Friction-induced slip band relief of -Hadfield steel single crystal oriented for multiple slip deformation

Wear 374-375 (2017) 5–14

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Friction-induced slip band relief of -Hadfield steel single crystal oriented for multiple slip deformation D.V. Lychagin a,b,d, A.V. Filippov b,c,n, O.S. Novitskaia c, Y.I. Chumlyakov a, E.A. Kolubaev b,c, O.V. Sizova c a

National Research Tomsk State University, 36, Lenin ave., Tomsk 634050, Russia National Research Tomsk Polytechnic University, 30, Lenin ave., Tomsk 634050, Russia c Institute of Strength Physics and Material Science of SB RAS, 2/4 Akademicheskiy ave., Tomsk 634055, Russia d Tomsk State University of Architecture and Building, Solyanaya Square 2, Tomsk 634003, Russia b

art ic l e i nf o

a b s t r a c t

Article history: Received 4 September 2016 Received in revised form 13 December 2016 Accepted 20 December 2016 Available online 27 December 2016

Hadfield steel is characterized both by high wear-resistance and ability to strain hardening. Due to these properties Hadfield steel is widely used in various industrial applications. The present investigation is aimed at analyzing the deformational behavior of Hadfield steel single crystals with [10 7 1] and ⎡⎣ 3 4̅ 2̅ ⎤⎦ compression and friction axis orientations, respectively. Consecutive experiments under constant loading conditions have demonstrated the deformation-induced relief development stages as well as succession of slip system activation in the process. Both slip band step height and inter-band space increased due to the development of the maximum stress concentration zone and distortions of the near-end zone. The sequence and direction of the shear in the analyzed systems are ascertained by analyzing the shear stress value and the deformation relief. & 2016 Elsevier B.V. All rights reserved.

Keywords: Sliding Friction Single crystal Hadfield steel Deformation relief Slip band

1. Introduction Hadfield steel is a material that combines a range of unique properties as follows: wear resistance, strength, and high ability to strain hardening. Due to these properties the Hadfield steel is widely employed in railway transport, mining industry, tracked vehicles and other high-power mechanisms, including those operating under the cyclic impact loading. It is known that high strain hardening is caused by low stacking-fault energy, which contributes to formation of micro- and nano-twins [1–3] starting even from the low strain levels as well as by a high concentration of interstitial atoms (C atoms of C-Mn pair), which enhance the mobile dislocations pinning [4–6]. Those twins are formed as a result of multiple dislocation slip, whereby local stress concentration occurs due to intersection of some gliding dislocations [7,8]. According to reference [4] C atoms in C-Mn clusters may interact with dislocations and cause their tangling of high density, which then enhances the short-range stress field. Stress concentration is formed because the dislocations pile-up in the primary slip planes against the Lomer-Cottrell-type barriers [2]. n Corresponding author at: Institute of Strength Physics and Material Science of SB RAS, 2/4 Akademicheskiy ave., Tomsk 634055, Russia. E-mail address: [email protected] (A.V. Filippov).

http://dx.doi.org/10.1016/j.wear.2016.12.028 0043-1648/& 2016 Elsevier B.V. All rights reserved.

Formation of interstitial stacking-fault defects leads to dislocation glide interruption and increasing the strain hardening rate [9]. Detailed studies on the Hadfield steel indicated that such deformation processes as twinning, dislocation slipg, twinning within the primary twins, inside-twin slip and void formation were observed during the deformation at various test temperatures. As it has been previously reported, two dominant systems of twinning and dislocation glide ip can be active during the plastic deformation of Hadfield steel single crystals under uniaxial tension [1] and compression [10]. Moreover, Astafurova et al. [11] reported that severe plastic deformation of Hadfield steel single crystals also contributed to the development of two active twinning systems under the high-pressure high-strain rate torsion. As a result, these twin systems interacted with each other and thus formed barriers that then blocked dislocation glide in the intersecting planes. This caused either partial detwinning at the cost of partial dislocations motion along twinned area boundaries or the movement of dislocations into the twinned area [12,13]. Recent studies [14,15] revealed that during the high-rate compression of Hadfield steel samples, both secondary and tertiary nanoscale twins formed and contributed to additional strain hardening due to more efficient energy dissipation as compared to that by means of either primary twinning or dislocations slip [16]. Bal et al. [15] indicated the that the mean distance between the

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gliding dislocations in parallel systems was changed and manifested as a slip band width change in the places of where the twin boundaries intersected by dislocations. As a result of the secondary twin formation, the average length of the dislocation free run is diminished thus enhancing the dislocation glide energy barrier. However, the multiple twinning also enabled the dislocations to achieve the higher energy levels [17] which, when a dislocation crossed a twin boundary, facilitated its division into Shockley's partial dislocations [16,18]. The similar observations have been provided in papers [16,18]. Kang et al. [19] studied the deformation behavior and fatigue properties of the polycrystalline Hadfield steel samples under the conditions of the low and high cyclic fatigue. It was revealed that at low strain the cyclic hardening of Hadfield steel still occurred and then followed by weakening under the condition of sufficient stress saturation. At high strain there was no saturation area and the weakening was accompanied by the sample fracture. The comparable deformation behavior has been described by Schilke [20]. Such a behavior may imply that the dislocation density reached its saturation and stopped the strain hardening when achieving a certain level strain. Besides, the authors [20] stated that the density of slip bands was connected with the strain level and a number of fatigue cycles. Previously, Suresh [21] has proved that both maximum stress and dislocation density remained relatively constant during cyclic saturation until the moment of fatigue failure due to the balance between the generation of dislocations and their annihilation. The investigation of plastic deformation in a sliding test is complicated by the multiple factor nature of the friction resulting from ambiguous impacts of numerous phenomena occurring in the tribological contact zone such as intense heat generation in contact spots, formation and detachment of wear particles, the «stick-slip» effect, the segmentation of surface and near-surface layers, and others). These phenomena change conditions of the friction process and the friction coefficient magnitude, which in its turn changes loading conditions in the tribo-contact zone and creates the strain inhomogeneity. To gain fundamental understanding of the essence of the deformation processes developing in sliding, it is more convenient conducting experiments on single crystals. The rationale behind this is an opportunity to control both the acting deformation mechanism and the number of slip systems involved by means of choosing the certain crystallographic orientation and the applied load direction. The previous studies [22,23] on the sliding-induced deformation of copper single crystals allowed displaying that complex hierarchically organized plastic deformation in sliding occurs in the order as follows: shear along slip planes; formation of a continuous type misorientations as a result of the accumulation of the excessive density of dislocations; generation of one or more reoriented layers; accumulation of misorientations in the reoriented layers with formation of sub-boundaries; formation of a layer with grain-subgrain structure; accumulation of misorientations and grain refining with further formation of a microcrystalline or nano-sized grain structure. The aim of this work is to investigate the deformation behavior of the Hadfield steel single crystals oriented for with the multiple slip under conditions of dry sliding at room temperature.

Fig. 1. Sliding «pin-on-disk» test scheme and Hadfield steel single crystal orientation.

follows: C ¼ 1.1%, Mn ¼12.5%, Si ¼0.4%, Ni¼0.15%, Cr ¼0.29%, V ¼0.035%, Co ¼0.04%, Ti¼0.007%, Fe¼balance. Stacking-fault energy of the Hadfield steel samples is γ ¼0,023 J/m2. Samples for testing were cut-off using an electrical discharge machine. The samples had sizes 10.0 70.1 mm height; 1.37 0.1 mm width and thickness. After the cut-off the single crystals had the compression and friction force axes orientations along ⎡⎣ 10 7 1⎤⎦ and ⎡⎣ 3 4¯ 2¯ ⎤⎦ , respectively. The accuracy of the single crystal face orientation was 71°. The samples were annealed in helium at 1050 °C for 1 h and then quenched in water to fix the austenitic structure. Mechanically deteriorated surface layer was removed by mechanical polishing followed by electro-polishing. The hardness of the single crystals after quenching was 580 MPa. Sliding test was performed using a TRIBOtechnik tribometer and «pin-on-disk» (Fig. 1) scheme at room t's orientation during the sliding. A steel 1470 MPa hardness disc served as a counterbody; the normal load was 4 H; the sliding speed was 0.1 m/s. The single test duration was 3 h. Three consecutive tests were performed under the same loading condition in order to reveal the slip band pattern evolution with the loading. The deformationinduced slip band surface pattern was examined using a confocal laser scanning microscope Olympus LEXT OLS4100 after each test.

3. Results 3.1. Coefficient of friction The friction coefficient behavior as depended on the sliding path length revealed that the duration of so-called running-in stage for the Hadfield steel single crystals was different for each of the three tests (Fig. 2). The running-in stages on the curves are denoted in Fig. 2 as «stage 1». The running-in stage was followed by a steady-state friction stage with only modest fluctuations of the friction coefficient magnitude. The periodicity (Δt) of these fluctuations is presented on the graphs by dashed lines and is almost equal to  24 min (see «stage 2» for tests 1 and 2; «stage 3» for test 3, Fig. 2). For test 3, a curve portion with less periodicity of the friction coefficient (  12 min) occured (Fig. 2, Δt1 «stage 2», test 3). This seems to be connected with deterioration by wear of the previously severely deformed subsurface layer. The phenomenon of friction coefficient periodic fluctuations might be caused by alternating processes of accumulation and removal of the debris resulted from oxidation wear.

̅ ) faces ̅ ̅ ), and (138 3.2. Slip band systems on (1̅ 38̅ ), (342 2. Materials and methods Hadfield steel single crystals were grown according to the Bridgman's method in a helium atmosphere, and homogenized in an inert gas at 1373 K for 24 h. The chemical composition was as

An enlarged optical microscopy image of a single crystal face ̅ ) after three tests and a scheme for determining the para(138 meters of the primary and secondary slip systems are shown in Fig. 3. The distances between the primary and secondary bands are

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(Fig. 4e). The slip band penetration below the worn surface was still 90 μm. Also there were clear secondary slip system bands intersecting the primary system ones. After test 3 (3 h additionally to test 2), the deformation relief ̅ ) was severely distorted. The priof the single crystal face (138 mary slip system bands became more pronounced and arranged at a greater distance from each other. The secondary system slip bands were barely visible due to severe deformation of the single crystal face. Fig. 5 shows 3D-images of the slip bands from Fig. 4 and their cross-sections. ̅ - face relief was only One can note that on test 1 the 138 slightly developed with the maximum band depth about  60 nm. This depth increased with the further loading so that after test 2 and test 3 it was  240 nm and 410 nm, respectively. Also with further deformation the surface relief becomes smoother. ̅ ), ̅ ̅ ), (342 Optical microscopy panoramic view images from ( 138 ̅ ) – faces of the Hadfield steel single crystal have been used and (138 to determine the geometry of the slip band formation on these faces (Fig. 6).

(

Fig. 2. The change of the friction coefficient during testing.

designated as hprim and hsec, respectively. The slip band slopes are denoted by indexes analogous to those of hprim and hsec i.e. αprim and αsec. To identify the primary and secondary slip systems we assume that the band slope of the primary system (αprim) is positive while that of secondary one (αsec) is negative. ̅ ) after Fig. 4 demonstrates the images of the sample's face (138 three consecutive tests conducted under constant loading and sliding speed. After test 1 single loading only one system of slip bands oc̅ ) -face (Fig. 4. a, d). These slip bands were curred on the (138 ̅ ) and ( 342 ̅ ) faces and concentrated near the edge between (138 penetrate 90 μm below the worn surface. The secondary system slip bands have never been observed on this sample. Double time loading by normal and friction forces resulted in the larger face's area occupied by the primary slip system bands

(

)

)

3.2.1. Slip band systems on the (1̅ 38̅ )-face ̅ ̅ ) - face was characterized by the The deformation relief on ( 138 presence of three slip band systems, which spreaded to a depth 80 μm below the worn surface and occupied total surface area 66,000 μm 2 (Fig. 5a, d, g). The primary (111) slip band system was clearly seen and inclined with respect to the worn surface at an angle αprim ¼21–27°. The distance between the slip bands is hprim ¼1.3.11 μm, as depended on the distance below the worn surface. The secondary slip band system intersected the primary one and had a slope of αsec ¼-(5–8)° with respect to the worn surface. The interband distance is hsec ¼0.4–4 μm. This system can be attributed to the shear plane (111̅ ). The third system of slip bands was revealed only after test 3 on the enlarged face image (Fig. 6, c, f, i), and had a slope of 85–87°, thus corresponded to shear plane (11̅ 1̅ ). ̅ ̅ ) as well as the Fig. 8 shows 3D-images of slip bands of face ( 138 slip band profiles after the third test. The obtained data indicate that the height of steps formed by the shear along the plane 111̅ is  200 nm. The shear on the plane (111) leads to the significantly greater step height, which amounts to  600 nm.

(

)

̅ ) - face 3.2.2. Slip band systems on the (342 ̅ ) - face had only one slip band system, which covered The (342 an area of 65,000 μm 2 and penetrated to the depth of 110 μm below the worn surface. The distance between the slip bands hprim increased with the distance below the worn surface in the range 0.47 to 4.3 μm; the slip band slope was αprim ¼ 18–20°. This corresponds to the shear plane (111), if macro-distortions of the single crystal face are taken into account. As in the case of the

̅ face and schematics for the analysis of slip band systems. Fig. 3. Slip band pattern on the 138

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(

)

̅ − face resulted from sliding under single (a, d), double (b, e) and triple (c, f) loading. Fig. 4. Optical images of slip band systems on the 138

Fig. 5. 3D-images and profiles of slip bands (side face from Fig. 2) after 1 (a), 2 (b) and 3 (c) tests.

̅ ) the development of the deformation relief on the face (138 ̅ ) – face occurred as growth of the band profile depth on the (342 the test duration time increased. After test 2 and test 3, the band profile depth is  280 nm and 400 nm, respectively. Fig. 7 presents ̅ ) slip bands after tests 2 and 3 together with 3D-images of face (342 the slip band profiles. Let us note that no slip band pattern has been observed on this face after test 1.

̅ )-face 3.2.3. Slip band systems on the (138 ̅ ) face which There were three slip band systems on the (138 totally occupied 40,000 μm2 of the total face area and still found at the depth of 90 μm below the worn surface. The primary system of slip bands had a slope αprim ¼20–25° with respect to the worn surface; the distance between the slip bands varied from hprim ¼0.4 to 5 μm with the distance below the worn surface. This system can be attributed to shear developed in the (111)-plane. The secondary system of slip bands intersected the primary one and had slope αsec ¼  7 to 8°; the distance between the slip bands hsec ¼0.85.5.1

μm, i.e. varied depending on the distance below the worn surface. This secondary system can be related to shear in (111̅ ) plane.

4. Crystallographic analysis of ideal and experimentally observed slip systems 4.1. Stress-strain state Fig. 9 illustrates the schematics of the Hadfield steel single crystal crystallographic orientation during the sliding test where shear planes and directions are shown with respect to loading from both normal and friction forces. According to the orientation chosen, the normal and friction force directions coincided with ⎣⎡ 10 7 1⎦⎤ and ⎣⎡ 34¯ 2¯ ⎦⎤ axes, respectively.

D.V. Lychagin et al. / Wear 374-375 (2017) 5–14

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̅ ̅ ) – (a, d, g), (342 ̅ ) – (b, e, h), (138 ̅ ) – (c, f, i). Fig. 6. Slip bands on single crystal faces: ( 138

̅ ) after tests 2 (b) and 3 (c). Fig. 7. Slip bands (a) and 3D-image of face (342

4.2. Schmid factor with respect to normal and friction forces Table 1 presents the Schmid factor magnitudes for 12 FCC metal slip systems calculated with respect to loading from either normal

or friction force [24]. The maximum Schmid factors correspond to sliding systems as follows: 111̅ ⎡⎣ 101⎤⎦, ( 111) ⎡⎣ 101̅ ⎤⎦, 111̅ ⎡⎣ 011⎤⎦ ̅ ⎡⎣ 01̅ 1̅ ⎤⎦, 111 ̅ ⎡⎣ 101̅ ⎤⎦ and ( 111) ⎡⎣ 011̅ ⎤⎦ for normal force and 111

(

)

(

for friction force.

)

( (

) )

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D.V. Lychagin et al. / Wear 374-375 (2017) 5–14

̅ ̅ ) after the third test: a) shear on plane (111̅ ), b) shear on plane (111). Fig. 8. 3D-image of shear bands of face ( 138

Fig. 9. The crystallographic scheme of the shear planes locations in the Hadfield steel single crystals with the orientation of the compression axis [ 10 ⎡⎣ 3 4̅ 2̅ ⎤⎦ .

According to Schmid factor magnitudes the order of the shear systems engagement into deformation was as follows: shear ̅ ) planes became instarted in the 111̅ -plane, then ( 111), (111

(

)

volved and the last one was the (11̅ 1̅ )plane.

4.3. Stress-strains state According to Backofen λ [25] shear stress acting in each of the sliding systems is given by the formula as follows:

3

ταβ =

7 1], friction axis

3

∑ ∑ lαi lβi σij i=1 j=1

(1)

Then, in accordance with the chosen orientation of the single crystal and directions of the normal and friction forces the following expressions for the resolved shear stresses may be obtained:

τzs = σz lnz lsz = σz cos λ cos φ; τys = σy lny lsy = σy cos λ cos φ; τxs = 0.

(2),)

D.V. Lychagin et al. / Wear 374-375 (2017) 5–14

¼0.75 is the mean value of the friction coefficient defined experimentally (see Fig. 2 in the Section 3). When calculating the total shear stress shear directions from the acting loads and their possible opposite directions were considered. According to the data obtained (see Table 2), the maximum value of the total stress acting in the slip system is attained in shear planes ( 111) and ( 111̅ ). The lower level τzy stress is regis̅ ), and the minimum one in plane (11̅ 1̅ ). tered in plane ( 111

Table 1 Maximum Schmid factors for normal and friction forces. Shear plane

Close-packed direction

(111)

⎡⎣ 011̅ ⎤⎦ ⎡⎣ 101̅ ⎤⎦

(111̅ )

̅ ) (111

(11̅ 1̅ )

n

Mnorm,

Close-packed direction

mfric, ⎡⎣ 3 4¯ 2¯ ⎤⎦n

0.29

⎡⎣ 011 ̅ ⎤⎦

 0.08

0.44

⎡⎣ 101̅ ⎤⎦

 0.21

⎡⎣ 110 ̅ ⎤⎦

0.15

⎡⎣ 110 ̅ ⎤⎦

 0.3

⎡⎣ 110 ̅ ⎤⎦

0.13

⎡⎣ 110 ̅ ⎤⎦

0.1

[ 101] [ 011]

0.48

[ 101]

0.01

0.35

⎡⎣ 01̅ 1̅ ⎤⎦

0.08

[ 011]

0.09

⎡⎣ 01̅ 1̅ ⎤⎦

0.42

⎡⎣ 101̅ ⎤⎦

0.1

⎡⎣ 101̅ ⎤⎦

0.35

[ 110]

0.19

⎡⎣ 1̅ 10 ̅ ⎤⎦

0.07

[ 110]

0.09

⎡⎣ 1̅ 10 ̅ ⎤⎦

0.13

⎡⎣ 011̅ ⎤⎦

0.03

⎡⎣ 011 ̅ ⎤⎦

0.25

[ 101]

0.06

[ 101]

0.13

[ 10 7 1]n

5. Discussion As a result of sliding at 4 N normal load, slip bands have been formed on the lateral faces of the Hadfield steel single crystals with the compression axis and friction force orientations along ⎡⎣ 10 7 1⎤⎦ and ⎡⎣ 3 4¯ 2¯ ⎤⎦ , respectively. These slip bands were still found up to 110 μm below the worn surface. Optical microscopy examination of the deformed crystal face topography allowed ̅ ), ( 138 ̅ ̅ ); discovering three slip band systems formed on faces (138 ̅ ). and only single slip band system on the face (342 The slopes of these slip bands with respect to horizontal faces have been measured and these slope angle values were compared to those known from the crystallography. The differences have been explained by the friction-induced macro-distortion of the sample face edges during so-called “lip” formation [23]. Further tribological testing resulted in larger Hadfield steel single crystal's face areas occupied by the slip bands. The slip band steps height increased in the process. Nevertheless, the face's area occupied by these slip bands retained at the level of  100 μm depth below the worn surface in all the tests performed. Therefore, the mechanical stresses exerted by both normal and friction forces seemed to be insufficient for overcoming the dislocation glide barriers and development of the slip bands throughout the single crystal thickness as it happened under uniaxial compression test [26]. Such a tendency to subsurface strain localization may be the result of inhomogeneous subsurface plastic flow under the action of friction force. It was observed [22] that even a zero Schmid factor slip system hasa been involved in the subsurface deformation during sliding. It is known that shear in each of the {111} FCC metal planes is possible with six close-packed directions. However, the shear is more likely to occur if there is an acute angle (λ angle) between the close-packed direction and the acting force. In accordance with this provision, the presumed shear directions were identified for the planes under consideration and the loads acting during the test (the force of the normal pressure and the friction force). Figs. 10–13 schematically illustrate the possible shear in those planes under loading from both normal and friction forces.

mnorm – Schmid factor for normal force, mfric – Schmid factor for friction.

Table 2 Nominal operating stresses. Shear plane

Closepacked direction

Normal pressure force stress [ 10 7 1]

Closepacked direction

(sz, MPa) (111)

(111̅ )

̅ ) (111

(11̅ 1̅ )

Friction force stress ⎡⎣ 3 4¯ 2¯ ⎤⎦ (sy, MPa)

Total tangential stress, (τxy, MPa)

⎡⎣ 011̅ ⎤⎦

0.70

⎡⎣ 011 ̅ ⎤⎦

 0.15

0.55

⎡⎣ 101̅ ⎤⎦

1.05

⎡⎣ 101̅ ⎤⎦

0.38

1.42

⎡⎣ 110 ̅ ⎤⎦

0.35

⎡⎣ 110 ̅ ⎤⎦

0.53

0.87

⎡⎣ 110 ̅ ⎤⎦

0.31

⎡⎣ 110 ̅ ⎤⎦

0.18

0.48

[ 101] [ 011]

1.14

[ 101]

0.03

1.16

0.83

⎡⎣ 01̅ 1̅ ⎤⎦

 0.15

0.68

[ 011]

0.21

⎡⎣ 01̅ 1̅ ⎤⎦

 0.75

0.54

⎡⎣ 101̅ ⎤⎦

0.23

⎡⎣ 101̅ ⎤⎦

0.63

0,86

[ 110]

0.44

⎡⎣ 1̅ 10 ̅ ⎤⎦

 0.13

0.31

[ 110]

0.22

⎡⎣ 1̅ 10 ̅ ⎤⎦

 0.23

0.01

⎡⎣ 011̅ ⎤⎦

0.08

⎡⎣ 011 ̅ ⎤⎦

 0.45

0.37

[ 101]

0.14

[ 101]

0.23

0.37

5.1. Shear strain development in (111)-plane

where rz is the normal force stress, ry is the friction force stress, φ is the angle between the normal to the shear plane and operating force direction, λ is the angle between the close-packed direction and operating force direction. The overall stress acting in the slip system may be expressed as a sum of stresses induced by normal and friction forces:

τzy = τzs + τys

11

(3)

Table 2 presents the nominal acting stresses calculated according to formulas (2) and (3). It is assumed in calculations that sz ¼ FN/s ¼ 2.37 MPa, where s ¼ 1. 69 mm2 is the nominal contact area defined by the sample size. The stress value acting in the direction of the friction force is sy ¼ sz∙f¼ 1.78 MPa, where f

Experimental data showed a single slip band system formed by ̅ )-face. For this plane high values of shear in ( 111)on the (138 Schmidt factors m ¼0.44 were determined both for normal and friction forces (see Table 1), as well as a high value of the total shear stress (see Table 2). According to the theoretical analysis of Schmidt factor values and resolved shear stress in this plane, the shear occurs in ⎡⎣ 101̅ ⎤⎦ - direction under the action of the normal pressure force. Then a step should be formed on the surface of the ̅ )-face which has beenactually observed from the experi( 138 mental data obtained (see Figs. 4 and 5). At the same time, a step ̅ ̅ )-face (see with the opposite profile slope was formed on the ( 138 Fig. 8 profile b). Under the action of the friction force the shear was developed ̅ ⎤⎦- direction because of Schmidt factor m ¼ by plane (111) in ⎡⎣ 110

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Fig. 10. Theoretically possible variants of the shear realization in plane (111) .

̅ ⎤⎦ should give a step on the 0.3. The shear in the direction ⎡⎣ 110 ̅ )-face and the reality again was in agreement with this sug(342 gestion (see Fig. 7). 5.2. Shear strain development in (111̅ )-plane The slip bands belonged to the (111̅ )-plane manifested themselves only after the second and third sliding tests. The maximum Schmidt factor value m ¼0.48 for normal force was found for this plane but in reality the shear stress level was lower than that of achieved in plane (111). It follows from the crystallography that the maximum Schmid factor m ¼0.48 for normal force compression corresponds to the ⎡⎣ 101⎤⎦-direction (see Fig. 10 and Table 1). The shear deformation in this direction should form a step on the ̅ ̅ )-face and it really does so as follows from the experimental ( 138 results (see Fig. 8 profile a). In its turn, the step protrusion on the ̅ ) face by shear in direction ⎡⎣ 101⎤⎦ is less possible (see Fig. 11), (342 and therefore it has never been observed experimentally (see Fig. 6).

5.3. Shear strain development in (111̅ )-plane The rationale behind the absence of shear traces on the (11̅ 1̅ )-plane after the first two tests may be too low normal stress values as well as the higher friction force Schmid factor m ¼0.25 as compared to that of the normal force one (see Table 1). According to a theoretical analysis a shear by this plane can be caused by the ̅ ⎤⎦ with the step formation on friction force acting in direction ⎡⎣ 011

̅ )-face (see Fig. 12). During the analysis of successive tests, the (138 ̅ )-face were observed after traces of slipping by plane (11̅ 1̅ ) on (138 the third test (see Fig. 6, c, f, i). The emergence of the slip bands only after the third test may be caused by reduced normal stress due to higher real contact surface area achieved as a result of the running-in, and consequently a dominating role played by the friction force in the subsurface deformation.

(

)

5.4. Shear strain development in 11̅ 1 plane According to schemes in Fig. 13 both normal and friction forces

Fig. 11. Theoretically possible variants of the shear realization in plane (111̅ ).

D.V. Lychagin et al. / Wear 374-375 (2017) 5–14

13

Fig. 12. Theoretically possible variants of the shear realization in plane (11̅ 1̅ ).

̅ ). Fig. 13. Theoretically possible variants of the shear realization in plane (111

̅ ) plane in several directions. One of may produce shear in the (111 them, namely ⎡⎣ 101̅ ⎤⎦ is available for unidirectional shear from both ̅ ⎤⎦ and ⎡⎣ 011⎤⎦- ⎡⎣ 01̅ 1̅ ⎤⎦ forces. Other directions such as ⎡⎣ 110⎤⎦- ⎡⎣ 1̅ 10 are available for oppositely directed shear, i.e. the overall shear stress in these directions will be low. Also the Schmid factor analysis allows suggesting that shear in direction ⎡⎣ 101̅ ⎤⎦ caused by the friction force might develop in this plane (see Table 1). However, no traces of shear by this plane have been revealed in the experiments. Such a finding can be explained by strong localization of the friction force-produced strain within a thin subsurface layer where we can hardly observe the slip bands. 6. Conclusions Sliding experiments on Hadfield steel single crystals oriented

for multiple slip have been carried out to study the evolution of a deformation-induced slip band pattern on the crystal's lateral faces. Different strain levels have been achieved by successive loading the samples by normal and friction forces for constant time periods. Also basing upon the experimental results and crystallography considerations we analyzed the critical resolved shear stress levels which allowed us making conclusions as follows: Both evolution of deformation-induced slip band pattern and slip plane activation order are related to the resolved shear stress levels as well as to shear strain localization and distortion below the worn surface. The slip plane activation order is dictated by the Schmid factor value as well as by stress levels in the normal [1,7,10] and friction force ⎡⎣ 3 4̅ 2̅ ⎤⎦ directions. Slipping started from the (111) –plane

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and then continued successively in (111̅ ) - and further in (11̅ 1̅ )planes. The evolution of slip band steps is manifested in increasing their heights and deformed layer thickness below the worn surface with the strain level accumulated during sliding tests. Strain localization below the worn surface and plastic flow of the sample's edges are the main contributors to the process.

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Acknowledgments The present study was partially supported by RFBR Grant no. 16-08-00377 а. Authors express their gratitude to Tarasov S.Yu. and Chumaevsky A.V. for valuable discussions and assistance.

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