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Initiation of basal slip and tensile twinning in magnesium alloys during nanoindentation
Journal of Alloys and Compounds 731 (2018) 620e630
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Initiation of basal slip and tensile twinning in magnesium alloys during nanoindentation Tingting Guo a, *, Filip Siska b, Jun Cheng a, Matthew Barnett a a b
Institute for Frontier Materials, Deakin University, Geelong, Victoria, 3216, Australia Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 513/22, 616 62, Brno, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 June 2017 Received in revised form 26 September 2017 Accepted 11 October 2017 Available online 13 October 2017
The present study addresses the challenge of determining the stress required for the initiation of deformation modes in Mg alloys. Nanoindentation is employed to detect the onset of basal slip and tensile twinning. A Mg-6 wt. % Zn alloy and a series of Mg-Gd binary alloys with concentrations between 0.3 and 4 wt. % Gd are examined in the extruded state. Nanoindentation tests were conducted on {1010} and {1120} crystal planes using a 5 mm radius spherical indenter. It is shown that the initial yielding point in the load trace corresponds to the appearance of basal slip lines on the sample surface. A pop-in event is seen to accompany the appearance of twinning. We find that the addition of Zn strengthens the basal slip but shows mild influence on twin initiation. For alloying with Gd, an impact on basal slip and twinning is only seen at the highest solute levels. A means of examining the alloying effect on twin growth is proposed and revealed that solute Zn has a greater impact on twin growth than initiation. Crown Copyright © 2017 Published by Elsevier B.V. All rights reserved.
Keywords: Nanoindentation Basal slip Twin Magnesium Solute strengthening
1. Introduction Basal slip and {1012} extension twinning frequently dominate the deformation of magnesium and often control yielding [1,2]. Understanding the respective critical resolved shear stress (CRSS) values of these two deformation modes e in the context of a polycrystal - is therefore of practical interest. A considerable range of values exist in the literature for both basal slip [1e4] and extension twinning [1,5]. This evidently reflects alloying effects [6e13] as well as potential variations due to the technique of measurement. The effect of Zn additions on twinning for example are in dispute, one of us has reported that the effect is minor [6] while others report it to be significant [9,10]. Gd has been shown to have a considerable impact on slip [12] whereas its impact on twinning is unknown. There is need for additional experimental clarification, particularly in regard to the separate processes of twin nucleation and growth. In the present work, we explore the extent to which nanoindentation technique can be usefully brought to bear on the problem, for the benefit of understanding rational alloy design for the micro- and nano- scaled structure. Somekawa and Schuh [14] employed cube corner indenter (up
* Corresponding author. E-mail addresses: [email protected], [email protected] (T. Guo). https://doi.org/10.1016/j.jallcom.2017.10.088 0925-8388/Crown Copyright © 2017 Published by Elsevier B.V. All rights reserved.
to loads of 1 mN) to compare the hardness and pop-in stress for a range of fine grained solute strengthened magnesium alloys. It was found that the increments in hardness values due to solute addition (Ca, Zn, Y, Al, Li) qualitatively followed theoretical predictions based on Yasi et al. [15] for basal slip, but fell 1.5 to 3 times higher in magnitude. They found the pop-in stress to be considerably less sensitive to solute addition. However, no distinction was made between deformation modes. Sanchez-Martin et al. [16] have recently taken some steps towards addressing this gap. They used crystal plasticity finite element (CPFE) modelling combined with Berkovich indentation (up to depth of ~300 nm) on electropolished surfaces. CPFE modelling was employed to map out the broad impact of relative CRSS values on the sensitivity of hardness to crystallographic indentation plane. The measurements are seen to be sensitive to the choice of CRSS values only within certain ranges of values. This, compared with the fact that in their model frame work three parameters are needed to describe the hardening for each of the four deformation modes, makes unique determination of characteristic CRSS values problematic. Their study also did not consider deformation twinning. Catoor et al. [17] have examined the apparent CRSS value corresponding to pop-in events seen in their nanoindentation tests. They employed a 3 mm radius spherical tip indenter and examined indentation of three chemically polished crystallographic planes
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using pure Mg single crystals. Twinning was observed in their study but the initial pop-in event was interpreted in each case to be due to slip. Nevertheless, complete rationalization of the pop-in events based on the nanoindentation Schmid factor was not possible. It was concluded, however, that the pop-in event probably corresponded to the homogeneous nucleation of dislocations at stresses between 0.6 and 1.2 GPa. In a previous work, we addressed the issue of associating nanoindentation yielding events with different deformation modes [18]. For Mg alloy AZ31, we found that basal slip and {1012} extension twinning events could be separated for spherical tip indentation (5 mm tip radius) on colloidal silica (OPS) polished planes containing the crystallographic c-axis. Atomic Force Microscopy (AFM) was employed to confirm that the initial yielding event corresponded to the appearance of copious basal slip lines on the surface, which is the onset of the plasticity during penetration. The apparent CRSS for the onset of basal slip for these experiments could be estimated using Hertzian elastic contact theory as [19]:
6Py E*2 p3 R2
!
=
tyielding ¼ S
1
3
(1)
where Py is the load of yielding and R is the indenter radius. E* is the reduced Young's modulus. S is defined as the elastic Indentation Schmid Factor (ISF) and the value is 0.18 for basal slip in {1010} and {1120} indentation [17,18]. Twins on the surface were only seen once a pop-in event had occurred after the yielding. Associating a CRSS value with the twinning event is more difficult in these tests because it relies on the estimation of the stresses under the indenter during plastic indentation immediately prior to the onset of twinning. Finite element crystal plasticity (CPFEM) simulations were employed to establish the relationship between indentation load and the resolved shear stress on twinning plane [18]. This was done for a range of candidate CRSS values for slip and the mean was recorded. With this relationship in hand, it is possible to convert the load corresponding to the pop-in to an estimate of the corresponding resolved shear stress on the most heavily stressed twinning system. The present study employs nanoindentation on planes containing the crystallographic c-axis in an attempt to discern the sensitivity of the CRSS values corresponding to the onset of basal slip and twinning to the addition of Zn and Gd to pure Mg. Our first objective is to verify that our previous findings, made on alloy AZ31 [18], hold for Mg alloys in general (i.e. that the yielding is due to slip and the following pop-in is due to twinning).
2. Materials and experimental method Cast Mg-6Zn billets (F ¼ 59.5 mm and h ¼ 40 mm) were solution treated at 335 C for 72 h and quenched in water. The billets were then extruded to plates 46 mm wide and 12 mm thick at 370 C and a ram speed of 0.1 mm/s. Samples for nanoindentation tests were annealed at 340 C for 3 h. Four magnesium alloys containing 0.3, 1, 2.5 and 4 wt. % Gd were cast and cut into billets measuring 59.5 mm 40 mm for extrusion. All the billets were homogenized at 450 C for 3 h. The extrusion schedule included preheating the billets at 400 C for 2 h, followed by extrusion at 400 C at a ram speed of 0.5 mm/s. The samples prepared for nanoindentation tests were annealed at 450 C for another 3 h. Asreceived cast pure Mg billets with a diameter of 29.8 mm and height of 20 mm were extruded into rods 8 mm in diameter at 370 C at a strain rate of 15 mm/s. The samples were immediately annealed at 450 C for 2 h followed by a water quench. The
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Table 1 Chemical composition of the materials in the present study (wt. %). Material
Zn
Gd
Mn
Mg
Mg-6 Zn Mg-0.3 Gd Mg-1Gd Mg-2.5 Gd Mg-4 Gd Pure Mg
6% e e e e 0.006%
0.0415% 0.304% 1.09% 2.51% 4.08% e
0.036% 0.0182% 0.0178% 0.0162% 0.0153% 0.0345%
balance balance balance balance balance 99.7%
chemical compositions of all the materials used in the study are given in Table 1. The dimension of the samples used for nanoindentation was 10 mm 10 mm 5 mm. The large surface was cut to be perpendicular to the extrusion direction, which was then selected as the testing surface. Similar to the previous experiment carried out on AZ31 in Ref. [18], all the tests were performed on planes within 5 of the {1010} and {1120} crystal planes. EBSD was employed on a pre-marked area to obtain the grain orientation data and the initial crystallographic texture (Fig. 1) by a field emission Leo 1530 Scanning Electron Microscope. The textures for pure Mg and Mg-6Zn were typical for extruded magnesium alloys with the basal planes aligned perpendicular to the extrusion direction. The texture in the Mg-Gd series alloys agreed with reference [20]. The <1121> texture increased with Gd addition. The testing surfaces for EBSD mapping were first wet ground using 1200 grit SiC paper, cleaned in ethanol in an ultrasonic bath and dried with flowing air. Then, 9 mm, 6 mm and 3 mm diamond suspensions were used for rough polishing on a Struers DP-Pan cloth, followed immediately by etching in acetic-nitric acid (15 ml acetic acid, 5 ml nitric acid, 60 ml ethanol and 20 ml distilled water) for 20 s. Samples for EBSD mapping were polished with 10% of OPS (colloidal silica) for 10 min in the middle of a Struers OP-chem cloth at a rotating speed of 150 r/min. Before the nanoindentation tests, samples were polished another 3 min with OPS and 2 min with ethanol. The purpose for this step is to get rid of the oxidation film and clean the colloidal silica thoroughly. Two to seven grains were selected for each orientation, depending on the grain size and quantity of {1010}w and {1120} oriented grains on the polished surface. Nanoindentation tests were conducted using a UMIS ultramicro indentation system (UMIS is the name of the machine manufactured by CSIRO Division of Applied Physics, Lindfield, Australia). A 5 mm radius diamond spherical tip are conical shaped with a spherical end, which were employed in the present work. Tests were performed under the closed loop control, ensuring reproducible and stable results. The loading rate was around 0.015 ± 0.005 mN/s (There is no influence of rate on the experimental results over this range.) The maximum applied load is 5 mN. On the indented surface, the grain boundaries are avoided (within ~10 indent diameters). Some tests were interrupted once the yielding or pop-in event was observed. The deformation around the indents was characterized using a Brucker Multimode 8 Atomic Force Microscopy (AFM) in the PeakForce error mode and analysed by software ‘NanoScope Analysis’. The occurrence of yielding and the pop-in events is sensitive to the surface damage caused by polishing [21,22]. Mechanical polishing can alter the dislocation density in the near-surface zone. We therefore examined the influence of mechanical polishing time on the yielding and pop-in load in a large grain in pure Mg. The tests were first carried out for chemical polished condition (60% ethanol, 20% distilled water, 5% nitric acid and 15% acetic acid for 5 min). It was found that a pop-in is the first and only event in 90% of the curves, which is consistent with the behaviour commonly seen in
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Fig. 1. EBSD maps with inverse pole figure colour and inverse pole figures referring to the extrusion direction for (a) pure Mg, (b) Mg-6Zn (c) Mg-0.3Gd (d) Mg-1Gd (e) Mg-2.5Gd (f) Mg-4Gd.
chemical and/or electropolished samples [17]. Subsequent OPS polishing for different times led to yielding as the first event and this was followed by a pop-in. As shown in Fig. 2, the difference of the yielding and pop-in load is quite small for the four polishing states, implying that polishing using OPS for up to 60 min generates a repeatable result. To correlate the indentation load with the resolved shear stress for the most heavily stressed {1012} twinning system, single CRSS values for the different slip systems were employed to fit the loaddepth curves before the pop-in event. Due to complexities relating to size effects [23], strain hardening was not introduced into the simulations. The fitted CRSS values reflect an effective value, applicable to the indenter shape and size employed. The actual values depend on the choice assumed to be basal (CRSS range: 20 MPae100 MPa), prismatic (CRSS range: 100 MPae150 MPa) and 2nd order pyramidal slip (CRSS range: 500 MPae1000 MPa) (see Ref. [18] for details). The simulation
results are shown in Fig. 3. The estimated twinning RSS is sensitive to the onset and extent of prismatic slip CRSS and this impacts upon both the slopes of the upper and lower limits and changes in these slopes with increasing load (see also [24]). The resolved shear stress can be approximated by a power law with an exponent of 1/3 (see Discussion). This, incidentally, is also the case for Hertzian contact, as evident in Equation (1). Due to the unknown values of the critical stresses for the slip systems, the apparent twinning CRSS reported for alloys in this paper is accurate to ~ ±15%. 3. Results 3.1. Deformation during nanoindentation in Mg-6Zn alloy To illustrate the basic features of the present nanoindentation tests and to verify the relationship between yielding events on the flow curve and the appearance of deformation activity on the
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are only observed once a pop-in event is observed in the load curve (Fig. 4 (b) and (c)). It is also seen that the selected twin variants for {1120} and {1010} indentation show different morphologies. One edge of the twin present after {1010} indentation is parallel to the basal plane traces while the twins are seen to extend at an angle to the basal traces in the case of {1120} indentation. This is quite consistent with the expected active twin variants [25,26]. The twin morphology seen here is also consistent with that observed by Kitahara et al. [27]. Interestingly, the basal slip lines in some cases can be seen to extend up to 15 mm from the indent impression, in the direction of the c-axis. A similar observation was reported by Zambaldi et al. [28]. This testifies to the existence, at certain locations in the structure, of easily activated dislocation sources. Fig. 5 presents a cumulative frequency plot of yielding and pop-
Fig. 2. Influence of mechanical polishing time on yielding and pop-in load tested in the same grain in pure Mg.
in loads on selected {1010} and {1120} oriented grains for Mg-6Zn. Data for pure Mg and AZ31 [18] are also given for the purpose of comparison. Each curve represents data from 3 to 7 grains. For yielding, the width of the distribution reflects the stochastic nature of the process [29,30]. The shape of the distribution curves also varies somewhat and this can be understood in terms of a higher than expected grain-to-grain variation encountered in the study. For yielding, the two crystallographic planes subjected to indentation show no systematic difference in load range. This is consistent with the idea that yielding is dominated by basal slip; the orientation factor for which is the same for {1010} and {1120} indentation. As expected, both AZ31 and Mg-6Zn show higher yielding loads than pure Mg. The pop-in load, on the other hand, shows an orientation dependence. The pop-in loads for {1120} indentation are higher than those for {1010} indentation. This is consistent with the difference in indentation Schmid factors for the twinning mode in Hertzian contact (0.297 for {1120} indentation and 0.306 for {1010} indentation). However, as noted above, plasticity due to slip is present prior to twinning. The simulated resolved stresses in Fig. 3 do predict that twinning during {1010} indentation should be activated under lower loads than {1120} indentation, but only for loads below a critical value. The difference between {1010} and {1120} in CPFE is not as stark as seen in experiment and this may be due to stress variations arising from the localized nature of slip, which is evident in the AFM images but which is not captured in the CPFE simulations. The pop-in loads also reveal strengthening in AZ31 and Mg-6Zn compared to pure Mg.
3.2. Deformation during nanoindentation in Mg-Gd alloys
Fig. 3. CPFEM simulation results showing the relationship between the max RSS on twinning plane and the indentation load [18]. The dashed line shows a power law to the exponent of 1/3 fitted between the upper and lower bounds.
sample surface, Fig. 4 shows representative load-penetration depth curves and corresponding AFM images of indents for the Mg-6Zn alloy. Indents on a {1120} plane are shown in Fig. 4 (a) and (b) and those on a {1010} plane are given in Fig. 4 (c). As expected, the initial part of the curve follows the Hertzian elastic contact prediction. A reduced Young's modulus of 42 GPa is fitted to the initial elastic stage and this is employed to locate the load corresponding to the initiation of basal slip. The behaviour is similar to that observed previously in AZ31 [18]. Basal slip is the only deformation mode seen for load curves without a pop-in event (Fig. 4 (a)). Twins
Representative load-penetration depth curves and corresponding AFM images for Mg-1Gd are displayed in Fig. 6. Fig. 6 (a) and (b) show the case of {1120} indentation. It is observed that only one twin was formed when the pop-in occurred at around 0.8 mN. Two twins were nucleated at the higher pop-in load of 1.6 mN and it is possible the two twins formed during the single pop-in, as no second pop-in was observed in this instance. Fig. 6 (c) and (d) show two cases of {1010} indentation with similar pop-in loads (0.6 mN and 0.8 mN). The difference between the two cases is the extent of indentation following the pop-in. With increasing indentation, the twin clearly extends and thickens. Indentation data for the most concentrated Gd alloy (Mg-4Gd) studied in the present paper are shown in Fig. 7. In the case of {1120} indentation, pile-up of material on one side of the indent can be seen (Fig. 7 (a) and (b)). Surface mapping (not shown here) reveals the convex nature of the pile-up. The indentation in Fig. 7 (a)
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Fig. 4. Load-penetration depth curves and corresponding AFM images of the indents for alloy Mg-6Zn indented on (a) (b) {1120} plane and (c) {1010} plane showing “yielding” and “pop-in” behaviours.
Fig. 5. Yielding and pop-in loads for Mg-6Zn, along with data for pure Mg and AZ31 for comparison.
also shows a particularly high level of penetration without triggering twinning. This, along with a uniformly round imprint, suggests the operation of copious slip on different systems despite the absence of clear slip lines. Extension twins can be seen following the pop-in at 15.9 mN (Fig. 7 (b)). Additional slip lines close to the tip of the twin can also be seen in Fig. 7 (b). These are perpendicular
to the basal slip lines in matrix but look similar to the basal slip lines and traverse the twin-matrix boundary. We interpret this as an indication of basal slip within the twin. After removal of the load, shrinkage of the twin is presumed to have occurred, leaving behind surface slip steps formed by basal slip in the twin. Fig. 7 (c) and (d) show {1010} indentation with features similar to those seen in the
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Fig. 6. Load-penetration depth curves and corresponding AFM images of the indents for Mg-1Gd alloy indented on the (a) (b) {1120} plane and (c) (d) {1010} plane showing “yielding” and “pop-in” behaviours.
Fig. 7. Load-penetration depth curve and corresponding AFM images of the corresponding indents for alloy Mg-4Gd indented on (a) (b) f1120g plane and (c) (d) {1010} plane showing “yielding” and “pop-in” behaviours. The enlarged image of slip lines close to the twin tip in (b) is also shown in top left corner.
cases discussed above. The effect of Gd on yielding and pop-in load is summarized in Fig. 8. In the case of yielding, little effect of orientation is evident except in Mg-4Gd. For twinning, a greater effect is seen. In a number of cases low numbers of successful readings were obtained on the {1010} plane and we bracket conditions with <10 successful readings, for further analysis. 4. Discussion Basal slip and {1012} extension twinning are the two plastic
deformation modes seen to be dominant in all the alloys in present study for both {1120} and {1010} indentations. As pointed out in the Introduction, this is as expected; these are the two most readily activated deformation modes in magnesium alloys. Due to the mechanical OPS polishing employed in the study, the onset of basal slip is marked not by a pop-in Ref. [17] but by gradual yielding, presumably due to the activation of pre-existing sources introduced during the OPS polishing [21,31]. That these sources are present at a reasonably consistent number density is testified by the absence of OPS polishing time on the yielding response for pure Mg up to 60 min of polishing. Twinning on the other hand is
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Fig. 8. Yielding and pop-in load variation for Mg-Gd alloys.
typically associated with a significant energy release and so it manifests itself clearly in the present experiments via a pop-in event. The association of twin observation after a pop-in event was observed in 51 separate indents and the presence of slip lines only for cases of no pop-in observation was seen on all 18 cases where we examined the surface of no pop-in indents using AFM. We do not claim that non-basal slip is not active in these tests (perhaps in small amounts or under the indenter). As was noted above, in the high Gd alloy, the observed deformation is suggestive of multiple slip modes (Fig. 7 (b)). Nevertheless, basal slip is the only detectable slip mode and we proceed assuming that its onset controls the yield point.
4.1. Glide stresses The apparent CRSS for basal slip corresponding to the onset of yielding (established using Equation (1)) in Mg-6Zn is plotted in Fig. 9 (a) along with values for pure Mg and AZ31 [18]. The absolute values are considerably higher than those reported in other studies using conventional ‘macro’ test techniques [1e4,32,33]. The difference is over an order of magnitude compared to polycrystal and up to two orders of magnitude for the pure Mg compared to single crystals. However, the basal CRSS values obtained by Catoor et al. [17] for indentation on {1010} on chemically polished single crystal Mg, are ~3 times higher than our values. Thus, while we have
Fig. 9. The CRSS of basal slip for (a) Mg-6Zn and (b) Mg-Gd alloys. The error bars represent one standard deviation. The markers for the two orientations are artificially separated for clarity.
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shows the addition of 4 wt. % of Gd gives rise to an increase in CRSS for basal slip initiation of ~60 MPa. In sample Mg-4Gd, a pile-up was observed adjacent to the indenter and it was noted above that other non-basal systems are quite likely operative following yielding. Furthermore, our CPFE modelling employed previously to establish the stresses immediately prior to the onset of twinning relied on the activation of some non-basal slip close to the yield surface. To assess if there are any obvious effects of non-basal slip on the relation shown in Fig. 3, the load-displacement curves are compared in Fig. 10 by plotting points corresponding to twin onset. Note, these values reflect an arbitrary choice of a point on the load displacement curve for each test in lieu of comparing entire curves, which would be too unwieldy to do graphically. The data in Fig. 10 fall remarkably along a common curve showing, rather surprisingly, that no obvious effect is present. Any changes in slip stresses in the present case are clearly too minor to be detected on the load trace. It is worth noting though that CPFEM simulations show a ‘robustness’ in the load trace to changes in CRSS values for basal and prism slip [24], presumably due to the significant role played by the elasticity of the material surrounding the plastic zone. 4.2. Twinning stresses
Fig. 10. Plot of pop-in load and the penetration depth when pop-in occurs for pure Mg and Mg-4Gd for {1120} and {1010} indentations.
introduced dislocation sources during OPS polishing, deformation may still be considered to be source controlled. Yielding, while gradual, is still subjected to the challenge of finding dislocation sources to activate within the relatively small highly stressed zone under the indenter. Fig. 9 (a) shows that the CRSS values for the initiation of basal slip increase by ~45 MPa for each of AZ31 compared to pure Mg and then Mg-6Zn compared to AZ31. Fig. 9 (b)
Fig. 11 (a) shows the apparent CRSS for twin initiation, based on the pop-in observed in the load-displacement curves. The CRSS value is established from the maximum resolved shear stress using Fig. 3, which is based on CPFE modelling [18]. This stress represents the condition under which both twin nucleation and propagation occurs. If one defines nucleation as the process by which a twin capable of rapid propagation is formed, then it is reasonable to associate the stress of ‘twin initiation’ with that of twin nucleation. In the present case, we are not entirely sure where in the stress field twin nucleation takes place so by presenting the maximum value of the twin initiation CRSS we note that it is an upper limit of the stress required for nucleation.
Fig. 11. Twin CRSS for (a) Mg-6Zn and (b) Mg-Gd alloys. The error bars represent one standard deviation. For a better observation, the markers for the two different orientations are slightly separated.
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Fig. 12. (a) Relation between twin thickness t measured in AFM images and the pop-in depth for {1010} indentation for all the materials studied. The proposed model d ¼ gt=2 is shown as the dashed line. The difference between the measured thickness and the model is defined as Dt, as shown in the figure. (b) Plot of jDtj and the penetration depth after the pop-in event. The fitted dash line through the data points is a guide for eyes.
It is clear that the stress increments arising from alloying addition in Fig. 11 are greater compared to those for basal slip. The alloy Mg-4Gd shows a similar twinning strength to AZ31. The Mg6Zn alloy does not display relative hardening compared to AZ31 as it does for basal slip. This reveals a weak potency in the ability of Zn to harden against twin formation, something that has been pointed out previously [9]. The higher hardening effect against twinning in AZ31 is probably influenced by the presence of particles and not to solute effects alone.
4.3. Analysis of the pop-in We have shown that the pop-in is caused by a twinning event. Thus it should be possible to relate the dimensions of the twin measured on the indented surface with the pop-in depth, d. A simple approximation can be made for the case of {1010} indentation where the active twin mode forms on a plane approximately 45 deg. to the sample surface. It is assumed that twinning is associated with the glide of twinning dislocations/disconnections along
Fig. 13. Relation between pop-in load and pop-in depth for (a) {1010} indentation and (b) {1120} indentation for materials investigated in present study. The dashed lines show the linear relation between the pop-in load and the depth for pure Mg and Mg-6Zn.
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the twin boundary [34]. The twinning disconnections are characterized as a step (h ¼ two crystal planes high in the present case [35]) with a Burgers vector, bT [36] (~0.05 nm [37]). The pop-in pffiffiffi depth should be approximately nbT/ 2 where n is the number of twinning dislocations that have passed over the twin interface, each thickening the twin by h. The thickness of the twin is thus nh pffiffiffi but on the surface plane the apparent twin thickness, t, is 2nh. Because the twinning shearg, is bT/h (¼0.13) we can write the following for the pop-in depth:
tg d¼ 2
(2)
where t is the thickness of the twin apparent on the sample surface. Fig. 12 (a) plots measured values of the twin thickness for {1010} indentation measured on AFM images against the pop-in depth. Equation (2) is also shown for comparison. The correlation is in reasonable agreement with Equation (2) but there are a few outlying points. We suspect the outlying points are, at least in part, due to either twins shrinking during release of the load (see e.g. Ref. [38]) or to twins being thickened by further increase of the load; events that were noted earlier. To test this, Fig. 12 (b) plots the difference Dt between the model and our measurements against the depth of continued penetration between the end of pop-in and the end of the test. This provides a rationale for most of the wayward points in Fig. 12 (a). The present phenomena are expected to be quite sensitive to surface inclination and roughness and it is possible that, despite our care, this may be an issue for one or two points in this figure. Nevertheless, one can see that the magnitude of the pop-in depth can be rationalized reasonably well by Equation (2). Finally, we turn to the relationship between the pop-in depth and the load. In the literature, it is not uncommon for a linear relation to be found between these two variables [39,40]. In the present case (Fig. 13) there is considerable scatter, particularly for the richer alloys. However, the leaner alloys display a reasonably tight linear trend. The pop-in depth is larger for {1010} indentation than for {1120} indentation at a given load and this is probably a reflection of the more favourable orientation of the twin planes in the {1010} indentation. The increased scatter in the case of {1120} indentation might be due to different or simultaneous twin variants forming. Nevertheless, a decrease in slope of the relationship between load and pop-in depth can be detected for increasing alloying addition for both crystal orientations. This indicates that for a constant load, a richer alloy will tend to display a shallower pop-in depth. Our interpretation for this is that with higher alloying addition, the effective friction stress on the twinning dislocations (see Ref. [41]) increases. This leads to greater levels of dissipation during the twinning event and therefore a smaller pop-in depth. The effect is clear here for Zn addition and this is rationalized in the following. We assume an ideal disk-shaped twin as a first approximation. Equation (2) can then be re-written in terms of the twin diameter, l, and aspect ratio, q, as:
d¼
glq 2
(3)
We make a further first approximation that the twin diameter is set by the distance from the surface to the stress contour equivalent to the twin friction stress tc . This is an under estimate. The twin is likely to propagate further into the stress field driven by the higher stresses near the indenter. However, the distance of propagation is still be expected to scale similarly with the level of the stress contours and the friction stress. To obtain an approximate value, we
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inspect Hertzian [42] and plastic [24] stress fields and note that in both cases, for depths greater than the contact radius, a, the shear stress contours on the symmetry axis (i.e. directly below the indenter) can be given approximately as:
t tmax
z 32 a
(4)
where z is the distance below the surface. We can thus write l as:
2 tmax 3 l¼a
tc
(5)
This expression can be completed using the definition of pffiffiffiffiffiffiffiffiffiffiffiffi indentation hardness, a ¼ P=pH (where the hardness is that for slip dominated flow prior to the twinning pop-in) and the power law approximation in Fig. 3 (tmax ¼ kðPE2 =R2 Þ1=3 where the dimensionless parameter k contains potential further dependencies on E and R e note, the expression has only been validated for the present indenter radius of 5 mm). The twin aspect ratio, q, for magnesium can be established from an Eshelby inclusion analysis and is given as [43]:
q¼
1 tmax tc 1 tmax 2 2 gG gG
(6)
Combining, we arrive at the following:
d¼
k5=3 P 19=18 E 10=9 pffiffiffiffiffiffiffi 2=3 R 4G pH tc
(7)
This expression agrees more or less with experiment in its near linear dependency on P. The dependency on friction stress e i.e. to the power of 2/3 - is dictated by the stress field away from the indenter and this result, as noted above, is general; it is also obtained if one repeats the analysis for Hertzian contact. In Equation (7), the pop-in depth also depends upon the hardness prior to the pop-in. The consistency of the load-depth traces in Fig. 10 suggest only modest variations in hardness amongst the present samples. Additional tests were carried out to verify this for pure Mg and Mg-6Zn and the respective hardness were found to be 650 and 1000 MPa. According to Equation (7), this difference corresponds to a decrease in pop-in depth of ~1.25 times. Inspection of Fig. 13 (a) reveals a drop in pop-in depth of ~3 times with 6% Zn addition. Assuming this is due to a change in the critical stress for twin thickening, Equation (7) returns a change in twin friction stress of ~3.7 times. This is a considerably greater effect than that seen for twin nucleation, where the increase in critical stress for twin thickening upon Zn addition is seen to be approximately 1.25 times.
5. Conclusions 1. It is verified that for indentation on {1010} and {1120} planes gradual yielding is due to dislocation glide characterized by distinct basal slip lines on the surface and the following pop-in is caused by the initiation of extension twinning. This is generally true for all Mg alloys studied. 2. The stresses for basal slip initiation can be estimated using a Hertzian analysis, which enables the critical indentation load to be converted into a critical resolved shear stress. CRSS values for tensile twinning require simulation of the stress field prior to twin initiation. CPFEM was employed to establish a relationship between load and the max resolved shear stress on the twinning planes.
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3. 6 wt. % Zn was found to harden basal slip with an increment approximately twice that seen for alloy AZ31 compared to pure Mg. The addition of 4 wt. % Gd hardened the initiation of basal slip by a similar amount as seen in AZ31. 4. Twin nucleation in Mg-6Zn was hardened (compared to pure Mg) less than that for alloy AZ31 and Mg-4Gd. 5. A simple geometrical model was developed to describe the relation between the measured twin thickness on the {1010} planes and the corresponding pop-in depth. Outlying data points can be explained by twin shrinkage during unloading and thickening during continued penetration. 6. A model was developed to explain the alloying effect on twin growth using the depth of the pop-in. The addition of Zn is shown to have a greater effect on twin thickening compared to nucleation. Acknowledgments The authors would like to thank David Grey, Jayant Jain, Steven Babaniaris, Lynton Leigh and Aiden Beer for their assistance with the material preparation and extrusion in this work.
[16] [17]
[18]
[19]
[20]
[21] [22]
[23]
[24] [25] [26]
References [1] S.R. Agnew, et al., Study of slip mechanisms in a magnesium alloy by neutron diffraction and modeling, Scr. Mater. 48 (8) (2003) 1003e1008. [2] S.R. Agnew, Plastic anisotropy of magnesium alloy AZ31B sheet, in: TMS Annual Meeting, 2002. Seattle, Washington, USA. [3] M.R. Barnett, A taylor model based description of the proof stress of magnesium AZ31 during hot working, Metall. Mater. Trans. A 34 (9) (2003) 1799e1806. [4] O. Mur ansky, et al., Investigation of deformation mechanisms involved in the plasticity of AZ31 Mg alloy: in situ neutron diffraction and EPSC modelling, Mater. Sci. Eng. A 496 (1e2) (2008) 14e24. [5] B. Clausen, et al., Reorientation and stress relaxation due to twinning: modeling and experimental characterization for Mg, Acta Mater. 56 (11) (2008) 2456e2468. [6] B. Raeisinia, S. Agnew, A. Akhtar, Incorporation of solid solution alloying effects into polycrystal modeling of Mg alloys, Metall. Mater. Trans. A 42 (5) (2011) 1418e1430. [7] C.H. C aceres, A. Blake, The strength of concentrated MgeZn solid solutions, Phys. Status Solidi (a) 194 (1) (2002) 147e158. [8] A. Akhtar, E. Teghtsoonian, Substitutional solution hardening of magnesium single crystals, Philos. Mag. 25 (1972) 897e916. [9] N. Stanford, M.R. Barnett, Solute strengthening of prismatic slip, basal slip and twinning in Mg and MgeZn binary alloys, Int. J. Plast. 47 (2013) 165e181. [10] B. Raeisinia, S.R. Agnew, Using polycrystal plasticity modeling to determine the effects of grain size and solid solution additions on individual deformation mechanisms in cast Mg alloys, Scr. Mater. 63 (7) (2010) 731e736. [11] N. Stanford, R.K.W. Marceau, M.R. Barnett, The effect of high yttrium solute concentration on the twinning behaviour of magnesium alloys, Acta Mater. 82 (2015) 447e456. [12] N. Stanford, D. Atwell, M.R. Barnett, The effect of Gd on the recrystallisation, texture and deformation behaviour of magnesium-based alloys, Acta Mater. 58 (20) (2010) 6773e6783. [13] N. Stanford, et al., Evaluating the effect of yttrium as a solute strengthener in magnesium using in situ neutron diffraction, Acta Mater. 78 (2014) 1e13. [14] H. Somekawa, C.A. Schuh, Effect of solid solution elements on nanoindentation hardness, rate dependence, and incipient plasticity in fine grained magnesium alloys, Acta Mater. 59 (20) (2011) 7554e7563. [15] J.A. Yasi, L.G. Hector Jr., D.R. Trinkle, First-principles data for solid-solution
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strengthening of magnesium: from geometry and chemistry to properties, Acta Mater. 58 (17) (2010) 5704e5713. nchez-Martín, et al., Measuring the critical resolved shear stresses in Mg R. Sa alloys by instrumented nanoindentation, Acta Mater. 71 (0) (2014) 283e292. D. Catoor, et al., Incipient plasticity and deformation mechanisms in singlecrystal Mg during spherical nanoindentation, Acta Mater. 61 (8) (2013) 2953e2965. T. Guo, F. Siska, M.R. Barnett, Distinguishing between slip and twinning events during nanoindentation of magnesium alloy AZ31, Scr. Mater. 110 (2016) 10e13. T.L. Li, et al., Indentation Schmid factor and orientation dependence of nanoindentation pop-in behavior of NiAl single crystals, J. Mech. Phys. Solids 59 (6) (2011) 1147e1162. N. Stanford, M.R. Barnett, The origin of “rare earth” texture development in extruded Mg-based alloys and its effect on tensile ductility, Mater. Sci. Eng. A 496 (1e2) (2008) 399e408. Z. Wang, et al., Influences of surface preparation on nanoindentation pop-in in single-crystal Mo, Scr. Mater. 65 (6) (2011) 469e472. A. Montagne, V. Audurier, C. Tromas, Influence of pre-existing dislocations on the pop-in phenomenon during nanoindentation in MgO, Acta Mater. 61 (13) (2013) 4778e4786. K.W. McElhaney, J.J. Vlassak, W.D. Nix, Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments, J. Mater. Res. 13 (5) (1998) 1300e1306. F. Siska, et al., Numerical study of stress distribution and size effect during AZ31 nanoindentation, Comput. Mater. Sci. 126 (2017) 393e399. Q. Yu, J. Wang, Y. Jiang, Inverse slip accompanying twinning and detwinning during cyclic loading of magnesium single crystal, J. Mater. 2013 (2013) 8. nchez-Martín, et al., Effect of indentation size on the nucleation and R. Sa propagation of tensile twinning in pure magnesium, Acta Mater. 93 (0) (2015) 114e128. H. Kitahara, et al., Anisotropic deformation induced by spherical indentation of pure Mg single crystals, Acta Mater. 78 (0) (2014) 290e300. C. Zambaldi, C. Zehnder, D. Raabe, Orientation dependent deformation by slip and twinning in magnesium during single crystal indentation, Acta Mater. 91 (0) (2015) 267e288. J.R. Morris, et al., Size effects and stochastic behavior of nanoindentation pop in, Phys. Rev. Lett. 106 (16) (2011) 165502. P. Sudharshan Phani, et al., A stochastic model for the size dependence of spherical indentation pop-in, J. Mater. Res. 28 (19) (2013) 2728e2739. A. Barnoush, M.T. Welsch, H. Vehoff, Correlation between dislocation density and pop-in phenomena in aluminum studied by nanoindentation and electron channeling contrast imaging, Scr. Mater. 63 (5) (2010) 465e468. N. Stanford, M.R. Barnett, Effect of particles on the formation of deformation twins in a magnesium-based alloy, Mater. Sci. Eng. A 516 (1e2) (2009) 226e234. S. Graff, W. Brocks, D. Steglich, Yielding of magnesium: from single crystal to polycrystalline aggregates, Int. J. Plast. 23 (12) (2007) 1957e1978. , (-1 0 1 2) Twinning nucleation mechanisms in J. Wang, J.P. Hirth, C.N. Tome hexagonal-close-packed crystals, Acta Mater. 57 (18) (2009) 5521e5530. J. Wang, et al., Nucleation of a (-1012) twin in hexagonal close-packed crystals, Scr. Mater. 61 (9) (2009) 903e906. L. Leclercq, L. Capolungo, D. Rodney, Atomic-scale comparison between twin growth mechanisms in magnesium, Mater. Res. Lett. 2 (3) (2014) 152e159. , An atomic and probabilistic perspective on J. Wang, I.J. Beyerlein, C.N. Tome twin nucleation in Mg, Scr. Mater. 63 (7) (2010) 741e746. M.R. Barnett, Z. Keshavarz, M.D. Nave, Microstructural features of rolled Mg3Al-1Zn, Metall. Mater. Trans. A 36 (7) (2005) 1697e1704. D.-I.A. Barnoush, Hydrogen Embrittlement, Revisited by in Situ Electrochemical Nanoindentation, 2007. A. Barnoush, Correlation between dislocation density and nanomechanical response during nanoindentation, Acta Mater. 60 (3) (2012) 1268e1277. M. Ghazisaeidi, L.G. Hector Jr., W.A. Curtin, Solute strengthening of twinning dislocations in Mg alloys, Acta Mater. 80 (2014) 278e287. A.C. Fischer-Cripps, in: F.F. Ling (Ed.), Nanoindentation. Mechanical Engineering Series, Springer-Verlag, , New York, 2002. M.R. Barnett, et al., Plastic relaxation of the internal stress induced by twinning, Acta Mater. 61 (20) (2013) 7859e7867.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Initiation of basal slip and tensile twinning in magnesium alloys during nanoindentation Tingting Guo a, *, Filip Siska b, Jun Cheng a, Matthew Barnett a a b
Institute for Frontier Materials, Deakin University, Geelong, Victoria, 3216, Australia Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 513/22, 616 62, Brno, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 June 2017 Received in revised form 26 September 2017 Accepted 11 October 2017 Available online 13 October 2017
The present study addresses the challenge of determining the stress required for the initiation of deformation modes in Mg alloys. Nanoindentation is employed to detect the onset of basal slip and tensile twinning. A Mg-6 wt. % Zn alloy and a series of Mg-Gd binary alloys with concentrations between 0.3 and 4 wt. % Gd are examined in the extruded state. Nanoindentation tests were conducted on {1010} and {1120} crystal planes using a 5 mm radius spherical indenter. It is shown that the initial yielding point in the load trace corresponds to the appearance of basal slip lines on the sample surface. A pop-in event is seen to accompany the appearance of twinning. We find that the addition of Zn strengthens the basal slip but shows mild influence on twin initiation. For alloying with Gd, an impact on basal slip and twinning is only seen at the highest solute levels. A means of examining the alloying effect on twin growth is proposed and revealed that solute Zn has a greater impact on twin growth than initiation. Crown Copyright © 2017 Published by Elsevier B.V. All rights reserved.
Keywords: Nanoindentation Basal slip Twin Magnesium Solute strengthening
1. Introduction Basal slip and {1012} extension twinning frequently dominate the deformation of magnesium and often control yielding [1,2]. Understanding the respective critical resolved shear stress (CRSS) values of these two deformation modes e in the context of a polycrystal - is therefore of practical interest. A considerable range of values exist in the literature for both basal slip [1e4] and extension twinning [1,5]. This evidently reflects alloying effects [6e13] as well as potential variations due to the technique of measurement. The effect of Zn additions on twinning for example are in dispute, one of us has reported that the effect is minor [6] while others report it to be significant [9,10]. Gd has been shown to have a considerable impact on slip [12] whereas its impact on twinning is unknown. There is need for additional experimental clarification, particularly in regard to the separate processes of twin nucleation and growth. In the present work, we explore the extent to which nanoindentation technique can be usefully brought to bear on the problem, for the benefit of understanding rational alloy design for the micro- and nano- scaled structure. Somekawa and Schuh [14] employed cube corner indenter (up
* Corresponding author. E-mail addresses: [email protected], [email protected] (T. Guo). https://doi.org/10.1016/j.jallcom.2017.10.088 0925-8388/Crown Copyright © 2017 Published by Elsevier B.V. All rights reserved.
to loads of 1 mN) to compare the hardness and pop-in stress for a range of fine grained solute strengthened magnesium alloys. It was found that the increments in hardness values due to solute addition (Ca, Zn, Y, Al, Li) qualitatively followed theoretical predictions based on Yasi et al. [15] for basal slip, but fell 1.5 to 3 times higher in magnitude. They found the pop-in stress to be considerably less sensitive to solute addition. However, no distinction was made between deformation modes. Sanchez-Martin et al. [16] have recently taken some steps towards addressing this gap. They used crystal plasticity finite element (CPFE) modelling combined with Berkovich indentation (up to depth of ~300 nm) on electropolished surfaces. CPFE modelling was employed to map out the broad impact of relative CRSS values on the sensitivity of hardness to crystallographic indentation plane. The measurements are seen to be sensitive to the choice of CRSS values only within certain ranges of values. This, compared with the fact that in their model frame work three parameters are needed to describe the hardening for each of the four deformation modes, makes unique determination of characteristic CRSS values problematic. Their study also did not consider deformation twinning. Catoor et al. [17] have examined the apparent CRSS value corresponding to pop-in events seen in their nanoindentation tests. They employed a 3 mm radius spherical tip indenter and examined indentation of three chemically polished crystallographic planes
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using pure Mg single crystals. Twinning was observed in their study but the initial pop-in event was interpreted in each case to be due to slip. Nevertheless, complete rationalization of the pop-in events based on the nanoindentation Schmid factor was not possible. It was concluded, however, that the pop-in event probably corresponded to the homogeneous nucleation of dislocations at stresses between 0.6 and 1.2 GPa. In a previous work, we addressed the issue of associating nanoindentation yielding events with different deformation modes [18]. For Mg alloy AZ31, we found that basal slip and {1012} extension twinning events could be separated for spherical tip indentation (5 mm tip radius) on colloidal silica (OPS) polished planes containing the crystallographic c-axis. Atomic Force Microscopy (AFM) was employed to confirm that the initial yielding event corresponded to the appearance of copious basal slip lines on the surface, which is the onset of the plasticity during penetration. The apparent CRSS for the onset of basal slip for these experiments could be estimated using Hertzian elastic contact theory as [19]:
6Py E*2 p3 R2
!
=
tyielding ¼ S
1
3
(1)
where Py is the load of yielding and R is the indenter radius. E* is the reduced Young's modulus. S is defined as the elastic Indentation Schmid Factor (ISF) and the value is 0.18 for basal slip in {1010} and {1120} indentation [17,18]. Twins on the surface were only seen once a pop-in event had occurred after the yielding. Associating a CRSS value with the twinning event is more difficult in these tests because it relies on the estimation of the stresses under the indenter during plastic indentation immediately prior to the onset of twinning. Finite element crystal plasticity (CPFEM) simulations were employed to establish the relationship between indentation load and the resolved shear stress on twinning plane [18]. This was done for a range of candidate CRSS values for slip and the mean was recorded. With this relationship in hand, it is possible to convert the load corresponding to the pop-in to an estimate of the corresponding resolved shear stress on the most heavily stressed twinning system. The present study employs nanoindentation on planes containing the crystallographic c-axis in an attempt to discern the sensitivity of the CRSS values corresponding to the onset of basal slip and twinning to the addition of Zn and Gd to pure Mg. Our first objective is to verify that our previous findings, made on alloy AZ31 [18], hold for Mg alloys in general (i.e. that the yielding is due to slip and the following pop-in is due to twinning).
2. Materials and experimental method Cast Mg-6Zn billets (F ¼ 59.5 mm and h ¼ 40 mm) were solution treated at 335 C for 72 h and quenched in water. The billets were then extruded to plates 46 mm wide and 12 mm thick at 370 C and a ram speed of 0.1 mm/s. Samples for nanoindentation tests were annealed at 340 C for 3 h. Four magnesium alloys containing 0.3, 1, 2.5 and 4 wt. % Gd were cast and cut into billets measuring 59.5 mm 40 mm for extrusion. All the billets were homogenized at 450 C for 3 h. The extrusion schedule included preheating the billets at 400 C for 2 h, followed by extrusion at 400 C at a ram speed of 0.5 mm/s. The samples prepared for nanoindentation tests were annealed at 450 C for another 3 h. Asreceived cast pure Mg billets with a diameter of 29.8 mm and height of 20 mm were extruded into rods 8 mm in diameter at 370 C at a strain rate of 15 mm/s. The samples were immediately annealed at 450 C for 2 h followed by a water quench. The
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Table 1 Chemical composition of the materials in the present study (wt. %). Material
Zn
Gd
Mn
Mg
Mg-6 Zn Mg-0.3 Gd Mg-1Gd Mg-2.5 Gd Mg-4 Gd Pure Mg
6% e e e e 0.006%
0.0415% 0.304% 1.09% 2.51% 4.08% e
0.036% 0.0182% 0.0178% 0.0162% 0.0153% 0.0345%
balance balance balance balance balance 99.7%
chemical compositions of all the materials used in the study are given in Table 1. The dimension of the samples used for nanoindentation was 10 mm 10 mm 5 mm. The large surface was cut to be perpendicular to the extrusion direction, which was then selected as the testing surface. Similar to the previous experiment carried out on AZ31 in Ref. [18], all the tests were performed on planes within 5 of the {1010} and {1120} crystal planes. EBSD was employed on a pre-marked area to obtain the grain orientation data and the initial crystallographic texture (Fig. 1) by a field emission Leo 1530 Scanning Electron Microscope. The textures for pure Mg and Mg-6Zn were typical for extruded magnesium alloys with the basal planes aligned perpendicular to the extrusion direction. The texture in the Mg-Gd series alloys agreed with reference [20]. The <1121> texture increased with Gd addition. The testing surfaces for EBSD mapping were first wet ground using 1200 grit SiC paper, cleaned in ethanol in an ultrasonic bath and dried with flowing air. Then, 9 mm, 6 mm and 3 mm diamond suspensions were used for rough polishing on a Struers DP-Pan cloth, followed immediately by etching in acetic-nitric acid (15 ml acetic acid, 5 ml nitric acid, 60 ml ethanol and 20 ml distilled water) for 20 s. Samples for EBSD mapping were polished with 10% of OPS (colloidal silica) for 10 min in the middle of a Struers OP-chem cloth at a rotating speed of 150 r/min. Before the nanoindentation tests, samples were polished another 3 min with OPS and 2 min with ethanol. The purpose for this step is to get rid of the oxidation film and clean the colloidal silica thoroughly. Two to seven grains were selected for each orientation, depending on the grain size and quantity of {1010}w and {1120} oriented grains on the polished surface. Nanoindentation tests were conducted using a UMIS ultramicro indentation system (UMIS is the name of the machine manufactured by CSIRO Division of Applied Physics, Lindfield, Australia). A 5 mm radius diamond spherical tip are conical shaped with a spherical end, which were employed in the present work. Tests were performed under the closed loop control, ensuring reproducible and stable results. The loading rate was around 0.015 ± 0.005 mN/s (There is no influence of rate on the experimental results over this range.) The maximum applied load is 5 mN. On the indented surface, the grain boundaries are avoided (within ~10 indent diameters). Some tests were interrupted once the yielding or pop-in event was observed. The deformation around the indents was characterized using a Brucker Multimode 8 Atomic Force Microscopy (AFM) in the PeakForce error mode and analysed by software ‘NanoScope Analysis’. The occurrence of yielding and the pop-in events is sensitive to the surface damage caused by polishing [21,22]. Mechanical polishing can alter the dislocation density in the near-surface zone. We therefore examined the influence of mechanical polishing time on the yielding and pop-in load in a large grain in pure Mg. The tests were first carried out for chemical polished condition (60% ethanol, 20% distilled water, 5% nitric acid and 15% acetic acid for 5 min). It was found that a pop-in is the first and only event in 90% of the curves, which is consistent with the behaviour commonly seen in
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Fig. 1. EBSD maps with inverse pole figure colour and inverse pole figures referring to the extrusion direction for (a) pure Mg, (b) Mg-6Zn (c) Mg-0.3Gd (d) Mg-1Gd (e) Mg-2.5Gd (f) Mg-4Gd.
chemical and/or electropolished samples [17]. Subsequent OPS polishing for different times led to yielding as the first event and this was followed by a pop-in. As shown in Fig. 2, the difference of the yielding and pop-in load is quite small for the four polishing states, implying that polishing using OPS for up to 60 min generates a repeatable result. To correlate the indentation load with the resolved shear stress for the most heavily stressed {1012} twinning system, single CRSS values for the different slip systems were employed to fit the loaddepth curves before the pop-in event. Due to complexities relating to size effects [23], strain hardening was not introduced into the simulations. The fitted CRSS values reflect an effective value, applicable to the indenter shape and size employed. The actual values depend on the choice assumed to be basal (CRSS range: 20 MPae100 MPa), prismatic (CRSS range: 100 MPae150 MPa) and 2nd order pyramidal
results are shown in Fig. 3. The estimated twinning RSS is sensitive to the onset and extent of prismatic slip CRSS and this impacts upon both the slopes of the upper and lower limits and changes in these slopes with increasing load (see also [24]). The resolved shear stress can be approximated by a power law with an exponent of 1/3 (see Discussion). This, incidentally, is also the case for Hertzian contact, as evident in Equation (1). Due to the unknown values of the critical stresses for the slip systems, the apparent twinning CRSS reported for alloys in this paper is accurate to ~ ±15%. 3. Results 3.1. Deformation during nanoindentation in Mg-6Zn alloy To illustrate the basic features of the present nanoindentation tests and to verify the relationship between yielding events on the flow curve and the appearance of deformation activity on the
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are only observed once a pop-in event is observed in the load curve (Fig. 4 (b) and (c)). It is also seen that the selected twin variants for {1120} and {1010} indentation show different morphologies. One edge of the twin present after {1010} indentation is parallel to the basal plane traces while the twins are seen to extend at an angle to the basal traces in the case of {1120} indentation. This is quite consistent with the expected active twin variants [25,26]. The twin morphology seen here is also consistent with that observed by Kitahara et al. [27]. Interestingly, the basal slip lines in some cases can be seen to extend up to 15 mm from the indent impression, in the direction of the c-axis. A similar observation was reported by Zambaldi et al. [28]. This testifies to the existence, at certain locations in the structure, of easily activated dislocation sources. Fig. 5 presents a cumulative frequency plot of yielding and pop-
Fig. 2. Influence of mechanical polishing time on yielding and pop-in load tested in the same grain in pure Mg.
in loads on selected {1010} and {1120} oriented grains for Mg-6Zn. Data for pure Mg and AZ31 [18] are also given for the purpose of comparison. Each curve represents data from 3 to 7 grains. For yielding, the width of the distribution reflects the stochastic nature of the process [29,30]. The shape of the distribution curves also varies somewhat and this can be understood in terms of a higher than expected grain-to-grain variation encountered in the study. For yielding, the two crystallographic planes subjected to indentation show no systematic difference in load range. This is consistent with the idea that yielding is dominated by basal slip; the orientation factor for which is the same for {1010} and {1120} indentation. As expected, both AZ31 and Mg-6Zn show higher yielding loads than pure Mg. The pop-in load, on the other hand, shows an orientation dependence. The pop-in loads for {1120} indentation are higher than those for {1010} indentation. This is consistent with the difference in indentation Schmid factors for the twinning mode in Hertzian contact (0.297 for {1120} indentation and 0.306 for {1010} indentation). However, as noted above, plasticity due to slip is present prior to twinning. The simulated resolved stresses in Fig. 3 do predict that twinning during {1010} indentation should be activated under lower loads than {1120} indentation, but only for loads below a critical value. The difference between {1010} and {1120} in CPFE is not as stark as seen in experiment and this may be due to stress variations arising from the localized nature of slip, which is evident in the AFM images but which is not captured in the CPFE simulations. The pop-in loads also reveal strengthening in AZ31 and Mg-6Zn compared to pure Mg.
3.2. Deformation during nanoindentation in Mg-Gd alloys
Fig. 3. CPFEM simulation results showing the relationship between the max RSS on twinning plane and the indentation load [18]. The dashed line shows a power law to the exponent of 1/3 fitted between the upper and lower bounds.
sample surface, Fig. 4 shows representative load-penetration depth curves and corresponding AFM images of indents for the Mg-6Zn alloy. Indents on a {1120} plane are shown in Fig. 4 (a) and (b) and those on a {1010} plane are given in Fig. 4 (c). As expected, the initial part of the curve follows the Hertzian elastic contact prediction. A reduced Young's modulus of 42 GPa is fitted to the initial elastic stage and this is employed to locate the load corresponding to the initiation of basal slip. The behaviour is similar to that observed previously in AZ31 [18]. Basal slip is the only deformation mode seen for load curves without a pop-in event (Fig. 4 (a)). Twins
Representative load-penetration depth curves and corresponding AFM images for Mg-1Gd are displayed in Fig. 6. Fig. 6 (a) and (b) show the case of {1120} indentation. It is observed that only one twin was formed when the pop-in occurred at around 0.8 mN. Two twins were nucleated at the higher pop-in load of 1.6 mN and it is possible the two twins formed during the single pop-in, as no second pop-in was observed in this instance. Fig. 6 (c) and (d) show two cases of {1010} indentation with similar pop-in loads (0.6 mN and 0.8 mN). The difference between the two cases is the extent of indentation following the pop-in. With increasing indentation, the twin clearly extends and thickens. Indentation data for the most concentrated Gd alloy (Mg-4Gd) studied in the present paper are shown in Fig. 7. In the case of {1120} indentation, pile-up of material on one side of the indent can be seen (Fig. 7 (a) and (b)). Surface mapping (not shown here) reveals the convex nature of the pile-up. The indentation in Fig. 7 (a)
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Fig. 4. Load-penetration depth curves and corresponding AFM images of the indents for alloy Mg-6Zn indented on (a) (b) {1120} plane and (c) {1010} plane showing “yielding” and “pop-in” behaviours.
Fig. 5. Yielding and pop-in loads for Mg-6Zn, along with data for pure Mg and AZ31 for comparison.
also shows a particularly high level of penetration without triggering twinning. This, along with a uniformly round imprint, suggests the operation of copious slip on different systems despite the absence of clear slip lines. Extension twins can be seen following the pop-in at 15.9 mN (Fig. 7 (b)). Additional slip lines close to the tip of the twin can also be seen in Fig. 7 (b). These are perpendicular
to the basal slip lines in matrix but look similar to the basal slip lines and traverse the twin-matrix boundary. We interpret this as an indication of basal slip within the twin. After removal of the load, shrinkage of the twin is presumed to have occurred, leaving behind surface slip steps formed by basal slip in the twin. Fig. 7 (c) and (d) show {1010} indentation with features similar to those seen in the
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Fig. 6. Load-penetration depth curves and corresponding AFM images of the indents for Mg-1Gd alloy indented on the (a) (b) {1120} plane and (c) (d) {1010} plane showing “yielding” and “pop-in” behaviours.
Fig. 7. Load-penetration depth curve and corresponding AFM images of the corresponding indents for alloy Mg-4Gd indented on (a) (b) f1120g plane and (c) (d) {1010} plane showing “yielding” and “pop-in” behaviours. The enlarged image of slip lines close to the twin tip in (b) is also shown in top left corner.
cases discussed above. The effect of Gd on yielding and pop-in load is summarized in Fig. 8. In the case of yielding, little effect of orientation is evident except in Mg-4Gd. For twinning, a greater effect is seen. In a number of cases low numbers of successful readings were obtained on the {1010} plane and we bracket conditions with <10 successful readings, for further analysis. 4. Discussion Basal slip and {1012} extension twinning are the two plastic
deformation modes seen to be dominant in all the alloys in present study for both {1120} and {1010} indentations. As pointed out in the Introduction, this is as expected; these are the two most readily activated deformation modes in magnesium alloys. Due to the mechanical OPS polishing employed in the study, the onset of basal slip is marked not by a pop-in Ref. [17] but by gradual yielding, presumably due to the activation of pre-existing sources introduced during the OPS polishing [21,31]. That these sources are present at a reasonably consistent number density is testified by the absence of OPS polishing time on the yielding response for pure Mg up to 60 min of polishing. Twinning on the other hand is
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Fig. 8. Yielding and pop-in load variation for Mg-Gd alloys.
typically associated with a significant energy release and so it manifests itself clearly in the present experiments via a pop-in event. The association of twin observation after a pop-in event was observed in 51 separate indents and the presence of slip lines only for cases of no pop-in observation was seen on all 18 cases where we examined the surface of no pop-in indents using AFM. We do not claim that non-basal slip is not active in these tests (perhaps in small amounts or under the indenter). As was noted above, in the high Gd alloy, the observed deformation is suggestive of multiple slip modes (Fig. 7 (b)). Nevertheless, basal slip is the only detectable slip mode and we proceed assuming that its onset controls the yield point.
4.1. Glide stresses The apparent CRSS for basal slip corresponding to the onset of yielding (established using Equation (1)) in Mg-6Zn is plotted in Fig. 9 (a) along with values for pure Mg and AZ31 [18]. The absolute values are considerably higher than those reported in other studies using conventional ‘macro’ test techniques [1e4,32,33]. The difference is over an order of magnitude compared to polycrystal and up to two orders of magnitude for the pure Mg compared to single crystals. However, the basal CRSS values obtained by Catoor et al. [17] for indentation on {1010} on chemically polished single crystal Mg, are ~3 times higher than our values. Thus, while we have
Fig. 9. The CRSS of basal slip for (a) Mg-6Zn and (b) Mg-Gd alloys. The error bars represent one standard deviation. The markers for the two orientations are artificially separated for clarity.
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shows the addition of 4 wt. % of Gd gives rise to an increase in CRSS for basal slip initiation of ~60 MPa. In sample Mg-4Gd, a pile-up was observed adjacent to the indenter and it was noted above that other non-basal systems are quite likely operative following yielding. Furthermore, our CPFE modelling employed previously to establish the stresses immediately prior to the onset of twinning relied on the activation of some non-basal slip close to the yield surface. To assess if there are any obvious effects of non-basal slip on the relation shown in Fig. 3, the load-displacement curves are compared in Fig. 10 by plotting points corresponding to twin onset. Note, these values reflect an arbitrary choice of a point on the load displacement curve for each test in lieu of comparing entire curves, which would be too unwieldy to do graphically. The data in Fig. 10 fall remarkably along a common curve showing, rather surprisingly, that no obvious effect is present. Any changes in slip stresses in the present case are clearly too minor to be detected on the load trace. It is worth noting though that CPFEM simulations show a ‘robustness’ in the load trace to changes in CRSS values for basal and prism slip [24], presumably due to the significant role played by the elasticity of the material surrounding the plastic zone. 4.2. Twinning stresses
Fig. 10. Plot of pop-in load and the penetration depth when pop-in occurs for pure Mg and Mg-4Gd for {1120} and {1010} indentations.
introduced dislocation sources during OPS polishing, deformation may still be considered to be source controlled. Yielding, while gradual, is still subjected to the challenge of finding dislocation sources to activate within the relatively small highly stressed zone under the indenter. Fig. 9 (a) shows that the CRSS values for the initiation of basal slip increase by ~45 MPa for each of AZ31 compared to pure Mg and then Mg-6Zn compared to AZ31. Fig. 9 (b)
Fig. 11 (a) shows the apparent CRSS for twin initiation, based on the pop-in observed in the load-displacement curves. The CRSS value is established from the maximum resolved shear stress using Fig. 3, which is based on CPFE modelling [18]. This stress represents the condition under which both twin nucleation and propagation occurs. If one defines nucleation as the process by which a twin capable of rapid propagation is formed, then it is reasonable to associate the stress of ‘twin initiation’ with that of twin nucleation. In the present case, we are not entirely sure where in the stress field twin nucleation takes place so by presenting the maximum value of the twin initiation CRSS we note that it is an upper limit of the stress required for nucleation.
Fig. 11. Twin CRSS for (a) Mg-6Zn and (b) Mg-Gd alloys. The error bars represent one standard deviation. For a better observation, the markers for the two different orientations are slightly separated.
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Fig. 12. (a) Relation between twin thickness t measured in AFM images and the pop-in depth for {1010} indentation for all the materials studied. The proposed model d ¼ gt=2 is shown as the dashed line. The difference between the measured thickness and the model is defined as Dt, as shown in the figure. (b) Plot of jDtj and the penetration depth after the pop-in event. The fitted dash line through the data points is a guide for eyes.
It is clear that the stress increments arising from alloying addition in Fig. 11 are greater compared to those for basal slip. The alloy Mg-4Gd shows a similar twinning strength to AZ31. The Mg6Zn alloy does not display relative hardening compared to AZ31 as it does for basal slip. This reveals a weak potency in the ability of Zn to harden against twin formation, something that has been pointed out previously [9]. The higher hardening effect against twinning in AZ31 is probably influenced by the presence of particles and not to solute effects alone.
4.3. Analysis of the pop-in We have shown that the pop-in is caused by a twinning event. Thus it should be possible to relate the dimensions of the twin measured on the indented surface with the pop-in depth, d. A simple approximation can be made for the case of {1010} indentation where the active twin mode forms on a plane approximately 45 deg. to the sample surface. It is assumed that twinning is associated with the glide of twinning dislocations/disconnections along
Fig. 13. Relation between pop-in load and pop-in depth for (a) {1010} indentation and (b) {1120} indentation for materials investigated in present study. The dashed lines show the linear relation between the pop-in load and the depth for pure Mg and Mg-6Zn.
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the twin boundary [34]. The twinning disconnections are characterized as a step (h ¼ two crystal planes high in the present case [35]) with a Burgers vector, bT [36] (~0.05 nm [37]). The pop-in pffiffiffi depth should be approximately nbT/ 2 where n is the number of twinning dislocations that have passed over the twin interface, each thickening the twin by h. The thickness of the twin is thus nh pffiffiffi but on the surface plane the apparent twin thickness, t, is 2nh. Because the twinning shearg, is bT/h (¼0.13) we can write the following for the pop-in depth:
tg d¼ 2
(2)
where t is the thickness of the twin apparent on the sample surface. Fig. 12 (a) plots measured values of the twin thickness for {1010} indentation measured on AFM images against the pop-in depth. Equation (2) is also shown for comparison. The correlation is in reasonable agreement with Equation (2) but there are a few outlying points. We suspect the outlying points are, at least in part, due to either twins shrinking during release of the load (see e.g. Ref. [38]) or to twins being thickened by further increase of the load; events that were noted earlier. To test this, Fig. 12 (b) plots the difference Dt between the model and our measurements against the depth of continued penetration between the end of pop-in and the end of the test. This provides a rationale for most of the wayward points in Fig. 12 (a). The present phenomena are expected to be quite sensitive to surface inclination and roughness and it is possible that, despite our care, this may be an issue for one or two points in this figure. Nevertheless, one can see that the magnitude of the pop-in depth can be rationalized reasonably well by Equation (2). Finally, we turn to the relationship between the pop-in depth and the load. In the literature, it is not uncommon for a linear relation to be found between these two variables [39,40]. In the present case (Fig. 13) there is considerable scatter, particularly for the richer alloys. However, the leaner alloys display a reasonably tight linear trend. The pop-in depth is larger for {1010} indentation than for {1120} indentation at a given load and this is probably a reflection of the more favourable orientation of the twin planes in the {1010} indentation. The increased scatter in the case of {1120} indentation might be due to different or simultaneous twin variants forming. Nevertheless, a decrease in slope of the relationship between load and pop-in depth can be detected for increasing alloying addition for both crystal orientations. This indicates that for a constant load, a richer alloy will tend to display a shallower pop-in depth. Our interpretation for this is that with higher alloying addition, the effective friction stress on the twinning dislocations (see Ref. [41]) increases. This leads to greater levels of dissipation during the twinning event and therefore a smaller pop-in depth. The effect is clear here for Zn addition and this is rationalized in the following. We assume an ideal disk-shaped twin as a first approximation. Equation (2) can then be re-written in terms of the twin diameter, l, and aspect ratio, q, as:
d¼
glq 2
(3)
We make a further first approximation that the twin diameter is set by the distance from the surface to the stress contour equivalent to the twin friction stress tc . This is an under estimate. The twin is likely to propagate further into the stress field driven by the higher stresses near the indenter. However, the distance of propagation is still be expected to scale similarly with the level of the stress contours and the friction stress. To obtain an approximate value, we
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inspect Hertzian [42] and plastic [24] stress fields and note that in both cases, for depths greater than the contact radius, a, the shear stress contours on the symmetry axis (i.e. directly below the indenter) can be given approximately as:
t tmax
z 32 a
(4)
where z is the distance below the surface. We can thus write l as:
2 tmax 3 l¼a
tc
(5)
This expression can be completed using the definition of pffiffiffiffiffiffiffiffiffiffiffiffi indentation hardness, a ¼ P=pH (where the hardness is that for slip dominated flow prior to the twinning pop-in) and the power law approximation in Fig. 3 (tmax ¼ kðPE2 =R2 Þ1=3 where the dimensionless parameter k contains potential further dependencies on E and R e note, the expression has only been validated for the present indenter radius of 5 mm). The twin aspect ratio, q, for magnesium can be established from an Eshelby inclusion analysis and is given as [43]:
q¼
1 tmax tc 1 tmax 2 2 gG gG
(6)
Combining, we arrive at the following:
d¼
k5=3 P 19=18 E 10=9 pffiffiffiffiffiffiffi 2=3 R 4G pH tc
(7)
This expression agrees more or less with experiment in its near linear dependency on P. The dependency on friction stress e i.e. to the power of 2/3 - is dictated by the stress field away from the indenter and this result, as noted above, is general; it is also obtained if one repeats the analysis for Hertzian contact. In Equation (7), the pop-in depth also depends upon the hardness prior to the pop-in. The consistency of the load-depth traces in Fig. 10 suggest only modest variations in hardness amongst the present samples. Additional tests were carried out to verify this for pure Mg and Mg-6Zn and the respective hardness were found to be 650 and 1000 MPa. According to Equation (7), this difference corresponds to a decrease in pop-in depth of ~1.25 times. Inspection of Fig. 13 (a) reveals a drop in pop-in depth of ~3 times with 6% Zn addition. Assuming this is due to a change in the critical stress for twin thickening, Equation (7) returns a change in twin friction stress of ~3.7 times. This is a considerably greater effect than that seen for twin nucleation, where the increase in critical stress for twin thickening upon Zn addition is seen to be approximately 1.25 times.
5. Conclusions 1. It is verified that for indentation on {1010} and {1120} planes gradual yielding is due to dislocation glide characterized by distinct basal slip lines on the surface and the following pop-in is caused by the initiation of extension twinning. This is generally true for all Mg alloys studied. 2. The stresses for basal slip initiation can be estimated using a Hertzian analysis, which enables the critical indentation load to be converted into a critical resolved shear stress. CRSS values for tensile twinning require simulation of the stress field prior to twin initiation. CPFEM was employed to establish a relationship between load and the max resolved shear stress on the twinning planes.
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3. 6 wt. % Zn was found to harden basal slip with an increment approximately twice that seen for alloy AZ31 compared to pure Mg. The addition of 4 wt. % Gd hardened the initiation of basal slip by a similar amount as seen in AZ31. 4. Twin nucleation in Mg-6Zn was hardened (compared to pure Mg) less than that for alloy AZ31 and Mg-4Gd. 5. A simple geometrical model was developed to describe the relation between the measured twin thickness on the {1010} planes and the corresponding pop-in depth. Outlying data points can be explained by twin shrinkage during unloading and thickening during continued penetration. 6. A model was developed to explain the alloying effect on twin growth using the depth of the pop-in. The addition of Zn is shown to have a greater effect on twin thickening compared to nucleation. Acknowledgments The authors would like to thank David Grey, Jayant Jain, Steven Babaniaris, Lynton Leigh and Aiden Beer for their assistance with the material preparation and extrusion in this work.
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