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Nanoforming behaviour and microstructural evolution during nanoimprinting of ultrafine-grained and nanocrystalline metals
Materials Science & Engineering A 568 (2013) 68–75
Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Nanoforming behaviour and microstructural evolution during nanoimprinting of ultrafine-grained and nanocrystalline metals J. Ast n, K. Durst Materials Science and Engineering, University Erlangen—N¨ urnberg, D-91058 Erlangen, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 September 2012 Received in revised form 13 November 2012 Accepted 15 November 2012 Available online 27 November 2012
The influences of microstructure and the macroscopic material behaviour on the nanoforming behaviour of nickel, copper and aluminium with grain sizes ranging from single crystalline to nanocrystalline were studied using a flat punch indenter with a double ring cavity and with a wheel-shaped die. Of main interest in this work was the flow of crystalline materials in submicron sized cavities during imprinting. The ring cavities which have widths of 650 nm and 80 nm were fabricated by focused ion beam (FIB) machining. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to evaluate the imprinted ring geometries. The microstructure after imprinting was investigated in detail by FIB cross sections and electron back scatter diffraction (EBSD) as well as by using finite element analysis (FEA) of the forming process. SX-Ni showed the smallest extrusion height together with a sinking-in of the formed region. This is accompanied by strong orientation gradients up to 181 below the cavities. The UFG samples exhibited the best formability, with a subgrain formation inside and around the cavities. The plastic flow is confined to the surface and a pile-up formation occurs. For the nanocrystalline material only a slight elongation of the grains inside the cavity was found, yielding moreover a smooth and homogeneous extruded geometry. These findings can be explained by the grain size to cavity width ratio as well as the yield strength and the work hardening behaviour of the materials. & 2012 Elsevier B.V. All rights reserved.
Keywords: Nanoforming Nanoimprinting Finite element analysis Grain size EBSD
1. Introduction The demand for micro-parts in today’s industrial applications in the fields of electronics, healthcare and automotive is rising. These parts such as miniaturised springs and screws have small dimensions in the sub-millimetre scale and complex geometries especially when used in micro-electro-mechanical-systems (MEMS). In reviews by Geiger et al. [1] and by Engel and Eckstein [2] an overview of mostly metallic micro-parts is given and emphasis is put on many obstacles one has to overcome when designing these versatile structures. Previous studies from Engel and Eckstein [2] and Wang et al. [3] have shown that the material’s microstructure, e.g. the grain size, has a decisive influence on the forming capability of the materials. When the grain size approximates about half of the cavity line width the local flow behaviour is at its lowest. Justinger and Hirt [4] showed that the crystallographic orientation of the grains in the forming zone is decisive for the forming accuracies and forces when the dimensions of the forming tool are in the same magnitude as those of the material’s microstructure. Durst et al. [5] explained that the grain size dependency found during imprinting is strongly
n
Corresponding author. Fax: þ49 91318527504. E-mail address: [email protected] (J. Ast).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.056
related to the work hardening behaviour of the material. UFGmetals with grain sizes below 1 mm exhibit nearly ideal plastic behaviour combined with pronounced strain-rate sensitivity and thus provide superior forming capabilities, as has been also found by Topic et al. [6] on the macroscopic scale. In this work the plastic flow of UFG- and nanocrystalline metals with grain sizes ranging from 80 nm up to 1.2 mm was studied by means of flat punch indentation experiments with forming cavities of less than 1 mm. The experimental setup, besides using static indentation, was quite similar to that of Cross et al. [7] who carried out nanoimprints on polymeric films on silicon with a FIB-milled flat punch. After imprinting, atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to evaluate the formed ring geometries in terms of extrusion height relative to residual imprinting depth. Via FIB cross sections and electron back scatter diffraction (EBSD) measurements, changes in the grain size and orientation inside of the formed geometry were investigated in detail. For all the EBSD analyses the software HKL CHANNEL5 by Oxford Instruments was chosen. Part of the experimental work was complemented by FEA of the forming process to further understand the effect of the macroscopic work hardening behaviour on the shape and size of the plastic zone around the cavities. Macroscopic stress–strain data measurements of the imprinted metals were taken as input for the finite element simulations.
J. Ast, K. Durst / Materials Science & Engineering A 568 (2013) 68–75
2. Experimental setup
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2.1. Materials and sample preparation
linear extrapolation
nano-Ni
The nanoforming experiments were performed on pure metallic Ni for grain sizes ranging from single crystalline to nanocrystalline as well as Cu and Al samples with grain sizes in the ultrafine-grained regime. Pulsed-electro-deposition (PED) was used to produce nanocrystalline Ni (‘‘nano-Ni’’). By annealing the PED-samples for 15 h at 300 1C an ultrafine-grained homogeneous microstructure was obtained—these samples will be referred to as ‘‘UFG-Ni’’. Furthermore, samples of ultrafine-grained Cu and Al as produced by equal channel angular pressing (ECAP) were prepared. The macroscopic deformation behaviour of all materials except for the singlecrystalline Ni was determined by uniaxial compression tests. The average grain size was determined on metallographic cross sections of the materials using the back scatter electron (BSE) contrast in a SEM. Details on the studied materials with their processing, microstructure and mechanical properties are discussed in general by Durst et al. [5] and specifically for Ni by Li et al. [8], for Cu by Li et al. [9] and for Al by May et al. [10]. Table 1 provides an overview of the used metals and grain sizes. All the samples were sectioned, ground and polished. Prior to the experiments a final electrolytic polishing with a solution of 230 ml demineralised water, 40 ml concentrated acetic acid and 230 ml 95–97% sulphuric acid was performed. The electrolytes D2 and A3 by Struers Inc. were chosen for the Cu and the Al samples, respectively. For the FE-calculations of the imprinting process, stress–strain input data as determined by compression testing of the samples were used. Regarding elastic properties, literature values were used (ENi ¼200 GPa, ECu ¼120 GPa and EAl ¼70 GPa) assuming a constant Poisson’s ratio of 0.33 for all materials.
Stress / MPa
1600
1200
UFG-Ni
800 UFG-Cu 400
CG-Ni UFG-Al
0 0.00
0.05
0.10 0.15 Plastic strain
0.20
0.25
Fig. 1. Stress–strain curves of the investigated materials produced by means of compression tests.
to provide a stiff forming die having a diameter of 8.3 mm. As shown in Fig. 2(a) a double ring cavity was then milled into its surface, providing a symmetric forming geometry. The outer ring’s diameter was set to 6.2 mm, its width to 650 nm and its depth to 750 nm. The inner ring’s diameter was set to 1.2 mm and its width and depth to about 80 nm. For material redeposition reasons the rings’ walls are not perfectly straight. For a second series of experiments on the materials, the indenter was modified again by FIB milling in order to obtain a wheel-shaped die which is shown in Fig. 2(b). For this the two cavities were connected by rectangular slits having a width of about 400–500 nm. The aim of this was to reduce the contact area and to enhance the extrusion height and furthermore to produce a more sophisticated wheel like structure on the nanoscale.
2.2. Compression testing 2.4. Imaging and evaluation procedure of the formed rings The true-stress plastic-strain data from compression tests are plotted in Fig. 1. By subtracting the elastic response from the truestress–true-strain data at a strain rate of 10 3 s 1, the plastic strain is obtained. Up to ten interpolation points were chosen as simulation input parameters in order to describe the materials’ hardening behaviour. Further details can be found in Durst et al. [5]. To approximate the behaviour of the SX-Ni in multiple slip conditions, stress–strain data for a conventionally-grained Ni sample (CG-Ni) with a grain size between 2 and 3 mm were chosen. Since the CG-Ni was well annealed and the grain size was rather large, similar behaviour is expected for both materials. 2.3. Fabrication of indenters for imprinting experiments For the nanoforming experiments a flat punch with a double circular cavity was fabricated by focused ion beam milling with a Zeiss Cross Beam 1540 FIB. A Berkovich-type diamond indenter was taken and modified by the FIB milling to produce a flat punch indenter. An aspect ratio (height/diameter) of about 1/3 was chosen Table 1 Investigated materials and grain sizes. Material
Grain size (nm)
Nano-Ni UFG-Ni SX-Ni UFG-Cu SX-Cu UFG-Al
80 740 1200 7280 – 750 7275 – 950 7280
The nanoforming experiments were performed at room temperature up to an indentation depth of 3 mm using a Nanoindenter XP. Prior to the experiments the sample surface had to be aligned to the punch. This was done by mounting the sample on a tripod equipped with adjustment screws to allow slight inclinations (up to 51) of the sample. By performing imprints at depths o500 nm a possible misalignment could thus be corrected. The loading rates were kept constant for all experiments and was 70 s for loading, 10 s peak hold time and 30 s for unloading. The formed rings’ topography was evaluated by means of AFM using a Dimension 3100 from Veeco in contact mode. Fig. 3(a) shows an AFM height mode image of a formed double ring structure in UFG-Al. In the cross section analysis (Fig. 3(b)) the total plastic indentation depth hind and the extrusion height hextr were quantitatively determined. In order to compensate a slight misalignment between the sample and the indenter surface, the wall height of the larger ring was evaluated at two opposite points. At least two imprints with the same indentation depth were evaluated for calculating the average values together with the standard deviation. The forming characteristics of the smaller inner ring are only qualitatively discussed regarding the hardening behaviour of the respective materials.
3. Results 3.1. Influence of work hardening behaviour on the nano-extrusion A series of imprints for different plastic depths is shown in Fig. 4 for UFG-Al for the double ring die. A slightly inclined contact
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J. Ast, K. Durst / Materials Science & Engineering A 568 (2013) 68–75
Fig. 2. SEM images of the modified flat punch nanoindenter with (a) double ring cavity and (b) wheel-like cavity.
Fig. 3. (a) AFM height mode image of an imprint in UFG-Al and (b) the associated cross section evaluation; indicated in blue is the indentation depth hind and in red the extrusion height hextr. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Series of SEM images of UFG-Al at different indentation depths as indicated in (a)–(d).
between the indenter and the sample surface leads initially to a slightly inhomogeneous material flow (Fig. 4(a)). The extrusion height is initially equal to the remaining indentation depth. At larger indentation depths, the grain structure becomes visible in the ring structure as well as at the outer side of the imprint, where the grains are slightly pushed out of the surface. The extrusion height
increases continuously and the contours of the smaller ring become more pronounced (Fig. 4(b), (c)). At still larger depth, the ring height saturates and the fully formed ring structure is pushed into the surface. In Fig. 5 the extrusion height from AFM analysis is shown as a function of plastic indentation depth for the different materials.
J. Ast, K. Durst / Materials Science & Engineering A 568 (2013) 68–75
Initially, a linear relation between the extrusion height and the indentation depth is expected for all materials [5]. For small depths (o500 nm), it is however difficult to determine the exact extrusion height as well as the exact indentation depth. Slight misalignments of the indenter as well as surface roughness lead to non-homogeneous not well defined extruded geometries. Yet for SX-Ni and especially for UFG-Al the linear trend with different slopes is clearly visible. Included in the plot is a line with a 451 slope, which indicates the same extrusion height as the remaining indentation depth. For UFGNi this ratio of hextr/hind is close to one whereas it is around 0.7 for the other UFG-materials and nano-Ni. SX-Ni shows very limited flow at this stage with a ratio of 0.3. At larger indentation depths (hind E500 nm), the extrusion heights deviate from the linear behaviour depending on the grain size and the hardening behaviour of the materials. It is well known from indentation testing that materials which have a pronounced work hardening rate like SX-Ni exhibit far reaching plastic zones underneath the imprints. However materials which do not work-harden and deform in an ideal plastic manner, show a constrained plastic flow at the surface, yielding extensive pileup behaviour also [11,12]. This behaviour also results in larger extrusion heights during nanoimprinting.
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The - prior to the experiments - severely deformed metals UFG-Al and UFG-Cu show a further increase of the extrusion height with large indentation depth and reach the highest values, whereas the nano-Ni saturates at quite an early stage (hind E700 nm). The fact that for UFG-Al the extrusion height values keep increasing with the plastic depth shows that the cavity depth is 4500 nm. The SX-Ni needs large indentation depths due to its strong hardening behaviour to achieve comparable ring wall heights and consequently shows the worst nanoimprinting behaviour. This will be also demonstrated by FE-simulations shown in the discussion chapter. Besides the grain size, the enhanced forming behaviour of UFG-Ni with respect to nano-Ni could be due to the higher Young’s modulus to yield stress ratio which is about 160 for nano-Ni and around 250 for UFG-Ni. At the same total applied strain or imprinting depth, UFG-Ni will respond with a much larger plastic strain contribution as compared to nano-Ni, which exhibits a large elastic recovery during unloading. It is therefore expected that during nanoimprinting of UFG-Ni better forming characteristics are achieved. To further understand this grain size dependence on the forming characteristics FIB cross sections of the extruded geometries were performed.
Extrusion height / nm
800
3.2. Deformation induced structure formation
UFG-Al UFG-Cu UFG-Ni nano-Ni SX-Ni
600 1 400
200
0
0
500
1000 1500 Indentation depth / nm
2000
2500
Fig. 5. Comparison of different materials in terms of the ring’s extrusion height.
In the following chapter the structure formation underneath the imprinted areas is analysed using FIB cross sections and EBSD measurements. Firstly, imprints made with the double ring die in UFG-Ni and nano-Ni were chosen to investigate the local material flow into the separate cavities in detail in dependency of the grain size. In a second step, the material flow was also analysed for imprints made with the more complex wheel-like die in SX-Ni and UFG-Ni. Fig. 6(a) and (b) shows top-view SEM images in BSE contrast of imprints in UFG and nano-Ni made with the double ring die. There the grain structure is clearly visible and it is obvious that for UFG-Ni a strong grain refining takes place in the ring wall–the calculated ratio of grain size to ring width is about 1.75 for UFGNi–whereas in the inner part of the formed geometry the grain size seems to be unaffected. This becomes even more apparent in the cross sectional analysis (c) where a strong grain refinement is
Fig. 6. SEM images of imprints in (a) and (c) UFG-Ni and (b) and (d) nano-Ni. The smaller inner ring could not be formed at the present imprinting depth of about 1.5 mm. Prior to the FIB cross sectioning a thin Pt-layer was deposited onto the imprints to avoid blur contour edges.
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Fig. 7. Side-view SEM images of imprints in (a) UFG-Ni and (b) SX-Ni at depths of about 1 mm, FIB cross sections of imprints in (c) UFG-Ni and (d) SX-Ni, EBSD-scans (euler angles) of the lateral surface of the UFG-Ni cross section (e) directly under the imprint and at a depth of about 10 mm, and (f) EBSD misorientation profile (texture component mapping) of the SX-Ni cross section. The outher shape of the weel-like indenter is schematically represented by a grey line. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
found for the edges of the formed geometry as well as the ring wall. In contrast to this, the grain structure and size appear hardly affected in the zone underneath the centre of the ring as well as at the surroundings of the imprint. As discussed more profoundly later on, these findings are in good accordance with the FEA predictions: The grains being sheared along the indenter flanks and deformed into the cavities are found in the zone with the highest plastic strains (indicated by a dashed line in Fig. 6(c)). Furthermore, the grains under the flat surface of the indenter as marked by an arrow are just pushed downwards with hardly any remarkable plastic deformation as the grain size remains unchanged. The situation is quite different for nano-Ni, where the ratio of grain size to ring width is about 0.10. Several grains have to move inside the cavity in order to form the extruded geometry. With the used SEM, no remarkable change in grain size could be detected. Yet the grains in the cavity-zone of highest plastic strains seem to be slightly elongated as a consequence of the extrusion process. This moreover leads to a much smoother and more homogeneous ring contour for nano-Ni compared to UFGNi, where local anisotropic effects play a decisive role.
For the wheel-like die it should be noted that this forming punch has a reduced flat punch contact as the inner ring is connected to the outer one. Imprints with this indenter are shown exemplarily in Fig. 7(a) and (b) for UFG-Ni and SX-Ni respectively. FIB cross sections for the same materials revealing the grain structure underneath the imprints are shown in Fig. 7(c) and (d). For the UFG-Ni a severely deformed microstructure is found below the whole imprint. By means of EBSD measurements shown in Fig. 7(e) of the cross section, the formation of many low-angle grain boundaries ( o 121)–indicated in green colour–is found underneath the surface. This is in contrast to the ring structure, where subgrain formation was restricted mainly to the large cavities. By performing line section analysis around the indenter flanks and in the cavities up to a depth of 1 mm the developed subgrain size is determined to be about 350 nm. As reference, the grain structure as determined by EBSD of the undeformed bulk material is also shown in Fig. 7(e) (see also Table 1). This time hardly any low-angle grain boundaries are found and the mean grain size with 1.2 mm is much larger.
J. Ast, K. Durst / Materials Science & Engineering A 568 (2013) 68–75
For the cross section of the imprint in SX-Ni shown in Fig. 7(d) a misorientation profile (texture component mapping) of the plastically deformed crystal structure is shown in Fig. 7(f). Euler angles outside the forming region were taken as reference. Remarkably high misorientations of up to 181 are found around the flanks of the indenter and cavities. It is noticeable that there exists a region centrally underneath the imprint which in dependency of the cavity dimensions appears nearly undeformed. This is most probably caused by frictional effects, which lead to an undeformed zone underneath the flat punch, comparable to compression tests. Subgrain formation underneath the imprint could not be found this time.
4. Discussion The imprinting behaviour of the different materials depends on different factors like grain size vs. cavity width as well as the work hardening behaviour of the material. The SX-Ni with the infinite grain size compared to the cavity width and pronounced work hardening showed only a limited material flow into the ring cavities whereas the UFG-materials with nearly ideal-plastic material behaviour in combination with high yield strengths achieved the highest extrusion heights. Since the grain size determined both strength and work hardening, it is hard to discern these two factors purely form the experiments. However using FEA of the nanoforming process, only the influence of the work hardening and the elastic–plastic deformation behaviour on the nanoforming can be analysed. For information on the FEA-model, the reader is referred to the work of Durst et al. [5]. In Fig. 8 the 2D-axisymmetric model used for the double ring forming process is shown for Ni with different elastic–plastic deformation behaviours. The model consists of an analytical rigid forming die which had approximately the same dimensions as those of the experimental punch and a deformable sample. Linear rectangular CAX4 elements in the vicinity of the punch and CAX3 elements for the rest of the sample were chosen as linear elements are needed when using the adaptive mesh algorithm by Abaqus/Explicit finite element code. The contact was modelled as ‘‘hard’’ and a Coulomb friction coefficient of 0.2 was applied. After imprinting the material it is found that the equivalent plastic strain is the highest (indicated in grey) in the vicinity of the cavities and at the flanks of the indenter. At low indentation depths ( o1 mm), the material in between the larger and the smaller cavity is shifted downwards elastically (indicated in blue). This is also well observable in the FIB cross sections in Fig. 6(c) for the UFG-Ni sample, where the grain structure remains rather
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undeformed and the grains are only pushed downwards. For the UFG-Ni which showed in the macroscopic compression tests nearly ideal-plastic material behaviour the plastic deformation is confined to the forming region directly under the punch, leading to a pile-up formation around the imprint also. The strongly work hardening SX-Ni sample thus leads to a more widely spread plastic zone and sink-in behaviour around the imprint. The formation of pile-up and sink-in has to be taken into account when determining the residual indentation depth. The comparison of the Ni samples with different grain sizes shown in Fig. 7 demonstrated the enhanced microformability of the UFG-Ni and especially its remarkable grain deformation along the indenter flanks and in the cavities. Here the development of a subgrain structure is necessary to fulfil the high amount of plastic strain due to the severe plastic deformation processes developed. Nevertheless underneath the centre and further away of the imprint the grain structure appears hardly deformed as the total plastic deformation during imprinting is carried by the grains in the described deformation zones where plastic strains are the highest according to the FEA. In the case of the nano-Ni the grain size remains more or less constant in relation to the undeformed state and consequently the shaped outer ring’s surface appears smooth. Fig. 9 presents a schematic comparison and summarizes the three different grain structures studied with the double ring cavity. In reality frictional effects vary in the FIB-cut cavities as well as under the indenter as the imprints are slightly inclined because of rough surfaces. To overcome friction, the experimental procedure was modified to imprint with small oscillations which were added onto the displacement upon loading. But as the maximum achievable amplitudes were only around 10 nm with the Nanoindenter XP the results in terms of extrusion height did not change. Finally one should also keep in mind that anisotropic material properties considerably influence the nanoimprinting behaviour once only a few grains or even just one single grain is located directly under the cavity. These different factors influencing the local imprinting behaviour are visually summarized again in Fig. 10 for UFG-Cu at an indentation depth of about 1 mm. A strong subgrain formation is found in the ring wall and the initial grain size is reduced from 750 nm down to 150 nm. The outer ring wall (left hand side in Fig. 10) is moreover inclined to the surface which is probably caused by redeposition from FIB milling. The width of the cavity decreases from 650 nm at the top of the indenter down to 300 nm at a depth of 400 nm. The inclined shape of the forming die is probably also one reason for the decreasing extrusion depths with indentation depth as seen in Fig. 5. From the FE modelling with a straight wall die a steadily increasing wall height is expected.
Fig. 8. FE-simulation and evaluation of the imprinting process with the double ring geometry. The equivalent plastic strain values (PEEQ) are indicated exemplarily for (a) UFG-Ni and (b) CG-Ni after an imprinting depth of about 400 nm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 10. SEM image of a FIB-cut of an imprint in UFG-Cu; the outer ring’s shape is strongly influenced by factors such as the inclined geometry of the cavities, local frictional conditions, the grain size and the local anisotropic material behaviour.
punch indenter with two specific forming geometries. By evaluating the imprinted structures in terms of extrusion height relative to residual indentation depth a quantification of the characteristic nanoimprinting behaviour could be achieved. The change in grain size and shape upon local plastic deformation of the material into the cavities was investigated in detail by FIB cross sections and EBSD measurements. Experiments as well as FEA of the imprinting process lead to the following two main conclusions. Firstly, grain size and its evolution during imprinting have a significant impact on the shape of the imprinted structures and the forming characteristics. When the ratio of grain size to cavity width is high the surface quality of the formed geometries becomes less smooth due to severe subgrain formation in and around the cavities. This was explicitly shown in the EBSD patterns for UFG-Ni and in Fig. 10, where the deformation of individual grains in the cavity is observed by means of a FIB cut. Secondly, concerning the macroscopic hardening behaviour the FEA supports well the experimental findings. The qualitative trend is the same and the estimation of the plastic zone size with the highest strains fits well to both the SE micrographs shown for the Ni samples and the EBSD patterns of the imprinted surfaces. This proves again qualitatively and in a very illustrative way the quantitative results of Durst et al. [5] considering the fact that even on a submicron-scale the macroscopic behaviour has a great influence on local material flow. Nevertheless precise quantitative results in order to directly compare experiment and simulation in this work cannot be given.
Acknowledgements
Fig. 9. 2D-Schematic of the right side of the flat punch indenter with the double ring cavity. (a) single-crystalline, (b) ultrafine and (c) nanocrystalline grain structure. Straight black lines indicate high-angle grain boundaries, dashed black lines indicate high-angle grain boundaries formed during the imprinting process and the symbols for edge-type dislocations represent on one hand side low-angle grain boundaries for the UFG-structure and on the other hand the regions of highest plastic deformation for the SX-material—as no low-angle grain boundaries were found here.
5. Conclusions The nanoforming behaviour of various metals with grain sizes ranging from 80 nm up to 1.2 mm was studied by means of a flat
The cluster of excellence ‘‘Engineering of advanced materials ¨ (EAM)’’ at the University Erlangen—Nurnberg is gratefully acknowledged for funding of this research. Vale´rie Neitzels help considering sample preparation and EBSD measurements is also kindly appreciated. References [1] M. Geiger, M. Kleiner, R. Eckstein, Ann. CIRP 50 (2001) 445–462. [2] U. Engel, R. Eckstein, J. Mater. Process. Technol. 125–126 (2002) 35–44. [3] C.J. Wang, D.B. Shan, J. Zhou, B. Guo, L.N. Sun, J. Mater. Process. Technol. 187–188 (2007) 256–259. [4] H. Justinger, G. Hirt, J. Mater. Process. Technol. 209 (2009) 2111–2121. ¨ [5] K. Durst, S. Hofmann, B. Backes, J. Mueller, M. Goken, J. Mater. Process. Technol. 210 (2010) 1787–1793. ¨ ¨ [6] I. Topic, H.W. Hoppel, M. Goken, Int. J. Mater. Res. 98 (2007) 320–324.
J. Ast, K. Durst / Materials Science & Engineering A 568 (2013) 68–75 ¨ zer, J.B. Pethica, Nano Lett. 7 (2007) [7] G.L.W. Cross, B.S. O’Connell, H.O. O 357–362. ¨ ¨ [8] Y.L. Li, J. Mueller, H.W. Hoppel, M. Goken, W. Blum, Acta Mater. 55 (2007) 5708–5717.
[9] [10] [11] [12]
Y.L. Li, R. Valiev, W. Blum, Mater. Sci. Eng. A 410-411 (2005) 451–456. J. May, H.W. Ho ppel, M. Go ken, Scr. Mater. 53 (2005) 189–194. ¨ B. Backes, K. Durst, M. Goken, Philos. Mag. 86 (2006) 5541–5551. ¨ K. Durst, B. Backes, M. Goken, Scr. Mater. 52 (2005) 1093–1097.
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Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Nanoforming behaviour and microstructural evolution during nanoimprinting of ultrafine-grained and nanocrystalline metals J. Ast n, K. Durst Materials Science and Engineering, University Erlangen—N¨ urnberg, D-91058 Erlangen, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 September 2012 Received in revised form 13 November 2012 Accepted 15 November 2012 Available online 27 November 2012
The influences of microstructure and the macroscopic material behaviour on the nanoforming behaviour of nickel, copper and aluminium with grain sizes ranging from single crystalline to nanocrystalline were studied using a flat punch indenter with a double ring cavity and with a wheel-shaped die. Of main interest in this work was the flow of crystalline materials in submicron sized cavities during imprinting. The ring cavities which have widths of 650 nm and 80 nm were fabricated by focused ion beam (FIB) machining. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to evaluate the imprinted ring geometries. The microstructure after imprinting was investigated in detail by FIB cross sections and electron back scatter diffraction (EBSD) as well as by using finite element analysis (FEA) of the forming process. SX-Ni showed the smallest extrusion height together with a sinking-in of the formed region. This is accompanied by strong orientation gradients up to 181 below the cavities. The UFG samples exhibited the best formability, with a subgrain formation inside and around the cavities. The plastic flow is confined to the surface and a pile-up formation occurs. For the nanocrystalline material only a slight elongation of the grains inside the cavity was found, yielding moreover a smooth and homogeneous extruded geometry. These findings can be explained by the grain size to cavity width ratio as well as the yield strength and the work hardening behaviour of the materials. & 2012 Elsevier B.V. All rights reserved.
Keywords: Nanoforming Nanoimprinting Finite element analysis Grain size EBSD
1. Introduction The demand for micro-parts in today’s industrial applications in the fields of electronics, healthcare and automotive is rising. These parts such as miniaturised springs and screws have small dimensions in the sub-millimetre scale and complex geometries especially when used in micro-electro-mechanical-systems (MEMS). In reviews by Geiger et al. [1] and by Engel and Eckstein [2] an overview of mostly metallic micro-parts is given and emphasis is put on many obstacles one has to overcome when designing these versatile structures. Previous studies from Engel and Eckstein [2] and Wang et al. [3] have shown that the material’s microstructure, e.g. the grain size, has a decisive influence on the forming capability of the materials. When the grain size approximates about half of the cavity line width the local flow behaviour is at its lowest. Justinger and Hirt [4] showed that the crystallographic orientation of the grains in the forming zone is decisive for the forming accuracies and forces when the dimensions of the forming tool are in the same magnitude as those of the material’s microstructure. Durst et al. [5] explained that the grain size dependency found during imprinting is strongly
n
Corresponding author. Fax: þ49 91318527504. E-mail address: [email protected] (J. Ast).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.056
related to the work hardening behaviour of the material. UFGmetals with grain sizes below 1 mm exhibit nearly ideal plastic behaviour combined with pronounced strain-rate sensitivity and thus provide superior forming capabilities, as has been also found by Topic et al. [6] on the macroscopic scale. In this work the plastic flow of UFG- and nanocrystalline metals with grain sizes ranging from 80 nm up to 1.2 mm was studied by means of flat punch indentation experiments with forming cavities of less than 1 mm. The experimental setup, besides using static indentation, was quite similar to that of Cross et al. [7] who carried out nanoimprints on polymeric films on silicon with a FIB-milled flat punch. After imprinting, atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to evaluate the formed ring geometries in terms of extrusion height relative to residual imprinting depth. Via FIB cross sections and electron back scatter diffraction (EBSD) measurements, changes in the grain size and orientation inside of the formed geometry were investigated in detail. For all the EBSD analyses the software HKL CHANNEL5 by Oxford Instruments was chosen. Part of the experimental work was complemented by FEA of the forming process to further understand the effect of the macroscopic work hardening behaviour on the shape and size of the plastic zone around the cavities. Macroscopic stress–strain data measurements of the imprinted metals were taken as input for the finite element simulations.
J. Ast, K. Durst / Materials Science & Engineering A 568 (2013) 68–75
2. Experimental setup
69
2000
2.1. Materials and sample preparation
linear extrapolation
nano-Ni
The nanoforming experiments were performed on pure metallic Ni for grain sizes ranging from single crystalline to nanocrystalline as well as Cu and Al samples with grain sizes in the ultrafine-grained regime. Pulsed-electro-deposition (PED) was used to produce nanocrystalline Ni (‘‘nano-Ni’’). By annealing the PED-samples for 15 h at 300 1C an ultrafine-grained homogeneous microstructure was obtained—these samples will be referred to as ‘‘UFG-Ni’’. Furthermore, samples of ultrafine-grained Cu and Al as produced by equal channel angular pressing (ECAP) were prepared. The macroscopic deformation behaviour of all materials except for the singlecrystalline Ni was determined by uniaxial compression tests. The average grain size was determined on metallographic cross sections of the materials using the back scatter electron (BSE) contrast in a SEM. Details on the studied materials with their processing, microstructure and mechanical properties are discussed in general by Durst et al. [5] and specifically for Ni by Li et al. [8], for Cu by Li et al. [9] and for Al by May et al. [10]. Table 1 provides an overview of the used metals and grain sizes. All the samples were sectioned, ground and polished. Prior to the experiments a final electrolytic polishing with a solution of 230 ml demineralised water, 40 ml concentrated acetic acid and 230 ml 95–97% sulphuric acid was performed. The electrolytes D2 and A3 by Struers Inc. were chosen for the Cu and the Al samples, respectively. For the FE-calculations of the imprinting process, stress–strain input data as determined by compression testing of the samples were used. Regarding elastic properties, literature values were used (ENi ¼200 GPa, ECu ¼120 GPa and EAl ¼70 GPa) assuming a constant Poisson’s ratio of 0.33 for all materials.
Stress / MPa
1600
1200
UFG-Ni
800 UFG-Cu 400
CG-Ni UFG-Al
0 0.00
0.05
0.10 0.15 Plastic strain
0.20
0.25
Fig. 1. Stress–strain curves of the investigated materials produced by means of compression tests.
to provide a stiff forming die having a diameter of 8.3 mm. As shown in Fig. 2(a) a double ring cavity was then milled into its surface, providing a symmetric forming geometry. The outer ring’s diameter was set to 6.2 mm, its width to 650 nm and its depth to 750 nm. The inner ring’s diameter was set to 1.2 mm and its width and depth to about 80 nm. For material redeposition reasons the rings’ walls are not perfectly straight. For a second series of experiments on the materials, the indenter was modified again by FIB milling in order to obtain a wheel-shaped die which is shown in Fig. 2(b). For this the two cavities were connected by rectangular slits having a width of about 400–500 nm. The aim of this was to reduce the contact area and to enhance the extrusion height and furthermore to produce a more sophisticated wheel like structure on the nanoscale.
2.2. Compression testing 2.4. Imaging and evaluation procedure of the formed rings The true-stress plastic-strain data from compression tests are plotted in Fig. 1. By subtracting the elastic response from the truestress–true-strain data at a strain rate of 10 3 s 1, the plastic strain is obtained. Up to ten interpolation points were chosen as simulation input parameters in order to describe the materials’ hardening behaviour. Further details can be found in Durst et al. [5]. To approximate the behaviour of the SX-Ni in multiple slip conditions, stress–strain data for a conventionally-grained Ni sample (CG-Ni) with a grain size between 2 and 3 mm were chosen. Since the CG-Ni was well annealed and the grain size was rather large, similar behaviour is expected for both materials. 2.3. Fabrication of indenters for imprinting experiments For the nanoforming experiments a flat punch with a double circular cavity was fabricated by focused ion beam milling with a Zeiss Cross Beam 1540 FIB. A Berkovich-type diamond indenter was taken and modified by the FIB milling to produce a flat punch indenter. An aspect ratio (height/diameter) of about 1/3 was chosen Table 1 Investigated materials and grain sizes. Material
Grain size (nm)
Nano-Ni UFG-Ni SX-Ni UFG-Cu SX-Cu UFG-Al
80 740 1200 7280 – 750 7275 – 950 7280
The nanoforming experiments were performed at room temperature up to an indentation depth of 3 mm using a Nanoindenter XP. Prior to the experiments the sample surface had to be aligned to the punch. This was done by mounting the sample on a tripod equipped with adjustment screws to allow slight inclinations (up to 51) of the sample. By performing imprints at depths o500 nm a possible misalignment could thus be corrected. The loading rates were kept constant for all experiments and was 70 s for loading, 10 s peak hold time and 30 s for unloading. The formed rings’ topography was evaluated by means of AFM using a Dimension 3100 from Veeco in contact mode. Fig. 3(a) shows an AFM height mode image of a formed double ring structure in UFG-Al. In the cross section analysis (Fig. 3(b)) the total plastic indentation depth hind and the extrusion height hextr were quantitatively determined. In order to compensate a slight misalignment between the sample and the indenter surface, the wall height of the larger ring was evaluated at two opposite points. At least two imprints with the same indentation depth were evaluated for calculating the average values together with the standard deviation. The forming characteristics of the smaller inner ring are only qualitatively discussed regarding the hardening behaviour of the respective materials.
3. Results 3.1. Influence of work hardening behaviour on the nano-extrusion A series of imprints for different plastic depths is shown in Fig. 4 for UFG-Al for the double ring die. A slightly inclined contact
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Fig. 2. SEM images of the modified flat punch nanoindenter with (a) double ring cavity and (b) wheel-like cavity.
Fig. 3. (a) AFM height mode image of an imprint in UFG-Al and (b) the associated cross section evaluation; indicated in blue is the indentation depth hind and in red the extrusion height hextr. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Series of SEM images of UFG-Al at different indentation depths as indicated in (a)–(d).
between the indenter and the sample surface leads initially to a slightly inhomogeneous material flow (Fig. 4(a)). The extrusion height is initially equal to the remaining indentation depth. At larger indentation depths, the grain structure becomes visible in the ring structure as well as at the outer side of the imprint, where the grains are slightly pushed out of the surface. The extrusion height
increases continuously and the contours of the smaller ring become more pronounced (Fig. 4(b), (c)). At still larger depth, the ring height saturates and the fully formed ring structure is pushed into the surface. In Fig. 5 the extrusion height from AFM analysis is shown as a function of plastic indentation depth for the different materials.
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Initially, a linear relation between the extrusion height and the indentation depth is expected for all materials [5]. For small depths (o500 nm), it is however difficult to determine the exact extrusion height as well as the exact indentation depth. Slight misalignments of the indenter as well as surface roughness lead to non-homogeneous not well defined extruded geometries. Yet for SX-Ni and especially for UFG-Al the linear trend with different slopes is clearly visible. Included in the plot is a line with a 451 slope, which indicates the same extrusion height as the remaining indentation depth. For UFGNi this ratio of hextr/hind is close to one whereas it is around 0.7 for the other UFG-materials and nano-Ni. SX-Ni shows very limited flow at this stage with a ratio of 0.3. At larger indentation depths (hind E500 nm), the extrusion heights deviate from the linear behaviour depending on the grain size and the hardening behaviour of the materials. It is well known from indentation testing that materials which have a pronounced work hardening rate like SX-Ni exhibit far reaching plastic zones underneath the imprints. However materials which do not work-harden and deform in an ideal plastic manner, show a constrained plastic flow at the surface, yielding extensive pileup behaviour also [11,12]. This behaviour also results in larger extrusion heights during nanoimprinting.
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The - prior to the experiments - severely deformed metals UFG-Al and UFG-Cu show a further increase of the extrusion height with large indentation depth and reach the highest values, whereas the nano-Ni saturates at quite an early stage (hind E700 nm). The fact that for UFG-Al the extrusion height values keep increasing with the plastic depth shows that the cavity depth is 4500 nm. The SX-Ni needs large indentation depths due to its strong hardening behaviour to achieve comparable ring wall heights and consequently shows the worst nanoimprinting behaviour. This will be also demonstrated by FE-simulations shown in the discussion chapter. Besides the grain size, the enhanced forming behaviour of UFG-Ni with respect to nano-Ni could be due to the higher Young’s modulus to yield stress ratio which is about 160 for nano-Ni and around 250 for UFG-Ni. At the same total applied strain or imprinting depth, UFG-Ni will respond with a much larger plastic strain contribution as compared to nano-Ni, which exhibits a large elastic recovery during unloading. It is therefore expected that during nanoimprinting of UFG-Ni better forming characteristics are achieved. To further understand this grain size dependence on the forming characteristics FIB cross sections of the extruded geometries were performed.
Extrusion height / nm
800
3.2. Deformation induced structure formation
UFG-Al UFG-Cu UFG-Ni nano-Ni SX-Ni
600 1 400
200
0
0
500
1000 1500 Indentation depth / nm
2000
2500
Fig. 5. Comparison of different materials in terms of the ring’s extrusion height.
In the following chapter the structure formation underneath the imprinted areas is analysed using FIB cross sections and EBSD measurements. Firstly, imprints made with the double ring die in UFG-Ni and nano-Ni were chosen to investigate the local material flow into the separate cavities in detail in dependency of the grain size. In a second step, the material flow was also analysed for imprints made with the more complex wheel-like die in SX-Ni and UFG-Ni. Fig. 6(a) and (b) shows top-view SEM images in BSE contrast of imprints in UFG and nano-Ni made with the double ring die. There the grain structure is clearly visible and it is obvious that for UFG-Ni a strong grain refining takes place in the ring wall–the calculated ratio of grain size to ring width is about 1.75 for UFGNi–whereas in the inner part of the formed geometry the grain size seems to be unaffected. This becomes even more apparent in the cross sectional analysis (c) where a strong grain refinement is
Fig. 6. SEM images of imprints in (a) and (c) UFG-Ni and (b) and (d) nano-Ni. The smaller inner ring could not be formed at the present imprinting depth of about 1.5 mm. Prior to the FIB cross sectioning a thin Pt-layer was deposited onto the imprints to avoid blur contour edges.
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Fig. 7. Side-view SEM images of imprints in (a) UFG-Ni and (b) SX-Ni at depths of about 1 mm, FIB cross sections of imprints in (c) UFG-Ni and (d) SX-Ni, EBSD-scans (euler angles) of the lateral surface of the UFG-Ni cross section (e) directly under the imprint and at a depth of about 10 mm, and (f) EBSD misorientation profile (texture component mapping) of the SX-Ni cross section. The outher shape of the weel-like indenter is schematically represented by a grey line. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
found for the edges of the formed geometry as well as the ring wall. In contrast to this, the grain structure and size appear hardly affected in the zone underneath the centre of the ring as well as at the surroundings of the imprint. As discussed more profoundly later on, these findings are in good accordance with the FEA predictions: The grains being sheared along the indenter flanks and deformed into the cavities are found in the zone with the highest plastic strains (indicated by a dashed line in Fig. 6(c)). Furthermore, the grains under the flat surface of the indenter as marked by an arrow are just pushed downwards with hardly any remarkable plastic deformation as the grain size remains unchanged. The situation is quite different for nano-Ni, where the ratio of grain size to ring width is about 0.10. Several grains have to move inside the cavity in order to form the extruded geometry. With the used SEM, no remarkable change in grain size could be detected. Yet the grains in the cavity-zone of highest plastic strains seem to be slightly elongated as a consequence of the extrusion process. This moreover leads to a much smoother and more homogeneous ring contour for nano-Ni compared to UFGNi, where local anisotropic effects play a decisive role.
For the wheel-like die it should be noted that this forming punch has a reduced flat punch contact as the inner ring is connected to the outer one. Imprints with this indenter are shown exemplarily in Fig. 7(a) and (b) for UFG-Ni and SX-Ni respectively. FIB cross sections for the same materials revealing the grain structure underneath the imprints are shown in Fig. 7(c) and (d). For the UFG-Ni a severely deformed microstructure is found below the whole imprint. By means of EBSD measurements shown in Fig. 7(e) of the cross section, the formation of many low-angle grain boundaries ( o 121)–indicated in green colour–is found underneath the surface. This is in contrast to the ring structure, where subgrain formation was restricted mainly to the large cavities. By performing line section analysis around the indenter flanks and in the cavities up to a depth of 1 mm the developed subgrain size is determined to be about 350 nm. As reference, the grain structure as determined by EBSD of the undeformed bulk material is also shown in Fig. 7(e) (see also Table 1). This time hardly any low-angle grain boundaries are found and the mean grain size with 1.2 mm is much larger.
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For the cross section of the imprint in SX-Ni shown in Fig. 7(d) a misorientation profile (texture component mapping) of the plastically deformed crystal structure is shown in Fig. 7(f). Euler angles outside the forming region were taken as reference. Remarkably high misorientations of up to 181 are found around the flanks of the indenter and cavities. It is noticeable that there exists a region centrally underneath the imprint which in dependency of the cavity dimensions appears nearly undeformed. This is most probably caused by frictional effects, which lead to an undeformed zone underneath the flat punch, comparable to compression tests. Subgrain formation underneath the imprint could not be found this time.
4. Discussion The imprinting behaviour of the different materials depends on different factors like grain size vs. cavity width as well as the work hardening behaviour of the material. The SX-Ni with the infinite grain size compared to the cavity width and pronounced work hardening showed only a limited material flow into the ring cavities whereas the UFG-materials with nearly ideal-plastic material behaviour in combination with high yield strengths achieved the highest extrusion heights. Since the grain size determined both strength and work hardening, it is hard to discern these two factors purely form the experiments. However using FEA of the nanoforming process, only the influence of the work hardening and the elastic–plastic deformation behaviour on the nanoforming can be analysed. For information on the FEA-model, the reader is referred to the work of Durst et al. [5]. In Fig. 8 the 2D-axisymmetric model used for the double ring forming process is shown for Ni with different elastic–plastic deformation behaviours. The model consists of an analytical rigid forming die which had approximately the same dimensions as those of the experimental punch and a deformable sample. Linear rectangular CAX4 elements in the vicinity of the punch and CAX3 elements for the rest of the sample were chosen as linear elements are needed when using the adaptive mesh algorithm by Abaqus/Explicit finite element code. The contact was modelled as ‘‘hard’’ and a Coulomb friction coefficient of 0.2 was applied. After imprinting the material it is found that the equivalent plastic strain is the highest (indicated in grey) in the vicinity of the cavities and at the flanks of the indenter. At low indentation depths ( o1 mm), the material in between the larger and the smaller cavity is shifted downwards elastically (indicated in blue). This is also well observable in the FIB cross sections in Fig. 6(c) for the UFG-Ni sample, where the grain structure remains rather
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undeformed and the grains are only pushed downwards. For the UFG-Ni which showed in the macroscopic compression tests nearly ideal-plastic material behaviour the plastic deformation is confined to the forming region directly under the punch, leading to a pile-up formation around the imprint also. The strongly work hardening SX-Ni sample thus leads to a more widely spread plastic zone and sink-in behaviour around the imprint. The formation of pile-up and sink-in has to be taken into account when determining the residual indentation depth. The comparison of the Ni samples with different grain sizes shown in Fig. 7 demonstrated the enhanced microformability of the UFG-Ni and especially its remarkable grain deformation along the indenter flanks and in the cavities. Here the development of a subgrain structure is necessary to fulfil the high amount of plastic strain due to the severe plastic deformation processes developed. Nevertheless underneath the centre and further away of the imprint the grain structure appears hardly deformed as the total plastic deformation during imprinting is carried by the grains in the described deformation zones where plastic strains are the highest according to the FEA. In the case of the nano-Ni the grain size remains more or less constant in relation to the undeformed state and consequently the shaped outer ring’s surface appears smooth. Fig. 9 presents a schematic comparison and summarizes the three different grain structures studied with the double ring cavity. In reality frictional effects vary in the FIB-cut cavities as well as under the indenter as the imprints are slightly inclined because of rough surfaces. To overcome friction, the experimental procedure was modified to imprint with small oscillations which were added onto the displacement upon loading. But as the maximum achievable amplitudes were only around 10 nm with the Nanoindenter XP the results in terms of extrusion height did not change. Finally one should also keep in mind that anisotropic material properties considerably influence the nanoimprinting behaviour once only a few grains or even just one single grain is located directly under the cavity. These different factors influencing the local imprinting behaviour are visually summarized again in Fig. 10 for UFG-Cu at an indentation depth of about 1 mm. A strong subgrain formation is found in the ring wall and the initial grain size is reduced from 750 nm down to 150 nm. The outer ring wall (left hand side in Fig. 10) is moreover inclined to the surface which is probably caused by redeposition from FIB milling. The width of the cavity decreases from 650 nm at the top of the indenter down to 300 nm at a depth of 400 nm. The inclined shape of the forming die is probably also one reason for the decreasing extrusion depths with indentation depth as seen in Fig. 5. From the FE modelling with a straight wall die a steadily increasing wall height is expected.
Fig. 8. FE-simulation and evaluation of the imprinting process with the double ring geometry. The equivalent plastic strain values (PEEQ) are indicated exemplarily for (a) UFG-Ni and (b) CG-Ni after an imprinting depth of about 400 nm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 10. SEM image of a FIB-cut of an imprint in UFG-Cu; the outer ring’s shape is strongly influenced by factors such as the inclined geometry of the cavities, local frictional conditions, the grain size and the local anisotropic material behaviour.
punch indenter with two specific forming geometries. By evaluating the imprinted structures in terms of extrusion height relative to residual indentation depth a quantification of the characteristic nanoimprinting behaviour could be achieved. The change in grain size and shape upon local plastic deformation of the material into the cavities was investigated in detail by FIB cross sections and EBSD measurements. Experiments as well as FEA of the imprinting process lead to the following two main conclusions. Firstly, grain size and its evolution during imprinting have a significant impact on the shape of the imprinted structures and the forming characteristics. When the ratio of grain size to cavity width is high the surface quality of the formed geometries becomes less smooth due to severe subgrain formation in and around the cavities. This was explicitly shown in the EBSD patterns for UFG-Ni and in Fig. 10, where the deformation of individual grains in the cavity is observed by means of a FIB cut. Secondly, concerning the macroscopic hardening behaviour the FEA supports well the experimental findings. The qualitative trend is the same and the estimation of the plastic zone size with the highest strains fits well to both the SE micrographs shown for the Ni samples and the EBSD patterns of the imprinted surfaces. This proves again qualitatively and in a very illustrative way the quantitative results of Durst et al. [5] considering the fact that even on a submicron-scale the macroscopic behaviour has a great influence on local material flow. Nevertheless precise quantitative results in order to directly compare experiment and simulation in this work cannot be given.
Acknowledgements
Fig. 9. 2D-Schematic of the right side of the flat punch indenter with the double ring cavity. (a) single-crystalline, (b) ultrafine and (c) nanocrystalline grain structure. Straight black lines indicate high-angle grain boundaries, dashed black lines indicate high-angle grain boundaries formed during the imprinting process and the symbols for edge-type dislocations represent on one hand side low-angle grain boundaries for the UFG-structure and on the other hand the regions of highest plastic deformation for the SX-material—as no low-angle grain boundaries were found here.
5. Conclusions The nanoforming behaviour of various metals with grain sizes ranging from 80 nm up to 1.2 mm was studied by means of a flat
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