- Email: [email protected]
Mechanism of shear banding during cold rolling of a bulk metallic glass
Accepted Manuscript Mechanism of shear banding during cold rolling of a bulk metallic glass Sergio Scudino PII:
S0925-8388(18)33560-6
DOI:
10.1016/j.jallcom.2018.09.302
Reference:
JALCOM 47721
To appear in:
Journal of Alloys and Compounds
Received Date: 26 April 2018 Revised Date:
30 August 2018
Accepted Date: 24 September 2018
Please cite this article as: S. Scudino, Mechanism of shear banding during cold rolling of a bulk metallic glass, Journal of Alloys and Compounds (2018), doi: https://doi.org/10.1016/j.jallcom.2018.09.302. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
ACCEPTED MANUSCRIPT Mechanism of shear banding during cold rolling of a bulk metallic glass
RI PT
Sergio Scudino
IFW Dresden, Institute for Complex Materials, Helmholtzstraße 20, D-01069 Dresden,
SC
Germany
Shear band formation within the roll bite is investigated for the cold-rolled
M AN U
Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass. The results indicate that shear bands originate on the surface of the specimen in contact with the rolls and propagate approximately at 45° towards the opposite surface. This is accompanied by the rotation of the shear offsets that depends on their position along the arc of contact. The rotation
TE D
is the medium that transmits the increasing pressure exerted by the rotating rolls to a propagating shear band, while the specimen progressively enters in the roll bite. This mechanism implies that the strain at opposite sides of a band changes sign from
EP
compressive to tensile, as indeed experimentally observed by strain analysis across an
AC C
individual shear band.
E-mail address. [email protected]
Keywords: Bulk metallic glasses; Shear bands; Cold rolling; Plastic deformation mechanisms
1
ACCEPTED MANUSCRIPT 1. Introduction A prerequisite for alleviating the characteristic room-temperature brittleness of bulk metallic glasses (BMGs) under tensile loading is to avoid catastrophic propagation of a
RI PT
single shear band [1]. This purpose can be achieved by distributing the plastic strain over several bands via shear band multiplication or through the reactivation of pre-
existing shear bands. Examples of methods promoting shear band multiplication are
SC
high-pressure torsion and imprinting [2,3], where the structural heterogeneities
generated by the mechanical processing represent obstacles to the formation of
M AN U
detrimental runaway shear bands. Pre-existing shear bands can be efficiently generated by cold rolling [4-6]. Because of the strain softening resulting from the accumulation of free volume within the shear bands (and in the surrounding elastic matrix [7]), these bands can become the preferential location of plastic deformation during subsequent
6,8,9].
TE D
tensile loading [8,9], enhancing the ductility compared with the as-cast material [4-
The reactivation of the pre-existing shear bands appears to depend on their
EP
orientation with respect to the loading axis; for example, early reports on metallic glass ribbons showed that tensile fracture occurs along the pre-existing bands when they are
AC C
orientated at angles larger than 64°, while fracture no longer takes place along the preexisting bands for angles smaller than 40° [10]. The strength of the material as well depends on the shear band orientation: ribbons fracturing along the pre-existing bands display lower fracture stresses [10]. This behavior is also observed in cold-rolled BMGs, where the reactivation of the bands oriented at about 45° (i.e., along the plane of maximum resolved shear stress) leads to reduced yield strength than the as-cast counterpart but, in addition, induces larger ductility and apparent work-hardening
2
ACCEPTED MANUSCRIPT behavior [9]. Finally, the direction of the shear bands has significant effect on the plastic deformation of BMGs under compressive loading, where specimens with bands oriented at ~45° display the largest plastic strain [11].
RI PT
The control of shear band orientation is, therefore, of primary importance for governing the mechanical behavior of metallic glasses, including strength, plastic
deformation and, most likely, fracture toughness, where crack propagation across the
SC
pre-existing shear bands promotes a tortuous crack trajectory [12]. To achieve this aim, the understanding of the fundamental aspects characterizing shear band formation and
M AN U
propagation is essential and a significant amount of knowledge about the phenomenon of shear banding in BMGs has been gathered recently. For example, nanoindentation and calorimetry investigations have shown that softening, accumulation of free volume and reduction of the Young´s modulus not only take place within a shear band, but also
TE D
occur in the material surrounding the band [7,13,14], pointing to a rather diffuse effect of shear banding. The results also suggest that the softening induced by shear bands is non-planar, which may then lead to long-range stress fields during their propagation
EP
[15], an aspect that has strong implications for shear band interaction and multiplication [16]. Shear bands are indeed not straight and display small deflections corresponding to
AC C
large density variations within the bands [17,18], a behavior compatible with a local mechanism based on the alignment of Eshelby-like quadrupoles [19]. Shear band formation induced by cold rolling has also been investigated. By using
digital image correlation, Binkowski et al. [20] analyzed the strain fields related to the propagation of an individual shear band and observed that adjacent areas of the shear band display strain components with opposite sign, indicative of a stick-slip behavior. Shear banding not only generates strain fields along the shear band direction, but also
3
ACCEPTED MANUSCRIPT creates strong strain fields that extend well into the material surrounding the band [21]; the comparison between experiments and simulations indicates that such fields are the mark left in the adjacent material by the structural rearrangements occurring within a
the atomistic mechanism of shear banding [22]
RI PT
shear band and suggests their possible use as a diagnostic for experimentally analyzing
In this work, the phenomenon of shear banding is further investigated by analyzing
SC
the formation of shear bands in the roll bite for the Zr52.5Ti5Cu18Ni14.5Al10 BMG (a
metallic glass extensively investigated [6,9,23,24] that represents well the distinctive
M AN U
behavior of cold-rolled amorphous metals). The analysis of shear band initiation and propagation within the roll bite is a very challenging task because of the fast dynamics of shear banding along with the characteristics of rolling, where plastic deformation occurs in a confined volume of material that travels along the specimen during the
TE D
process. To achieve this purpose, here the shear band morphology generated at an intermediate stage of rolling, when the process is stopped approximately in the middle of the sample, is examined; this approach permits one to identify the characteristics of
EP
shear band formation within the roll bite. Finally, the combination of the shear band morphology with the structural information gained from high-energy x-ray strain
AC C
analysis is used to describe the mechanism of shear band formation induced by rolling.
2. Experimental
A plate with nominal composition Zr52.5Ti5Cu18Ni14.5Al10 (at.%) and dimensions
35×40×1.7 mm3 was synthesized by copper mold casting. From this plate, specimens for cold rolling with dimensions 6x×3y×1.7z mm3 were prepared by wire erosion. Cold rolling was carried out at room temperature using a laboratory rolling mill. In order to
4
ACCEPTED MANUSCRIPT reduce the friction arising during rolling at the interfaces between rolls and samples and, therefore, to preserve the shear band morphology on the x-y plane (for the coordinate system used in this work refer to Fig. 1(a)), the samples were encapsulated into a Cu
RI PT
jacket (thickness ~0.2 mm) before rolling. The shear band morphology of the rolled specimens was evaluated by scanning electron microscopy (SEM) using a Gemini 1530 microscope. Strain analysis was performed on the Zr52.5Ti5Cu18Ni14.5Al10 BMG cold
SC
rolled at room temperature to a thickness reduction of about 3 % (measured by using a microcaliper) achieved by multiple reductions of ~0.25 %. Such a small reduction does
M AN U
not change the characteristic shear band morphology of cold-rolled BMGs and guarantees the shear band spacing to be much larger than the beam size [9,22], which thus allows one to accurately analyze the elastic strain induced by the shear band in the surrounding material. The structure of a cold-rolled specimen with thickness of about 100 µm was studied by x-ray diffraction (XRD) in transmission using a high-intensity
TE D
high-energy monochromatic synchrotron beam (λ = 0.1897 Å) at the ID11 beamline of the European Synchrotron Radiation Facility (ESRF). The specimen for XRD analysis
EP
was prepared by carefully grinding and polishing a 3 % rolled sample (original dimensions 6x×3y×1.7z mm3) down to a thickness of 100 µm. Diffraction patterns were
AC C
collected on the x-z plane at about 1 mm from the side of the specimen every 2.0 µm across an individual shear band using a beam with size of 2×2 µm2. The position of the shear band was identified by using a Cu marker. The XRD patterns were collected using a two-dimensional charge coupled device (CCD) Frelon camera [25]. The twodimensional patterns were integrated in 10° azimuthal slices between 0 and 360° using the Fit2D program [26] to give the XRD intensity distributions I(q,θ) as a function of the scattering vector q and azimuthal angle θ = 10…360°. The position of the first
5
ACCEPTED MANUSCRIPT scattering maximum q1, which can be used to evaluate the structural changes occurring in the medium-range order [27], was determined by fitting using a pseudo-Voigt function. The strain was measured through the shift of q1 with respect of the reference
RI PT
0 value q1 as ߝ = (qଵ − ݍଵ )/ݍଵ. In order to minimize possible errors introduced by the 0 uncertainty of the sample-to-detector distance, q1 was selected within the investigated
sample by choosing a position far enough from the shear band and, thus, less affected
SC
by shear banding. The components of the strain tensor (parallel, ߝଵଵ , and perpendicular, ߝଶଶ , to the shear band and the in-plane shear strain ߝଵଶ ) for each point scanned across
AC C
EP
TE D
M AN U
the band were determined according to the method described in Poulsen et al. [28].
Fig. 1. (a) Cold rolling setup and coordinate system used in this work. (b) Characteristic shear band morphology of the Zr52.5Ti5Cu18Ni14.5Al10 BMG rolled with Cu jacket to a thickness reduction of 10 % showing on the x-z plane the creation of an array of parallel shear bands forming an angle of approximately 45° with the rolling direction. (c) The shear offsets display a rotation of about 8° around the y-axis.
6
ACCEPTED MANUSCRIPT 3. Results and discussion 3.1 Shear band morphology The shear band morphology generated by cold rolling in the Zr52.5Ti5Cu18Ni14.5Al10
RI PT
BMG has been reported elsewhere [9]. However, some key aspects have to be reported here. On the x-z plane, the rolled BMG exhibits straight shear bands forming an angle of approximately 45° with the rolling direction (Figs. 1(b) and 1(c)). These shear bands
SC
propagate for about 100 µm along the y-axis and then they branch and intersect,
generating a rather irregular shear band morphology on the x-y plane. The shear offsets
M AN U
related to the straight bands are not parallel to the rolling direction but display a rotation of about 8° around the y-axis (Fig. 1(c)). The friction arising during rolling at the interface between rolls and specimen drastically affects the shear band morphology on the x-y plane, where the shear bands are not visible in the absence of the Cu jacket [9],
TE D
whereas it does not change the shear band arrangement on the x-z plane, where the bands are oriented at about 45° in both high and low friction conditions [9]. The arrangement of the shear bands shown in Figs. 1(b) and 1(c) is the final result
EP
of cold rolling, that is, after that the confined volume where plastic deformation occurs has traveled along the entire specimen. In order to understand the mechanism of shear
AC C
band formation, the process of cold rolling would require to be analyzed in-situ. This approach, however, poses the problem of examining the shear banding phenomenon through the Cu jacket necessary to preserve the morphology of the bands. A way to overcome this problem is to stop the rolling process at an intermediate stage, where the plastic deformation front comes to an end within the sample. The resulting shear band morphology at the front end would thus exhibit the characteristic features generated in the roll bite.
7
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Fig. 2. (a) Shear band morphology for the cold-rolled Zr52.5Ti5Cu18Ni14.5Al10 BMG when the rolling process is stopped approximately in the middle of the sample; the white dashed lines mark the position of shear bands with different morphologies, while the yellow full lines represent the rolls. (b,c) Magnified view of the shear band morphology corresponding to the red and blue dashed boxes in (a). (d) SEM
TE D
micrograph revealing that the shear bands (marked by red arrows) do not propagate beyond the green dashed line, which can be approximately considered as the roll bite entry.
EP
An example of this approach is shown in Fig. 2(a), which displays a Zr52.5Ti5Cu18Ni14.5Al10 BMG sample cold rolled up to about its half-length. The shape of
AC C
the specimen is no longer flat and the curvature imparted by the rotating cylindrical rolls (represented by yellow full lines in Fig. 2(a)) is evident. The shear band morphology is irregular near the sample edge, where curved and intersecting shear bands are formed. The morphology becomes more regular towards the center of the sample with the formation of parallel and straight shear bands (marked by dashed white lines). Shear offsets are formed on both rolled surfaces (Figs. 2(b) and 2(c)) and their angle varies along the arc of contact from about 2° to values oscillating around 8° (Fig. 3). This
8
ACCEPTED MANUSCRIPT indicates that the rotation around the y-axis observed in Fig. 1(c) is a dynamic process and that the orientation of the shear offsets changes within the roll bite. The shear bands propagating toward the center of the specimen do not go beyond the green dashed line
M AN U
SC
RI PT
in Fig. 2(d), which can be approximately considered as the roll bite entry.
Fig. 3. Representative variation of the angle formed by the shear offsets within the roll bite after rotation around the y-axis (see inset for the orientation of the offsets). The dashed green line represents the roll
TE D
bite entry.
EP
3.2 Mechanism of shear band formation
The arrangement of the shear bands shown in the previous section provides useful
AC C
information regarding their formation in the gap between the rolls, where the material is progressively subjected to plastic deformation, as schematically described in Fig. 4(a). Along the arc of contact between the rolls and the specimen delimited by the curve ab, the pressure P exerted by the rolls increases along the rolling direction from the roll bite entry, passes through a maximum at the neutral point N and subsequently decreases towards the roll bite exit [29]. This pressure profile creates two elastic zones at entry
9
ACCEPTED MANUSCRIPT and exit of the roll gap that enclose the zone undergoing plastic deformation (dark grey area in Fig. 4(a)), which defines the volume where the shear bands can form. Shear bands generated by cold rolling of BMGs form an angle of about 45° with the
RI PT
rolling direction [4,5,9]. Because of this orientation, shear bands generated at the entry of the plastic zone, where the yield strength of the BMG is exceeded, can propagate
until they encounter the elastic zone, where they are stopped, as observed in Fig. 2(d).
SC
This behavior can be better understood by considering Figs. 4(b) and 4(c), which show schematically the propagation of shear bands within the roll bite at two consecutive
M AN U
stages of rolling. During the first stage (Fig. 4(b)), shear bands (red full lines) can form and propagate within the plastic zone and their propagation is then interrupted at the elastic zone. In the following stage (Fig. 4(c)), when a new portion of material enters the roll bite and, correspondingly, the plastic zone travels in the opposite direction, new
TE D
shear bands (black full line) can be generated and the shear bands formed in the previous stage can propagate further. This process gradually drives the shear bands across the sample until they eventually emerge on the opposite side, shearing a portion
AC C
EP
of material with respect to the adjacent one.
10
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
EP
Fig. 4. Schematic illustrations of: (a) rolling setup showing the main features characterizing the roll bite and (b,c) shear band propagation within the roll bite at two consecutive stages of rolling. The full lines
AC C
oriented at 45° in (b,c) represent the shear bands formed in the plastic zone (dark grey), while the dotted lines indicate the bands not propagating through the elastic zone (light grey).
After having qualitatively described the progressive shear band propagation within
the roll bite, it is now necessary to discuss the mechanism leading to this process and, in particular, how the pressure exerted by the rolls is transmitted to the propagating band. As already observed in Fig. 2, shear bands nucleate on the surface of the rolled BMG and propagate at about 45° towards the opposite surface. The shear offsets visible on the
11
ACCEPTED MANUSCRIPT sample surface display a rotation around the y-axis that depends on the position along the arc of contact (Fig. 3). Shear band propagation and the rotation of the shear offsets,
M AN U
SC
RI PT
therefore, appear to be correlated.
Fig. 5. (a,b) Schematic representation of shear band propagation. The vertical lines in (a) represent the undeformed condition and the horizontal dashed line marks the position of the shear band formed in (b). The vertical lines are distorted in (b) due to the formation of the shear band, inducing opposite strain fields at the two sides of the band. (c) Variation of the components of the strain tensor evaluated by high-
TE D
energy XRD across a shear band generated by cold rolling the Zr52.5Ti5Cu18Ni14.5Al10 BMG. ε11 and ε22 represent the strain components respectively parallel and perpendicular to the shear band, while ε12 is the shear strain. The horizontal dashed line in (c) marks the position of the shear band. The colors in (b) are
EP
not derived experimentally and are solely intended to represent the strain profile in (c).
AC C
A possible explanation for this behavior is given in Figs. 5(a) and 5(b), which schematically show a shear band and the corresponding shear offset formed from an undeformed initial condition (represented by the vertical lines in Fig. 5(a)). Once the shear band is initiated, the rotation of the shear offset imparted by the roll is progressively transmitted to the shear band, driving its propagation. According to this hypothesis, the rotation would induce atomic displacements with opposite directions at the two sides of the band (represented by the distorted lines in Fig. 5(b)) and, for the shear band represented in Fig. 5(b), which comes to an end within the material, strain
12
ACCEPTED MANUSCRIPT compatibility with the neighboring unsheared material would induce tensile and compressive strains in the direction parallel to the band [22]. The validity of this hypothesis was examined by analyzing the variation of the components of the strain
RI PT
tensor across an individual band estimated by high-energy XRD (Fig. 5(c)). The results confirm the hypothesis: the strain parallel to the shear band (ε11) displays a sigmoidal
profile with the sign changing from compressive to tensile at opposite sides of the band.
SC
An inverse trend (i.e. from tension to compression) is exhibited by the strain component perpendicular to the band (ε22). The shear strain (ε12) displays the smallest variation,
M AN U
indicating that most of the strain is accommodated along the directions parallel and perpendicular to the shear band. Interestingly, the amount of strain at the two sides of the band is not equal: the compressive strain is larger than the tensile strain along the shear band direction (ε11), whereas the tensile strain is larger in the direction
TE D
perpendicular to the band (ε22). The origin of this behavior is unclear and additional experiments involving strain mapping of a series of shear bands are needed to clarify whether this is a distinctive feature of shear banding or simply the result of a local
EP
asymmetry of the stress distribution during rolling. The strain profiles in Fig. 5(c) represent only a glimpse of the strain distribution
AC C
generated across a shear band, which continuously changes as the band propagates through the specimen, as recently shown by molecular dynamics simulations [22]. The observed strain is the microscopic manifestation of the mechanism of shear banding at the nanoscale, which evolves from an antisymmetric character for a band not transecting the entire specimen to a symmetric profile for a mature shear band emerging on the opposite side of the sample [22]. It is also tempting to correlate this behavior to the serrations of opposite sign (tensile and compressive) observed by Wright et al. [30]
13
ACCEPTED MANUSCRIPT under uniaxial compression; a correlation which would suggest that the effect of shear band formation spans different length scales from the atomic level to the macroscale. The mechanism outlined in Fig. 5 has strong similarities with the one proposed by
RI PT
Qu et al. [31] for explaining shear band propagation under uniaxial compression. According to the interpretation of Qu et al. [31], shear bands are often initiated at stress concentrators, such as surface imperfections or defects, even if the applied stress is
SC
below the yield strength of the material. The formation of a shear offset on the sample surface would then induce contraction and traction of atoms/clusters at opposite sides of
M AN U
the shear band while it propagates approximately at 45° towards the opposite surface
AC C
EP
TE D
[31], as experimentally observed here in Fig. 5(c).
14
ACCEPTED MANUSCRIPT Fig. 6. Schematic illustrations of: (a) deformation of the metallic glass within the roll bite represented by a unit specimen (light blue rectangle) undergoing a series of consecutive compression tests at increasing loads (red-blue areas); (b1,c1) stress profiles across the specimen and (b2,c2) corresponding degree of sample deformation for the unit specimen compressed within the (b) elastic and (c) plastic zones. The
RI PT
dotted boxes in (b2,c2) represent the undeformed unit specimen. The colors and stress profiles in (b,c) are not derived experimentally and are exclusively intended to give a descriptive explanation of the proposed mechanism.
SC
Stress concentration may also be generated during rolling. The regular shear band
M AN U
spacing characterizing BMGs cold rolled to small thickness reductions (Fig. 1) suggests that the mechanism of shear band formation may act in a periodic fashion. In analogy with the work of Song et al. [32], the deformation of the material within the roll bite can thus be represented by a unit specimen undergoing a series of consecutive compression tests at increasing loads (Fig. 6(a)). The load, however, would not be applied
TE D
homogeneously to the unit specimen because of the variation of stress along the arc of contact [29] (schematically depicted in Figs. 6(b) and 6(c)), a condition similar to that
EP
met during compression tests when the ends of a specimen are misaligned with respect to the applied load. As reported by Chen et al. [33] for a Cu-Zr-Al BMG, such a
AC C
misalignment induces the generation of a stress gradient within the sample, which leads to the formation of a high density of shear bands in the regions exhibiting comparatively higher stresses. Accordingly, once the unit specimen accesses the elastic zone at entry (Fig. 6(b)), the stress would become heterogeneously distributed. In analogy with the work of Qu et al. [31], the formation of a shear band within a unit specimen can then be qualitatively illustrated by considering how the critical stress required to activate a shear band (σy) would change across the specimen (Figs. 6(b1) and 6(c1)). In the elastic zone,
15
ACCEPTED MANUSCRIPT the maximum stress achievable is by definition below σy and no shear band is expected to be initiated at this stage. Within the plastic zone (Fig. 6(c)), the critical stress σy is exceeded and a shear band as well as the corresponding shear offset can be formed. The
RI PT
shear band would propagate only within the region of the sample where the σ ≥ σy [31], i.e. in the plastic zone, in agreement with the results displayed in Fig. 2(d), and
additional compression steps might be necessary to drive the band through the entire
SC
unit specimen. The reiteration of these steps in adjacent unit specimens leads to the
formation of new shear bands and to their propagation across the sample, progressively
M AN U
deforming the material. Due to the symmetry of the roll setup (Fig. 4(a)), this scenario would imply the symmetric formation and propagation of shear bands from each roll, giving rise to their intersection approximately at the center of the specimen. In contrast, the generation of only a pattern of parallel shear bands is observed here (Figs. 1 and 2).
TE D
This behavior is not unusual and has been ascribed to the non-perfectly symmetric rolling process combined with the asymmetric character of shear band formation [5]; two symmetric and conjugated families of shear bands can, however, be generated by
AC C
proposed here.
EP
changing the rolling direction by 180° [5], a behavior in agreement with the mechanism
4. Conclusions
The formation of shear bands within the roll bite has been investigated for the
Zr52.5Ti5Cu18Ni14.5Al10 BMG by examining the shear band morphology generated at an intermediate stage of rolling, i.e. when the rolling process is stopped approximately in the middle of the sample. Because of the orientation at about 45°, shear bands nucleated at the entry of the plastic zone, where the yield strength of the material is exceeded, can
16
ACCEPTED MANUSCRIPT propagate until they encounter the elastic zone, where they are stopped. The comparison with the shear band formation during compression tests suggests that the stress gradient generated along the arc of contact possibly triggers the formation of shear bands and the
RI PT
corresponding shear offsets on the surface of the rolled specimen. The offsets display a rotation that depends on their position along the arc of contact. The rotation transmits
the pressure exerted by the rotating rolls to the shear bands, driving their propagation.
SC
This mechanism requires that the strain at opposite sides of the band changes sign from compressive to tensile, as indeed experimentally observed by high-energy XRD across
M AN U
an individual shear band.
Acknowledgements The author thanks R.N. Shahid and J. Han for technical assistance, the European Synchrotron Radiation Facility for provision of synchrotron radiation
AC C
EP
TE D
facilities and J. Wright for assistance in using beamline ID11.
17
ACCEPTED MANUSCRIPT References [1] M.W. Chen, Mechanical behavior of metallic glasses: microscopic understanding of strength and ductility, Annu. Rev. Mater. Res. 38 (2008) 445-469.
RI PT
[2] S.-H. Joo, D.-H. Pi, A.D.H. Setyawan, H. Kato, M. Janecek, Y.C. Kim, S. Lee, H.S. Kim, Work-hardening induced tensile ductility of bulk metallic glasses via highpressure torsion, Sci. Rep. 5 (2015) 9660.
SC
[3] S. Scudino, B. Jerliu, S. Pauly, K.B. Surreddi, U. Kühn, J. Eckert, Ductile bulk
metallic glasses produced through designed heterogeneities, Scripta Mater. 65 (2011)
M AN U
815-818.
[4] Y. Yokoyama, K. Inoue, K. Fukaura, Cold-rolled Zr50Cu30Ni10Al10 bulk amorphous alloys with tensile plastic elongation at room temperature, Mater. Trans. 12 (2002) 3199-3205.
TE D
[5] Q.P. Cao, J.W. Liu, K.J. Yang, F. Xu, Z.Q. Yao, A. Minkow, H.J. Fecht, J. Ivanisenko, L.Y. Chen, X.D. Wang, S.X. Qu, J.Z. Jiang, Effect of pre-existing shear bands on the tensile mechanical properties of a bulk metallic glass, Acta Mater. 58
EP
(2010) 1276-1292.
[6] S. Scudino, B. Jerliu, K.B. Surreddi, U. Kühn, J. Eckert, Effect of cold rolling on
AC C
compressive and tensile mechanical properties of Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass, J. Alloys Compd. 509 (2011) 128-130. [7] M. Stolpe, J.J. Kruzic, R. Busch, Evolution of shear bands, free volume and hardness during cold rolling of a Zr-based bulk metallic glass, Acta Mater. 64 (2014) 231-240. [8] Y. Yokoyama, Ductility improvement of Zr–Cu–Ni–Al glassy alloy, J. Non-Cryst. Solids 316 (2003) 104-113.
18
ACCEPTED MANUSCRIPT [9] S. Scudino, K.B. Surreddi, Shear band morphology and fracture behavior of coldrolled Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass under tensile loading, J. Alloys Compd. 708 (2017) 722-727.
(rolling deformation), J. Mater. Sci. 16 (1981) 2411-2418.
RI PT
[10] S. Takayama, Work-hardening and susceptibility to plastic flow in metallic glasses
[11] J. Kobata, T. Kimura, Y. Takigawa, T. Uesugi, H. Kimura, K. Higashi, Effect of
metallic glass, Mater. Trans. 50 (2009) 2355-2358.
SC
pre-introduced shear bands direction on deformation behavior in Zr55Al10Ni5Cu30 bulk
M AN U
[12] S. Xie, J.J. Kruzic, Cold rolling improves the fracture toughness of a Zr-based bulk metallic glass, J. Alloys Compd. 694 (2017) 1109-1120.
[13] J. Pan, Q. Chen, L. Liu, Y. Li, Softening and dilatation in a single shear band, Acta Mater. 59 (2011) 5146-5158.
TE D
[14] R. Maaß, K. Samwer, W. Arnold, C.A. Volkert, A single shear band in a metallic glass: Local core and wide soft zone, Appl. Phys. Lett. 105 (2014) 171902. [15] R. Maaß, P. Birckigt, C. Borchers, K. Samwer, C.A. Volkert, Long range stress
EP
fields and cavitation along a shear band in a metallic glass: The local origin of fracture, Acta Mater. 98 (2015) 94-102.
AC C
[16] D.P. Wang, B.A. Sun, X.R. Niu, Y. Yang, W.H. Wang, C.T. Liu, Mutual interaction of shear bands in metallic glasses, Intermetallics 85 (2017) 48-53. [17] V. Schmidt, H. Rösner, M. Peterlechner, G. Wilde, Quantitative measurement of density in a shear band of metallic glass monitored along its propagation direction, Phys. Rev. Lett. 115 (2015) 035501. [18] C. Liu, V. Roddatis, P. Kenesei, R. Maaß, Shear-band thickness and shear-band cavities in a Zr-based metallic glass, Acta Mater. 140 (2017) 206-216.
19
ACCEPTED MANUSCRIPT [19] V. Hieronymus-Schmidt, H. Rösner, G. Wilde, A. Zaccone, Shear banding in metallic glasses described by alignments of Eshelby quadrupoles, Phys. Rev. B 95 (2017) 134111.
RI PT
[20] I. Binkowski, S. Schlottbom, J. Leuthold, S. Ostendorp, S.V. Divinski, G. Wilde, Sub-micron strain analysis of local stick-slip motion of individual shear bands in a bulk metallic glass, Appl. Phys. Lett. 107 (2015) 221902.
SC
[21] H. Shakur Shahabi, S. Scudino, I. Kaban, M. Stoica, B. Escher, S. Menzel, G.B.M. Vaughan, U. Kühn, J. Eckert, Mapping of residual strains around a shear band in bulk
M AN U
metallic glass by nanobeam x-ray diffraction, Acta Mater. 111 (2016) 187-193. [22] S. Scudino, D. Şopu, Strain distribution across an individual shear band in real and simulated metallic glasses, Nano Lett. 18 (2018) 1221-1227.
[23] P.N. Zhang, J.F. Li, Y. Hu, Y.H. Zhou, Effect of rolling on the microstructure and
462 (2008) 88-93.
TE D
mechanical property of Zr52.5Cu17.9Ni14.6Al10Ti5 bulk metallic glass, J. Alloys Compd.
[24] C.T. Liu, L. Heatherly, D.S. Easton, C.A. Carmichael, J.H. Schneibel, C.H. Chen,
EP
J.L. Wright, M.H. Yoo, J.A. Horton, A. Inoue, Test environments and mechanical properties of Zr-base bulk amorphous alloys, Metall. Mater. Trans. A 29 (1998) 1811-
AC C
1820.
[25] J.C. Labiche, O. Mathon, S. Pascarelli, M.A. Newton, G.G. Ferre, C. Curfs, G. Vaughan, A. Homs, D.F. Carreiras, The fast readout low noise camera as a versatile xray detector for time resolved dispersive extended x-ray absorption fine structure and diffraction studies of dynamic problems in materials science, chemistry, and catalysis, Rev. Sci. Instrum. 78 (2007) 091301.
20
ACCEPTED MANUSCRIPT [26] A.P. Hammersley, S.O. Svensson, M. Hanfland, A.N. Fitch, D. Hausermann, Twodimensional detector software: From real detector to idealised image or two-theta scan, High Press. Res. 14 (1996) 235
RI PT
[27] S. Scudino, M. Stoica, I. Kaban, K.G. Prashanth, G.B.M. Vaughan, J. Eckert, Length scale-dependent structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 metallic glass, J. Alloys Compd. 639 (2015) 465-469.
SC
[28] H.F. Poulsen, J.A. Wert, J. Neuefeind, V. Honkimäki, M. Daymond, Measuring strain distributions in amorphous materials, Nature Mater. 4 (2005) 33-36.
M AN U
[29] M. Kazeminezhad, A. Karimi Taheri, Calculation of the rolling pressure distribution and force in wire flat rolling process, J. Mater. Proc. Tech. 171 (2006) 253258.
[30] W.J. Wright, M.W. Samale, T.C. Hufnagel, M.M. LeBlanc, J.N. Florando, Studies
TE D
of shear band velocity using spatially and temporally resolved measurements of strain during quasistatic compression of a bulk metallic glass, Acta Mater. 57 (2009) 46394648.
EP
[31] R.T. Qu, Z.Q. Liu, G. Wang, Z.F. Zhang, Progressive shear band propagation in metallic glasses under compression, Acta Mater. 91 (2015) 19-33.
AC C
[32] K.K. Song, S. Pauly, Y. Zhang, S. Scudino, P. Gargarella, K.B. Surreddi, U. Kühn, J. Eckert, Significant tensile ductility induced by cold rolling in Cu47.5Zr47.5Al5 bulk metallic glass, Intermetallics 19 (2011) 1394-1398. [33] L.Y. Chen, Q. Ge, S. Qu, Q.K. Jiang, X.P. Nie, J.Z. Jiang, Achieving large macroscopic compressive plastic deformation and work-hardening-like behavior in a monolithic bulk metallic glass by tailoring stress distribution, Appl. Phys. Lett. 92 (2008) 211905.
21
ACCEPTED MANUSCRIPT Figure captions Fig. 1. (a) Cold rolling setup and coordinate system used in this work. (b) Characteristic shear band morphology of the Zr52.5Ti5Cu18Ni14.5Al10 BMG rolled with Cu jacket to a
RI PT
thickness reduction of 10 % showing on the x-z plane the creation of an array of parallel shear bands forming an angle of approximately 45° with the rolling direction. (c) The
SC
shear offsets display a rotation of about 8° around the y-axis.
Fig. 2. (a) Shear band morphology for the cold-rolled Zr52.5Ti5Cu18Ni14.5Al10 BMG
M AN U
when the rolling process is stopped approximately in the middle of the sample; the white dashed lines mark the position of shear bands with different morphologies, while the yellow full lines represent the rolls. (b,c) Magnified view of the shear band morphology corresponding to the red and blue dashed boxes in (a). (d) SEM micrograph
TE D
revealing that the shear bands (marked by red arrows) do not propagate beyond the green dashed line, which can be approximately considered as the roll bite entry.
EP
Fig. 3. Representative variation of the angle formed by the shear offsets within the roll bite after rotation around the y-axis (see inset for the orientation of the offsets). The
AC C
dashed green line represents the roll bite entry.
Fig. 4. Schematic illustrations of: (a) rolling setup showing the main features characterizing the roll bite and (b,c) shear band propagation within the roll bite at two consecutive stages of rolling. The full lines oriented at 45° in (b,c) represent the shear bands formed in the plastic zone (dark grey), while the dotted lines indicate the bands not propagating through the elastic zone (light grey).
22
ACCEPTED MANUSCRIPT
Fig. 5. (a,b) Schematic representation of shear band propagation. The vertical lines in (a) represent the undeformed condition and the horizontal dashed line marks the position of
RI PT
the shear band formed in (b). The vertical lines are distorted in (b) due to the formation of the shear band, inducing opposite strain fields at the two sides of the band. (c)
Variation of the components of the strain tensor evaluated by high-energy XRD across a
SC
shear band generated by cold rolling the Zr52.5Ti5Cu18Ni14.5Al10 BMG. ε11 and ε22
represent the strain components respectively parallel and perpendicular to the shear
M AN U
band, while ε12 is the shear strain. The horizontal dashed line in (c) marks the position of the shear band. The colors in (b) are not derived experimentally and are solely intended to represent the strain profile in (c).
TE D
Fig. 6. Schematic illustrations of: (a) deformation of the metallic glass within the roll bite represented by a unit specimen (light blue rectangle) undergoing a series of consecutive compression tests at increasing loads (red-blue areas); (b1,c1) stress
EP
profiles across the specimen and (b2,c2) corresponding degree of sample deformation for the unit specimen compressed within the (b) elastic and (c) plastic zones. The dotted
AC C
boxes in (b2,c2) represent the undeformed unit specimen. The colors and stress profiles in (b,c) are not derived experimentally and are exclusively intended to give a descriptive explanation the proposed mechanism.
23
ACCEPTED MANUSCRIPT
EP
TE D
M AN U
SC
RI PT
Shear band mechanism within the roll bite in cold-rolled bulk metallic glass Shear offset rotation transmits the pressure from rolls to propagating shear band Strain at opposite sides of shear band changes sign from compressive to tensile
AC C
• • •
S0925-8388(18)33560-6
DOI:
10.1016/j.jallcom.2018.09.302
Reference:
JALCOM 47721
To appear in:
Journal of Alloys and Compounds
Received Date: 26 April 2018 Revised Date:
30 August 2018
Accepted Date: 24 September 2018
Please cite this article as: S. Scudino, Mechanism of shear banding during cold rolling of a bulk metallic glass, Journal of Alloys and Compounds (2018), doi: https://doi.org/10.1016/j.jallcom.2018.09.302. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
ACCEPTED MANUSCRIPT Mechanism of shear banding during cold rolling of a bulk metallic glass
RI PT
Sergio Scudino
IFW Dresden, Institute for Complex Materials, Helmholtzstraße 20, D-01069 Dresden,
SC
Germany
Shear band formation within the roll bite is investigated for the cold-rolled
M AN U
Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass. The results indicate that shear bands originate on the surface of the specimen in contact with the rolls and propagate approximately at 45° towards the opposite surface. This is accompanied by the rotation of the shear offsets that depends on their position along the arc of contact. The rotation
TE D
is the medium that transmits the increasing pressure exerted by the rotating rolls to a propagating shear band, while the specimen progressively enters in the roll bite. This mechanism implies that the strain at opposite sides of a band changes sign from
EP
compressive to tensile, as indeed experimentally observed by strain analysis across an
AC C
individual shear band.
E-mail address. [email protected]
Keywords: Bulk metallic glasses; Shear bands; Cold rolling; Plastic deformation mechanisms
1
ACCEPTED MANUSCRIPT 1. Introduction A prerequisite for alleviating the characteristic room-temperature brittleness of bulk metallic glasses (BMGs) under tensile loading is to avoid catastrophic propagation of a
RI PT
single shear band [1]. This purpose can be achieved by distributing the plastic strain over several bands via shear band multiplication or through the reactivation of pre-
existing shear bands. Examples of methods promoting shear band multiplication are
SC
high-pressure torsion and imprinting [2,3], where the structural heterogeneities
generated by the mechanical processing represent obstacles to the formation of
M AN U
detrimental runaway shear bands. Pre-existing shear bands can be efficiently generated by cold rolling [4-6]. Because of the strain softening resulting from the accumulation of free volume within the shear bands (and in the surrounding elastic matrix [7]), these bands can become the preferential location of plastic deformation during subsequent
6,8,9].
TE D
tensile loading [8,9], enhancing the ductility compared with the as-cast material [4-
The reactivation of the pre-existing shear bands appears to depend on their
EP
orientation with respect to the loading axis; for example, early reports on metallic glass ribbons showed that tensile fracture occurs along the pre-existing bands when they are
AC C
orientated at angles larger than 64°, while fracture no longer takes place along the preexisting bands for angles smaller than 40° [10]. The strength of the material as well depends on the shear band orientation: ribbons fracturing along the pre-existing bands display lower fracture stresses [10]. This behavior is also observed in cold-rolled BMGs, where the reactivation of the bands oriented at about 45° (i.e., along the plane of maximum resolved shear stress) leads to reduced yield strength than the as-cast counterpart but, in addition, induces larger ductility and apparent work-hardening
2
ACCEPTED MANUSCRIPT behavior [9]. Finally, the direction of the shear bands has significant effect on the plastic deformation of BMGs under compressive loading, where specimens with bands oriented at ~45° display the largest plastic strain [11].
RI PT
The control of shear band orientation is, therefore, of primary importance for governing the mechanical behavior of metallic glasses, including strength, plastic
deformation and, most likely, fracture toughness, where crack propagation across the
SC
pre-existing shear bands promotes a tortuous crack trajectory [12]. To achieve this aim, the understanding of the fundamental aspects characterizing shear band formation and
M AN U
propagation is essential and a significant amount of knowledge about the phenomenon of shear banding in BMGs has been gathered recently. For example, nanoindentation and calorimetry investigations have shown that softening, accumulation of free volume and reduction of the Young´s modulus not only take place within a shear band, but also
TE D
occur in the material surrounding the band [7,13,14], pointing to a rather diffuse effect of shear banding. The results also suggest that the softening induced by shear bands is non-planar, which may then lead to long-range stress fields during their propagation
EP
[15], an aspect that has strong implications for shear band interaction and multiplication [16]. Shear bands are indeed not straight and display small deflections corresponding to
AC C
large density variations within the bands [17,18], a behavior compatible with a local mechanism based on the alignment of Eshelby-like quadrupoles [19]. Shear band formation induced by cold rolling has also been investigated. By using
digital image correlation, Binkowski et al. [20] analyzed the strain fields related to the propagation of an individual shear band and observed that adjacent areas of the shear band display strain components with opposite sign, indicative of a stick-slip behavior. Shear banding not only generates strain fields along the shear band direction, but also
3
ACCEPTED MANUSCRIPT creates strong strain fields that extend well into the material surrounding the band [21]; the comparison between experiments and simulations indicates that such fields are the mark left in the adjacent material by the structural rearrangements occurring within a
the atomistic mechanism of shear banding [22]
RI PT
shear band and suggests their possible use as a diagnostic for experimentally analyzing
In this work, the phenomenon of shear banding is further investigated by analyzing
SC
the formation of shear bands in the roll bite for the Zr52.5Ti5Cu18Ni14.5Al10 BMG (a
metallic glass extensively investigated [6,9,23,24] that represents well the distinctive
M AN U
behavior of cold-rolled amorphous metals). The analysis of shear band initiation and propagation within the roll bite is a very challenging task because of the fast dynamics of shear banding along with the characteristics of rolling, where plastic deformation occurs in a confined volume of material that travels along the specimen during the
TE D
process. To achieve this purpose, here the shear band morphology generated at an intermediate stage of rolling, when the process is stopped approximately in the middle of the sample, is examined; this approach permits one to identify the characteristics of
EP
shear band formation within the roll bite. Finally, the combination of the shear band morphology with the structural information gained from high-energy x-ray strain
AC C
analysis is used to describe the mechanism of shear band formation induced by rolling.
2. Experimental
A plate with nominal composition Zr52.5Ti5Cu18Ni14.5Al10 (at.%) and dimensions
35×40×1.7 mm3 was synthesized by copper mold casting. From this plate, specimens for cold rolling with dimensions 6x×3y×1.7z mm3 were prepared by wire erosion. Cold rolling was carried out at room temperature using a laboratory rolling mill. In order to
4
ACCEPTED MANUSCRIPT reduce the friction arising during rolling at the interfaces between rolls and samples and, therefore, to preserve the shear band morphology on the x-y plane (for the coordinate system used in this work refer to Fig. 1(a)), the samples were encapsulated into a Cu
RI PT
jacket (thickness ~0.2 mm) before rolling. The shear band morphology of the rolled specimens was evaluated by scanning electron microscopy (SEM) using a Gemini 1530 microscope. Strain analysis was performed on the Zr52.5Ti5Cu18Ni14.5Al10 BMG cold
SC
rolled at room temperature to a thickness reduction of about 3 % (measured by using a microcaliper) achieved by multiple reductions of ~0.25 %. Such a small reduction does
M AN U
not change the characteristic shear band morphology of cold-rolled BMGs and guarantees the shear band spacing to be much larger than the beam size [9,22], which thus allows one to accurately analyze the elastic strain induced by the shear band in the surrounding material. The structure of a cold-rolled specimen with thickness of about 100 µm was studied by x-ray diffraction (XRD) in transmission using a high-intensity
TE D
high-energy monochromatic synchrotron beam (λ = 0.1897 Å) at the ID11 beamline of the European Synchrotron Radiation Facility (ESRF). The specimen for XRD analysis
EP
was prepared by carefully grinding and polishing a 3 % rolled sample (original dimensions 6x×3y×1.7z mm3) down to a thickness of 100 µm. Diffraction patterns were
AC C
collected on the x-z plane at about 1 mm from the side of the specimen every 2.0 µm across an individual shear band using a beam with size of 2×2 µm2. The position of the shear band was identified by using a Cu marker. The XRD patterns were collected using a two-dimensional charge coupled device (CCD) Frelon camera [25]. The twodimensional patterns were integrated in 10° azimuthal slices between 0 and 360° using the Fit2D program [26] to give the XRD intensity distributions I(q,θ) as a function of the scattering vector q and azimuthal angle θ = 10…360°. The position of the first
5
ACCEPTED MANUSCRIPT scattering maximum q1, which can be used to evaluate the structural changes occurring in the medium-range order [27], was determined by fitting using a pseudo-Voigt function. The strain was measured through the shift of q1 with respect of the reference
RI PT
0 value q1 as ߝ = (qଵ − ݍଵ )/ݍଵ. In order to minimize possible errors introduced by the 0 uncertainty of the sample-to-detector distance, q1 was selected within the investigated
sample by choosing a position far enough from the shear band and, thus, less affected
SC
by shear banding. The components of the strain tensor (parallel, ߝଵଵ , and perpendicular, ߝଶଶ , to the shear band and the in-plane shear strain ߝଵଶ ) for each point scanned across
AC C
EP
TE D
M AN U
the band were determined according to the method described in Poulsen et al. [28].
Fig. 1. (a) Cold rolling setup and coordinate system used in this work. (b) Characteristic shear band morphology of the Zr52.5Ti5Cu18Ni14.5Al10 BMG rolled with Cu jacket to a thickness reduction of 10 % showing on the x-z plane the creation of an array of parallel shear bands forming an angle of approximately 45° with the rolling direction. (c) The shear offsets display a rotation of about 8° around the y-axis.
6
ACCEPTED MANUSCRIPT 3. Results and discussion 3.1 Shear band morphology The shear band morphology generated by cold rolling in the Zr52.5Ti5Cu18Ni14.5Al10
RI PT
BMG has been reported elsewhere [9]. However, some key aspects have to be reported here. On the x-z plane, the rolled BMG exhibits straight shear bands forming an angle of approximately 45° with the rolling direction (Figs. 1(b) and 1(c)). These shear bands
SC
propagate for about 100 µm along the y-axis and then they branch and intersect,
generating a rather irregular shear band morphology on the x-y plane. The shear offsets
M AN U
related to the straight bands are not parallel to the rolling direction but display a rotation of about 8° around the y-axis (Fig. 1(c)). The friction arising during rolling at the interface between rolls and specimen drastically affects the shear band morphology on the x-y plane, where the shear bands are not visible in the absence of the Cu jacket [9],
TE D
whereas it does not change the shear band arrangement on the x-z plane, where the bands are oriented at about 45° in both high and low friction conditions [9]. The arrangement of the shear bands shown in Figs. 1(b) and 1(c) is the final result
EP
of cold rolling, that is, after that the confined volume where plastic deformation occurs has traveled along the entire specimen. In order to understand the mechanism of shear
AC C
band formation, the process of cold rolling would require to be analyzed in-situ. This approach, however, poses the problem of examining the shear banding phenomenon through the Cu jacket necessary to preserve the morphology of the bands. A way to overcome this problem is to stop the rolling process at an intermediate stage, where the plastic deformation front comes to an end within the sample. The resulting shear band morphology at the front end would thus exhibit the characteristic features generated in the roll bite.
7
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Fig. 2. (a) Shear band morphology for the cold-rolled Zr52.5Ti5Cu18Ni14.5Al10 BMG when the rolling process is stopped approximately in the middle of the sample; the white dashed lines mark the position of shear bands with different morphologies, while the yellow full lines represent the rolls. (b,c) Magnified view of the shear band morphology corresponding to the red and blue dashed boxes in (a). (d) SEM
TE D
micrograph revealing that the shear bands (marked by red arrows) do not propagate beyond the green dashed line, which can be approximately considered as the roll bite entry.
EP
An example of this approach is shown in Fig. 2(a), which displays a Zr52.5Ti5Cu18Ni14.5Al10 BMG sample cold rolled up to about its half-length. The shape of
AC C
the specimen is no longer flat and the curvature imparted by the rotating cylindrical rolls (represented by yellow full lines in Fig. 2(a)) is evident. The shear band morphology is irregular near the sample edge, where curved and intersecting shear bands are formed. The morphology becomes more regular towards the center of the sample with the formation of parallel and straight shear bands (marked by dashed white lines). Shear offsets are formed on both rolled surfaces (Figs. 2(b) and 2(c)) and their angle varies along the arc of contact from about 2° to values oscillating around 8° (Fig. 3). This
8
ACCEPTED MANUSCRIPT indicates that the rotation around the y-axis observed in Fig. 1(c) is a dynamic process and that the orientation of the shear offsets changes within the roll bite. The shear bands propagating toward the center of the specimen do not go beyond the green dashed line
M AN U
SC
RI PT
in Fig. 2(d), which can be approximately considered as the roll bite entry.
Fig. 3. Representative variation of the angle formed by the shear offsets within the roll bite after rotation around the y-axis (see inset for the orientation of the offsets). The dashed green line represents the roll
TE D
bite entry.
EP
3.2 Mechanism of shear band formation
The arrangement of the shear bands shown in the previous section provides useful
AC C
information regarding their formation in the gap between the rolls, where the material is progressively subjected to plastic deformation, as schematically described in Fig. 4(a). Along the arc of contact between the rolls and the specimen delimited by the curve ab, the pressure P exerted by the rolls increases along the rolling direction from the roll bite entry, passes through a maximum at the neutral point N and subsequently decreases towards the roll bite exit [29]. This pressure profile creates two elastic zones at entry
9
ACCEPTED MANUSCRIPT and exit of the roll gap that enclose the zone undergoing plastic deformation (dark grey area in Fig. 4(a)), which defines the volume where the shear bands can form. Shear bands generated by cold rolling of BMGs form an angle of about 45° with the
RI PT
rolling direction [4,5,9]. Because of this orientation, shear bands generated at the entry of the plastic zone, where the yield strength of the BMG is exceeded, can propagate
until they encounter the elastic zone, where they are stopped, as observed in Fig. 2(d).
SC
This behavior can be better understood by considering Figs. 4(b) and 4(c), which show schematically the propagation of shear bands within the roll bite at two consecutive
M AN U
stages of rolling. During the first stage (Fig. 4(b)), shear bands (red full lines) can form and propagate within the plastic zone and their propagation is then interrupted at the elastic zone. In the following stage (Fig. 4(c)), when a new portion of material enters the roll bite and, correspondingly, the plastic zone travels in the opposite direction, new
TE D
shear bands (black full line) can be generated and the shear bands formed in the previous stage can propagate further. This process gradually drives the shear bands across the sample until they eventually emerge on the opposite side, shearing a portion
AC C
EP
of material with respect to the adjacent one.
10
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
EP
Fig. 4. Schematic illustrations of: (a) rolling setup showing the main features characterizing the roll bite and (b,c) shear band propagation within the roll bite at two consecutive stages of rolling. The full lines
AC C
oriented at 45° in (b,c) represent the shear bands formed in the plastic zone (dark grey), while the dotted lines indicate the bands not propagating through the elastic zone (light grey).
After having qualitatively described the progressive shear band propagation within
the roll bite, it is now necessary to discuss the mechanism leading to this process and, in particular, how the pressure exerted by the rolls is transmitted to the propagating band. As already observed in Fig. 2, shear bands nucleate on the surface of the rolled BMG and propagate at about 45° towards the opposite surface. The shear offsets visible on the
11
ACCEPTED MANUSCRIPT sample surface display a rotation around the y-axis that depends on the position along the arc of contact (Fig. 3). Shear band propagation and the rotation of the shear offsets,
M AN U
SC
RI PT
therefore, appear to be correlated.
Fig. 5. (a,b) Schematic representation of shear band propagation. The vertical lines in (a) represent the undeformed condition and the horizontal dashed line marks the position of the shear band formed in (b). The vertical lines are distorted in (b) due to the formation of the shear band, inducing opposite strain fields at the two sides of the band. (c) Variation of the components of the strain tensor evaluated by high-
TE D
energy XRD across a shear band generated by cold rolling the Zr52.5Ti5Cu18Ni14.5Al10 BMG. ε11 and ε22 represent the strain components respectively parallel and perpendicular to the shear band, while ε12 is the shear strain. The horizontal dashed line in (c) marks the position of the shear band. The colors in (b) are
EP
not derived experimentally and are solely intended to represent the strain profile in (c).
AC C
A possible explanation for this behavior is given in Figs. 5(a) and 5(b), which schematically show a shear band and the corresponding shear offset formed from an undeformed initial condition (represented by the vertical lines in Fig. 5(a)). Once the shear band is initiated, the rotation of the shear offset imparted by the roll is progressively transmitted to the shear band, driving its propagation. According to this hypothesis, the rotation would induce atomic displacements with opposite directions at the two sides of the band (represented by the distorted lines in Fig. 5(b)) and, for the shear band represented in Fig. 5(b), which comes to an end within the material, strain
12
ACCEPTED MANUSCRIPT compatibility with the neighboring unsheared material would induce tensile and compressive strains in the direction parallel to the band [22]. The validity of this hypothesis was examined by analyzing the variation of the components of the strain
RI PT
tensor across an individual band estimated by high-energy XRD (Fig. 5(c)). The results confirm the hypothesis: the strain parallel to the shear band (ε11) displays a sigmoidal
profile with the sign changing from compressive to tensile at opposite sides of the band.
SC
An inverse trend (i.e. from tension to compression) is exhibited by the strain component perpendicular to the band (ε22). The shear strain (ε12) displays the smallest variation,
M AN U
indicating that most of the strain is accommodated along the directions parallel and perpendicular to the shear band. Interestingly, the amount of strain at the two sides of the band is not equal: the compressive strain is larger than the tensile strain along the shear band direction (ε11), whereas the tensile strain is larger in the direction
TE D
perpendicular to the band (ε22). The origin of this behavior is unclear and additional experiments involving strain mapping of a series of shear bands are needed to clarify whether this is a distinctive feature of shear banding or simply the result of a local
EP
asymmetry of the stress distribution during rolling. The strain profiles in Fig. 5(c) represent only a glimpse of the strain distribution
AC C
generated across a shear band, which continuously changes as the band propagates through the specimen, as recently shown by molecular dynamics simulations [22]. The observed strain is the microscopic manifestation of the mechanism of shear banding at the nanoscale, which evolves from an antisymmetric character for a band not transecting the entire specimen to a symmetric profile for a mature shear band emerging on the opposite side of the sample [22]. It is also tempting to correlate this behavior to the serrations of opposite sign (tensile and compressive) observed by Wright et al. [30]
13
ACCEPTED MANUSCRIPT under uniaxial compression; a correlation which would suggest that the effect of shear band formation spans different length scales from the atomic level to the macroscale. The mechanism outlined in Fig. 5 has strong similarities with the one proposed by
RI PT
Qu et al. [31] for explaining shear band propagation under uniaxial compression. According to the interpretation of Qu et al. [31], shear bands are often initiated at stress concentrators, such as surface imperfections or defects, even if the applied stress is
SC
below the yield strength of the material. The formation of a shear offset on the sample surface would then induce contraction and traction of atoms/clusters at opposite sides of
M AN U
the shear band while it propagates approximately at 45° towards the opposite surface
AC C
EP
TE D
[31], as experimentally observed here in Fig. 5(c).
14
ACCEPTED MANUSCRIPT Fig. 6. Schematic illustrations of: (a) deformation of the metallic glass within the roll bite represented by a unit specimen (light blue rectangle) undergoing a series of consecutive compression tests at increasing loads (red-blue areas); (b1,c1) stress profiles across the specimen and (b2,c2) corresponding degree of sample deformation for the unit specimen compressed within the (b) elastic and (c) plastic zones. The
RI PT
dotted boxes in (b2,c2) represent the undeformed unit specimen. The colors and stress profiles in (b,c) are not derived experimentally and are exclusively intended to give a descriptive explanation of the proposed mechanism.
SC
Stress concentration may also be generated during rolling. The regular shear band
M AN U
spacing characterizing BMGs cold rolled to small thickness reductions (Fig. 1) suggests that the mechanism of shear band formation may act in a periodic fashion. In analogy with the work of Song et al. [32], the deformation of the material within the roll bite can thus be represented by a unit specimen undergoing a series of consecutive compression tests at increasing loads (Fig. 6(a)). The load, however, would not be applied
TE D
homogeneously to the unit specimen because of the variation of stress along the arc of contact [29] (schematically depicted in Figs. 6(b) and 6(c)), a condition similar to that
EP
met during compression tests when the ends of a specimen are misaligned with respect to the applied load. As reported by Chen et al. [33] for a Cu-Zr-Al BMG, such a
AC C
misalignment induces the generation of a stress gradient within the sample, which leads to the formation of a high density of shear bands in the regions exhibiting comparatively higher stresses. Accordingly, once the unit specimen accesses the elastic zone at entry (Fig. 6(b)), the stress would become heterogeneously distributed. In analogy with the work of Qu et al. [31], the formation of a shear band within a unit specimen can then be qualitatively illustrated by considering how the critical stress required to activate a shear band (σy) would change across the specimen (Figs. 6(b1) and 6(c1)). In the elastic zone,
15
ACCEPTED MANUSCRIPT the maximum stress achievable is by definition below σy and no shear band is expected to be initiated at this stage. Within the plastic zone (Fig. 6(c)), the critical stress σy is exceeded and a shear band as well as the corresponding shear offset can be formed. The
RI PT
shear band would propagate only within the region of the sample where the σ ≥ σy [31], i.e. in the plastic zone, in agreement with the results displayed in Fig. 2(d), and
additional compression steps might be necessary to drive the band through the entire
SC
unit specimen. The reiteration of these steps in adjacent unit specimens leads to the
formation of new shear bands and to their propagation across the sample, progressively
M AN U
deforming the material. Due to the symmetry of the roll setup (Fig. 4(a)), this scenario would imply the symmetric formation and propagation of shear bands from each roll, giving rise to their intersection approximately at the center of the specimen. In contrast, the generation of only a pattern of parallel shear bands is observed here (Figs. 1 and 2).
TE D
This behavior is not unusual and has been ascribed to the non-perfectly symmetric rolling process combined with the asymmetric character of shear band formation [5]; two symmetric and conjugated families of shear bands can, however, be generated by
AC C
proposed here.
EP
changing the rolling direction by 180° [5], a behavior in agreement with the mechanism
4. Conclusions
The formation of shear bands within the roll bite has been investigated for the
Zr52.5Ti5Cu18Ni14.5Al10 BMG by examining the shear band morphology generated at an intermediate stage of rolling, i.e. when the rolling process is stopped approximately in the middle of the sample. Because of the orientation at about 45°, shear bands nucleated at the entry of the plastic zone, where the yield strength of the material is exceeded, can
16
ACCEPTED MANUSCRIPT propagate until they encounter the elastic zone, where they are stopped. The comparison with the shear band formation during compression tests suggests that the stress gradient generated along the arc of contact possibly triggers the formation of shear bands and the
RI PT
corresponding shear offsets on the surface of the rolled specimen. The offsets display a rotation that depends on their position along the arc of contact. The rotation transmits
the pressure exerted by the rotating rolls to the shear bands, driving their propagation.
SC
This mechanism requires that the strain at opposite sides of the band changes sign from compressive to tensile, as indeed experimentally observed by high-energy XRD across
M AN U
an individual shear band.
Acknowledgements The author thanks R.N. Shahid and J. Han for technical assistance, the European Synchrotron Radiation Facility for provision of synchrotron radiation
AC C
EP
TE D
facilities and J. Wright for assistance in using beamline ID11.
17
ACCEPTED MANUSCRIPT References [1] M.W. Chen, Mechanical behavior of metallic glasses: microscopic understanding of strength and ductility, Annu. Rev. Mater. Res. 38 (2008) 445-469.
RI PT
[2] S.-H. Joo, D.-H. Pi, A.D.H. Setyawan, H. Kato, M. Janecek, Y.C. Kim, S. Lee, H.S. Kim, Work-hardening induced tensile ductility of bulk metallic glasses via highpressure torsion, Sci. Rep. 5 (2015) 9660.
SC
[3] S. Scudino, B. Jerliu, S. Pauly, K.B. Surreddi, U. Kühn, J. Eckert, Ductile bulk
metallic glasses produced through designed heterogeneities, Scripta Mater. 65 (2011)
M AN U
815-818.
[4] Y. Yokoyama, K. Inoue, K. Fukaura, Cold-rolled Zr50Cu30Ni10Al10 bulk amorphous alloys with tensile plastic elongation at room temperature, Mater. Trans. 12 (2002) 3199-3205.
TE D
[5] Q.P. Cao, J.W. Liu, K.J. Yang, F. Xu, Z.Q. Yao, A. Minkow, H.J. Fecht, J. Ivanisenko, L.Y. Chen, X.D. Wang, S.X. Qu, J.Z. Jiang, Effect of pre-existing shear bands on the tensile mechanical properties of a bulk metallic glass, Acta Mater. 58
EP
(2010) 1276-1292.
[6] S. Scudino, B. Jerliu, K.B. Surreddi, U. Kühn, J. Eckert, Effect of cold rolling on
AC C
compressive and tensile mechanical properties of Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass, J. Alloys Compd. 509 (2011) 128-130. [7] M. Stolpe, J.J. Kruzic, R. Busch, Evolution of shear bands, free volume and hardness during cold rolling of a Zr-based bulk metallic glass, Acta Mater. 64 (2014) 231-240. [8] Y. Yokoyama, Ductility improvement of Zr–Cu–Ni–Al glassy alloy, J. Non-Cryst. Solids 316 (2003) 104-113.
18
ACCEPTED MANUSCRIPT [9] S. Scudino, K.B. Surreddi, Shear band morphology and fracture behavior of coldrolled Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass under tensile loading, J. Alloys Compd. 708 (2017) 722-727.
(rolling deformation), J. Mater. Sci. 16 (1981) 2411-2418.
RI PT
[10] S. Takayama, Work-hardening and susceptibility to plastic flow in metallic glasses
[11] J. Kobata, T. Kimura, Y. Takigawa, T. Uesugi, H. Kimura, K. Higashi, Effect of
metallic glass, Mater. Trans. 50 (2009) 2355-2358.
SC
pre-introduced shear bands direction on deformation behavior in Zr55Al10Ni5Cu30 bulk
M AN U
[12] S. Xie, J.J. Kruzic, Cold rolling improves the fracture toughness of a Zr-based bulk metallic glass, J. Alloys Compd. 694 (2017) 1109-1120.
[13] J. Pan, Q. Chen, L. Liu, Y. Li, Softening and dilatation in a single shear band, Acta Mater. 59 (2011) 5146-5158.
TE D
[14] R. Maaß, K. Samwer, W. Arnold, C.A. Volkert, A single shear band in a metallic glass: Local core and wide soft zone, Appl. Phys. Lett. 105 (2014) 171902. [15] R. Maaß, P. Birckigt, C. Borchers, K. Samwer, C.A. Volkert, Long range stress
EP
fields and cavitation along a shear band in a metallic glass: The local origin of fracture, Acta Mater. 98 (2015) 94-102.
AC C
[16] D.P. Wang, B.A. Sun, X.R. Niu, Y. Yang, W.H. Wang, C.T. Liu, Mutual interaction of shear bands in metallic glasses, Intermetallics 85 (2017) 48-53. [17] V. Schmidt, H. Rösner, M. Peterlechner, G. Wilde, Quantitative measurement of density in a shear band of metallic glass monitored along its propagation direction, Phys. Rev. Lett. 115 (2015) 035501. [18] C. Liu, V. Roddatis, P. Kenesei, R. Maaß, Shear-band thickness and shear-band cavities in a Zr-based metallic glass, Acta Mater. 140 (2017) 206-216.
19
ACCEPTED MANUSCRIPT [19] V. Hieronymus-Schmidt, H. Rösner, G. Wilde, A. Zaccone, Shear banding in metallic glasses described by alignments of Eshelby quadrupoles, Phys. Rev. B 95 (2017) 134111.
RI PT
[20] I. Binkowski, S. Schlottbom, J. Leuthold, S. Ostendorp, S.V. Divinski, G. Wilde, Sub-micron strain analysis of local stick-slip motion of individual shear bands in a bulk metallic glass, Appl. Phys. Lett. 107 (2015) 221902.
SC
[21] H. Shakur Shahabi, S. Scudino, I. Kaban, M. Stoica, B. Escher, S. Menzel, G.B.M. Vaughan, U. Kühn, J. Eckert, Mapping of residual strains around a shear band in bulk
M AN U
metallic glass by nanobeam x-ray diffraction, Acta Mater. 111 (2016) 187-193. [22] S. Scudino, D. Şopu, Strain distribution across an individual shear band in real and simulated metallic glasses, Nano Lett. 18 (2018) 1221-1227.
[23] P.N. Zhang, J.F. Li, Y. Hu, Y.H. Zhou, Effect of rolling on the microstructure and
462 (2008) 88-93.
TE D
mechanical property of Zr52.5Cu17.9Ni14.6Al10Ti5 bulk metallic glass, J. Alloys Compd.
[24] C.T. Liu, L. Heatherly, D.S. Easton, C.A. Carmichael, J.H. Schneibel, C.H. Chen,
EP
J.L. Wright, M.H. Yoo, J.A. Horton, A. Inoue, Test environments and mechanical properties of Zr-base bulk amorphous alloys, Metall. Mater. Trans. A 29 (1998) 1811-
AC C
1820.
[25] J.C. Labiche, O. Mathon, S. Pascarelli, M.A. Newton, G.G. Ferre, C. Curfs, G. Vaughan, A. Homs, D.F. Carreiras, The fast readout low noise camera as a versatile xray detector for time resolved dispersive extended x-ray absorption fine structure and diffraction studies of dynamic problems in materials science, chemistry, and catalysis, Rev. Sci. Instrum. 78 (2007) 091301.
20
ACCEPTED MANUSCRIPT [26] A.P. Hammersley, S.O. Svensson, M. Hanfland, A.N. Fitch, D. Hausermann, Twodimensional detector software: From real detector to idealised image or two-theta scan, High Press. Res. 14 (1996) 235
RI PT
[27] S. Scudino, M. Stoica, I. Kaban, K.G. Prashanth, G.B.M. Vaughan, J. Eckert, Length scale-dependent structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 metallic glass, J. Alloys Compd. 639 (2015) 465-469.
SC
[28] H.F. Poulsen, J.A. Wert, J. Neuefeind, V. Honkimäki, M. Daymond, Measuring strain distributions in amorphous materials, Nature Mater. 4 (2005) 33-36.
M AN U
[29] M. Kazeminezhad, A. Karimi Taheri, Calculation of the rolling pressure distribution and force in wire flat rolling process, J. Mater. Proc. Tech. 171 (2006) 253258.
[30] W.J. Wright, M.W. Samale, T.C. Hufnagel, M.M. LeBlanc, J.N. Florando, Studies
TE D
of shear band velocity using spatially and temporally resolved measurements of strain during quasistatic compression of a bulk metallic glass, Acta Mater. 57 (2009) 46394648.
EP
[31] R.T. Qu, Z.Q. Liu, G. Wang, Z.F. Zhang, Progressive shear band propagation in metallic glasses under compression, Acta Mater. 91 (2015) 19-33.
AC C
[32] K.K. Song, S. Pauly, Y. Zhang, S. Scudino, P. Gargarella, K.B. Surreddi, U. Kühn, J. Eckert, Significant tensile ductility induced by cold rolling in Cu47.5Zr47.5Al5 bulk metallic glass, Intermetallics 19 (2011) 1394-1398. [33] L.Y. Chen, Q. Ge, S. Qu, Q.K. Jiang, X.P. Nie, J.Z. Jiang, Achieving large macroscopic compressive plastic deformation and work-hardening-like behavior in a monolithic bulk metallic glass by tailoring stress distribution, Appl. Phys. Lett. 92 (2008) 211905.
21
ACCEPTED MANUSCRIPT Figure captions Fig. 1. (a) Cold rolling setup and coordinate system used in this work. (b) Characteristic shear band morphology of the Zr52.5Ti5Cu18Ni14.5Al10 BMG rolled with Cu jacket to a
RI PT
thickness reduction of 10 % showing on the x-z plane the creation of an array of parallel shear bands forming an angle of approximately 45° with the rolling direction. (c) The
SC
shear offsets display a rotation of about 8° around the y-axis.
Fig. 2. (a) Shear band morphology for the cold-rolled Zr52.5Ti5Cu18Ni14.5Al10 BMG
M AN U
when the rolling process is stopped approximately in the middle of the sample; the white dashed lines mark the position of shear bands with different morphologies, while the yellow full lines represent the rolls. (b,c) Magnified view of the shear band morphology corresponding to the red and blue dashed boxes in (a). (d) SEM micrograph
TE D
revealing that the shear bands (marked by red arrows) do not propagate beyond the green dashed line, which can be approximately considered as the roll bite entry.
EP
Fig. 3. Representative variation of the angle formed by the shear offsets within the roll bite after rotation around the y-axis (see inset for the orientation of the offsets). The
AC C
dashed green line represents the roll bite entry.
Fig. 4. Schematic illustrations of: (a) rolling setup showing the main features characterizing the roll bite and (b,c) shear band propagation within the roll bite at two consecutive stages of rolling. The full lines oriented at 45° in (b,c) represent the shear bands formed in the plastic zone (dark grey), while the dotted lines indicate the bands not propagating through the elastic zone (light grey).
22
ACCEPTED MANUSCRIPT
Fig. 5. (a,b) Schematic representation of shear band propagation. The vertical lines in (a) represent the undeformed condition and the horizontal dashed line marks the position of
RI PT
the shear band formed in (b). The vertical lines are distorted in (b) due to the formation of the shear band, inducing opposite strain fields at the two sides of the band. (c)
Variation of the components of the strain tensor evaluated by high-energy XRD across a
SC
shear band generated by cold rolling the Zr52.5Ti5Cu18Ni14.5Al10 BMG. ε11 and ε22
represent the strain components respectively parallel and perpendicular to the shear
M AN U
band, while ε12 is the shear strain. The horizontal dashed line in (c) marks the position of the shear band. The colors in (b) are not derived experimentally and are solely intended to represent the strain profile in (c).
TE D
Fig. 6. Schematic illustrations of: (a) deformation of the metallic glass within the roll bite represented by a unit specimen (light blue rectangle) undergoing a series of consecutive compression tests at increasing loads (red-blue areas); (b1,c1) stress
EP
profiles across the specimen and (b2,c2) corresponding degree of sample deformation for the unit specimen compressed within the (b) elastic and (c) plastic zones. The dotted
AC C
boxes in (b2,c2) represent the undeformed unit specimen. The colors and stress profiles in (b,c) are not derived experimentally and are exclusively intended to give a descriptive explanation the proposed mechanism.
23
ACCEPTED MANUSCRIPT
EP
TE D
M AN U
SC
RI PT
Shear band mechanism within the roll bite in cold-rolled bulk metallic glass Shear offset rotation transmits the pressure from rolls to propagating shear band Strain at opposite sides of shear band changes sign from compressive to tensile
AC C
• • •