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On the interaction between transformation induced plasticity and the austenitic stainless steel anisotropy (AISI 304) under shear loading path
Materials and Design 32 (2011) 3765–3771
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
On the interaction between transformation induced plasticity and the austenitic stainless steel anisotropy (AISI 304) under shear loading path Zied Ktari a, Zoubeir Tourki a,b,⇑, Habib Sidhom a, Med Amene Gahbiche c a
Laboratoire de Mécanique, Matériaux et Procédés (LMMP), Ecole Supérieure des Sciences et Techniques de Tunis, 5, Av Taha Hussein, 1008 Tunis, Tunisia Ecole Nationale d’Ingénieurs de Sousse, Technopole de Sousse, Tunisia c Laboratoire Génie Mécanique (LGM), Ecole Nationale d’Ingénieurs de Monastir, Rue Ibn Aljazzar, 5000 Monastir, Tunisia b
a r t i c l e
i n f o
Article history: Received 6 January 2011 Accepted 18 March 2011 Available online 22 March 2011 Keywords: Microstructure X-ray analysis Plastic behavior
a b s t r a c t It is well known that for the AISI 304 austenitic stainless steel some parameters such as temperature, strain rate, material anisotropy and loading path are the main factors which strongly affect the kinetic of transformation induced plasticity (TRIP) in this material. In literature, tensile and compression tests represent the commonly experimental tools studied on this material. Under such type of loading, dissymmetry plastic behavior was obtained due to the martensitic kinetic evolution. The aim of the present work is to highlight the role of the TRIP phenomenon on the initial material anisotropy of the AISI 304 material using appropriate experimental framework. The cross-coupled effect of the phase transformation on initial anisotropy is studied through special loading test (simple shear test (SST)) conducted at various temperatures. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In automotive industry, the association of the strength and the excellent formability of steels remain an increasing need for economical reasons. Combining these properties, plastic instability may not occur without large deformations. During the forming process when the austenitic stainless steel (AISI 304) is subjected to specific load conditions at low temperature a new martensitic phase is formed. It is well known that under these conditions process forming a combination of new properties lead to high ductility and good tensile strength [1–7]. This transformation induced plasticity phenomenon called TRIP effect is attributed to the progressive transformation phase from the metastable fcc austenite (c) to the new variant bcc martensite (a0 ). Mangonon and Thomas [8] showed that the sequence of the martensitic transformation in the austenitic stainless steel AISI 304, is generally produced as follows: Austenite c ? martensite e ? martensite a0 . On the other hand, it has been established that the temperature, the strain rate, the loading path and the material anisotropy are the most current factors which strongly affect the martensitic transformation kinetics [5–7]. Many microstructure studies were carried out to elucidate the martensitic transformation mechanisms and ⇑ Corresponding author at: Laboratoire de Mécanique, Matériaux et Procédés (LMMP), Ecole Supérieure des Sciences et Techniques de Tunis, 5, Av Taha Hussein, 1008 Tunis, Tunisia. Tel.: +216 73 369 501; fax: +216 73 220 470. E-mail addresses: [email protected] (Z. Ktari), [email protected], [email protected] (Z. Tourki), [email protected] (M.A. Gahbiche). 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2011.03.043
to find the appropriate models describing the kinetics of this process. Many authors [1,2,6,9,10] have established the evolution of the martensitic volume fraction in monotonic tensile and compression test. They have showed that the amount of the martensite is more developed with decreasing of the temperature and/or increasing of plastic deformation. Alternatively, Powell et al. [11] and Kubler et al. [12] were interested to identify the effect of the loading path on the martensitic transformation kinetics. They have showed that the martensitic volume fraction is more important in tensile load than that in compression or torsion test and the hardening rate is also modified. Stringfellow et al. [10] have generalized the Olson and Cohen model [5] by introducing the stress state effect. The effect of nonproportional loading during tensile–torsion tests on austenitic stainless has been carried out by Calloch and Marquis [13] and Calloch et al. [14]. Gallee et al. [15] have expected that the hardening levels in cyclic tensile–torsion may be twice higher than that in tensile–compression loading. Moreover, Olson and Cohen [5] have deduced that the transformation could be emphasized by strong values of the three-dimensional stress state. This fact was also observed by Jacques et al. [16] on a general TRIP steels during tensile test. Okutani et al. [17] carried out various experimental tests (uniaxial tension, compression, equibiaxial compression and deep drawing) on a 304 austenitic stainless steel at room temperature. They have reported that the martensite volume fraction increases with hydrostatic stress pressure under uniaxial tension. However, these authors have found that martensitic volume fraction is higher for compression test than that for tensile test. Lebedev and
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Kosarchuk [4] have studied the influence of the stress state on the martensitic transformation kinetics for two types of stainless steel (steel A: 16.4%Cr, 9.6%Ni and steel B: 15.4%Cr, 12.3%Ni). The steel B was subjected to compression and torsion tests and leads to more production of martensite a0 volume fraction in tension test compared to torsion and compression one. However, more important e martensite variants in torsion test was obtained which rapidly vanishes, where a0 particles nucleation take place under high plastic deformation level. The aim of the present work is to highlight the effect of the plastic strain-induced martensitic phase (TRIP effect) on the initial material anisotropy for a shear loading experiment. Studies have been carried on AISI 304 austenitic stainless steel at various temperatures subjected to a large deformation in order to enhance the martensite phase production [1]. 2. Experimental procedure A stainless steel X4CrNi18-9 (AISI 304) with chemical composition shown in Table 1 was used for this study. The material is supplied as a thin cold rolled sheet with 1 mm thick. The nuance AISI 304 is considered as austenitic metastable phase. Specimens were cut from 1 mm thick laminated sheet by a laser cutting process along three anisotropic directions: rolling direction (RD), direction at 45° (D45) and transverse direction (TD). This process is useful since it allows a precise cut and avoids stress concentration and providing a high range of homogenous strains. Along the adopted three directions (RD, D45 and TD) tensile tests performed by Ktari et al. [3] at room temperature have shown that the material exhibits stress anisotropy behavior. The average anisotropy coefficient r ¼ ðr 0 þ r 90 þ 2r 45 Þ=4 which characterizes the normal anisotropy have been introduced by Gahbiche [18] and given in Table 2, whereas the more significant measured anisotropic coefficient is given by Dr ¼ ðr 0 þ r 90 2r45 Þ=2. To identify the material behavior, it is convenient to obtain more information on the materials response under various strain states and temperatures. Thus, two loading paths were adopted: plane strain test (PST) and simple shear test (SST). In the present work only the SST experimental data will be discussed. The shape and dimensions of the sample are presented in Fig. 1. The sample contains two shearing areas, where the maximum of shear strain will occur. Low temperature experiments were conducted at room temperature 23 °C, in ice to obtain 0 °C, in salt–ice mixture for 10 °C, in dry ice for 40 °C and finally in liquid nitrogen to obtain the lowest temperature value 196 °C. The low temperatures coupled with an additional mechanical loading promote the transformation of austenitic into martensite which is enhanced by the low nickel proportion (less than 12%, see Table 1). For each loading path a specific experimental set-up device is used (Figs. 2a–c). A specific thermal enclosure (see Fig. 2d) has been designed and manufactured for these experiments. This enclosure will contain the mechanical set-up device and the cryogenic environment. Plane strain and shear test were applied in a universal tensile machine of maximum capacity of 300 kN. For simple shear tests a cross-head of 4 mm/mn is imposed leading to a nominal strain rate _ 0 of almost 20.2 103 mm s1, where b0 = 3.3 mm is the of c_ ¼ d=b width of the shearing zone (see Fig. 2a). Natural shear strain as well as the Cauchy stress are used in the present work. The specimens
Table 2 Values of anisotropy coefficients of the AISI 304 obtained at room temperature. r0
r45
r90
r
Dr
a^
^ b
1.24
0.99
1.2
1.1
0.23
2
2.6
were maintained for 20 min in the thermal chamber before test in order to homogenize the sample temperature. Tests were performed using a specific device carried out by Gahbiche [18]. As it is shown in Fig. 2a, the symmetry of the device makes it useful for the two stretching directions. This device was then settled on the testing machine and instrumented by the adjunction of an extensometer to measure the local displacement d of shear zone in the sample (see Fig. 2b). In addition, the volume fraction of both phases (a0 -martensite and c-austenite) was measured by X-ray diffraction method applied on the surface fractured of specimen. 3. Results and discussion Fig. 3 shows a typical deformed sample at 196 °C along the direction D45 which represents the final shape of the shear zone (dash-points). We note that the shear deformation is stopped when the cross-head of the tensile machine reaches a predetermined deformation level ranging between 0% and 100%. This is to avoid the deformation of the used specimen at the lips area. Fig. 4a–c present the experimental true stress–strain curves (s–c) in the RD, D45 and TD directions respectively at the different temperatures used in this study i.e., from 23 to 196 °C. It should be noted that for the three orthotropic directions the stress level increases with decreasing temperature especially for the RD and TD directions. This result is in agreement with the general martensitic transformation behavior of the stainless steel material as reported by Bargui et al. [1] for the uniaxial loading. We also showed from these figures that for all curve the total elongation in shear test is close to each other. This phenomenon has well been interpreted by Olson and Cohen [5] as a result of the induced transformed phase in a certain proportion with a given transformation rate. However, at 40 °C and in RD and TD direction the stress level presents the highest value at strain between 8% and 30% compared to the stress curves obtained for the other temperatures. This behavior observed for all orthotropic directions can be attributed to the saturation phenomenon of the new martensite particles in relation with the shear bands produced in this loading path. In addition, it is important to note that for all orthotropic directions the effect of temperature seems to start only at 0 °C. At lower temperatures, however all curves become closely to each other. Such tendency is more significant in the D45 and RD directions as seen in
Table 1 Chemical composition of AISI 304 stainless steel. AISI 304
Chemical composition
Elements Wt.%
Cr 18.3
Ni 9.2
C 0.04
Mn 1.5
Si 0.5
Mo 0.18
Fig. 1. The used specimen geometry in the simple shear test (units: mm).
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(a)
(b)
Extensometer l δ b
(c)
Specimen
(d)
Fig. 2. Experimental apparatus used for the Simple Shear Test (SST). (a) Kinematics of the SST device, (b) the SST device with the extensometer settled in tensile machine, (c) specimen inserted into the SST device, and (d) thermal enclosure inserted in the tensile machine.
Fig. 4a and b. Moreover, these figures clearly indicate a change of the yield stress with temperature in the three orthotropic directions. Hence, we can deduce that the stress–strain behavior of the used material changes substantially when the deformation increases for the three orthotropic directions. This is an expected result that will be discussed in the following paragraph. Fig. 5a–e present the experimental s–c curves along RD, D45 and TD at 23 °C, 0 °C, 10 °C, 40 °C and 196 °C respectively. They show a clearly decrease of stress anisotropy especially for low temperatures (i.e., the discrepancy between the three curves is reduced gradually as the temperature decreases). Moreover, the maximum stress level reached in the three orthotropic directions changes from 600 MPa at 23 °C (Fig. 5a) to around 800 MPa at the others temperatures. It can also be seen from Fig. 5b–d that at D45 direction, the work-hardening is slightly more important than the ones obtained in the RD and DT directions for the negative range of temperatures except for 40 °C. Under 20% strain, this
Fig. 3. Deformed sample after simple shear test along direction D45 at 196 °C.
behavior depends strongly on temperature test and no generalization can yet be confirmed. Furthermore, the s–c curves have reversed position along the RD and TD directions at each temperature jump as shown in Fig. 5a–d. This behavior is repeated until temperature reaches 196 °C, where all curves become superposed. The dependence of stress–strain curves on temperature as well as on orthotropic direction becomes very strong over a large strain and the saturation of the martensite volume fraction. Indeed, Fig. 5a–e clearly show that the stress–strain curves become much closer as the temperature decreases. At temperature of 196 °C the three orthotropic directions give almost the same stress–strain curves (see Fig. 5e). On the other hand, from the microstructural point of view, it is well known that the martensitic transformation which is produced by the slip in individual grains has a strong effect on the grain size and shape [19]. According to the elastic accommodation, the grain boundaries movements promotes the generation of the internal stress at the interface and this process intensifies with strain in initial stage of plastic deformation [20]. Reaching a given temperature and strain levels, the grain boundaries have no effect on the process which is responsible for energy storage. This phenomenon may explain the reversible behavior observed between RD and TD at low temperature. Wiera et al. [20] have reported that the storage of the rate energy is caused not only by the rise of dislocation density but also by the increase of stress at grain boundaries. The increase of stress results from the increase of the additional storage energy below a certain threshold. In fact, the increase of the internal stress should stimulate the slip in new systems which act as a dislocation activity in these systems. This effect is called elastic accommodation [21]. Hence, the rate of energy dissipation increases. We believe that part of such energy is converted into heat while the rest is needed for the self energy dislocation. As a result, the rate of storage energy ceases to increase when reaching its maximum value.
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Fig. 4. s–c curves at various temperatures (from 23 °C until 196 °C) along; (a) RD, (b) D45 and (c) TD.
Since the grain size is quite sensitive to strain-induced transformation the mechanical characteristics and the texture of material induced by transformation are strongly affected by the loading path and temperatures changes caused by the irreversible work. Consequently, the observed neutralizing effect of anisotropy at low temperatures (Fig. 5e) could be attributed to the change of the grain’s shape which in turn affects the crystallographic texture. To confirm such tendency, microscopic analyses have been achieved in this study and the results are given in Fig. 6. We identify many shear band intersections acting as preferential nucleation sites for a0 embryos. These bands may represent an obstacle to slip systems and they favor the a0 particles growth. They also contribute to the change of the grain size at the onset of necking. According to the interaction between strain-induced martensite and initial anisotropy newly found it may be considered that the initial anisotropic effect of the AISI 304 stainless steel tends to be inhibited. In addition, this crystallographic texture reorientation can be interpreted as a consequence of the new martensite particles nucleation which grows rapidly and homogenizes the material structure (see Fig. 6). This microstructure disorientation could be responsible for the inhibition of the initial anisotropy produced by the TRIP phenomenon. For the next we will discuss the kinetics of the strain-induced transformation relative to the transverse direction (DT). Fig. 7 shows the X-ray diffraction patterns of the deformed DT sample at the temperature range between 196 °C and 23 °C. From the constant ratio of the two phases observed in this figure, we distinguish clearly the volume fraction distribution of each phase (austenite and martensite). The dashed points represent the new martensitic phase and the residual austenitic phase distributions. The solid line shows the theoretical volume fraction distribution of the martensitic phase as a function of temperature. The
measurements are obtained with an error of ±5%. During the experimental treatment the texture effect has not been considered. This assumption has been taken into account since the Xray analysis results show that all the studied specimens have the same texture. We note that the global volume fraction of the induced phase is in agreement with macroscopic results obtained through the stress–strain behavior for all temperatures values. 4. Equations for TRIP modeling Based on our experimental results, the orthotropic quadratic Hill’s model should be used taking into account the microstructure evolution according to the continued martensitic transformation progress. This criterion takes into account the initial anisotropy of the studied material and can be written for the plane stress case along the principal axes of the orthotropic referential as follows:
f ðrÞ ¼ req ðrÞ rs ðeÞ
ð1Þ
where f is the yield surface, r is the Cauchy plane stress tensor given in the orthotropic axes and rs ðeÞ is the hardening law which will be identified to the shear stress sðcÞ. In plastic behavior, the stress tensor is described according to Voigt notation as follows:
2
3
r11 7 r¼6 4 r22 5 s
ð2Þ
The establishment of the identification procedure which have been conducted according to the obtained experimental results in shear stress loading can be expressed by the following equations:
Z. Ktari et al. / Materials and Design 32 (2011) 3765–3771
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Fig. 5. s–c curves according to directions RD, D45 and DT at the following temperatures: (a) 23 °C, (b) 0 °C, (c) 10 °C, (d) 40 °C and (e) 196 °C.
req ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð1 þ 2rÞ s and 1 þ r
epeq ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð1 þ r Þ c 1 þ 2r
ð3Þ
where s ¼ FS ¼ leF ¼ l0Fe0 and c ¼ bd0 is the shear stress and strain and d is the local displacement given by the extensometer. Olson and Cohen have established a model (OC model) for strain-induced martensitic transformation kinetics in which the intersection of the shear band in the austenite phase was considered to be the dominant mechanism of strain-induced transformation. They have developed a physical model which can also predict the effect of temperature in the strain-induced martensitic transformation. Under constant temperature and strain rate the law of the kinetics of the volume fraction of martensite is written as follows:
fa0 ¼ 1 expfb½1 expðaepeq Þn g
ð4Þ
where a is the rate of shear bands formation depending on stacking faults energy, b is the probability that an intersection of shear band will nucleate a martensite embryo, n is a geometrical constant equal to 4,5 and epeq represents the equivalent plastic strain as described by Eq. (3). This law is established based only on uniaxial tests (e.g. tensile and compression experiments). In order to predict the kinetics of the martensite volume fraction under various loading path (shear test (ST) and plane strain test (PS)), a and b parameters of Eq. (4) are determined and expressed in Eq. (5), taking into account the initial anisotropy of material AISI 304 via the average anisotropy coefficient r .
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tigated in order to express the effect of the kinetic of martensitic volume fraction transformation in an austenitic stainless steel on the initial material anisotropy. The study leads to the following conclusions:
Fig. 6. SEM micrograph taken from AISI 304 specimen at room temperature at failure in uniaxial tensile test.
(1) For all the orthotropic directions the strengthening increases when temperature goes down. (2) In the shear loading path the effect of temperature becomes more significant starting from 0 °C. Furthermore, an increasing of the hardening and high ductility of the material has been identified when the temperature decreases. Therefore, it is advisable to consider this phenomenon as a consequence of the TRIP effect in the modeling of the austenitic stainless steel. (3) A microstructure observations provide an illustration of the new a0 -martensite particle nucleation. The growth of these particles plays an important role on the initial austenitic grain size changes which is in good accordance with the interaction results between the martensitic transformation and the textural reorientation. (4) Based on the measure of the volume fraction of the new martensite phase in the SST loading path, the proposed model is able to describe the TRIP effect in the numerical approach. (5) By coupling anisotropy stress with the generation of the new martensite phase the initial material anisotropy may be inhibited especially when temperature decreases.
References
Fig. 7. X-ray diffraction of the residual austenite and martensite volume fraction measured on a fractured specimen as a function of absolute temperature. In solid line, the proposed model (Eq. (5)) giving the theoretical martensitic volume fraction.
8 a^ ðxþ1Þ ^ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > < aðT; x; rÞ ¼ AðTÞ þ a 3 1þx2 2xr =ð1þr Þ ^ bðxþ1Þ > ^ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi : bðT; x; rÞ ¼ CðTÞ þ b 2 3
ð5Þ
1þx 2xr =ð1þrÞ
where A and C are the temperature-dependent parameters (see Ref. ^ are constants given in Table 2 and ^ and b [7] for more details), a x ¼ rII =rI represents the principal stress ratio. The Eq. (5) shows the anisotropic-dependent parameters that must be updated during the strain process. This model is represented in Fig. 6 which shows a good correlation between the volume fraction of martensite obtained from the X-ray diffraction method and from the proposed model. In this work, an original identification procedure has been conducted on the fraction martensitic evolution according to the shear loading path which has not been detailed in the present paper. This work is in going and will appear in the near future. 5. Conclusion Simple shear tests carried on the AISI 304 stainless steel and according to three anisotropic directions (RD, D45 and TD) at temperatures ranging from room temperature to 196 °C were inves-
[1] Bargui H, Sidhom H, Tourki Z. Martensite induite: incidence sur le comportement en écrouissage et sur la limite de formage de l’acier inoxydable AISI 304. Matériaux Tech 2000;11–12:31–41. [2] Iwamoto T, Tsuta T, Tomita Y. Investigation on deformation mode dependence of strain-induced martensitic transformation in TRIP steels and modelling of transformation kinetics. Int J Mech Sci 1998;40(2–3):173–82. [3] Ktari Z, Tourki Z, Sidhom H, Gahbiche A. Identification de la transformation martensitique induite par déformation plastique dans le cas de la déformation plane: expérience et validation numérique. 2ème CMSM 2007. Tunisia: Monastir; 2007. [4] Lebedev A, Kosarchuk V. Influence of phase transformations on the mechanical properties of austenitic stainless steel. Int J Plast 2000;16:749–67. [5] Olson GB, Cohen M. Kinetics of strain-induced martensitic nucleation. Metall Trans A 1975;6A:791–5. [6] Tourki Z, Bargui H, Sidhom H. The kinetic of induced martensitic formation and its effect on forming limit curves in AISI 304 stainless steel. J Mater Process Technol 2003;00:330–6. [7] Tourki Z, Sidhom H, Cherkaoui M. Plastic strain induced martensitic in type 304 austenitic stainless steel: modeling and numerical simulation of deep drawing processes. Int J Forming Process 2005;8(2–3):201–26. [8] Mangonon PL, Thomas G. The martensite phases in 304 stainless steel. Metall Trans 1970;A1:1577–86. [9] Angel T. Formation of martensite in austenitic stainless steels. J Iron Steel Inst 1954;00:165–74. [10] Stringfellow RG, Parks DM, Olson GB. A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels. Acta Metall Mater 1992;40(7):1703–16. [11] Powell GW, Marshall ER, Backofen WA. Strain hardening of austenitic stainless steel. ASM Trans Q 1958;50:478–9. [12] Kubler R, Berveiller M, Buessler P. Modélisation du comportement des aciers à effet TRIP par une approche simplifiée. In: 16ème Congrès Français de Mécanique Nice; 1–5 septembre, 2003. [13] Calloch S, Marquis D. Additional hardening due to tension–torsion nonproportional loadings: influence of the loading path shape. In: Kalluri S, Bonacuse PJ, editors. Multiaxial fatigue and deformation testing techniques, ASTM STP 1280. American Society for Testing and Materials; 1997. pp. 113–30. [14] Portier L, Calloch S, Marquis D, Geyer P. Ratchetting under tension–torsion loadinds: experiments and modelling. Int J Plast 2000;16:303–35. [15] Gallee S, Manach PY, Thuillier S. Mechanical behavior of a metastable austenitic stainless steel under simple and complex loading paths. Mater Sci Eng A 2007;466:47–55. [16] Jacques P, Furmemont Q, Pardoen T, Delannay F. On the role of martensitic transformation on damage and cracking resistance in trip-assisted multiphase steels. Acta Mater 2001;49:139–52.
Z. Ktari et al. / Materials and Design 32 (2011) 3765–3771 [17] Okutani T, Yukawa N, Ishikawa K, Jinma T. The strain-induced martensitic transformation of SUS304 under various stress states. In: Proceedings of the Japanese society and technical plasticity’95 spring; 1995. pp. 331–2. [18] Gahbiche A. Caractérisation expérimentale des tôles d’emboutissage, application à l’identification des lois de comportement, Thèse de Doctorat, LGM/ENIM Tunisia; 2006. [19] Ping H, Huang P, Lopez HF. Strain induced e-martensite in Co–Cr–Mo alloy: grain size effects. Mater Lett 1999;39:244–8.
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[20] Weira O, Andrzej K, Maciej WG. Mode of deformation and the rate of energy storage during uniaxial tensile deformation of austenitic steel. Mater Sci Eng 1996;A220:123–8. [21] Korbel A, Bochniak W. The structure based design of metal forming operations. J Mater Process Technol 1995;53:229–37.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
On the interaction between transformation induced plasticity and the austenitic stainless steel anisotropy (AISI 304) under shear loading path Zied Ktari a, Zoubeir Tourki a,b,⇑, Habib Sidhom a, Med Amene Gahbiche c a
Laboratoire de Mécanique, Matériaux et Procédés (LMMP), Ecole Supérieure des Sciences et Techniques de Tunis, 5, Av Taha Hussein, 1008 Tunis, Tunisia Ecole Nationale d’Ingénieurs de Sousse, Technopole de Sousse, Tunisia c Laboratoire Génie Mécanique (LGM), Ecole Nationale d’Ingénieurs de Monastir, Rue Ibn Aljazzar, 5000 Monastir, Tunisia b
a r t i c l e
i n f o
Article history: Received 6 January 2011 Accepted 18 March 2011 Available online 22 March 2011 Keywords: Microstructure X-ray analysis Plastic behavior
a b s t r a c t It is well known that for the AISI 304 austenitic stainless steel some parameters such as temperature, strain rate, material anisotropy and loading path are the main factors which strongly affect the kinetic of transformation induced plasticity (TRIP) in this material. In literature, tensile and compression tests represent the commonly experimental tools studied on this material. Under such type of loading, dissymmetry plastic behavior was obtained due to the martensitic kinetic evolution. The aim of the present work is to highlight the role of the TRIP phenomenon on the initial material anisotropy of the AISI 304 material using appropriate experimental framework. The cross-coupled effect of the phase transformation on initial anisotropy is studied through special loading test (simple shear test (SST)) conducted at various temperatures. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In automotive industry, the association of the strength and the excellent formability of steels remain an increasing need for economical reasons. Combining these properties, plastic instability may not occur without large deformations. During the forming process when the austenitic stainless steel (AISI 304) is subjected to specific load conditions at low temperature a new martensitic phase is formed. It is well known that under these conditions process forming a combination of new properties lead to high ductility and good tensile strength [1–7]. This transformation induced plasticity phenomenon called TRIP effect is attributed to the progressive transformation phase from the metastable fcc austenite (c) to the new variant bcc martensite (a0 ). Mangonon and Thomas [8] showed that the sequence of the martensitic transformation in the austenitic stainless steel AISI 304, is generally produced as follows: Austenite c ? martensite e ? martensite a0 . On the other hand, it has been established that the temperature, the strain rate, the loading path and the material anisotropy are the most current factors which strongly affect the martensitic transformation kinetics [5–7]. Many microstructure studies were carried out to elucidate the martensitic transformation mechanisms and ⇑ Corresponding author at: Laboratoire de Mécanique, Matériaux et Procédés (LMMP), Ecole Supérieure des Sciences et Techniques de Tunis, 5, Av Taha Hussein, 1008 Tunis, Tunisia. Tel.: +216 73 369 501; fax: +216 73 220 470. E-mail addresses: [email protected] (Z. Ktari), [email protected], [email protected] (Z. Tourki), [email protected] (M.A. Gahbiche). 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2011.03.043
to find the appropriate models describing the kinetics of this process. Many authors [1,2,6,9,10] have established the evolution of the martensitic volume fraction in monotonic tensile and compression test. They have showed that the amount of the martensite is more developed with decreasing of the temperature and/or increasing of plastic deformation. Alternatively, Powell et al. [11] and Kubler et al. [12] were interested to identify the effect of the loading path on the martensitic transformation kinetics. They have showed that the martensitic volume fraction is more important in tensile load than that in compression or torsion test and the hardening rate is also modified. Stringfellow et al. [10] have generalized the Olson and Cohen model [5] by introducing the stress state effect. The effect of nonproportional loading during tensile–torsion tests on austenitic stainless has been carried out by Calloch and Marquis [13] and Calloch et al. [14]. Gallee et al. [15] have expected that the hardening levels in cyclic tensile–torsion may be twice higher than that in tensile–compression loading. Moreover, Olson and Cohen [5] have deduced that the transformation could be emphasized by strong values of the three-dimensional stress state. This fact was also observed by Jacques et al. [16] on a general TRIP steels during tensile test. Okutani et al. [17] carried out various experimental tests (uniaxial tension, compression, equibiaxial compression and deep drawing) on a 304 austenitic stainless steel at room temperature. They have reported that the martensite volume fraction increases with hydrostatic stress pressure under uniaxial tension. However, these authors have found that martensitic volume fraction is higher for compression test than that for tensile test. Lebedev and
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Kosarchuk [4] have studied the influence of the stress state on the martensitic transformation kinetics for two types of stainless steel (steel A: 16.4%Cr, 9.6%Ni and steel B: 15.4%Cr, 12.3%Ni). The steel B was subjected to compression and torsion tests and leads to more production of martensite a0 volume fraction in tension test compared to torsion and compression one. However, more important e martensite variants in torsion test was obtained which rapidly vanishes, where a0 particles nucleation take place under high plastic deformation level. The aim of the present work is to highlight the effect of the plastic strain-induced martensitic phase (TRIP effect) on the initial material anisotropy for a shear loading experiment. Studies have been carried on AISI 304 austenitic stainless steel at various temperatures subjected to a large deformation in order to enhance the martensite phase production [1]. 2. Experimental procedure A stainless steel X4CrNi18-9 (AISI 304) with chemical composition shown in Table 1 was used for this study. The material is supplied as a thin cold rolled sheet with 1 mm thick. The nuance AISI 304 is considered as austenitic metastable phase. Specimens were cut from 1 mm thick laminated sheet by a laser cutting process along three anisotropic directions: rolling direction (RD), direction at 45° (D45) and transverse direction (TD). This process is useful since it allows a precise cut and avoids stress concentration and providing a high range of homogenous strains. Along the adopted three directions (RD, D45 and TD) tensile tests performed by Ktari et al. [3] at room temperature have shown that the material exhibits stress anisotropy behavior. The average anisotropy coefficient r ¼ ðr 0 þ r 90 þ 2r 45 Þ=4 which characterizes the normal anisotropy have been introduced by Gahbiche [18] and given in Table 2, whereas the more significant measured anisotropic coefficient is given by Dr ¼ ðr 0 þ r 90 2r45 Þ=2. To identify the material behavior, it is convenient to obtain more information on the materials response under various strain states and temperatures. Thus, two loading paths were adopted: plane strain test (PST) and simple shear test (SST). In the present work only the SST experimental data will be discussed. The shape and dimensions of the sample are presented in Fig. 1. The sample contains two shearing areas, where the maximum of shear strain will occur. Low temperature experiments were conducted at room temperature 23 °C, in ice to obtain 0 °C, in salt–ice mixture for 10 °C, in dry ice for 40 °C and finally in liquid nitrogen to obtain the lowest temperature value 196 °C. The low temperatures coupled with an additional mechanical loading promote the transformation of austenitic into martensite which is enhanced by the low nickel proportion (less than 12%, see Table 1). For each loading path a specific experimental set-up device is used (Figs. 2a–c). A specific thermal enclosure (see Fig. 2d) has been designed and manufactured for these experiments. This enclosure will contain the mechanical set-up device and the cryogenic environment. Plane strain and shear test were applied in a universal tensile machine of maximum capacity of 300 kN. For simple shear tests a cross-head of 4 mm/mn is imposed leading to a nominal strain rate _ 0 of almost 20.2 103 mm s1, where b0 = 3.3 mm is the of c_ ¼ d=b width of the shearing zone (see Fig. 2a). Natural shear strain as well as the Cauchy stress are used in the present work. The specimens
Table 2 Values of anisotropy coefficients of the AISI 304 obtained at room temperature. r0
r45
r90
r
Dr
a^
^ b
1.24
0.99
1.2
1.1
0.23
2
2.6
were maintained for 20 min in the thermal chamber before test in order to homogenize the sample temperature. Tests were performed using a specific device carried out by Gahbiche [18]. As it is shown in Fig. 2a, the symmetry of the device makes it useful for the two stretching directions. This device was then settled on the testing machine and instrumented by the adjunction of an extensometer to measure the local displacement d of shear zone in the sample (see Fig. 2b). In addition, the volume fraction of both phases (a0 -martensite and c-austenite) was measured by X-ray diffraction method applied on the surface fractured of specimen. 3. Results and discussion Fig. 3 shows a typical deformed sample at 196 °C along the direction D45 which represents the final shape of the shear zone (dash-points). We note that the shear deformation is stopped when the cross-head of the tensile machine reaches a predetermined deformation level ranging between 0% and 100%. This is to avoid the deformation of the used specimen at the lips area. Fig. 4a–c present the experimental true stress–strain curves (s–c) in the RD, D45 and TD directions respectively at the different temperatures used in this study i.e., from 23 to 196 °C. It should be noted that for the three orthotropic directions the stress level increases with decreasing temperature especially for the RD and TD directions. This result is in agreement with the general martensitic transformation behavior of the stainless steel material as reported by Bargui et al. [1] for the uniaxial loading. We also showed from these figures that for all curve the total elongation in shear test is close to each other. This phenomenon has well been interpreted by Olson and Cohen [5] as a result of the induced transformed phase in a certain proportion with a given transformation rate. However, at 40 °C and in RD and TD direction the stress level presents the highest value at strain between 8% and 30% compared to the stress curves obtained for the other temperatures. This behavior observed for all orthotropic directions can be attributed to the saturation phenomenon of the new martensite particles in relation with the shear bands produced in this loading path. In addition, it is important to note that for all orthotropic directions the effect of temperature seems to start only at 0 °C. At lower temperatures, however all curves become closely to each other. Such tendency is more significant in the D45 and RD directions as seen in
Table 1 Chemical composition of AISI 304 stainless steel. AISI 304
Chemical composition
Elements Wt.%
Cr 18.3
Ni 9.2
C 0.04
Mn 1.5
Si 0.5
Mo 0.18
Fig. 1. The used specimen geometry in the simple shear test (units: mm).
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(a)
(b)
Extensometer l δ b
(c)
Specimen
(d)
Fig. 2. Experimental apparatus used for the Simple Shear Test (SST). (a) Kinematics of the SST device, (b) the SST device with the extensometer settled in tensile machine, (c) specimen inserted into the SST device, and (d) thermal enclosure inserted in the tensile machine.
Fig. 4a and b. Moreover, these figures clearly indicate a change of the yield stress with temperature in the three orthotropic directions. Hence, we can deduce that the stress–strain behavior of the used material changes substantially when the deformation increases for the three orthotropic directions. This is an expected result that will be discussed in the following paragraph. Fig. 5a–e present the experimental s–c curves along RD, D45 and TD at 23 °C, 0 °C, 10 °C, 40 °C and 196 °C respectively. They show a clearly decrease of stress anisotropy especially for low temperatures (i.e., the discrepancy between the three curves is reduced gradually as the temperature decreases). Moreover, the maximum stress level reached in the three orthotropic directions changes from 600 MPa at 23 °C (Fig. 5a) to around 800 MPa at the others temperatures. It can also be seen from Fig. 5b–d that at D45 direction, the work-hardening is slightly more important than the ones obtained in the RD and DT directions for the negative range of temperatures except for 40 °C. Under 20% strain, this
Fig. 3. Deformed sample after simple shear test along direction D45 at 196 °C.
behavior depends strongly on temperature test and no generalization can yet be confirmed. Furthermore, the s–c curves have reversed position along the RD and TD directions at each temperature jump as shown in Fig. 5a–d. This behavior is repeated until temperature reaches 196 °C, where all curves become superposed. The dependence of stress–strain curves on temperature as well as on orthotropic direction becomes very strong over a large strain and the saturation of the martensite volume fraction. Indeed, Fig. 5a–e clearly show that the stress–strain curves become much closer as the temperature decreases. At temperature of 196 °C the three orthotropic directions give almost the same stress–strain curves (see Fig. 5e). On the other hand, from the microstructural point of view, it is well known that the martensitic transformation which is produced by the slip in individual grains has a strong effect on the grain size and shape [19]. According to the elastic accommodation, the grain boundaries movements promotes the generation of the internal stress at the interface and this process intensifies with strain in initial stage of plastic deformation [20]. Reaching a given temperature and strain levels, the grain boundaries have no effect on the process which is responsible for energy storage. This phenomenon may explain the reversible behavior observed between RD and TD at low temperature. Wiera et al. [20] have reported that the storage of the rate energy is caused not only by the rise of dislocation density but also by the increase of stress at grain boundaries. The increase of stress results from the increase of the additional storage energy below a certain threshold. In fact, the increase of the internal stress should stimulate the slip in new systems which act as a dislocation activity in these systems. This effect is called elastic accommodation [21]. Hence, the rate of energy dissipation increases. We believe that part of such energy is converted into heat while the rest is needed for the self energy dislocation. As a result, the rate of storage energy ceases to increase when reaching its maximum value.
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Fig. 4. s–c curves at various temperatures (from 23 °C until 196 °C) along; (a) RD, (b) D45 and (c) TD.
Since the grain size is quite sensitive to strain-induced transformation the mechanical characteristics and the texture of material induced by transformation are strongly affected by the loading path and temperatures changes caused by the irreversible work. Consequently, the observed neutralizing effect of anisotropy at low temperatures (Fig. 5e) could be attributed to the change of the grain’s shape which in turn affects the crystallographic texture. To confirm such tendency, microscopic analyses have been achieved in this study and the results are given in Fig. 6. We identify many shear band intersections acting as preferential nucleation sites for a0 embryos. These bands may represent an obstacle to slip systems and they favor the a0 particles growth. They also contribute to the change of the grain size at the onset of necking. According to the interaction between strain-induced martensite and initial anisotropy newly found it may be considered that the initial anisotropic effect of the AISI 304 stainless steel tends to be inhibited. In addition, this crystallographic texture reorientation can be interpreted as a consequence of the new martensite particles nucleation which grows rapidly and homogenizes the material structure (see Fig. 6). This microstructure disorientation could be responsible for the inhibition of the initial anisotropy produced by the TRIP phenomenon. For the next we will discuss the kinetics of the strain-induced transformation relative to the transverse direction (DT). Fig. 7 shows the X-ray diffraction patterns of the deformed DT sample at the temperature range between 196 °C and 23 °C. From the constant ratio of the two phases observed in this figure, we distinguish clearly the volume fraction distribution of each phase (austenite and martensite). The dashed points represent the new martensitic phase and the residual austenitic phase distributions. The solid line shows the theoretical volume fraction distribution of the martensitic phase as a function of temperature. The
measurements are obtained with an error of ±5%. During the experimental treatment the texture effect has not been considered. This assumption has been taken into account since the Xray analysis results show that all the studied specimens have the same texture. We note that the global volume fraction of the induced phase is in agreement with macroscopic results obtained through the stress–strain behavior for all temperatures values. 4. Equations for TRIP modeling Based on our experimental results, the orthotropic quadratic Hill’s model should be used taking into account the microstructure evolution according to the continued martensitic transformation progress. This criterion takes into account the initial anisotropy of the studied material and can be written for the plane stress case along the principal axes of the orthotropic referential as follows:
f ðrÞ ¼ req ðrÞ rs ðeÞ
ð1Þ
where f is the yield surface, r is the Cauchy plane stress tensor given in the orthotropic axes and rs ðeÞ is the hardening law which will be identified to the shear stress sðcÞ. In plastic behavior, the stress tensor is described according to Voigt notation as follows:
2
3
r11 7 r¼6 4 r22 5 s
ð2Þ
The establishment of the identification procedure which have been conducted according to the obtained experimental results in shear stress loading can be expressed by the following equations:
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Fig. 5. s–c curves according to directions RD, D45 and DT at the following temperatures: (a) 23 °C, (b) 0 °C, (c) 10 °C, (d) 40 °C and (e) 196 °C.
req ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð1 þ 2rÞ s and 1 þ r
epeq ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð1 þ r Þ c 1 þ 2r
ð3Þ
where s ¼ FS ¼ leF ¼ l0Fe0 and c ¼ bd0 is the shear stress and strain and d is the local displacement given by the extensometer. Olson and Cohen have established a model (OC model) for strain-induced martensitic transformation kinetics in which the intersection of the shear band in the austenite phase was considered to be the dominant mechanism of strain-induced transformation. They have developed a physical model which can also predict the effect of temperature in the strain-induced martensitic transformation. Under constant temperature and strain rate the law of the kinetics of the volume fraction of martensite is written as follows:
fa0 ¼ 1 expfb½1 expðaepeq Þn g
ð4Þ
where a is the rate of shear bands formation depending on stacking faults energy, b is the probability that an intersection of shear band will nucleate a martensite embryo, n is a geometrical constant equal to 4,5 and epeq represents the equivalent plastic strain as described by Eq. (3). This law is established based only on uniaxial tests (e.g. tensile and compression experiments). In order to predict the kinetics of the martensite volume fraction under various loading path (shear test (ST) and plane strain test (PS)), a and b parameters of Eq. (4) are determined and expressed in Eq. (5), taking into account the initial anisotropy of material AISI 304 via the average anisotropy coefficient r .
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tigated in order to express the effect of the kinetic of martensitic volume fraction transformation in an austenitic stainless steel on the initial material anisotropy. The study leads to the following conclusions:
Fig. 6. SEM micrograph taken from AISI 304 specimen at room temperature at failure in uniaxial tensile test.
(1) For all the orthotropic directions the strengthening increases when temperature goes down. (2) In the shear loading path the effect of temperature becomes more significant starting from 0 °C. Furthermore, an increasing of the hardening and high ductility of the material has been identified when the temperature decreases. Therefore, it is advisable to consider this phenomenon as a consequence of the TRIP effect in the modeling of the austenitic stainless steel. (3) A microstructure observations provide an illustration of the new a0 -martensite particle nucleation. The growth of these particles plays an important role on the initial austenitic grain size changes which is in good accordance with the interaction results between the martensitic transformation and the textural reorientation. (4) Based on the measure of the volume fraction of the new martensite phase in the SST loading path, the proposed model is able to describe the TRIP effect in the numerical approach. (5) By coupling anisotropy stress with the generation of the new martensite phase the initial material anisotropy may be inhibited especially when temperature decreases.
References
Fig. 7. X-ray diffraction of the residual austenite and martensite volume fraction measured on a fractured specimen as a function of absolute temperature. In solid line, the proposed model (Eq. (5)) giving the theoretical martensitic volume fraction.
8 a^ ðxþ1Þ ^ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > < aðT; x; rÞ ¼ AðTÞ þ a 3 1þx2 2xr =ð1þr Þ ^ bðxþ1Þ > ^ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi : bðT; x; rÞ ¼ CðTÞ þ b 2 3
ð5Þ
1þx 2xr =ð1þrÞ
where A and C are the temperature-dependent parameters (see Ref. ^ are constants given in Table 2 and ^ and b [7] for more details), a x ¼ rII =rI represents the principal stress ratio. The Eq. (5) shows the anisotropic-dependent parameters that must be updated during the strain process. This model is represented in Fig. 6 which shows a good correlation between the volume fraction of martensite obtained from the X-ray diffraction method and from the proposed model. In this work, an original identification procedure has been conducted on the fraction martensitic evolution according to the shear loading path which has not been detailed in the present paper. This work is in going and will appear in the near future. 5. Conclusion Simple shear tests carried on the AISI 304 stainless steel and according to three anisotropic directions (RD, D45 and TD) at temperatures ranging from room temperature to 196 °C were inves-
[1] Bargui H, Sidhom H, Tourki Z. Martensite induite: incidence sur le comportement en écrouissage et sur la limite de formage de l’acier inoxydable AISI 304. Matériaux Tech 2000;11–12:31–41. [2] Iwamoto T, Tsuta T, Tomita Y. Investigation on deformation mode dependence of strain-induced martensitic transformation in TRIP steels and modelling of transformation kinetics. Int J Mech Sci 1998;40(2–3):173–82. [3] Ktari Z, Tourki Z, Sidhom H, Gahbiche A. Identification de la transformation martensitique induite par déformation plastique dans le cas de la déformation plane: expérience et validation numérique. 2ème CMSM 2007. Tunisia: Monastir; 2007. [4] Lebedev A, Kosarchuk V. Influence of phase transformations on the mechanical properties of austenitic stainless steel. Int J Plast 2000;16:749–67. [5] Olson GB, Cohen M. Kinetics of strain-induced martensitic nucleation. Metall Trans A 1975;6A:791–5. [6] Tourki Z, Bargui H, Sidhom H. The kinetic of induced martensitic formation and its effect on forming limit curves in AISI 304 stainless steel. J Mater Process Technol 2003;00:330–6. [7] Tourki Z, Sidhom H, Cherkaoui M. Plastic strain induced martensitic in type 304 austenitic stainless steel: modeling and numerical simulation of deep drawing processes. Int J Forming Process 2005;8(2–3):201–26. [8] Mangonon PL, Thomas G. The martensite phases in 304 stainless steel. Metall Trans 1970;A1:1577–86. [9] Angel T. Formation of martensite in austenitic stainless steels. J Iron Steel Inst 1954;00:165–74. [10] Stringfellow RG, Parks DM, Olson GB. A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels. Acta Metall Mater 1992;40(7):1703–16. [11] Powell GW, Marshall ER, Backofen WA. Strain hardening of austenitic stainless steel. ASM Trans Q 1958;50:478–9. [12] Kubler R, Berveiller M, Buessler P. Modélisation du comportement des aciers à effet TRIP par une approche simplifiée. In: 16ème Congrès Français de Mécanique Nice; 1–5 septembre, 2003. [13] Calloch S, Marquis D. Additional hardening due to tension–torsion nonproportional loadings: influence of the loading path shape. In: Kalluri S, Bonacuse PJ, editors. Multiaxial fatigue and deformation testing techniques, ASTM STP 1280. American Society for Testing and Materials; 1997. pp. 113–30. [14] Portier L, Calloch S, Marquis D, Geyer P. Ratchetting under tension–torsion loadinds: experiments and modelling. Int J Plast 2000;16:303–35. [15] Gallee S, Manach PY, Thuillier S. Mechanical behavior of a metastable austenitic stainless steel under simple and complex loading paths. Mater Sci Eng A 2007;466:47–55. [16] Jacques P, Furmemont Q, Pardoen T, Delannay F. On the role of martensitic transformation on damage and cracking resistance in trip-assisted multiphase steels. Acta Mater 2001;49:139–52.
Z. Ktari et al. / Materials and Design 32 (2011) 3765–3771 [17] Okutani T, Yukawa N, Ishikawa K, Jinma T. The strain-induced martensitic transformation of SUS304 under various stress states. In: Proceedings of the Japanese society and technical plasticity’95 spring; 1995. pp. 331–2. [18] Gahbiche A. Caractérisation expérimentale des tôles d’emboutissage, application à l’identification des lois de comportement, Thèse de Doctorat, LGM/ENIM Tunisia; 2006. [19] Ping H, Huang P, Lopez HF. Strain induced e-martensite in Co–Cr–Mo alloy: grain size effects. Mater Lett 1999;39:244–8.
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[20] Weira O, Andrzej K, Maciej WG. Mode of deformation and the rate of energy storage during uniaxial tensile deformation of austenitic steel. Mater Sci Eng 1996;A220:123–8. [21] Korbel A, Bochniak W. The structure based design of metal forming operations. J Mater Process Technol 1995;53:229–37.