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Compatible deformation and extra strengthening by heterogeneous nanolayer composites
Scripta Materialia 179 (2020) 30–35
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Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Compatible deformation and extra strengthening by heterogeneous nanolayer composites Jianjun Li a,b,c, Wenjun Lu c,∗, James Gibson d, Siyuan Zhang e, Sandra Korte-Kerzel d, Dierk Raabe c,∗ a
School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, Hunan, China State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, Hunan, China Department of Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany d Institute of Physical Metallurgy and Materials Physics, RWTH Aachen University, Aachen 52062, Germany e Nanoanalytics and Interfaces, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany b c
a r t i c l e
i n f o
Article history: Received 7 November 2019 Revised 21 December 2019 Accepted 6 January 2020
Keywords: Compression test Multilayers Nanocrystalline materials Plastic deformation Sputtering
a b s t r a c t A topologically heterogeneous microstructure design is introduced in a Cu/Zr nanolayered composite, in which each soft 100 nm Cu or Zr layer is surrounded on both sides by several hard 10 nm Cu/Zr bilayers. This design aims to impose a full geometrical constraint on all of the soft layers. Micropillar compression tests demonstrate that the composite deforms in a compatible fashion among the layers, in which no extrusion of the soft layers occurs. An elevated strength of 730 MPa is achieved in the composite compared with the strength prediction based on the linear rule of mixtures.
Due to the high density of the hetero-interfaces that are created by alternatively stacked, dissimilar constituent materials [1–13], nanolayered (NL) metals possess good mechanical properties, such as ultra-high strength [14], high thermal stability [15–19] and excellent resistance to radiation damage [20–22]. However, homogeneous NL materials (Fig. 1a) often exhibit a severe deformation incompatibility among the constituent layers with identical thickness owing to their usually high mechanical contrast, leading to a pronounced mechanical heterogeneity upon mechanical loading. Experiments have shown that there are two types of deformation incompatibility depending on the layer thickness. The first phenomenon observed in that context includes severe shear instabilities for NL composites with very thin layers (h is in the range of approximately 1–5 nm) because of the cutting of dislocations through the interfaces that promoted joint soft deformation modes [1,23–25]. A representative example is the through-thickness formation of shear zones and shear cracks observed during rolling of Cu/Nb NL materials with a 4 nm initial layer thickness [26]. The profuse shear bands in Cu/Au [27–29], Cu/Cr [30], and Cu/amorphous CuZr [31] NL materials produced by nano-/microindentation also demonstrated this type of shear in-
∗
Corresponding authors. E-mail addresses: [email protected] (W. Lu), [email protected] (D. Raabe).
https://doi.org/10.1016/j.scriptamat.2020.01.006 1359-6462/© 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
© 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
stability behavior. The second type of deformation incompatibility is the non-matching deformation of constituent layers with a large layer thickness (h is in the range of tens of nanometres to 100 nm). A typical phenomenon is the strong extrusion of the soft constituent layer (e.g., Cu), as observed in Cu/Zr [32,33], Cu/Cr [30] or Cu/amorphous CuZr [34,35] micropillars under compression. The deformation incompatibility described above leads to very limited tensile ductility in NL materials (usually below 4% failure elongation [36–39]), which is insufficient for engineering applications. Efforts have been made to alleviate the deformation incompatibility problem, thus improving the plasticity and ductility of NL materials [26,40,41]. For example, Misra and Hoagland [26] and Wynn et al. [40] designed a bimodal NL structure that contained alternatively stacked 4 nm and 40 nm Cu/Nb bilayers, where the shear cracks that previously appeared in the 4 nm Cu/Nb NL materials were suppressed during rolling. The finding above showed that the first type of deformation incompatibility might have been overcome by a bimodal NL structure. However, our micropillar compression tests of a Cu/Zr composite showed that the bimodal design did not solve the second challenge, viz., deformation concentration and squeezing-out (extrusion) effects occurred in the soft regions [33]. This bimodal microstructure showed severe extrusion of the soft 100 nm Cu layers relative to the 100 nm Zr layers (see Fig. 5d in [33]). The problem with the bimodal NL design
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Fig. 1. Schematic of homogeneous (a), bimodal (b), and newly designed heterogeneous (c, d) nanolayer Cu/Zr structures, i.e., H1, H2 and H3, where the numeral represents the number of the 10 nm Cu/Zr bilayers that cover each side of the 100 nm layer (d). In (d), the dashed lines denote the interface between the 10 nm Cu and Zr individual layers, while the solid lines designate the 10 nm bilayer interface.
is that only one side of the 100 nm Cu or Zr layer is covered by the 10 nm bilayers (Fig. 1b). Unlike the bimodal design in pure metals, where a soft domain with large grains is completely constrained by a hard domain with small grains to produce a sufficiently large strain gradient [42–45], the 10 nm layers in the bimodal NL composite were consequently unable to produce an effective constraint on the 100 nm layers. To achieve full constraint of each 100 nm layer and produce significant strain gradient-induced strengthening, we designed a new heterogeneous nanolayer composite structure where each of the 100 nm Cu and Zr layers (the soft phase) was coated on both sides by 10 nm Cu/Zr bilayers (the hard phase) (Fig. 1c). This topology ensured that an effective constraint of the soft phase was imposed by the hard phase. The deformed pillars showed no extrusion of the soft Cu layers, as observed by scanning transmission electron microscopy (STEM) probing. The heterogeneous composite had a yield strength that is 60% much higher than that expected from the linear rule of mixtures. Three heterogeneous samples, i.e., H1, H2 and H3, were prepared by magnetron sputtering, where the numerals denote the number of coated 10 nm Cu/Zr bilayers on each side of the 100 nm layer (Fig. 1c and d). The corresponding volume fractions of the 10 nm layers in H1, H2 and H3 were 16.7%, 28.6% and 37.5%, respectively. The nominal sample thicknesses of H1, H2 and H3 were 1.44 μm, 1.40 μm and 1.2 μm, respectively. The reduced elastic moduli of the prepared samples were measured by nanoindentation. Micropillar compression tests were performed to investigate the deformation behavior of the heterogeneous layered samples and the underlying deformation response was mapped by STEM imaging of the cross sections. Details of preparation, testing, and characterization are given in the Supplementary Note 1. Fig. 2 shows the detailed analysis of the microstructures for samples H1–H3. Fig. 2a1 presents an overall of H1 with the brightfield TEM image and the corresponding selected area electron diffraction (SAED). In the TEM data, the polycrystalline grains with equiaxed morphology were observed in both 10 nm Cu/Zr and 100 nm Cu/Zr multilayers without lamellar structures (e.g., annealing twins) detected. The inset SAED reveals strong Cu {111} and Zr {0 0 02} texture. LAADF-STEM image (Fig. 2b1 ) caused by the strain-contrast [46] further confirms that the equiaxed grains with ~10 nm and ~100 nm in size have been formed within the
10 nm Cu/Zr and 100 nm Cu/Zr multilayers, respectively, leading to a fabrication of heterogeneous layered structure containing six repeated blocks. Here one block is defined as one 100 nm Cu layer and one 100 nm Zr layer plus the added 10 nm layers on the top surface of these 100 nm layers (see the numerals in Fig. 3). The enlarged LAADF-STEM view with EDS scanning in Fig. 2c1 clearly shows the heterogeneously distributed layer thicknesses (i.e., 100 nm and 10 nm) and elements (i.e., Cu and Zr). Besides, the high-resolution TEM images of the interface (Fig. 2d1 and e1 ) with fast Fourier transforms (FFTs) exhibit the typical orientation relationship between Cu and Zr layers of <110>Cu//<11–20>Zr; {111}Cu//{0 0 02}Zr. In comparison to sample H1, both sample H2 (five repeated blocks in Fig. 2a2 –e2 ) and sample H3 (four repeated blocks in Fig. 2a3 –e3 ) show similar microstructure features, e.g., grain size: ~10 nm in 10 nm Cu/Zr nanolayers and ~100 nm Cu/Zr in 100 nm multilayers; morphology: equiaxed grain; texture (Supplementary Fig. 1): Cu {111} and Zr {0 0 02}; and interface: <110>Cu//<11–20>Zr; {111}Cu//{0 0 02}Zr. As a result, the main difference of the three samples are the number of the 10 nm bilayers that are inserted among the 100 nm Cu and Zr layers (Fig. 1d). Fig. 3 summarizes the pillar compression deformation of the three heterogeneous samples (H1, H2 and H3) under approximately 20% and 30% globally applied strains. The results showed that the deformation of sample H1 was fully compatible, i.e., extrusion of the soft Cu layer did not occur among all the constituent layers under both strains (Fig. 3a–d). The reduction in material extrusion was clearly revealed by the smooth and continuous pillar boundaries, as shown in the HAADF-STEM images of the deformed pillar cross sections (Fig. 3b and d), which is in contrast to that observed in the homogeneous 100 nm samples (see the red arrows in Fig. 3m–p) [33]. The compatible deformation was also evident by the very close thicknesses of the 100 nm Cu and Zr layers after compression and the comparable strains of all constituent layers in each block (Supplementary Fig. 2). The difference in the layer strains and thicknesses in the different blocks was due to the taper of the pillar because the top accommodated more strain than the bottom. However, the deformation of sample H2 was less compatible than that of sample H1 (Fig. 3e–h). Under a relatively small globally applied strain of 23%, the HAADF-STEM image indicated a small movement of the 100 nm Cu layer in the right-hand side in
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Fig. 2. Microstructure analysis of the heterogeneous Cu/Zr nanolayer samples: H1 (a1 -e1 ), H2 (a2 -e2 ) and H3 (a3 -e3 ). (a1 –a3 ) Bright-field TEM images of the H1–H3 samples. The insets are the corresponding SAEDs. (b1 –b3 ) Its corresponding LAADF-STEM images. (c1 –c3 ) Enlarged areas of the interlayers between the 100 nm layers from (b1 –b3 ). The insets are the corresponding EDS maps showing the distribution of principle elements, i.e., Cu (red) and Zr (green). (d1 –d3 ) and (e1 –e3 ) Enlarged positions in (c1 –c3 ) show high-resolution TEM images of the interface between Zr and Cu layers. The insets in (e1 –e3 ) are the corresponding FFTs for both Zr and Cu structures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
block 4 (and block 3) relative to the 10 nm bilayers in block 3 (and block 2) (red arrows in Fig. 3f). As the applied strain increased up to 32%, the magnitude of the relative motion between the neighboring blocks increased compared with that for the small strain (red arrows in Fig. 3h). Fig. 3j shows that in sample H3, the relative motion among the 100 nm Cu layer in block 3 and the 10 nm bilayers in block 2 increased compared with that for sample H2 under the approximately same applied strain (ɛa ≈ 21%). The extrusion further expanded to the interface between blocks 2 and 1 as the applied strain increased to 29% (Fig. 3k and l). This means that some degree of deformation incompatibility appears among all the neighboring blocks in sample H3. These findings show that sample H1 had the best and most compatible deformation among all the samples and that additional compatible deformation in heterogeneous samples can be achieved when the lowest number of 10 nm Cu/Zr bilayers is used. Fig. 4a shows the typical engineering stress–strain curves for the three heterogeneous nanolayer samples. The stress-strain relations were obtained using the method presented in Supplementary Note 2. The yield strengths were calculated as the flow stress at 3% plastic strain and are presented in Fig. 4b. Four to seven stress-strain curves were used to calculate the yield strength for each heterogeneous sample. The linear rule of mixtures (ROM) calculations under iso-stress conditions [47] are also shown for comparison based on the yield strength of the homogeneous 100 nm Cu/Zr sample and that of the 10 nm Cu/Zr sample, as listed in Supplementary Table 1. The ROM results can be expressed as
σROM =
f (1 − f ) + σ100 σ10
−1 (1)
where σ100 = 1.01 GPa and σ10 = 3.04 GPa are the yield strengths of the homogeneous 10 nm and 100 nm Cu/Zr samples, respectively, and f denotes the volume fraction of the 10 nm Cu/Zr bilayers. The results show that the observed yield strength levels of the heterogeneously layered samples were much higher than those expected from the linear ROM predictions. The increase in
the strength was 730 MPa for sample H1, 790 MPa for sample H2 and 780 MPa for sample H3 (Fig. 4c), which has been reproduced by our dislocation model (Supplementary Note 3). The significantly elevated yield strength (approximately 60% higher than the ROM predictions) indicated that the constituent layers were additionally strengthened during deformation in all three heterogeneous samples. There are three key factors that must be present for the newly designed heterogeneous structure to achieve compatible deformation and extra strength. The first key factor is the topological arrangement of the 10 nm and 100 nm layers, where each soft 100 nm Cu or Zr layer (with a yield strength of approximately 1 GPa) is coated on both surfaces by strong 10 nm Cu/Zr bilayers (with a yield strength of 3.04 GPa). This topology is effective in creating a strong geometrical constraint on the soft layer that is otherwise able to deform freely. The strong geometrical constraint produces a large strain partitioning and in turn strong strain gradient in the soft 100 nm layers due to the strength difference between the 100 nm and 10 nm layers. The strain gradient can be accommodated by a substantial number of geometrically necessary dislocations (GNDs) [44,48–50]. As suggested by previous experimental findings [14], dislocations can pile-up at interfaces when layer thicknesses are larger than 50 nm. Therefore, the accumulation and pile-up of the GNDs leads to a substantial amount of extra strengthening in the soft 100 nm layers [42,44,50,51]. The above physical picture is incorporated in a dislocation-based model (Supplementary Note 3). Consequently, the strength of the 100 nm and 10 nm layers after strengthening can be comparable, thus leading to a compatible deformation. For example, the yield strengths of the 100 nm Cu and Zr layers after strengthening are 2.1 GPa and 2.16 GPa, respectively. This is different from the bimodal nanolayer structure, in which only one surface of each 100 nm Cu or Zr layer is covered by the 10 nm layers [26,33]. The incomplete constraint in the bimodal microstructure is unable to generate a sufficiently large strain gradient in the soft layers. The second key point is a sufficiently small volume fraction of the 10 nm layers to ensure a small strain difference between the
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Fig. 3. Deformation of the heterogeneous nanolayer samples, i.e., H1 (1st line, a–d), H2 (2nd line, e–h) and H3 (3rd line, i–l), under approximately 20% (1st column) and 30% (2nd column) global compression strains, ε a . For each sample at each applied strain, the left and right figures are SEM and STEM images, respectively. The deformation of the homogeneous 100 nm Cu/Zr samples (m–p) was adopted from [33] for comparison, in which dark-field TEM images are used. The numerals on the right side of the HAADF-STEM and TEM images denote the number of each block. Scale bar: 200 nm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
10 nm bilayers and the 100 nm layers (sample H1). For example, the plastic strain difference is 3.9% for sample H1, 4.8% for sample H2, and 5.6% for sample H3 at yielding (Supplementary Fig. 5a). The sufficiently small strain difference in sample H1 provides a relatively small shear stress at interfaces. Otherwise, the 10 nm100 nm interface is broken due to the larger shear stress, as exhibited by the interface sliding in samples H2 and H3 (see arrows in Fig. 3f, h, j and l). The compatible deformation is also attributed to the high resistance to shear banding in sample H1, in contrast to the extrusion that corresponds to the onset of shear banding (see the position as pointed by the arrow near numeral ‘2’ in Fig. 3h and l). According to our dislocation model, the third one is the sufficiently large difference between the two layer thicknesses to induce high strength variations, which is able to lead to suffi-
ciently strong strain gradient to strengthen the soft layers. Here we adopted a 10 nm-100 nm combination. Other layer thickness combination could also be possible to achieve compatible deformation, such as 5 nm-50 nm, 5 nm-100 nm, which requires further experimental efforts. Furthermore, as demonstrated by the microstructure analysis presented in Fig. 2, the three samples have very similar grain morphology and sizes, which suggests that the grain size might have ignorable influence on the compatible deformation and extra strengthening of the heterogeneous composite. The texture of the three samples are also similar (e.g., Cu {111} and Zr {0 0 02}), as evidenced by SAEDs (Fig. 2). Note that the yield strength of the three samples varies almost linearly with the volume fraction of the 10 nm bilayers (Fig. 4b), which indicates that the texture plays an insignificant role in strengthening the composite. In addition,
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Fig. 4. Typical engineering stress–strain curves for heterogeneous nanolayer samples, i.e., H1, H2 and H3, under micropillar compression (a). Yield strengths of the three heterogeneous samples (b). Corresponding yield strength increase of the three heterogeneous samples as compared with the ROM results (c). The dashed lines in (b) denote the results calculated from the linear rule of mixtures (ROM) by Eq. (1). The dislocation-based model predictions are also presented in (c).
all the heterogeneous samples have similar grain size and texture to their homogeneous counterparts [33]. The interface structure is also identical among heterogeneous and homogeneous structures. All these findings suggest that it is the addition and the variation of the number of the 10 nm bilayers that play the key role in rendering the extra strengthening and compatible deformation. In summary, we overcame the deformation incompatibility problem of nanolayered Cu/Zr composites by introducing a novel heterogeneous layer topology. The complete constraint of the soft 100 nm layers imposed by the hard 10 nm layers enables fully compatible deformation and a substantial amount of extra strengthening in the new composite if one 10 nm Cu/Zr bilayer is coated on both sides of each 100 nm Cu or Zr layer. The present work showed how to improve the deformation compatibility in thin film samples. The underlying microstructure architecture principle in terms of a heterogeneous design in both material and topology can be generally employed to fabricate bulk multilayered samples, for instance through a localized phase transformation in dual-phase or reversion steels [52,53] or by accumulative roll bonding. Declaration of Competing Interest None. Funding This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11872380), the Natural Science
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Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Compatible deformation and extra strengthening by heterogeneous nanolayer composites Jianjun Li a,b,c, Wenjun Lu c,∗, James Gibson d, Siyuan Zhang e, Sandra Korte-Kerzel d, Dierk Raabe c,∗ a
School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, Hunan, China State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, Hunan, China Department of Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany d Institute of Physical Metallurgy and Materials Physics, RWTH Aachen University, Aachen 52062, Germany e Nanoanalytics and Interfaces, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany b c
a r t i c l e
i n f o
Article history: Received 7 November 2019 Revised 21 December 2019 Accepted 6 January 2020
Keywords: Compression test Multilayers Nanocrystalline materials Plastic deformation Sputtering
a b s t r a c t A topologically heterogeneous microstructure design is introduced in a Cu/Zr nanolayered composite, in which each soft 100 nm Cu or Zr layer is surrounded on both sides by several hard 10 nm Cu/Zr bilayers. This design aims to impose a full geometrical constraint on all of the soft layers. Micropillar compression tests demonstrate that the composite deforms in a compatible fashion among the layers, in which no extrusion of the soft layers occurs. An elevated strength of 730 MPa is achieved in the composite compared with the strength prediction based on the linear rule of mixtures.
Due to the high density of the hetero-interfaces that are created by alternatively stacked, dissimilar constituent materials [1–13], nanolayered (NL) metals possess good mechanical properties, such as ultra-high strength [14], high thermal stability [15–19] and excellent resistance to radiation damage [20–22]. However, homogeneous NL materials (Fig. 1a) often exhibit a severe deformation incompatibility among the constituent layers with identical thickness owing to their usually high mechanical contrast, leading to a pronounced mechanical heterogeneity upon mechanical loading. Experiments have shown that there are two types of deformation incompatibility depending on the layer thickness. The first phenomenon observed in that context includes severe shear instabilities for NL composites with very thin layers (h is in the range of approximately 1–5 nm) because of the cutting of dislocations through the interfaces that promoted joint soft deformation modes [1,23–25]. A representative example is the through-thickness formation of shear zones and shear cracks observed during rolling of Cu/Nb NL materials with a 4 nm initial layer thickness [26]. The profuse shear bands in Cu/Au [27–29], Cu/Cr [30], and Cu/amorphous CuZr [31] NL materials produced by nano-/microindentation also demonstrated this type of shear in-
∗
Corresponding authors. E-mail addresses: [email protected] (W. Lu), [email protected] (D. Raabe).
https://doi.org/10.1016/j.scriptamat.2020.01.006 1359-6462/© 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
© 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
stability behavior. The second type of deformation incompatibility is the non-matching deformation of constituent layers with a large layer thickness (h is in the range of tens of nanometres to 100 nm). A typical phenomenon is the strong extrusion of the soft constituent layer (e.g., Cu), as observed in Cu/Zr [32,33], Cu/Cr [30] or Cu/amorphous CuZr [34,35] micropillars under compression. The deformation incompatibility described above leads to very limited tensile ductility in NL materials (usually below 4% failure elongation [36–39]), which is insufficient for engineering applications. Efforts have been made to alleviate the deformation incompatibility problem, thus improving the plasticity and ductility of NL materials [26,40,41]. For example, Misra and Hoagland [26] and Wynn et al. [40] designed a bimodal NL structure that contained alternatively stacked 4 nm and 40 nm Cu/Nb bilayers, where the shear cracks that previously appeared in the 4 nm Cu/Nb NL materials were suppressed during rolling. The finding above showed that the first type of deformation incompatibility might have been overcome by a bimodal NL structure. However, our micropillar compression tests of a Cu/Zr composite showed that the bimodal design did not solve the second challenge, viz., deformation concentration and squeezing-out (extrusion) effects occurred in the soft regions [33]. This bimodal microstructure showed severe extrusion of the soft 100 nm Cu layers relative to the 100 nm Zr layers (see Fig. 5d in [33]). The problem with the bimodal NL design
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Fig. 1. Schematic of homogeneous (a), bimodal (b), and newly designed heterogeneous (c, d) nanolayer Cu/Zr structures, i.e., H1, H2 and H3, where the numeral represents the number of the 10 nm Cu/Zr bilayers that cover each side of the 100 nm layer (d). In (d), the dashed lines denote the interface between the 10 nm Cu and Zr individual layers, while the solid lines designate the 10 nm bilayer interface.
is that only one side of the 100 nm Cu or Zr layer is covered by the 10 nm bilayers (Fig. 1b). Unlike the bimodal design in pure metals, where a soft domain with large grains is completely constrained by a hard domain with small grains to produce a sufficiently large strain gradient [42–45], the 10 nm layers in the bimodal NL composite were consequently unable to produce an effective constraint on the 100 nm layers. To achieve full constraint of each 100 nm layer and produce significant strain gradient-induced strengthening, we designed a new heterogeneous nanolayer composite structure where each of the 100 nm Cu and Zr layers (the soft phase) was coated on both sides by 10 nm Cu/Zr bilayers (the hard phase) (Fig. 1c). This topology ensured that an effective constraint of the soft phase was imposed by the hard phase. The deformed pillars showed no extrusion of the soft Cu layers, as observed by scanning transmission electron microscopy (STEM) probing. The heterogeneous composite had a yield strength that is 60% much higher than that expected from the linear rule of mixtures. Three heterogeneous samples, i.e., H1, H2 and H3, were prepared by magnetron sputtering, where the numerals denote the number of coated 10 nm Cu/Zr bilayers on each side of the 100 nm layer (Fig. 1c and d). The corresponding volume fractions of the 10 nm layers in H1, H2 and H3 were 16.7%, 28.6% and 37.5%, respectively. The nominal sample thicknesses of H1, H2 and H3 were 1.44 μm, 1.40 μm and 1.2 μm, respectively. The reduced elastic moduli of the prepared samples were measured by nanoindentation. Micropillar compression tests were performed to investigate the deformation behavior of the heterogeneous layered samples and the underlying deformation response was mapped by STEM imaging of the cross sections. Details of preparation, testing, and characterization are given in the Supplementary Note 1. Fig. 2 shows the detailed analysis of the microstructures for samples H1–H3. Fig. 2a1 presents an overall of H1 with the brightfield TEM image and the corresponding selected area electron diffraction (SAED). In the TEM data, the polycrystalline grains with equiaxed morphology were observed in both 10 nm Cu/Zr and 100 nm Cu/Zr multilayers without lamellar structures (e.g., annealing twins) detected. The inset SAED reveals strong Cu {111} and Zr {0 0 02} texture. LAADF-STEM image (Fig. 2b1 ) caused by the strain-contrast [46] further confirms that the equiaxed grains with ~10 nm and ~100 nm in size have been formed within the
10 nm Cu/Zr and 100 nm Cu/Zr multilayers, respectively, leading to a fabrication of heterogeneous layered structure containing six repeated blocks. Here one block is defined as one 100 nm Cu layer and one 100 nm Zr layer plus the added 10 nm layers on the top surface of these 100 nm layers (see the numerals in Fig. 3). The enlarged LAADF-STEM view with EDS scanning in Fig. 2c1 clearly shows the heterogeneously distributed layer thicknesses (i.e., 100 nm and 10 nm) and elements (i.e., Cu and Zr). Besides, the high-resolution TEM images of the interface (Fig. 2d1 and e1 ) with fast Fourier transforms (FFTs) exhibit the typical orientation relationship between Cu and Zr layers of <110>Cu//<11–20>Zr; {111}Cu//{0 0 02}Zr. In comparison to sample H1, both sample H2 (five repeated blocks in Fig. 2a2 –e2 ) and sample H3 (four repeated blocks in Fig. 2a3 –e3 ) show similar microstructure features, e.g., grain size: ~10 nm in 10 nm Cu/Zr nanolayers and ~100 nm Cu/Zr in 100 nm multilayers; morphology: equiaxed grain; texture (Supplementary Fig. 1): Cu {111} and Zr {0 0 02}; and interface: <110>Cu//<11–20>Zr; {111}Cu//{0 0 02}Zr. As a result, the main difference of the three samples are the number of the 10 nm bilayers that are inserted among the 100 nm Cu and Zr layers (Fig. 1d). Fig. 3 summarizes the pillar compression deformation of the three heterogeneous samples (H1, H2 and H3) under approximately 20% and 30% globally applied strains. The results showed that the deformation of sample H1 was fully compatible, i.e., extrusion of the soft Cu layer did not occur among all the constituent layers under both strains (Fig. 3a–d). The reduction in material extrusion was clearly revealed by the smooth and continuous pillar boundaries, as shown in the HAADF-STEM images of the deformed pillar cross sections (Fig. 3b and d), which is in contrast to that observed in the homogeneous 100 nm samples (see the red arrows in Fig. 3m–p) [33]. The compatible deformation was also evident by the very close thicknesses of the 100 nm Cu and Zr layers after compression and the comparable strains of all constituent layers in each block (Supplementary Fig. 2). The difference in the layer strains and thicknesses in the different blocks was due to the taper of the pillar because the top accommodated more strain than the bottom. However, the deformation of sample H2 was less compatible than that of sample H1 (Fig. 3e–h). Under a relatively small globally applied strain of 23%, the HAADF-STEM image indicated a small movement of the 100 nm Cu layer in the right-hand side in
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Fig. 2. Microstructure analysis of the heterogeneous Cu/Zr nanolayer samples: H1 (a1 -e1 ), H2 (a2 -e2 ) and H3 (a3 -e3 ). (a1 –a3 ) Bright-field TEM images of the H1–H3 samples. The insets are the corresponding SAEDs. (b1 –b3 ) Its corresponding LAADF-STEM images. (c1 –c3 ) Enlarged areas of the interlayers between the 100 nm layers from (b1 –b3 ). The insets are the corresponding EDS maps showing the distribution of principle elements, i.e., Cu (red) and Zr (green). (d1 –d3 ) and (e1 –e3 ) Enlarged positions in (c1 –c3 ) show high-resolution TEM images of the interface between Zr and Cu layers. The insets in (e1 –e3 ) are the corresponding FFTs for both Zr and Cu structures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
block 4 (and block 3) relative to the 10 nm bilayers in block 3 (and block 2) (red arrows in Fig. 3f). As the applied strain increased up to 32%, the magnitude of the relative motion between the neighboring blocks increased compared with that for the small strain (red arrows in Fig. 3h). Fig. 3j shows that in sample H3, the relative motion among the 100 nm Cu layer in block 3 and the 10 nm bilayers in block 2 increased compared with that for sample H2 under the approximately same applied strain (ɛa ≈ 21%). The extrusion further expanded to the interface between blocks 2 and 1 as the applied strain increased to 29% (Fig. 3k and l). This means that some degree of deformation incompatibility appears among all the neighboring blocks in sample H3. These findings show that sample H1 had the best and most compatible deformation among all the samples and that additional compatible deformation in heterogeneous samples can be achieved when the lowest number of 10 nm Cu/Zr bilayers is used. Fig. 4a shows the typical engineering stress–strain curves for the three heterogeneous nanolayer samples. The stress-strain relations were obtained using the method presented in Supplementary Note 2. The yield strengths were calculated as the flow stress at 3% plastic strain and are presented in Fig. 4b. Four to seven stress-strain curves were used to calculate the yield strength for each heterogeneous sample. The linear rule of mixtures (ROM) calculations under iso-stress conditions [47] are also shown for comparison based on the yield strength of the homogeneous 100 nm Cu/Zr sample and that of the 10 nm Cu/Zr sample, as listed in Supplementary Table 1. The ROM results can be expressed as
σROM =
f (1 − f ) + σ100 σ10
−1 (1)
where σ100 = 1.01 GPa and σ10 = 3.04 GPa are the yield strengths of the homogeneous 10 nm and 100 nm Cu/Zr samples, respectively, and f denotes the volume fraction of the 10 nm Cu/Zr bilayers. The results show that the observed yield strength levels of the heterogeneously layered samples were much higher than those expected from the linear ROM predictions. The increase in
the strength was 730 MPa for sample H1, 790 MPa for sample H2 and 780 MPa for sample H3 (Fig. 4c), which has been reproduced by our dislocation model (Supplementary Note 3). The significantly elevated yield strength (approximately 60% higher than the ROM predictions) indicated that the constituent layers were additionally strengthened during deformation in all three heterogeneous samples. There are three key factors that must be present for the newly designed heterogeneous structure to achieve compatible deformation and extra strength. The first key factor is the topological arrangement of the 10 nm and 100 nm layers, where each soft 100 nm Cu or Zr layer (with a yield strength of approximately 1 GPa) is coated on both surfaces by strong 10 nm Cu/Zr bilayers (with a yield strength of 3.04 GPa). This topology is effective in creating a strong geometrical constraint on the soft layer that is otherwise able to deform freely. The strong geometrical constraint produces a large strain partitioning and in turn strong strain gradient in the soft 100 nm layers due to the strength difference between the 100 nm and 10 nm layers. The strain gradient can be accommodated by a substantial number of geometrically necessary dislocations (GNDs) [44,48–50]. As suggested by previous experimental findings [14], dislocations can pile-up at interfaces when layer thicknesses are larger than 50 nm. Therefore, the accumulation and pile-up of the GNDs leads to a substantial amount of extra strengthening in the soft 100 nm layers [42,44,50,51]. The above physical picture is incorporated in a dislocation-based model (Supplementary Note 3). Consequently, the strength of the 100 nm and 10 nm layers after strengthening can be comparable, thus leading to a compatible deformation. For example, the yield strengths of the 100 nm Cu and Zr layers after strengthening are 2.1 GPa and 2.16 GPa, respectively. This is different from the bimodal nanolayer structure, in which only one surface of each 100 nm Cu or Zr layer is covered by the 10 nm layers [26,33]. The incomplete constraint in the bimodal microstructure is unable to generate a sufficiently large strain gradient in the soft layers. The second key point is a sufficiently small volume fraction of the 10 nm layers to ensure a small strain difference between the
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Fig. 3. Deformation of the heterogeneous nanolayer samples, i.e., H1 (1st line, a–d), H2 (2nd line, e–h) and H3 (3rd line, i–l), under approximately 20% (1st column) and 30% (2nd column) global compression strains, ε a . For each sample at each applied strain, the left and right figures are SEM and STEM images, respectively. The deformation of the homogeneous 100 nm Cu/Zr samples (m–p) was adopted from [33] for comparison, in which dark-field TEM images are used. The numerals on the right side of the HAADF-STEM and TEM images denote the number of each block. Scale bar: 200 nm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
10 nm bilayers and the 100 nm layers (sample H1). For example, the plastic strain difference is 3.9% for sample H1, 4.8% for sample H2, and 5.6% for sample H3 at yielding (Supplementary Fig. 5a). The sufficiently small strain difference in sample H1 provides a relatively small shear stress at interfaces. Otherwise, the 10 nm100 nm interface is broken due to the larger shear stress, as exhibited by the interface sliding in samples H2 and H3 (see arrows in Fig. 3f, h, j and l). The compatible deformation is also attributed to the high resistance to shear banding in sample H1, in contrast to the extrusion that corresponds to the onset of shear banding (see the position as pointed by the arrow near numeral ‘2’ in Fig. 3h and l). According to our dislocation model, the third one is the sufficiently large difference between the two layer thicknesses to induce high strength variations, which is able to lead to suffi-
ciently strong strain gradient to strengthen the soft layers. Here we adopted a 10 nm-100 nm combination. Other layer thickness combination could also be possible to achieve compatible deformation, such as 5 nm-50 nm, 5 nm-100 nm, which requires further experimental efforts. Furthermore, as demonstrated by the microstructure analysis presented in Fig. 2, the three samples have very similar grain morphology and sizes, which suggests that the grain size might have ignorable influence on the compatible deformation and extra strengthening of the heterogeneous composite. The texture of the three samples are also similar (e.g., Cu {111} and Zr {0 0 02}), as evidenced by SAEDs (Fig. 2). Note that the yield strength of the three samples varies almost linearly with the volume fraction of the 10 nm bilayers (Fig. 4b), which indicates that the texture plays an insignificant role in strengthening the composite. In addition,
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Fig. 4. Typical engineering stress–strain curves for heterogeneous nanolayer samples, i.e., H1, H2 and H3, under micropillar compression (a). Yield strengths of the three heterogeneous samples (b). Corresponding yield strength increase of the three heterogeneous samples as compared with the ROM results (c). The dashed lines in (b) denote the results calculated from the linear rule of mixtures (ROM) by Eq. (1). The dislocation-based model predictions are also presented in (c).
all the heterogeneous samples have similar grain size and texture to their homogeneous counterparts [33]. The interface structure is also identical among heterogeneous and homogeneous structures. All these findings suggest that it is the addition and the variation of the number of the 10 nm bilayers that play the key role in rendering the extra strengthening and compatible deformation. In summary, we overcame the deformation incompatibility problem of nanolayered Cu/Zr composites by introducing a novel heterogeneous layer topology. The complete constraint of the soft 100 nm layers imposed by the hard 10 nm layers enables fully compatible deformation and a substantial amount of extra strengthening in the new composite if one 10 nm Cu/Zr bilayer is coated on both sides of each 100 nm Cu or Zr layer. The present work showed how to improve the deformation compatibility in thin film samples. The underlying microstructure architecture principle in terms of a heterogeneous design in both material and topology can be generally employed to fabricate bulk multilayered samples, for instance through a localized phase transformation in dual-phase or reversion steels [52,53] or by accumulative roll bonding. Declaration of Competing Interest None. Funding This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11872380), the Natural Science
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