Scholarly article on topic 'Stress-strain Response for Twinning-induced Plasticity Steel with Temperature'

Stress-strain Response for Twinning-induced Plasticity Steel with Temperature Academic research paper on "Materials engineering"

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Procedia Engineering
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{"TWIP steels" / "Dislocation-based model" / "Strain hardening" / Temperature}

Abstract of research paper on Materials engineering, author of scientific article — Fei Liu, Weigang Zhang, Wenjiao Dan

Abstract This paper presents a physical computational model to study the influence of temperature on the strain hardening of Twinning-induced Plasticity (TWIP) steel in tensile loading with the dislocation and twinning formulation. In this model, the evolution of microstructure can be considered as the result of the competition between the rate of production and annihilation of dislocation controlled by temperature. The model is confirmed by the experimental data from Curtze et al. (Acta Materialia 58, 5129–5141, 2010). The stress-strain curve, hardening rate, strain hardening exponent are verified by the experimental data. The dislocation density and twinning volume fraction are calculated to predict the influence of temperature on the strain hardening of TWIP steel.

Academic research paper on topic "Stress-strain Response for Twinning-induced Plasticity Steel with Temperature"

Procedía Engineering

www.elsevier.com/locate/procedia

11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014,

Nagoya Congress Center, Nagoya, Japan

Stress-strain response for twinning-induced plasticity steel with

temperature

Fei Liu, Weigang Zhang, Wenjiao Dan*

Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China

Abstract

This paper presents a physical computational model to study the influence of temperature on the strain hardening of Twinning-induced Plasticity (TWIP) steel in tensile loading with the dislocation and twinning formulation. In this model, the evolution of microstructure can be considered as the result of the competition between the rate of production and annihilation of dislocation controlled by temperature. The model is confirmed by the experimental data from Curtze et al. (Acta Materialia 58, 5129-5141, 2010). The stress-strain curve, hardening rate, strain hardening exponent are verified by the experimental data. The dislocation density and twinning volume fraction are calculated to predict the influence of temperature on the strain hardening of TWIP steel.

© 2014 The Authors.PublishedbyElsevier Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University Keywords: TWIP steels; Dislocation-based model; Strain hardening; Temperature

1. Introduction

Twinning-induced plasticity (TWIP) steels have an extraordinary combination of ductility and strength simultaneously due to austenite twinning in plastic deformation process. These desirable properties satisfy the design requirements of modern automobiles with energy economy, environmental protection and personal safety.

The investigations have shown that the deformation temperature is essential to survey the reliability of the mechanical properties of TWIP steels. The flow stress and work-hardening decreased as the deformation

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Procedia Engineering 81 (2014) 1330- 1335

* Corresponding author. Tel.: +86-21- 34203084; fax: +86-21- 34203084. E-mail address: : wjdan@sjtu.edu.cn

1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi:10.1016/j.proeng.2014.10.152

temperature increasing (Curtze et al., 2010, Hokka et al., 2006, Jung et al. 2013 and Koyama et al., 2011). The modulus anomaly changed due to the spontaneous volume magnetostriction during the paramagnetic to antiferromagnetic transition below the Neel temperature (Jung et al., 2012). The mechanical parameters (i.e., yield strength, ultimate tensile strength, uniform elongation and total elongation) decreased as the deformation temperature increasing (Jung et al. 2013). Those results were related to the dislocation glide over obstacles by thermally assisted (Allain et al., 2002, Allain et al., 2010, Barbier et al., 2012, Dancette et al., 2012, Kim et al., 2010, Prakash et al., 2008 and Shiekhelsouk et al. 2009). The stacking fault energy was also temperature dependent (Tsuchida et al. 20011), as was the deformation twinning kinetics (Remy, 1978). Temperature changes also influenced the dynamic strain aging (Lee et al., 2011). The experimental results also found the twins became less with deformation temperature rising (Zhang et al., 2011) and revealed the dependence of deformation twinning on grain orientation at all test temperatures (Fang et al., 2011).

In this paper, a physical model is proposed to study the temperature effect on the strain hardening of TWIP steel in tensile loading based on the dislocation formulation with austenite twinning, where the evolution of microstructure results from the competition between the rate of accumulation and annihilation of dislocation controlled by the temperature. The stress-strain curve, hardening rate, strain hardening exponent are verified by the experimental data.

Nomenclature

a material constant

b Burgers vector

d grain size

e twinning thickness

£ effective strain of material

fo material constant

f J tw volume fraction of twins

G shear modulus

Y effective shear strain

Yg shear strain by dislocation gliding

h twinning shear strain

P dislocation density

k material constant

m material parameter

M Taylor factor

n material constant

T ambient temperature

T m referent temperature

^0 yield stress

2. Dislocation-based model

To take into account the twinning contribution to the total plastic shear strain, a mixture law expressed as follows has been used (Remy 1978):

dy = {\ - f * )drg + YAft*, (1)

_ . . . . ..... J2 . . .

where y is the effective shear strain, yg is the shear strain by dislocation gliding, yt = ~ is the twinning shear

strain, f w is the volume fraction of twins.

The stress response of TWIP steels is assumed to obey the classical relation between flow stress and the total dislocation density (Allain et al., 2002):

a = a0 + aMGbfp , (2)

where <t0 is the yield stress of material, (X is material constant, M is Taylor factor. G , b and p are shear modulus, Burgers vector and dislocation density, respectively.

With the Mecking-Kocks theory (Mecking et al., 1981), the evolution of single phase can be considered as the result of the competition between the production rate and annihilation rate of dislocation, and the annihilation rate of dislocation is supposed to be influenced the ambient temperature. It can be described as:

_ _ _|__¿Jw_

~d 2e(l - fw )"

kJp- f0 •

where d the grain size, e is the twinning thickness, k is a material constant, f and n are material constant, T

is the ambient temperature, Tm is the referent temperature.

The Taylor factor links the cumulative shear strain to the macroscopic tensile deformation as follows y = Ms , (4)

where £ is the effective strain of material.

With the assumption of Olson and Cohen's assumption (1974), the relationship between the twinning volume fraction and the macroscopic tensile deformation can be defined as

dfw - fw )md£ , (5)

where m is material parameter. From equations above, the evolution of the dislocation density is expressed as follows

f mM (1 - fw

M (1 - fw )

+^ ({"' f \+kj~p d 2e l1 - fw )

3. Materials

Two TWIP steel grades were used in the paper and its chemical compositions are presented in Tab. 1 (Curtze et al. 2010), in which the content of Mn in TWIP steels is 28% and 25%. The mechanical behaviour of the tested TWIP steels with different temperature in tensile loading are shown in Tab.2, in which the yield strength, ultimate tensile strength, uniform elongation and total elongation of materials are related to deformation temperature. The parameters for the new model in section 2 are shown in Tab.3.

Table 1. Chemical compositions of the tested TWIP steels.

Material Mn(%) Al(%) Si(%) C(%) Cr+Mo(%) Nb(%) Fe(%)

TWIP1 28 1.6 0.28 0.08 <0.01 <0.001 Bal.

TWIP2 25 1.6 0.24 0.08 <0.01 0.05 Bal.

Table 2. Mechanical behaviors of the tested TWIP steels in tensile loading.

Temperature YS(MPa) TWIP1 UTS(MPa) UE(%) TE(%) YS(MPa) TWIP2 UTS(MPa) UE(%) TE(%)

223K 409 552 29 32 471.5 723.5 49 54

248K 383 550 60 68 421.5 674.5 59 71

298K 325 495 48 64 375.5 538 50 61

YS: yield strength, UTS: ultimate tensile strength, UE: uniform elongation, TE: total elongation.

4. Results and discussions

The stress-strain responses of TWIP1 and TWIP2 are calculated with the new model and compared with experimental data from Fig. 1 to Fig. 3, where stress-strain curve, hardening rate and strain hardening exponent are

shown in Fig.2, Fig.3 and Fig.4 respectively. The ambient temperature in tensile deformation is 223K, 248K and 298K.

Table 3. Parameters for model.

T n fo m k ^0 M a d e b G

unit K -- -- -- -- MPa -- -- /um nm /um GPa

223 2.50 1.80 0.025 409

TWIP1 248 0.82 1.40 0.015 370

298 223 -0.25 0.70 1.00 0.80 1.60 0.012 0.023 325 480 3.00 0.30 30 30 0.3 72

TWIP2 248 298 0.82 0.55 1.40 1.00 0.02 0.0115 420 375

TWIP1 Exp. Cal. 223K ■ — 248K o 298K *

Exp. Cal.

223K ■ -

248K o —

298K *

0.2 0.3

Strain

(a) TWIPl

0.0 0.1 0.2 0.3 0.4 0.5

Strain

(b) TWIP2

Fig. 1 Stress-strain curve comparison at different temperatures.

3000-,

Exp. Cal.

223K ■ —

248K o —

298K *

^ 2000-

"CD 1500-□J

~ 1000-

CD "Ö

<5 500 H

Exp. Cal.

223K ■ —

248K o —

298K *

Strain

(a) TWIPl

0.2 0.3

Strain

(b) TWIP2

Fig.2 Hardening rate comparison at different temperatures.

The results in Fig. 1 show that the stress is lower with the ambient temperature raising. And the elongation of TWIP steel at 248K is better than 223K and 298K. The results in Fig. 2(a) show that hardening rate at 223 K is the highest at begin and decreases rapidly with strain increasing, the hardening rate of TWIP1 at 248 K is highest in large deformation process. However, the results in Fig. 2(b) indicate that the hardening rate decreases as forming temperature up. According to TRIP1, the strain hardening exponent with 248 K is highest and that with 223 K is lowest (in Fig.3(a)). But for the TWIP2, the material has the lowest strain hardening exponent at 298K. The results show that the stress response of TWIP steels is depended on the forming temperature, and its work-hardening is related to the microstructure evolution, i.e., twinning, dislocation and phase transformation, controlled by Stacking fault energy influenced by temperature, chemical compositions.

-i-1—c

Exp. Cal.

223K ■ —

248K o —

298K -*-

Strain

(a) TWIP1

0.2 0.3

Strain

(b) TWIP2

Fig.3 Strain hardening exponent comparison at different temperatures

223 K ■

248 K o

298K V;

Strain

(a) TWIP1

Fig.4 Dislocation density evolution at different temperatures.

Strain

(b) TWIP2

C 0.50 O

5 0 40

<1) 0.35

O 0.25

0.10 0.05 0.00

m 223K

O 248K

ft 298K

005 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Strain

(a) TWIP1

0.00 0.05 0.10 0.15 0,20 0,25 0.30 0.35 0,40 0.45 0.50

Strain

(b) TWIP2

Fig.5 Twinning volume fraction at different temperatures.

The dislocation density and twinning volume fraction in plastic process are evaluated with ambient temperature 223K, 248K and 298K (in Figs.4 and 5). The results show that the dislocation density in TWIP2 is higher than that of TWIP1 at same temperature and the dislocation density increases as temperature decreasing expect that of TWIP1 at 223K (in Fig. 4). The twinning volume fraction increases with temperature decreasing (Zhang et al. 2011, Fang et al. 2011) (in Fig. 5). At that time, twinning in the early stages of deformation leads to decreasing elongation values with temperature decreasing, although more twins are formed during plastic deformation in lower temperature (Grassel et al., 2000). Both the uniform and total elongations show maximum values at a certain temperature, below and above which the elongation values decrease. Then, the SFE is lowered into the region where twinning as a deformation mechanism becomes energetically favoured over dislocation motion (Curtze et al., 2010).

5. Conclusions

A dislocation-based physical model is proposed to study the influence of temperature on the strain hardening of TWIP steels in tensile loading, in which the evolution of microstructure results from the competition between the rate of accumulation and annihilation of dislocation controlled by the temperature. The model is evaluated by the experimental data from two fully austenitic high manganese TWIP steels. The strain hardening behaviour is analyzed and verified by the experimental data. The dislocation density and twinning volume fraction are calculated to predict the influence of temperature on the strain hardening of TWIP steels. The results show that the stress response of TWIP steels is depended on the forming temperature, and its work-hardening is related to the microstructure evolution.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.51275296, No. 51375307, No. 51222505and No. 51075266).

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