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The morphology of the deformation relief and the grain boundary role in the bicrystals of AISI 316 steel
Solid State Sciences 99 (2020) 106060
Contents lists available at ScienceDirect
Solid State Sciences journal homepage: http://www.elsevier.com/locate/ssscie
The morphology of the deformation relief and the grain boundary role in the bicrystals of AISI 316 steel Ekaterina Alfyorova a, *, Andrey Filippov b a b
National Research Tomsk Polytechnic University, Lenin Av., 30, Tomsk, 634050, Russia Institute of Strength Physics and Materials Sciences SB RAS, Pr. Akademicheskii, 2/4, Tomsk, 634055, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords: Stainless steel Plastic deformation Self-organization of deformation relief Grain boundary Scratch testing
The morphology of the deformation relief bicrystals of AISI 316 steel was described in terms of statistical pa rameters and using nonparametric roughness criteria. The presence of two large-scale levels of plastic defor mation self-organization and scaling was established. Coordinated shear in bundles of parallel shear planes was the key mechanism at the mesolevel. The processes of self-organization in the dislocation substructure was the key mechanism at the microlevel. The deformation relief close to the grain boundary was investigated. Several shear systems in two grains was active at the grain boundaries. Due to this fact, it was waited inconsistency of deformation and more rough relief at the grain boundaries then into grains. However, there was not the high values of root mean square surface roughness at the grain boundaries. In addition, the scratch testing experiment showed that the grain boundary did not have a dramatic effect in this case. The connection between the statistical parameters of the surface morphology and the stages of the stress strain curve was established.
1. Introduction The main properties of polycrystalline deformation are related to the heterogeneity of the internal structure (the presence of grains, grain boundaries, grain sizes, etc.) [1,2]. Therefore, when studying a poly crystal, the attention of researchers is often focused on two questions; plastic deformation of a single grain and the transfer of deformation across the grain boundaries. In a number of papers [3–7], various grain deformation schemes are discussed. The Taylor and Bishop-Hill schemes are close to each other and suggest that the polycrystal deformation is homogeneous. At the same time, stresses and deformations are contin uous even at the grain boundaries. This assumption, however, is ques tionable, since a number of authors experimentally [8,9] showed that the grain boundaries are the places of the deformation localization and the formation of accommodation bands. The next significant issue is the question of how the transfer of deformation between neighboring grains is carried out. Cottrell A.K. [10], Gold I., et al. [11] suggested that shear stress concentrator is necessary for the slip transfer from one grain to the next. The specified concentrator should be formed near the boundaries of plane accumu lations of dislocations. Stresses from the accumulation of dislocations at the grain boundary can elastically propagate through the boundary and
activate Frank-Read sources in the neighboring grain. Moreover, it is believed that deformation localization is typical for the grain bound aries. In addition, a number of works drew attention to the fact that the deformation behavior of surface grains and grains inside the sample differ. This circumstance is associated with the difference in the stress state of the grains inside the sample from the surface grains. Wouters O. et al. [2]. showed that the surface roughness (i.e., deformation relief) of a number of materials could be determined by several grains layers and not just by the grains on the surface of the material. In particular, they assume that the spatial variation of the Schmid factor (defined along the column below a certain point) determines the local value of the height of the surface. The development of plastic deformation leads to a change in the morphology of the surface. These changes can be quantified by the pa rameters of roughness and fractal surface dimensions. The results sug gested that the morphology of the surface and its evolution are associated with changes in the internal structure of the material. In addition, the change in the deformation relief on the surface shows the ability of self-organization. For instance, the methods of fractal analysis are sensitive both to external conditions and to the internal parameters of the material [12]. Moreover, the fractal dimension can estimate the surface regardless of the shape of its elements, their density and the
* Corresponding author. E-mail addresses: [email protected] (E. Alfyorova), [email protected] (A. Filippov). https://doi.org/10.1016/j.solidstatesciences.2019.106060 Received 17 May 2019; Received in revised form 30 October 2019; Accepted 30 October 2019 Available online 31 October 2019 1293-2558/© 2019 Elsevier Masson SAS. All rights reserved.
E. Alfyorova and A. Filippov
Solid State Sciences 99 (2020) 106060
physical regularities of plastic deformation inside the grains and in the grain boundaries. This research based on AISI 316 steel bicrystals in which the boundary passes through the entire volume of the sample. Therefore, there is no additional complication of the stress state scheme due to the influence of internal grains. 2. Material and techniques AISI 316 austenitic steel (i.e., FCC crystalline structure) was used for the current study. The sample is a bicrystal. Fig. 1 shows the appearance of the sample and the method for shooting. Fig. 1 schematically shows shear traces during deformation. Due to this choice of sample, it was possible to investigate the deformation relief both in individual single crystals and at the boundary of their interface. Sample size is 3 � 3 � 6 mm. Mechanical grinding; polishing and final electrolytic polishing prepared the surface of the specimens. Compression deformation was carried out on УТС 110М-100 1-У testing machine at a speed of 1 mm/min at room temperature. Olympus LEXT OLS4100 confocal laser-scanning microscope were used for analysing the deformation relief pattern after each loading step. Experiments were carried out in the strain interval 0.7–28%. The size of the scanned region in each case was 0.066 mm2 (0.256 � 0.256 mm2). The depth resolution was 0.06 μm. The size of the scanned region in this case sets a limit on the self-organization scale being established. The fractal analysis of the deformation pattern based on the height–height correlation function H(r) was used to reveal scaleinvariant regularities [38,39]. H(r)¼<[Z(r’) – Z(r’– r)]2> where Z(r) is the function of the surface height over all pairs of points separated by a fixed distance r; angle brackets indicate averaging over all pairs of points. The slope of the initial segment of the curve describing the height–height correlation function H(r) and plotted in logarithmic axes can be used for determining the Hurst exponent (H) and correlation length (L). The correlation length is determined by the projection of the linear segment onto the abscissa. At the same time, it is known that for a self-affine surface, then for the function H (r) the following holds true:where α is the scaling coef ficient or Hurst exponent (N), or roughness index; ξ (L) is the lateral correlation length, it defines the upper limit of the region of self-affinity and characterizes the irregularity of the surface in the lateral direction. Height fluctuations at r « ξ (small scale) are correlated, dependent, and at r » ξ (large scale), uncorrelated, random. The width of the interface (ω) is a characteristic of the irregularity of the surface in the vertical direction, it is also called the correlation length in the vertical direction or the root mean square surface roughness (ω ¼ Sq) [38–42]. Thus, the description of the deformation relief in terms of statistical parameters allows to combine information on large-scale roughness (parameter ω ¼ Sq) and small scale correlations (scaling coefficient α/Hurst exponent H) and to determine typical correlation lengths at which the deformation relief develops (correlation length ξ/L). The mean square value of the surface height of a limited scale Sq was esti mated based on ISO 25178-2: 2012. The nonparametric approach to the assessment of surface morphology was also applied. It is based on the use of such nonparametric criteria as a function of the density distribution of the ordi nates of the profile. This function contains about 95% of the surface information and describes the surface microrelief with high accuracy [43]. To study the mechanical characteristics and the establishment of features of the deformation relief formation in neighboring grains and when crossing the grain boundary, was used scratch testing. CSM In strument macro scratch tester was used in experiments. Normal load is
Fig. 1. Sampling scheme.
nature of the distribution, which makes it a universal parameter. Currently, fractal analysis is increasingly used in the description and analysis of microscopic images of the surfaces of materials. This method enable the scientists to describe the structure of a deformed surface and fractures, analyze the deformation mechanisms, try to assess the degree of material damage and predict the residual resource [13–21]. The self-organization process is manifested in the fact that traces of shear (characteristic of the onset of deformation) develop into structural elements of the relief of a qualitatively new level and scale. This development of the relief is due only to internal factors, without external specific effects. A distinctive feature of self-organization is a focused and at the same time natural, spontaneous process, which is relatively autonomous. Its purpose is to preserve the integrity of the system when an external load is applied. There are a number of papers describing the development of defor mation relief under various types of loading. Some of them do not provide estimates of the degree of self-organization, as mentioned in Refs. [22–29]. On the contrary, a number of works give quantitative estimates of the degree of self-organization of the deformation relief [18, 30–37]. Thus, the use of fractal assessments to describe the deformation relief and the degree of self-organization demonstrates its prospects, and together with identifying the physical background of these processes is of considerable interest for the development of materials science. However, when using data obtained from the sample surface, it is difficult to separate the contribution of surface and internal grains. The purposes of this study is 1) to describe the morphology of the deformed surface in terms of statistical parameters; 2) to identify the 2
E. Alfyorova and A. Filippov
Solid State Sciences 99 (2020) 106060
Fig. 2. 3D picture of the deformation relief (a–b) and the graph of distribution density of ordinates (profile heights) for zone in Fig. 2, a (c), for zone in Fig. 2, b (d), ε ¼ 0.7%.
100 N. The scratch length is 3 mm. The scratching velocity is constant and equals 10 mm/min. The deformation relief is examined with Olympus LEXT 4100 laser scanning microscope.
of micrometers (average value is 25.8 � 9.4 μm), i.e. it was observed a correlated formation of groups of parallel tracks, i.e. formation of a quasi-periodic surface profile. Let us analyze the literature data on the dislocation substructure evolution in AISI 316 steel and compare them with our results. Feaugas X [44]. reports that at the stages I-II of the stress-strain curve, the pro portion of dislocation tangles and walls increases, while there are no dislocation cells. The low value of the stacking fault energy AISI 316 (30 mJ/m2) prevents the cross-slip of dislocations at low straining. In stage II, the activation of cross-slip and multiple slip promotes the for mation of heterogeneous dislocation structures like patches, walls and cells. During the transition from stage II to III, the proportion of dislo cation walls decreases sharply, and the proportion of dislocation cells increases sharply. By the middle of stage II, Feaugas X [44]. notes the presence of the maximum number of dislocation tangles, which de creases to almost zero in the transition to stage III. The share of dislo cation cells is still growing. Thus, the statistical parameters describing the morphology of the surface reflect changes in the dislocation struc ture and consistent with the stages of the strain-stress curve. There are works that reveal scaling laws and the processes of selforganization in the dislocation structure. For instance, Hughes D.A [45]. reports that various materials demonstrate similarities in the microstructural patterns arising from monotonic deformation. The re sults were obtained for polycrystals of Ni, Cu, Al and 304 L steel, as well as on Cu and Al single crystals under various loading conditions (compression, rolling, forging, torsion and friction). This indicate that similar dislocation mechanisms work for a wide range of materials and deformation conditions. Hughes D.A [45]. also showed that a sufficient three-dimensional dislocation mobility to create three-dimensional structures is a necessary condition. In the present work, the root-mean-square roughness Sq was esti mated on a scale of length over 70 μm. The magnitude of the root-meansquare roughness increases linearly with increasing degree of deforma tion (Fig. 4) for the cases considered in this paper. Interestingly, the approximating curve obtained for zone 1–2 lies between the curves for zones 1 and 2. It should also be noted that the values of Sq for the boundary zone 1–2 have the greatest scatter. This reflects the fact that at
3. Experiment and discussion Fig. 2 shows a 3D picture of the deformation relief (Fig. 2, a – b, the arrow points to the grain boundary) and the distribution density of or dinates (profile heights) for different zones of the sample at ε ¼ 0.7% (Fig. 2, c – d). The deformation relief is represented by shear traces, the surface profile is quasi-periodic in nature. A nonparametric approach was used to describe the surface morphology. Graph of distribution function of ordinates for them is close to the normal distribution law. For zone 1, the extremum of the function is not shifted to the right or left, the graph is moderately extended in height (Fig. 2, c). This allows us to describe shear traces as an element of relief, for which low irregularities of approximately equal height are characteristic. Graph of distribution function of ordinates constructed for the interface of the two crystals has a bimodal height distribution, which reflects the action of the two sys tems of shear traces (Fig. 2, d). To identify the scale-invariant regularities of the crystals plastic deformation process and a statistical description of the surface morphology a fractal analysis of the deformation pattern was used. For the analysis, the height-height correlation function H (r) was applied. Fig. 3 shows the change in the Hurst exponent H1 and H2 with increasing deformation. Thus, our results show that there are two large-scale levels of plastic deformation self-organization with a similar behavior of the Hurst exponent. The exponential curves y(x) ¼ aebx with exponent b ¼ 0.16 � 0.02 describe well the behavior of the Hurst exponents H1 and H2 in the compression process (Fig. 3). The qualitative nature of the curves is similar, therefore there is scaling, yet the quantitative values of the Hurst exponent are different this fact means different mechanisms are involved. The correlation length L1 is about 2.1 � 0.7 μm, therefore, it can suppose that the dislocation substructure controls formation of the selfconsistent relief on this scale. The correlation length of L2 is several tens 3
E. Alfyorova and A. Filippov
Solid State Sciences 99 (2020) 106060
Fig. 3. Hurst exponent H1 (a) and H2 (b), the stress-strain curve in box.
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of two grains in order to preserve the survivability of the system. It is reasonable to assume that the root-mean-square roughness of Sq is caused and reflects microstructural differences in the grain scale, in particular, the orientation of the grains and, therefore, the presence of a grain boundary. The scratch testing experiment was conducted in such a way that the scratch crossed the grain boundaries. Fig. 5 shows the dependence of the friction force on the magnitude of the normal load. The friction force increases with increasing normal load. When comparing the Ft-Fn curve with the scratch image, it was found that when the indenter approaches the grain boundary, there is first a slight increase in the friction force, and then when it crosses the boundary, it decreases. A sharp increase in the friction force at the end of the scratch is due to the formation of a volume of material in front of the indenter. Fig. 6 shows a pattern of shear traces to the left (Fig. 6, c) and right (Fig. 6, d) of the grain boundary. It can be stated that when crossing the grain boundary, the orientation of the shear traces changes, but only slightly (Fig. 6, b-c). With the resolution used, the intersection of the grain boundary was not marked by shear traces. The results of scratch testing allowed revealing that metal is ploughed and pushed aside by the moving indenter thus forming a pileup on the scratch edges as well as a leading burr in front of the moving indenter. The maximum pile-up height h was determined on the scratch site before and after the grain boundary. The maximum pile-up h is close for both cases and is about 14 μm, however, the nature of the formation of piles is different (Fig. 7). This reflects the influence of the orientation of the shear systems in neighboring grains. Wang Y. et al. [46]. based on Cu
Fig. 4. The root-mean-square roughness Sq.
the grain boundary the complex of slip systems from grain 1 and 2 works and the relief changes more actively. On the other hand, usually the grain boundaries are places of localization of deformation and the roughness near them is higher. In this case, there is a different result. The 3D image of the surface at the grain boundary shows that the relief is not outstanding here (Fig. 2, b). In addition, in this case there is no influence of internal grains, which, as is known, dramatically effects the local surface height [2]. Thus, an adjustment of the deformation relief occurs at the boundary
Fig. 5. Scratch image (а), the scratch friction force (Ft) vs normal load (Fn) (Ft-Fn curve) (b), scheme of scratch position in box.
Fig. 6. Pattern of shear traces (a, c) to the left (b) and right (d) of the grain boundary. 5
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Solid State Sciences 99 (2020) 106060
a
b Fig. 7. The scratch test groove profiles left (a) and right (b) of the grain boundary (area L and R in Fig. 6).
single crystals showed that the pile-up patterns depend strongly on the crystallographic orientation of the indented surface. The influence of crystallographic orientation on the deformation relief in scratch test for single and polycrystals was noted in the works [47–49]. Moreover, the effect of grain boundaries is not seen very clearly during scratch testing. Mohit Kothari et al. [48]. also indicated that the grain boundary force does not have much influence.
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4. Conclusion The morphology of a deformed surface was described in terms of statistical parameters (Hurst exponent, correlation length, the rootmean-square roughness of Sq) and using nonparametric roughness criteria. The presence of two large-scale levels of plastic deformation selforganization and scaling was established. It was revealed that various physical mechanisms of plastic deformation are involved at the microand mesolevel. These are the processes of self-organization in the dislocation substructure and the coordinated shear in bundles of parallel shear planes, respectively. The connection between the surface morphology and the stress strain curve is established due to the statistical parameters of the deformation relief description. The paper shows that at the grain boundaries plastic deformations self-organizes in order to preserve the continuity of the sample under loading. Acknowledgments "The results have been obtained with financial support from Fundamental Research Program of State Academies for 2013–2020 (project No III.23.2.4)" financial support provided by the Institute of Strength Physics and Materials Science of Siberian Branch of Russian Academy of Sciences, Tomsk, Russia.. "The research is supported by Tomsk Polytechnic University within the framework of Tomsk Polytechnic University Competitiveness Enhancement Program" support (not financial) provided by Tomsk Polytechnic University, Tomsk, Russia. References [1] Z. Zhao, R. Radovitzky, A. Cuiti~ no, A study of surface roughening in fcc metals using direct numerical simulation, Acta Mater. 52 (20) (2004) 5791–5804. [2] O. Wouters, et al., Effects of crystal structure and grain orientation on the roughness of deformed polycrystalline metals, Acta Mater. 54 (10) (2006) 2813–2821.
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Contents lists available at ScienceDirect
Solid State Sciences journal homepage: http://www.elsevier.com/locate/ssscie
The morphology of the deformation relief and the grain boundary role in the bicrystals of AISI 316 steel Ekaterina Alfyorova a, *, Andrey Filippov b a b
National Research Tomsk Polytechnic University, Lenin Av., 30, Tomsk, 634050, Russia Institute of Strength Physics and Materials Sciences SB RAS, Pr. Akademicheskii, 2/4, Tomsk, 634055, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords: Stainless steel Plastic deformation Self-organization of deformation relief Grain boundary Scratch testing
The morphology of the deformation relief bicrystals of AISI 316 steel was described in terms of statistical pa rameters and using nonparametric roughness criteria. The presence of two large-scale levels of plastic defor mation self-organization and scaling was established. Coordinated shear in bundles of parallel shear planes was the key mechanism at the mesolevel. The processes of self-organization in the dislocation substructure was the key mechanism at the microlevel. The deformation relief close to the grain boundary was investigated. Several shear systems in two grains was active at the grain boundaries. Due to this fact, it was waited inconsistency of deformation and more rough relief at the grain boundaries then into grains. However, there was not the high values of root mean square surface roughness at the grain boundaries. In addition, the scratch testing experiment showed that the grain boundary did not have a dramatic effect in this case. The connection between the statistical parameters of the surface morphology and the stages of the stress strain curve was established.
1. Introduction The main properties of polycrystalline deformation are related to the heterogeneity of the internal structure (the presence of grains, grain boundaries, grain sizes, etc.) [1,2]. Therefore, when studying a poly crystal, the attention of researchers is often focused on two questions; plastic deformation of a single grain and the transfer of deformation across the grain boundaries. In a number of papers [3–7], various grain deformation schemes are discussed. The Taylor and Bishop-Hill schemes are close to each other and suggest that the polycrystal deformation is homogeneous. At the same time, stresses and deformations are contin uous even at the grain boundaries. This assumption, however, is ques tionable, since a number of authors experimentally [8,9] showed that the grain boundaries are the places of the deformation localization and the formation of accommodation bands. The next significant issue is the question of how the transfer of deformation between neighboring grains is carried out. Cottrell A.K. [10], Gold I., et al. [11] suggested that shear stress concentrator is necessary for the slip transfer from one grain to the next. The specified concentrator should be formed near the boundaries of plane accumu lations of dislocations. Stresses from the accumulation of dislocations at the grain boundary can elastically propagate through the boundary and
activate Frank-Read sources in the neighboring grain. Moreover, it is believed that deformation localization is typical for the grain bound aries. In addition, a number of works drew attention to the fact that the deformation behavior of surface grains and grains inside the sample differ. This circumstance is associated with the difference in the stress state of the grains inside the sample from the surface grains. Wouters O. et al. [2]. showed that the surface roughness (i.e., deformation relief) of a number of materials could be determined by several grains layers and not just by the grains on the surface of the material. In particular, they assume that the spatial variation of the Schmid factor (defined along the column below a certain point) determines the local value of the height of the surface. The development of plastic deformation leads to a change in the morphology of the surface. These changes can be quantified by the pa rameters of roughness and fractal surface dimensions. The results sug gested that the morphology of the surface and its evolution are associated with changes in the internal structure of the material. In addition, the change in the deformation relief on the surface shows the ability of self-organization. For instance, the methods of fractal analysis are sensitive both to external conditions and to the internal parameters of the material [12]. Moreover, the fractal dimension can estimate the surface regardless of the shape of its elements, their density and the
* Corresponding author. E-mail addresses: [email protected] (E. Alfyorova), [email protected] (A. Filippov). https://doi.org/10.1016/j.solidstatesciences.2019.106060 Received 17 May 2019; Received in revised form 30 October 2019; Accepted 30 October 2019 Available online 31 October 2019 1293-2558/© 2019 Elsevier Masson SAS. All rights reserved.
E. Alfyorova and A. Filippov
Solid State Sciences 99 (2020) 106060
physical regularities of plastic deformation inside the grains and in the grain boundaries. This research based on AISI 316 steel bicrystals in which the boundary passes through the entire volume of the sample. Therefore, there is no additional complication of the stress state scheme due to the influence of internal grains. 2. Material and techniques AISI 316 austenitic steel (i.e., FCC crystalline structure) was used for the current study. The sample is a bicrystal. Fig. 1 shows the appearance of the sample and the method for shooting. Fig. 1 schematically shows shear traces during deformation. Due to this choice of sample, it was possible to investigate the deformation relief both in individual single crystals and at the boundary of their interface. Sample size is 3 � 3 � 6 mm. Mechanical grinding; polishing and final electrolytic polishing prepared the surface of the specimens. Compression deformation was carried out on УТС 110М-100 1-У testing machine at a speed of 1 mm/min at room temperature. Olympus LEXT OLS4100 confocal laser-scanning microscope were used for analysing the deformation relief pattern after each loading step. Experiments were carried out in the strain interval 0.7–28%. The size of the scanned region in each case was 0.066 mm2 (0.256 � 0.256 mm2). The depth resolution was 0.06 μm. The size of the scanned region in this case sets a limit on the self-organization scale being established. The fractal analysis of the deformation pattern based on the height–height correlation function H(r) was used to reveal scaleinvariant regularities [38,39]. H(r)¼<[Z(r’) – Z(r’– r)]2> where Z(r) is the function of the surface height over all pairs of points separated by a fixed distance r; angle brackets indicate averaging over all pairs of points. The slope of the initial segment of the curve describing the height–height correlation function H(r) and plotted in logarithmic axes can be used for determining the Hurst exponent (H) and correlation length (L). The correlation length is determined by the projection of the linear segment onto the abscissa. At the same time, it is known that for a self-affine surface, then for the function H (r) the following holds true:where α is the scaling coef ficient or Hurst exponent (N), or roughness index; ξ (L) is the lateral correlation length, it defines the upper limit of the region of self-affinity and characterizes the irregularity of the surface in the lateral direction. Height fluctuations at r « ξ (small scale) are correlated, dependent, and at r » ξ (large scale), uncorrelated, random. The width of the interface (ω) is a characteristic of the irregularity of the surface in the vertical direction, it is also called the correlation length in the vertical direction or the root mean square surface roughness (ω ¼ Sq) [38–42]. Thus, the description of the deformation relief in terms of statistical parameters allows to combine information on large-scale roughness (parameter ω ¼ Sq) and small scale correlations (scaling coefficient α/Hurst exponent H) and to determine typical correlation lengths at which the deformation relief develops (correlation length ξ/L). The mean square value of the surface height of a limited scale Sq was esti mated based on ISO 25178-2: 2012. The nonparametric approach to the assessment of surface morphology was also applied. It is based on the use of such nonparametric criteria as a function of the density distribution of the ordi nates of the profile. This function contains about 95% of the surface information and describes the surface microrelief with high accuracy [43]. To study the mechanical characteristics and the establishment of features of the deformation relief formation in neighboring grains and when crossing the grain boundary, was used scratch testing. CSM In strument macro scratch tester was used in experiments. Normal load is
Fig. 1. Sampling scheme.
nature of the distribution, which makes it a universal parameter. Currently, fractal analysis is increasingly used in the description and analysis of microscopic images of the surfaces of materials. This method enable the scientists to describe the structure of a deformed surface and fractures, analyze the deformation mechanisms, try to assess the degree of material damage and predict the residual resource [13–21]. The self-organization process is manifested in the fact that traces of shear (characteristic of the onset of deformation) develop into structural elements of the relief of a qualitatively new level and scale. This development of the relief is due only to internal factors, without external specific effects. A distinctive feature of self-organization is a focused and at the same time natural, spontaneous process, which is relatively autonomous. Its purpose is to preserve the integrity of the system when an external load is applied. There are a number of papers describing the development of defor mation relief under various types of loading. Some of them do not provide estimates of the degree of self-organization, as mentioned in Refs. [22–29]. On the contrary, a number of works give quantitative estimates of the degree of self-organization of the deformation relief [18, 30–37]. Thus, the use of fractal assessments to describe the deformation relief and the degree of self-organization demonstrates its prospects, and together with identifying the physical background of these processes is of considerable interest for the development of materials science. However, when using data obtained from the sample surface, it is difficult to separate the contribution of surface and internal grains. The purposes of this study is 1) to describe the morphology of the deformed surface in terms of statistical parameters; 2) to identify the 2
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Solid State Sciences 99 (2020) 106060
Fig. 2. 3D picture of the deformation relief (a–b) and the graph of distribution density of ordinates (profile heights) for zone in Fig. 2, a (c), for zone in Fig. 2, b (d), ε ¼ 0.7%.
100 N. The scratch length is 3 mm. The scratching velocity is constant and equals 10 mm/min. The deformation relief is examined with Olympus LEXT 4100 laser scanning microscope.
of micrometers (average value is 25.8 � 9.4 μm), i.e. it was observed a correlated formation of groups of parallel tracks, i.e. formation of a quasi-periodic surface profile. Let us analyze the literature data on the dislocation substructure evolution in AISI 316 steel and compare them with our results. Feaugas X [44]. reports that at the stages I-II of the stress-strain curve, the pro portion of dislocation tangles and walls increases, while there are no dislocation cells. The low value of the stacking fault energy AISI 316 (30 mJ/m2) prevents the cross-slip of dislocations at low straining. In stage II, the activation of cross-slip and multiple slip promotes the for mation of heterogeneous dislocation structures like patches, walls and cells. During the transition from stage II to III, the proportion of dislo cation walls decreases sharply, and the proportion of dislocation cells increases sharply. By the middle of stage II, Feaugas X [44]. notes the presence of the maximum number of dislocation tangles, which de creases to almost zero in the transition to stage III. The share of dislo cation cells is still growing. Thus, the statistical parameters describing the morphology of the surface reflect changes in the dislocation struc ture and consistent with the stages of the strain-stress curve. There are works that reveal scaling laws and the processes of selforganization in the dislocation structure. For instance, Hughes D.A [45]. reports that various materials demonstrate similarities in the microstructural patterns arising from monotonic deformation. The re sults were obtained for polycrystals of Ni, Cu, Al and 304 L steel, as well as on Cu and Al single crystals under various loading conditions (compression, rolling, forging, torsion and friction). This indicate that similar dislocation mechanisms work for a wide range of materials and deformation conditions. Hughes D.A [45]. also showed that a sufficient three-dimensional dislocation mobility to create three-dimensional structures is a necessary condition. In the present work, the root-mean-square roughness Sq was esti mated on a scale of length over 70 μm. The magnitude of the root-meansquare roughness increases linearly with increasing degree of deforma tion (Fig. 4) for the cases considered in this paper. Interestingly, the approximating curve obtained for zone 1–2 lies between the curves for zones 1 and 2. It should also be noted that the values of Sq for the boundary zone 1–2 have the greatest scatter. This reflects the fact that at
3. Experiment and discussion Fig. 2 shows a 3D picture of the deformation relief (Fig. 2, a – b, the arrow points to the grain boundary) and the distribution density of or dinates (profile heights) for different zones of the sample at ε ¼ 0.7% (Fig. 2, c – d). The deformation relief is represented by shear traces, the surface profile is quasi-periodic in nature. A nonparametric approach was used to describe the surface morphology. Graph of distribution function of ordinates for them is close to the normal distribution law. For zone 1, the extremum of the function is not shifted to the right or left, the graph is moderately extended in height (Fig. 2, c). This allows us to describe shear traces as an element of relief, for which low irregularities of approximately equal height are characteristic. Graph of distribution function of ordinates constructed for the interface of the two crystals has a bimodal height distribution, which reflects the action of the two sys tems of shear traces (Fig. 2, d). To identify the scale-invariant regularities of the crystals plastic deformation process and a statistical description of the surface morphology a fractal analysis of the deformation pattern was used. For the analysis, the height-height correlation function H (r) was applied. Fig. 3 shows the change in the Hurst exponent H1 and H2 with increasing deformation. Thus, our results show that there are two large-scale levels of plastic deformation self-organization with a similar behavior of the Hurst exponent. The exponential curves y(x) ¼ aebx with exponent b ¼ 0.16 � 0.02 describe well the behavior of the Hurst exponents H1 and H2 in the compression process (Fig. 3). The qualitative nature of the curves is similar, therefore there is scaling, yet the quantitative values of the Hurst exponent are different this fact means different mechanisms are involved. The correlation length L1 is about 2.1 � 0.7 μm, therefore, it can suppose that the dislocation substructure controls formation of the selfconsistent relief on this scale. The correlation length of L2 is several tens 3
E. Alfyorova and A. Filippov
Solid State Sciences 99 (2020) 106060
Fig. 3. Hurst exponent H1 (a) and H2 (b), the stress-strain curve in box.
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of two grains in order to preserve the survivability of the system. It is reasonable to assume that the root-mean-square roughness of Sq is caused and reflects microstructural differences in the grain scale, in particular, the orientation of the grains and, therefore, the presence of a grain boundary. The scratch testing experiment was conducted in such a way that the scratch crossed the grain boundaries. Fig. 5 shows the dependence of the friction force on the magnitude of the normal load. The friction force increases with increasing normal load. When comparing the Ft-Fn curve with the scratch image, it was found that when the indenter approaches the grain boundary, there is first a slight increase in the friction force, and then when it crosses the boundary, it decreases. A sharp increase in the friction force at the end of the scratch is due to the formation of a volume of material in front of the indenter. Fig. 6 shows a pattern of shear traces to the left (Fig. 6, c) and right (Fig. 6, d) of the grain boundary. It can be stated that when crossing the grain boundary, the orientation of the shear traces changes, but only slightly (Fig. 6, b-c). With the resolution used, the intersection of the grain boundary was not marked by shear traces. The results of scratch testing allowed revealing that metal is ploughed and pushed aside by the moving indenter thus forming a pileup on the scratch edges as well as a leading burr in front of the moving indenter. The maximum pile-up height h was determined on the scratch site before and after the grain boundary. The maximum pile-up h is close for both cases and is about 14 μm, however, the nature of the formation of piles is different (Fig. 7). This reflects the influence of the orientation of the shear systems in neighboring grains. Wang Y. et al. [46]. based on Cu
Fig. 4. The root-mean-square roughness Sq.
the grain boundary the complex of slip systems from grain 1 and 2 works and the relief changes more actively. On the other hand, usually the grain boundaries are places of localization of deformation and the roughness near them is higher. In this case, there is a different result. The 3D image of the surface at the grain boundary shows that the relief is not outstanding here (Fig. 2, b). In addition, in this case there is no influence of internal grains, which, as is known, dramatically effects the local surface height [2]. Thus, an adjustment of the deformation relief occurs at the boundary
Fig. 5. Scratch image (а), the scratch friction force (Ft) vs normal load (Fn) (Ft-Fn curve) (b), scheme of scratch position in box.
Fig. 6. Pattern of shear traces (a, c) to the left (b) and right (d) of the grain boundary. 5
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Solid State Sciences 99 (2020) 106060
a
b Fig. 7. The scratch test groove profiles left (a) and right (b) of the grain boundary (area L and R in Fig. 6).
single crystals showed that the pile-up patterns depend strongly on the crystallographic orientation of the indented surface. The influence of crystallographic orientation on the deformation relief in scratch test for single and polycrystals was noted in the works [47–49]. Moreover, the effect of grain boundaries is not seen very clearly during scratch testing. Mohit Kothari et al. [48]. also indicated that the grain boundary force does not have much influence.
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4. Conclusion The morphology of a deformed surface was described in terms of statistical parameters (Hurst exponent, correlation length, the rootmean-square roughness of Sq) and using nonparametric roughness criteria. The presence of two large-scale levels of plastic deformation selforganization and scaling was established. It was revealed that various physical mechanisms of plastic deformation are involved at the microand mesolevel. These are the processes of self-organization in the dislocation substructure and the coordinated shear in bundles of parallel shear planes, respectively. The connection between the surface morphology and the stress strain curve is established due to the statistical parameters of the deformation relief description. The paper shows that at the grain boundaries plastic deformations self-organizes in order to preserve the continuity of the sample under loading. Acknowledgments "The results have been obtained with financial support from Fundamental Research Program of State Academies for 2013–2020 (project No III.23.2.4)" financial support provided by the Institute of Strength Physics and Materials Science of Siberian Branch of Russian Academy of Sciences, Tomsk, Russia.. "The research is supported by Tomsk Polytechnic University within the framework of Tomsk Polytechnic University Competitiveness Enhancement Program" support (not financial) provided by Tomsk Polytechnic University, Tomsk, Russia. References [1] Z. Zhao, R. Radovitzky, A. Cuiti~ no, A study of surface roughening in fcc metals using direct numerical simulation, Acta Mater. 52 (20) (2004) 5791–5804. [2] O. Wouters, et al., Effects of crystal structure and grain orientation on the roughness of deformed polycrystalline metals, Acta Mater. 54 (10) (2006) 2813–2821.
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