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Hardness and shear band evolution in bulk metallic glasses after plastic deformation and annealing
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Acta Materialia 56 (2008) 5202–5213 www.elsevier.com/locate/actamat
Hardness and shear band evolution in bulk metallic glasses after plastic deformation and annealing q S. Xie a, E.P. George a,b,* a
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
b
Received 30 September 2007; accepted 2 July 2008 Available online 11 August 2008
Abstract Strain-induced hardening and annealing-induced softening are typical in crystalline metals. Bulk metallic glasses (BMG) exhibit the opposite behavior, namely, strain-induced softening and annealing-induced hardening. In addition, reversible softening–hardening–softening occurs in a BMG subjected to a three-step deformation–annealing–deformation process. The hardness changes after deformation and annealing can be correlated with the shear band patterns around/underneath Vickers indents. Shear bands produced during indentation of as-cast BMG are semicircular and radial, consistent with the stress distribution beneath the indenter. In contrast, the shear bands in the pre-strained BMG are irregular and convoluted, and appear to be a mixture of the shear bands produced during the prior compression and those in the as-cast BMG. After annealing, the shear bands tend to recover their semicircular and radial shapes consistent with the annealing-induced hardening. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Metallic glasses; Plastic deformation; Shear bands; Hardness; Annealing
1. Introduction Metallic glasses have interesting properties, including high strength, high elastic limit (2%) and good corrosion resistance [1–4]. However, their high strength is often accompanied by limited plastic deformation (<2%) at low homologous temperatures (relative to the glass-transition temperature Tg). Metallic glasses undergo plastic deformation by the nucleation and propagation of shear bands [5]. In uniaxial tension and compression, once a few shear bands are formed, plastic deformation remains highly localized there, which prevents the generation of new shear bands and makes the existing shear bands propagate rapidly through the samples, resulting in catastrophic failure q This article was presented at the Symposium on Phase Stability and Defect Structures in Honor of Professor Austin Chang, held in Orlando, FL, February 28–March 2, 2007. * Corresponding author. Address: Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA. E-mail address: [email protected] (E.P. George).
[5–7]. This shear localization appears to be a result of strain softening, which has been observed to occur in heavily deformed metallic glasses [8–11]. This behavior contrasts sharply with the strain hardening typically seen in crystalline materials, which tends to produce more uniform plastic deformation [12]. To characterize the response of bulk metallic glasses (BMG) to plastic deformation, some researchers have performed indentation tests and examined the deformation zones around/underneath the indent. Pile-ups and incomplete circular shear bands have been observed around the perimeters of Vickers [13,14], Berkovich [10,15,16] and spherical [17,18] indents. Several sets of shear bands that looked like slip lines were observed beneath a Vickers indenter and explained using slip-line field theory [19]. However, in many other experiments, roughly semicircular shear bands were observed which are not predicted by the slip-line theory. These bands and their associated hemispherical plastic zone beneath the Vickers indent were explained using the expanding cavity model [13,14].
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.07.009
S. Xie, E.P. George / Acta Materialia 56 (2008) 5202–5213
Finally, nearly symmetrical radial shear bands were observed beneath a cylindrical indent and shown to be consistent with the numerically simulated shear band pattern [20]. None of these studies addressed deformation behavior and shear banding in pre-strained BMG, although it is generally thought that pre-existing shear bands are preferred sites for subsequent deformation [5,21]. The detailed structure of shear bands, which accommodate plastic deformation in metallic glasses [8,22,23], is not known. Certain structural changes, such as an increase in free volume after plastic deformation [24–26], and a decrease in free volume after annealing at temperatures below Tg [27–30], have been observed in shear bands. However, only limited information is available on the effects of annealing on the hardness of pre-strained BMG. To the authors’ knowledge, the only available data are those of Jiang et al. [10], who showed that the hardness of 45.5% cold-rolled Al–Ni–Y amorphous ribbon (22 lm thick) increased from 3.48 to 4.05 GPa after annealing at 110 °C for 1 h. Systematic investigations have yet to be performed on the effects of annealing temperature and time on the hardness of pre-strained BMG and the structural relaxation of shear bands. In this paper, the hardness response of metallic glasses after plastic deformation and annealing below Tg is investigated. The evolution of hardness is correlated with shear band patterns around/underneath indents. The observed shear band patterns show the role of pre-existing shear bands in subsequent deformation and indicate the structural relaxation of shear bands upon annealing. 2. Experimental procedures Bulk metallic glass of composition Zr–10Al–5Ti– 17.9Cu–14.6Ni (at.%) [6,31] was prepared by arc melting the elemental constituents in argon atmosphere, followed by drop casting into cylindrical Cu molds measuring 6.7 mm in diameter and 72 mm in length. Before being drop cast, the arc-melted buttons were flipped over and re-melted five or six times to enhance compositional homogeneity. The amorphous structure of the specimens was confirmed by X-ray diffraction (XRD) and differential scanning calorimetry (DSC) at a heating rate of 20 K min1. Disc-shaped specimens 3.5 mm thick were cut transverse to the long axis of the drop-cast rods using electric-discharge machining (EDM). Some of these specimens were compressed at room temperature (up to 80% plastic strain) using a servo-hydraulic machine (MTS 8100) at an engineering strain rate of 1 103 s1. The plastic strain is defined here as ep = (l0l)/l0, where l0 and l are specimen thicknesses before and after compression. The as-cast and plastically deformed samples were annealed in vacuum (5 106 Torr) for times up to 16 h at 373, 473 and 633 K (all of which are lower than the glass-transition temperature for this BMG, Tg = 663 K). Some of the annealed samples were compressed again to explore reversible softening in metallic glasses. After anneal-
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ing, the samples were polished with SiC paper through 600 grit and then with 0.5 lm Al2O3 to obtain a mirror finish. Vickers hardness tests were conducted on the polished surfaces using a Buehler Micromet 2001 microhardness tester (1000 g load and 20 s holding time). The perimeters of the indents were examined using interference optical microscopy (IOM) and optical microscopy (OM). To reveal shear band patterns underneath hardness indents, the bonded interface technique has typically been used in the past [13,14,18–20,33–35]. Here, the use of an adhesive at the interface is eschewed, and two pieces of BMG are simply clamped with surfaces that have been polished to a mirror finish. When the two halves are separated after indentation, they reveal more clearly the correlation between the shear-band morphology and the indentation/ compression stress fields than if an adhesive had been used. The entire assembly, including vice and tightly clamped samples, was cold-mounted in epoxy resin, and a surface transverse to the clamped interface was ground through 600 grit SiC and polished with 0.5 lm Al2O3 to a mirror finish. Vickers indents (using a 1000 g load and 20 s hold time) were made at the interface and away from the interface. In the former case, two different orientations were chosen with the indenter diagonal either parallel to the interface (Fig. 1a) or at 45° to the interface (Fig. 1b). At the clamped interface, the gap between the two halves was 2–4 lm, which was smaller than the 6-lm gap reported for the bonded interface technique [14]. No further separation between the two halves was observed for the indentation load (1000 g), indicating that the interface remained tightly clamped. After indentation, the clamped assembly was extricated from the epoxy resin, and the vice unclamped to separate the two halves. The indents that were made at locations away from the interface were examined using IOM and OM. The shear bands at the interface (underneath the indents) were examined by scanning electron microscopy (SEM) and atomic force microscopy (AFM). 3. Results 3.1. Effect of plastic deformation and annealing on the hardness of metallic glasses The effects of compressive plastic strain (ep) and subsequent annealing on hardness (H) are shown in Fig. 2. The hardness of the deformed BMG (square symbols) decreases linearly with increasing plastic strain. Using earlier results [8], namely that the shear band spacing (d) decreases linearly with increasing plastic strain (d1 = 0.14ep), the hardness decrease shown in Fig. 2 may be expressed as a function of shear band spacing as follows: 1 H ¼ H m A1 ð1Þ d where Hm is the hardness of as-cast BMG, and A1 is a proportionality constant equal to the softening induced by
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Fig. 1. Top-surface view of Vickers indents made at clamped interfaces between polished BMG specimens: (a) indenter diagonal parallel to the interface; (b) indenter diagonal at 45° to the interface.
shear bands that are spaced 1 lm apart. Upon annealing, the hardness of the deformed BMG increases (Fig. 2), which may be expressed as follows: 1 H anneal ¼ H anneal 0 A2 ð2Þ d where Hanneal_0 is the hardness of the as-cast glass after annealing, and A2 is another proportionality constant (A1 > A2). By combining Eqs. (1) and (2), the change in hardness upon annealing is obtained as: DH ¼ H anneal H ¼ ðH anneal 0 H m Þ þ ðA1 A2 Þ
Fig. 2. Effect of compressive strain and subsequent annealing on the Vickers hardness of Zr52.5Al10Ti5Cu17.9Ni14.6 bulk metallic glass as a function of (a) time and (b) temperature.
1 d
ð3Þ
After annealing at 373 K for 2 h, it is seen that Hanneal_0 Hm, which yields an inverse relationship between the hardness change and shear band spacing, DH / d1. That is, hardness recovers much faster in the more heavily deformed specimens (containing closely spaced shear bands) than in the lightly deformed ones. Note that the hardness recovery can occur at a relatively low temperature (373 K) compared with the Tg for this BMG (663 K) and at relatively short times (2 h). With increasing annealing time (Fig. 2a) and temperature (Fig. 2b), there is a further increase in Hanneal_0, but relatively little change in the slope A2. This means that once the hardness recovers to Hm, the amount of pre-strain (i.e., shear band density) has little effect on any further hardness increase, in contrast to the DH / d1 relation that was obtained for annealing at 373 K for 2 h. The extent to which the above annealing treatments produce irreversible changes in the strain softening behavior was investigated next. For this, BMG specimens that had already undergone a compression and annealing cycle were re-compressed (see Table 1 for the specimens and their processing conditions). Table 2 shows the amount of compressive strain (per cent reduction in thickness) that was possible during the second deformation cycle for various annealing temperatures and times. In general, the BMG
S. Xie, E.P. George / Acta Materialia 56 (2008) 5202–5213 Table 1 Identifications of specimens subjected to different deformation and annealing steps Sample name
Processing
D33 D50 D50A373 D50A473 D50A633 D33A373 D33A473 D33A373D
33% plastic 50% plastic 50% plastic 50% plastic 50% plastic 33% plastic 33% plastic 33% plastic strain D33A473D 33% plastic strain
strain strain strain + annealed strain + annealed strain + annealed strain + annealed strain + annealed strain + annealed
at at at at at at
373 K 473 K 633 K 373 K 473 K 373 K
for for for for for for
2h 2h 2h 2h 2h 2 h+33% plastic
strain + annealed at 473 K for 2 h+33% plastic
Table 2 Effects of annealing treatments on the compressive strain to failure in the second deformation step of a deform-anneal-deform process Annealing time (h)
2 4 16
Temperature 473 K
573 K
633 K
– >50% 50%
– 50% <5%
<5% – –
became more brittle the higher the annealing temperature and time. After annealing at 633 K, the material could not be compressed more than 5%. Significant compression (50%) was possible after annealing at 473 and 573 K, provided the annealing times were kept below 16 and 4 h, respectively. Although it is not listed in Table 2, extensive compression (>50%) was possible after 16 h anneals at 373 K. Table 3 summarizes the hardness changes in the BMG specimens subjected to a three-step deformation–annealing–deformation process. Consider specimen D33A373D (Table 1), which was deformed (ep = 33%), annealed (373 K for 2 h) and deformed again (ep = 33%). As shown in Table 3, it has the same hardness (567 HV) as specimen D33 (569 HV), which started out in the as-cast state and was compressed just once (Table 1). That is, the hardness returns to the same value after the second compression cycle as after the first. To the authors’ knowledge, this is the first time that such a reversible strain softening behavior has been observed in a metallic glass. Next, consider specimen D33A473D (Table 1), which was deformed (ep = 33%), annealed at a higher temperature (473 K for 2 h) and deformed again (ep = 33%). This specimen has a
Table 3 Hardness of our BMG after various processing steps Specimen
Hardness (HV)
Specimen
Hardness (HV)
As-cast D33A373 D33A473
596 593 627
D33 D33A373D D33A473D
569 567 598
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hardness of 598 HV, which is higher than that of specimen D33 (569 HV) which was compressed only once. However, if one compares the degree of compression-induced softening after annealing at 373 and 473 K, that is the decrease in hardness between samples D33A473 and D33A473D, on the one hand, and samples D33A373 and D33A373D, on the other, the softening in both cases is 5% for ep = 33%. 3.2. Shear band patterns induced by micro-indentation 3.2.1. Top surface Fig. 3a shows a top-surface view of a 1000-g Vickers indent in the as-cast sample. There are incomplete circular shear bands around the edges of the indent but no cracks, including at the corners. Surface profilometry using IOM along a line from A to B reveals pile-ups at the edges that rise to a height of 24% of the indent depth (Fig. 3b). Compared with the as-cast sample, the indent in a sample compressed 50% is slightly bigger (Fig. 3c), consistent with the measured strain softening. In addition, the shear bands around the indent become irregular and convoluted (Fig. 3c) with smaller pile-up height (12% of indent depth) than in the as-cast sample (Fig. 3d). After the 50% compressed sample is annealed at 633 K for 2 h, the smooth, incomplete, circular shear bands return (Fig. 3e), and the pile-up height increases to 25% of the indent depth (Fig. 3f), as in the as-cast sample (Fig. 3a and b). 3.2.2. Underneath the indent 3.2.2.1. As-cast BMG. As mentioned before, the shear band morphology underneath microhardness indents was investigated by clamping together two polished BMG surfaces and indenting the interface with a Vickers indenter and a 1000-g load. Fig. 4 shows the shear band morphology in the as-cast sample when the indentation was carried out with the Vickers diagonal oriented parallel to the clamped interface. There are two sets of shear bands: semicircular and radial. Within the plastic deformation zone (40 lm), defined as the region from the indenter tip to the furthest shear band, there are many more semicircular shear bands than radial ones, as shown in Fig. 4a. The radial shear bands intersect the semicircular shear bands and leave behind shear-offsets that decrease in magnitude with increasing distance from the indenter tip (Fig. 4b). Therefore, it is concluded that the semicircular bands were generated prior to the radial bands, and that the direction of propagation of the radial bands was away from the indenter tip. Where the radial bands are not present, the semicircular bands are smooth and do not exhibit any shear offsets (Fig. 4c). The spacing between the semicircular shear bands increases linearly with increasing distance from the tip of the indenter, as plotted in Fig. 4d. This relationship can be expressed by: d indent ¼ 0:11h 0:24
ð4Þ
where dindent is the shear band spacing (units lm), and h is the distance from the indenter tip (units lm). Note that
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Fig. 3. Optical images showing shear bands around the perimeter of a Vickers indent and the corresponding line-scan profiles in (a,b) as-cast BMG, (c,d) 50% pre-strained BMG, and (e,f) pre-strained plus annealed BMG.
both the semicircular and the radial shear bands reach the top surface but neither extends beyond the diagonal of the Vickers indent (Fig. 4a). Fig. 5 shows the shear band morphology in the as-cast sample when the Vickers diagonal is at 45° to the clamped interface. Here, too, the plastic zone size is 40 lm (Fig. 5a); there are many more semicircular shear bands that are intersected by the fewer radial bands and leave behind shear-offsets (Fig. 5b); the semicircular bands are continuous and smooth in regions where the radial bands are not present
(Fig. 5c); and the spacing between the semicircular bands increases linearly with increasing distance from the tip of the indenter (Fig. 5d), which can be expressed by: d indent ¼ 0:11h þ 0:04
ð5Þ
The only noticeable difference between these two orientations is that, when the indenter diagonal is at 45° to the interface, shear bands extend beyond the indent impression (white lines in Fig. 5a), but not when the diagonal is parallel to the interface.
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Fig. 4. (a) Shear band morphology beneath a Vickers indent in as-cast BMG when the interface is parallel to the indenter diagonal, and higher magnification images showing (b) radial shear bands around indenter tip intersecting the semicircular shear bands, and (c) smooth semicircular shear bands in regions without radial bands. (d) The shear band spacing between the semicircular bands increases with increasing distance from the indenter tip.
Fig. 5. (a) Shear band morphology beneath a Vickers indent in as-cast BMG when the interface is at 45° to the indenter diagonal, and higher magnification images showing (b) radial shear bands intersecting the semicircular shear bands and (c) smooth semicircular shear bands in regions without radial bands. (d) The shear band spacing between the semicircular bands increases with increasing distance from the indenter tip.
The plastic zones beneath Vickers indents were also examined by AFM. Fig. 6a and d are shear band patterns and the corresponding line scan profiles showing the displacements resulting from the indentation. Overall, mate-
rial is seen to protrude out of the plane (i.e., into the clamped interface), with the amount of protrusion higher closer to the indenter. As mentioned earlier, there is a small gap at the clamped interface, which allows material to flow
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Fig. 6. SEM/AFM images and line scans showing the shear band patterns and topology beneath the Vickers indenter in as-cast BMG: (a) SEM image showing the entire plastic zone; (d) corresponding line scan from A to B indicating out-of-plane material flow; (b) higher magnification AFM image showing smooth semicircular shear bands; (e) corresponding line scan from C to D revealing increasing out-of-plane displacement for shear bands that are closer to the indenter tip; (c) AFM image showing radial shear bands; (f) corresponding line scan from E to F indicating the out-of-plane displacement of the radial bands.
into the interface during indentation. This out-of-plane flow is inhomogeneous, as evidenced by the serrated AFM line scan. The higher magnification AFM image of the semicircular shear bands (Fig. 6b) and the corresponding line scan from C to D (Fig. 6e), reveal that each serration on the line scan is associated with one shear band. The thickness of the shear bands, defined as the width of the shear band valleys in Fig. 6e, ranges from 150 to 500 nm, which is comparable to reported shear band thicknesses of 200–1000 nm [32]. For comparison, an AFM image of the radial shear bands and the corresponding line scan are shown in Fig. 6c and f, respectively. It can be seen that the radial bands produce displacements not only parallel to the clamped interface (as evidenced by shear-offsets on the semicircular bands), but also out of the interface plane (serrations in the line scan). 3.2.2.2. Plastically deformed BMG. Vickers indents were made in a specimen that was previously compressed to 50% reduction in thickness, and Fig. 7 shows shear band patterns beneath such an indent. Similar to what was observed in the as-cast BMG, the plastic zone size is 40 lm for both orientations of the interface and indenter diagonal, indicating a hemispherical shape of the plastic zone underneath a Vickers indenter. Overall, the shear bands are irregular, convoluted and rough, unlike the regular smooth bands in the as-cast BMG. In some regions, semicircular and radial shear bands can be discerned (Fig. 7c), similar to those in the as-cast sample. However, in many other regions (Fig. 7d), the shear bands are irregular and often totally deviate from the semicircular shape. Fig. 7e shows the variation in shear band spacing with
distance from the indenter tip. Consistent with their irregular shapes, the shear band spacings show considerable scatter (cf., Figs. 4d and 5d), with a larger fraction located in the small spacing region compared with the as-cast sample. Fig. 7f shows the surface height obtained by an AFM line scan from A to B in Fig. 7b. As in the as-cast specimen, material flows into the interface, and its amount increases closer to the indenter tip. The serrations in the line-scan profile associated with individual shear bands reveal that the irregular or convoluted bands can produce higher shear steps (arrows in Fig. 7f) than smooth semicircular bands. 3.2.2.3. Plastically deformed and annealed BMG. Fig. 8 shows shear band patterns beneath a Vickers indent in the 50% pre-strained and annealed samples (D50A373, D50A473 and D50A633 in Table 1). Irregular shear bands were observed in samples (D50A373 and D50A473) annealed at the lower temperatures (373 and 473 K). However, the shear bands in both these specimens were much less convoluted than in the as-deformed specimen not subjected to any annealing (Fig. 7a). With increasing annealing temperature, the shear bands became increasingly smoother, until, at 633 K (Fig. 8c and d) their appearance was similar to that in the as-cast specimen (Figs. 4a and 5a), indicating enhanced structural relaxation at higher temperatures. Overall, the Vickers indenter produces shear band patterns in D50A633 that are similar to those in the as-cast glass (Figs. 4 and 5). The semicircular shear bands extend beyond the indent edge (Fig. 8d), but not beyond the indent corner (Fig. 8c); the size of plastic zone is 40 lm regardless of the indent orientation, indicating a hemispherical plastic zone beneath the Vickers indent;
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Fig. 7. Shear band morphologies beneath a Vickers indent in the 50% pre-strained sample D50: (a) clamped interface parallel to the indenter diagonal; (b) interface at 45° to the indenter diagonal; (c) higher magnification image showing semicircular and radial bands; (d) higher magnification image showing pre-existing shear bands reactivated during subsequent indentation; (e) variation in shear band spacing with distance from the indenter tip; (f) line scan profile from A to B in image (b).
where the semicircular bands are intersected by the propagation of radial bands, shear offsets are created on the former (Fig. 8e). From a higher magnification SEM image (Fig. 9), it is seen that a polishing scratch (black arrows) is displaced by the radial bands, but not by the semicircular bands, consistent with the AFM observations (Fig. 6) which show that the semicircular shear bands are the result purely of out-of-plane shearing, but the radial bands are caused by both out-of-plane and in-plane shearing. 4. Discussion As shown in Fig. 2, the Vickers microhardness of our Zr-based BMG decreases with increasing amounts of compressive strain. The shear bands generated underneath the Vickers indent in the as-cast BMG are smooth, regular and either semicircular or radial in shape (Figs. 4 and 5), consistent with indentation stress field. In pre-strained
specimens, however, the shear bands under the Vickers indent are irregular and quite convoluted in shape (Fig. 7). As illustrated in Fig. 10, these shear band patterns are consistent with the strain softening implied by the hardness results (Fig. 2). The irregular convoluted shear bands (Fig. 10e and f) appear to be a mixture of the shear bands produced during pre-straining by uniaxial compression (Fig. 10a and b) and those produced during indentation of as-cast material (Fig. 10c and d). Because the as-cast BMG is isotropic, there are no preferred planes for plastic deformation during indentation, and the shear bands follow the stress contours. However, in the previously compressed specimens, there are pre-existing shear bands (Fig. 10a and b) which, because they are softer than the surrounding undeformed material [8], become preferred locations for subsequent deformation [33]. This makes it impossible for the subsequent indentation-induced deformation to take place strictly along the stress contours.
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Fig. 8. Shear band morphologies beneath a Vickers indent in (a) sample D50A373, (b) sample D50A473, (c) and (d) sample D50A633 with the interface parallel to the indenter diagonal and at 45° to the indenter diagonal, respectively; (e) higher magnification image showing the interaction between radial and semicircular bands; (f) smooth semicircular bands in regions without radial bands.
Fig. 9. High-magnification image showing a scratch (black arrows) that is offset by radial bands but not by semicircular bands, indicating that the former have in-plane displacements, but not the latter.
However, not all pre-existing bands are reactivated during the indentation. If the maximum stress at a point underneath the indent is not along the pre-existing bands [14], the stress may not be high enough to reactivate them, even if they are weaker. Only those pre-existing bands, for which
the critical resolved shear stress is exceeded, reappear during the subsequent indentation. In addition, new shear bands (identifiable because of their semicircular and radial shapes, Fig. 7) are also created when the pre-strained specimens are indented. Thus, deformation in the pre-strained specimens occurs at both pre-existing and new shear bands. It is worth noting that we decided to use the clampedinterface technique here, instead of the widely used bonded-interface technique [13,14,19,20], to better reveal the shear band patterns underneath microhardness indents. In the bonded interface technique, the presence of the adhesive between the samples affects the appearance of the shear band patterns, because the interface does not consist of two free surfaces as it does in the present case. In this study, during indentation, material is able to flow freely into the gap between the two halves, allowing high-quality images to be obtained of the shear band patterns, which show a much better correspondence with the indentation and compression stress fields.
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Fig. 10. SEM images and schematic diagrams illustrating how the irregular shear band patterns underneath the indent in sample D50 (e,f) can be viewed as a mixture of shear bands produced by 50% plastic strain (a,b) and shear bands underneath the indent in the as-cast BMG (c,d).
One reason to look underneath the indent is because a shear band becomes visible on the top surface only if it propagates beyond the indent impression. As shown in Figs. 4a, 7a and 8c, none of the shear bands extends beyond the indent corner, i.e., all of them would be hidden by the indent impression when viewed from the top. Consistent with this, no shear bands are visible at the corners in the top-surface views in Fig. 3a, c and e. In contrast, there are multiple shear bands that extend beyond the indent edge in Figs. 5a, 7b and 8d, many of which are visible on the top surface around the indent edges (Fig. 3a, c and e). In general [13,14,18,19], many more shear bands are visible underneath an indent than on the top surface [cf., Fig. 3 and Figs. 4–8]. Upon annealing for 2 h at 373 K, the hardness of all the pre-strained specimens recovers to the hardness value of the as-cast BMG (Fig. 2). That this recovery happens at such a low homologous temperature (relative to Tg) suggests that many deformation-induced structural changes that occur within the shear bands do not require long-range diffusion for reversal. Consistent with these hardness
changes, Fig. 8a shows that, after annealing for 2 h at 373 K, the shear bands underneath the Vickers indent become less convoluted and more semicircular. However, they do not become as smooth and regular as those in the as-cast BMG (Figs. 4 and 5), suggesting that shear band morphologies are more sensitive to structural relaxation than are hardness values. Upon annealing at higher temperatures, the shear bands become progressively more smooth (Fig. 8) and eventually look almost identical to those in the as-cast material. However, at the higher temperatures needed to recover the shear band patterns, there are irreversible changes occurring in mechanical behavior (Tables 2 and 3 and Fig. 2) suggesting the need for additional work in the future to determine the effects of longer anneals at the lower temperatures. The evolution of hardness and shear band patterns in BMG provides only indirect evidence of any structural changes that might be occurring in the shear bands during plastic deformation and annealing. Such changes might include short/medium range ordering/disordering, clustering or changes in the free volume. Here, free volume is
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considered as a parameter to characterize the structural changes in the shear bands, and Spaepen’s model [21] is used, where free volume annihilation is due to a diffusion process, and the amount of free volume annihilated per second (Dt) is expressed as: Dt ¼
t ct DG Þ N cexpð Þexpð kT nD tf
ð6Þ
where ntD is the amount of free volume annihilated per jump, t* is the atomic volume, nD is the number of diffusion jumps needed to annihilate free volume equal to t*, N cexpð cttf Þexpð DG Þ is the number of jumps per second, kT N is the total number of atoms, c is a geometry factor between 1 and ½, tf is the average free volume of an atom, DG is the activation energy for atomic motion, k is Boltzmann’s constant, and T is the absolute temperature. In addition to the free volume present in the as-cast glass, extra free volume is created during plastic deformation, which is expected to be located mostly within shear bands. During the annealing process, free volume annihilation is known to occur [10,34–36]. In the plastically deformed specimens, annihilation will occur both in the shear bands and in the undeformed regions. At a given temperature, the annihilation rates will depend on diffusivity. By analogy with the higher diffusivity in dislocation cores and grain boundaries in crystalline materials [37], diffusivity will be significantly higher within the shear bands than in the matrix (because of the larger free volume in the shear bands). As shown in Fig. 2, for 2-h anneals at 373 K, hardness recovery is faster, the greater the amount of plastic strain in the specimen. Spaepen’s model suggests that this may be a consequence of the faster annihilation of free volume in the more heavily deformed specimens (which contain a higher density of shear bands [8]). When sufficiently annealed, however, the free-volume in the shear bands will eventually become similar to that in the undeformed matrix, resulting in eradication of all pre-strain effects, including strain softening and the convoluted shear banding. 5. Summary The hardness of plastically deformed Zr52.5Al10Ti5Cu17.9Ni14.6 BMG decreases linearly with increasing plastic strain. This strain softening is reversed upon annealing, i.e., the deformed BMG becomes harder after annealing, in contrast to crystalline metals which usually strain harden and soften upon annealing. When annealed for 2 h at 373 K, the hardness initially recovers more rapidly in heavily deformed specimens than in lightly deformed ones, at a rate that varies inversely as the shear band spacing. With increasing annealing time and temperature, hardness increases further, but pre-strain (i.e., the density of preexisting shear bands) has little effect on hardness in this regime. If the deformed and annealed BMG is plastically deformed again, reversible softening is observed.
The above hardness changes were correlated with shear band patterns around/underneath Vickers indents. In the as-cast BMG, indentation produces incomplete circular shear bands on the top surface, and semicircular and radial shear bands beneath the indent. In the 50% pre-strained BMG, shear bands induced by indentation are irregular and convoluted, and appear to be a mixture of the shear bands produced during the preceding compression and those in as-cast BMG. This indicates that pre-existing shear bands are softer than the surrounding undeformed matrix and act as preferred sites for subsequent deformation, consistent with the macroscopic strain softening observed after plastic deformation. In pre-strained plus annealed samples, shear bands induced by indentation tend to approach the morphology of those in the as-cast BMG, consistent with the observation that the hardness also approaches that of the as-cast BMG when the deformed specimens are annealed. This eradication of the pre-strain effects happens at relatively low temperatures and short times (e.g., 2 h at 373 K in the BMG that has a Tg of 663 K) suggesting that whatever structural changes are occurring within the shear bands during deformation and annealing are not the result of long-range atomic motion. Spaepen’s free volume model suggests that, initially, the free volume annihilation rate in shear bands is much faster than that in the undeformed matrix, which results in faster annealing-induced hardness increase in the more heavily deformed specimens that have a higher shear band density. Once the excess free volume in the shear bands is annihilated, further densification occurs at about the same rate everywhere in the specimens, and the annealing-induced hardness increase no longer depends on the degree of pre-strain. Acknowledgments This research was sponsored by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, US Department of Energy, under contract DEAC05-00OR22725 with UT-Battelle, LLC. The authors are grateful to George Pharr for letting them use his interference optical microscope, and to Sanghoon Shim for AFM training (S.X.). References [1] Johnson WL. MRS Bull 1999;24:42. [2] Inoue A. Acta Mater 2000;48:279. [3] Schuh CA, Hufnagel TC, Ramamurty U. Acta Mater 2007;55: 4067. [4] Wang WH, Dong C, Shek CH. Mater Sci Eng R 2004;44:45. [5] Pampillo CA. J Mater Sci 1975;10:1194. [6] Liu CT et al. Metall Mater Trans A 1998;29:1811. [7] Shiflet GJ, He Y, Poon SJ. J Appl Phys 1988;64:6863. [8] Bei H, Xie S, George EP. Phys Rev Lett 2006;96:105503. [9] Tang C, Li Y, Zeng K. Mater Sci Eng A 2004;384:215. [10] Jiang WH, Pinkerton FE, Atzmon M. Acta Mater 2005;53:3469. [11] Bhowmick R, Raghavan R, Chattopadhyay K. Acta Mater 2006;54:4221.
S. Xie, E.P. George / Acta Materialia 56 (2008) 5202–5213 [12] Dieter GE. Mechanical metallurgy. New York: McGraw-Hill; 1986. [13] Ramamurty U, Jana S, Kawamura Y, Chattopadhyay K. Acta Mater 2005;53:705. [14] Zhang H, Jing X, Subhash G, Kecskes LJ, Dowding RJ. Acta Mater 2005;53:3849. [15] Vaidynathan R, Dao M, Ravichandran G, Suresh S. Acta Mater 2001;49:3781. [16] Kim JJ, Choi Y, Suresh S, Argon AS. Science 2002;295:654. [17] Donovan PE. J Mater Sci 1989;24:523. [18] Patnaik MNM, Narasimhan R, Ramamurty U. Acta Mater 2004;52:3335. [19] Jana S, Ramamurty U, Chattopadhyay K, Kawamura Y. Mater Sci Eng A 2004:375–7. [20] Su C, Anand L. Acta Mater 2006;54:179. [21] Spaepen F. Acta Mater 1975;25:407. [22] Argon AS. Acta Mater 1979;27:47. [23] Steif PS, Spaepen F, Hutchinson JW. Acta Mater 1982;30:441.
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[24] Hajlaoui K, Benameur T, Vaughan G, Yavari AR. Scripta Mater 2004;51:843. [25] Wright JL, Hufnagel TC, Nix WD. J Appl Phys 2003;93:1432. [26] Kristiakova K, Sve P, Kristiak J, Sausa O, Duhaj PJ. J Non-Cryst Solids 1995;193:277. [27] Murali P, Ramamurty U. Acta Mater 2005;53:1467. [28] Tsao SS, Spaepen F. Acta Mater 1985;33:881. [29] Taub AI, Spaepen F. Acta Mater 1980;28:1781. [30] Duine PA, Sietsma J, VandenBeukel A. Acta Mater 1992;40:753. [31] Lin XH, Johnson WL, Rhim WK. Mater Trans JIM 1997;38:473. [32] Lewandowski JJ, Greer AL. Nat Mater 2006;5:15. [33] Krishnanand KD, Cahn RW. Scripta Mater 1975;9:1259. [34] Wen P et al. Phys Rev B 2003;67:212201. [35] Nagel C, Ratzke K, Schmidtke E, Faupel F. Phys Rev B 1999;60:9212. [36] Nagel C et al. Phys Rev B 1998;57:1998. [37] Shewmon PG. Diffusion in solids. New York: McGraw-Hill; 1963.
Acta Materialia 56 (2008) 5202–5213 www.elsevier.com/locate/actamat
Hardness and shear band evolution in bulk metallic glasses after plastic deformation and annealing q S. Xie a, E.P. George a,b,* a
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
b
Received 30 September 2007; accepted 2 July 2008 Available online 11 August 2008
Abstract Strain-induced hardening and annealing-induced softening are typical in crystalline metals. Bulk metallic glasses (BMG) exhibit the opposite behavior, namely, strain-induced softening and annealing-induced hardening. In addition, reversible softening–hardening–softening occurs in a BMG subjected to a three-step deformation–annealing–deformation process. The hardness changes after deformation and annealing can be correlated with the shear band patterns around/underneath Vickers indents. Shear bands produced during indentation of as-cast BMG are semicircular and radial, consistent with the stress distribution beneath the indenter. In contrast, the shear bands in the pre-strained BMG are irregular and convoluted, and appear to be a mixture of the shear bands produced during the prior compression and those in the as-cast BMG. After annealing, the shear bands tend to recover their semicircular and radial shapes consistent with the annealing-induced hardening. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Metallic glasses; Plastic deformation; Shear bands; Hardness; Annealing
1. Introduction Metallic glasses have interesting properties, including high strength, high elastic limit (2%) and good corrosion resistance [1–4]. However, their high strength is often accompanied by limited plastic deformation (<2%) at low homologous temperatures (relative to the glass-transition temperature Tg). Metallic glasses undergo plastic deformation by the nucleation and propagation of shear bands [5]. In uniaxial tension and compression, once a few shear bands are formed, plastic deformation remains highly localized there, which prevents the generation of new shear bands and makes the existing shear bands propagate rapidly through the samples, resulting in catastrophic failure q This article was presented at the Symposium on Phase Stability and Defect Structures in Honor of Professor Austin Chang, held in Orlando, FL, February 28–March 2, 2007. * Corresponding author. Address: Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA. E-mail address: [email protected] (E.P. George).
[5–7]. This shear localization appears to be a result of strain softening, which has been observed to occur in heavily deformed metallic glasses [8–11]. This behavior contrasts sharply with the strain hardening typically seen in crystalline materials, which tends to produce more uniform plastic deformation [12]. To characterize the response of bulk metallic glasses (BMG) to plastic deformation, some researchers have performed indentation tests and examined the deformation zones around/underneath the indent. Pile-ups and incomplete circular shear bands have been observed around the perimeters of Vickers [13,14], Berkovich [10,15,16] and spherical [17,18] indents. Several sets of shear bands that looked like slip lines were observed beneath a Vickers indenter and explained using slip-line field theory [19]. However, in many other experiments, roughly semicircular shear bands were observed which are not predicted by the slip-line theory. These bands and their associated hemispherical plastic zone beneath the Vickers indent were explained using the expanding cavity model [13,14].
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.07.009
S. Xie, E.P. George / Acta Materialia 56 (2008) 5202–5213
Finally, nearly symmetrical radial shear bands were observed beneath a cylindrical indent and shown to be consistent with the numerically simulated shear band pattern [20]. None of these studies addressed deformation behavior and shear banding in pre-strained BMG, although it is generally thought that pre-existing shear bands are preferred sites for subsequent deformation [5,21]. The detailed structure of shear bands, which accommodate plastic deformation in metallic glasses [8,22,23], is not known. Certain structural changes, such as an increase in free volume after plastic deformation [24–26], and a decrease in free volume after annealing at temperatures below Tg [27–30], have been observed in shear bands. However, only limited information is available on the effects of annealing on the hardness of pre-strained BMG. To the authors’ knowledge, the only available data are those of Jiang et al. [10], who showed that the hardness of 45.5% cold-rolled Al–Ni–Y amorphous ribbon (22 lm thick) increased from 3.48 to 4.05 GPa after annealing at 110 °C for 1 h. Systematic investigations have yet to be performed on the effects of annealing temperature and time on the hardness of pre-strained BMG and the structural relaxation of shear bands. In this paper, the hardness response of metallic glasses after plastic deformation and annealing below Tg is investigated. The evolution of hardness is correlated with shear band patterns around/underneath indents. The observed shear band patterns show the role of pre-existing shear bands in subsequent deformation and indicate the structural relaxation of shear bands upon annealing. 2. Experimental procedures Bulk metallic glass of composition Zr–10Al–5Ti– 17.9Cu–14.6Ni (at.%) [6,31] was prepared by arc melting the elemental constituents in argon atmosphere, followed by drop casting into cylindrical Cu molds measuring 6.7 mm in diameter and 72 mm in length. Before being drop cast, the arc-melted buttons were flipped over and re-melted five or six times to enhance compositional homogeneity. The amorphous structure of the specimens was confirmed by X-ray diffraction (XRD) and differential scanning calorimetry (DSC) at a heating rate of 20 K min1. Disc-shaped specimens 3.5 mm thick were cut transverse to the long axis of the drop-cast rods using electric-discharge machining (EDM). Some of these specimens were compressed at room temperature (up to 80% plastic strain) using a servo-hydraulic machine (MTS 8100) at an engineering strain rate of 1 103 s1. The plastic strain is defined here as ep = (l0l)/l0, where l0 and l are specimen thicknesses before and after compression. The as-cast and plastically deformed samples were annealed in vacuum (5 106 Torr) for times up to 16 h at 373, 473 and 633 K (all of which are lower than the glass-transition temperature for this BMG, Tg = 663 K). Some of the annealed samples were compressed again to explore reversible softening in metallic glasses. After anneal-
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ing, the samples were polished with SiC paper through 600 grit and then with 0.5 lm Al2O3 to obtain a mirror finish. Vickers hardness tests were conducted on the polished surfaces using a Buehler Micromet 2001 microhardness tester (1000 g load and 20 s holding time). The perimeters of the indents were examined using interference optical microscopy (IOM) and optical microscopy (OM). To reveal shear band patterns underneath hardness indents, the bonded interface technique has typically been used in the past [13,14,18–20,33–35]. Here, the use of an adhesive at the interface is eschewed, and two pieces of BMG are simply clamped with surfaces that have been polished to a mirror finish. When the two halves are separated after indentation, they reveal more clearly the correlation between the shear-band morphology and the indentation/ compression stress fields than if an adhesive had been used. The entire assembly, including vice and tightly clamped samples, was cold-mounted in epoxy resin, and a surface transverse to the clamped interface was ground through 600 grit SiC and polished with 0.5 lm Al2O3 to a mirror finish. Vickers indents (using a 1000 g load and 20 s hold time) were made at the interface and away from the interface. In the former case, two different orientations were chosen with the indenter diagonal either parallel to the interface (Fig. 1a) or at 45° to the interface (Fig. 1b). At the clamped interface, the gap between the two halves was 2–4 lm, which was smaller than the 6-lm gap reported for the bonded interface technique [14]. No further separation between the two halves was observed for the indentation load (1000 g), indicating that the interface remained tightly clamped. After indentation, the clamped assembly was extricated from the epoxy resin, and the vice unclamped to separate the two halves. The indents that were made at locations away from the interface were examined using IOM and OM. The shear bands at the interface (underneath the indents) were examined by scanning electron microscopy (SEM) and atomic force microscopy (AFM). 3. Results 3.1. Effect of plastic deformation and annealing on the hardness of metallic glasses The effects of compressive plastic strain (ep) and subsequent annealing on hardness (H) are shown in Fig. 2. The hardness of the deformed BMG (square symbols) decreases linearly with increasing plastic strain. Using earlier results [8], namely that the shear band spacing (d) decreases linearly with increasing plastic strain (d1 = 0.14ep), the hardness decrease shown in Fig. 2 may be expressed as a function of shear band spacing as follows: 1 H ¼ H m A1 ð1Þ d where Hm is the hardness of as-cast BMG, and A1 is a proportionality constant equal to the softening induced by
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Fig. 1. Top-surface view of Vickers indents made at clamped interfaces between polished BMG specimens: (a) indenter diagonal parallel to the interface; (b) indenter diagonal at 45° to the interface.
shear bands that are spaced 1 lm apart. Upon annealing, the hardness of the deformed BMG increases (Fig. 2), which may be expressed as follows: 1 H anneal ¼ H anneal 0 A2 ð2Þ d where Hanneal_0 is the hardness of the as-cast glass after annealing, and A2 is another proportionality constant (A1 > A2). By combining Eqs. (1) and (2), the change in hardness upon annealing is obtained as: DH ¼ H anneal H ¼ ðH anneal 0 H m Þ þ ðA1 A2 Þ
Fig. 2. Effect of compressive strain and subsequent annealing on the Vickers hardness of Zr52.5Al10Ti5Cu17.9Ni14.6 bulk metallic glass as a function of (a) time and (b) temperature.
1 d
ð3Þ
After annealing at 373 K for 2 h, it is seen that Hanneal_0 Hm, which yields an inverse relationship between the hardness change and shear band spacing, DH / d1. That is, hardness recovers much faster in the more heavily deformed specimens (containing closely spaced shear bands) than in the lightly deformed ones. Note that the hardness recovery can occur at a relatively low temperature (373 K) compared with the Tg for this BMG (663 K) and at relatively short times (2 h). With increasing annealing time (Fig. 2a) and temperature (Fig. 2b), there is a further increase in Hanneal_0, but relatively little change in the slope A2. This means that once the hardness recovers to Hm, the amount of pre-strain (i.e., shear band density) has little effect on any further hardness increase, in contrast to the DH / d1 relation that was obtained for annealing at 373 K for 2 h. The extent to which the above annealing treatments produce irreversible changes in the strain softening behavior was investigated next. For this, BMG specimens that had already undergone a compression and annealing cycle were re-compressed (see Table 1 for the specimens and their processing conditions). Table 2 shows the amount of compressive strain (per cent reduction in thickness) that was possible during the second deformation cycle for various annealing temperatures and times. In general, the BMG
S. Xie, E.P. George / Acta Materialia 56 (2008) 5202–5213 Table 1 Identifications of specimens subjected to different deformation and annealing steps Sample name
Processing
D33 D50 D50A373 D50A473 D50A633 D33A373 D33A473 D33A373D
33% plastic 50% plastic 50% plastic 50% plastic 50% plastic 33% plastic 33% plastic 33% plastic strain D33A473D 33% plastic strain
strain strain strain + annealed strain + annealed strain + annealed strain + annealed strain + annealed strain + annealed
at at at at at at
373 K 473 K 633 K 373 K 473 K 373 K
for for for for for for
2h 2h 2h 2h 2h 2 h+33% plastic
strain + annealed at 473 K for 2 h+33% plastic
Table 2 Effects of annealing treatments on the compressive strain to failure in the second deformation step of a deform-anneal-deform process Annealing time (h)
2 4 16
Temperature 473 K
573 K
633 K
– >50% 50%
– 50% <5%
<5% – –
became more brittle the higher the annealing temperature and time. After annealing at 633 K, the material could not be compressed more than 5%. Significant compression (50%) was possible after annealing at 473 and 573 K, provided the annealing times were kept below 16 and 4 h, respectively. Although it is not listed in Table 2, extensive compression (>50%) was possible after 16 h anneals at 373 K. Table 3 summarizes the hardness changes in the BMG specimens subjected to a three-step deformation–annealing–deformation process. Consider specimen D33A373D (Table 1), which was deformed (ep = 33%), annealed (373 K for 2 h) and deformed again (ep = 33%). As shown in Table 3, it has the same hardness (567 HV) as specimen D33 (569 HV), which started out in the as-cast state and was compressed just once (Table 1). That is, the hardness returns to the same value after the second compression cycle as after the first. To the authors’ knowledge, this is the first time that such a reversible strain softening behavior has been observed in a metallic glass. Next, consider specimen D33A473D (Table 1), which was deformed (ep = 33%), annealed at a higher temperature (473 K for 2 h) and deformed again (ep = 33%). This specimen has a
Table 3 Hardness of our BMG after various processing steps Specimen
Hardness (HV)
Specimen
Hardness (HV)
As-cast D33A373 D33A473
596 593 627
D33 D33A373D D33A473D
569 567 598
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hardness of 598 HV, which is higher than that of specimen D33 (569 HV) which was compressed only once. However, if one compares the degree of compression-induced softening after annealing at 373 and 473 K, that is the decrease in hardness between samples D33A473 and D33A473D, on the one hand, and samples D33A373 and D33A373D, on the other, the softening in both cases is 5% for ep = 33%. 3.2. Shear band patterns induced by micro-indentation 3.2.1. Top surface Fig. 3a shows a top-surface view of a 1000-g Vickers indent in the as-cast sample. There are incomplete circular shear bands around the edges of the indent but no cracks, including at the corners. Surface profilometry using IOM along a line from A to B reveals pile-ups at the edges that rise to a height of 24% of the indent depth (Fig. 3b). Compared with the as-cast sample, the indent in a sample compressed 50% is slightly bigger (Fig. 3c), consistent with the measured strain softening. In addition, the shear bands around the indent become irregular and convoluted (Fig. 3c) with smaller pile-up height (12% of indent depth) than in the as-cast sample (Fig. 3d). After the 50% compressed sample is annealed at 633 K for 2 h, the smooth, incomplete, circular shear bands return (Fig. 3e), and the pile-up height increases to 25% of the indent depth (Fig. 3f), as in the as-cast sample (Fig. 3a and b). 3.2.2. Underneath the indent 3.2.2.1. As-cast BMG. As mentioned before, the shear band morphology underneath microhardness indents was investigated by clamping together two polished BMG surfaces and indenting the interface with a Vickers indenter and a 1000-g load. Fig. 4 shows the shear band morphology in the as-cast sample when the indentation was carried out with the Vickers diagonal oriented parallel to the clamped interface. There are two sets of shear bands: semicircular and radial. Within the plastic deformation zone (40 lm), defined as the region from the indenter tip to the furthest shear band, there are many more semicircular shear bands than radial ones, as shown in Fig. 4a. The radial shear bands intersect the semicircular shear bands and leave behind shear-offsets that decrease in magnitude with increasing distance from the indenter tip (Fig. 4b). Therefore, it is concluded that the semicircular bands were generated prior to the radial bands, and that the direction of propagation of the radial bands was away from the indenter tip. Where the radial bands are not present, the semicircular bands are smooth and do not exhibit any shear offsets (Fig. 4c). The spacing between the semicircular shear bands increases linearly with increasing distance from the tip of the indenter, as plotted in Fig. 4d. This relationship can be expressed by: d indent ¼ 0:11h 0:24
ð4Þ
where dindent is the shear band spacing (units lm), and h is the distance from the indenter tip (units lm). Note that
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Fig. 3. Optical images showing shear bands around the perimeter of a Vickers indent and the corresponding line-scan profiles in (a,b) as-cast BMG, (c,d) 50% pre-strained BMG, and (e,f) pre-strained plus annealed BMG.
both the semicircular and the radial shear bands reach the top surface but neither extends beyond the diagonal of the Vickers indent (Fig. 4a). Fig. 5 shows the shear band morphology in the as-cast sample when the Vickers diagonal is at 45° to the clamped interface. Here, too, the plastic zone size is 40 lm (Fig. 5a); there are many more semicircular shear bands that are intersected by the fewer radial bands and leave behind shear-offsets (Fig. 5b); the semicircular bands are continuous and smooth in regions where the radial bands are not present
(Fig. 5c); and the spacing between the semicircular bands increases linearly with increasing distance from the tip of the indenter (Fig. 5d), which can be expressed by: d indent ¼ 0:11h þ 0:04
ð5Þ
The only noticeable difference between these two orientations is that, when the indenter diagonal is at 45° to the interface, shear bands extend beyond the indent impression (white lines in Fig. 5a), but not when the diagonal is parallel to the interface.
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Fig. 4. (a) Shear band morphology beneath a Vickers indent in as-cast BMG when the interface is parallel to the indenter diagonal, and higher magnification images showing (b) radial shear bands around indenter tip intersecting the semicircular shear bands, and (c) smooth semicircular shear bands in regions without radial bands. (d) The shear band spacing between the semicircular bands increases with increasing distance from the indenter tip.
Fig. 5. (a) Shear band morphology beneath a Vickers indent in as-cast BMG when the interface is at 45° to the indenter diagonal, and higher magnification images showing (b) radial shear bands intersecting the semicircular shear bands and (c) smooth semicircular shear bands in regions without radial bands. (d) The shear band spacing between the semicircular bands increases with increasing distance from the indenter tip.
The plastic zones beneath Vickers indents were also examined by AFM. Fig. 6a and d are shear band patterns and the corresponding line scan profiles showing the displacements resulting from the indentation. Overall, mate-
rial is seen to protrude out of the plane (i.e., into the clamped interface), with the amount of protrusion higher closer to the indenter. As mentioned earlier, there is a small gap at the clamped interface, which allows material to flow
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Fig. 6. SEM/AFM images and line scans showing the shear band patterns and topology beneath the Vickers indenter in as-cast BMG: (a) SEM image showing the entire plastic zone; (d) corresponding line scan from A to B indicating out-of-plane material flow; (b) higher magnification AFM image showing smooth semicircular shear bands; (e) corresponding line scan from C to D revealing increasing out-of-plane displacement for shear bands that are closer to the indenter tip; (c) AFM image showing radial shear bands; (f) corresponding line scan from E to F indicating the out-of-plane displacement of the radial bands.
into the interface during indentation. This out-of-plane flow is inhomogeneous, as evidenced by the serrated AFM line scan. The higher magnification AFM image of the semicircular shear bands (Fig. 6b) and the corresponding line scan from C to D (Fig. 6e), reveal that each serration on the line scan is associated with one shear band. The thickness of the shear bands, defined as the width of the shear band valleys in Fig. 6e, ranges from 150 to 500 nm, which is comparable to reported shear band thicknesses of 200–1000 nm [32]. For comparison, an AFM image of the radial shear bands and the corresponding line scan are shown in Fig. 6c and f, respectively. It can be seen that the radial bands produce displacements not only parallel to the clamped interface (as evidenced by shear-offsets on the semicircular bands), but also out of the interface plane (serrations in the line scan). 3.2.2.2. Plastically deformed BMG. Vickers indents were made in a specimen that was previously compressed to 50% reduction in thickness, and Fig. 7 shows shear band patterns beneath such an indent. Similar to what was observed in the as-cast BMG, the plastic zone size is 40 lm for both orientations of the interface and indenter diagonal, indicating a hemispherical shape of the plastic zone underneath a Vickers indenter. Overall, the shear bands are irregular, convoluted and rough, unlike the regular smooth bands in the as-cast BMG. In some regions, semicircular and radial shear bands can be discerned (Fig. 7c), similar to those in the as-cast sample. However, in many other regions (Fig. 7d), the shear bands are irregular and often totally deviate from the semicircular shape. Fig. 7e shows the variation in shear band spacing with
distance from the indenter tip. Consistent with their irregular shapes, the shear band spacings show considerable scatter (cf., Figs. 4d and 5d), with a larger fraction located in the small spacing region compared with the as-cast sample. Fig. 7f shows the surface height obtained by an AFM line scan from A to B in Fig. 7b. As in the as-cast specimen, material flows into the interface, and its amount increases closer to the indenter tip. The serrations in the line-scan profile associated with individual shear bands reveal that the irregular or convoluted bands can produce higher shear steps (arrows in Fig. 7f) than smooth semicircular bands. 3.2.2.3. Plastically deformed and annealed BMG. Fig. 8 shows shear band patterns beneath a Vickers indent in the 50% pre-strained and annealed samples (D50A373, D50A473 and D50A633 in Table 1). Irregular shear bands were observed in samples (D50A373 and D50A473) annealed at the lower temperatures (373 and 473 K). However, the shear bands in both these specimens were much less convoluted than in the as-deformed specimen not subjected to any annealing (Fig. 7a). With increasing annealing temperature, the shear bands became increasingly smoother, until, at 633 K (Fig. 8c and d) their appearance was similar to that in the as-cast specimen (Figs. 4a and 5a), indicating enhanced structural relaxation at higher temperatures. Overall, the Vickers indenter produces shear band patterns in D50A633 that are similar to those in the as-cast glass (Figs. 4 and 5). The semicircular shear bands extend beyond the indent edge (Fig. 8d), but not beyond the indent corner (Fig. 8c); the size of plastic zone is 40 lm regardless of the indent orientation, indicating a hemispherical plastic zone beneath the Vickers indent;
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Fig. 7. Shear band morphologies beneath a Vickers indent in the 50% pre-strained sample D50: (a) clamped interface parallel to the indenter diagonal; (b) interface at 45° to the indenter diagonal; (c) higher magnification image showing semicircular and radial bands; (d) higher magnification image showing pre-existing shear bands reactivated during subsequent indentation; (e) variation in shear band spacing with distance from the indenter tip; (f) line scan profile from A to B in image (b).
where the semicircular bands are intersected by the propagation of radial bands, shear offsets are created on the former (Fig. 8e). From a higher magnification SEM image (Fig. 9), it is seen that a polishing scratch (black arrows) is displaced by the radial bands, but not by the semicircular bands, consistent with the AFM observations (Fig. 6) which show that the semicircular shear bands are the result purely of out-of-plane shearing, but the radial bands are caused by both out-of-plane and in-plane shearing. 4. Discussion As shown in Fig. 2, the Vickers microhardness of our Zr-based BMG decreases with increasing amounts of compressive strain. The shear bands generated underneath the Vickers indent in the as-cast BMG are smooth, regular and either semicircular or radial in shape (Figs. 4 and 5), consistent with indentation stress field. In pre-strained
specimens, however, the shear bands under the Vickers indent are irregular and quite convoluted in shape (Fig. 7). As illustrated in Fig. 10, these shear band patterns are consistent with the strain softening implied by the hardness results (Fig. 2). The irregular convoluted shear bands (Fig. 10e and f) appear to be a mixture of the shear bands produced during pre-straining by uniaxial compression (Fig. 10a and b) and those produced during indentation of as-cast material (Fig. 10c and d). Because the as-cast BMG is isotropic, there are no preferred planes for plastic deformation during indentation, and the shear bands follow the stress contours. However, in the previously compressed specimens, there are pre-existing shear bands (Fig. 10a and b) which, because they are softer than the surrounding undeformed material [8], become preferred locations for subsequent deformation [33]. This makes it impossible for the subsequent indentation-induced deformation to take place strictly along the stress contours.
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Fig. 8. Shear band morphologies beneath a Vickers indent in (a) sample D50A373, (b) sample D50A473, (c) and (d) sample D50A633 with the interface parallel to the indenter diagonal and at 45° to the indenter diagonal, respectively; (e) higher magnification image showing the interaction between radial and semicircular bands; (f) smooth semicircular bands in regions without radial bands.
Fig. 9. High-magnification image showing a scratch (black arrows) that is offset by radial bands but not by semicircular bands, indicating that the former have in-plane displacements, but not the latter.
However, not all pre-existing bands are reactivated during the indentation. If the maximum stress at a point underneath the indent is not along the pre-existing bands [14], the stress may not be high enough to reactivate them, even if they are weaker. Only those pre-existing bands, for which
the critical resolved shear stress is exceeded, reappear during the subsequent indentation. In addition, new shear bands (identifiable because of their semicircular and radial shapes, Fig. 7) are also created when the pre-strained specimens are indented. Thus, deformation in the pre-strained specimens occurs at both pre-existing and new shear bands. It is worth noting that we decided to use the clampedinterface technique here, instead of the widely used bonded-interface technique [13,14,19,20], to better reveal the shear band patterns underneath microhardness indents. In the bonded interface technique, the presence of the adhesive between the samples affects the appearance of the shear band patterns, because the interface does not consist of two free surfaces as it does in the present case. In this study, during indentation, material is able to flow freely into the gap between the two halves, allowing high-quality images to be obtained of the shear band patterns, which show a much better correspondence with the indentation and compression stress fields.
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Fig. 10. SEM images and schematic diagrams illustrating how the irregular shear band patterns underneath the indent in sample D50 (e,f) can be viewed as a mixture of shear bands produced by 50% plastic strain (a,b) and shear bands underneath the indent in the as-cast BMG (c,d).
One reason to look underneath the indent is because a shear band becomes visible on the top surface only if it propagates beyond the indent impression. As shown in Figs. 4a, 7a and 8c, none of the shear bands extends beyond the indent corner, i.e., all of them would be hidden by the indent impression when viewed from the top. Consistent with this, no shear bands are visible at the corners in the top-surface views in Fig. 3a, c and e. In contrast, there are multiple shear bands that extend beyond the indent edge in Figs. 5a, 7b and 8d, many of which are visible on the top surface around the indent edges (Fig. 3a, c and e). In general [13,14,18,19], many more shear bands are visible underneath an indent than on the top surface [cf., Fig. 3 and Figs. 4–8]. Upon annealing for 2 h at 373 K, the hardness of all the pre-strained specimens recovers to the hardness value of the as-cast BMG (Fig. 2). That this recovery happens at such a low homologous temperature (relative to Tg) suggests that many deformation-induced structural changes that occur within the shear bands do not require long-range diffusion for reversal. Consistent with these hardness
changes, Fig. 8a shows that, after annealing for 2 h at 373 K, the shear bands underneath the Vickers indent become less convoluted and more semicircular. However, they do not become as smooth and regular as those in the as-cast BMG (Figs. 4 and 5), suggesting that shear band morphologies are more sensitive to structural relaxation than are hardness values. Upon annealing at higher temperatures, the shear bands become progressively more smooth (Fig. 8) and eventually look almost identical to those in the as-cast material. However, at the higher temperatures needed to recover the shear band patterns, there are irreversible changes occurring in mechanical behavior (Tables 2 and 3 and Fig. 2) suggesting the need for additional work in the future to determine the effects of longer anneals at the lower temperatures. The evolution of hardness and shear band patterns in BMG provides only indirect evidence of any structural changes that might be occurring in the shear bands during plastic deformation and annealing. Such changes might include short/medium range ordering/disordering, clustering or changes in the free volume. Here, free volume is
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considered as a parameter to characterize the structural changes in the shear bands, and Spaepen’s model [21] is used, where free volume annihilation is due to a diffusion process, and the amount of free volume annihilated per second (Dt) is expressed as: Dt ¼
t ct DG Þ N cexpð Þexpð kT nD tf
ð6Þ
where ntD is the amount of free volume annihilated per jump, t* is the atomic volume, nD is the number of diffusion jumps needed to annihilate free volume equal to t*, N cexpð cttf Þexpð DG Þ is the number of jumps per second, kT N is the total number of atoms, c is a geometry factor between 1 and ½, tf is the average free volume of an atom, DG is the activation energy for atomic motion, k is Boltzmann’s constant, and T is the absolute temperature. In addition to the free volume present in the as-cast glass, extra free volume is created during plastic deformation, which is expected to be located mostly within shear bands. During the annealing process, free volume annihilation is known to occur [10,34–36]. In the plastically deformed specimens, annihilation will occur both in the shear bands and in the undeformed regions. At a given temperature, the annihilation rates will depend on diffusivity. By analogy with the higher diffusivity in dislocation cores and grain boundaries in crystalline materials [37], diffusivity will be significantly higher within the shear bands than in the matrix (because of the larger free volume in the shear bands). As shown in Fig. 2, for 2-h anneals at 373 K, hardness recovery is faster, the greater the amount of plastic strain in the specimen. Spaepen’s model suggests that this may be a consequence of the faster annihilation of free volume in the more heavily deformed specimens (which contain a higher density of shear bands [8]). When sufficiently annealed, however, the free-volume in the shear bands will eventually become similar to that in the undeformed matrix, resulting in eradication of all pre-strain effects, including strain softening and the convoluted shear banding. 5. Summary The hardness of plastically deformed Zr52.5Al10Ti5Cu17.9Ni14.6 BMG decreases linearly with increasing plastic strain. This strain softening is reversed upon annealing, i.e., the deformed BMG becomes harder after annealing, in contrast to crystalline metals which usually strain harden and soften upon annealing. When annealed for 2 h at 373 K, the hardness initially recovers more rapidly in heavily deformed specimens than in lightly deformed ones, at a rate that varies inversely as the shear band spacing. With increasing annealing time and temperature, hardness increases further, but pre-strain (i.e., the density of preexisting shear bands) has little effect on hardness in this regime. If the deformed and annealed BMG is plastically deformed again, reversible softening is observed.
The above hardness changes were correlated with shear band patterns around/underneath Vickers indents. In the as-cast BMG, indentation produces incomplete circular shear bands on the top surface, and semicircular and radial shear bands beneath the indent. In the 50% pre-strained BMG, shear bands induced by indentation are irregular and convoluted, and appear to be a mixture of the shear bands produced during the preceding compression and those in as-cast BMG. This indicates that pre-existing shear bands are softer than the surrounding undeformed matrix and act as preferred sites for subsequent deformation, consistent with the macroscopic strain softening observed after plastic deformation. In pre-strained plus annealed samples, shear bands induced by indentation tend to approach the morphology of those in the as-cast BMG, consistent with the observation that the hardness also approaches that of the as-cast BMG when the deformed specimens are annealed. This eradication of the pre-strain effects happens at relatively low temperatures and short times (e.g., 2 h at 373 K in the BMG that has a Tg of 663 K) suggesting that whatever structural changes are occurring within the shear bands during deformation and annealing are not the result of long-range atomic motion. Spaepen’s free volume model suggests that, initially, the free volume annihilation rate in shear bands is much faster than that in the undeformed matrix, which results in faster annealing-induced hardness increase in the more heavily deformed specimens that have a higher shear band density. Once the excess free volume in the shear bands is annihilated, further densification occurs at about the same rate everywhere in the specimens, and the annealing-induced hardness increase no longer depends on the degree of pre-strain. Acknowledgments This research was sponsored by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, US Department of Energy, under contract DEAC05-00OR22725 with UT-Battelle, LLC. The authors are grateful to George Pharr for letting them use his interference optical microscope, and to Sanghoon Shim for AFM training (S.X.). References [1] Johnson WL. MRS Bull 1999;24:42. [2] Inoue A. Acta Mater 2000;48:279. [3] Schuh CA, Hufnagel TC, Ramamurty U. Acta Mater 2007;55: 4067. [4] Wang WH, Dong C, Shek CH. Mater Sci Eng R 2004;44:45. [5] Pampillo CA. J Mater Sci 1975;10:1194. [6] Liu CT et al. Metall Mater Trans A 1998;29:1811. [7] Shiflet GJ, He Y, Poon SJ. J Appl Phys 1988;64:6863. [8] Bei H, Xie S, George EP. Phys Rev Lett 2006;96:105503. [9] Tang C, Li Y, Zeng K. Mater Sci Eng A 2004;384:215. [10] Jiang WH, Pinkerton FE, Atzmon M. Acta Mater 2005;53:3469. [11] Bhowmick R, Raghavan R, Chattopadhyay K. Acta Mater 2006;54:4221.
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