- Email: [email protected]
The effect of alloying elements on the stacking fault energy of a TWIP steel
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Procedia Manufacturing00 (2018) 137–142 Available online atatwww.sciencedirect.com Available www.sciencedirect.com Procediaonline Manufacturing00 (2018) 137–142
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Procedia Manufacturing 22 (2018) 129–134 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
11th International Conference Interdisciplinarity in Engineering, INTER-ENG 2017, 5-6 October 11th International Conference Interdisciplinarity in Engineering, 2017, Tirgu-Mures, Romania INTER-ENG 2017, 5-6 October 2017, Tirgu-Mures, Romania
The effect of alloying elements on the stacking fault energy of a
The effectEngineering of alloying elements onConference the stacking fault energy ofJune a Manufacturing Society International 2017, MESIC 2017, 28-30 TWIP steel 2017, Vigo (Pontevedra), TWIP steel Spain a
a
b,
Hamza Essoussia, Said Ettaqia, Elhachmi Essadiqib, * Costing models for capacity optimization in Industry Hamza Essoussi , Said Ettaqi , Elhachmi Essadiqi *4.0: Trade-off Laboratory of Materials, Metallurgy and Process Engineering, ENSAM, Meknes, Morocco used capacity operational efficiency Laboratory of Materials, MetallurgyEnergy and and Process Engineering, ENSAM, Meknes, Morocco Salé, Morocco Universitébetween Internatonale de Rabat (UIR), Renewable & Advanced Materials Research (LERMA),Rabat P
P
P
P
P
P0F
P
P
P
P
P
P0F
a P
P
a
b
P
P
P
P
b P
Université Internatonale de Rabat (UIR), Renewable Energy & Advanced Materials Research (LERMA),Rabat Salé, Morocco P
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract Abstract
a
University of Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil
High manganese twinning induced plasticity steels present good mechanical properties that depend firstly on the High manganese twinning plasticity value steels of present good mechanical properties firstly by on: the stacking fault energy (SFE),induced with decreasing this energy the plasticity of these that steelsdepend is achieved (i) stackingoffault energy decreasing of this twinning, energy the(iii) plasticity of these steels is achieved : (i) gliding partial and (SFE), perfect with dislocations, (ii)value mechanical martensitic transformation. In thisbypaper gliding of partial andused perfect dislocations, (ii) mechanical twinning,temperatures (iii) martensitic transformation. In this paper one TWIP steel was in the aim to predict the SFE at different and different percentage in weight Abstract one TWIP steel was by used in the aim predict the SFE at different temperatures andproposed differentbypercentage in weight of alloying elements following thetothermodynamic modeling approach originally Olsen –Cohen. of alloying elementsPublished by "Industry following the modelingwill approach originally proposed by Olsen –Cohen. © 2018 The concept Authors. by Elsevier B.V. Under the of 4.0",thermodynamic production processes be pushed to be increasingly interconnected, © 2018 The under Authors. Published by Elsevier B.V.committee Peer-review responsibility ofthe scientific of the 11thmore International Conference Interdisciplinarity in information based on a real time basis and, necessarily, much efficient. In this context, capacity optimization © 2018 The Authors. Published by Elsevier B.V. committee of the 11th International Conference Interdisciplinarity in Peer-review under responsibility ofthe scientific Engineering. goes beyond the responsibility traditional aim of scientific capacity maximization, contributing alsoConference for organization’s profitability and value. Peer-review under of the committee of the 11th International Interdisciplinarity in Engineering. Engineering. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of Keywords: Stacking fault energy; Temperature; Alloying elements; TWIP steels. maximization. The ofTemperature; capacity optimization and TWIP costing models is an important research topic that deserves Keywords: Stacking faultstudy energy; Alloying elements; steels. contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been 1. Introduction developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted is shownmechanisms that capacity High mechanical properties of TWIP steels are closely related to the presenceand of itdifferent of optimization might hide operational inefficiency. High mechanical of TWIP steels closely related to the(SFE), presence of deformation which areproperties in first order controlled by are the stacking fault energy whileofthedifferent value ofmechanisms SFE in its turn © 2017 The Authors. Published byorder Elsevier B.V. deformation which are inelement first by the the aim stacking fault energy while value of SFE inelements its turn depends on the alloying and controlled temperature, of this paper is to(SFE), highlight the the effect of alloying Peer-review responsibility of the scientific committee theofManufacturing Society International Conference depends onunder the alloying element and temperature, the of aim paper isEngineering to exploit highlight effect of alloying elements on SFE especially at temperatures of hot forming processes inthis order to fully thethe TWIP effect. 2017. on SFE especially at temperatures of hot forming processes in order to fully exploit the TWIP effect. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction * Corresponding author. Tel.: +212-06-71-85-09-02.
* E-mail: Corresponding author. Tel.: +212-06-71-85-09-02. [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail: [email protected]
in modern production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789© 2018 The Authors. Published by Elsevier 2351-9789© 2018 The Authors. Published by Elsevier B.V.hours Peer-review responsibility ofthe scientific committee of the 11th Conference in Engineering. in several under ways: tons of production, available of International manufacturing, etc. Interdisciplinarity The management of the idle capacity Peer-review underTel.: responsibility scientific committee of741 the 11th International Conference Interdisciplinarity in Engineering. * Paulo Afonso. +351 253 ofthe 510 761; fax: +351 253 604 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 11th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2018.03.020
Hamza EssoussiProcedia et al. / Procedia Manufacturing (2018) 129–134 Hamza ESSOUSSI/ Manufacturing00 (2018)22 137–142
130 138
Nomenclature SFE ∆𝐺𝐺 𝛾𝛾/𝜀𝜀 σ ρ 𝑏𝑏�⃗
Stacking Fault Energy Change of molar Gibbs free energy due to the transformation of (CFC) austenite to (HCP) martensite Interfacial energy of the γ/ε interface Molar surface density along {111} planes Burgers vector
2. Hot stamping Generally forming processes are divided into major types: hot and cold stamping. For the last one it is reported recently in the works of S,Allain et al [1], that cold stamping has allowed to have good surface quality and good hardening of classic steels sheets , however with TWIP steel sheets it caused some defects like cracking and spring back. In order to avoid this defects hot stamping is an alternative solution that requires high temperatures that change the behavior of material by affecting the stacking fault energy which is first parameter that controls the mechanisms of deformation. Hot stamping is considered as the viable alternative solution for manufacturing several components (Front bumper, Door beam, Tunnel…) of body in white of cars [2], as it is reported in Fig.1, it is based on heating metals to austenisation temperature range, transferring the austenitized sheet from the furnace to a press, forming and simultaneously quenched. This variation of temperature involves direct and indirect effect on the stacking fault energy.
Fig. 1. Components manufactured using hot stamping [2].
3. Stacking fault energy 3.1 Stacking fault condition SFE is defined as the energy that measured thestability of hexagonal closed packed phase (phase ε) against the faced centered cubic phase (phase γ) [3], this stability is due to the diminution of free molar enthalpy of martensitic phase formation compared to austenitic phase. Generally the dissociation of perfect dislocations to partial dislocations is the first generator of stacking fault. 𝑏𝑏 → 𝑏𝑏1 + 𝑏𝑏2 𝑎𝑎 2
𝑎𝑎
(1) 𝑎𝑎
[1� 10] → [1� 21� ] + [2� 11] 6
6
(2)
Hamza Essoussi et al. / Procedia Manufacturing 22 (2018) 129–134 Hamza ESSOUSSI/ Procedia Manufacturing 00 (2018) 137–142
131 139
Fig. 2. Dissociation of perfect dislocation into partials dislocations [3].
The energy of dislocation’s line is proportional to the square of Burgers vector, therefore the dissociation according to the relationship (1) occurs if: 𝑎𝑎2 2
>
𝑎𝑎2 6
+
𝑎𝑎2
(3)
6
3.2 Stacking fault energy modeling A widely used approach to calculate an ideal SFE was proposed by Olsen and Cohen [1], which defines the required Gibbs free energy to form an intrinsic stacking fault by the movement of a single Shockley partial dislocation occurring on every second plane, a hexagonal close packed (hcp) crystalline structure is formed with thickness of two atomic layers. The core equation to calculate the SFE is: 𝑆𝑆𝑆𝑆𝑆𝑆 = 2𝜌𝜌∆𝐺𝐺 𝛾𝛾→𝜀𝜀 + 2𝜎𝜎 𝛾𝛾/𝜀𝜀
(4)
The Gibbs free energy of 𝛾𝛾 → 𝜀𝜀 phase transformation ∆𝐺𝐺 𝛾𝛾→𝜀𝜀 was intensively discussed in several works in literature like those of S, Allain and P,Dummy [1,5], and its detail expression was divided into magnetic and chemical contribution. 𝜑𝜑
𝜑𝜑
𝐺𝐺 𝜑𝜑 = 𝐺𝐺𝑐𝑐ℎ𝑖𝑖𝑖𝑖 + 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚
(5)
The chemical effect was also divided in two terms one of alloying element and the other is only for carbon effect (effect of interstitial element). 𝛾𝛾→𝜀𝜀
𝛾𝛾→𝜀𝜀
𝛾𝛾→𝜀𝜀
∆𝐺𝐺 𝛾𝛾→𝜀𝜀 = ∆𝐺𝐺𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 + 𝑥𝑥𝑐𝑐 ∆𝐺𝐺𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹/𝐶𝐶 + ∆𝐺𝐺𝑚𝑚𝑚𝑚
(6)
The details values of all expressions mentioned above are found in the literature [1,5]. The Table 1 shows the chemical composition of the TWIP steel used in this paper for SFE calculation. Table 1. Chemical composition of the tested TWIP steel [5]. Alloying elements
Mn
C
Al
Cr+Mo
Cu
Si
Nb
Wt %
28
0.08
1.6
<0.01
0
0.28
0.05
4. Results & discussions Understanding the overall variation of the SFE of TWIP steel as a function of temperature and the percentage in weight of alloying elements becomes relatively complex, since the variation of temperature from room temperature to the hot stamping temperature can change the effect of some alloying elements on the SFE.
Hamza Essoussi et al. / Procedia Manufacturing 22 (2018) 129–134 Hamza ESSOUSSI/ Procedia Manufacturing00 (2018) 137–142
132 140
4.1. Effect of temperature In Fig. 3. the SFE of TWIP steel is shown as a function of temperature together with the contributions of the individual magnetic, chemical and total terms. It can be clearly seen that the magnetic contribution to the SFE is very strong at low temperatures, whereas at temperatures above the Néel temperature of γ-phase which calculated as Tγ Néel=394.04K the magnetic contribution decreases and becomes almost negligible, so that the SFE is dominated by the chemical contribution at high temperatures. The value of SFE calculated at room temperature is 27.05 mJ/m2 it is closely the value found in the reference [5]. 150
Total SFE Chemical contribution Magnetic contribution
100
SFE [mJ/m2]
50
0
0
200
400
600
800
1000
Temperature [K]
-50
-100 Fig. 3. The predicted effect of temperature on the SFE.
4.2. Effect of alloying elements Fig. 4 shows the result when adding each alloying element to the Fe28Mn0.08C steel. Aluminium and copper increase the SFE, contrary to silicon and chromium. Silicon has a complex effect on SFE, increasing SFE for small quantities and decreasing it at high ones. However this effect changes with temperature as we will discuss in the following section. 80 70
SFE [mJ/m2]
60
Al
Cr
Cu
Si
50 40 30 20 10 0
X( Al, Cr, Cu, Si) wt% 0
1
2
3
4
5
6
7
8
Fig. 4.The predicted effect of Al, Cr, Cu and Si on the SFE of TWIP steel used at T=300K.
9
Hamza Essoussi et al. / Procedia Manufacturing 22 (2018) 129–134 Hamza ESSOUSSI/ Procedia Manufacturing 00 (2018) 137–142
133 141
4.3. Coupled effect By comparing the slopes at different temperature shown in Fig. 5 results that Aluminum increases the SFE regardless the temperature, as well as according to the Fig. 7, Copper has a constant effect that appears in parallel horizontal slopes. However Silicon and Chromium as it is shown in Fig. 6 and Fig.8 have a complex effect which is increasing slightly SFE at room temperature and decreasing it strongly at high temperatures for high percentage of their addition 300
Al (300K) Al (900K)
SFE [mJ/m2]
250
Al (600K) Al (1200K)
200 150 100 50
Al (wt%)
0
0
1
2
3
4
5
6
7
8
9
Fig. 5. Variation of the predicted effect of Aluminum on the SFE with temperature. 250
Cr (300K) Cr (900K)
SFE [mJ/m2]
200
Cr (600K) Cr (1200K)
150 100 50 0
Cr (wt%) 0
1
2
3
4
5
6
7
8
9
Fig. 6. Variation of the predicted effect of Chromium on the SFE with temperature. 250 Cu (300K) Cu (600K)
Cu (900K)
SFE [mJ/m2]
200
Cu (1200K)
150 100 50 0
Cu (wt%) 0
1
2
3
4
5
6
7
8
Fig. 7. Variation of the predicted effect of Copper on the SFE with temperature.
9
Hamza Essoussi et al. / Procedia Manufacturing (2018) 129–134 Hamza ESSOUSSI/ Procedia Manufacturing00 (2018) 22 137–142
134 142
250
Si (300K) Si (900K)
SFE [mJ/m2]
200
Si (600K) Si (1200K)
150 100 50 0
Si (wt%) 0
1
2
3
4
5
6
7
8
9
Fig. 8. Variation of the predicted effect of Silicon on the SFE with temperature.
5. Conclusion We have presented a model of the SFE that is based on the thermo chemical approach, the results are in good agreement with other author's works. as well as we reach to conclude that there is an indirect effect of temperature on the SFE, which is changing the effect of some alloying elements especially here the effect of Cr and Si . So in alloys design it is necessary to predict the temperature and composition dependence with the SFE in order to adjust the alloy’s grade to their forming process. References [1] S. Allain, J.P. Chateau, O. Bouaziz, S. Migot, N. Guelton, Correlations between the calculated stacking fault energy and the plasticity mechanisms in Fe–Mn–C alloys. Materials Science and Engineering. A 387–389 (2004) 158–162. doi:10.1016/j.msea.2004.01.059. [2] A. Naganathan, Hot stamping of manganese boron steel (technology review and preliminary finite element simulations). PhD Thesis. The Ohio State University, 2010. [3] S. Altintas, J.W. Morris Jr., Computer simulation of dislocation glide—I. Comparison with statistical theories., Acta Metall., 34 (1986) 801807. [4] S. Allain, Mechanical behavior of steels: from fundamental mechanisms to macroscopic deformation. arXiv preprint arXiv:1401.2099, 2014 [5] S. Curtze, V.T. Kuokkala, Dependence of tensile deformation behavior of TWIP steels on stacking fault energy, temperature and strain rate. Acta Materialia. 58 (2010) 5129–5141. doi:10.1016/j.actamat.2010.05.049.
ScienceDirect ScienceDirect
Procedia Manufacturing00 (2018) 137–142 Available online atatwww.sciencedirect.com Available www.sciencedirect.com Procediaonline Manufacturing00 (2018) 137–142
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 22 (2018) 129–134 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
11th International Conference Interdisciplinarity in Engineering, INTER-ENG 2017, 5-6 October 11th International Conference Interdisciplinarity in Engineering, 2017, Tirgu-Mures, Romania INTER-ENG 2017, 5-6 October 2017, Tirgu-Mures, Romania
The effect of alloying elements on the stacking fault energy of a
The effectEngineering of alloying elements onConference the stacking fault energy ofJune a Manufacturing Society International 2017, MESIC 2017, 28-30 TWIP steel 2017, Vigo (Pontevedra), TWIP steel Spain a
a
b,
Hamza Essoussia, Said Ettaqia, Elhachmi Essadiqib, * Costing models for capacity optimization in Industry Hamza Essoussi , Said Ettaqi , Elhachmi Essadiqi *4.0: Trade-off Laboratory of Materials, Metallurgy and Process Engineering, ENSAM, Meknes, Morocco used capacity operational efficiency Laboratory of Materials, MetallurgyEnergy and and Process Engineering, ENSAM, Meknes, Morocco Salé, Morocco Universitébetween Internatonale de Rabat (UIR), Renewable & Advanced Materials Research (LERMA),Rabat P
P
P
P
P
P0F
P
P
P
P
P
P0F
a P
P
a
b
P
P
P
P
b P
Université Internatonale de Rabat (UIR), Renewable Energy & Advanced Materials Research (LERMA),Rabat Salé, Morocco P
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract Abstract
a
University of Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil
High manganese twinning induced plasticity steels present good mechanical properties that depend firstly on the High manganese twinning plasticity value steels of present good mechanical properties firstly by on: the stacking fault energy (SFE),induced with decreasing this energy the plasticity of these that steelsdepend is achieved (i) stackingoffault energy decreasing of this twinning, energy the(iii) plasticity of these steels is achieved : (i) gliding partial and (SFE), perfect with dislocations, (ii)value mechanical martensitic transformation. In thisbypaper gliding of partial andused perfect dislocations, (ii) mechanical twinning,temperatures (iii) martensitic transformation. In this paper one TWIP steel was in the aim to predict the SFE at different and different percentage in weight Abstract one TWIP steel was by used in the aim predict the SFE at different temperatures andproposed differentbypercentage in weight of alloying elements following thetothermodynamic modeling approach originally Olsen –Cohen. of alloying elementsPublished by "Industry following the modelingwill approach originally proposed by Olsen –Cohen. © 2018 The concept Authors. by Elsevier B.V. Under the of 4.0",thermodynamic production processes be pushed to be increasingly interconnected, © 2018 The under Authors. Published by Elsevier B.V.committee Peer-review responsibility ofthe scientific of the 11thmore International Conference Interdisciplinarity in information based on a real time basis and, necessarily, much efficient. In this context, capacity optimization © 2018 The Authors. Published by Elsevier B.V. committee of the 11th International Conference Interdisciplinarity in Peer-review under responsibility ofthe scientific Engineering. goes beyond the responsibility traditional aim of scientific capacity maximization, contributing alsoConference for organization’s profitability and value. Peer-review under of the committee of the 11th International Interdisciplinarity in Engineering. Engineering. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of Keywords: Stacking fault energy; Temperature; Alloying elements; TWIP steels. maximization. The ofTemperature; capacity optimization and TWIP costing models is an important research topic that deserves Keywords: Stacking faultstudy energy; Alloying elements; steels. contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been 1. Introduction developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted is shownmechanisms that capacity High mechanical properties of TWIP steels are closely related to the presenceand of itdifferent of optimization might hide operational inefficiency. High mechanical of TWIP steels closely related to the(SFE), presence of deformation which areproperties in first order controlled by are the stacking fault energy whileofthedifferent value ofmechanisms SFE in its turn © 2017 The Authors. Published byorder Elsevier B.V. deformation which are inelement first by the the aim stacking fault energy while value of SFE inelements its turn depends on the alloying and controlled temperature, of this paper is to(SFE), highlight the the effect of alloying Peer-review responsibility of the scientific committee theofManufacturing Society International Conference depends onunder the alloying element and temperature, the of aim paper isEngineering to exploit highlight effect of alloying elements on SFE especially at temperatures of hot forming processes inthis order to fully thethe TWIP effect. 2017. on SFE especially at temperatures of hot forming processes in order to fully exploit the TWIP effect. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction * Corresponding author. Tel.: +212-06-71-85-09-02.
* E-mail: Corresponding author. Tel.: +212-06-71-85-09-02. [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail: [email protected]
in modern production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789© 2018 The Authors. Published by Elsevier 2351-9789© 2018 The Authors. Published by Elsevier B.V.hours Peer-review responsibility ofthe scientific committee of the 11th Conference in Engineering. in several under ways: tons of production, available of International manufacturing, etc. Interdisciplinarity The management of the idle capacity Peer-review underTel.: responsibility scientific committee of741 the 11th International Conference Interdisciplinarity in Engineering. * Paulo Afonso. +351 253 ofthe 510 761; fax: +351 253 604 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 11th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2018.03.020
Hamza EssoussiProcedia et al. / Procedia Manufacturing (2018) 129–134 Hamza ESSOUSSI/ Manufacturing00 (2018)22 137–142
130 138
Nomenclature SFE ∆𝐺𝐺 𝛾𝛾/𝜀𝜀 σ ρ 𝑏𝑏�⃗
Stacking Fault Energy Change of molar Gibbs free energy due to the transformation of (CFC) austenite to (HCP) martensite Interfacial energy of the γ/ε interface Molar surface density along {111} planes Burgers vector
2. Hot stamping Generally forming processes are divided into major types: hot and cold stamping. For the last one it is reported recently in the works of S,Allain et al [1], that cold stamping has allowed to have good surface quality and good hardening of classic steels sheets , however with TWIP steel sheets it caused some defects like cracking and spring back. In order to avoid this defects hot stamping is an alternative solution that requires high temperatures that change the behavior of material by affecting the stacking fault energy which is first parameter that controls the mechanisms of deformation. Hot stamping is considered as the viable alternative solution for manufacturing several components (Front bumper, Door beam, Tunnel…) of body in white of cars [2], as it is reported in Fig.1, it is based on heating metals to austenisation temperature range, transferring the austenitized sheet from the furnace to a press, forming and simultaneously quenched. This variation of temperature involves direct and indirect effect on the stacking fault energy.
Fig. 1. Components manufactured using hot stamping [2].
3. Stacking fault energy 3.1 Stacking fault condition SFE is defined as the energy that measured thestability of hexagonal closed packed phase (phase ε) against the faced centered cubic phase (phase γ) [3], this stability is due to the diminution of free molar enthalpy of martensitic phase formation compared to austenitic phase. Generally the dissociation of perfect dislocations to partial dislocations is the first generator of stacking fault. 𝑏𝑏 → 𝑏𝑏1 + 𝑏𝑏2 𝑎𝑎 2
𝑎𝑎
(1) 𝑎𝑎
[1� 10] → [1� 21� ] + [2� 11] 6
6
(2)
Hamza Essoussi et al. / Procedia Manufacturing 22 (2018) 129–134 Hamza ESSOUSSI/ Procedia Manufacturing 00 (2018) 137–142
131 139
Fig. 2. Dissociation of perfect dislocation into partials dislocations [3].
The energy of dislocation’s line is proportional to the square of Burgers vector, therefore the dissociation according to the relationship (1) occurs if: 𝑎𝑎2 2
>
𝑎𝑎2 6
+
𝑎𝑎2
(3)
6
3.2 Stacking fault energy modeling A widely used approach to calculate an ideal SFE was proposed by Olsen and Cohen [1], which defines the required Gibbs free energy to form an intrinsic stacking fault by the movement of a single Shockley partial dislocation occurring on every second plane, a hexagonal close packed (hcp) crystalline structure is formed with thickness of two atomic layers. The core equation to calculate the SFE is: 𝑆𝑆𝑆𝑆𝑆𝑆 = 2𝜌𝜌∆𝐺𝐺 𝛾𝛾→𝜀𝜀 + 2𝜎𝜎 𝛾𝛾/𝜀𝜀
(4)
The Gibbs free energy of 𝛾𝛾 → 𝜀𝜀 phase transformation ∆𝐺𝐺 𝛾𝛾→𝜀𝜀 was intensively discussed in several works in literature like those of S, Allain and P,Dummy [1,5], and its detail expression was divided into magnetic and chemical contribution. 𝜑𝜑
𝜑𝜑
𝐺𝐺 𝜑𝜑 = 𝐺𝐺𝑐𝑐ℎ𝑖𝑖𝑖𝑖 + 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚
(5)
The chemical effect was also divided in two terms one of alloying element and the other is only for carbon effect (effect of interstitial element). 𝛾𝛾→𝜀𝜀
𝛾𝛾→𝜀𝜀
𝛾𝛾→𝜀𝜀
∆𝐺𝐺 𝛾𝛾→𝜀𝜀 = ∆𝐺𝐺𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 + 𝑥𝑥𝑐𝑐 ∆𝐺𝐺𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹/𝐶𝐶 + ∆𝐺𝐺𝑚𝑚𝑚𝑚
(6)
The details values of all expressions mentioned above are found in the literature [1,5]. The Table 1 shows the chemical composition of the TWIP steel used in this paper for SFE calculation. Table 1. Chemical composition of the tested TWIP steel [5]. Alloying elements
Mn
C
Al
Cr+Mo
Cu
Si
Nb
Wt %
28
0.08
1.6
<0.01
0
0.28
0.05
4. Results & discussions Understanding the overall variation of the SFE of TWIP steel as a function of temperature and the percentage in weight of alloying elements becomes relatively complex, since the variation of temperature from room temperature to the hot stamping temperature can change the effect of some alloying elements on the SFE.
Hamza Essoussi et al. / Procedia Manufacturing 22 (2018) 129–134 Hamza ESSOUSSI/ Procedia Manufacturing00 (2018) 137–142
132 140
4.1. Effect of temperature In Fig. 3. the SFE of TWIP steel is shown as a function of temperature together with the contributions of the individual magnetic, chemical and total terms. It can be clearly seen that the magnetic contribution to the SFE is very strong at low temperatures, whereas at temperatures above the Néel temperature of γ-phase which calculated as Tγ Néel=394.04K the magnetic contribution decreases and becomes almost negligible, so that the SFE is dominated by the chemical contribution at high temperatures. The value of SFE calculated at room temperature is 27.05 mJ/m2 it is closely the value found in the reference [5]. 150
Total SFE Chemical contribution Magnetic contribution
100
SFE [mJ/m2]
50
0
0
200
400
600
800
1000
Temperature [K]
-50
-100 Fig. 3. The predicted effect of temperature on the SFE.
4.2. Effect of alloying elements Fig. 4 shows the result when adding each alloying element to the Fe28Mn0.08C steel. Aluminium and copper increase the SFE, contrary to silicon and chromium. Silicon has a complex effect on SFE, increasing SFE for small quantities and decreasing it at high ones. However this effect changes with temperature as we will discuss in the following section. 80 70
SFE [mJ/m2]
60
Al
Cr
Cu
Si
50 40 30 20 10 0
X( Al, Cr, Cu, Si) wt% 0
1
2
3
4
5
6
7
8
Fig. 4.The predicted effect of Al, Cr, Cu and Si on the SFE of TWIP steel used at T=300K.
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133 141
4.3. Coupled effect By comparing the slopes at different temperature shown in Fig. 5 results that Aluminum increases the SFE regardless the temperature, as well as according to the Fig. 7, Copper has a constant effect that appears in parallel horizontal slopes. However Silicon and Chromium as it is shown in Fig. 6 and Fig.8 have a complex effect which is increasing slightly SFE at room temperature and decreasing it strongly at high temperatures for high percentage of their addition 300
Al (300K) Al (900K)
SFE [mJ/m2]
250
Al (600K) Al (1200K)
200 150 100 50
Al (wt%)
0
0
1
2
3
4
5
6
7
8
9
Fig. 5. Variation of the predicted effect of Aluminum on the SFE with temperature. 250
Cr (300K) Cr (900K)
SFE [mJ/m2]
200
Cr (600K) Cr (1200K)
150 100 50 0
Cr (wt%) 0
1
2
3
4
5
6
7
8
9
Fig. 6. Variation of the predicted effect of Chromium on the SFE with temperature. 250 Cu (300K) Cu (600K)
Cu (900K)
SFE [mJ/m2]
200
Cu (1200K)
150 100 50 0
Cu (wt%) 0
1
2
3
4
5
6
7
8
Fig. 7. Variation of the predicted effect of Copper on the SFE with temperature.
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134 142
250
Si (300K) Si (900K)
SFE [mJ/m2]
200
Si (600K) Si (1200K)
150 100 50 0
Si (wt%) 0
1
2
3
4
5
6
7
8
9
Fig. 8. Variation of the predicted effect of Silicon on the SFE with temperature.
5. Conclusion We have presented a model of the SFE that is based on the thermo chemical approach, the results are in good agreement with other author's works. as well as we reach to conclude that there is an indirect effect of temperature on the SFE, which is changing the effect of some alloying elements especially here the effect of Cr and Si . So in alloys design it is necessary to predict the temperature and composition dependence with the SFE in order to adjust the alloy’s grade to their forming process. References [1] S. Allain, J.P. Chateau, O. Bouaziz, S. Migot, N. Guelton, Correlations between the calculated stacking fault energy and the plasticity mechanisms in Fe–Mn–C alloys. Materials Science and Engineering. A 387–389 (2004) 158–162. doi:10.1016/j.msea.2004.01.059. [2] A. Naganathan, Hot stamping of manganese boron steel (technology review and preliminary finite element simulations). PhD Thesis. The Ohio State University, 2010. [3] S. Altintas, J.W. Morris Jr., Computer simulation of dislocation glide—I. Comparison with statistical theories., Acta Metall., 34 (1986) 801807. [4] S. Allain, Mechanical behavior of steels: from fundamental mechanisms to macroscopic deformation. arXiv preprint arXiv:1401.2099, 2014 [5] S. Curtze, V.T. Kuokkala, Dependence of tensile deformation behavior of TWIP steels on stacking fault energy, temperature and strain rate. Acta Materialia. 58 (2010) 5129–5141. doi:10.1016/j.actamat.2010.05.049.