Characterization of localized plastic deformation behaviors associated with dynamic strain aging in pipeline steels using digital image correlation

International Journal of Plasticity xxx (xxxx) xxx–xxx

Contents lists available at ScienceDirect

International Journal of Plasticity journal homepage: www.elsevier.com/locate/ijplas

Characterization of localized plastic deformation behaviors associated with dynamic strain aging in pipeline steels using digital image correlation Taylor R. Jacobsa,b,∗, David K. Matlockb, Kip O. Findleyb a b

Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM, 87544, USA Colorado School of Mines, Advanced Steel Processing and Products Research Center, 1500 Illinois Street, Hill Hall, Golden, CO, 80401, USA

ABSTRACT

Localized deformation behavior in X52 and X70 pipeline steels during dynamic strain aging (or DSA, caused by interstitial atom-dislocation interactions during plastic deformation) were systematically assessed using digital image correlation with incremental strain analysis during elevated temperature tensile testing in the range of 25–350 °C. Similar to materials that use substitutional atoms for DSA, deformation band propagation and nucleation behaviors in the steels were directly related to the morphologies of flow curves from the tensile data. Comparisons between the steels and substitutional DSA systems were made. The type of localized deformation behavior was dependent on the temperature and strain rate conditions of the tensile test and the total amount of strain in the sample. Plastic flow was primarily dominated by deformation band propagation and nucleation at relatively low and high temperatures respectively within the DSA regime. It was theorized that the changing serration morphologies and deformation behaviors at different temperature-strain rate conditions were due to relative differences between the mobility of the solute atoms and the velocity of the mobile dislocations throughout the DSA regime. The dislocation density (which increases due to strain hardening during a tensile test) also influenced deformation behavior at relatively low and high strains.

1. Introduction Dynamic strain aging (DSA) is a metallurgical phenomenon that influences mechanical properties of many engineering metals through interactions of mobile dislocations and solute atoms during plastic deformation (Li and Leslie, 1978). Specifically, DSA typically increases the flow strength, reduces ductility, and results in negative strain rate sensitivities. Aluminum alloys (Morris, 1974; Benallal et al., 2008; Zavattieri et al., 2009; Anjabin et al., 2013;Klusemann, 2015; Yuzbekova, 2017; Zhemchuzhnikova et al., 2018), steels and iron alloys (Cuddy and Leslie, 1972; Li and Leslie, 1978; Choudhary et al., 1999; Gonzalez et al., 2003; Wagner et al., 1998; Okamoto et al., 1991; Gilat and Wu, 1997), stainless steels (Rodriguez, 1984), titanium alloys (Prasad, 2010), superalloys (Swaminathan et al., 2015), high entropy alloys (Chen et al., 2015; Brechtl et al., 2018; Zhemchuzhnikova et al., 2017) and potentially twinning induced plasticity steels (De Cooman et al., 2012; Kim et al., 2015; Hector and Zavattieri, 2010; Renard et al., 2010) have exhibited evidence of DSA under specific, material-dependent temperature-strain rate conditions during tensile testing. Substitutional and interstitial atoms can contribute to DSA (Robinson and Shaw, 1994). For example, steels containing interstitial carbon and nitrogen typically exhibit DSA within an approximate temperature range of 100–200 °C, and iron alloys with substitutional alloy additions, e.g. Si, Mn, Ni, Ru, Rh, Re, Ir, or Pt, exhibit DSA in the approximate temperature range of 230–500 °C during quasi-static tensile testing (Cuddy and Leslie, 1972). The microscopic mechanism of DSA in interstitial-containing alloys is different from substitutional-containing alloys (Sarkar et al., 2007). Substitutional atoms require vacancy-assisted diffusion or dislocationassisted cross-core diffusion of solutes over long distances (Curtin et al., 2006). Interstitials can diffuse more freely in the crystal

∗

Corresponding author. Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM, 87544, USA. E-mail address: [email protected] (T.R. Jacobs).

https://doi.org/10.1016/j.ijplas.2019.07.010 Received 26 March 2019; Received in revised form 8 July 2019; Accepted 11 July 2019 0749-6419/ Published by Elsevier Ltd.

Please cite this article as: Taylor R. Jacobs, David K. Matlock and Kip O. Findley, International Journal of Plasticity, https://doi.org/10.1016/j.ijplas.2019.07.010

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 1. Schematic stress-strain curves demonstrating the different types of serrated yielding morphologies associated with DSA and the relative critical strain ( c ) associated with each type. Figure was first published by Rodriguez (1984).

without the need for vacancy or dislocation assisted diffusion. Hence, DSA from interstitial-dislocation interactions can typically happen at relatively lower temperatures. A common manifestation of DSA in tensile data is the presence of serrations (or load drops) in the flow curve and the presence of localized plastic flow. Rodriguez (1984) identified, as shown in Fig. 1, various stress-strain curve appearances caused by DSA that were dependent on the test temperature and strain rate. The different serration types are commonly referred to as Types A-E (Rodriguez, 1984; Robinson and Shaw, 1994), and it is possible for a single material to exhibit all five types of serration morphologies under different temperature-strain rate conditions. Different types of serrations are associated with different critical strains ( c ) to initiate DSA in a sample. It is also possible for multiple types of serrations to be observed simultaneously (e.g. Type A + B or Type D + B). Rodriguez (1984) indicated that Types A and B serrations exhibit lower critical strains (i.e. serrations initiate closer to the yield point) than Type C. The serrations depicted in Fig. 1 are based on observations from DSA caused by substitutional atomdislocation interactions (e.g. Al–Mg alloys and stainless steels). Serrations observed in materials that exhibit DSA through interstitial atom-dislocation interactions (e.g. steels) are reported to be more complex than the schematic plots in Fig. 1 (Robinson and Shaw, 1994). While DSA is active, stable localized plastic deformation (i.e. localized deformation without necking) occurs in the gauge length of the tensile specimen. Deformation markings are often visible on polished tensile samples and are commonly referred to as deformation bands, stretcher-strain markings, Portevin-Le Chatelier (PLC) bands, or Lüders bands (Robinson and Shaw, 1994). Deformation bands can either nucleate and arrest or nucleate and then propagate within the tensile specimen gauge length. Nucleation and propagation behavior of deformation bands are directly related to the morphology of the serrations in the stress-strain curve (Rodriguez, 1984). In general, the flow curve morphologies shown schematically in Fig. 1 can be divided based on serration frequency: low for Types A, D and E and high for Types B and C. Plastic flow primarily occurs through propagation of deformation bands for low frequency serrations and nucleation of deformation bands for high frequency serrations. Detailed descriptions of the deformation behaviors associated with the serration types discussed by Rodriguez (1984) are provided below. Localized deformation from DSA has been studied using various methods. Initially, highly polished tensile samples were used to reveal surface markings (Cuddy and Leslie, 1972; Chihab et al., 1987; Robinson and Shaw, 1994). Other experimental methods have included strain gauges located along the gauge length (Cuddy and Leslie, 1972; Matlock et al., 1979, Benallal et al., 2008), thermal imaging (Ait-Amokhtar et al., 2008; Nogueira De Codes et al., 2011; Lee et al., 2011; De Cooman et al., 2012) and digital image correlation (DIC) (Ait-Amokhtar et al., 2006; Hector and Zavattieri, 2010; Benallal et al., 2008; Renard et al., 2010; Nogueira De Codes et al., 2011; Anjabin et al., 2013; Kim et al., 2015; Swaminathan et al., 2015; Cai et al., 2016). The ability to resolve individual band formation and relationships of the bands to the overall deformation behavior depends on test technique. Direct observations from surface markings are often difficult to detect, especially at elevated temperatures with samples that develop surface oxide layers during testing. In comparison to thermal imaging or DIC, strain gauge methods which average in-plane surface strains have a lower ability to resolve localized deformation. Thermal imaging which assesses temperature changes within localized bands due to adiabatic heating, also has limitations due to the rate of heat dissipation compared to the strain rate of the sample. Digital image correlation is effective at studying localized deformation because it is unaffected by localized adiabatic heating and provides sufficient spatial resolution to detect deformation bands. While relationships between serration morphology and localized deformation resulting from substitutional atom-dislocation interactions have been studied extensively, serration morphologies caused by interstitial atom-dislocation interactions were reported to be irregular and more challenging to classify (Robinson and Shaw, 1994). The goal of the present study was to use DIC to correlate physical localized deformation behavior to serration morphologies in pipeline steels at temperatures up to 350 °C. High strength 2

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Table 1 Chemical compositions of the X52 and X70 steels (in wt pct). (wt pct)

C

Mn

Si

Mo

Ti

Nb

V

Al

N

X52 X70

0.048 0.045

1.19 1.57

0.17 0.30

0.040 0.094

0.003 0.015

0.001 0.065

0.046 0.005

0.035 0.026

0.0109 0.0049

pipeline steels are under development for applications in heavy oil extraction that utilize high pressure steam to provide heat at operating temperatures up to approximately 350 °C. Recent studies (Jacobs et al., 2016, 2017; Jacobs, 2018) have evaluated the elevated temperature mechanical properties of X70 pipeline steels and have shown some unique correlations between the presence of DSA, strength-ductility combinations, and the development of localized plastic deformation. It was hypothesized that steels (which use interstitials for DSA in the temperature range of interest) exhibit the same deformation band nucleation and propagation behaviors as materials with substitutional atoms contributing to DSA. Thus, a second goal is to compare the results obtained here to studies of materials where DSA is caused by substitutional-dislocation interactions. 2. Experimental methods 2.1. Materials Two commercially produced plate steels for use in the construction of pipe were selected for analysis. The steels, designated X52 and X70, had compositions summarized in Table 1 and were respectively received as 13.5 and 12.7 mm thick plate. Micrographs of the X52 and X70 steels have been published elsewhere (Jacobs et al., 2016; Jacobs, 2018). The X52 steel had a ferrite-pearlite microstructure with an approximate ferrite grain size of 16 μm. The X70 steel had a quasi-polygonal ferrite microstructure with martensite-austenite and austenite islands and an approximate ferrite grain size of 2.4 μm. 2.2. Elevated temperature tensile testing Cylindrical tensile samples were machined parallel to the rolling direction with a reduced gauge diameter of 6.35 mm and a nominal gauge length of 25.4 mm. Tensile tests of as-received material were conducted in air in the temperature range of 25–400 °C, at engineering strain rates ranging between 1.67 × 10−4 and 1.67 × 10−3 s−1 on a standard electro-mechanical test frame equipped with a clamshell furnace. Samples tested at the low and high strain rates are identified below as 10−4 and 10−3 s−1, respectively. Temperatures were measured with a Type K thermocouple spot welded to the surface of the tensile specimen gauge of each sample. Samples were speckled with a high temperature boron nitride spray for DIC analysis. Prior to testing, sample temperatures were stabilized for a minimum of 1200 s at each test temperature. Complete details of the experimental techniques and test matrix are published elsewhere (Jacobs, 2018). 2.3. Photography Two-dimensional (2D) DIC was used to map surface strains in situ during elevated temperature straining of the X52 and X70 steels. A single camera was used with a 50 mm f/2.8 manual lens. Light was polarized using filters at the light source and camera lens. The speckled tensile specimens were viewed through an extensometer port in the clamshell furnace. The maximum camera frame rate was 1 Hz. For most of the DIC analyses, 1.0 and 0.1 Hz were used for samples tested at 10−3 and 10−4 s−1, respectively. The different frame rates allowed for identical strain increments between images for both strain rate conditions in the DIC analysis. Selected samples that exhibited high frequency serrations at 10−4 s−1 were also analyzed with an imaging frequency of 0.33 Hz (exact frequencies are indicated with presented figures). Tensile testing and imaging were manually initiated simultaneously with a start time (i.e. t = 0) error of less than 0.5 s. 2.4. Digital image correlation The recorded DIC images were analyzed with ARAMIS software from GOM. Two general types of strain calculations based on planar displacements between dots in two images were possible. Displacements between sequential images were used to calculate incremental strains, while displacements between any two images were used to calculate average engineering strains. Fig. 2 shows a schematic diagram to define engineering and incremental strains from a series of speckled pattern images. Engineering strains were calculated from images of the un-deformed and deformed sample (i.e. comparing t0 and tn) and were used to analyze accumulated surface strains throughout an experiment. Incremental strains are defined as the amount of surface strain measured within a distinct time increment during deformation. While speckle pattern displacements can be used to analyze in-plane strains in different directions, all strain measurements with 2D DIC in the present work were based on displacements parallel to the tensile axis. The depth of field with the 2D DIC camera was high enough to focus the entire gauge length of the circular cross-sectional geometry of the tensile specimen. The primary purpose of DIC in the current work was to study localized plastic deformation during DSA and compare the behavior 3

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 2. Schematic representation of how engineering and incremental strains are calculated using DIC. Schematic images of tensile specimens from left to right represent un-deformed and increasing strain levels. Arrows indicate the two images used to calculate engineering and incremental strains (adapted from an unpublished diagram from B. Goshert, 2018).

to serration morphologies. Fig. 3 shows an example (X52 steel at 98 °C 10−4 s−1) of how incremental strain analysis was performed and how the results are reported in the discussion below. Engineering stress-time data were plotted in Fig. 3a and used to analyze serration morphology (note, serration morphologies had the same appearance for stress-strain and stress-time data). Incremental strain maps were then generated at all time increments during the tensile test using the ARAMIS software, and a map for one time during the test is shown in Fig. 3b. From the data used to create Fig. 3b, plots of the incremental strain data as a function of position along the gauge length obtained along a single dashed reference line (or section) parallel to the tensile axis were generated as shown

Fig. 3. Example diagram of the procedure for relating localized deformation behavior to serration morphology using incremental strain analysis. The (a) morphologies of the engineering stress-time plots were compared to DIC data in the form of (b) incremental strain maps. Data along a section of the incremental strain maps were plotted (c) sequentially from one fillet (0 mm) to the opposite end of the reduced gauge section and as an incremental strain contour plot (d). The example shown is from the X52 98 °C 10−4 s−1 sample. The time increment for the DIC analysis was 0.1 Hz. Color in this image represents incremental stain values. Blue indicates approximately zero incremental strain and transitions to lighter colors (white, yellow, red) to indicate higher levels of incremental strain. Note, there is a difference between color scales for the incremental strain map and the 3D incremental section data plot. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 4

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

in Fig. 3c. Localized deformation is evident in Fig. 3c by the presence of the data peak at a location which changes with time and reflects band propagation during a test. Strain profile data (i.e. Fig. 3c) for each time step throughout a tensile test were used to create three-dimensional contour plots at the same time scale as the flow curves; one example is shown in Fig. 3d. The number of displacement measurement points and correspondingly, the number of strain data values along the incremental strain profiles were constant. However, the distances between measurement points increased with deformation. Thus, position values on the contour plots are relative to the fillets of the tensile bar (i.e. each plot covers the entire gauge length of the tensile specimen). The number reported at the top of the contour plot is the conversion factor between relative position and actual position (in mm) at time equals zero. The color scale of the contour map was selected to highlight statistically significant incremental strain values above background noise. Incremental strains above 0.32 pct were considered statistically significant by performing DIC on 30 images of an unstrained sample and taking the range of strain calculations across the entire sample. Transitions from blue to white to red on the contour plots indicated increased levels of incremental strain. Deformation band propagation, nucleation, and plastic instability resulted in distinct features on the contour plots (all of which are present in the example shown in Fig. 3d). Continuous propagation of a localized deformation band (i.e. strain peak) is represented by continuous diagonal “lines” on the contour plot. At times less than about 700 s, the example in Fig. 3b illustrates four incidences where bands nucleated at the same end and propagated completely across the gauge length (i.e. diagonal lines are essentially parallel). Above about 700 s, one band appears to reverse direction (i.e. slope of diagonal line reversed) and propagate completely through the gauge length. Discontinuities (or jumps) in locations of the incremental strain peaks or isolated peaks indicate deformation band nucleation. Nucleation events were observed at approximately 300, 390, 530, and 720 s in Fig. 3d. Above about 1000 s, the band location remains fixed signifying formation of a final neck at that location and strain increases in intensity with time until final fracture. 2.5. Classification system for serration morphologies and localized deformation behavior To assist in the description of DSA observed in this study, a serration morphology/deformation band behavior classification system was developed for the X52 and X70 steels. The goal of the modified classification system was to clearly describe the localized deformation behavior in relation to the serration morphologies observed. Table 2 shows an outline of the DSA deformation classification system used here. DIC results were related to the serration type system outlined by Rodriguez (1984) based on load fluctuations and deformation band kinematics. The proposed classification system provides a more specific description of the relationship between serration morphology and deformation band kinematics compared to the classic system (Rodriguez, 1984). Deformation types were classified as either propagating or nucleating localized bands, which are related to low or high frequency serrations respectively. Propagating deformation band behaviors are classified as continuous propagation (CP) or reflected continuous propagation (RCP). Systematic nucleation (SN), constrained nucleation (CN) and reflected constrained nucleation (RCN) are used to describe deformation through the nucleation of localized bands. A description of Lüders bands, associated with yield point elongation (YPE) in the flow curve, is also included in Table 2. Lüders band formation was considered independent from types of serrations due to the difference in flow curve morphologies compared to serrations associated with DSA. Fig. 4 schematically presents examples of flow curve appearances and deformation behaviors considered in the present study. Each schematic in Fig. 4 correlates the incremental strain contour plot to flow curve morphology. In addition, the red boxes along the schematic gauge lengths below the contour plot indicate the approximate locations of plastic deformation at different times associated with the corresponding flow curves and incremental strain contour plots. For conditions where the sample experiences uniform strain (e.g. Fig. 4a), deformation is shown to be uniform throughout the gauge length. Lüders bands (Fig. 4a) occur after elastic deformation; nucleation usually occurs at one of the fillets (i.e. the end of the sample), and then the bands propagate along the entire gauge length once during YPE. After Lüders band propagation, uniform plastic strain (e.g. Fig. 4a) or serrated flow can occur depending on testing temperature and strain rate. Uniform plastic strain results in Table 2 Deformation band classification system for DSA. Rodriguez (1984) Defined Serration Classification

Current Classification

Description of Band Behavior

Yield Point Elongation (YPE)

Lüders Bands

Type A

Continuous Propagation (CP)

Types D or E

Reflected Continuous Propagation (RCP) (Reflected) Constrained Nucleation ((R)CN)

Nucleation and propagation of localized deformation associated with a yield point in the flow curve. Continuous unidirectional propagation of bands with nucleation events that occur when the deformation band reaches one end of the gauge length. Continuous propagation of bands that result in a relative direction change when the bands reach one end of the gauge length. Nucleation of bands where the potential nucleation sites are constrained to occur within the vicinity of the previous deformation band location. Deformation behavior appears similar to CP and RCP. Nucleation of bands that occur anywhere along gauge length at favorable sites; which are typically locations that have relatively low total strains. Behavior can appear somewhat random.

Types A + B or D + B Types B or C

Systematic Nucleation (SN)

5

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 4. Schematic diagrams of (from top to bottom) stress-time curves showing different flow curve morphologies, associated incremental strain contour plots, and physical location of deformation along the gauge length at various times. Types of deformation depicted are (a) Lüders bands and uniform deformation, (b) continuous propagation, (c) reflected continuous propagation, (d) constrained nucleation, and (e) systematic nucleation.

approximately constant incremental strain values along the gauge length due to the constant imposed strain rate of the tensile test. As discussed above, serrations from DSA are related to different localized deformation behaviors. Deformation bands with CP character (Fig. 4b) nucleate at one end of the gauge length and propagation occurs unidirectionally. The resulting incremental strain contour plot exhibits multiple diagonal lines of positive or negative slope that indicate the region of local plastic deformation moves continuously along the gauge length in a single direction. Deformation bands with RCP character (Fig. 4c) propagate continuously back and forth along the gauge length. The resulting incremental strain contour plot exhibits lines with cycling positive and negative slopes as the local deformation changes direction at the ends of the sample gauge length. Deformation bands with CP and RCP behavior can have similar appearances to Lüders bands in the incremental strain contour plots. The classifications are distinguished based on flow curve appearances. Lüders bands are associated with YPE, which does not result in macroscopic strain hardening, and serrations from DSA are associated with appreciable strain hardening. 6

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 5. Engineering stress-time curves obtained at 25 °C and associated contour plots of the incremental strain profiles of (a) X52 at 10−4 s−1, and (b) X70 steel at 10−3 s−1. The X52 samples exhibited YPE and Lüders band propagation during yielding and both materials exhibited uniform deformation prior to necking.

Testing conditions that induce higher frequency serrations in flow curves are associated with deformation band nucleation. Deformation bands with CN character (Fig. 4d) are also associated with CP or RCP morphologies in the flow curve. Instead of deformation band propagation, the bands nucleate adjacent to previously formed bands. The overall appearance on the incremental strain contour plot is similar to either CP or RCP behavior. However, similar to SN deformation bands (see below), plastic deformation only occurs at load drops. The resulting appearance in the incremental strain contour plot is individual spots with an ordered behavior. Deformation bands with SN character (Fig. 4e) occur quasi-randomly along the gauge length. At each load drop in the flow curve, a deformation band nucleates at a favorable location along the gauge length. Since deformation is associated with strain hardening, favorable nucleation locations include regions that have experienced the lowest levels of strain hardening. Also, since deformation bands nucleate at load drops, negligible plastic strain is detected between load drops (i.e. as the load increases). Therefore, the incremental strain contour plots exhibit individual spots that are associated with the nucleation of deformation bands. 3. Results and discussion 3.1. DIC observations Figs. 5–8 present data pairs consisting of engineering stress vs. time (i.e. strain) and DIC contour plots, each pair aligned to match the x-axis time scales. In the figures discussed below, time is used on the x-axis in lieu of strain to be able to directly compare the deformation behavior of the constant engineering strain rate tests to the DIC data recorded in fixed time increments. Data are presented for samples selected to illustrate variations in the character of band nucleation and propagation observed in this study. At room temperature, the X52 steels exhibited YPE and the X70 steels exhibited continuous yielding as shown in Fig. 5a and b respectively. For both steels at higher strains, continuous uniform deformation was observed up to the peak stress followed by localized strain associated with necking instability. For the X52 steel, the contour plot in Fig. 5a shows that YPE was associated with nucleation of a Lüders band at approximately 180 s and propagation from one end of the reduced gauge section to the other end. After band propagation, uniform deformation occurred without nucleation of additional bands. As indicated by the calibrated color intensity band at the right of the contour plot, maximum incremental strains observed during Lüders band propagation were greater than approximately 1.0 pct. In contrast, the X70 steel contour plot in Fig. 5b shows a complete absence of band formation at low strains consistent with continuous yielding. For both steels, uniform deformation exhibited approximately constant incremental strains of 0.3–0.4 pct along the gauge length and appeared as a light blue color in the incremental strain contour plots. In both steels the development of diffuse necking is evident by a region of light blue over an extended portion of the gauge length initiated at approximately the location of maximum stress in the engineering stress-time curve. This behavior is particularly visible 7

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 6. Engineering stress-time and associated contour plots of the incremental strain profiles of (a) X52 149 °C 10−3 s−1, and (b) X70 200 °C 10−3 s−1. Samples exhibited Lüders bands with YPE (X52 only), CP and RCP localized deformation behaviors at relatively low and high strains, respectively, followed by necking.

Fig. 7. Engineering stress-time and associated contour plots of the incremental strain profiles of (a) X70 149 °C 10−4 s−1 and (b) X70 225 °C 10−4 s−1. Samples exhibited independent RCP serration and deformation band behaviors. Vertical dashed lines indicate the time of the critical strain.

for the X70 steel for times between about 80 and 100 s and for the X52 steels for times above about 1200 s. As shown in Fig. 5b, with time after the initial formation of a diffuse neck, strain concentrates (distinct red region) in the localized necked region immediately preceding fracture. 8

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 8. Engineering stress-time and associated contour plots of the incremental strain profiles of the X52 151 °C 10−4 s−1 condition. An image frequency of 0.33 Hz was used to attempt to detect individual deformation band nucleation. (a) Overall serration and deformation band behavior. (b–d) Higher magnifications of (a) showing deformation behaviors in different regions of the flow curve.

The X52 98 °C 10−4 s−1 sample from Fig. 3 exhibited continuous propagation (CP) type behavior at relatively low strains after yielding. Fig. 6 shows engineering stress-time curves and associated incremental strain contour plots for two additional specimens that exhibited CP behavior at relatively low strains. The X52 149 °C 10−3 s−1 (Fig. 6a) specimen initially exhibited YPE, followed by CP (low strains), and then reflected continuous propagation (RCP) behavior at high strains associated with DSA prior to necking. Deformation band propagation was the primary deformation mechanism with nucleation events at 35 and 46 s. The X70 200 °C 10−3 s−1 (Fig. 6b) specimen also exhibited CP and RCP behavior at relatively low and high strains, respectively, prior to necking. One CP nucleation event was observed at 35 s in the X70 200 °C 10−3 s−1 specimen. In contrast to the sample shown in Fig. 3, Lüders bands in the X52 149 °C 10−3 s−1 specimen (Fig. 6a) propagated along the gauge length in the opposite direction compared to the CP deformation bands. Deformation bands from DSA also exhibited lower incremental strains, around 0.6 pct, compared to the Lüders 9

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

incremental strains of approximately 1.0 pct. As noted in the discussion above regarding Table 2 and Fig. 4, CP behavior is equivalent to the Type A serrations classified by Rodriguez (1984). The schematic incremental strain plot in Fig. 4b demonstrates the appearance of repeating diagonal lines with the same-sign slope that are related to the unidirectional propagation of deformation bands along the sample. The data in the range of 30–58 s and 26–44 s in Fig. 6a and b, respectively, show similarities to CP behavior depicted in Fig. 4a. Most samples exhibited a transition to RCP deformation band behavior and serration morphology at relatively high strains (a phenomenon shown schematically in Fig. 1 as Type E). Continuous propagation behavior, indicated by a direction change at the fillets (as depicted in Fig. 4), was observed from 60 to 100 s and 44–64 s in Fig. 6a and b, respectively. After the initial nucleation event, deformation consisted entirely of band propagation when classified as RCP. The maximum incremental strains measured in the RCP regions were approximately equal to the values measured in the CP regions of the tensile curve. As the samples approached the point of necking instability, the width of the localized deformation region increased, and necking initiated near the location of the last RCP deformation bands to propagate. The flow curve morphologies past the point of necking instability were smooth for all samples, and localized deformation within the necking region was not detected with DIC. Some samples exhibited exclusively RCP deformation band behavior after yielding at both relatively low and high strains. For the X70 steel, Fig. 7 shows two engineering stress-time curves and associated contour plots of the incremental strain profiles of samples that exhibited independent RCP behavior (i.e. RCP behavior at high and low strains). The morphologies of the flow curves were similar to Types D or E serrations discussed by Rodriguez (1984). Note the temperature and critical strain times for the two samples. At a strain rate of 10−4 s−1, the X70 149 °C (Fig. 7a) sample was tested at an intermediate temperature within the DSA regime, and the X70 225 °C (Fig. 7b) sample was tested at the high temperature boundary of the DSA regime (discussed in further detail below). Both samples exhibited RCP behaviors, but the higher temperature sample (Fig. 7b) exhibited a relatively large critical strain (εc = 2.7 pct engineering strain) compared to the lower temperature sample in Fig. 7a (εc = 0.9 pct engineering strain). However, the deformation band behaviors were equivalent for the two RCP examples. Deformation band propagation direction changes were associated with the local minima in the flow curves, and maximum incremental strains were approximately the same as CP bands. Uniform deformation (similar to that shown in Fig. 5) was observed prior to the critical strain for both samples. Plastic instability for both samples presented in Fig. 7 initiated in the same manner as what was discussed above for Fig. 6. The DIC camera framerate used to analyze CP and RCP behaviors (0.1 Hz for the slower strain rate discussed above) resulted in substantial aliasing errors for testing conditions that exhibited the high frequency SN and CN behaviors. Aliasing errors can occur when two sets of signals with different frequencies are compared. All deformation band nucleation events were associated with higher load drop frequencies compared to CP/RCP behaviors and were the source of the aliasing errors. To assess the consequences of aliasing errors and provide increased resolution in incremental strain contour plots, selected tests were run with a higher DIC camera frame rate of 0.33 Hz for the 10−4 s−1 strain rate condition to characterize the deformation band nucleation behavior of SN and CN testing conditions and results are presented in Fig. 8. Fig. 8 shows the engineering stress-time and associated incremental strain contour plots of the X52 151 °C 10−4 s−1 sample that exhibited two types of high load drop frequency behaviors. Fig. 8a shows the overall deformation behavior and Fig. 8b–d shows higher magnifications of different parts of the flow curve and incremental strain profiles (indicated by the boxes in Fig. 8a) that exhibited various localized deformation behaviors. The incremental strain contour plot in Fig. 8a exhibited features similar to the independent RCP behavior shown in Fig. 7a. However, the morphology of the engineering stress-time curve was substantially different due to the presence of high frequency load drops. Lüders bands were observed within the YPE region, followed by a combination of SN, RCN, and RCP behaviors at higher strains prior to necking. High frequency serrations were observed during YPE (170–230 s in Fig. 8). Similar to the observations in Figs. 5 and 6, maximum incremental strains during YPE were greater than maximum incremental strains measured during DSA after yielding. Maximum incremental strains in YPE and serration regions were approximately 0.45 and 0.25 pct, respectively (note that calculated incremental strain values are lower than previous samples because of the greater imaging frame rate). However, the Lüders bands changed behavior in the presence of the high frequency serrations within the YPE region (labeled as discontinuous YPE in Fig. 8b). Instead of continuous propagation of the Lüders bands along the gauge length (see Figs. 5a and 6a), YPE in the presence of secondary high frequency serrations corresponded to Lüders band nucleation at somewhat random locations followed by propagation along part of the gauge length, with nucleation of new Lüders bands in previously undeformed sections of the gauge length. The formation of a Lüders band results in local strain hardening within the band. Regions along the gauge length that experienced local plastic strain have an elevated flow stress compared to locations with only elastic deformation and are therefore unlikely to nucleate an additional Lüders band until the entire gauge length has experienced an equal amount of deformation. As a consequence, the number of possible nucleation sites decreased throughout the YPE region as the sample approached an approximately uniform amount of total strain throughout the gauge length. High frequency serrations (related to the systematic nucleation of deformation bands) were observed just after the YPE region at times between 228 and 287 s (Fig. 8b). Within the region of SN behavior, deformation bands nucleated throughout the gauge length somewhat randomly. However, the locations of the incremental strain peaks associated with SN deformation bands rarely appeared at the same relative position along the gauge length. The SN deformation band behavior was therefore classified as quasi-random nucleation. The quasi-random behavior was again thought to be influenced by local strain hardening in a manner similar to what was discussed above regarding YPE and Lüders bands. The number of possible nucleation sites was therefore dependent on the distribution of the total strain throughout the gauge length. Locations with the lowest amount of total strain had the lowest flow stress along the gauge length and therefore the highest probability of nucleating the next deformation bands. At relatively high strains, the X52 151 °C 10−4 s−1 sample (Fig. 8c and d) exhibited a combination of RCN and RCP deformation 10

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 9. Serration maps showing the temperature/strain rate conditions for different types of deformation behaviors observed in the (a) X52 and (b) X70 steels. Deformation behaviors are identified as uniform deformation (NO DSA), continuous propagation (CP), reflected continuous propagation (RCP), systematic nucleation (SN), constrained nucleation (CN), and reflected constrained nucleation (RCN). Regions identified as high εc means the critical strain for serrations was relatively high and uniform deformation was observed prior to serrations and localized deformation. Open and filled shapes indicate regions of propagation and nucleation dominated deformation behaviors, respectively. The dashed line in (a) indicates the maximum temperature where YPE and Lüders bands were detected.

bands. The overall behavior (Fig. 8a) has similarities to RCP (see Fig. 7), with deformation bands moving up and down the gauge length until plastic instability. However, closer inspection reveals alternating propagation and nucleation behaviors. Due to the overall appearance, propagation and nucleation regions were characterized as RCP and RCN respectively. High frequency load drops were associated with RCN behavior near the fillets of the tensile specimen and were observed as distinct incremental strain peaks. The deformation band nucleation behavior is classified as constrained because the nucleation sites only appeared adjacent to previously formed deformation bands and followed the overall trend of RCP behavior. Sections where the engineering stress-time curve was relatively smooth are associated with RCP deformation band behavior. The distinct incremental strain peaks associated with RCN behavior exhibited slightly greater maximum incremental strains compared to the RCP peaks. The DIC data discussed above provide unique observations related to localized deformation band formation in materials that exhibit DSA and provide additional data to complement the historical approach to band characterization. Discussions relating the observations above to interpretations of changes in local plastic deformation and dislocation-interstitial interactions at various temperature-strain rate conditions are included in the next section. 3.2. Application of DIC results to enhanced interpretation of DSA in steels Previously, serration maps were developed to illustrate, in log strain rate – inverse temperature space, regions where distinct load fluctuations were observed (Leslie, 1971; Rodriguez, 1984; Robinson and Shaw, 1994; Mogucheva et al., 2016). Previously published serration maps (Leslie, 1971; Rodriguez, 1984; Robinson and Shaw, 1994) divided the temperature-strain rate space into three or more distinct regions: DSA regions where serrations (often separated by type) are observed bounded by lower and higher temperature regions where serrations are absent for all imposed strain rates. Fig. 9 shows detailed serration maps for the X52 and X70 steels in the strain rate range of 10−4 to 2 × 10−3 s−1. The serration maps identify the temperature-strain rate conditions for the DSA regime and indicate the testing conditions for the various types of serration/localized deformation band behaviors discussed above. The X52 and X70 steels exhibited distinct changes in deformation band behavior that are defined by linear lines on the serration maps. The lines that indicate changes in deformation band behaviors are approximate boundaries based on experiments performed. The temperature range (at all strain rates tested) of the DSA regime is slightly greater for the X52 steel compared to the X70 steel. Most noticeably, the lower boundary of the DSA regime occurred at lower temperatures in the X52 steel compared to the X70 steel. At the highest strain rates tested, the lower temperature boundary of the DSA regime was approximately 112 and 143 °C for the X52 and X70 steels, respectively. It is hypothesized that nitrogen interstitial/dislocation interactions could be responsible for the differences in the lower temperature boundary of the DSA regime in the X52 steel. Interstitial nitrogen is slightly more mobile than carbon in ferrite (Leslie, 1981). Therefore, steels with nitrogen and carbon interstitials would exhibit DSA at lower temperatures than steels with just carbon interstitials. Due to the chemical compositions and processing histories of the pipeline steels tested, it is assumed that nitrogen atoms were mostly present as nitrides because of the relatively high concentrations of stable nitride forming elements. However, the X52 steel had relatively fewer strong nitride forming elements compared to the X70 steel, so there is a higher probability for free nitrogen to be present in the X52, which is reflected in the low temperature DSA boundary. 11

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Both steels exhibited relatively high critical strain (εc) RCP behavior (e.g. Fig. 7b) near the upper and lower boundaries of the DSA regime (critical strains were the amount of plastic deformation required for the onset of serrated yielding). The high critical strain RCP regions were observed over a narrow temperature range at both of the high and low temperature boundaries. Higher dislocation densities achieved through strain hardening likely aid the activation of DSA near the high and low temperature boundaries, where the solute diffusion-dislocation velocity relationship is less optimal. At relatively low temperatures within the DSA regime, both steels primarily exhibited propagating type deformation bands. Most samples exhibited CP behavior at low strains and transitioned to RCP at high strains (e.g. Fig. 6). However, it was possible for samples to exhibit RCP behavior (e.g. Fig. 7a) throughout the entire plastic deformation region prior to necking. Deformation band nucleation behavior was observed at relatively high temperatures within the DSA regime for both steels. However, the serration morphologies and deformation band behaviors were slightly different for the two steels discussed. In the X70 steel with increasing testing temperature, deformation behavior transitioned from CP→RCP or independent RCP, to RCN behaviors over a relatively narrow temperature range, and then to SN→RCP behavior. As testing temperature increased, the X52 steel exhibited a transition from CP→RCP to primarily SN→RCN behavior (a few samples exhibited CN behavior at higher temperatures and strain rates). Prior to the high critical strain RCP behavior near the high temperature boundary of the DSA regime, three samples in the X52 exhibited high critical strain CN behavior. The disappearance of Lüders bands at the onset of yielding was also observed in the CN region (indicated by the dashed line in Fig. 9). 3.3. Comparison between interstitial atom-dislocation and substitutional atom-dislocation interactions In many instances, serration morphologies and deformation behaviors were similar, with minor differences, when comparing materials that exhibited DSA through interstitial-dislocation and substitutional-dislocation interactions. For example, CP serrations exhibited relatively large, abrupt load drops in the flow curve that were related to the nucleation of a new deformation band across the sample. The morphologies of the CP serrations observed in the pipeline steels are slightly more complicated than what is depicted in some DSA studies involving substitutional atom-dislocation interactions (Rodriguez, 1984; Zavattieri et al., 2009). While distinct load drops were observed with relatively low frequencies, the morphologies of the flow curves between the distinct load drops appear more irregular than what was expected based on results from Rodriguez (1984) and Zavattieri et al. (2009), having a comparable appearance to the relatively high strain RCP (equivalent to Type E) serrations. However, highly irregular serration morphologies observed in the present study are also comparable to the appearance of some studies involving DSA through substitutional atomdislocation interactions (Ait-Amokhtar and Fressengeas, 2010; Chihab et al., 1987; Jiang et al., 2007; Benallal et al., 2008; Anjabin et al., 2013). Three notable differences in serration/deformation behaviors were observed when comparing materials that exhibit DSA from substitutional atom-dislocation and interstitial atom-dislocation interactions. The first is that RCP behavior (Types D/E) are uncommon for substitutionals (Wijler et al., 1972), but were observed in almost every testing condition for both steels in the present work. The second difference is related to the transition of deformation band behaviors from low to high strains in testing conditions where high frequency serrations (SN, CN, and RCN) were observed. It is common for substitutional DSA systems to exhibit a transition from low frequency serrations to high frequency serrations. However, steels only exhibited high frequency serration behaviors at high strains when high frequency serrations were also observed at low strains. For example, the Al–Mg alloy at 5 × 10−3 s−1 from Ait-Amokhtar and Fressengeas (2010) and the 316 stainless steel at 550 °C from Rodriguez (1984) exhibited CP (Type A) behavior at low strains and CN (Type A + B) behavior at high strains. The third is that substitutional atom-dislocation interactions commonly exhibit high frequency serrations at all strains in the high strain-rate, high temperature regions of the DSA regime (Rodriguez, 1984; Ait-Amokhtar and Fressengeas, 2010), where the steels studied in the present work tend to transition to RCP behaviors at high strains. 3.4. Solute atom-dislocation interactions in relation to observed deformation behaviors It is hypothesized that the changing serration morphologies and deformation behaviors at different temperature-strain rate conditions are due to transitions in operative DSA mechanisms based on relative differences between the mobility of the solute atoms and the velocity of the mobile dislocations throughout the DSA regime. Two different solute-dislocation interaction models are primarily discussed in the DSA literature (Leslie, 1981; Dieter, 1986): (1) the rapid pinning and unpinning of dislocations during deformation; and (2) the permanent pinning of dislocations by solutes causing the rapid generation of new mobile dislocations necessary for deformation to continue. The latter model is typically associated with steels (Li and Leslie, 1978; Leslie, 1981) and is based on results which show substantial increases in dislocation density during DSA compared to room temperature results where DSA is not observed. However, Leslie's model does not account for changes in deformation behaviors at different temperature-strain rate conditions within the DSA regime. Deformation at multiple length scales is considered for the discussion below, based on the following assumptions. For the purpose of this discussion, strain rate (and mobile dislocation velocity) is assumed to be constant, and interstitial atom mobility increases at higher temperatures. Therefore, within the DSA regime, dislocations are pinned faster at higher temperatures. Leslie's model is assumed applicable for interstitial-dislocation interactions at all testing conditions, which means that dislocation sources within grains must be activated to cause deformation of an individual grain. During deformation of individual grains, dislocation pileups at grain boundaries increase the flow strength of the grain, increase the dislocation density, and generate an internal stress which is applied to and activates dislocation sources in neighboring grains. Fig. 10 shows a schematic representation of the Hall-Petch derivation (Honeycombe, 1984), which includes the internal stress needed to activate dislocation sources in adjacent grains due to 12

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 10. Schematic representation of a deforming tensile specimen and the Hall-Petch derivation. As a result of a dislocation pileup in Grain 1, an internal stress is applied on Grain 2. If the internal stress is greater than n the dislocation source (S2) will be activated. Figure was adapted from Honeycombe (1984).

dislocation pileups ( n ). Localized deformation bands from DSA are macroscopic (on the order of a few mm in length and schematically represented in Fig. 10), so all the grains within a deformation band experience plastic deformation and grains in the rest of the sample are statically loaded (i.e. no plastic deformation) and likely exhibit non-uniform levels of strain aging and stress relaxation. During tensile testing on the cylindrical samples considered here, plastic deformation within a deformation band causes the band to increase in length and decease in diameter, effectively creating a small notch (i.e. stress concentrator) in the tensile bar (shown schematically in Fig. 10). The presence of the small notch may cause the next deformation band to form adjacent to the previous band in lieu of forming at other stress concentrations present in the sample, e.g. at the machined fillets associated with the reduced gage section. As discussed in above, DSA is associated with different types of localized deformation. Deformation band propagation and nucleation is generally associated with low and high temperatures, respectively (see Fig. 9). The transition from propagation to nucleation of deformation bands is related to the speed that the interstitial atoms can pin mobile dislocations. At lower temperatures carbon atoms have a lower diffusivity and take longer to diffuse to mobile dislocation cores. As a result, the deforming grains within a deformation band deform for relatively longer times. Fig. 11 shows incremental strain section data for selected times during tensile tests of samples that exhibited propagation and nucleation behaviors. The peaks associated with localized deformation were

Fig. 11. Section data of the incremental strain maps of (a) X70 149 °C 10−4 s−1 and (b) X70 225 °C 10−3 s−1 samples at select instances during tensile testing. The low (a) and high (b) temperature samples exhibited RCP and SN behaviors, respectively. 13

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Fig. 12. Partial engineering stress-time curves for X52 149 °C 10−3 s−1 specimen. The schematic tensile bar and letters indicate the location of deformation bands at different points of the flow curve (based on DIC analysis). Propagation and nucleation observations are indicated.

asymmetric for deformation band propagation and more symmetric for deformation band nucleation. During deformation band propagation (Fig. 11a), grains at the deformation band front exhibited the greatest amount strain. Grains behind the deformation band front continued to deform at a decaying rate as more time was allowed to pin the mobile dislocations. When the tail end of the deformation band peak has negligible incremental strain (i.e. plastic deformation has stopped), all of the mobile dislocations have been pinned and the grains have higher flow stress due to strain hardening. The stress concentration notch effect of the deformation band front causes the internal stress of the deforming grains to exceed n in the grains just ahead of the front. The result is a cascade of grain deformation along the tensile bar which is characterized as deformation band propagation. As an example, refer to the schematic of grains at the deformation band front in Fig. 10. Pileups of mobile dislocations in grains within the deformation band (e.g. grain 1) impart an internal stress on adjacent grains ahead of the deformation band front (e.g. grain 2) to activate the dislocation sources (S2) and propagate the deformation band front forward. Fig. 12 shows examples of a sample that exhibited CP behavior at low strains (Fig. 12a) and RCP behavior at high strains (Fig. 12b). The primary difference between CP and RCP behavior is the observed response when the deformation band front reaches the end of the sample (point D in this example). For CP behavior, the deformation band front propagates from point A to point D followed by nucleation of an additional band at A. For RCP behavior, the deformation band front propagates from point A to point D and changes direction to continue propagation toward point B. The type of behavior observed is dependent on the local flow stress of grains at points A and C compared to the local stress needed to activate dislocation sources at each location ( n, A and n, C ). Since the two propagation conditions typically occur in the same sample, the primary difference between the two conditions is the strain, and thus the dislocation density. Lower and higher dislocation densities support CP and RCP behaviors, respectively. At low strains, n, A must be less than n, C and at high strains, n, A must be greater than n, C . Since dislocation density is greater at high strains, the internal stress acting on grains adjacent to the deformation band front is higher. It is therefore easier to activate dislocation sources in grains adjacent to the deformation band front and change the direction of propagation at high strains. Non-uniform levels of strain hardening and strain aging can account for differences in local flow stress along the gauge length. Strain hardening only occurs during local plastic deformation, and strain aging requires time to occur after local deformation. For example in Fig. 12b, n, C at 59 and 60 s are both 455 MPa, but n, A changes from 432 MPa at 46 s to 455 MPa at 74 s. Due to RCP deformation behavior, points A and C had 28 and 1 s, respectively, of strain aging to influence the local engineering flow stress. When a nucleation event occurs between points D and A (see Fig. 12a), a large load drop of approximately 10 MPa is observed at 46 s. Since point C has had little time for strain aging, n, C at 46 s is approximately equal to n, C at 45 s, which was 441 MPa. The flow stress at point A was 432 MPa at 46 s. Since n, A was less than n, C , deformation continued as CP behavior. At higher temperatures, where deformation band nucleation was observed, interstitial atoms have a higher diffusivity and can pin mobile dislocations at a much higher rate. During nucleation behaviors, dislocations are immediately arrested after the deformation bands form. An example of this behavior is shown in Fig. 8c at times between 340 and 360 s. Incremental strain intensity (related to plastic deformation) was only observed immediately following a load drop in the tensile curve. Between load drops, only elastic deformation was observed along the tensile sample gauge length. Peaks related to nucleation behavior in the incremental strain section data (Fig. 11b) were more symmetric (for both SN and CN behaviors). More symmetric peaks indicated that plastic deformation occurred more uniformly around the nucleation site of a deformation band compared to a propagating front. In the X52 steel, SN behaviors were typically observed at lower strains compared to CN behaviors. Conditions where deformation behaviors 14

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

transitioned from SN to CN with increasing strain were likely dependent on dislocation density and the notch effect in a similar manner to what was discussed above with respect to the transition from CP to RCP. 4. Conclusions Pipeline steel tensile samples tested at various deformation temperatures and strain rates were evaluated in the DSA regime to systematically relate serration morphologies to localized deformation behaviors that result from interstitial atom-dislocation interactions. Deformation band propagation and nucleation behaviors were directly related to low (CP and RCP) and high (SN, CN, and RCN) frequency flow curve serration morphologies, respectively. Observed serration morphologies/deformation band behaviors were dependent on the relative temperature, strain rate, and strain within DSA testing conditions. At a constant strain rate, the following list defines the general DSA testing conditions where all types of localized deformation were observed in pipeline steels:

• CP (Type A) – low strains and low temperatures. • RCP (Type D/E) – high strains and all temperatures (also observed at low strains at 10 • SN (Type B/C) – low strains and high temperatures. • CN (Type A + B) – all strains and high temperatures (only observed at 10 s ). • RCN (Type D + B) – high strains and high temperatures. −3

−4

s−1).

−1

The deformation behavior observed was dependent on the solute atom mobility-mobile dislocation velocity relationship (which changes with temperature and strain rate) and the local flow stress of groups of grains within a deformation band due to strain hardening (and rises in dislocation density). Within the DSA regime, increases in solute atom mobility (i.e. increasing temperature) promoted a transition from propagation to nucleation behaviors. Increases in dislocation density from strain hardening promoted a transition from CP or SN behaviors to RCP or CN/RCN behaviors. Serration morphologies and deformation behaviors exhibited many similarities for materials that experience DSA through interstitial (e.g. steels studied here) and substitutional (e.g. Au–Mg) atom-dislocation interactions. The main notable differences between the two types of materials were:

• RCP behavior is uncommon in substitutional DSA systems, but observed in almost all steel testing conditions. • Substitutional DSA systems commonly exhibit a transition from CP to CN/RCN behaviors from low to high strains. The steels •

studied in the present work only exhibited nucleation behaviors at high strains when nucleation behaviors were also observed at low strains. At relatively high temperatures, substitutional DSA systems tend to exhibit deformation band nucleation behaviors at all strains, but steels tend to transition to RCP prior to necking instability.

Funding sources and acknowledgements The authors acknowledge the support of the corporate sponsors of the Advanced Steel Processing and Products Research Center, an industry/university corporate research center at the Colorado School of Mines. References Ait-Amokhtar, H., Vacher, P., Boudrahem, S., 2006. Kinematics fields and spatial activity of Portevin-Le Chatelier bands using the digital image correlation method. Acta Mater. 54, 4365–4371. Ait-Amokhtar, H., Fressengeas, C., Boudrahem, S., 2008. The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography. Mater. Sci. Eng. A 488, 540–546. Ait-Amokhtar, H., Fressengeas, C., 2010. Crossover from continuous to discontinuous propagation in the Portevin-Le Chatelier effect. Acta Mater. 58, 1342–1349. Anjabin, N., Karimi Taheri, A., Kim, H.S., 2013. Simulation and experimental analyses of dynamic strain aging of a supersaturated age hardenable aluminum alloy. Mater. Sci. Eng. A 585, 165–173. Benallal, A., Berstad, T., Børivk, T., Hopperstad, O.S., Koutiri, I., Rogueria de Codes, R., 2008. An experimental and numerical investigation of the behavior of AA5083 aluminum alloy in presence of the Portevin-Le Chatelier effect. Int. J. Plast. 24, 1916–1945. Brechtl, J., Chen, S.Y., Xie, X., Ren, Y., Qiao, J.W., Liaw, P.K., Zinkle, S.J., 2019. Towards a greater understanding of serrated flows in an Al-containing high-entropybased alloy. Int. J. Plast. (115), 71–92. https://doi.org/10.1016/j.ijplas.2018.11.011. Cai, Y.L., Yang, S.L., Wang, Y.H., Fu, S.H., Zhang, Q.C., 2016. Characterization of the deformation behaviors associated with the serrated flow of a 5456 Al-based alloy using two orthogonal digital image correlation systems. Mater. Sci. Eng. A 664, 155–164. Chen, S., Xie, X., Chen, B.L., Qiao, J.W., Zhang, Y., Ren, Y., Dahmen, K.A., Liaw, P.K., 2015. Effects of temperature on serrated flows of Al0.5CoCrCuFeNi high-entropy alloy. J. Occup. Med. 67, 2314–2320. Chihab, K., Estrin, Y., Kubin, L.P., Vergnol, J., 1987. The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy. Scr. Metall. 21, 203–208. Choudhary, B.K., Bhanu Sankara Rao, K., Mannan, S.L., Kashyap, B.P., 1999. Serrated yielding in 9Cr-1Mo ferritic steel. Mater. Sci. Technol. 15, 791–797. Cuddy, L.J., Leslie, W.C., 1972. Some aspects of serrated yielding in substitutional solid solutions of iron. Acta Metall. 20, 1157–1167. Curtin, W.A., Olmsted, D.L., Hector, L.G., 2006. A predictive mechanism for dynamic strain aging in aluminum-magnesium alloys. Nat. Mater. 5, 875–880. De Cooman, B.C., Kim, J., Lee, S., 2012. Heterogeneous deformation in twinning-induced plasticity steel. Scr. Mater. 66, 986–991. Dieter, G.E., 1986. Mechanical Metallurgy, third ed. McGraw-Hill, New York, pp. 201–203. Gilat, A., Wu, X., 1997. Plastic deformation of 1020 steel over a wide range of strain rates and temperatures. Int. J. Plast. 13, 611–632. Gonzalez, B.M., Marchi, L.A., Fonseca, E.J., Modenesi, P.J., Buono, V.T.L., 2003. Measurement of dynamic strain aging in pearlitic steels by tensile test. ISIJ Int. 43, 428–432. Goshert, B., 2018. Unpublished diagram of incremental strain measurement. Colorado School of Mines.

15

International Journal of Plasticity xxx (xxxx) xxx–xxx

T.R. Jacobs, et al.

Hector, L.G., Zavattieri, P.D., 2010. Nucleation and propagation of Portevin-Le Chatelier bands in austenitic steel with twinning induced plasticity. In: Conference Proceedings of the Society for Experimental Mechanics Series 17, vol. 6. pp. 855–863. Honeycombe, R.W.K., 1984. The Plastic Deformation of Metals, second ed. Edward Arnold, London, pp. 244–251. Jacobs, T.R., Matlock, D.K., Findley, K.O., Collins, L., 2016. The short and long term effects of elevated temperature on the mechanical properties of line pipe steels. In: Conference Proceedings of the 11th ASME International Pipeline Conference. Vol 3. Operations, Monitoring and Maintenance; Materials and Joining. Jacobs, T.R., Matlock, D.K., Findley, K.O., 2017. Fractographic analysis of anisotropic deformation behavior after tensile testing at elevated temperatures. Mater. Sci. Eng. A 708, 478–481. Jacobs, T.R., 2018. Elevated Temperature Mechanical Properties of Line Pipe Steels. Colorado School of Mines (Ph.D. Thesis). Jiang, H., Zhang, Q., Chen, X., Chen, Z., Jiang, Z., Wu, X., Fan, J., 2007. Three types of Portevin-Le Chatelier effects: experiment and modelling. Acta Mater. 55, 2219–2228. Kim, J.G., Hong, S., Anjabin, N., Park, B.H., Kim, S.K., Chin, K.-G., Lee, S., Kim, H.S., 2015. Dynamic strain aging of twinning-induced plasticity (TWIP) steel in tensile testing and deep drawing. Mater. Sci. Eng. A 633, 136–143. Klusemann, B., Fischer, G., Böhlke, T., Svendsen, B., 2015. Thermomechanical characterization of Portevin-Le Chatelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin-McCormick approach. Int. J. Plast. 67, 192–216. Lee, S., Kim, J., Lee, S.J., De Cooman, B., 2011. Effect of nitrogen on the critical strain for dynamic strain aging in high-manganese twinning-induced plasticity steel. Scr. Mater. 65, 528–531. Leslie, W.C., 1971. Iron and its dilute substitutional solid solutions. Metallurgical Transactions 3, 5–26. Leslie, W.C., 1981. The Physical Metallurgy of Steels, first ed. Hemisphere Publishing Corporation, pp. 68–96. Li, C.C., Leslie, W.C., 1978. Effects of dynamic strain aging on the subsequent mechanical properties of carbon steels. Metallurgical Transactions A 9A, 1765–1775. Matlock, D.K., Krauss, G., Ramos, L.F., Huppi, G.S., 1979. A Correlation of Processing Variables with Deformation Behavior of Dual Phase Steels. Published in Structure and Properties of Dual Phase Steels. TMS, AIME, Warrendale Pennsylvania, pp. 62–90. Mogucheva, A., Yuzbekova, D., Kaibyshev, R., Lebedkina, T., Lebyodkin, M., 2016. Effect of grain refinement on jerky flow in an Al-Mg-Sc alloy. Metall. Mater. Trans. A 47A, 2093–2106. Morris, J.G., 1974. Dynamic strain aging in aluminum alloys. Mater. Sci. Eng. 13, 101–108. Nogueira De Codes, R., Hopperstad, O.S., Engler, O., Lademo, O.,-G., Embury, J.D., Benallal, A., 2011. Spatial and temporal characteristics of propagating deformation bands in AA5182 alloy at room temperature. Metall. Mater. Trans. A 42A, 3358–3369. Okamoto, S., Matlock, D.K., Krauss, G., 1991. The transition from serrated to non-serrated flow in low-carbon martensite at 150 °C. Scr. Metall. Mater. 25, 39–44. Prasad, K., 2010. Influence of dynamic strain aging on plastic instability behaviour of near alpha titanium alloy Timetal 834. Mater. Sci. Technol. 26, 1068–1072. Renard, K., Ryelandt, S., Jacques, P.J., 2010. Characterization of the Portevin-Le Chatelier effect affecting an austenitic TWIP steel based on digital image correlation. Mater. Sci. Eng. 527, 2969–2977. Robinson, J.M., Shaw, M.P., 1994. Microstructural and mechanical influences on dynamic strain aging phenomena. Int. Mater. Rev. 39, 113–122. Rodriguez, P., 1984. Serrated plastic flow. Bull. Mater. Sci. 6, 653–663. Sarkar, A., Chatterjee, A., Barat, P., Mukherjee, P., 2007. Comparative study of the Portevin-Le Chatelier effect in interstitial and substitutional alloy. Mater. Sci. Eng. A 459, 361–365. Swaminathan, B., Abuzaid, W., Sehitoglu, H., Lambros, J., 2015. Investigation using digital image correlation of Portevin-Le Chatelier effect in Hastelloy X under thermos-mechanical loading. Int. J. Plast. 64, 177–192. Wagner, D., Moreno, J.C., Prioul, C., 1998. Dynamic strain aging sensitivity of heat affected zones in C-Mn steels. J. Nucl. Mater. 252, 257–265. Wijler, A., Schade Van Westrum, J., Van Den Beukel, A., 1972. A new type of stress-strain curve and the Portevin-Le Chatelier effect in Au (14 at% Cu). Acta Metall. 20, 355–362. Yuzbekova, D., Mogucheva, A., Zhemchuzhnikova, D., Lebedkina, T., Lebyodkin, M., Kaibyshev, R., 2017. Effect of microstructure on continuous propagation of the Portevin-Le Chatelier deformation bands. Int. J. Plast. 96, 210–226. Zavattieri, P.D., Savic, V., Hector Jr., L.G., Fekete, J.R., Tong, W., Xuan, Y., 2009. Spatio-temporal characteristics of the Portevin-Le Chatelier effect in austenitic steel with twinning induced plasticity. Int. J. Plast. 25, 2298–2330. Zhemchuzhnikova, D., Lebyodkin, M., Lebedkina, T., Mogucheva, A., Yuzbekova, D., Kaibyshev, R., 2017. Peculiar spatiotemporal behavior of unstable plastic flow in an AlMgMnScZr alloy with coarse and ultrafine grains. Metals 7, 325. Zhemchuzhnikova, D., Lebyodkin, M., Yuzbekova, D., Lebedkina, T., Mogucheva, A., Kaibyshev, R., 2018. Interrelation between the Portevin Le-Chatelier effect and necking in AlMg alloys. Int. J. Plast. 110, 95–109.

16