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Strain hardening behavior and microstructural evolution during plastic deformation of dual phase, non-grain oriented electrical and AISI 304 steels
Author’s Accepted Manuscript Strain hardening behavior and microstructural evolution during plastic deformation of dual phase, non-grain oriented electrical and AISI 304 steels Guilherme Corrêa Soares, Berenice Mendonça Gonzalez, Leandro de Arruda Santos www.elsevier.com/locate/msea
PII: DOI: Reference:
S0921-5093(16)31595-7 http://dx.doi.org/10.1016/j.msea.2016.12.094 MSA34525
To appear in: Materials Science & Engineering A Received date: 5 October 2016 Revised date: 19 December 2016 Accepted date: 20 December 2016 Cite this article as: Guilherme Corrêa Soares, Berenice Mendonça Gonzalez and Leandro de Arruda Santos, Strain hardening behavior and microstructural evolution during plastic deformation of dual phase, non-grain oriented electrical and AISI 304 steels, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2016.12.094 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Strain hardening behavior and microstructural evolution during plastic deformation of dual phase, non-grain oriented electrical and AISI 304 steels Guilherme Corrêa Soares, Berenice Mendonça Gonzalez, Leandro de Arruda Santos* Department of Metallurgical and Materials Engineering, School of Engineering, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil. [email protected] *
Correspondence. Professor Leandro de Arruda Santos Department of Metallurgical
and Materials Engineering, Universidade Federal de Minas Gerais Av. Antonio Carlos, 6627–Campus Pampulha 31270-901, Belo Horizonte, MG, Brazil. Phone: +55 31 34091782, Fax: +55 31 3409-1815
Abstract Strain hardening behavior and microstructural evolution of non-grain oriented electrical, dual phase, and AISI 304 steels, subjected to uniaxial tensile tests, were investigated in this study. Tensile tests were performed at room temperature and the strain hardening behavior of the steels was characterized by three different parameters: modified Crussard–Jaoul stages, strain hardening rate and instantaneous strain hardening exponent. Optical microscopic analysis, X-ray diffraction measurements, phase quantification by Rietveld refinement and hardness tests were also carried out in order to correlate the microstructural and mechanical responses to plastic deformation. Distinct strain hardening stages were observed in the steels in terms of the instantaneous strain hardening exponent and the strain hardening rate. The dual phase and non-grain oriented steels exhibited a two-stage strain hardening behavior while the AISI 304 steel displayed multiple stages, resulting in a more complex strain hardening behavior. The dual phase steels showed a high work hardening capacity in stage 1, which was
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gradually reduced in stage 2. On the other hand, the AISI 304 steel showed high strain hardening capacity, which continued to increase up to the tensile strength. This is a consequence of its additional strain hardening mechanism, based on a strain-induced martensitic transformation, as shown by the X-ray diffraction and optical microscopic analyses. Keywords: strain hardening behavior, strain hardening rate, instantaneous strain hardening exponent, Crussard–Jaoul analysis.
1. Introduction In the need for high strength and good formability, steel sheet producers have been investing efforts in the increasing of the strain hardening capacity of steels. Strain hardening is the strengthening of a material as a response to plastic deformation and it plays a central role in the development of advanced high strength steels (AHSS), such as dual-phase steels [1,2]. The mechanisms responsible for strain hardening are mostly related to the interaction of dislocations with strain fields and obstacles in the crystal structure, such as other dislocations, strain-induced phases or twin boundaries. These obstacles are introduced in the structure by the deformation process and decrease the dislocation mobility [3,4]. To better understand the strain hardening behavior of a material, it is useful to establish different strain hardening stages along plastic deformation. A modified Crussard–Jaoul (C–J) analysis is a mathematical analysis used to determine strain hardening stages, being known for revealing a most clear distinction between these stages in comparison with other mathematical approaches [5-9]and is given by: ( )
–
–
(1)
2
Where is the true stress, is the logarithmic strain (also referred as true strain), m is the C–J strain hardening exponent, and KS is the wift’s strength coefficient. (d/d) is the strain hardening rate and (1 – m) is the slope of ln (d/d) vs. ln plot. Changes in this slope characterize different strain hardening stages. Furthermore, the strain hardening behavior of a material can be analyzed by variations in the strain hardening rate and the instantaneous strain hardening exponent, ni, which is a parameter that describes the work hardening behavior of metals and is given by: (2)
i
This parameter is erive from the Ho omo ’s equation:
= KHn,
(3)
Where the strain hardening exponent (n a
the Ho omo ’s strength coefficient (KH)
are constants. As shown in other studies, considering the strain hardening exponent as a constant is not accurate, since it measures the strain hardening capacity of a material, which may vary during the plastic deformation [4,10,11]. Thus, ni is more adequate than a constant strain hardening exponent to describe this behavior [11] and can be applied to the analysis of practical situations, such as forming operations [12]. The objective of this study is to contribute a deeper understanding regarding the different mechanical responses of steels that are subjected to plastic deformation. To achieve this, the instantaneous strain hardening behavior and microstructural evolution during plastic deformation of the dual phase (DP), AISI 304, and non-grain oriented electrical (NGOE) steels undergoing uniaxial tensile tests were investigated. The selection of these steels was based on their different strain hardening mechanisms. DP steels are one grade of AHSS, which are known for presenting higher rates of work hardening due to the presence of martensite in a ferritic matrix. AISI 304 steels present transformation induced plasticity (TRIP), since their austenitic microstructure is
3
transformed to martensite during deformation, resulting in severe strain hardening. On the other hand, NGOE steels have a simple ferritic microstructure and were selected as a reference group. The strain hardening behaviors were analyzed based on three different parameters: instantaneous strain hardening exponent (ni), C–J modified analysis and strain hardening rate. Although these are well known parameters, to the best of the author’s knowledge, no study combined these three parameters to compare the strain hardening behavior of these steels. The microstructural evolution during plastic deformation was also investigated using optical microscopy, X-ray diffraction (XRD) and hardness tests.
2. Materials and Methods Three steels were selected for this study: stainless AISI 304, DP and NGOE. The samples were received as thin cold rolled sheets and their chemical compositions are listed in Table 1. The mechanical properties and the work hardening behavior were evaluated by means of uniaxial tensile tests performed at room temperature and at a constant strain rate of 10-3 s-1 using a universal testing machine (Instron 5582, Canton, MA, USA). The specimens for these tests were machined according to ASTM A370 standards [13] and the gauge length and width of these specimens were controlled by means of a profile projector, PJ311 (Mitutoyo, Chicago, IL, USA). The tensile tests were performed until different strain values in order to characterize the changes in the microstructure of the steels as a function of the strain. Flow curves were deducted from engineering stress-strain curves in terms of = s (1 + e) and = ln (1 + e), where s and e are the engineering stress and strain, respectively. The C–J analysis was applied to the resultant flow curves and different strain hardening
4
stages were determined for each steel. Then, the strain hardening rate and the instantaneous strain hardening exponent were calculated as a function of the logarithmic strain. The constant strain hardening exponent, n, was also calculated to be compared with ni. Samples cut from the tensile tested specimens were analyzed by hardness tests and used for microstructural characterization by XRD analysis and optical microscopy. The hardness tests performed on the samples of DP and AISI 304 steels were carried out using a Zwick & Co. KG. machine Model Z302 (Zwick & Co. KG, Ulm, BW, Germany) and microhardness analysis was applied to the NGOE samples by using a Future-Tech FM-700 Microhardness tester (FUTURE-TECH CORP., Kawasaki-City, Kanagawa Prefecture, Japan). The microstructural analysis was performed in the longitudinal sections of the specimens, which were prepared by standard metallographic techniques. The DP and NGOE steels were etched with 2% Nital and the AISI 304 steel was etched with Behara. The microstructures were observed in a Metallux II Metallographic Microscope (Leitz, Wetzlar, Germany). The XRD analyses were carried out in a Philips PW 1710 (Philips Instrument, Eindhoven, The Netherlands) with Bragg–Brentano geometry a
usi g Cu Kα
radiation (= 0.15418 nm). The measurements were performed at room temperature, in a range of 20° to 90° and 0.02 °s-1 step. The resulting XRD patterns were then used to identify the phases by comparison with patters of a crystallographic database [14]. Phase quantification using the Rietveld refinement was applied to the samples of AISI 304 steel subjected to different strain percentages, using the GSAS software and EXPGUI interface, in order to evaluate the weight fraction of martensite as a function of strain.
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3. Results and Discussion The strain hardening behavior of the NGOE, DP and AISI 304 steels is characterized by multiple stages. The number of stages depends on the steel and is related directly to the strain hardening rate and strain hardening exponent. The following discussion aims to establish connections between the microstructural aspects and these strain hardening stages. Through these data, comparisons can be made among different industrial steels, a better understanding of the mechanical properties can be achieved, and correlations can be made with previously published results regarding the same subject [3,5-12,15].
3.1 General Mechanical Behavior The engineering stress–strain and flow curves for the NGOE, DP and AISI 304 steels are shown in Figures 1 (a) and (b), respectively. The values of the tensile strength (SR), yield strength (Se), uniform elongation (eu), constant strain hardening coefficient (n) and Hollomon’s strength coefficient (KH) are listed in Table 2. The DP and AISI 304 steels presented continuous yielding while the NGOE steel had a yield point elongation, which is typical of ferritic steels. AISI 304 steel exhibited the highest strain hardening capacity among the studied steels, with the lowest yield strength and the highest tensile strength. Consequently, AISI 304’s n is remarkably higher than the other calculated coefficients. On the other hand, comparing NGOE and DP steels, the former seems to exhibit a lower strain hardening capacity when one analyses the values of the yield and tensile strengths. Nevertheless, NGOE presented a higher n when compared with the DP steel. Then, in this case, it seems essential to investigate the variations in the ni of these steels, since the constant exponent is not enough to describe their strain hardening behavior. Furthermore, it is important to
6
notice that the DP steel has a relatively higher KH than the NGOE steel, which is also a constant parameter used to analyze the strain hardening capacity of a material. The hardness measurements as a function of the logarithmic strain are shown in Figure 2 and a good correlation can be made with the mechanical properties obtained by the stress–strain curves. The NGOE steel presented higher increase in hardness in comparison with the DP steel. This is consistent with the values of n calculated for these steels. As expected, the AISI 304 steel undergoes the highest hardness increase as a function of the logarithmic strain.
3.2 Non-grain Oriented Electrical Steel 3.2.1 Microstructural Evolution Optical microscopy was performed in order to confirm the monophasic ferritic microstructure. The XRD patterns for the steel as received and after strained up to = 0.219 strain value are shown in Figure 3. The results show the patterns of a bcc ferritic structure with {110}, {200} and {211}reflections. The main difference observed between the patterns is the peak broadening of the strained sample’s pattern, which is expected in plastically deformed structures because of the introduction of lattice defects such as dislocations and faulting [16].
3.2.2 Strain Hardening Behavior Figure 4 shows the strain hardening behavior analyses for the NGOE steel. The ln (d/d) vs. ln curve, Figure 4 (a), displays a slope change at 1 = 0.039, dividing the strain hardening behavior into two distinct stages. The strain hardening rate, Figure 4 (b), significantly decreases after the beginning of the plastic deformation (stage 1) and steadily decreases at an ever lower rate at the end of uniform elongation (stage 2). The
7
instantaneous strain hardening exponent, Figure 4 (c), remained nearly stable during uniform deformation. The constant strain hardening exponent (n = 0.240) appears to be a credible estimate for the entire strain hardening behavior of the NGOE steel. The NGOE steel is not a structural steel, therefore, there are only a few studies related to its strain hardening behavior and microstructural evolution, while most of the investigations are associated with magnetic properties [17-19]. It has been observed that the constant strain hardening exponent exhibited a reasonable linear relationship with the degradation of magnetic properties; hence, it seems important to better understand the strain hardening behavior of NGOE steel [19]. Considering that the NGOE steel is entirely ferritic and no phase transformation or twinning was observed in the microstructural characterization, dislocation interaction with defects in its crystal lattice is presumably the main strain hardening mechanism. This behavior was used as a reference to be compared with the more complex behavior presented by the DP and AISI 304 steels.
3.3 Dual Phase Steel 3.3.1 Microstructural Evolution DP steels are low carbon micro-alloyed steels, which consist of hard martensite grains dispersed in a ductile ferritic matrix [1, 2, 20-22]. This coexistence allows the material to combine good ductility and high tensile strength. The microstructure of the as received DP steel is shown in Figure 5 and exhibits a typical DP microstructure. Depending on the process route, the microstructure of these steels may present a high degree of complexity, especially regarding the dispersed hard phase. In fact, their constitution may also incorporate other constituents, such as retained austenite, bainite, and carbides [21], which are very difficult to identify only by micrographic images.
8
XRD was applied to complement the micrographic analysis and the results are shown in Figure 6. XRD were performed on the as received sample and on the sample strained up to = 0.209. The XRD pattern of the as received steel revealed a microstructure composed of ferrite + martensite, identified by the {110}, {200} and {211} peaks, containing traces of retained austenite, identified by the {200} and {220} peaks. Two main differences were observed after straining the steel up to = 0.209: 1) the absence of retained austenite, which was transformed to martensite; and 2) peak broadening of the diffraction profile, which is expected in plastically deformed structures.
3.3.2 Strain Hardening Behavior The main factor that differentiates DP steels from the ferritic steels during plastic deformation is the continuous yielding, which was observed in Figure 1. This factor, combined with a high initial strain-hardening rate, is the basis for the excellent sheetforming presented by these steels [21]. The strain hardening behavior analyses of the DP steel are shown in Figure 7 and it is observed that the strain hardening occurs in two stages, Figure 7 (a), which are the same number of stages found for the NGOE steel. The main difference is the high strain hardening rate in the stage 1 of the DP steel, Figure 7 (b), and it can be assumed as the most important stage for forming processes, responsible for the rapid increase in work hardening of this steel. As expected, the strain hardening rate progressively decreased as a function of the deformation as observed in Figure 7 (b). The instantaneous strain hardening exponent, seen in Figure 7 (c), rapidly increased in stage 1 and reached a maximum in the beginning of stage 2, where it remained practically constant. This rapid increase is also related to the high strain hardening rate observed in stage 1 and it distinguishes from the NGOE’s exponent that remained nearly constant during the different stages. Comparing the constant strain
9
hardening exponent (n = 0.219) with the instantaneous strain hardening exponent, it becomes evident that the former is a good estimate for stage 2, although not accurate to describe stage 1. These results are consistent with previous investigations, in which two stages of work hardening were also calculated for DP steels [11,23-25]. The continuous yielding and the high strain hardening rate found for this steel are a consequence of the austenite-martensite transformation during the heat treatment, which involves volume expansion [2,20-22,26,27]. The strain produced by this transformation generates residual stresses in the surrounding grains of ferrite. These stresses facilitate the plastic flow, reducing the yield strength and being responsible for the absence of yield point [20,26]. Moreover, the strain generated by the volume expansion creates a high density of mobile dislocation in the vicinity of martensite. The movement of these mobile dislocations also contribute to eliminate the yield point and to reduce the yield strength. Finally, the interaction of these dislocation with each other and with the martensite grains result in the high strain hardening rate observed in stage 1 [2,20,26,27] and the increase of ni until a maximum in stage 2. After this maximum, the strain hardening behavior of the DP steel seems similar to the NGOE steel, with a nearly constant ni, gradual decrease in strain hardening rate and continuous deformation of the ferritic matrix. During the deformation of ferritic grains as a consequence of the volume expansion, geometrically necessary dislocations (GNDs) are formed to guarantee the continuity of the lattice [20,26,27]. It is known that GNDs increase the local hardness of the surrounding ferrite grains, as demonstrated by Tsipouridis et al. [2]. However, the role of these dislocation in the strain hardening behavior, combined with the residual stress, is not completely known [20,21].
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3.4 AISI 304 Steel 3.4.1 Microstructural Evolution The XRD analysis and the Rietveld refinement of the AISI 304 steel as received and after being strained up to = 0.1, 0.2, 0.3, 0.4 and 0.425 are shown in Figure 8. The XRD analysis shows a completely austenitic structure in the non-deformed steel, identified by the {111}, {200} and {220} peaks. However, as a response to the plastic deformation, the material undergoes athermal phase transformation, where martensite (’ is strai -induced from austenite (). The samples exhibited an increase in the proportion of strain-induced martensite as a function of the plastic deformation, detected by the increasing intensities of the {111}’, {200}’ a
{221}’ peaks.
Traces of hexagonal martensite were also identified in samples strained up to 0.2 and 0.3 logarithmic strains. Presumably, martensite acts as a precursor for the formation of tetragonal ’ martensite in early stages of deformation [3,28]. At = 0.425, the XRD pattern shows a mostly martensitic structure with some retained austenite. It is also worth noting that traces of martensite were detected in this analysis only for a limited range of plastic deformation, indicating that the strain-induced phase transformation also occurs with the help of mechanical twinning [28]. The ’ martensite weight fraction, weighted profile R-factor (Rwp) and goodness of fit (χ2) obtained by the Rietveld refinement of the X-ray patterns are listed in Table 3. Both Rwp and χ2 are important parameters to evaluate the quality of the refinement, and the literature states that acceptable Rwp values of a refinement performed with X-ray data should be approximately 10% and χ2 values should be approximately 1 [29,30]. The Rwp values determined in the refinements were approximately 13% and χ2 values were barely higher than 1, confirming the reliability of the refinement. Considering that the Rietveld refinement was developed to analyze powder diffraction patterns, a spherical
11
harmonics preferred orientation function was utilized in order to reduce possible errors associated with texture. The reflections regarding martensite presented very low intensities, then the quantity of this phase was neglected. The quantitative analysis indicate that most of the martensite is induced in early values of logarithmic strain. Optical micrographic images of the AISI 304 steel as received and after being strained up to = 0.2 and 0.425 are shown in Figure 9. The micrographic analysis is in agreement with the XRD results and shows that the as received samples (Figure 9 (a)) is constituted by an austenitic matrix (containing some traces of martensite. Considering that martensite was not identified in the XRD analysis, it is reasonable to assume that it was formed during the metallographic preparation. After being strained up to a 0.2 logarithmic strain, seen in Figure 9 (b), the presence of ’ a
strain-
induced martensite is notable, and it is evident that the formation of ’ martensite occurs at the intersection of martensite platelets [31]. A mainly ’ martensitic microstructure with isles of retained austenite was identified at = 0.425 as seen in Figure 9 (c).
3.4.2 Strain Hardening Behavior The strain hardening behavior analyses, ’ weight fractio a
’ tra sformatio rate as
a function of the logarithmic strain of the AISI 304 steel are shown in Figure 10. The ln (d/d) vs. ln curve, seen in Figure 10 (a), revealed five recognizable strain hardening stages with limits at four critical values: 1 = 0.033, 2 = 0.080, 3 = 0.111 and 4 = 0.269. The strain hardening rate, seen in Figure 10 (b), continuously decreased in stages 1 and 2, reaching a minimum in stage 3, and increased in stage 4, reaching a local maximum before stage 5 in where the rate started decreasing again. Contrary to the observations in the other steels, the instantaneous strain hardening exponent, seen in 12
Figure 10 (c), increased in the first four stages to a value as high as approximately 0.8 before decreasing in the following stage. The constant strain hardening exponent (n = 0.463) does not appear to be an accurate parameter to describe strain hardening in this case, since it strongly deviates from the instantaneous values in almost every stage. At lower logarithmic strain values, the transformation of austenite to martensite is the main strain hardening mechanism, since precedes ’. This is confirmed by the fact that ’ tra sformatio rate starts to increase in later stages, such as stage 2 and 3, indicating that the ’ marte site starts to be respo sib e for the strain hardening in these stages. Despite the decreasing values of the ’ tra sformatio rate in the last stages, the ’ martensitic transformation still occurs and certainly affects the strain hardening behavior. These results are in agreement with previous studies, which indicated that strain-induced martensitic transformation played an important role in strain hardening behavior [3,32]. The observed strain hardening behavior of AISI 304 steel and multiple strain hardening stages are consistent with previous investigations [15,32]. In stages 1, the interaction of mobile dislocations and dynamic strain softening appears to be the predominant strain hardening mechanism, as established in previous studies [6,32]. Stage 2 represents the onset of martensite formation, which occurs preferably at low strain values and only after a certain stress threshold is reached [10,31-33]. Optical microscopy observations are in accordance with this premise, as the formation of parallel martensite platelets was observed at low strain values. At the beginning of stage 2, the microstructure is mostly austenitic with platelets of martensite. Stage 3 is associated with the formation of ’ marte site c usters, a non-homogeneous plastic deformation of the matrix and a subsequent enhanced generation of geometrically necessary dislocations [31-35] as a consequence of the athermal transformations. This explains the increase in the strain
13
hardening rate observed in the following stage. In stage 4, a critical ’ marte site fraction of 0.3~0.4 is formed, and plastic deformation of austenite is no longer able to completely accommodate martensite [32]. In this stage, percolating clusters of ’ martensite are formed and generate a composite strengthening effect, increasing even more the strain hardening rate [31,36]. Accor i g to the XRD patter s, ε marte site is no longer detected in stages 4 and 5, hinting to the fact that ’ formatio is no longer associated with the formation of an intermediate phase. This is in agreement with the decrease in slope of the ’ transformation rate’s curve as seen in Figure 10 (d). During stage 5, both instantaneous strain hardening exponent, seen in Figure 10 (c), and the strain hardening rate, seen in Figure 10 (b), decrease, indicating that less strain hardening mechanisms are active. The strain-induced martensitic transformation is not the major strain hardening mechanism in stages 5, as indicated by the transformation rate in Figure 10 (d). At such high strains, strain hardening is dominated by plastic deformation and dynamic recovery of a ’ saturate microstructure, which resemb es the behavior of a single phase material [28,31,32].
4. Conclusions In the present study, the microstructural evolution as a function of plastic deformation and the strain hardening behavior of the DP, NGOE and AISI 304 steels were studied. Based on the results, the main conclusions can be summarized as follows: (1) The C–J analysis clearly revealed a two-stage hardening behavior for the NGOE steel, which is possibly associated with dynamic recovery and the interaction of dislocations with a deformed lattice. The instantaneous strain hardening exponent remained nearly constant.
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(2) The DP steel also exhibited a two-stage strain hardening behavior. In stage 1, it was observed a high strain hardening rate and increasing instantaneous strain hardening exponent. This is due to the presence of mobile dislocations that are introduced in the ferrite by the martensitic transformation during the manufacturing process of the alloy. (3) The AISI 304 steel featured a complex five-stage strain hardening behavior. The formation of strain-induced and ’ marte site has a major influence on its behavior. Therefore, this complexity comes from the activation of a variety of strain hardening mechanisms during the strain induced phase transformation.
Acknowledgements This work was partially supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES/PROEX), Brasília, DF, Brazil; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brasília, DF, Brazil; Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Belo Horizonte, MG, Brazil; and Pró-Reitoria de Pesquisa da Universidade Federal de Minas Gerais (PRPq/UFMG), Belo Horizonte, MG, Brazil. The authors would like to thank Aperam South America, Timóteo, MG, Brazil for providing the AISI 304 and NGOE steels, and Usiminas, Ipatinga, MG, Brazil for providing the DP steel. The authors deny any conflict of interest.
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[28] J.Y. Choi, W. Jin, Strain induced martensite formation and its effect on strain hardening behavior in the cold drawn 304 austenitic stainless steels, Scr. Mater. 36 (1997) 99-104. [29] B.H.R. Toby, R factors in Rietveld analysis: How good is good enough?, Powder Diffr. 21 (2006) 67-70. [30] L.B. McCusker, R.B. Von Dreele, D.E. Cox, D. Louër, P. Scardi, Rietveld refinement guidelines, J. Appl. Crystallogr. 32 (1999) 36-50. [31] A.K. De, G. Speer, D.K. Matlock, D.C. Murdock, M.C. Mataya, R.J. Comstock, Deformation-induced phase transformation and strain hardening in type 304 austenitic stainless steel, Metall. Mater. Trans. A. 37A (2006) 1875-1886. [32] J. Talonen, Effect of microstructural evolution on mechanical properties. In: Effect of strain-i
uce α’-martensite transformation on mechanical properties of metastable
austenitic stainless steels [Dissertation]. Espoo, Helsinki University of Technology, 2007, pp. 102-109. [33] J. Talonen, H. H. Hanninen, Formation of shear bands and strain-induced martensite during plastic deformation of metastable austenitic stainless steels, Acta. Mater. 55 (2007) 6108-6118. [34] T.F.A. Santos, M.S. Andrade, Internal friction on AISI 304 stainless steel with low tensile deformations at temperatures between -50 and 20°C, Adv. Mater. Sci. Eng. 2010 (2010) 1-8. [35] A. Weiß, H. Gutte, J. Mola, Contribuitions of and TRIP effects to the strength and ductility of AISI 304 (X5CrNi18-10) austenitic stainless steel, Met. Metall. Mater. Trans. A 47 (2015) 112-122.
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[36] M. Milad, N. Zreiba, F. Elhalouani, C. Baradai. The effect of cold work on structure and properties of AISI 304 stainless steel, Mater. Process. Technol. 203 (2008) 80-85.
Figure 1. (a) Engineering stress–strain curves and (b) flow curves of DP, NGOE and AISI 304 steels. Figure 2. Hardness tests as a function of the logarithmic strain. Figure 3. XRD patterns of the NGOE steel before and after deformation. Figure 4. Strain hardening behavior analysis of the NGOE steel: (a) ln (d /dε) vs. ln curve for the modified C–J analysis; (b) relation between strain hardening rate and logarithmic strain; (c) relation between the instantaneous strain hardening exponent and the logarithmic strain and a comparison with its constant strain hardening exponent. Figure 5. Optical micrograph of the DP steel, containing ferrite (F) and martensite (M). Figure 6. XRD patterns of the DP steel before and after deformation. Figure 7. Strain hardening behavior analyses of the DP steel: (a) ln (d /dε) vs. ln curve for the modified C–J analysis; (b) relation between strain hardening rate and logarithmic strain; (c) relation between the instantaneous strain hardening exponent and logarithmic strain and a comparison with its constant strain hardening exponent. Figure 8. XRD patterns (black lines) and Rietveld refinement analysis (gray lines) for the AISI 304 steel before and after deformations up to = 0.1, 0.2, 0.3, 0.4 and 0.425. Figure 9. Optical micrographs of the AISI 304 steel: (a) as received, (b) deformed up to
= 0.2 and (c) deformed up to = 0.425. Figure 10. Strain hardening behavior analysis of the AISI 304 steel: (a) ln (d /dε) vs. ln curve for the modified C-J analysis; (b) relation between strain hardening rate and logarithmic strain; (c) relation between the instantaneous strain hardening exponent and
20
the logarithmic strain and a comparison with its constant strain hardening exponent; (d) α’ weight fractio a
α’ transformation rate as a function of the logarithmic strain.
Table 1. Chemical composition of the investigated steels (in wt%). Steel
C
Mn
Si
P
S
Cr
Ni
Al
AISI 304
0.0427
0.0039
0.3597
0.0247
0.0018
18.1023
8.0261
0.0024
NGOE
0.0039
1.1773
2.1278
0.0131
0.0003
-
-
0.0024
DP
0.10
1.8
0.51
0.018
0.007
-
-
0.035
Table 2. Mechanical properties determined in tensile testing. Steel
SR (MPa)
Se (MPa)
eu (%)
n
KH (MPa)
DP
664.5 ± 6.6
368.6 ± 6.1
22.5 ± 0.5
0.219 ± 0.003
1138.1 ± 9.2
NGOE
433.7 ± 7.7
315.2 ± 1.4
23.9 ± 1.15
0.240 ± 0.004
778.2 ± 11.9
AISI 304
785.8 ± 15.3
262.6 ± 5.3
55.0 ± 3.5
0.463 ± 0.007
1485.5 ± 17.5
Table 3. Quantitative analyses results and parameters from Rietveld refinement of deformed AISI 304 steel samples.
’ Weight Rwp (%)
χ2
Fraction (%) 0.1
42.1
13.52
1.385
0.2
63.7
13.12
1.397
0.3
71.6
12.37
1.307
0.4
80.3
12.31
1.285
0.425
80.5
12.88
1.428
21
22
23
24
25
26
27
PII: DOI: Reference:
S0921-5093(16)31595-7 http://dx.doi.org/10.1016/j.msea.2016.12.094 MSA34525
To appear in: Materials Science & Engineering A Received date: 5 October 2016 Revised date: 19 December 2016 Accepted date: 20 December 2016 Cite this article as: Guilherme Corrêa Soares, Berenice Mendonça Gonzalez and Leandro de Arruda Santos, Strain hardening behavior and microstructural evolution during plastic deformation of dual phase, non-grain oriented electrical and AISI 304 steels, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2016.12.094 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Strain hardening behavior and microstructural evolution during plastic deformation of dual phase, non-grain oriented electrical and AISI 304 steels Guilherme Corrêa Soares, Berenice Mendonça Gonzalez, Leandro de Arruda Santos* Department of Metallurgical and Materials Engineering, School of Engineering, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil. [email protected] *
Correspondence. Professor Leandro de Arruda Santos Department of Metallurgical
and Materials Engineering, Universidade Federal de Minas Gerais Av. Antonio Carlos, 6627–Campus Pampulha 31270-901, Belo Horizonte, MG, Brazil. Phone: +55 31 34091782, Fax: +55 31 3409-1815
Abstract Strain hardening behavior and microstructural evolution of non-grain oriented electrical, dual phase, and AISI 304 steels, subjected to uniaxial tensile tests, were investigated in this study. Tensile tests were performed at room temperature and the strain hardening behavior of the steels was characterized by three different parameters: modified Crussard–Jaoul stages, strain hardening rate and instantaneous strain hardening exponent. Optical microscopic analysis, X-ray diffraction measurements, phase quantification by Rietveld refinement and hardness tests were also carried out in order to correlate the microstructural and mechanical responses to plastic deformation. Distinct strain hardening stages were observed in the steels in terms of the instantaneous strain hardening exponent and the strain hardening rate. The dual phase and non-grain oriented steels exhibited a two-stage strain hardening behavior while the AISI 304 steel displayed multiple stages, resulting in a more complex strain hardening behavior. The dual phase steels showed a high work hardening capacity in stage 1, which was
1
gradually reduced in stage 2. On the other hand, the AISI 304 steel showed high strain hardening capacity, which continued to increase up to the tensile strength. This is a consequence of its additional strain hardening mechanism, based on a strain-induced martensitic transformation, as shown by the X-ray diffraction and optical microscopic analyses. Keywords: strain hardening behavior, strain hardening rate, instantaneous strain hardening exponent, Crussard–Jaoul analysis.
1. Introduction In the need for high strength and good formability, steel sheet producers have been investing efforts in the increasing of the strain hardening capacity of steels. Strain hardening is the strengthening of a material as a response to plastic deformation and it plays a central role in the development of advanced high strength steels (AHSS), such as dual-phase steels [1,2]. The mechanisms responsible for strain hardening are mostly related to the interaction of dislocations with strain fields and obstacles in the crystal structure, such as other dislocations, strain-induced phases or twin boundaries. These obstacles are introduced in the structure by the deformation process and decrease the dislocation mobility [3,4]. To better understand the strain hardening behavior of a material, it is useful to establish different strain hardening stages along plastic deformation. A modified Crussard–Jaoul (C–J) analysis is a mathematical analysis used to determine strain hardening stages, being known for revealing a most clear distinction between these stages in comparison with other mathematical approaches [5-9]and is given by: ( )
–
–
(1)
2
Where is the true stress, is the logarithmic strain (also referred as true strain), m is the C–J strain hardening exponent, and KS is the wift’s strength coefficient. (d/d) is the strain hardening rate and (1 – m) is the slope of ln (d/d) vs. ln plot. Changes in this slope characterize different strain hardening stages. Furthermore, the strain hardening behavior of a material can be analyzed by variations in the strain hardening rate and the instantaneous strain hardening exponent, ni, which is a parameter that describes the work hardening behavior of metals and is given by: (2)
i
This parameter is erive from the Ho omo ’s equation:
= KHn,
(3)
Where the strain hardening exponent (n a
the Ho omo ’s strength coefficient (KH)
are constants. As shown in other studies, considering the strain hardening exponent as a constant is not accurate, since it measures the strain hardening capacity of a material, which may vary during the plastic deformation [4,10,11]. Thus, ni is more adequate than a constant strain hardening exponent to describe this behavior [11] and can be applied to the analysis of practical situations, such as forming operations [12]. The objective of this study is to contribute a deeper understanding regarding the different mechanical responses of steels that are subjected to plastic deformation. To achieve this, the instantaneous strain hardening behavior and microstructural evolution during plastic deformation of the dual phase (DP), AISI 304, and non-grain oriented electrical (NGOE) steels undergoing uniaxial tensile tests were investigated. The selection of these steels was based on their different strain hardening mechanisms. DP steels are one grade of AHSS, which are known for presenting higher rates of work hardening due to the presence of martensite in a ferritic matrix. AISI 304 steels present transformation induced plasticity (TRIP), since their austenitic microstructure is
3
transformed to martensite during deformation, resulting in severe strain hardening. On the other hand, NGOE steels have a simple ferritic microstructure and were selected as a reference group. The strain hardening behaviors were analyzed based on three different parameters: instantaneous strain hardening exponent (ni), C–J modified analysis and strain hardening rate. Although these are well known parameters, to the best of the author’s knowledge, no study combined these three parameters to compare the strain hardening behavior of these steels. The microstructural evolution during plastic deformation was also investigated using optical microscopy, X-ray diffraction (XRD) and hardness tests.
2. Materials and Methods Three steels were selected for this study: stainless AISI 304, DP and NGOE. The samples were received as thin cold rolled sheets and their chemical compositions are listed in Table 1. The mechanical properties and the work hardening behavior were evaluated by means of uniaxial tensile tests performed at room temperature and at a constant strain rate of 10-3 s-1 using a universal testing machine (Instron 5582, Canton, MA, USA). The specimens for these tests were machined according to ASTM A370 standards [13] and the gauge length and width of these specimens were controlled by means of a profile projector, PJ311 (Mitutoyo, Chicago, IL, USA). The tensile tests were performed until different strain values in order to characterize the changes in the microstructure of the steels as a function of the strain. Flow curves were deducted from engineering stress-strain curves in terms of = s (1 + e) and = ln (1 + e), where s and e are the engineering stress and strain, respectively. The C–J analysis was applied to the resultant flow curves and different strain hardening
4
stages were determined for each steel. Then, the strain hardening rate and the instantaneous strain hardening exponent were calculated as a function of the logarithmic strain. The constant strain hardening exponent, n, was also calculated to be compared with ni. Samples cut from the tensile tested specimens were analyzed by hardness tests and used for microstructural characterization by XRD analysis and optical microscopy. The hardness tests performed on the samples of DP and AISI 304 steels were carried out using a Zwick & Co. KG. machine Model Z302 (Zwick & Co. KG, Ulm, BW, Germany) and microhardness analysis was applied to the NGOE samples by using a Future-Tech FM-700 Microhardness tester (FUTURE-TECH CORP., Kawasaki-City, Kanagawa Prefecture, Japan). The microstructural analysis was performed in the longitudinal sections of the specimens, which were prepared by standard metallographic techniques. The DP and NGOE steels were etched with 2% Nital and the AISI 304 steel was etched with Behara. The microstructures were observed in a Metallux II Metallographic Microscope (Leitz, Wetzlar, Germany). The XRD analyses were carried out in a Philips PW 1710 (Philips Instrument, Eindhoven, The Netherlands) with Bragg–Brentano geometry a
usi g Cu Kα
radiation (= 0.15418 nm). The measurements were performed at room temperature, in a range of 20° to 90° and 0.02 °s-1 step. The resulting XRD patterns were then used to identify the phases by comparison with patters of a crystallographic database [14]. Phase quantification using the Rietveld refinement was applied to the samples of AISI 304 steel subjected to different strain percentages, using the GSAS software and EXPGUI interface, in order to evaluate the weight fraction of martensite as a function of strain.
5
3. Results and Discussion The strain hardening behavior of the NGOE, DP and AISI 304 steels is characterized by multiple stages. The number of stages depends on the steel and is related directly to the strain hardening rate and strain hardening exponent. The following discussion aims to establish connections between the microstructural aspects and these strain hardening stages. Through these data, comparisons can be made among different industrial steels, a better understanding of the mechanical properties can be achieved, and correlations can be made with previously published results regarding the same subject [3,5-12,15].
3.1 General Mechanical Behavior The engineering stress–strain and flow curves for the NGOE, DP and AISI 304 steels are shown in Figures 1 (a) and (b), respectively. The values of the tensile strength (SR), yield strength (Se), uniform elongation (eu), constant strain hardening coefficient (n) and Hollomon’s strength coefficient (KH) are listed in Table 2. The DP and AISI 304 steels presented continuous yielding while the NGOE steel had a yield point elongation, which is typical of ferritic steels. AISI 304 steel exhibited the highest strain hardening capacity among the studied steels, with the lowest yield strength and the highest tensile strength. Consequently, AISI 304’s n is remarkably higher than the other calculated coefficients. On the other hand, comparing NGOE and DP steels, the former seems to exhibit a lower strain hardening capacity when one analyses the values of the yield and tensile strengths. Nevertheless, NGOE presented a higher n when compared with the DP steel. Then, in this case, it seems essential to investigate the variations in the ni of these steels, since the constant exponent is not enough to describe their strain hardening behavior. Furthermore, it is important to
6
notice that the DP steel has a relatively higher KH than the NGOE steel, which is also a constant parameter used to analyze the strain hardening capacity of a material. The hardness measurements as a function of the logarithmic strain are shown in Figure 2 and a good correlation can be made with the mechanical properties obtained by the stress–strain curves. The NGOE steel presented higher increase in hardness in comparison with the DP steel. This is consistent with the values of n calculated for these steels. As expected, the AISI 304 steel undergoes the highest hardness increase as a function of the logarithmic strain.
3.2 Non-grain Oriented Electrical Steel 3.2.1 Microstructural Evolution Optical microscopy was performed in order to confirm the monophasic ferritic microstructure. The XRD patterns for the steel as received and after strained up to = 0.219 strain value are shown in Figure 3. The results show the patterns of a bcc ferritic structure with {110}, {200} and {211}reflections. The main difference observed between the patterns is the peak broadening of the strained sample’s pattern, which is expected in plastically deformed structures because of the introduction of lattice defects such as dislocations and faulting [16].
3.2.2 Strain Hardening Behavior Figure 4 shows the strain hardening behavior analyses for the NGOE steel. The ln (d/d) vs. ln curve, Figure 4 (a), displays a slope change at 1 = 0.039, dividing the strain hardening behavior into two distinct stages. The strain hardening rate, Figure 4 (b), significantly decreases after the beginning of the plastic deformation (stage 1) and steadily decreases at an ever lower rate at the end of uniform elongation (stage 2). The
7
instantaneous strain hardening exponent, Figure 4 (c), remained nearly stable during uniform deformation. The constant strain hardening exponent (n = 0.240) appears to be a credible estimate for the entire strain hardening behavior of the NGOE steel. The NGOE steel is not a structural steel, therefore, there are only a few studies related to its strain hardening behavior and microstructural evolution, while most of the investigations are associated with magnetic properties [17-19]. It has been observed that the constant strain hardening exponent exhibited a reasonable linear relationship with the degradation of magnetic properties; hence, it seems important to better understand the strain hardening behavior of NGOE steel [19]. Considering that the NGOE steel is entirely ferritic and no phase transformation or twinning was observed in the microstructural characterization, dislocation interaction with defects in its crystal lattice is presumably the main strain hardening mechanism. This behavior was used as a reference to be compared with the more complex behavior presented by the DP and AISI 304 steels.
3.3 Dual Phase Steel 3.3.1 Microstructural Evolution DP steels are low carbon micro-alloyed steels, which consist of hard martensite grains dispersed in a ductile ferritic matrix [1, 2, 20-22]. This coexistence allows the material to combine good ductility and high tensile strength. The microstructure of the as received DP steel is shown in Figure 5 and exhibits a typical DP microstructure. Depending on the process route, the microstructure of these steels may present a high degree of complexity, especially regarding the dispersed hard phase. In fact, their constitution may also incorporate other constituents, such as retained austenite, bainite, and carbides [21], which are very difficult to identify only by micrographic images.
8
XRD was applied to complement the micrographic analysis and the results are shown in Figure 6. XRD were performed on the as received sample and on the sample strained up to = 0.209. The XRD pattern of the as received steel revealed a microstructure composed of ferrite + martensite, identified by the {110}, {200} and {211} peaks, containing traces of retained austenite, identified by the {200} and {220} peaks. Two main differences were observed after straining the steel up to = 0.209: 1) the absence of retained austenite, which was transformed to martensite; and 2) peak broadening of the diffraction profile, which is expected in plastically deformed structures.
3.3.2 Strain Hardening Behavior The main factor that differentiates DP steels from the ferritic steels during plastic deformation is the continuous yielding, which was observed in Figure 1. This factor, combined with a high initial strain-hardening rate, is the basis for the excellent sheetforming presented by these steels [21]. The strain hardening behavior analyses of the DP steel are shown in Figure 7 and it is observed that the strain hardening occurs in two stages, Figure 7 (a), which are the same number of stages found for the NGOE steel. The main difference is the high strain hardening rate in the stage 1 of the DP steel, Figure 7 (b), and it can be assumed as the most important stage for forming processes, responsible for the rapid increase in work hardening of this steel. As expected, the strain hardening rate progressively decreased as a function of the deformation as observed in Figure 7 (b). The instantaneous strain hardening exponent, seen in Figure 7 (c), rapidly increased in stage 1 and reached a maximum in the beginning of stage 2, where it remained practically constant. This rapid increase is also related to the high strain hardening rate observed in stage 1 and it distinguishes from the NGOE’s exponent that remained nearly constant during the different stages. Comparing the constant strain
9
hardening exponent (n = 0.219) with the instantaneous strain hardening exponent, it becomes evident that the former is a good estimate for stage 2, although not accurate to describe stage 1. These results are consistent with previous investigations, in which two stages of work hardening were also calculated for DP steels [11,23-25]. The continuous yielding and the high strain hardening rate found for this steel are a consequence of the austenite-martensite transformation during the heat treatment, which involves volume expansion [2,20-22,26,27]. The strain produced by this transformation generates residual stresses in the surrounding grains of ferrite. These stresses facilitate the plastic flow, reducing the yield strength and being responsible for the absence of yield point [20,26]. Moreover, the strain generated by the volume expansion creates a high density of mobile dislocation in the vicinity of martensite. The movement of these mobile dislocations also contribute to eliminate the yield point and to reduce the yield strength. Finally, the interaction of these dislocation with each other and with the martensite grains result in the high strain hardening rate observed in stage 1 [2,20,26,27] and the increase of ni until a maximum in stage 2. After this maximum, the strain hardening behavior of the DP steel seems similar to the NGOE steel, with a nearly constant ni, gradual decrease in strain hardening rate and continuous deformation of the ferritic matrix. During the deformation of ferritic grains as a consequence of the volume expansion, geometrically necessary dislocations (GNDs) are formed to guarantee the continuity of the lattice [20,26,27]. It is known that GNDs increase the local hardness of the surrounding ferrite grains, as demonstrated by Tsipouridis et al. [2]. However, the role of these dislocation in the strain hardening behavior, combined with the residual stress, is not completely known [20,21].
10
3.4 AISI 304 Steel 3.4.1 Microstructural Evolution The XRD analysis and the Rietveld refinement of the AISI 304 steel as received and after being strained up to = 0.1, 0.2, 0.3, 0.4 and 0.425 are shown in Figure 8. The XRD analysis shows a completely austenitic structure in the non-deformed steel, identified by the {111}, {200} and {220} peaks. However, as a response to the plastic deformation, the material undergoes athermal phase transformation, where martensite (’ is strai -induced from austenite (). The samples exhibited an increase in the proportion of strain-induced martensite as a function of the plastic deformation, detected by the increasing intensities of the {111}’, {200}’ a
{221}’ peaks.
Traces of hexagonal martensite were also identified in samples strained up to 0.2 and 0.3 logarithmic strains. Presumably, martensite acts as a precursor for the formation of tetragonal ’ martensite in early stages of deformation [3,28]. At = 0.425, the XRD pattern shows a mostly martensitic structure with some retained austenite. It is also worth noting that traces of martensite were detected in this analysis only for a limited range of plastic deformation, indicating that the strain-induced phase transformation also occurs with the help of mechanical twinning [28]. The ’ martensite weight fraction, weighted profile R-factor (Rwp) and goodness of fit (χ2) obtained by the Rietveld refinement of the X-ray patterns are listed in Table 3. Both Rwp and χ2 are important parameters to evaluate the quality of the refinement, and the literature states that acceptable Rwp values of a refinement performed with X-ray data should be approximately 10% and χ2 values should be approximately 1 [29,30]. The Rwp values determined in the refinements were approximately 13% and χ2 values were barely higher than 1, confirming the reliability of the refinement. Considering that the Rietveld refinement was developed to analyze powder diffraction patterns, a spherical
11
harmonics preferred orientation function was utilized in order to reduce possible errors associated with texture. The reflections regarding martensite presented very low intensities, then the quantity of this phase was neglected. The quantitative analysis indicate that most of the martensite is induced in early values of logarithmic strain. Optical micrographic images of the AISI 304 steel as received and after being strained up to = 0.2 and 0.425 are shown in Figure 9. The micrographic analysis is in agreement with the XRD results and shows that the as received samples (Figure 9 (a)) is constituted by an austenitic matrix (containing some traces of martensite. Considering that martensite was not identified in the XRD analysis, it is reasonable to assume that it was formed during the metallographic preparation. After being strained up to a 0.2 logarithmic strain, seen in Figure 9 (b), the presence of ’ a
strain-
induced martensite is notable, and it is evident that the formation of ’ martensite occurs at the intersection of martensite platelets [31]. A mainly ’ martensitic microstructure with isles of retained austenite was identified at = 0.425 as seen in Figure 9 (c).
3.4.2 Strain Hardening Behavior The strain hardening behavior analyses, ’ weight fractio a
’ tra sformatio rate as
a function of the logarithmic strain of the AISI 304 steel are shown in Figure 10. The ln (d/d) vs. ln curve, seen in Figure 10 (a), revealed five recognizable strain hardening stages with limits at four critical values: 1 = 0.033, 2 = 0.080, 3 = 0.111 and 4 = 0.269. The strain hardening rate, seen in Figure 10 (b), continuously decreased in stages 1 and 2, reaching a minimum in stage 3, and increased in stage 4, reaching a local maximum before stage 5 in where the rate started decreasing again. Contrary to the observations in the other steels, the instantaneous strain hardening exponent, seen in 12
Figure 10 (c), increased in the first four stages to a value as high as approximately 0.8 before decreasing in the following stage. The constant strain hardening exponent (n = 0.463) does not appear to be an accurate parameter to describe strain hardening in this case, since it strongly deviates from the instantaneous values in almost every stage. At lower logarithmic strain values, the transformation of austenite to martensite is the main strain hardening mechanism, since precedes ’. This is confirmed by the fact that ’ tra sformatio rate starts to increase in later stages, such as stage 2 and 3, indicating that the ’ marte site starts to be respo sib e for the strain hardening in these stages. Despite the decreasing values of the ’ tra sformatio rate in the last stages, the ’ martensitic transformation still occurs and certainly affects the strain hardening behavior. These results are in agreement with previous studies, which indicated that strain-induced martensitic transformation played an important role in strain hardening behavior [3,32]. The observed strain hardening behavior of AISI 304 steel and multiple strain hardening stages are consistent with previous investigations [15,32]. In stages 1, the interaction of mobile dislocations and dynamic strain softening appears to be the predominant strain hardening mechanism, as established in previous studies [6,32]. Stage 2 represents the onset of martensite formation, which occurs preferably at low strain values and only after a certain stress threshold is reached [10,31-33]. Optical microscopy observations are in accordance with this premise, as the formation of parallel martensite platelets was observed at low strain values. At the beginning of stage 2, the microstructure is mostly austenitic with platelets of martensite. Stage 3 is associated with the formation of ’ marte site c usters, a non-homogeneous plastic deformation of the matrix and a subsequent enhanced generation of geometrically necessary dislocations [31-35] as a consequence of the athermal transformations. This explains the increase in the strain
13
hardening rate observed in the following stage. In stage 4, a critical ’ marte site fraction of 0.3~0.4 is formed, and plastic deformation of austenite is no longer able to completely accommodate martensite [32]. In this stage, percolating clusters of ’ martensite are formed and generate a composite strengthening effect, increasing even more the strain hardening rate [31,36]. Accor i g to the XRD patter s, ε marte site is no longer detected in stages 4 and 5, hinting to the fact that ’ formatio is no longer associated with the formation of an intermediate phase. This is in agreement with the decrease in slope of the ’ transformation rate’s curve as seen in Figure 10 (d). During stage 5, both instantaneous strain hardening exponent, seen in Figure 10 (c), and the strain hardening rate, seen in Figure 10 (b), decrease, indicating that less strain hardening mechanisms are active. The strain-induced martensitic transformation is not the major strain hardening mechanism in stages 5, as indicated by the transformation rate in Figure 10 (d). At such high strains, strain hardening is dominated by plastic deformation and dynamic recovery of a ’ saturate microstructure, which resemb es the behavior of a single phase material [28,31,32].
4. Conclusions In the present study, the microstructural evolution as a function of plastic deformation and the strain hardening behavior of the DP, NGOE and AISI 304 steels were studied. Based on the results, the main conclusions can be summarized as follows: (1) The C–J analysis clearly revealed a two-stage hardening behavior for the NGOE steel, which is possibly associated with dynamic recovery and the interaction of dislocations with a deformed lattice. The instantaneous strain hardening exponent remained nearly constant.
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(2) The DP steel also exhibited a two-stage strain hardening behavior. In stage 1, it was observed a high strain hardening rate and increasing instantaneous strain hardening exponent. This is due to the presence of mobile dislocations that are introduced in the ferrite by the martensitic transformation during the manufacturing process of the alloy. (3) The AISI 304 steel featured a complex five-stage strain hardening behavior. The formation of strain-induced and ’ marte site has a major influence on its behavior. Therefore, this complexity comes from the activation of a variety of strain hardening mechanisms during the strain induced phase transformation.
Acknowledgements This work was partially supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES/PROEX), Brasília, DF, Brazil; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brasília, DF, Brazil; Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Belo Horizonte, MG, Brazil; and Pró-Reitoria de Pesquisa da Universidade Federal de Minas Gerais (PRPq/UFMG), Belo Horizonte, MG, Brazil. The authors would like to thank Aperam South America, Timóteo, MG, Brazil for providing the AISI 304 and NGOE steels, and Usiminas, Ipatinga, MG, Brazil for providing the DP steel. The authors deny any conflict of interest.
References
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Figure 1. (a) Engineering stress–strain curves and (b) flow curves of DP, NGOE and AISI 304 steels. Figure 2. Hardness tests as a function of the logarithmic strain. Figure 3. XRD patterns of the NGOE steel before and after deformation. Figure 4. Strain hardening behavior analysis of the NGOE steel: (a) ln (d /dε) vs. ln curve for the modified C–J analysis; (b) relation between strain hardening rate and logarithmic strain; (c) relation between the instantaneous strain hardening exponent and the logarithmic strain and a comparison with its constant strain hardening exponent. Figure 5. Optical micrograph of the DP steel, containing ferrite (F) and martensite (M). Figure 6. XRD patterns of the DP steel before and after deformation. Figure 7. Strain hardening behavior analyses of the DP steel: (a) ln (d /dε) vs. ln curve for the modified C–J analysis; (b) relation between strain hardening rate and logarithmic strain; (c) relation between the instantaneous strain hardening exponent and logarithmic strain and a comparison with its constant strain hardening exponent. Figure 8. XRD patterns (black lines) and Rietveld refinement analysis (gray lines) for the AISI 304 steel before and after deformations up to = 0.1, 0.2, 0.3, 0.4 and 0.425. Figure 9. Optical micrographs of the AISI 304 steel: (a) as received, (b) deformed up to
= 0.2 and (c) deformed up to = 0.425. Figure 10. Strain hardening behavior analysis of the AISI 304 steel: (a) ln (d /dε) vs. ln curve for the modified C-J analysis; (b) relation between strain hardening rate and logarithmic strain; (c) relation between the instantaneous strain hardening exponent and
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the logarithmic strain and a comparison with its constant strain hardening exponent; (d) α’ weight fractio a
α’ transformation rate as a function of the logarithmic strain.
Table 1. Chemical composition of the investigated steels (in wt%). Steel
C
Mn
Si
P
S
Cr
Ni
Al
AISI 304
0.0427
0.0039
0.3597
0.0247
0.0018
18.1023
8.0261
0.0024
NGOE
0.0039
1.1773
2.1278
0.0131
0.0003
-
-
0.0024
DP
0.10
1.8
0.51
0.018
0.007
-
-
0.035
Table 2. Mechanical properties determined in tensile testing. Steel
SR (MPa)
Se (MPa)
eu (%)
n
KH (MPa)
DP
664.5 ± 6.6
368.6 ± 6.1
22.5 ± 0.5
0.219 ± 0.003
1138.1 ± 9.2
NGOE
433.7 ± 7.7
315.2 ± 1.4
23.9 ± 1.15
0.240 ± 0.004
778.2 ± 11.9
AISI 304
785.8 ± 15.3
262.6 ± 5.3
55.0 ± 3.5
0.463 ± 0.007
1485.5 ± 17.5
Table 3. Quantitative analyses results and parameters from Rietveld refinement of deformed AISI 304 steel samples.
’ Weight Rwp (%)
χ2
Fraction (%) 0.1
42.1
13.52
1.385
0.2
63.7
13.12
1.397
0.3
71.6
12.37
1.307
0.4
80.3
12.31
1.285
0.425
80.5
12.88
1.428
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