig. 4b). The reason why n _{0} increases with σ _{0} could be explained as a TWIP steel with a higher σ _{0} value may exhibit stronger twins which are more effective as obstacles for dislocation movement as demonstrated by the recent TEM study [15].
Summary
The present study extends a previous physical model to include the effect of carbon content on the work hardening behaviour of a wide range of Fe–Mn–C TWIP steels. The model captures well the effect of carbon by adjusting one physical parameter n _{0} meaning that carbon mainly controls the maximum number of dislocations piled up at the twin boundary. Higher carbon content leads to more dislocations piled up at the twin boundary, resulting in higher backstresses (i.e. kinematic hardening) and therefore higher work hardening rate. This analysis seems to be in agreement with recent TEM observations [15], but future researches are required to provide more insight information to understand such a dependence.
Notes
Acknowledgements
MH gratefully acknowledges the financial support from the University Research Committee of The University of Hong Kong (Project code: 201009159012).
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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