materials

Article as a Means to Investigate Grain Size and Strain Rate Effect on Plastic Deformation of 316 L Nanocrystalline Stainless-Steel

Abdelrahim Husain 1,2 , Peiqing La 1,*, Yue Hongzheng 1 and Sheng Jie 1

1 State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals, Lanzhou University of Technology, Lanzhou 730050, China; [email protected] (A.H.); [email protected] (Y.H.); [email protected] (S.J.) 2 Department of Physics, Faculty of Science and Technology, University of Shendi, Shendi P.O. Box 407, Sudan * Correspondence: [email protected]; Tel.: +86-138-9316-6172

 Received: 24 June 2020; Accepted: 16 July 2020; Published: 20 July 2020 

Abstract: In the present study, molecular dynamics simulations were employed to investigate the effect of strain rate on the plastic deformation mechanism of nanocrystalline 316 L stainless-steel, wherein there was an average grain of 2.5–11.5 nm at room temperature. The results showed that the critical grain size was 7.7 nm. Below critical grain size, grain boundary activation was dominant (i.e., grain boundary sliding and grain rotation). Above critical grain size, dislocation activities were dominant. There was a slight effect that occurred during the plastic deformation mechanism transition from dislocation-based plasticity to grain boundaries, as a result of the stress rate on larger grain sizes. There was also a greater sensitive on the strain rate for smaller grain sizes than the larger grain sizes. We chose samples of 316 L nanocrystalline stainless-steel with mean grain sizes of 2.5, 4.1, and 9.9 nm. The values of strain rate sensitivity were 0.19, 0.22, and 0.14, respectively. These values indicated that small grain sizes in the plastic deformation mechanism, such as grain boundary sliding and grain boundary rotation, were sensitive to strain rates bigger than those of the larger grain sizes. We found that the stacking fault was formed by partial dislocation in all samples. These stacking faults were obstacles to partial dislocation emission in more sensitive stress rates. Additionally, the results showed that mechanical properties such as yield stress and flow stress increased by increasing the strain rate.

Keywords: strain rate; 316 L austenitic stainless-steel; grain size; plastic deformation mechanisms; molecular dynamics; embedded atom method (EAM)

1. Introduction The study of the nanocrystalline (NC) austenitic stainless-steel plastic deformation process is important due to these materials’ influence on mechanical properties during the production process [1,2]. When the alloy is plastically deformed, its shear strain is usually produced by deformation twinning and/or dislocation slip, particularly at low strain rates. Other deformation mechanisms include grain rotation, grain boundary sliding, and grain migration, but these mechanisms only become important at high temperatures, especially when the grain sizes are large. Deformation twinning is a common and significant mechanism in metals and alloys. The stacking fault energy (SFE) is a significant parameter in the plastic deformation mechanism of a face-centered cubic (fcc), where the twinning tendency of an fcc metal is largely determined by its SFE. For example, coarse-grained (CG) fcc metals with high stacking fault energies such as Ni normally deform by dislocation slip, while fcc metals with low SFE such as Ag [3] and austenitic steels [4,5] primarily deform by twinning. Deformation twinning has

Materials 2020, 13, 3223; doi:10.3390/ma13143223 www.mdpi.com/journal/materials Materials 2020, 13, 3223 2 of 12 been extensively observed in CG austenitic steels with low SFE during severe plastic deformation (SPD). For NC fcc materials, twinning is one of the major deformation mechanisms even with high SFE. Therefore, the focus of this paper is plastic deformation on NC fcc 316 L stainless-steel. NC materials are defined as substances that have a grain size less than 100 nm [6]. These nanocrystalline materials are required in the research field because they have excellent properties, such as high strength and hardness, compared to CG materials. However, ductility is usually significantly reduced. Ultrafine-grained materials are synthesized using two methods: nano-powder synthesis and SPD. For instance, SPD, high-pressure torsion, equal channel angular processing, accumulative roll-ponding, accumulative press-bonding, milling, multidirectional forging, and so on, are used to produce grain size in the nanostructure. As the grain boundaries play a significant role in defining the mechanical properties of nanomaterials, they are often in non-equilibrium states, or more rigorously, they are diffuse boundaries between dislocation cells in the nanocrystalline produced by SPD. Moreover, there are many other defects like stacking faults and twins, and these defects and non-equilibrium grain boundaries may significantly influence mechanical behavior. The mechanical properties of nanocrystalline stainless-steel, including flow stress, yield stress, and ductility are controlled by plastic deformation mechanisms. Plastic deformations may occur through different mechanisms, such as partial dislocations formed from grain boundaries [7,8], deformation twinning [9–13], perfect dislocation gliding [14], grain boundary sliding [15,16], phase transformation [17,18], and grain boundary rotation [19,20]. The phase transformation is one of the most important mechanisms, where phase transformation from a face-centered cubic to a body-centered cubic (fcc bcc) plays an important role in determining the mechanical properties of CG → 316 L stainless-steel. In this study, we focused only on the deformation mechanisms that occur in NC fcc 316 L stainless-steel. Deformation twinning and dislocation slip are two competitive deformations. Interactions between deformation twinning and dislocation slip occur in the grain boundary. Dislocation slip and twinning activities enhance the strength and ductility of nanocrystalline materials. Deformation twinning has been extramaritally observed in CG metals and alloys. Deformation twinning occurs in fcc metals with low SFE. Molecular dynamics (MD) simulation has been previously used to examine the mechanical properties and plastic deformation mechanisms of nanocrystalline metals with average grain sizes [21,22]. Moreover, MD simulation has been employed to study the strain rate impact on the plastic deformation with the different grain sizes at room temperature. Zhou et al. [23] used MD simulations to investigate the influence of grain size on NC copper, indicating that the plastic deformation mechanism transits from the dislocation-mediated plasticity to grain boundary sliding in a small grain size around 10 nm. Schiøtz et al. [24] used MD simulation to study nanocrystalline copper plastic deformation, showing that flow stress decreases when the strain rate decreases. Further, they observed a transition from dislocation-mediated plasticity to grain boundary sliding for larger grain sizes. Since it is difficult to produce NC materials for experimental studies, early studies were conducted on NC samples created by inert gas condensation, which had no clean grain boundaries or defects, such as cracks. In this study, we used MD simulation, which has many advantages compared to other experimental researches, making it a powerful tool to study NC. MD simulations can expound atomic-level deformation mechanisms in NC material in a degree of detail that cannot be obtained via experimental studies. Moreover, it has the ability to investigate deformation mechanisms in real-time, such as twinning, stacking faults, and other faults. It can deform samples into extensive plastic strains, making it possible to explore the deformation mechanism with high dislocations. In this study, we created 316 L of NC stainless-steel samples with a mean grain size between 2.5 to 11.5 nm. MD simulation was used to explain the effect of strain rate on these samples. Further, we discuss plastic deformation mechanisms at different strain rates. Materials 2019, 12, x FOR PEER REVIEW 3 of 12

The Voronoi construction method [25] and ATOMSK [26] (Materials and Transformations Unit, Bât. C6, Univ. Lille 1, 59655 Villeneuve d´Ascq, France) were used to create three-dimensional (3D) polycrystalline stainless-steel samples with mean grain sizes ranging from 2.5 to 11.5 nm. A polycrystalline simulation box contained fcc iron (Fe) (200 × 200 × 200 Å 3) and a sum of 691,554 atoms. The nickel (Ni) and chromium (Cr) elements were replacement atoms and were randomly handed out in the sample. The sample was composed of Ni-12%, Cr-17%, and Fe-71%, as shown in Figure 1a. Although other alloy elements, such as Mo, Mn, C, and N, are reported to play a crucialMaterials role2020, in13, determining 3223 the mechanical properties of nanocrystalline 316 L stainless-steel, given3 of 12 the complexity and lack of reliable interatomic potentials of multiple elements, the current work only considers the influence of alloy elements, namely Fe, Cr, and Ni. Grain directions were randomly 2. Simulation Methods organized in the samples. Figure 1b,c present a sample with a mean grain size of 2.5 nm. AfterThe Voronoi the polycryst constructionalline methodstainless [-25steel] and samples ATOMSK were [26 created,] software molecular (Materials dynamics and Transformations simulations (LAMMPS)Unit, Bât. C6, progressed Univ. Lille by 1, the 59655 Sandia Villeneuve National d´Ascq, Laboratories France) [27] were were used implemented to create three-dimensional using a large- (3D)scale polycrystallineatomic molecular stainless-steel massively parallel samples simulator. with mean Periodic grain boundary sizes ranging conditions from were 2.5 to applied 11.5 nm. in Ax-,polycrystalline y-, and z-dimensions. simulation The embedded box contained atom fcc method iron (Fe) (EAM), (200 developed200 200 by Å Zhou3) and et a al. sum [28], of was 691,554 also × × utilized.atoms. The All polycrystalline nickel (Ni) and samples chromium were (Cr) minimized elements using were the replacement conjugate atomsgradient and algorithm were randomly to get a steadyhanded atom out in configuration. the sample. The The sample simulation was composed sample was of Ni-12%, applied Cr-17%, at 300 K and using Fe-71%, a Nose as shown–Hoover in thermostatFigure1a. Although (Research other School alloy of elements, Chemistry, such Australian as Mo, Mn, National C, and University, N, are reported G.P.O. to play Box a4, crucial Canberra, role ACT.in determining 2601, Australia the mechanical) [29,30] under properties the time of nanocrystalline steps of 2 femtoseconds. 316 L stainless-steel, Before deformation given the simulation, complexity theand samples lack of reliable were relaxed interatomic at 300 potentials k and a pressure of multiple of elements,0 bar with the a time current step work of 2 onlyfs for considers time 40 theps, measuredinfluence of using alloy elements, a Nose–Hoover namely Fe, thermostat Cr, and Ni. and Grain Parrinello directions–Rahman were randomly barostat organized (NPT). Tensile in the deformationsamples. Figure along1b,c the present x-axis a is sample simulated with at a strain mean rates grain of size 6 × of 10 2.59 and nm. 1 × 1010 s−1 at 300 K.

Figure 1. InitialInitial configuration configuration of the the polycrystalline polycrystalline stainless stainless-steel-steel alloy with an average grain size of 2.5 nm. ( aa)) Element Element container, container, ( b) grain identity number, andand ((cc)) commoncommon neighborneighbor analysis.analysis.

After therelaxation, polycrystalline the bulk stainless-steel NC 316 L austenit samplese stainless were created,-steel was molecular tensile loaded dynamics and simulations applied at (LAMMPS)room temperature. progressed A constant by the Sandia strain Nationalrate (1.0 × Laboratories 1010 s−1) was [ 27implemented] were implemented in which using the length a large-scale (in the xatomic-direction) molecular of the massivelybulk NC 316 parallel L austenite simulator. stainless Periodic-steel boundary was measured. conditions The wereatomic applied configuration in x-, y-, thrandoughout z-dimensions. the simulation The embedded was atom visualized method using (EAM), OVITO developed software by Zhou (Institute et al. [28 for], Materials was also utilized. Science, All polycrystalline samples were minimized using the conjugate gradient algorithm to get a steady atom configuration. The simulation sample was applied at 300 K using a Nose–Hoover thermostat (Research School of Chemistry, Australian National University, G.P.O. Box 4, Canberra, ACT. 2601, Australia) [29,30] under the time steps of 2 femtoseconds. Before deformation simulation, the samples were relaxed at 300 k and a pressure of 0 bar with a time step of 2 fs for time 40 ps, measured using a Nose–Hoover thermostat and Parrinello–Rahman barostat (NPT). Tensile deformation along the x-axis is simulated at strain rates of 6 109 and 1 1010 s 1 at 300 K. × × − Materials 2020, 13, 3223 4 of 12

After relaxation, the bulk NC 316 L austenite stainless-steel was tensile loaded and applied at room temperature. A constant strain rate (1.0 1010 s 1) was implemented in which the length (in the × − x-direction)Materials 2019, of12, thex FOR bulk PEER NC REVIEW 316 L austenite stainless-steel was measured. The atomic configuration4 of 12 throughout the simulation was visualized using OVITO software (Institute for Materials Science, Technical University Darmstadt, Petersenstr, Darmstadt, Germany) [31]. The common-neighbor analysis Technical University Darmstadt, Petersenstr, Darmstadt, Germany) [31]. The common-neighbor technique (CNA) was used to visualize the defects and local atomic structure [32]. Different analysis technique (CNA) was used to visualize the crystal defects and local atomic structure [32]. types of crystal defects and atoms were marked in colors such as green for fcc structure, blue for bcc Different types of crystal defects and atoms were marked in colors such as green for fcc structure, structure, red for stacking faults, and white for grain boundaries or dislocation cores. blue for bcc structure, red for stacking faults, and white for grain boundaries or dislocation cores. 3. Results and Discussion 3. Results and Discussion

3.1.3.1. TensileTensile DeformationDeformation FigureFigure2 2illustrates illustrates the the tensile tensile stress–strain stress–strain curves curves for for NC NC 316 316 L L stainless-steel stainless-steel for for various various average average graingrain sizes.sizes. StrainStrain rate rate was was applied applied to to all all samples samples ranging ranging from from 1 1 10× 1010 10s s1−1to to 6 6 × 101099 ss−1,, respectively. respectively. × − × − YieldYield stress stress increasedincreased with with a a higher higherstrain strainrate. rate. In In all all investigated investigated samples, samples, a a linear linear correlation correlation betweenbetween stressstress andand strainstrain meantmeant thatthat stainless-steelstainless-steel alloysalloys withwith didifferentfferent graingrain sizessizes hadhad anan elasticelastic region,region, which which cancan be be obtained obtained from from the the elastic elastic constant constant by by fitting fitting thethe initial initial linearlinear elastic elastic region. region. PlasticPlastic deformation deformation might might happen happen in in the the linear linear elastic elastic phase phase at at a a high high strain strain rate. rate. These These plastic plastic deformationsdeformations occurred within within the the grain grain boundaries boundaries such such as the as thegrain grain boundary boundary movement movement and could and couldnot be not observed be observed by any by any grai grainn boundary boundary dislocation dislocation activity activity in in the the elastic elastic region region during the the deformationdeformation simulation.simulation.

7 7 (a) (b)

6 6

5 5

4 4

3 3 10 -1 1x10 s 10 -1

Truestress(GPa) Truestress (GPa) 1x10 s 2 9 -1 2 8x10 s 9 -1 Grain size 2.5 nm 8x10 s 9 -1 Grain size 3.6 nm 6x10 s 9 -1 1 1 6x10 s

0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 True strain True strain

7 7 (c) (d)

6 6

5 5

4 4

3 3

10 -1

Truestress (GPa) Truesrtess (GPa) 1x10 s 2 10 -1 2 Grain size 4.1 nm 9 -1 1x10 s 8x10 s Grain size 7.7 nm 9 -1 9 -1 8x10 s 6x10 s 1 1 9 -1 6x10 s

0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 True strain True strain Figure 2. Cont.

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7 7 (e) (f)

6 6

5 5

4 4

3 3

Truestress (GPa) Truestress (GPa) 10 -1 1x10 s 10 -1 2 2 1x10 s 9 -1 Grain size 9.9 nm 8x10 s 9 -1 8x10 s 9 -1 1 6x10 s 1 9 -1 Grain size 11.5 nm 6x10 s

0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 True strain True strain FigureFigure 2. 2. (a(a––ff) )True True stress stress–strain–strain curves curves for for nanocrystalline nanocrystalline (NC) (NC) 316 316 L L stainless stainless-steel-steel with with different different 9 1 10 1 mean grain sizes and at different strain rates (6 109 −s1 to 1 10 −1 s ). mean grain sizes and at different strain rates (6 ×× 10 s − to 1 × 10× s ). −

ForFor samples samples with with a grain a grain size size above above the critical the critical grain grain sizes, sizes, an increase an increase in the neck in the in neckthe stress in the– stress–strain curves (Figure2e,f) can be noted, particularly for high strain rates. This can be explained strain curves (Figure 2e,f) can be noted, particularly for high strain rates. This can be explained by theby the fact fact that that there there was was insufficient insufficient time time for for nucleated nucleated dislocations dislocations when when the the plastic plastic deformation deformation appeared through large grain sizes and high strain rates. For samples below the critical grain size appeared through large grain sizes and high strain rates. For samples below the critical grain size (3.6 and(3.6 4.1 and nm), 4.1 fluctuations nm), fluctuations in the inloading the loading tensile tensilecurves curvesat various at variousstrain rates strain were rates observed were observed (Figure 2b(Figure,c). This2b,c). may This indicate may indicate that the that dominant the dominant mechanism mechanism was the was grain the grainboundary boundary movement movement and andnot thenot dislocations. the dislocations. FigureFigure 3 illustratesillustrates thethe Hall–PetchHall–Petch (H–P)(H–P) relationship’srelationship’s transition transition from from normal normal to to inverse, inverse, which which is isdependent dependent on on the the flow flow stress stress at at various various strainstrain rates.rates. In Figure 33,, thethe extremeextreme inin thethe flowflow stressstress corresponds to 7.7 nm for strain rates of 1 1010 s 1 and decreases when strain rate decreases. corresponds to 7.7 nm for strain rates of 1 × 10× 10 s−1 and− decreases when strain rate decreases. The transitionThe transition from from a normal a normal to inverse to inverse H–P H–P relationship relationship was was noted noted in inNC NC material material via via MD MD simulations. simulations. ThisThis transition transition occurred occurred after after a a shift shift in in grain grain boundary, boundary, which which was was mediated mediated by by dislocation dislocation-based-based plasticity.plasticity. Figure Figure 4 shows how the flow flow stress stress increased increased when the the strain strain rate rate increased increased below below a a critical critical graingrain size (d (d< ˂7.7 7.7 nm). nm). Samples Samples with with a high a high flow stressflow stress had small had strain small rate strain sensitivity. rate sensitivity. The maximum The maximumflow stress flow was stress observed was usingobserved MD using simulations MD simulations in copper in NC copper at a mean NC at grain a mean size grain around size 8–20around nm. 8Figure–20 nm.4 illustrates Figure 4 illustrates flow stress flow dependence stress dependence on the strain on rate.the strain For all rate. samples, For all the samples, flow stress the flow increments stress incrementsexpanded theexpanded strain rate,the strain especially rate, especially for the sample for the with sample a grain with sizea grain of 7.7size nm of 7.7 at anm strain at a ratestrain of 1 1010 s 1. The strain rate sensitivity dependence of the different grain size was investigated in the rate× of 1 × −1010 s−1. The strain rate sensitivity dependence of the different grain size was investigated inNC the stainless-steel NC stainless- samples.steel samples. The sample The sample with awith grain a grain size of size 9.9 of nm 9.9 flow nm stressflow stress slowly slowly increased increased when the strain rate increased. When the strain rate increments moved from 6 109 s 1 to 1 1010 s 1, when the strain rate increased. When the strain rate increments moved from× 6 × 109− s−1 to 1× × 1010 s−1, strainstrain rate rate sensitivity incrementsincrements moved moved from from 0.122 0.122 to to 0.135. 0.135. For For a small a small grain grain size size of 2.5 of nm, 2.5 flownm, stressflow increments quickly expanded the strain rate. When the strain rate increased from 6 109 s 1 to stress increments quickly expanded the strain rate. When the strain rate increased from 6× × 109 s−−1 to 1 1010 s 1, the volume of the strain rate sensitivity moved from 0.19 to 0.22. 1 ×× 1010 s−1,− the volume of the strain rate sensitivity moved from 0.19 to 0.22.

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11.5 9.9 7.7 Grain size (nm)4.1 2.5 5.3 11.5 9.9 7.7 4.1 102.5 -1 1x10 s 5.25.3 10 -1 1x109 -1s 5.15.2 8x10 s 99-1-1 5.05.1 6x10 8x10ss 9 -1 4.95.0 6x10 s 4.84.9 4.74.8

4.64.7

4.54.6 4.44.5

Flow stress(GPa) 4.34.4

Flow stress(GPa) 4.24.3 Hall-Petch inverse Hall-Petch 4.14.2 Hall-Petch inverse Hall-Petch 4.04.1 4.00.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.25 0.30 0.35 0.40-1/20.45 -1/20.50 0.55 0.60 0.65 d (nm ) -1/2 -1/2 d (nm ) Figure 3. Relationship between flow stress and grain size under different strain rates. FigureFigure 3. 3.Relationship Relationship between between flow flow stress stress and and grain grain size size under under di differentfferent strain strain rates. rates.

5.2 m=0.19 5.15.2 m=0.19 5.05.1 m=0.14 m=0.135 4.95.0 m=0.14 m=0.135 m=0.19 4.84.9 m=0.135 m=0.19 4.74.8 m=0.135 4.7 4.6 m=0.22

4.54.6 m=0.23 m=0.22 4.44.5 m=0.23

Flow stress(GPa) 2.5 nm 4.34.4 m=0.15 m=0.22 3.6 nm Flow stress(GPa) 2.5 nm 4.24.3 m=0.15 m=0.22 4.1 3.6 nm nm 4.14.2 m=0.19 7.7 4.1 nm nm 9.9 7.7 nm nm 4.04.1 m=0.19 9.9 nm 4.0 0.006 0.007 0.008 0.009 0.010 0.006 0.007 0.008 -1 0.009 0.010 Strain rate(s ) -1 Strain rate(s ) Figure 4. Flow stress as a function of strain rate for NC 316 L stainless-steel, with various mean Figure 4. Flow stress as a function of strain rate for NC 316 L stainless-steel, with various mean grain grain sizes. sizes.Figure 4. Flow stress as a function of strain rate for NC 316 L stainless-steel, with various mean grain 3.2. Deformationsizes. Mechanism 3.2. Deformation Mechanism 3.2. ToDeformation investigate Mechanism the effect of strain rate on the plastic deformation of NC stainless-steel, we chose two samples:To investigate one with the aeffect mean of small strain grain rate sizeon the of 3.6plastic nm deformation and one with of a largeNC stainless grain size-steel, of 9.9 we nm. chose two Forsamples:To theinvestigate smaller one with grainthe a effect mean size, of Figuresmall strain 5grain showsrate size on the the of NC 3.6plastic stainless-steelnm anddeformation one with sample ofa largeNC with stainless grain a mean size-steel, grain of 9.9 we size nm. chose of two Forsamples: the smaller one with grain a mean size,9 Fismall1gure grain 5 shows size10 the of1 3.6NC nm stainless and one-steel with sample a large with grain a meansize of grain 9.9 nm. size 3.5 nm at strain rates of 6 10 s− and 1 10 s− , respectively. When the applied strain was 0.075, For the smaller grain× size,9 Fi9 1gure−1 5 ×shows10 the−1 NC stainless-steel sample with a mean grain size forof 3.5 the nm lesser at strain strain rates rate (6of 6 10× 10s− s ) partialand 1 x dislocations 10 s , respectively. are observed When emitted the applied from grain strain boundaries was 0.075, × 9 −1 10 −1 andforof 3.5the propagated nmless ater strainstrain in grains, ratesrate (of6 as ×6 10 shown× 109 s−1 s) partial in and Figure 1 dislocationsx 105a. Ins , Figure respectively. are5 observed, partial When dislocations emitted the applied from were grain strain indicated boundaries was 0.075, by blackandfor thepropagated arrows, lesser while strain in stackinggrains, rate (6 as faults× shown109 s were−1) partialin indicatedFigure dislocations 5a by. In yellow Figure are arrows 5,observed partial and dislocations twinsemitted indicated from were grain by indicated blue boundaries arrows. by Figureblackand propagated5arrows,a shows while an in increase grains,stacking inas the faultsshown thickness were in Figure indicated of grain 5a. boundaries,In by Figure yellow 5, wherepartialarrows smalldislocations and grainstwins disappearedind wereicated indicated by after blue by anarrows.black increase arrows, Figure in grain while 5a shows boundary stacking an inthickness,faultscrease were in merging theindicated thickness with by larger yellow of grain grains. arrows boundaries, This and merger twins where ind and icated small the increase by grains blue indisappearedarrows. the thickness Figure after grain 5a an shows increase boundaries an in in graincrease indicated boundary in the a grain thickness thickness, rotation of merging and grain grain boundaries,with sliding larger at grains. where the highest This small merger stress grains anddisappeared the increase10 1 after in anthe increase thickness in graingrain boundariesboundary thickness, indicated merginga grain rotation with larger and graingrains. slidi Thisng merger at the of 1 10 s− . Partial dislocations emitted from grain boundaries delayed emission and very few and× the increase in the thickness grain boundaries indicated a grain rotation and grain sliding at the

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highest stress of 1 × 1010 s−1. Partial dislocations emitted from grain boundaries delayed emission and compared to those shown in Figure5a. At the same strain (0.075; see Figure5d), there were very few very few compared to those shown in Figure 5a. At the same strain (0.075; see Figure 5d), there were stacking faults that appeared behind the partial dislocation. When increase strains were 0.125 and very few stacking faults that appeared behind the partial dislocation. When increase strains were 0.15, many stacking faults were observed. Stacking faults were observed in a 6 109 s 1 strain rate. − 9 −1 0.125 and 0.15, many stacking faults10 were1 observed. Stacking faults were observed× in a 6 × 10 s This compares well with the 1 10 s− strain rate. In smaller grain sizes, the stacking fault mainly strain rate. This compares well× with the 1 × 1010 s−1 strain rate. In smaller grain sizes, the stacking fault parallels in each grain; this was different from the larger mean grain sizes, where many stacking faults mainly parallels in each grain; this was different from the larger mean grain sizes, where many crisscrossed with one another at the same strain rates. stacking faults crisscrossed with one another at the same strain rates.

Figure 5. Snapshots of the simulated stainless-steel with a mean grain size of 3.6 nm, deformed at Figure 5. Snapshots of the 9simulated1 stainless-steel10 with1 a mean grain size of 3.6 nm, deformed at strain rates of (a,c,e) 6 10 s− and (b,d,f) 1 10 s− .(a,b) present 0.075 true strain; (c,d) present × 9 −1 × 10 −1 0.125strain true rates strain; of (a, (ce,e,f)) 6 present × 10 s 0.15 and true (b, strain.d,f) 1 × Black10 s arrows. (a) and in ((ab,b) )present indicate 0.075 partial true dislocation. strain; (c) and Yellow (d) arrowspresent in 0.125 (a,d true) indicate strain; the (e) stacking and (f) present fault, while 0.15 true blue strain. arrows Black indicate arrows deformation in (a) and twins.(b) indicate partial dislocation. Yellow arrows in (a) and (d) indicate the stacking fault, while blue arrows indicate Asdeformation previously twins. mentioned, the dominate mechanism on the small grain size was the grain sliding and grain rotation. Figure5a shows that this mechanism was more active at a strain rate of 6 109 s 1. × − FigureAs5e previously shows that mentioned, at the strain the rate dominate of 6 10 mechanism9 s 1, a smaller on the grain small size grain appeared size was due the to agrain decrease sliding in × − thicknessand grain grainrotation. boundary. Figure 5a Some shows grain that boundaries this mechanism became was narrow. more active For the at strain a strain rate rate of of 1 6 10× 1010 9s s−11,. × − someFigure grain 5e shows boundaries that at disappeared, the strain rate indicated of 6 × 10 by9 s− the1, a smaller long black grain arrow size inappeared Figure5f. due The to fraction a decrease atom in inthickness the grain grain boundary boundary. at 1 Some1010 s grain1 was boundaries greater than became 6 109 narrow.s 1 in the For same the applied strain rate strain. of The1 × 10 plastic10 s−1, × − × − deformationsome grain boundaries at a lower straindisappeared, rate resulted indicated in atom by t relaxationhe long black within arrow grain in boundaries.Figure 5f. The Thus, fraction the grainatom boundaryin the grain network boundary remained at 1 × 10 significantly10 s−1 was greater unchanged. than 6 × 109 s−1 in the same applied strain. The plastic deformation at a lower strain rate resulted in atom relaxation within grain boundaries. Thus, the grain boundary network remained significantly unchanged.

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The dominant mechanism of the small grain size was grain sliding and grain rotation, but, interestingly, the stacking fault that resulted from partial dissociation and twin activities could still be seen in the sample for each of the strain rates (Figure5c,f). Its presence as a twin and stacking fault meant that grain boundary deformation mechanisms needed collaboration for all partial dislocation activities. Moreover, the strain rate dependency of the flow stress was mainly related to grain boundary movement mechanisms for mean grain size samples below the critical grain size (i.e., 2.5 nm). In the current study, these mechanisms included the grain boundary sliding, grain rotation, and grain boundary migration. Hence, the value of strain rate sensitivity for these grain boundary activities was 0.19 for strain rates below 1 1010 s 1 (Figure4), which was smaller than the thermally activated grain × − boundary activities. With the increase of the strain from 0.15 to 0.2 (Figure5c–f), the density of stacking faults increased. However, the flow stress was about steady when the strain increased (Figure2a). In this region, we confirmed that the density of stacking faults did not affect flow stress, given that the stacking faults act as barriers to the motion of partial dislocations. Figure6 shows the sample of NC stainless-steel with a mean grain size of 9.9 nm at strain rates of 6 109 s 1 and 1 1010 s 1, respectively. When the strain increased to 0.075, the partial dislocation × − × − emissions from the grain boundary mobilized in the grains (grain 1), while partial dislocations of the sample (grain 1) at 1 1010 s 1 and at the same strain (0.075) nucleated the grain boundaries × − and did not emit inside the grain (Figure6b). The plastic deformation was mostly accommodated by grain boundary activities. Dislocation activities and deformation twinning dominated plastic deformation in the sample with an average grain size of 9.9 nm. The partial dislocation emission from the grain boundary (Shockley dislocation) is indicated by black arrows in Figure6a at a strain rate of 6 109 s 1, while impartial dislocation emission had a strain rate of 1 1010 s 1 at the same strain. × − × − This demonstrates that the strain rate impacted partial dislocation activities. The stacking faults were generated by increasing partial dislocations. Figure6c,d show the stacking faults via yellow arrows at a strain of 0.125. For a strain rate of 6 109 s 1, deformation twins and stacking faults were parallel × − in grain 1 and grain 2 and were also created by the consecutive nucleated partial dislocation at the neighbor atom planes. For a high strain rate of 1 1010 s 1, many stacking faults crossed with one × − another in most grains due to two types of partial dislocations moving in two different directions, forming intersecting stacking faults. These stacking faults hindered the movement of the partial dislocations. When the strain increased to 0.15, many deformation twins and stacking faults were observed in both strain rates. The stacking faults were formed by partial dislocation and were parallel in some grains (1 and 3). According to our simulation, we concluded that stacking faults hindered the movement of partial dislocation and increased flow stress with a higher stress rate. When analyzing the microstructure of the grain size of 9.9 nm at different strain rates, in addition to analyzing partial dislocations occurring inside the grain, one can notice grain boundary activities, such as grain migration. Grain 4 in Figure6a, indicated by the black dotted circle, was split into two grains. Grain boundary activities at a strain rate of 6 109 s 1 were compared with a strain rate of × − 1 1010 s 1 (Figure6c,d). Therefore, we found that the strain rate had a clear e ffect on grain boundary × − movement. At a high strain rate, the grain boundary movement was reduced, but a local strike was observed around the grain boundary. Figure7 illustrates how the strain increased to 0.2. Moreover, Figure7 shows how the stacking faults and twins increased. Finally, when the grain size is large, the dominant plastic deformation mechanism dislocates and deforms twins in the sample, and the directions produced by the twins are mostly perpendicular to each other. Moreover, other types of twins were formed through successive partial dislocations and interfered between two extended neighboring slip planes. Materials 2020, 13, 3223 9 of 12 Materials 2019, 12, x FOR PEER REVIEW 9 of 12

Figure 6. Snapshots of the simulated stainless-steel with a mean grain size of 9.9 nm, deformed at strainFigure rates 6. Snapshots of (a,c,e) 6of the109 simulateds 1 and (b stainless,d,f) 1 -10steel10 s with1.(a ,ab mean) present grain 0.075 size true of 9.9 strain; nm, (cdeformed,d) present at × − × − 0.125strain true rates strain; of (a (,ce,,ef) present6 × 109 s 0.15−1 and true (b, strain.d,f) 1 x Black 1010 s arrows−1. (a) and in ((ab,b) )present indicate 0.075 partial true dislocation, strain; (c) yellowand (d) arrowspresent in 0.125 (c,d) true indicate strain; the (e stacking) and (f) present fault, and 0.15 blue true arrows strain. indicate Black arrows deformation in (a) and twins. (b) indicate partial dislocation, yellow arrows in (c) and (d) indicate the stacking fault, and blue arrows indicate Furtherdeformation investigations twins. were conducted on samples sized 2.5 nm and 9.9 nm at a strain of 0.2. We observed plastic deformation on portions of the sample. For the 2.5 nm-sized (Figure7a,c), the dominantWhen analyzing plastic deformation the microstructure experienced of the grain boundarysize of 9.9 nm movement. at different However, strain rates, large in numbers addition ofto stackinganalyzing faults partial and dislocations twinning occurring were observed. inside the For grain, thesample one canwith notice 9.9 grain nm boundary average grain activities, size (Figuresuch as7 b,d),grain themigration. dominant Grain plastic 4 in Figure deformation 6a, indicated experienced by the dislocatedblack dotted and circle, deformed was split twinning. into two Manygrains. stacking Grain boundary faults were activities generated at a by strain partial rate dissociation of 6 × 109 s movements−1 were compared at high with strain a strain rates andrate mostof 1 × plastic1010 s−1 deformation (Figure 6c,d was). Therefore, absorbed we into found the sample. that the strain rate had a clear effect on grain boundary movement. At a high strain rate, the grain boundary movement was reduced, but a local strike was observed around the grain boundary. Figure 7 illustrates how the strain increased to 0.2. Moreover, Figure 7 shows how the stacking faults and twins increased. Finally, when the grain size is large, the dominant plastic deformation mechanism dislocates and deforms twins in the sample, and the directions produced by the twins are mostly perpendicular to each other. Moreover, other types of twins were formed through successive partial dislocations and interfered between two extended neighboring slip planes.

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Figure 7. SnapshotsSnapshots of of the simulated stainlessstainless-steel-steel with the strain increases to 0.20. 0.20. Each sample 9 1 10 1 shows the strain accumulation for the sample at 6 910−1 s and 1 10 10−1 s . This is presented in shows the strain accumulation for the sample at 6 × 10× s and− 1 × 10 × s . This− is presented in (a) and (ca),c with) with grain grain size size 2.5 2.5 nm; nm; (b ()b and,d) with (d) with grain grain size size 9.9 nm, 9.9 nm, respectively. respectively. 4. Conclusions Further investigations were conducted on samples sized 2.5 nm and 9.9 nm at a strain of 0.2. We observedVoronoi plastic construction deformation was performed on portions to create of the NC sample. stainless-steel For the samples 2.5 nm-sized with mean (Figure grain 7a sizes,c), the of dominant2.5 and 9.9 plastic nm. These deformation samples experienced were investigated grain usingboundary molecular movement. dynamics However, simulation large to numbers determine of 9 1 stackingthe effect faults of strain and ratetwinning on NC were stainless-steel observed. plasticFor the deformationsample with at9.9 the nm strain average rates grain of 6 size10 (Figures− to 10 1 × 17b,d10), thes− dominant. The results plastic of this deformation study can be experienced summarized dislocated as follows: and deformed twinning. Many × stacking faults were generated by partial dissociation movements at high strain rates and most plastic 1. The result showed that grain sliding and grain rotation dominated in small grain sizes. deformation was absorbed into the sample. Additionally, dislocation activities and twins were observed for large grain sizes. 4.2. ConclusionsTransitioning between plastic deformation mechanisms and dislocation-based plasticity to grain boundaries was observed. 3. VoronoiThe influence construction of strain was rates performed on small grainto create sizes NC was stainless greater-steel than samples on large with grain mean sizes. grain Therefore, sizes of 2.5strain and rate 9.9 nm.sensitivity These increased samples were when investigated the grain size using decreased. molecular The stackingdynamics fault simulation created by to determinepartial the dislocation effect of strain was observed rate on NC in every stainless sample.-steel plastic deformation at the strain rates of 6 × 109 s−1 to 1 × 1010 s−1. The results of this study can be summarized as follows: 4. For small grain sizes or lower strain rates, the stacking fault had a partial dislocation emission. 1. TheTherefore, result the showed grain boundary that grain movement sliding and was grain the most rotation active dominated in the small in grain. small grain sizes. 5. AFordditionally, large grain dislocation sizes or high activities strain and rates, twins the stackingwere observed fault did for not large represent grain sizes. any impediment to 2. Transitioningthe movement between of partial plastic dislocations. deformation Therefore, mechanisms the twin and was dislocation formed through-based plasticity the stacking to grain fault boundariesand was spread was observed. inside the grains. 3.6. ThePartial influence dislocation of strain was rates observed on small at a grain lower sizes strain was rate, greater before than it was on large observed grain at sizes. a higher Therefore, strain strainrate, at rate the sensitivity same applied increased strain. when the grain size decreased. The stacking fault created by 7. partialAs the dislocation strain rate was was observed increased, in every mechanical sample. properties such as the yield stress and flow 4. Forstress small increased. grain sizes or lower strain rates, the stacking fault had a partial dislocation emission. Therefore, the grain boundary movement was the most active in the small grain. 5. For large grain sizes or high strain rates, the stacking fault did not represent any impediment to the movement of partial dislocations. Therefore, the twin was formed through the stacking fault and was spread inside the grains.

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Author Contributions: A.H. conducted part of simulation work and wrote the preliminary version of the paper. P.L. conducted part of the simulation work and discussed the results with other authors. Y.H. discussed the results with other authors and revised the paper. S.J. took part in the simulation, writing, and revising work of the paper. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (51164022) and the Gansu Provincial Science and Technology Support Program (1304GKCA027). This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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