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Evolution of microstructures, dislocation density and arrangement during deformation of low carbon lath martensitic steels
Journal Pre-proof Evolution of microstructures, dislocation density and arrangement during deformation of low carbon lath martensitic steels Md Shamsujjoha PII:
S0921-5093(20)30127-1
DOI:
https://doi.org/10.1016/j.msea.2020.139039
Reference:
MSA 139039
To appear in:
Materials Science & Engineering A
Received Date: 16 October 2019 Revised Date:
29 January 2020
Accepted Date: 31 January 2020
Please cite this article as: M. Shamsujjoha, Evolution of microstructures, dislocation density and arrangement during deformation of low carbon lath martensitic steels, Materials Science & Engineering A (2020), doi: https://doi.org/10.1016/j.msea.2020.139039. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2020 Published by Elsevier B.V.
Credit Author Statement Md Shamsujjoha is the sole author of this paper.
Evolution of Microstructures, Dislocation Density and Arrangement During Deformation of Low Carbon Lath Martensitic Steels Md Shamsujjoha ArcelorMittal Global R&D, East Chicago, IN-46312. Abstract In this paper, the role of solute carbon on the strengthening and work hardening behavior of lath martensite was studied by analyzing the microstructures and dislocation density in the undeformed and deformed conditions. An increase in carbon content from 0.18% to 0.30% decreases the martensite start (Ms) temperature, leading to refinement of both the block and lath widths. Although reduction of the “effective grain size” is observed via Electron Backscatter Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI) techniques, this effect is considered secondary in increasing the strength of lath martensite with increased carbon content. The higher strength is attributed mainly to the phase transformation-induced dislocation density in the high-carbon martensite. Comparing this total dislocation density calculated using a Convolutional Multiple Whole Profile (CMWP) fitting procedure with the estimated geometrically necessary dislocations (GND) from the misorientation distribution of EBSD analysis, it appears that a high fraction of the dislocations in lath martensitic steel is GND. Furthermore, the analysis of the samples strained to a different level suggests that the dislocation density shows minimal change during deformation, whereas the dislocation arrangement rapidly decreases at the beginning of the plastic deformation. Finally, the strain hardening behavior of the lath martensitic steel is quantitatively described by considering lath width, dislocation density, and dislocation arrangement parameters through the α coefficient in Taylor’s equation. Key words: Lath martensite, Carbon concentration, Dislocation density, Dislocation arrangement
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1. Introduction Lath martensite consists of hierarchically arranged substructures within a prior-austenite grain (PAG), namely the packets and blocks of laths. A block contains laths with the same orientation, while a packet is a group of blocks with the same habit plane [1-3]. These intricate arrangements of sub-structures accommodate the distortions due to the crystallographic transformation of martensite from the austenite. A high dislocation density in the order of ~1015 m-2 has been reported to be produced from these austenite-martensite phase transformation [5–8]. The boundary and dislocation strengthening are the two primary strengthening mechanisms that contribute to the initial high yield strength of the martensitic steel [3]. Among the alloying elements, carbon has the most crucial impact on the development of microstructure and strength of the low carbon lath martensitic steels. Carbon refines the microstructural parameters such as block size and increases dislocation density as well [8]. However, the respective contributions of dislocation strengthening and lath boundary strengthening to the yield stress of martensite have not yet been quantified. Martensitic steels exhibit a high level of work hardening at the beginning of plastic deformation despite having a high yield strength. However, the relationship between dislocation density and plastic strain is not well understood. Nakashima et al. [9] studied the change in dislocation density (ρ) of ultra-low carbon lath martensitic Fe–18Ni alloy using X-ray diffraction. Results of the Williamson-Hall method revealed that the dislocation density decreases just after yielding and reaches a constant value at a low plastic strain. A similar reduction in dislocation density
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with plastic deformation is also reported in [7, 10, 11]. The decrease in dislocation density with increased work hardening is perplexing. Harjo et al. [7] noted that while the average dislocation density remains unchanged, the dislocation arrangement parameter (M) decreases rapidly during plastic deformation. They suggested that the deformation behavior of lath martensitic steel cannot be justified based solely on the change in dislocation density; the rearrangement of the dislocation should also be considered. As seen from the preceding discussion, despite the vast body of prior work, an entirely physical, predictive model linking the composition, microstructure, and mechanical properties of the martensitic steels is yet to be established. To the best of this author’s knowledge, no systematic study investigating the role of solute carbon on the microstructure development and evolution of dislocation during plastic deformation has been published to date. Therefore, such an investigation is undertaken in the present work to provide a quantitative characterization of martensitic steel with different carbon content, as this will be the baseline for understanding the deformation behavior of martensite in fully martensitic or multiphase steel. 2. Methods Low carbon martensitic steels with three different C contents, i.e., 0.18, 0.25, and 0.30 weight percent carbon, are used in this study. Other alloying elements include 0.48% Mn, 0.18%Si, 0.45% Ti, 0.01% P, 0.015% S and ≤0.01% B. These steels are termed as 0.18C, 0.25C and 0.30C martensitic steels in this manuscript. Following the typical hot and cold rolling, the final heat treatment was carried out on a water-quenched continuous annealing line.
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Uniaxial tensile tests along the rolling direction of the sheet material were performed using an Instron system with a nominal strain rate of 1×10-3 s-1 at room temperature. A mechanical clipon extensometer was used to measure axial strain in the sample gage upon loading. For microstructural analysis, samples were sectioned using the conventional band saw, and slow-speed diamond saw methods, mounted in Polyfast and mechanically ground up to 1200 grit silicon carbide paper, polished with diamond pastes of 3 and 1 µm, and finally, re-polished using 0.05 µm colloidal silica. The microstructure was examined using Electron Backscatter Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI) in a Scanning Electron Microscope (SEM) JEOL-7600F equipped with an EDAX EBSD system. EBSD measurement was conducted at an operative voltage of 20 kV and a working distance ranging from 18 to 22 mm. A step size of 50nm was used during the EBSD data collection. Geometrically necessary dislocations (GND) were assessed from the kernel averaged misorientation (KAM) obtained from EBSD analysis. In this analysis, KAM was determined up to the second-nearest neighbor; misorientation values exceeding a threshold value of 5° were excluded from the KAM calculation. X-ray diffraction (XRD) was used to characterize the dislocation density of undeformed and deformed samples. All XRD measurements were performed using a conventional PANalytical X’Pert Pro MPD (multipurpose diffractometer) X-ray diffractometer with a Co-Kα sealed-tube source operated at 30 kV and 50 mA. Similar sample surface preparation methods were used for the X-ray diffraction analysis as used for microstructural characterization.
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Bragg–Brentano focusing geometry was used to collect diffraction patterns over the 2θ range from 40°–120° with a step size of 0.004° and counting time of 40 seconds per step for phase quantification and dislocation density measurement. PANalytical X’Celerator linear positionsensitive detector was used to collect the diffracted beam during this θ:2θ scans. A sample spinner programmed to a revolution time of 2 seconds was used to obtain better grainsampling statistics. Instrumental broadening effects were evaluated and corrected using a silicon standard. For the quantitative analysis of dislocation density, the X-ray diffraction patterns were evaluated by the CMWP fitting procedure. In CMWP, the peak profile functions are calculated as the convolution of the size, strain, and instrumental broadening. The measured diffraction pattern is then fitted with the calculated profile function using a nonlinear least-squares method [12][13]. Anisotropic elastic constants C11 = 185.3, C12 = 109.1, and C44 = 114.8 GPa were used to determine the average dislocation contrast factors, considering the mixed dislocations (equal proportion of edge and screw types), by Anizc software [14]. 3. Results 3.1 Initial Microstructures ECCI micrographs in Figure 1 exhibit typical microstructures of low carbon martensite consist of prior austenite grain (PAG) (red arrow), packets (yellow arrow), blocks, and laths (green arrow) within the PAGs. High-resolution ECCI images are employed to reveal lath structures. (see Figure 2). A combination of coarse (width ~1 µm) and fine laths (width ~50 nm) are present in
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all three steel grades under investigation. A relatively higher dislocation density was observed inside and along the boundaries of the fine laths compare to coarser laths. Besides, occasional nano-scale carbide precipitates are observed inside the coarse laths, which indicates these laths are tempered (see Figure 3). A small fraction of twins was also observed; however, for the interest of space, it is not shown here.
Figure 1: Typical microstructures of low carbon lath martensite showing prior austenite grain(red), packet (yellow), lath and block (green) boundaries.
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Lath width was measured from high magnification ECCI micrographs using the line intercept method. The distributions of lath widths based on approximately 300 laths of each sample are presented in Figures 2(d), 2(e), 2(f) for 0.18C, 0.25C and 0.30C martensitic steels, respectively. The mean value of lath width decreases with increasing carbon content. Histograms in Figure 2 show that the number of fractions in lath width < 100 nm increases, while fractions in lath width >550nm decrease with increasing solute carbon content, which is consistent with a higher dislocation density in the higher carbon lath martensite. This will be discussed in more detail later in this manuscript.
Figure 2: Effects of solute carbon content on the distribution of lath width for a, d) 0.18C, b, e) 0.25C, and c, f) 0.30C martensitic steel are shown.
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Figure 3: Nano-scale carbide precipitates inside coarser laths. ARPGRE reconstruction software [15] was employed to analyze crystallographic orientation using EBSD data to identify the PAG, and block boundaries. It is well accepted that there exists a Kurdjumov–Sachs (K–S) relationship ({111}A// {011}M, <110>A//<111>M, where subscripts A and M denote austenite and martensite, respectively) between martensite and prior austenite grain in low carbon martensitic steel. Because of the symmetry in the K–S relationship, there are 24 equivalent crystallographic variants of martensite that can be transformed from a single austenite grain. Figures 4(a), 4(b), 4(c) exhibit the PAGs and block boundaries, where PAGs are drawn in black lines, and each color represents a block, of 0.18C, 0.25C, and 0.30C martensitic steels, respectively. The block width distributions of 0.18C, 0.25C, and 0.30C martensitic steels are shown in Figure 4(d), 4(e), and 4(f), respectively. Similar to lath width, the block size also decreases with increasing solute carbon content. However, no
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significant difference in PAG size as a function of carbon content was observed. It should be noted that the size of a limited number of PAGs has been analyzed during this study, and it might not be statistically significant to draw any conclusion of the PAG size.
Figure 4: Effects of solute carbon content on the distribution of block for a, d) 0.18C, b, e) 0.25C, and c, f) 0.30C martensitic steel are shown. 3.2 Mechanical Properties True stress-strain and work hardening rate (Ө)-strain curves for martensitic steels with different solute carbon contents are shown in Figures 5(a) and 5(b), respectively. For each material, the result of only one of the three tensile tests is shown. All steels under investigation reveal continuous yielding and a high initial strain hardening rate. With increasing carbon content, the yield and tensile strength increased remarkably, whereas the uniform and total elongation are not affected. Analysis reveals that the initial strain-hardening rate is increased by increasing
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carbon content, but it is nearly the same for 0.25C and 0.30C steels. At a strain level of 0.025, hardening curves for these steels converge with that of 0.18 C steel, indicating a diminishing impact of increasing carbon content on the hardening rate (see Figure 5).
Figure 5: Figure shows the tensile properties of the martensitic steels: a) true stress vs. true strain, and b) work hardening rate. 3.3 Microstructure evolution during straining Strained samples were analyzed to evaluate the microstructure evolution during deformation. As an example, Figure 6 shows the ECCI images of 0.30C martensitic steel deformed to a strain level a) 2% strain, b) 6% strain (true strain at failure). Lath width does not change with a strain increment (see Figure 6). No conclusions regarding the evolution of dislocation density during deformation can be drawn from these high-resolution ECCI micrographs; however, there is a frequent indication of the formation of dislocation cell structures within the lath boundaries (as indicated by the red arrow). Transmission Electron Microscopy (TEM) analysis is needed for confirmation. Nevertheless, prior studies [10], [16] have shown the formation of cellular dislocation structures during the deformation of lath martensite using TEM.
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Figure 6: ECCI images of 0.3C martensitic steel at different true strain level a) 2% strain, and b) ~6% (true strain at failure). Red arrow indicates the possible formation of dislocation cells within lath boundaries. KAM maps created through EBSD are employed to analyze the evolution of substructure and linked it to a relevant deformation mechanism. KAM provides orientation gradients (typically up to 5 degrees) within individual grains. Figure 7 shows the KAM distributions of undeformed and fractured samples of 0.18C (Figure 7 a and d), 0.25C (Figure 7 b and e), and 0.30C (Figure 7c and f) martensitic steels. As shown by KAM maps, there are wide regions of low KAM values surrounded by higher KAM values. These low KAM value regions correspond to the core of coarse laths, while a high misorientation angle is observed in the lath/block boundaries. This observation is consistent with ECCI analysis, where it shows a low dislocation density in the interior of auto-tempered coarse laths. These KAM maps also show a global increase of lattice distortion (higher average KAM value) as the lath boundary density increases with increasing
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carbon content (see Figures 7(a-c)). There are still regions of low KAM value in higher carbon steel; however, the density of areas with high KAM value increases. KAM maps (see Figures 7 (d-f)) of samples deformed to 6% strain, i.e., the strain at fracture, demonstrate a slight increase in local misorientation in the lath/block boundary region, while the lath interiors do not display any significant misorientation change.
Figure 7: Kernel average misorientation (KAM) maps of undeform and fracture samples of a, d) 0.18C, c, e) 0.25C, and d, f) 0.30C martensitic steel.
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GND can be estimated from average KAM value using the following formula [17]: ≅
2
where b is the Burgers vector magnitude (0.248 nm for BCC iron) and d is the step size. GND density of the steel grades under investigation at different strain level are listed in Table 1. GND density value increases with the increasing carbon content of lath martensite, while local KAM value at the boundaries increases with straining, GND related to average KAM value hardly increases with straining, especially in 0.18C and 0.30C martensitic steels. This KAM based analysis provides useful information concerning the influence of solute content and deformation on GND distribution; however, it does not provide any information regarding global dislocation density, i.e., combination of geometrically necessary dislocation (GND) and statistically stored dislocation (SSD), or their characteristics, which are better assessed by XRD method. Table 1: Geometrically necessary dislocation (GND) density of lath martensitic steels at different strain level. -2
GND (m ) Undeform 15
0.18C
2.2×10
0.25C
2.8×10
0.3C
3.0×10
15
15
2% strain 15
2.3×10
15
3.1×10
15
3.0×10
6% strain 15
2.3×10
15
3.1×10
15
3.0×10
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3.4 Dislocation density evolution during straining Line broadening analysis performed using the CMWP method is shown in Figure 8 for 0.25C lath martensite. The black and red lines show the measured and fitted data, respectively, with residual presented at the bottom of the figure, which exhibits a good fit between measured and theoretical profile. Among the parameters, i.e., dislocation density (ρ), dislocation arrangement parameter (M), dislocation character (screw or edge), and crystalline size, that can be garnered from CMWP fit, a focus is given to the result concerning ρ and M in this study.
Figure 8: Measured and fitted diffraction patterns obtained using CMWP of 0.25C undeformed martensitic steel.
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Dislocation density (ρ) and dislocation arrangement parameter (M) obtained from the CMWP are presented in Figure 9. Similar to GND results obtained from the EBSD examination, the total dislocation density (ρtot) of undeformed lath martensite increases with increasing carbon content. ρtot estimated to be (2.3 ±0.3) × 1015 m-2, (3.5 ±0.05) × 1015 m-2, and (4.4 ±0.2) × 1015 m2
, respectively, for 0.18C, 0.25C and 0.30C materials prior deformation. Comparing the
estimated total dislocation density with GND value, it appears that the fraction of GNDs decreases with carbon content. GND is estimated to account for about 95%, 80%, and 67% of the total dislocation densities of 0.18C, 0.25C, and 0.30C lath martensite, respectively. The uncertainties of the dislocation density reported here were calculated using error propagation of the uncertainties in the parameters of the CMWP fitting routine. All the materials under investigation exhibit M>1 in the undeformed state; M values are estimated to be 5.5 ± 0.5, 3.1 ± 0.25 and 2.6 ± 0.96 for 0.18C, 0.25C, and 0.30C steels, respectively, indicating that the dislocations in the undeformed state have a weak dipole character. The value of parameter q, which is related to the dislocation types, is calculated to be approximately 2.0 for the materials under investigation before deformation. For the BCC slip system, the theoretical value of q is 1.3 for an edge dislocation and 2.6 for a screw dislocation. Thus, the q value of 2.1 indicates that the screw-type dislocation is dominant in the lath martensite. The evolution of ρtot and M as a function of plastic strain is shown in Figure 9 for 0.25C and 0.30C steel. Considering the error associated with the line broadening analysis, it can be concluded that the dislocation density in both materials remains constant during straining, notwithstanding an increase in flow stress (see Figure 5). This finding is contrary to the results
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published in [5, 10, 11], where they reported a reduction in ρtot with increasing plastic strain using the classical Williamson-Hall method. It should be noted that during line broadening analysis, it was assumed that the peak remains symmetric during plastic deformation. M values decrease to 0.61±0.04 and 0.51±0.01, respectively, for 0.25C and 0.3C steel at 2% plastic strain and hardly changes beyond this point. The q value remains between 2.0-2.2 throughout the deformation. It appears from the results presented in Figure 9 that the evolution characteristics of ρtot, M, q with plastic strain are very similar and merely depend on carbon content for the concentration range under investigation; thus the evolution of ρtot, M, q as a function of plastic strain was not measured for 0.18C steels.
Figure 9: Dislocation density (ρ) and average arrangement parameter (M) estimated from the XRD line broadening analysis using CMWP fitting procedure.
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4. Discussions a. Yield strength Yield strength (σy) of lath martensite can be expressed as a linear combination of the different strengthening mechanisms contributing to the strength of martensite: =
+
+
√
Here σ0 is contribution from Peierls-Nabarro stress and solid solution strengthening; second term is contribution from dislocation strengthening, i.e., the Taylor model, and third term is contribution from grain boundary strengthening. Also, α is proportionality constant, G is shear modulus (80 GPa for lath martensite), b is Burger’s vector, ρ is dislocation density, KHP is coefficient of Hall-Petch relation and d is “effective grain size” of lath martensite. Considering a low volume fraction of auto-tempered martensite, precipitation hardening effect is not considered in the yield strength calculation. σ0 is considered independent of solid solution strengthening by carbon. Elemental mapping of carbon using atom probe tomography has revealed that the carbon segregates to the lath boundaries or in the dislocations core rather than forming a random solid solution even in the as-quenched state [18]. Jo et al. [19] estimated σ0 to be 201 MPa for a 0.3C lath martensite steel based on Rodriguez and Gutierrez’s method. The same value of σ0 is also used in this study.
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The individual contribution of solid solution, grain size, and dislocation density on the yield strength are shown in Figure 10. The experimental value of yield strength (YS) is plotted as a reference. It should be noted here that stress at 0.2% offset strain is considered as yield strength. Calculated yield strength exhibits a good agreement with the experimentally measured value. It is also worth noting here that total dislocation density estimated from the XRD analysis is used in Taylor’s model, and “block size” is considered as the “effective grain size” for the YS calculation. The figure shows that the strengthening by forest dislocation is the main contributor to the strength of the martensite. The effect of lath width on the overall strengthening was also considered; however, this overestimates the grain size effects on yield strength as noted by the higher difference between calculated and experimentally measured yield strength. Lath width, carbon content, and dislocation density are interrelated. This correlation between composition, substructure size and defect density can be explained based on the plastic strain accommodation in prior austenite grain during martensite transformation. Researchers have shown the formation of accommodated dislocations at the martensite/austenite interface using high-resolution TEM [20] and EBSD analysis [21]. Martensitic transformation (MS) temperature decreases with increasing carbon content. Reduced MS, as well as increased carbon content, resulting in higher accommodated dislocations in PAGs, which increase the energy barrier for the migration of lath boundaries. The inherited dislocation density in martensite also increases with increasing accommodated dislocations in PAGs. In addition, the extent of auto-tempering, which causes coarsening of lath boundaries and reduction of dislocation density during martensitic transformation, reduced
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with decreasing MS. This suggests that while carbon can modify both martensitic substructures and dislocation density, the strength increment is mostly correlated to dislocation density changes due to increasing carbon concentration. This conclusion is contrary to the well-known relation between YS and the square root of carbon content in martensitic steel, which is related to the solid solution strengthening effects of carbon.
Figure 10: Contribution of solid solution, grain size and dislocation density on the yield strength (YS). Experimental value of YS also plotted as a reference.
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b. Work hardening behavior In general, the increment in flow stress (Δσ) is attributed to the increment in dislocation density with increasing plastic strain using Taylor’s model. However, while the dislocation density remains almost constant during straining, a stress increment >200 MPa beyond the yield strength was observed for lath martensite. This peculiarity in the deformation behavior of martensite is also reported in [7, 22, 23], which leads to the special classification of “in-lath” and “out-of-lath” plane slip of lath martensite. The critical resolved stress value is significantly lower in in-lath plane slip systems (soft packet) compared to that of out-of-lath slip systems (hard packet). Lath packets with active Burgers vectors in the lath plane work soften, whereas the packets with active Burgers vectors out of the lath plane work harden. Ungar et al. [23] using in-situ high-resolution neutron diffraction revealed that during plastic straining of 0.22C lath martensite, the initial symmetric diffraction profile became an asymmetric profile, which can be deconvoluted to calculate the evolution of dislocation density in soft and hard packets. Dislocation density increases in hard packets while it decreases in soft packets. However, no such asymmetry in the diffraction pattern of the deformed sample was observed in this study. Nevertheless, in both cases, change in average dislocation density shows a similar trend, i.e., a minimal change during straining. In addition, the dislocation arrangement parameter (M) shows minimal changes in soft packets (M>1), while it rapidly decreases from a value of M>1 to M<1 in the hard packet. A similar decrease in dislocation arrangement parameter (M) is also observed in this study considering symmetric diffraction profile. This decrease in M suggests that the dislocations arranged themselves in lower energy dislocation structures (LEDSs). The coefficient
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α in the Taylor model increases with increasing cell wall volume fraction of these LEDSs. Thus, a decrease in M is linked with the increase in α. In general, α is considered constant during deformation; however, researchers have shown that α also changes during straining, especially when the material system undergoes a significant rearrangement of dislocation structure during deformation [22–24]. In this study, the α needs to increase from the initial value of 0.25 to 0.35 in order to account for the increment in flow strength. It is interesting to note that interactions between dislocations and solute carbon atoms do not affect dislocations rearrangement, and thus α is also independent of carbon concentration. 5. Conclusions The effects of solute carbon content on microstructure and dislocation density evolution during deformation of lath martensite were examined in this study. The following conclusions can be drawn from this investigation:
i)
The block and lath width of lath martensite decreases with increasing carbon content. The decrease in lath width correlates with the increase in dislocation density. Dislocation density increases from 2.3× 1015 m-2 for 0.18 C material to 3.5× 1015 for 0.25 C and 4.6× 1015 for 0.3 C martensitic steels.
ii)
Contributions of different strengthening mechanisms to yield strength were estimated. Block size is perceived to be the “effective grain size” of lath martensite. Dislocation strengthening was determined to be the most crucial factor, contributing
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up to 65% of the yield strength. The increase in yield strength with increasing carbon content is attributed to the increase in dislocation density. iii)
Dislocation density remains constant during deformation, but the parameter M related to dislocation arrangement decreases with straining. The work hardening in lath martensite is speculated to stem from the rearrangement of dislocations toward stronger dipole character, which increases the coefficient α in Taylor’s model.
iv)
Solute carbon atoms have little or no effect on the strain hardening behavior of lowcarbon martensite.
Acknowledgements The author thanks ArcelorMittal Global R&D management for their permission to publish the work. The author is also grateful to Loretta Bock for metallography and tensile test and Warren Bolton for XRD measurement. The author also extends his appreciation to Cayron Cyril for providing a copy of ARPGE reconstruction software.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0921-5093(20)30127-1
DOI:
https://doi.org/10.1016/j.msea.2020.139039
Reference:
MSA 139039
To appear in:
Materials Science & Engineering A
Received Date: 16 October 2019 Revised Date:
29 January 2020
Accepted Date: 31 January 2020
Please cite this article as: M. Shamsujjoha, Evolution of microstructures, dislocation density and arrangement during deformation of low carbon lath martensitic steels, Materials Science & Engineering A (2020), doi: https://doi.org/10.1016/j.msea.2020.139039. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2020 Published by Elsevier B.V.
Credit Author Statement Md Shamsujjoha is the sole author of this paper.
Evolution of Microstructures, Dislocation Density and Arrangement During Deformation of Low Carbon Lath Martensitic Steels Md Shamsujjoha ArcelorMittal Global R&D, East Chicago, IN-46312. Abstract In this paper, the role of solute carbon on the strengthening and work hardening behavior of lath martensite was studied by analyzing the microstructures and dislocation density in the undeformed and deformed conditions. An increase in carbon content from 0.18% to 0.30% decreases the martensite start (Ms) temperature, leading to refinement of both the block and lath widths. Although reduction of the “effective grain size” is observed via Electron Backscatter Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI) techniques, this effect is considered secondary in increasing the strength of lath martensite with increased carbon content. The higher strength is attributed mainly to the phase transformation-induced dislocation density in the high-carbon martensite. Comparing this total dislocation density calculated using a Convolutional Multiple Whole Profile (CMWP) fitting procedure with the estimated geometrically necessary dislocations (GND) from the misorientation distribution of EBSD analysis, it appears that a high fraction of the dislocations in lath martensitic steel is GND. Furthermore, the analysis of the samples strained to a different level suggests that the dislocation density shows minimal change during deformation, whereas the dislocation arrangement rapidly decreases at the beginning of the plastic deformation. Finally, the strain hardening behavior of the lath martensitic steel is quantitatively described by considering lath width, dislocation density, and dislocation arrangement parameters through the α coefficient in Taylor’s equation. Key words: Lath martensite, Carbon concentration, Dislocation density, Dislocation arrangement
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1. Introduction Lath martensite consists of hierarchically arranged substructures within a prior-austenite grain (PAG), namely the packets and blocks of laths. A block contains laths with the same orientation, while a packet is a group of blocks with the same habit plane [1-3]. These intricate arrangements of sub-structures accommodate the distortions due to the crystallographic transformation of martensite from the austenite. A high dislocation density in the order of ~1015 m-2 has been reported to be produced from these austenite-martensite phase transformation [5–8]. The boundary and dislocation strengthening are the two primary strengthening mechanisms that contribute to the initial high yield strength of the martensitic steel [3]. Among the alloying elements, carbon has the most crucial impact on the development of microstructure and strength of the low carbon lath martensitic steels. Carbon refines the microstructural parameters such as block size and increases dislocation density as well [8]. However, the respective contributions of dislocation strengthening and lath boundary strengthening to the yield stress of martensite have not yet been quantified. Martensitic steels exhibit a high level of work hardening at the beginning of plastic deformation despite having a high yield strength. However, the relationship between dislocation density and plastic strain is not well understood. Nakashima et al. [9] studied the change in dislocation density (ρ) of ultra-low carbon lath martensitic Fe–18Ni alloy using X-ray diffraction. Results of the Williamson-Hall method revealed that the dislocation density decreases just after yielding and reaches a constant value at a low plastic strain. A similar reduction in dislocation density
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with plastic deformation is also reported in [7, 10, 11]. The decrease in dislocation density with increased work hardening is perplexing. Harjo et al. [7] noted that while the average dislocation density remains unchanged, the dislocation arrangement parameter (M) decreases rapidly during plastic deformation. They suggested that the deformation behavior of lath martensitic steel cannot be justified based solely on the change in dislocation density; the rearrangement of the dislocation should also be considered. As seen from the preceding discussion, despite the vast body of prior work, an entirely physical, predictive model linking the composition, microstructure, and mechanical properties of the martensitic steels is yet to be established. To the best of this author’s knowledge, no systematic study investigating the role of solute carbon on the microstructure development and evolution of dislocation during plastic deformation has been published to date. Therefore, such an investigation is undertaken in the present work to provide a quantitative characterization of martensitic steel with different carbon content, as this will be the baseline for understanding the deformation behavior of martensite in fully martensitic or multiphase steel. 2. Methods Low carbon martensitic steels with three different C contents, i.e., 0.18, 0.25, and 0.30 weight percent carbon, are used in this study. Other alloying elements include 0.48% Mn, 0.18%Si, 0.45% Ti, 0.01% P, 0.015% S and ≤0.01% B. These steels are termed as 0.18C, 0.25C and 0.30C martensitic steels in this manuscript. Following the typical hot and cold rolling, the final heat treatment was carried out on a water-quenched continuous annealing line.
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Uniaxial tensile tests along the rolling direction of the sheet material were performed using an Instron system with a nominal strain rate of 1×10-3 s-1 at room temperature. A mechanical clipon extensometer was used to measure axial strain in the sample gage upon loading. For microstructural analysis, samples were sectioned using the conventional band saw, and slow-speed diamond saw methods, mounted in Polyfast and mechanically ground up to 1200 grit silicon carbide paper, polished with diamond pastes of 3 and 1 µm, and finally, re-polished using 0.05 µm colloidal silica. The microstructure was examined using Electron Backscatter Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI) in a Scanning Electron Microscope (SEM) JEOL-7600F equipped with an EDAX EBSD system. EBSD measurement was conducted at an operative voltage of 20 kV and a working distance ranging from 18 to 22 mm. A step size of 50nm was used during the EBSD data collection. Geometrically necessary dislocations (GND) were assessed from the kernel averaged misorientation (KAM) obtained from EBSD analysis. In this analysis, KAM was determined up to the second-nearest neighbor; misorientation values exceeding a threshold value of 5° were excluded from the KAM calculation. X-ray diffraction (XRD) was used to characterize the dislocation density of undeformed and deformed samples. All XRD measurements were performed using a conventional PANalytical X’Pert Pro MPD (multipurpose diffractometer) X-ray diffractometer with a Co-Kα sealed-tube source operated at 30 kV and 50 mA. Similar sample surface preparation methods were used for the X-ray diffraction analysis as used for microstructural characterization.
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Bragg–Brentano focusing geometry was used to collect diffraction patterns over the 2θ range from 40°–120° with a step size of 0.004° and counting time of 40 seconds per step for phase quantification and dislocation density measurement. PANalytical X’Celerator linear positionsensitive detector was used to collect the diffracted beam during this θ:2θ scans. A sample spinner programmed to a revolution time of 2 seconds was used to obtain better grainsampling statistics. Instrumental broadening effects were evaluated and corrected using a silicon standard. For the quantitative analysis of dislocation density, the X-ray diffraction patterns were evaluated by the CMWP fitting procedure. In CMWP, the peak profile functions are calculated as the convolution of the size, strain, and instrumental broadening. The measured diffraction pattern is then fitted with the calculated profile function using a nonlinear least-squares method [12][13]. Anisotropic elastic constants C11 = 185.3, C12 = 109.1, and C44 = 114.8 GPa were used to determine the average dislocation contrast factors, considering the mixed dislocations (equal proportion of edge and screw types), by Anizc software [14]. 3. Results 3.1 Initial Microstructures ECCI micrographs in Figure 1 exhibit typical microstructures of low carbon martensite consist of prior austenite grain (PAG) (red arrow), packets (yellow arrow), blocks, and laths (green arrow) within the PAGs. High-resolution ECCI images are employed to reveal lath structures. (see Figure 2). A combination of coarse (width ~1 µm) and fine laths (width ~50 nm) are present in
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all three steel grades under investigation. A relatively higher dislocation density was observed inside and along the boundaries of the fine laths compare to coarser laths. Besides, occasional nano-scale carbide precipitates are observed inside the coarse laths, which indicates these laths are tempered (see Figure 3). A small fraction of twins was also observed; however, for the interest of space, it is not shown here.
Figure 1: Typical microstructures of low carbon lath martensite showing prior austenite grain(red), packet (yellow), lath and block (green) boundaries.
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Lath width was measured from high magnification ECCI micrographs using the line intercept method. The distributions of lath widths based on approximately 300 laths of each sample are presented in Figures 2(d), 2(e), 2(f) for 0.18C, 0.25C and 0.30C martensitic steels, respectively. The mean value of lath width decreases with increasing carbon content. Histograms in Figure 2 show that the number of fractions in lath width < 100 nm increases, while fractions in lath width >550nm decrease with increasing solute carbon content, which is consistent with a higher dislocation density in the higher carbon lath martensite. This will be discussed in more detail later in this manuscript.
Figure 2: Effects of solute carbon content on the distribution of lath width for a, d) 0.18C, b, e) 0.25C, and c, f) 0.30C martensitic steel are shown.
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Figure 3: Nano-scale carbide precipitates inside coarser laths. ARPGRE reconstruction software [15] was employed to analyze crystallographic orientation using EBSD data to identify the PAG, and block boundaries. It is well accepted that there exists a Kurdjumov–Sachs (K–S) relationship ({111}A// {011}M, <110>A//<111>M, where subscripts A and M denote austenite and martensite, respectively) between martensite and prior austenite grain in low carbon martensitic steel. Because of the symmetry in the K–S relationship, there are 24 equivalent crystallographic variants of martensite that can be transformed from a single austenite grain. Figures 4(a), 4(b), 4(c) exhibit the PAGs and block boundaries, where PAGs are drawn in black lines, and each color represents a block, of 0.18C, 0.25C, and 0.30C martensitic steels, respectively. The block width distributions of 0.18C, 0.25C, and 0.30C martensitic steels are shown in Figure 4(d), 4(e), and 4(f), respectively. Similar to lath width, the block size also decreases with increasing solute carbon content. However, no
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significant difference in PAG size as a function of carbon content was observed. It should be noted that the size of a limited number of PAGs has been analyzed during this study, and it might not be statistically significant to draw any conclusion of the PAG size.
Figure 4: Effects of solute carbon content on the distribution of block for a, d) 0.18C, b, e) 0.25C, and c, f) 0.30C martensitic steel are shown. 3.2 Mechanical Properties True stress-strain and work hardening rate (Ө)-strain curves for martensitic steels with different solute carbon contents are shown in Figures 5(a) and 5(b), respectively. For each material, the result of only one of the three tensile tests is shown. All steels under investigation reveal continuous yielding and a high initial strain hardening rate. With increasing carbon content, the yield and tensile strength increased remarkably, whereas the uniform and total elongation are not affected. Analysis reveals that the initial strain-hardening rate is increased by increasing
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carbon content, but it is nearly the same for 0.25C and 0.30C steels. At a strain level of 0.025, hardening curves for these steels converge with that of 0.18 C steel, indicating a diminishing impact of increasing carbon content on the hardening rate (see Figure 5).
Figure 5: Figure shows the tensile properties of the martensitic steels: a) true stress vs. true strain, and b) work hardening rate. 3.3 Microstructure evolution during straining Strained samples were analyzed to evaluate the microstructure evolution during deformation. As an example, Figure 6 shows the ECCI images of 0.30C martensitic steel deformed to a strain level a) 2% strain, b) 6% strain (true strain at failure). Lath width does not change with a strain increment (see Figure 6). No conclusions regarding the evolution of dislocation density during deformation can be drawn from these high-resolution ECCI micrographs; however, there is a frequent indication of the formation of dislocation cell structures within the lath boundaries (as indicated by the red arrow). Transmission Electron Microscopy (TEM) analysis is needed for confirmation. Nevertheless, prior studies [10], [16] have shown the formation of cellular dislocation structures during the deformation of lath martensite using TEM.
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Figure 6: ECCI images of 0.3C martensitic steel at different true strain level a) 2% strain, and b) ~6% (true strain at failure). Red arrow indicates the possible formation of dislocation cells within lath boundaries. KAM maps created through EBSD are employed to analyze the evolution of substructure and linked it to a relevant deformation mechanism. KAM provides orientation gradients (typically up to 5 degrees) within individual grains. Figure 7 shows the KAM distributions of undeformed and fractured samples of 0.18C (Figure 7 a and d), 0.25C (Figure 7 b and e), and 0.30C (Figure 7c and f) martensitic steels. As shown by KAM maps, there are wide regions of low KAM values surrounded by higher KAM values. These low KAM value regions correspond to the core of coarse laths, while a high misorientation angle is observed in the lath/block boundaries. This observation is consistent with ECCI analysis, where it shows a low dislocation density in the interior of auto-tempered coarse laths. These KAM maps also show a global increase of lattice distortion (higher average KAM value) as the lath boundary density increases with increasing
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carbon content (see Figures 7(a-c)). There are still regions of low KAM value in higher carbon steel; however, the density of areas with high KAM value increases. KAM maps (see Figures 7 (d-f)) of samples deformed to 6% strain, i.e., the strain at fracture, demonstrate a slight increase in local misorientation in the lath/block boundary region, while the lath interiors do not display any significant misorientation change.
Figure 7: Kernel average misorientation (KAM) maps of undeform and fracture samples of a, d) 0.18C, c, e) 0.25C, and d, f) 0.30C martensitic steel.
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GND can be estimated from average KAM value using the following formula [17]: ≅
2
where b is the Burgers vector magnitude (0.248 nm for BCC iron) and d is the step size. GND density of the steel grades under investigation at different strain level are listed in Table 1. GND density value increases with the increasing carbon content of lath martensite, while local KAM value at the boundaries increases with straining, GND related to average KAM value hardly increases with straining, especially in 0.18C and 0.30C martensitic steels. This KAM based analysis provides useful information concerning the influence of solute content and deformation on GND distribution; however, it does not provide any information regarding global dislocation density, i.e., combination of geometrically necessary dislocation (GND) and statistically stored dislocation (SSD), or their characteristics, which are better assessed by XRD method. Table 1: Geometrically necessary dislocation (GND) density of lath martensitic steels at different strain level. -2
GND (m ) Undeform 15
0.18C
2.2×10
0.25C
2.8×10
0.3C
3.0×10
15
15
2% strain 15
2.3×10
15
3.1×10
15
3.0×10
6% strain 15
2.3×10
15
3.1×10
15
3.0×10
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3.4 Dislocation density evolution during straining Line broadening analysis performed using the CMWP method is shown in Figure 8 for 0.25C lath martensite. The black and red lines show the measured and fitted data, respectively, with residual presented at the bottom of the figure, which exhibits a good fit between measured and theoretical profile. Among the parameters, i.e., dislocation density (ρ), dislocation arrangement parameter (M), dislocation character (screw or edge), and crystalline size, that can be garnered from CMWP fit, a focus is given to the result concerning ρ and M in this study.
Figure 8: Measured and fitted diffraction patterns obtained using CMWP of 0.25C undeformed martensitic steel.
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Dislocation density (ρ) and dislocation arrangement parameter (M) obtained from the CMWP are presented in Figure 9. Similar to GND results obtained from the EBSD examination, the total dislocation density (ρtot) of undeformed lath martensite increases with increasing carbon content. ρtot estimated to be (2.3 ±0.3) × 1015 m-2, (3.5 ±0.05) × 1015 m-2, and (4.4 ±0.2) × 1015 m2
, respectively, for 0.18C, 0.25C and 0.30C materials prior deformation. Comparing the
estimated total dislocation density with GND value, it appears that the fraction of GNDs decreases with carbon content. GND is estimated to account for about 95%, 80%, and 67% of the total dislocation densities of 0.18C, 0.25C, and 0.30C lath martensite, respectively. The uncertainties of the dislocation density reported here were calculated using error propagation of the uncertainties in the parameters of the CMWP fitting routine. All the materials under investigation exhibit M>1 in the undeformed state; M values are estimated to be 5.5 ± 0.5, 3.1 ± 0.25 and 2.6 ± 0.96 for 0.18C, 0.25C, and 0.30C steels, respectively, indicating that the dislocations in the undeformed state have a weak dipole character. The value of parameter q, which is related to the dislocation types, is calculated to be approximately 2.0 for the materials under investigation before deformation. For the BCC slip system, the theoretical value of q is 1.3 for an edge dislocation and 2.6 for a screw dislocation. Thus, the q value of 2.1 indicates that the screw-type dislocation is dominant in the lath martensite. The evolution of ρtot and M as a function of plastic strain is shown in Figure 9 for 0.25C and 0.30C steel. Considering the error associated with the line broadening analysis, it can be concluded that the dislocation density in both materials remains constant during straining, notwithstanding an increase in flow stress (see Figure 5). This finding is contrary to the results
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published in [5, 10, 11], where they reported a reduction in ρtot with increasing plastic strain using the classical Williamson-Hall method. It should be noted that during line broadening analysis, it was assumed that the peak remains symmetric during plastic deformation. M values decrease to 0.61±0.04 and 0.51±0.01, respectively, for 0.25C and 0.3C steel at 2% plastic strain and hardly changes beyond this point. The q value remains between 2.0-2.2 throughout the deformation. It appears from the results presented in Figure 9 that the evolution characteristics of ρtot, M, q with plastic strain are very similar and merely depend on carbon content for the concentration range under investigation; thus the evolution of ρtot, M, q as a function of plastic strain was not measured for 0.18C steels.
Figure 9: Dislocation density (ρ) and average arrangement parameter (M) estimated from the XRD line broadening analysis using CMWP fitting procedure.
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4. Discussions a. Yield strength Yield strength (σy) of lath martensite can be expressed as a linear combination of the different strengthening mechanisms contributing to the strength of martensite: =
+
+
√
Here σ0 is contribution from Peierls-Nabarro stress and solid solution strengthening; second term is contribution from dislocation strengthening, i.e., the Taylor model, and third term is contribution from grain boundary strengthening. Also, α is proportionality constant, G is shear modulus (80 GPa for lath martensite), b is Burger’s vector, ρ is dislocation density, KHP is coefficient of Hall-Petch relation and d is “effective grain size” of lath martensite. Considering a low volume fraction of auto-tempered martensite, precipitation hardening effect is not considered in the yield strength calculation. σ0 is considered independent of solid solution strengthening by carbon. Elemental mapping of carbon using atom probe tomography has revealed that the carbon segregates to the lath boundaries or in the dislocations core rather than forming a random solid solution even in the as-quenched state [18]. Jo et al. [19] estimated σ0 to be 201 MPa for a 0.3C lath martensite steel based on Rodriguez and Gutierrez’s method. The same value of σ0 is also used in this study.
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The individual contribution of solid solution, grain size, and dislocation density on the yield strength are shown in Figure 10. The experimental value of yield strength (YS) is plotted as a reference. It should be noted here that stress at 0.2% offset strain is considered as yield strength. Calculated yield strength exhibits a good agreement with the experimentally measured value. It is also worth noting here that total dislocation density estimated from the XRD analysis is used in Taylor’s model, and “block size” is considered as the “effective grain size” for the YS calculation. The figure shows that the strengthening by forest dislocation is the main contributor to the strength of the martensite. The effect of lath width on the overall strengthening was also considered; however, this overestimates the grain size effects on yield strength as noted by the higher difference between calculated and experimentally measured yield strength. Lath width, carbon content, and dislocation density are interrelated. This correlation between composition, substructure size and defect density can be explained based on the plastic strain accommodation in prior austenite grain during martensite transformation. Researchers have shown the formation of accommodated dislocations at the martensite/austenite interface using high-resolution TEM [20] and EBSD analysis [21]. Martensitic transformation (MS) temperature decreases with increasing carbon content. Reduced MS, as well as increased carbon content, resulting in higher accommodated dislocations in PAGs, which increase the energy barrier for the migration of lath boundaries. The inherited dislocation density in martensite also increases with increasing accommodated dislocations in PAGs. In addition, the extent of auto-tempering, which causes coarsening of lath boundaries and reduction of dislocation density during martensitic transformation, reduced
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with decreasing MS. This suggests that while carbon can modify both martensitic substructures and dislocation density, the strength increment is mostly correlated to dislocation density changes due to increasing carbon concentration. This conclusion is contrary to the well-known relation between YS and the square root of carbon content in martensitic steel, which is related to the solid solution strengthening effects of carbon.
Figure 10: Contribution of solid solution, grain size and dislocation density on the yield strength (YS). Experimental value of YS also plotted as a reference.
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b. Work hardening behavior In general, the increment in flow stress (Δσ) is attributed to the increment in dislocation density with increasing plastic strain using Taylor’s model. However, while the dislocation density remains almost constant during straining, a stress increment >200 MPa beyond the yield strength was observed for lath martensite. This peculiarity in the deformation behavior of martensite is also reported in [7, 22, 23], which leads to the special classification of “in-lath” and “out-of-lath” plane slip of lath martensite. The critical resolved stress value is significantly lower in in-lath plane slip systems (soft packet) compared to that of out-of-lath slip systems (hard packet). Lath packets with active Burgers vectors in the lath plane work soften, whereas the packets with active Burgers vectors out of the lath plane work harden. Ungar et al. [23] using in-situ high-resolution neutron diffraction revealed that during plastic straining of 0.22C lath martensite, the initial symmetric diffraction profile became an asymmetric profile, which can be deconvoluted to calculate the evolution of dislocation density in soft and hard packets. Dislocation density increases in hard packets while it decreases in soft packets. However, no such asymmetry in the diffraction pattern of the deformed sample was observed in this study. Nevertheless, in both cases, change in average dislocation density shows a similar trend, i.e., a minimal change during straining. In addition, the dislocation arrangement parameter (M) shows minimal changes in soft packets (M>1), while it rapidly decreases from a value of M>1 to M<1 in the hard packet. A similar decrease in dislocation arrangement parameter (M) is also observed in this study considering symmetric diffraction profile. This decrease in M suggests that the dislocations arranged themselves in lower energy dislocation structures (LEDSs). The coefficient
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α in the Taylor model increases with increasing cell wall volume fraction of these LEDSs. Thus, a decrease in M is linked with the increase in α. In general, α is considered constant during deformation; however, researchers have shown that α also changes during straining, especially when the material system undergoes a significant rearrangement of dislocation structure during deformation [22–24]. In this study, the α needs to increase from the initial value of 0.25 to 0.35 in order to account for the increment in flow strength. It is interesting to note that interactions between dislocations and solute carbon atoms do not affect dislocations rearrangement, and thus α is also independent of carbon concentration. 5. Conclusions The effects of solute carbon content on microstructure and dislocation density evolution during deformation of lath martensite were examined in this study. The following conclusions can be drawn from this investigation:
i)
The block and lath width of lath martensite decreases with increasing carbon content. The decrease in lath width correlates with the increase in dislocation density. Dislocation density increases from 2.3× 1015 m-2 for 0.18 C material to 3.5× 1015 for 0.25 C and 4.6× 1015 for 0.3 C martensitic steels.
ii)
Contributions of different strengthening mechanisms to yield strength were estimated. Block size is perceived to be the “effective grain size” of lath martensite. Dislocation strengthening was determined to be the most crucial factor, contributing
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up to 65% of the yield strength. The increase in yield strength with increasing carbon content is attributed to the increase in dislocation density. iii)
Dislocation density remains constant during deformation, but the parameter M related to dislocation arrangement decreases with straining. The work hardening in lath martensite is speculated to stem from the rearrangement of dislocations toward stronger dipole character, which increases the coefficient α in Taylor’s model.
iv)
Solute carbon atoms have little or no effect on the strain hardening behavior of lowcarbon martensite.
Acknowledgements The author thanks ArcelorMittal Global R&D management for their permission to publish the work. The author is also grateful to Loretta Bock for metallography and tensile test and Warren Bolton for XRD measurement. The author also extends his appreciation to Cayron Cyril for providing a copy of ARPGE reconstruction software.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: