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Effect of strain and strain rate on the development of deformation heterogeneity during tensile deformation of a solution annealed 304 LN austenitic stainless steel: An EBSD study
Materials Science & Engineering A 773 (2020) 138854
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Materials Science & Engineering A journal homepage: http://www.elsevier.com/locate/msea
Effect of strain and strain rate on the development of deformation heterogeneity during tensile deformation of a solution annealed 304 LN austenitic stainless steel: An EBSD study Amrita Kundu a, *, David P. Field b, Pravash Chandra Chakraborti a a b
Metallurgical and Material Engineering Department, Jadavpur University, Kolkata, 700032, India School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, 99164-2920, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Tensile deformation Geometrically necessary dislocation density Electron backscatter diffraction Electron channeling contrast imaging 304 LN austenitic stainless steel
Evolution of the microstructure and geometrically necessary dislocation (GND) structure was studied during tensile deformation of a solution annealed 304 LN austenitic stainless steel. Microstructures of the steel at varying engineering strains and strain rates (i.e., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1) were analyzed using electron back scatter diffraction (EBSD) and electron channelling contrast imaging (ECCI) at ambient tempera ture. EBSD was used to quantify the evolution of the GND structure and the martensite formed during tensile straining to reveal the deformation mechanisms in the presence of microstructural heterogeneities. The average GND density and the amount of deformation induced martensite increased with increasing plastic strain at a faster rate than expected, following a concave up pattern that accelerated GND formation as strain increased. ECCI was used to examine the dislocation storage arrangements with plastic strain. Various strain rates were imposed on the steel specimens and the results show that the average GND density increased only slightly with increasing engineering strain rate. This substantiates the small decrease in strain rate sensitivity of the steel that was observed as the plastic strain increased. Therefore, the steel is tolerant to a change in the strain rate during forming. This study provides an understanding for the way in which the plastic deformation behavior of the steel is influenced by the evolution of GND density in the presence of microstructural heterogeneities, and by deformation induced martensitic transformations.
1. Introduction Austenitic stainless steels demonstrate high ductility and work hardening as they are subjected to forming operations. Therefore, strain rate dependent deformation behavior is important. The yield stress, ul timate tensile strength, work hardening rate, and uniform elongation depend strongly on the strain rate. The influence of strain rate on tensile deformation of any material at constant strain and temperature is quantified by its strain rate sensitivity (m). Strain rate sensitivity of different materials is dependent upon dislocation density, dislocation velocity, and the barriers against dislocation motion. Therefore, a nexus exists between strain rate sensitivity and true strain [1–4]. Strain rate is governed by the mobile dislocation density and the dislocation velocity. Deformation at different strain rates causes a change in the observable dislocation structure within the material [2]. Alloy composition, stress, strain, strain rate, mode of loading,
temperature of deformation, and initial texture govern the evolution of the deformation microstructure and dislocation substructure [1–5]. Therefore, it is prudent to investigate the change in dislocation density with strain and strain rate as this allows understanding of the develop ment of microstructure in each processing stage during manufacturing [1–4]. Traditionally, transmission electron microscopy (TEM) has been used to visualize the dislocation structure developed during deformation [2,6]. Plastic deformation takes place by slip in austenitic stainless steel, which is associated with the movement of dislocations in the slip planes [1,2]. The characteristics of the dislocation structure in the austenitic stainless steel, having medium to low stacking fault energy, consists of randomly distributed dislocations as well as dislocation cells, subgrains and shear bands, etc. [2,3,5–9]. At low plastic strain, the dislocation tangles and other dislocation structures can be formed [2,6]. Cells and subgrains are the small volume elements which are separated by low
* Corresponding author. E-mail address: [email protected] (A. Kundu). https://doi.org/10.1016/j.msea.2019.138854 Received 18 July 2019; Received in revised form 17 December 2019; Accepted 20 December 2019 Available online 23 December 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.
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mode at a strain rate of 1x10-3 s-1 to five different strains, e.g., 4.87, 9.53, 13.97, 18.23 and 33.64%, and then slowly unloaded. Tensile tests were repeated to a strain of 13.97% at 1x10-4 s-1 and 1x10-2 s-1 strain rates. Following tensile deformation, small coupons were machined from the central part of the gauge section of the deformed and the remaining undeformed specimens for microstructural observation. This was done by slow speed cutting, using an Al2O3 abrasive disc in a Struers SecoTom 10 abrasive cutter. For EBSD characterisation, the polishing of the deformed and un deformed specimens was carried out following a standard polishing method [29]. Final polishing was done using a dilute solution of 0.05 μm colloidal silica suspension for 300 min to eliminate the surface defor mation, introduced during metallographic preparation. After polishing, the samples were cleaned for 30 min in an ultrasonic bath. EBSD scans were performed using a hexagonal measurement grid in a Quanta 450 FEG-SEM equipped with an EDAX EDS/EBSD system. The EBSD scan area was positioned at the centre of the specimen to eliminate edge ef fects. The final polishing step using colloidal silica suspension provides a pristine surface for analysis since the pH of the suspension (10.3) pro vides a slight chemical attack that assists with the mechanical polishing. An area corresponding to 600 to 800 grains was covered in each scan. At least 2500 grains were scanned in both the deformed and solution annealed specimens using a 0.1 μm step size, an operating voltage of 20 keV and the working distance of 15 mm, respectively. TSL OIM software was used to analyse the raw EBSD data. There was no EBSD data ‘‘clean up’’ and data having a confidence index (CI) of less than 0.1 were dis regarded. The rate of the EBSD pattern indexing with CI > 0.1 was over 90%. ECCI examination of the deformed specimens was performed using the same SEM at 20 keV operating voltage and using a working distance of 7 mm.
angle boundaries [2,6]. Following large strain, orientation gradients can be found in individual grains in polycrystalline materials. The shear bands can propagate through several grains [6]. The dislocation struc ture in the austenitic steels has planar character that is a signature of the medium to low stacking fault energy materials [2,5–9]. The dislocation density in austenite during tensile straining increases due to the generation of both statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) [1,2,6,10]. SSDs are generated during deformation and result in strain hardening of the austenite during tensile deformation [2,10]. GND structure evolves in order to maintain compatibility between the deforming grains, and also contributes to strain hardening by refining the mean free path for dislocation movement [2,10]. Characterisation of dislocation structures containing SSDs and GNDs using TEM suffers from the difficulty in specimen preparation and statistically relevant areas of investigation [2, 5,6]. X ray and neutron diffraction can also be used to track the devel opment of dislocation structures on a global scale [11–15]. In the pre sent investigation, electron backscatter diffraction (EBSD) is used to estimate the GND content following incremental tensile deformation of a solution treated 304 LN austenitic stainless steel at ambient tempera ture. The theory of using EBSD in the determination of GND structure is based on Nye’s dislocation density tensor [16]. This will be discussed in the results and discussion section. This technique does not offer any measurements of SSD density. The advantage of using EBSD to estimate GND density is that a statistically relevant number of grains can be analyzed [17–21]. Austenitic stainless steels are prone to phase transformation to martensite during tensile deformation. Austenite to martensite phase transformation imparts high work hardening and helps to increase tensile ductility in the steel. An extensive amount of research has been carried out to understand the mechanisms of martensitic transformation during deformation of austenitic strainless steels [1,3,22–24]. Defor mation induced phase transformation is governed by the alloy compo sition, strain rate, strain, stress state, and temperature of deformation [1, 22–24]. Formation of hard martensite in soft austenite changes the local deformation mechanisms of the steel [1,3,19,22–28] since the disloca tions do not move as easily through the martensitic regions as they do through the austenitic structure [1,3,19,25–28]. The objective of the present study is to characterize the evolution of the microstructure and dislocation structure of a solution annealed 304 LN austenitic stainless steel subjected to tensile deformation at different strains and strain rates (i.e., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1) using coupled imaging methods of EBSD and electron channeling contrast imaging (ECCI). We also estimate the GND density of the steel in the presence of deformation induced martensite, at various strains and strain rates using EBSD. Additionally, ECCI is used to reveal the details of the dislocation structures. The influence of microstructural hetero geneities on the change in mechanical properties is discussed.
3. Results and discussion 3.1. Tensile properties Engineering stress strain behavior of the steel at varying strain rates is plotted in Fig. 1(a). Yield strength (YS) is more sensitive to the change in strain rate as opposed to the tensile strength (UTS). YS gradually in creases with increasing strain rates due to high lattice resistance [1,2]. This was reported for 304 austenitic stainless steel previously [1–4]. The deformation of austenitic stainless steel occurs in three different stages. This can be demonstrated by plotting work hardening rate with plastic strain for different strain rates, Fig. 1(b). Fig. 1(c–e) shows the variation of work hardening rate and plastic strain on logarithmic scales demonstrating three stages of plastic deformation. The change of deformation stage with strain and strain rate is listed in Table 1. The transition strain corresponding to three different stages of deformation is found to decrease with increasing strain rate. Kundu and Chakraborti [1] reported similar transition strains in solution annealed 304 austen itic stainless steel. During stage I of strain hardening, in FCC materials, deformation occurs by easy glide. In this stage, existing dislocations and residual stress in a specimen interact with the applied stress. Deforma tion takes place on a single slip system depending on the grain size and stacking fault energy of the materials [2]. In stage II of work hardening, the occurrence of dislocation cross slips increases with increasing strain. Dislocation cell structures form. The excess dislocations are packed in the cells, and the cell size decreases resulting in a reduction in the work hardening rate [1,4]. Stage III hardening consists of dislocation cross slip and cell structure formation resulting in dynamic recovery [1,4]. At higher strain rates, multiple slip and cross slip can begin to accommodate the higher rate of deformation, resulting in diminished strain hardening and lower transition strain at higher strain rates as presented in Fig. 1(c–e) and Table 1. There is also formation of martensite during deformation. Suzuki et al. [25] explained that the
2. Experimental details In the present investigation, a commercial 304 LN austenitic stainless steel cylindrical rod of 12 mm diameter was used. The chemical composition of the steel in weight percent is C - 0.027, Mn - 1.64, Si 0.374, S - 0.028, P - 0.015, Ni – 10.06, Cr – 16.85, Mo – 2.11, Ti – 0.0008, N – 0.057. The solution annealing treatment of the as received steel was done at 1100 � C for 45 min and then quenched in normal water at ambient temperature (28 � C). Tension tests to fracture were carried out on the specimens with gauge length of 30 mm and gauge diameter of 6.25 mm, fabricated out of solution annealed specimen blanks following ASTM standard E8/E8M, using three different engineering strain rates, e.g., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1 under ambient condition. The tests were carried out by attaching an extensometer of 25.00 mm gauge length to the specimen surface using a universal testing machine, INSTRON 8501R, of �100 kN capacity. Additionally, five tensile tests were done using strain-control 2
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Fig. 1. (a). Engineering stress strain plot of 304 LN austenitic stainless steel generated from tensile tests at varying engineering strain rates, 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1. (b). Work hardening rate vs true plastic strain plot of 304 LN austenitic stainless steel at engineering strain rates of 1x10-1 s-1 to 1x10-4 s-1 generated after plotting (dσ/dεP) as a function of true plastic strain (εP). Work hardening rate (dσ/dεP) vs true plastic strain (εP) plotted on logarithmic scales at engineering strain rates of (c)1x10-2 s-1, (d) 1x10-3 s-1 and (e) 1x10-4 s-1.
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deformation is characterized using EBSD. The specimens are unloaded after five different true plastic strains; 4.87%, 9.53%, 13.97%, 18.23% and 33.64%. The orientation maps of the specimens deformed to the plastic strains of 0%–33.64% is presented in Fig. 3 (a) to (f). The colours indicate the representation of the crystallographic poles aligned with the surface normal orientation of the specimens. With increasing strain, orientation gradients develop within the grains. The development of significant deformation heterogeneities is revealed from these maps. Martensite is formed during tensile deformation and can be charac terized by the higher lattice distortion and dislocation density. It appears darker in the image quality (IQ) map because of the strained and twinned structures inherent in martensite [19]. IQ map can be utilized to separate the martensite from ferrite, while austenite has a distinguish able crystal structure using EBSD. In this study, the quality of the EBSD patterns was poor for martensite and good for austenite, even after deformation, so IQ was used to distinguish between the phases in this work. The presence of martensite is shown in Fig. 4(a) in the specimen deformed up to a plastic strain of 33.64%. The corresponding phase map is shown in Fig. 4(b). The darker regions in the IQ map (Fig. 4(a)) overlap with the martensite in the phase map (Fig. 4(b)). Intersecting shear bands are present in the IQ map (Fig. 4(a)). These are favorable sites for nucleation of the martensite [3,25]. Martensite nucleation can also take place within single shear bands, grain boundaries, triple junctions, grain boundary/shear band intersection points, etc. [3,5,25, 27,28]. TEM investigation generally has been used to characterize the nucleation sites of deformation induced martensite, but this is beyond the scope of the present investigation [25,27,28]. The amount of martensite that formed during tensile deformation is quantified from the phase maps and presented in Fig. 4 (c). The signif icant increase in the amount of martensite, starts from the plastic strain of 13.9%. Mechanical driving force, which is supplied by the applied stress, increases with increasing strain [25,27]. In addition, with increasing strain, more slip systems are activated resulting in an increasing number of intersecting shear bands and martensite fraction [25,27]. Das et al. [28], for AISI 304 LN stainless steel and Talolen et al. [3], for AISI 301 LN stainless steel, reported nonlinear variations in the amount of deformation induced martensite with the true strain. With the progress of deformation, there is a change in the staking fault energy (SFE). SFE increases with increasing deformation, [3,25,27] promoting formation of martensite at higher strains. Deformation induced martensite has a significant influence on the strain hardening behavior of the steel. The flow stress can be controlled by the static hardening effect of the martensite particles [1,2]. The transformation of austenite to martensite introduces dislocations in the austenite, and the GND component of this structure can be readily analyzed from the EBSD data, but not the SSD component of the dislo cation structure. The dislocation structure of austenite shows a signifi cant change in the presence of deformation induced martensite during
Table 1 Change of deformation stages at various engineering strain rates and plastic strains. Engineering strain rate (s-1)
Transition strain (%) (Stage I to II)
Transition strain (%) (Stage II to III)
1x10-2 1x10-3 1x10-4
3.6 5.2 5.4
21.2 26.7 28.5
martensite could nucleate at the shear bands and result in a low work hardening rate as deformation progresses at lower loads with the help of the available driving force for martensitic transformation [1,3,4]. Dynamic recovery increases with increasing strain energy and with increasing strain rate [1,4]. As a result, further deformation becomes easier, resulting in lower strain hardening rates with increasing strain rates. In stage III of deformation, the marginally higher work hardening rate of 1x10-3 s-1 as compared to the specimen deformed at 1x10-4 s-1 is due to multiple mechanisms related to dislocation mobility and increased martensite generation in stage III strains [1,3]. Deformation induced martensite formation is increased with decreasing strain rate [1, 3,28], resulting in generation of GNDs, susceptible to recovery during stage III hardening [10]. Formation of deformation induced martensite also results in refinement of the dislocation structures [1,2,6,19,24], decreasing the trapping of dislocations, mainly SSDs, in the micro structure. The stage III deformation at 1x10-4 s-1 strain rate results in higher dynamic recovery of the dislocation structure, contributing to slightly diminished work hardening rate at 1x10-4 s-1 strain rate. This is consistent with the observation by Kundu and Chakraborti [1], Lich tenfeld et al. [4], Samuel et al. [7], Suzuki et al. [25] and Benzing et al. [30]. 3.2. Strain rate sensitivity Fig. 2 (a) shows that over the strain (ε) interval of 5–30%, flow stress (σ) increases slightly with increasing instantaneous true strain rate (_ε) at a decreasing rate following a power law relationship (R2 ¼ 0.95 to 0.97). The increase in flow stress with the strain can be explained as usual by the generation of dislocations and the interaction of dislocations and microstructural barriers [1,2,4]. The exponents of these power re lationships correspond to the strain rate sensitivity (m) of the steel for different constant true strains. As a result, m shows a small decrease (0.028–0.0076) as a function of increasing true strain (Fig. 2 (b)). The change in substructure at varying strain rates can contribute to small change in m with strain, which will be discussed in Section 3.5. 3.3. Evolution of the microstructure during tensile deformation The development of the microstructures of the steel during tensile
Fig. 2. Variation of (a) flow stress with strain rate and (b) strain rate sensitivity (m) with true strain. 4
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Fig. 3. Inverse pole figure (IPF) maps of the specimens deformed at various plastic strains of (a) 0% (b) 4.87% (c) 9.53% (d) 13.97% (e) 18.23% and (f) 33.64% using a strain rate of 1x10-3 s-1. The tensile loading direction is along A1.
plastic deformation. In EN 1.4318–1 austenitic stainless steel, deformed using 3�10-4 s-1 strain rate, dislocation density in austenite, determined using x-ray line broadening, shows linear increase with strain [31]. This implies change of SSD density with martensitic transformation. It is also reflected in the increase of flow stress with deformation induced martensitic transformation [1,3,31]. The dislocation storage with plastic strain and strain rate will be discussed in the next section.
types that are present in the given crystal system [17–20]:
α¼
ρk b k � z k
�
k¼1
or in component form
αij ¼
K X
�
ρk bki zkj
�
(2)
k¼1
3.4. GND density evolution during deformation at a strain rate 1x10-3 s-1
In equation (2), ρk is the dislocation density of the kth type of dislocation that is defined by a Burgers vector of bk and a line direction of zk. Crystal structure governs the total number of dislocations of type, k. For the present steel (FCC crystal structure) both {111}<110> edge and screw dislocations can be present. It is not possible to obtain a unique solution using the set of equations described in equation (2). Several techniques can be utilized to generate minimum dislocation density associated with the measured crystal lat tice curvature. In the present study, an L2 minimisation procedure was used to obtain values for the total GND density at a given position, ρ, as this measurement procedure offers rapid calculation time [17–20]. L2 minimisation does not yield estimates of the densities of various types of dislocations nor does it include explicit line energy minimisation criteria. It is used purely as a mathematical convenience in obtaining an estimate of the GND content. The procedure does not measure the elastic strain. Lattice curvatures perpendicular to the plane of measurement are not measured in the present study (2D measurements). SSD density cannot be measured using this technique. The GND estimation is dependent upon the step size of the measurement and the precision of
Nye’s dislocation density tensor [16,17,32] can be measured using EBSD data. The components of the curvature tensor give the estimation of Nye’s dislocation density tensor [17–19] using the equation below:
αij ¼ eikl (εejl,k þ gjl,k)
K X
(1)
where αij is the dislocation density tensor, eikl is the permutation tensor, εejl,k is the gradient of the elastic strain and gjl,k is the lattice curvature. The gradient in lattice orientation is measured directly by using EBSD [17,32]. In the present work, the elastic strain components of the dislocation density tensor are assumed to be small in relation to the uncertainty in orientation measurement using EBSD [17–20], and these are neglected. 2D EBSD data are used in the present study, so the cur vature in crystallite lattice orientation along a direction normal to the plane of the EBSD map [17–20] is unknown. The dislocation density tensor is measured directly by the EBSD measurements with these ca veats (though, only five components of the tensor are determined when measurements are made on a plane section). Nye’s tensor is alternatively represented by the Burgers vectors and line directions for all dislocation
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Fig. 4. (a) IQ map (b) phase map of the specimen deformed at true plastic strains of 33.64% demonstrating the deformation induced martensite. (c) Variation of deformation induced martensite fraction with true plastic strain.
the orientation determination. This method of estimation of GND den sity is not affected by the physics of the dislocation structure. This measurement procedure offers a lower bound estimate of the GND density which can lead to formation of the measured lattice curvature. GND density measurement using this technique depends on the distance over which the lattice curvature/misorientation is measured. This is known as the step size of the measurements. Typically, this can be taken as the scale of the microstructural information. In this case, it is the diameter of the dislocation cells present in the lattice [17–20]. In the present study, 0.5 μm is used as the step size of the measurements. Fig. 5(a–f) demonstrates the EBSD derived estimates of the stored GND density maps at progressively larger tensile plastic strains. 0.5 μm step size and 5o misorientation criterion are used to define the grain size. The average stored GND density shows a gradual increase from 0.4x1013 m-2 to 8x1013 m-2 following a concave up pattern, presented in Fig. 5(g). The GND density shows a rapid rate of increase with plastic strain, particularly as strain increases to larger values. Deformation re sults in the slow buildup of GND density to 9.53% of plastic strain. At higher plastic strains, the diffraction pattern quality diminishes due to the increasing presence of dislocations and strain gradients within the interaction volume [17–21]. Therefore, the number of points available for GND calculations decreases with increasing plastic strains. In the present study, the amount of indexing with high confidence was in excess of 90%, so the quality of the raw data obtained is generally good.
The GND density distribution becomes heterogeneous at plastic strains of 13.97%. The GND storage is found to be higher at the austenite-austenite grain boundaries, austenite martensite grain boundaries and at the shear bands. The GND density, at the centre of the austenite grains is in the range of 2x1013 m-2 and at the grain boundaries is 4x1013 m-2 at plastic strain of 13.97%. The gradient in GND density between austenite grain centres to the austenite grain boundaries in creases with increase in the plastic strain (e.g. Fig. 5(d)). The disloca tions glide from the grain interior and the pile ups are formed at the grain boundaries. The grain boundaries and the austenite-martensite phase boundaries are regions of greater misfit or strain in compatibility. These are the potential sites for greater GND storage. At the austenite-martensite interfaces, there is also the presence of higher GND density. This happens to accommodate the volume expansion associated with the martensitic transformation [19,24,26]. There is significant increase in the amount of martensitic transformation after plastic strain of 13.97%. This is consistent with the faster increase of the GND density (Fig. 5(g)) with the plastic strain following a concave up pattern. The austenite and deformation induced martensite has a semi coherent interface [24]. That results in the increased requirements of the GNDs at the austenite martensite interface. Fig. 5(f) shows that at the austenite martensite interface, the GND density is ~ 4x1014 m-2 which is one order of magnitude higher than the GND density measured at the centre of the austenite grains. 6
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Fig. 5. GND density maps of the specimens deformed at true plastic strains of (a) 0%, (b) 4.87%, (c) 9.53%, (d) 13.97%, (e) 18.23% and (f) 33.64%. (g) Variation of average GND density of the specimens deformed at various true plastic strains at a strain rate of 1x10-3 s-1. Representative dislocation structure exposed using ECCI after deformation at the tensile plastic strains of (h) 9.53% (i) 13.97% and (j) 33.64%.
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Fig. 5. (continued).
ECCI was used to reveal the formation of the dislocation arrange ments in the specimens deformed to strains of 9.53%, 13.97% and 33.64% (Fig. 5(h–j)). The representative images reveal progressive refinement of the dislocation structure with the deformation explaining the reduction in the work hardening rate with progressive tensile strain. Intersecting shear bands in the microstructure are visible at 33.64% tensile strain (Fig. 5(j)). At this strain, stacking faults become unstable due to higher stress and diverge on the slip plane, making cross-slip more difficult [31]. That results in the formation of the shear bands [31]. Appearance of intersecting shear bands is a symptom of the operation of multiple slip systems. The higher amount of deformation induced martensite at 33.64% tensile strain is due to the presence of the intersecting shear bands in the microstructure producing heterogeneity in the dislocation structure as shown in Fig. 5(f). Dislocation densities are measured using microstrain and domain size method in EN 1.4318–1 and EN 1.4301 steels using tensile defor mation at a strain rate of 3x10-4 s-1 for comparable plastic strains [31]. It is in the range of 1014 m-2. This is higher than the measured average GND density in the present study. Microstrain, domain size based approach of calculating dislocation density, takes into account the SSD density component, which cannot be measured in the EBSD based measurement. This explains the lower value of the estimated GND density in the present study. The difference can also arise due to the difference in the steel grades. Total dislocation density is also estimated using X ray line broadening method in the same study for EN 1.4318–1 and EN 1.4301 steels subjected to tensile deformation at a strain rate of 3x10-4 s-1. It is in the range of 2.5 x1013 m-2 for the same strain range [3, 31]. This is consistent with the present study. The reliability of the GND measurement depends on the accuracy of the misorientation measurement. The curvature tensor used in the estimation of GND is the ratio of the change of lattice orientation to a measurement distance (or EBSD scan step size). It is necessary to assess the accuracy of the misorientation measurement [17,19–21,26,33–35].
Misorientation measurement mostly depends on the pattern centre calibration [17,19–21,26,34] and the parameters of the image analysis routines that are used in identifying the Kikuchi band positions in the patterns [17,19–21,26,33–35]. In the present study, the misorientation measurement accuracy is of the order of 0.2o [19,20]. The Kernel Average Misorientation (KAM) is used to assess a quan titative rotation angle of the specimen over an arbitrary step size. KAM is the average misorientation around that pixel with respect to a defined set of nearest neighbouring points at a distance of 500 nm (step size used in the present study). The KAM and the GND density maps of the un deformed and the deformed samples at a plastic strain of 18.23% are shown in Fig. 6 (a) to (d). With plastic deformation, the misorientation (KAM) spread increases across the austenite grain boundaries, shown in Fig. 6(c). The regions of higher KAM values necessarily correspond to the regions of higher GND values (Fig. 6(d)) establishing the direct connection of the KAM and GND as discussed in the measurement pro cedure of GND. The GND measurements show significant dependence on the step size, when the step size is very small. This has been discussed thoroughly in the case of dual phase steel [19] where it has been shown that step size greater than 0.5 μm has very little effect on the GND estimation. The dislocation cell size is determined using the KAM and GND maps (Fig. 6(a–d)). It is in the range of 0.5 μm. Therefore, in the present study, 0.5 μm step size is used. The GND density measured in the present study, agrees well with the literature [3,31]. Talonen et al. [3] reported that the flow stress of AISI 301 LN stainless steel linearly increases with the increase in the square root of the martensite content. Fang and Dahl [27] found same dependence in their study. Flow stress follows a linear relationship with the square root of the dislocation density [3,27]. Gradual buildup of GND density and the presence of deformation induced martensite during tensile straining results in the superior work hardening behavior of the present steel. In literature, attempts have been made to isolate the hardening effect due to dislocations and that due to the formation of martensite during 8
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Fig. 6. (a) Kernel average misorientation (KAM) map (b) GND density map of the undeformed solution annealed specimen (c) KAM map (d) GND density map of the specimen deformed to 18.23% strain showing direct correlation between KAM and GND at both strain levels.
deformation [25,27]. Spencer et al. [15], using in-situ neutron diffrac tion in AISI 316 L showed that martensite phase can bear a significantly higher amount of stress than austenite. Because of the gradient in the hardness of the martensite and austenite, the microstructure behaves as a composite of soft austenite matrix and hard martensite dispersions under load. With the progress of martensitic transformation during deformation, the requirement of compatibility between the austenite and martensite increases resulting in progressively higher buildup of the GND content with plastic strain (Fig. 5(g)). This increases the defor mation heterogeneity. It was reported that dislocation density of the austenite phase, measured using microstrain and domain size method, increases linearly with the plastic strain in EN 1.4318–1 and EN 1.4301 austenitic stainless steels, deformed at 3�10-4 s-1 strain rate [31] and flow stress scales linearly with the square root of dislocation density [3,27,31]. In the present investigation, GND density generates faster with tensile defor mation. It deviates from linearity with plastic strain. As a result, GND density alone cannot be utilized as an alternative of the total dislocation density. Strain hardening of austenitic stainless steel predominantly arises due to evolution of SSDs [10]. Therefore, to describe the defor mation behavior of the steel, it is necessary to consider the SSD density, GND density and deformation induced martensite leading to generation of the microstructural heterogeneities.
increasing strain rate due to adiabatic heating at the higher strain rates [1,3,5,28] leading to limited contribution in the accumulation of GNDs. Measurement of total dislocation density or SSD is not in the scope of the present study. However, literature offer evidence of linear variation of flow stress with the square root of dislocation density during tensile deformation of EN 1.4301 austenitic steel at varying strain rates of 3�10-4 and 10-1 s-1 [31]. It was also shown that, strain rate has small effect on the flow stress and dislocation density for austenitic stainless steel [1,4,31]. Therefore, small increase of flow stress with increasing engineering strain rates, as seen in the present study, indicates small change in dislocation density including SSDs and GNDs. The increase in dislocation density results in an increase in the YS and UTS with increasing strain rates and positive strain rate sensitivity. The increase in the YS can be explained by the requirement of higher stress to maintain higher dislocation velocity. The increase in UTS with strain rate is attributed to the accumulation of dislocations with the progress of deformation. This has been shown in Figs. 5 and 7. This slow rate of increase of dislocation density (and flow stress) with engineering strain rate further validates the small change of strain rate sensitivity (0.028–0.0076) with deformation. 4. Conclusions The quasi static tensile properties of the solution annealed AISI 304 LN austenitic stainless steel are investigated in the current work at strain rates ranging from 1x10-4 s-1 to 1x10-2 s-1. The major conclusions are as follows:
3.5. GND density evolution during deformation using varying strain rates In the present study, specimens with 13.97% plastic strain are chosen to investigate the development of the GND structure with varying en gineering strain rates. The GND density maps of the deformed specimens at 13.97% plastic strain with strain rates from 1x10-4 s-1 to 1x10-2 s-1 are shown in Fig. 7 (a) to (c). The GND density map of the undeformed specimen is available in Fig. 5(a). The GND concentration near austenite grain boundaries spreads to the centre of the grains at higher engi neering strain rates. The variation of GND density with strain rate is plotted in Fig. 7 (d). The rate of increase of the GND density, reduces at higher strain rate. There is evidence in the literature that indicates that the amount of deformation induced martensite decreases with
1. Experimental investigation shows that the yield stress and ultimate tensile strength increases with strain rate at a decreasing rate. Tensile deformation of austenitic stainless steel was found to occur in three different stages. The strain hardening rate decreases with increase in the strain rate. Strain rate sensitivity of the steel was found to show a small decrease (0.028–0.0076) with true strain. 2. GND density was estimated using EBSD measurements. GND density follows a concave up variation with the plastic strain. The increased rate in the buildup of GND density with plastic strain can be 9
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Fig. 7. Maps of GND density with the engineering strain rates (a) 1x10-4 s-1 (b) 1x10-3 s-1 (c) 1x10-2 s-1. (d) Variation of GND density with the engineering strain rates when deformation was carried out at a plastic strain of 13.97%.
explained by the formation of deformation induced martensite. The variation of deformation induced martensite follows the same trend with the plastic strain which was observed for the GND density (concave up). 3. The distribution of GND shows significant gradient throughout the microstructure. The preferred sites for GND storage are the grain boundaries, triple junctions, shear bands and deformation induced martensite particles. The smaller austenite grains exhibit more GND storage than the coarser austenite grains. 4. It was demonstrated that for a fixed amount of plastic strain (ε ¼ 13.97%), GND density increases at a reduced rate with increasing strain rate leading to small increase in the flow stress and positive strain rate sensitivity. The small decrease of strain rate sensitivity with strain is linked to the small change in GND density and total dislocation density with increasing engineering strain rate.
interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The financial support of the work has been received from Science and Engineering Research Board, Department of Science and technology, Government of India (file no.: ECR/2016/000260) under early career research award. The OIM research facility at Metallurgical and Material Engineering Department, Jadavpur University was used in the work. References [1] A. Kundu, P.C. Chakraborti, J. Mater. Sci. 45 (2010) 5482–5489. [2] G.E. Dieter, Mechanical Metallurgy, McGraw Hill Book Company, UK, 1988. [3] J. Talonen, P. Nenonen, G. Pape, H. H€ anninen, Metall. Mater. Trans. A 36 A (2005) 421–432. [4] J.A. Lichtenfeld, C.J. Van Tyne, M.C. Mataya, Metall. Mater. Trans. A 37 (2006) 147–161. [5] A. Kundu, D.P. Field, P.C. Chakraborti, Mater. Sci. Eng. A (2019) 762, https://doi. org/10.1016/j.msea.2019.138090. [6] J.F. Humphreys, M. Hatherly, Recrystallisation and Related Annealing Phenomena, Pergamon Press, Kidlington, Oxford, UK, 1995. [7] E. Isaac Samuel, B.K. Choudhary, K. Bhanu Sankara Rao, Scripta Matter 46 (2002) 507–512. [8] A.A. Tiamiyu, J.A. Szpunar, A.G. Odeshi, Mater. Char. 154 (2019) 7–19. [9] W.S. Lee, C.F. Lin, Mater. Sci. Eng. A 308 (2001) 124–135. [10] M.F. Ashby, Philos. Mag. 21 (1970) 399–424. [11] M. Griffiths, D. Sage, R.A. Holt, C.N. Tome, Metall. Mater. Trans. A 33 (2002) 859–865. [12] T. Narutani, G.B. Olson, M. Cohen, J. Phys. 43 (C4) (1982). C4-429-C4-434.
Author contribution statement Amrita Kundu: Conceptualization, Investigation, Writing- Original draft preparation, Reviewing and Editing, Funding Acquisition, Project administration. David P. Field: Conceptualization, Writing- Reviewing and Editing. Pravash Chandra Chakraborti: Conceptualization. Declaration of competing interest The authors declare that they have no known competing financial 10
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Materials Science & Engineering A 773 (2020) 138854 [25] T. Suzuki, H. Kojima, K. Suzuki, T. Hashimoto, M. Ichihara, Acta Metall. 25 (1977) 1151–1162. [26] M. Calcagnotto, D. Ponge, E. Demir, D. Raabe, Mater. Sci. Eng. A 527 (2010) 2738–2746. [27] X.F. Fang, W. Dahl, Mater. Sci. Eng. A 141 (1991) 189–198. [28] A. Das, S. Sivaprasad, M. Ghosh, P.C. Chakraborti, S. Tarafder, Mater. Sci. Eng. A 486 (2008) 283–286. [29] S.I. Wright, M.M. Nowell, Microsc. Microanal. 12 (2006) 72–84. [30] J.T. Benzing, W.A. Poling, D.T. Pierce, J. Bentley, K.O. Findley, D. Raabe, J. E. Wittig, Mater. Sci. Eng. A 711 (2018) 78–92. [31] J. Talonen, Ph.D. Thesis, Helsinki University of Technology, Finland, 2007. [32] B.S. El-Dasher, B.L. Adams, A.D. Rollett, Scr. Mater. 48 (2003) 141–145. [33] T.B. Britton, A.J. Wilkinson, Ultramicroscopy 111 (2011) 1395–1404. [34] M. Kamaya, Mater. Char. 60 (2009) 1454–1462. [35] M. Kamaya, A.J. Wilkinson, J.M. Titchmarsh, Acta Mater. 54 (2006) 539–548.
[13] H. Li, G. Sun, W. Woo, J. Gong, B. Chen, Y. Wang, Y.Q. Fu, C. Huang, L. Xie, S. Peng, J. Nucl. Mater. 446 (2014) 134–141. [14] F. Christien, M.T.F. Telling, K.S. Knight, Scripta Matter 68 (2013) 506–509. [15] K. Spencer, J.D. Embury, K.T. Conlon, M. V�eron, Y. Br� echet, Mater. Sci. Eng. A 387–389 (2004) 873–881. [16] J.F. Nye, Acta Metall. 1 (1953) 153–162. [17] D.P. Field, C.C. Merriman, N. Allain-Bonasso, F. Wagner, Model. Simul. Mater. Sci. Eng. 20 (2012), https://doi.org/10.1088/0965–0393/20/2/024007. [18] J. Jiang, T.B. Britton, A.J. Wilkinson, Acta Mater. 61 (2013) 7227–7239. [19] A. Kundu, D.P. Field, Mater. Sci. Eng. A 667 (2016) 435–443. [20] A. Kundu, D.P. Field, Metall. Mater. Trans. A 49 (2018) 3274–3282. [21] E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer, Acta Mater. 57 (2009) 559–569. [22] G.B. Olson, M. Cohen, Metall. Trans. A 7 (1976) 1897–1904. [23] G.B. Olson, M. Cohen, Metall. Trans. A 7 (1976) 1905–1914. [24] H.K.D.H. Bhadeshia, Geometry of Crystals, second ed., Institute of Materials, London, 2006.
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Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: http://www.elsevier.com/locate/msea
Effect of strain and strain rate on the development of deformation heterogeneity during tensile deformation of a solution annealed 304 LN austenitic stainless steel: An EBSD study Amrita Kundu a, *, David P. Field b, Pravash Chandra Chakraborti a a b
Metallurgical and Material Engineering Department, Jadavpur University, Kolkata, 700032, India School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, 99164-2920, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Tensile deformation Geometrically necessary dislocation density Electron backscatter diffraction Electron channeling contrast imaging 304 LN austenitic stainless steel
Evolution of the microstructure and geometrically necessary dislocation (GND) structure was studied during tensile deformation of a solution annealed 304 LN austenitic stainless steel. Microstructures of the steel at varying engineering strains and strain rates (i.e., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1) were analyzed using electron back scatter diffraction (EBSD) and electron channelling contrast imaging (ECCI) at ambient tempera ture. EBSD was used to quantify the evolution of the GND structure and the martensite formed during tensile straining to reveal the deformation mechanisms in the presence of microstructural heterogeneities. The average GND density and the amount of deformation induced martensite increased with increasing plastic strain at a faster rate than expected, following a concave up pattern that accelerated GND formation as strain increased. ECCI was used to examine the dislocation storage arrangements with plastic strain. Various strain rates were imposed on the steel specimens and the results show that the average GND density increased only slightly with increasing engineering strain rate. This substantiates the small decrease in strain rate sensitivity of the steel that was observed as the plastic strain increased. Therefore, the steel is tolerant to a change in the strain rate during forming. This study provides an understanding for the way in which the plastic deformation behavior of the steel is influenced by the evolution of GND density in the presence of microstructural heterogeneities, and by deformation induced martensitic transformations.
1. Introduction Austenitic stainless steels demonstrate high ductility and work hardening as they are subjected to forming operations. Therefore, strain rate dependent deformation behavior is important. The yield stress, ul timate tensile strength, work hardening rate, and uniform elongation depend strongly on the strain rate. The influence of strain rate on tensile deformation of any material at constant strain and temperature is quantified by its strain rate sensitivity (m). Strain rate sensitivity of different materials is dependent upon dislocation density, dislocation velocity, and the barriers against dislocation motion. Therefore, a nexus exists between strain rate sensitivity and true strain [1–4]. Strain rate is governed by the mobile dislocation density and the dislocation velocity. Deformation at different strain rates causes a change in the observable dislocation structure within the material [2]. Alloy composition, stress, strain, strain rate, mode of loading,
temperature of deformation, and initial texture govern the evolution of the deformation microstructure and dislocation substructure [1–5]. Therefore, it is prudent to investigate the change in dislocation density with strain and strain rate as this allows understanding of the develop ment of microstructure in each processing stage during manufacturing [1–4]. Traditionally, transmission electron microscopy (TEM) has been used to visualize the dislocation structure developed during deformation [2,6]. Plastic deformation takes place by slip in austenitic stainless steel, which is associated with the movement of dislocations in the slip planes [1,2]. The characteristics of the dislocation structure in the austenitic stainless steel, having medium to low stacking fault energy, consists of randomly distributed dislocations as well as dislocation cells, subgrains and shear bands, etc. [2,3,5–9]. At low plastic strain, the dislocation tangles and other dislocation structures can be formed [2,6]. Cells and subgrains are the small volume elements which are separated by low
* Corresponding author. E-mail address: [email protected] (A. Kundu). https://doi.org/10.1016/j.msea.2019.138854 Received 18 July 2019; Received in revised form 17 December 2019; Accepted 20 December 2019 Available online 23 December 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.
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mode at a strain rate of 1x10-3 s-1 to five different strains, e.g., 4.87, 9.53, 13.97, 18.23 and 33.64%, and then slowly unloaded. Tensile tests were repeated to a strain of 13.97% at 1x10-4 s-1 and 1x10-2 s-1 strain rates. Following tensile deformation, small coupons were machined from the central part of the gauge section of the deformed and the remaining undeformed specimens for microstructural observation. This was done by slow speed cutting, using an Al2O3 abrasive disc in a Struers SecoTom 10 abrasive cutter. For EBSD characterisation, the polishing of the deformed and un deformed specimens was carried out following a standard polishing method [29]. Final polishing was done using a dilute solution of 0.05 μm colloidal silica suspension for 300 min to eliminate the surface defor mation, introduced during metallographic preparation. After polishing, the samples were cleaned for 30 min in an ultrasonic bath. EBSD scans were performed using a hexagonal measurement grid in a Quanta 450 FEG-SEM equipped with an EDAX EDS/EBSD system. The EBSD scan area was positioned at the centre of the specimen to eliminate edge ef fects. The final polishing step using colloidal silica suspension provides a pristine surface for analysis since the pH of the suspension (10.3) pro vides a slight chemical attack that assists with the mechanical polishing. An area corresponding to 600 to 800 grains was covered in each scan. At least 2500 grains were scanned in both the deformed and solution annealed specimens using a 0.1 μm step size, an operating voltage of 20 keV and the working distance of 15 mm, respectively. TSL OIM software was used to analyse the raw EBSD data. There was no EBSD data ‘‘clean up’’ and data having a confidence index (CI) of less than 0.1 were dis regarded. The rate of the EBSD pattern indexing with CI > 0.1 was over 90%. ECCI examination of the deformed specimens was performed using the same SEM at 20 keV operating voltage and using a working distance of 7 mm.
angle boundaries [2,6]. Following large strain, orientation gradients can be found in individual grains in polycrystalline materials. The shear bands can propagate through several grains [6]. The dislocation struc ture in the austenitic steels has planar character that is a signature of the medium to low stacking fault energy materials [2,5–9]. The dislocation density in austenite during tensile straining increases due to the generation of both statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) [1,2,6,10]. SSDs are generated during deformation and result in strain hardening of the austenite during tensile deformation [2,10]. GND structure evolves in order to maintain compatibility between the deforming grains, and also contributes to strain hardening by refining the mean free path for dislocation movement [2,10]. Characterisation of dislocation structures containing SSDs and GNDs using TEM suffers from the difficulty in specimen preparation and statistically relevant areas of investigation [2, 5,6]. X ray and neutron diffraction can also be used to track the devel opment of dislocation structures on a global scale [11–15]. In the pre sent investigation, electron backscatter diffraction (EBSD) is used to estimate the GND content following incremental tensile deformation of a solution treated 304 LN austenitic stainless steel at ambient tempera ture. The theory of using EBSD in the determination of GND structure is based on Nye’s dislocation density tensor [16]. This will be discussed in the results and discussion section. This technique does not offer any measurements of SSD density. The advantage of using EBSD to estimate GND density is that a statistically relevant number of grains can be analyzed [17–21]. Austenitic stainless steels are prone to phase transformation to martensite during tensile deformation. Austenite to martensite phase transformation imparts high work hardening and helps to increase tensile ductility in the steel. An extensive amount of research has been carried out to understand the mechanisms of martensitic transformation during deformation of austenitic strainless steels [1,3,22–24]. Defor mation induced phase transformation is governed by the alloy compo sition, strain rate, strain, stress state, and temperature of deformation [1, 22–24]. Formation of hard martensite in soft austenite changes the local deformation mechanisms of the steel [1,3,19,22–28] since the disloca tions do not move as easily through the martensitic regions as they do through the austenitic structure [1,3,19,25–28]. The objective of the present study is to characterize the evolution of the microstructure and dislocation structure of a solution annealed 304 LN austenitic stainless steel subjected to tensile deformation at different strains and strain rates (i.e., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1) using coupled imaging methods of EBSD and electron channeling contrast imaging (ECCI). We also estimate the GND density of the steel in the presence of deformation induced martensite, at various strains and strain rates using EBSD. Additionally, ECCI is used to reveal the details of the dislocation structures. The influence of microstructural hetero geneities on the change in mechanical properties is discussed.
3. Results and discussion 3.1. Tensile properties Engineering stress strain behavior of the steel at varying strain rates is plotted in Fig. 1(a). Yield strength (YS) is more sensitive to the change in strain rate as opposed to the tensile strength (UTS). YS gradually in creases with increasing strain rates due to high lattice resistance [1,2]. This was reported for 304 austenitic stainless steel previously [1–4]. The deformation of austenitic stainless steel occurs in three different stages. This can be demonstrated by plotting work hardening rate with plastic strain for different strain rates, Fig. 1(b). Fig. 1(c–e) shows the variation of work hardening rate and plastic strain on logarithmic scales demonstrating three stages of plastic deformation. The change of deformation stage with strain and strain rate is listed in Table 1. The transition strain corresponding to three different stages of deformation is found to decrease with increasing strain rate. Kundu and Chakraborti [1] reported similar transition strains in solution annealed 304 austen itic stainless steel. During stage I of strain hardening, in FCC materials, deformation occurs by easy glide. In this stage, existing dislocations and residual stress in a specimen interact with the applied stress. Deforma tion takes place on a single slip system depending on the grain size and stacking fault energy of the materials [2]. In stage II of work hardening, the occurrence of dislocation cross slips increases with increasing strain. Dislocation cell structures form. The excess dislocations are packed in the cells, and the cell size decreases resulting in a reduction in the work hardening rate [1,4]. Stage III hardening consists of dislocation cross slip and cell structure formation resulting in dynamic recovery [1,4]. At higher strain rates, multiple slip and cross slip can begin to accommodate the higher rate of deformation, resulting in diminished strain hardening and lower transition strain at higher strain rates as presented in Fig. 1(c–e) and Table 1. There is also formation of martensite during deformation. Suzuki et al. [25] explained that the
2. Experimental details In the present investigation, a commercial 304 LN austenitic stainless steel cylindrical rod of 12 mm diameter was used. The chemical composition of the steel in weight percent is C - 0.027, Mn - 1.64, Si 0.374, S - 0.028, P - 0.015, Ni – 10.06, Cr – 16.85, Mo – 2.11, Ti – 0.0008, N – 0.057. The solution annealing treatment of the as received steel was done at 1100 � C for 45 min and then quenched in normal water at ambient temperature (28 � C). Tension tests to fracture were carried out on the specimens with gauge length of 30 mm and gauge diameter of 6.25 mm, fabricated out of solution annealed specimen blanks following ASTM standard E8/E8M, using three different engineering strain rates, e.g., 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1 under ambient condition. The tests were carried out by attaching an extensometer of 25.00 mm gauge length to the specimen surface using a universal testing machine, INSTRON 8501R, of �100 kN capacity. Additionally, five tensile tests were done using strain-control 2
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Fig. 1. (a). Engineering stress strain plot of 304 LN austenitic stainless steel generated from tensile tests at varying engineering strain rates, 1x10-4 s-1, 1x10-3 s-1 and 1x10-2 s-1. (b). Work hardening rate vs true plastic strain plot of 304 LN austenitic stainless steel at engineering strain rates of 1x10-1 s-1 to 1x10-4 s-1 generated after plotting (dσ/dεP) as a function of true plastic strain (εP). Work hardening rate (dσ/dεP) vs true plastic strain (εP) plotted on logarithmic scales at engineering strain rates of (c)1x10-2 s-1, (d) 1x10-3 s-1 and (e) 1x10-4 s-1.
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deformation is characterized using EBSD. The specimens are unloaded after five different true plastic strains; 4.87%, 9.53%, 13.97%, 18.23% and 33.64%. The orientation maps of the specimens deformed to the plastic strains of 0%–33.64% is presented in Fig. 3 (a) to (f). The colours indicate the representation of the crystallographic poles aligned with the surface normal orientation of the specimens. With increasing strain, orientation gradients develop within the grains. The development of significant deformation heterogeneities is revealed from these maps. Martensite is formed during tensile deformation and can be charac terized by the higher lattice distortion and dislocation density. It appears darker in the image quality (IQ) map because of the strained and twinned structures inherent in martensite [19]. IQ map can be utilized to separate the martensite from ferrite, while austenite has a distinguish able crystal structure using EBSD. In this study, the quality of the EBSD patterns was poor for martensite and good for austenite, even after deformation, so IQ was used to distinguish between the phases in this work. The presence of martensite is shown in Fig. 4(a) in the specimen deformed up to a plastic strain of 33.64%. The corresponding phase map is shown in Fig. 4(b). The darker regions in the IQ map (Fig. 4(a)) overlap with the martensite in the phase map (Fig. 4(b)). Intersecting shear bands are present in the IQ map (Fig. 4(a)). These are favorable sites for nucleation of the martensite [3,25]. Martensite nucleation can also take place within single shear bands, grain boundaries, triple junctions, grain boundary/shear band intersection points, etc. [3,5,25, 27,28]. TEM investigation generally has been used to characterize the nucleation sites of deformation induced martensite, but this is beyond the scope of the present investigation [25,27,28]. The amount of martensite that formed during tensile deformation is quantified from the phase maps and presented in Fig. 4 (c). The signif icant increase in the amount of martensite, starts from the plastic strain of 13.9%. Mechanical driving force, which is supplied by the applied stress, increases with increasing strain [25,27]. In addition, with increasing strain, more slip systems are activated resulting in an increasing number of intersecting shear bands and martensite fraction [25,27]. Das et al. [28], for AISI 304 LN stainless steel and Talolen et al. [3], for AISI 301 LN stainless steel, reported nonlinear variations in the amount of deformation induced martensite with the true strain. With the progress of deformation, there is a change in the staking fault energy (SFE). SFE increases with increasing deformation, [3,25,27] promoting formation of martensite at higher strains. Deformation induced martensite has a significant influence on the strain hardening behavior of the steel. The flow stress can be controlled by the static hardening effect of the martensite particles [1,2]. The transformation of austenite to martensite introduces dislocations in the austenite, and the GND component of this structure can be readily analyzed from the EBSD data, but not the SSD component of the dislo cation structure. The dislocation structure of austenite shows a signifi cant change in the presence of deformation induced martensite during
Table 1 Change of deformation stages at various engineering strain rates and plastic strains. Engineering strain rate (s-1)
Transition strain (%) (Stage I to II)
Transition strain (%) (Stage II to III)
1x10-2 1x10-3 1x10-4
3.6 5.2 5.4
21.2 26.7 28.5
martensite could nucleate at the shear bands and result in a low work hardening rate as deformation progresses at lower loads with the help of the available driving force for martensitic transformation [1,3,4]. Dynamic recovery increases with increasing strain energy and with increasing strain rate [1,4]. As a result, further deformation becomes easier, resulting in lower strain hardening rates with increasing strain rates. In stage III of deformation, the marginally higher work hardening rate of 1x10-3 s-1 as compared to the specimen deformed at 1x10-4 s-1 is due to multiple mechanisms related to dislocation mobility and increased martensite generation in stage III strains [1,3]. Deformation induced martensite formation is increased with decreasing strain rate [1, 3,28], resulting in generation of GNDs, susceptible to recovery during stage III hardening [10]. Formation of deformation induced martensite also results in refinement of the dislocation structures [1,2,6,19,24], decreasing the trapping of dislocations, mainly SSDs, in the micro structure. The stage III deformation at 1x10-4 s-1 strain rate results in higher dynamic recovery of the dislocation structure, contributing to slightly diminished work hardening rate at 1x10-4 s-1 strain rate. This is consistent with the observation by Kundu and Chakraborti [1], Lich tenfeld et al. [4], Samuel et al. [7], Suzuki et al. [25] and Benzing et al. [30]. 3.2. Strain rate sensitivity Fig. 2 (a) shows that over the strain (ε) interval of 5–30%, flow stress (σ) increases slightly with increasing instantaneous true strain rate (_ε) at a decreasing rate following a power law relationship (R2 ¼ 0.95 to 0.97). The increase in flow stress with the strain can be explained as usual by the generation of dislocations and the interaction of dislocations and microstructural barriers [1,2,4]. The exponents of these power re lationships correspond to the strain rate sensitivity (m) of the steel for different constant true strains. As a result, m shows a small decrease (0.028–0.0076) as a function of increasing true strain (Fig. 2 (b)). The change in substructure at varying strain rates can contribute to small change in m with strain, which will be discussed in Section 3.5. 3.3. Evolution of the microstructure during tensile deformation The development of the microstructures of the steel during tensile
Fig. 2. Variation of (a) flow stress with strain rate and (b) strain rate sensitivity (m) with true strain. 4
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Fig. 3. Inverse pole figure (IPF) maps of the specimens deformed at various plastic strains of (a) 0% (b) 4.87% (c) 9.53% (d) 13.97% (e) 18.23% and (f) 33.64% using a strain rate of 1x10-3 s-1. The tensile loading direction is along A1.
plastic deformation. In EN 1.4318–1 austenitic stainless steel, deformed using 3�10-4 s-1 strain rate, dislocation density in austenite, determined using x-ray line broadening, shows linear increase with strain [31]. This implies change of SSD density with martensitic transformation. It is also reflected in the increase of flow stress with deformation induced martensitic transformation [1,3,31]. The dislocation storage with plastic strain and strain rate will be discussed in the next section.
types that are present in the given crystal system [17–20]:
α¼
ρk b k � z k
�
k¼1
or in component form
αij ¼
K X
�
ρk bki zkj
�
(2)
k¼1
3.4. GND density evolution during deformation at a strain rate 1x10-3 s-1
In equation (2), ρk is the dislocation density of the kth type of dislocation that is defined by a Burgers vector of bk and a line direction of zk. Crystal structure governs the total number of dislocations of type, k. For the present steel (FCC crystal structure) both {111}<110> edge and screw dislocations can be present. It is not possible to obtain a unique solution using the set of equations described in equation (2). Several techniques can be utilized to generate minimum dislocation density associated with the measured crystal lat tice curvature. In the present study, an L2 minimisation procedure was used to obtain values for the total GND density at a given position, ρ, as this measurement procedure offers rapid calculation time [17–20]. L2 minimisation does not yield estimates of the densities of various types of dislocations nor does it include explicit line energy minimisation criteria. It is used purely as a mathematical convenience in obtaining an estimate of the GND content. The procedure does not measure the elastic strain. Lattice curvatures perpendicular to the plane of measurement are not measured in the present study (2D measurements). SSD density cannot be measured using this technique. The GND estimation is dependent upon the step size of the measurement and the precision of
Nye’s dislocation density tensor [16,17,32] can be measured using EBSD data. The components of the curvature tensor give the estimation of Nye’s dislocation density tensor [17–19] using the equation below:
αij ¼ eikl (εejl,k þ gjl,k)
K X
(1)
where αij is the dislocation density tensor, eikl is the permutation tensor, εejl,k is the gradient of the elastic strain and gjl,k is the lattice curvature. The gradient in lattice orientation is measured directly by using EBSD [17,32]. In the present work, the elastic strain components of the dislocation density tensor are assumed to be small in relation to the uncertainty in orientation measurement using EBSD [17–20], and these are neglected. 2D EBSD data are used in the present study, so the cur vature in crystallite lattice orientation along a direction normal to the plane of the EBSD map [17–20] is unknown. The dislocation density tensor is measured directly by the EBSD measurements with these ca veats (though, only five components of the tensor are determined when measurements are made on a plane section). Nye’s tensor is alternatively represented by the Burgers vectors and line directions for all dislocation
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Fig. 4. (a) IQ map (b) phase map of the specimen deformed at true plastic strains of 33.64% demonstrating the deformation induced martensite. (c) Variation of deformation induced martensite fraction with true plastic strain.
the orientation determination. This method of estimation of GND den sity is not affected by the physics of the dislocation structure. This measurement procedure offers a lower bound estimate of the GND density which can lead to formation of the measured lattice curvature. GND density measurement using this technique depends on the distance over which the lattice curvature/misorientation is measured. This is known as the step size of the measurements. Typically, this can be taken as the scale of the microstructural information. In this case, it is the diameter of the dislocation cells present in the lattice [17–20]. In the present study, 0.5 μm is used as the step size of the measurements. Fig. 5(a–f) demonstrates the EBSD derived estimates of the stored GND density maps at progressively larger tensile plastic strains. 0.5 μm step size and 5o misorientation criterion are used to define the grain size. The average stored GND density shows a gradual increase from 0.4x1013 m-2 to 8x1013 m-2 following a concave up pattern, presented in Fig. 5(g). The GND density shows a rapid rate of increase with plastic strain, particularly as strain increases to larger values. Deformation re sults in the slow buildup of GND density to 9.53% of plastic strain. At higher plastic strains, the diffraction pattern quality diminishes due to the increasing presence of dislocations and strain gradients within the interaction volume [17–21]. Therefore, the number of points available for GND calculations decreases with increasing plastic strains. In the present study, the amount of indexing with high confidence was in excess of 90%, so the quality of the raw data obtained is generally good.
The GND density distribution becomes heterogeneous at plastic strains of 13.97%. The GND storage is found to be higher at the austenite-austenite grain boundaries, austenite martensite grain boundaries and at the shear bands. The GND density, at the centre of the austenite grains is in the range of 2x1013 m-2 and at the grain boundaries is 4x1013 m-2 at plastic strain of 13.97%. The gradient in GND density between austenite grain centres to the austenite grain boundaries in creases with increase in the plastic strain (e.g. Fig. 5(d)). The disloca tions glide from the grain interior and the pile ups are formed at the grain boundaries. The grain boundaries and the austenite-martensite phase boundaries are regions of greater misfit or strain in compatibility. These are the potential sites for greater GND storage. At the austenite-martensite interfaces, there is also the presence of higher GND density. This happens to accommodate the volume expansion associated with the martensitic transformation [19,24,26]. There is significant increase in the amount of martensitic transformation after plastic strain of 13.97%. This is consistent with the faster increase of the GND density (Fig. 5(g)) with the plastic strain following a concave up pattern. The austenite and deformation induced martensite has a semi coherent interface [24]. That results in the increased requirements of the GNDs at the austenite martensite interface. Fig. 5(f) shows that at the austenite martensite interface, the GND density is ~ 4x1014 m-2 which is one order of magnitude higher than the GND density measured at the centre of the austenite grains. 6
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Fig. 5. GND density maps of the specimens deformed at true plastic strains of (a) 0%, (b) 4.87%, (c) 9.53%, (d) 13.97%, (e) 18.23% and (f) 33.64%. (g) Variation of average GND density of the specimens deformed at various true plastic strains at a strain rate of 1x10-3 s-1. Representative dislocation structure exposed using ECCI after deformation at the tensile plastic strains of (h) 9.53% (i) 13.97% and (j) 33.64%.
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Fig. 5. (continued).
ECCI was used to reveal the formation of the dislocation arrange ments in the specimens deformed to strains of 9.53%, 13.97% and 33.64% (Fig. 5(h–j)). The representative images reveal progressive refinement of the dislocation structure with the deformation explaining the reduction in the work hardening rate with progressive tensile strain. Intersecting shear bands in the microstructure are visible at 33.64% tensile strain (Fig. 5(j)). At this strain, stacking faults become unstable due to higher stress and diverge on the slip plane, making cross-slip more difficult [31]. That results in the formation of the shear bands [31]. Appearance of intersecting shear bands is a symptom of the operation of multiple slip systems. The higher amount of deformation induced martensite at 33.64% tensile strain is due to the presence of the intersecting shear bands in the microstructure producing heterogeneity in the dislocation structure as shown in Fig. 5(f). Dislocation densities are measured using microstrain and domain size method in EN 1.4318–1 and EN 1.4301 steels using tensile defor mation at a strain rate of 3x10-4 s-1 for comparable plastic strains [31]. It is in the range of 1014 m-2. This is higher than the measured average GND density in the present study. Microstrain, domain size based approach of calculating dislocation density, takes into account the SSD density component, which cannot be measured in the EBSD based measurement. This explains the lower value of the estimated GND density in the present study. The difference can also arise due to the difference in the steel grades. Total dislocation density is also estimated using X ray line broadening method in the same study for EN 1.4318–1 and EN 1.4301 steels subjected to tensile deformation at a strain rate of 3x10-4 s-1. It is in the range of 2.5 x1013 m-2 for the same strain range [3, 31]. This is consistent with the present study. The reliability of the GND measurement depends on the accuracy of the misorientation measurement. The curvature tensor used in the estimation of GND is the ratio of the change of lattice orientation to a measurement distance (or EBSD scan step size). It is necessary to assess the accuracy of the misorientation measurement [17,19–21,26,33–35].
Misorientation measurement mostly depends on the pattern centre calibration [17,19–21,26,34] and the parameters of the image analysis routines that are used in identifying the Kikuchi band positions in the patterns [17,19–21,26,33–35]. In the present study, the misorientation measurement accuracy is of the order of 0.2o [19,20]. The Kernel Average Misorientation (KAM) is used to assess a quan titative rotation angle of the specimen over an arbitrary step size. KAM is the average misorientation around that pixel with respect to a defined set of nearest neighbouring points at a distance of 500 nm (step size used in the present study). The KAM and the GND density maps of the un deformed and the deformed samples at a plastic strain of 18.23% are shown in Fig. 6 (a) to (d). With plastic deformation, the misorientation (KAM) spread increases across the austenite grain boundaries, shown in Fig. 6(c). The regions of higher KAM values necessarily correspond to the regions of higher GND values (Fig. 6(d)) establishing the direct connection of the KAM and GND as discussed in the measurement pro cedure of GND. The GND measurements show significant dependence on the step size, when the step size is very small. This has been discussed thoroughly in the case of dual phase steel [19] where it has been shown that step size greater than 0.5 μm has very little effect on the GND estimation. The dislocation cell size is determined using the KAM and GND maps (Fig. 6(a–d)). It is in the range of 0.5 μm. Therefore, in the present study, 0.5 μm step size is used. The GND density measured in the present study, agrees well with the literature [3,31]. Talonen et al. [3] reported that the flow stress of AISI 301 LN stainless steel linearly increases with the increase in the square root of the martensite content. Fang and Dahl [27] found same dependence in their study. Flow stress follows a linear relationship with the square root of the dislocation density [3,27]. Gradual buildup of GND density and the presence of deformation induced martensite during tensile straining results in the superior work hardening behavior of the present steel. In literature, attempts have been made to isolate the hardening effect due to dislocations and that due to the formation of martensite during 8
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Fig. 6. (a) Kernel average misorientation (KAM) map (b) GND density map of the undeformed solution annealed specimen (c) KAM map (d) GND density map of the specimen deformed to 18.23% strain showing direct correlation between KAM and GND at both strain levels.
deformation [25,27]. Spencer et al. [15], using in-situ neutron diffrac tion in AISI 316 L showed that martensite phase can bear a significantly higher amount of stress than austenite. Because of the gradient in the hardness of the martensite and austenite, the microstructure behaves as a composite of soft austenite matrix and hard martensite dispersions under load. With the progress of martensitic transformation during deformation, the requirement of compatibility between the austenite and martensite increases resulting in progressively higher buildup of the GND content with plastic strain (Fig. 5(g)). This increases the defor mation heterogeneity. It was reported that dislocation density of the austenite phase, measured using microstrain and domain size method, increases linearly with the plastic strain in EN 1.4318–1 and EN 1.4301 austenitic stainless steels, deformed at 3�10-4 s-1 strain rate [31] and flow stress scales linearly with the square root of dislocation density [3,27,31]. In the present investigation, GND density generates faster with tensile defor mation. It deviates from linearity with plastic strain. As a result, GND density alone cannot be utilized as an alternative of the total dislocation density. Strain hardening of austenitic stainless steel predominantly arises due to evolution of SSDs [10]. Therefore, to describe the defor mation behavior of the steel, it is necessary to consider the SSD density, GND density and deformation induced martensite leading to generation of the microstructural heterogeneities.
increasing strain rate due to adiabatic heating at the higher strain rates [1,3,5,28] leading to limited contribution in the accumulation of GNDs. Measurement of total dislocation density or SSD is not in the scope of the present study. However, literature offer evidence of linear variation of flow stress with the square root of dislocation density during tensile deformation of EN 1.4301 austenitic steel at varying strain rates of 3�10-4 and 10-1 s-1 [31]. It was also shown that, strain rate has small effect on the flow stress and dislocation density for austenitic stainless steel [1,4,31]. Therefore, small increase of flow stress with increasing engineering strain rates, as seen in the present study, indicates small change in dislocation density including SSDs and GNDs. The increase in dislocation density results in an increase in the YS and UTS with increasing strain rates and positive strain rate sensitivity. The increase in the YS can be explained by the requirement of higher stress to maintain higher dislocation velocity. The increase in UTS with strain rate is attributed to the accumulation of dislocations with the progress of deformation. This has been shown in Figs. 5 and 7. This slow rate of increase of dislocation density (and flow stress) with engineering strain rate further validates the small change of strain rate sensitivity (0.028–0.0076) with deformation. 4. Conclusions The quasi static tensile properties of the solution annealed AISI 304 LN austenitic stainless steel are investigated in the current work at strain rates ranging from 1x10-4 s-1 to 1x10-2 s-1. The major conclusions are as follows:
3.5. GND density evolution during deformation using varying strain rates In the present study, specimens with 13.97% plastic strain are chosen to investigate the development of the GND structure with varying en gineering strain rates. The GND density maps of the deformed specimens at 13.97% plastic strain with strain rates from 1x10-4 s-1 to 1x10-2 s-1 are shown in Fig. 7 (a) to (c). The GND density map of the undeformed specimen is available in Fig. 5(a). The GND concentration near austenite grain boundaries spreads to the centre of the grains at higher engi neering strain rates. The variation of GND density with strain rate is plotted in Fig. 7 (d). The rate of increase of the GND density, reduces at higher strain rate. There is evidence in the literature that indicates that the amount of deformation induced martensite decreases with
1. Experimental investigation shows that the yield stress and ultimate tensile strength increases with strain rate at a decreasing rate. Tensile deformation of austenitic stainless steel was found to occur in three different stages. The strain hardening rate decreases with increase in the strain rate. Strain rate sensitivity of the steel was found to show a small decrease (0.028–0.0076) with true strain. 2. GND density was estimated using EBSD measurements. GND density follows a concave up variation with the plastic strain. The increased rate in the buildup of GND density with plastic strain can be 9
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Fig. 7. Maps of GND density with the engineering strain rates (a) 1x10-4 s-1 (b) 1x10-3 s-1 (c) 1x10-2 s-1. (d) Variation of GND density with the engineering strain rates when deformation was carried out at a plastic strain of 13.97%.
explained by the formation of deformation induced martensite. The variation of deformation induced martensite follows the same trend with the plastic strain which was observed for the GND density (concave up). 3. The distribution of GND shows significant gradient throughout the microstructure. The preferred sites for GND storage are the grain boundaries, triple junctions, shear bands and deformation induced martensite particles. The smaller austenite grains exhibit more GND storage than the coarser austenite grains. 4. It was demonstrated that for a fixed amount of plastic strain (ε ¼ 13.97%), GND density increases at a reduced rate with increasing strain rate leading to small increase in the flow stress and positive strain rate sensitivity. The small decrease of strain rate sensitivity with strain is linked to the small change in GND density and total dislocation density with increasing engineering strain rate.
interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The financial support of the work has been received from Science and Engineering Research Board, Department of Science and technology, Government of India (file no.: ECR/2016/000260) under early career research award. The OIM research facility at Metallurgical and Material Engineering Department, Jadavpur University was used in the work. References [1] A. Kundu, P.C. Chakraborti, J. Mater. Sci. 45 (2010) 5482–5489. [2] G.E. Dieter, Mechanical Metallurgy, McGraw Hill Book Company, UK, 1988. [3] J. Talonen, P. Nenonen, G. Pape, H. H€ anninen, Metall. Mater. Trans. A 36 A (2005) 421–432. [4] J.A. Lichtenfeld, C.J. Van Tyne, M.C. Mataya, Metall. Mater. Trans. A 37 (2006) 147–161. [5] A. Kundu, D.P. Field, P.C. Chakraborti, Mater. Sci. Eng. A (2019) 762, https://doi. org/10.1016/j.msea.2019.138090. [6] J.F. Humphreys, M. Hatherly, Recrystallisation and Related Annealing Phenomena, Pergamon Press, Kidlington, Oxford, UK, 1995. [7] E. Isaac Samuel, B.K. Choudhary, K. Bhanu Sankara Rao, Scripta Matter 46 (2002) 507–512. [8] A.A. Tiamiyu, J.A. Szpunar, A.G. Odeshi, Mater. Char. 154 (2019) 7–19. [9] W.S. Lee, C.F. Lin, Mater. Sci. Eng. A 308 (2001) 124–135. [10] M.F. Ashby, Philos. Mag. 21 (1970) 399–424. [11] M. Griffiths, D. Sage, R.A. Holt, C.N. Tome, Metall. Mater. Trans. A 33 (2002) 859–865. [12] T. Narutani, G.B. Olson, M. Cohen, J. Phys. 43 (C4) (1982). C4-429-C4-434.
Author contribution statement Amrita Kundu: Conceptualization, Investigation, Writing- Original draft preparation, Reviewing and Editing, Funding Acquisition, Project administration. David P. Field: Conceptualization, Writing- Reviewing and Editing. Pravash Chandra Chakraborti: Conceptualization. Declaration of competing interest The authors declare that they have no known competing financial 10
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