Fabrication and thermo-mechanical behavior of ultra-fine porous copper
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Porous materials with ligament sizes in the submicrometer to nanometer regime have a high potential for future applications such as catalysts, actuators, or radiation tolerant materials, which require properties like high strength-to-weight ratio, high surface-to-volume ratio, or large interface density as for radiation tolerance. The objective of this work was to manufacture ultra-fine porous copper, to determine the thermo-mechanical properties, and to elucidate the deformation behavior at room as well as elevated temperatures via nanoindentation. The experimental approach for manufacturing the foam structures used high pressure torsion, subsequent heat treatments, and selective dissolution. Nanoindentation at different temperatures was successfully conducted on the ultra-fine porous copper, showing a room temperature hardness of 220 MPa. During high temperature experiments, oxidation of the copper occurred due to the high surface area. A model, taking into account the mechanical properties of the copper oxides formed during the test, to describe the measured mechanical properties in dependence on the proceeding oxidation was developed. The strain rate sensitivity of the copper foam at room temperature was ∼0.03 and strongly correlated with the strain rate sensitivity of ultra-fine grained bulk copper. Although oxidation occurred near the surface, the rate-controlling process was still the deformation of the underlying copper. An increase in the strain rate sensitivity was observed, comparably to that of ultra-fine-grained copper, which can be linked to thermally activated processes at grain boundaries. Important insights into the effects of oxidation on the deformation behavior were obtained by assessing the activation volume. Oxidation of the ultra-fine porous copper foam, thereby hindering dislocations to exit to the surface, resulted in a pronounced reduction of the apparent activation volume from ~800 to ~50 b 3, as also typical for ultra-fine grained materials.
KeywordsFoam Cu2O Activation Volume Copper Oxide Equal Channel Angular Pressing
Nanoporous or ultra-fine porous materials are enormously interesting for a number of future applications due to many excellent properties including: high surface-to-volume ratio, high strength-to-weight ratio, and electrical and thermal conductivity . In addition, it has been shown that materials with high interface fractions can accommodate large amounts of helium and radiation-induced defects, as observed in some nuclear applications . In the past these interfaces were found as Kurdjumov–Sachs interfaces in bcc/fcc metals. However, a free surface can be considered as the ultimate defect sink and, therefore, little damage can accumulate within the metal leading to a rather radiation tolerant material . The excellent properties listed above can be used for combining structural purpose and functional use in the same material. The extraordinary strength-to-weight ratio is based on the fact that decreasing the length-scale of the ligaments to nanometers leads to an increase of the yield strength of the individual ligaments, approaching the theoretical strength of the material [4, 5, 6, 7]. Therefore, an individual small scale ligament carries more load than the same volume in a dense bulk material, leading to a weight reduction.
The ligament size and morphology can be controlled during the synthesis process by heat treatments or chemical treatments. Adjusting these parameters will allow tailoring foams for certain purposes.
A classical method to obtain nanoporous structures is selective dissolution from an alloy, which has been used previously to fabricate metal foams such as Ag, Au, Cu, Pd, or Pt . Notably, in this well known approach the first step is the preparation of an alloy consisting of two miscible elements, followed by a dealloying step of one of the elements, resulting in a nanoporous foam with ligaments in the range of few nanometers . We developed another procedure that can avoid the steps of alloying and dealloying. Therefore, in this work, the Cu–Fe system was used, which shows a high immiscibility of Cu and Fe  at room temperature. Our approach is to utilize high pressure torsion (HPT) as a powder consolidation step and to subsequently produce the ultra-fine grained (UFG) composite microstructure by applying large amounts of shear deformation. Subsequently, selective dissolution of Fe from the composite results in a remaining ultra-fine porous (UFP) Cu foam structure.
In order to utilize these foams in future applications, it is necessary to acquire information about the foam manufacturing, their thermo-mechanical properties, and the plastic deformation mechanisms even if the application has a functional purpose. Nanoindentation is a well-suited method to obtain mechanical properties for micro- and nanoporous structures with high lateral and depth resolution [4, 5]. Important data can be obtained to determine the dominant deformation processes and mechanical behavior even at elevated temperatures. The rate dependent deformation mechanisms can be obtained locally by strain rate jump, relaxation, or indentation creep tests [10, 11, 12, 13]. There are several characteristic properties of a material that can be used for a description of the time and strain rate dependent mechanisms inside the material. The strain rate sensitivity m and the activation volume A are two of these characteristic properties. Previously, nanoindentation was mostly used to determine m and A for UFG and coarse-grained (CG) bulk metals [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], but not for porous metal foams. In this work, m and A were determined by local stress relaxation tests in order to obtain more insight into the dominating deformation mechanisms of UFP materials at elevated temperatures.
The sample material was produced directly from commercially available powders via HPT processing. The powders used were copper (99.9 % purity, −170 + 400 mesh, 37–88 μm) and iron (99.9 % purity, −100 + 200 mesh, 74 – 149 μm) obtained from Alpha Aesa (Ward Hill, USA). Both powders were premixed in a ratio of 50 at.% Cu and 50 at.% Fe (Cu50Fe50). The mixed powders were consolidated with a novel two-step HPT process, originally introduced by Bachmaier et al. . The resulting product was an 8 mm diameter disk with a thickness of 1 mm. To reduce the amount of forced mechanical mixing between Cu and Fe, a heat treatment was conducted at 500 °C for 1 h in a vacuum furnace (SERIES XRETORT, Xerion Advanced Heating Ofentechnik GmbH, Germany). The vacuum pressure never exceeded 3 × 10−4 mbar during the heat treatment. The heating rate of the furnace was 10 °C per minute and then cooling down to RT required 8 h. The solubility of Cu in Fe at 500 °C can be found in  between 0.02 and 0.2 wt% and, therefore, it can be stated that in the worst case this amount of Cu will be still in the Fe.
The bulk UFP copper was prepared by selective leaching of iron using a 5 wt% hydrochloric acid (HCl) solution for 35 h at a temperature of 55 °C. After 35 h the samples were removed from the solution and cleaned with acetone and ethanol to remove the residual HCl-solution. This resulted in dissolution of the Fe from the composite top and bottom surface to a depth of ~ 50 µm. Notably, this is much deeper that the subsequent nanoindentation experiments will probe. The compact composite sample core is important, as it serves to prevent penetration of any form of glue or cement used for fixation of the samples for subsequent nanoindentation testing.
Foam characterization and testing
All microstructural investigations were made in axial and/or tangential direction at a radius of 3 mm on the HPT disks, related to the high grade of deformation at this radius. After the dealloying process the morphologies and structures of the UFP Cu were investigated to confirm a successful dissolution process. To verify the morphologies of the produced UFP Cu throughout, the samples were investigated using scanning electron microscopy. The microstructural investigations were performed in axial direction using a scanning electron microscope (SEM; LEO type 1525, Carl Zeiss GmbH, Germany) equipped with an energy dispersive X-ray spectrometer (EDX) or a dual beam focused ion beam (FIB)-SEM (Quanta 3D FEG, FEI, USA). EDX spectra were collected from the UFP Cu over an axial region to estimate the remaining Fe concentration. A more accurate method to obtain information about the porosity is to evaluate the relative density from micrographs. SEM images were processed using the computer software AnalySIS (AnalySIS Pro 5.0, Olympus Soft Imaging Solutions GmbH, Germany). This phase analysis was performed for SEM images of different magnifications and also compared to manual image analysis in order to identify parameters that deliver repeatable and reliable measurements. Local cross-sectioning of the samples and subsequently SEM imaging was conducted using a Quanta 3D FEG FIB in order to investigate the structure and morphology beneath the surface of the foam.
The depth-time curve of the dwell period can be separated into two distinct regions, called Stage a and Stage b as proposed by Peykov et al. , where Stage a represents the creep behavior within the first 20 s of constant loading and Stage b describes the mechanical behavior up to 200 s.
Hereby, h 0 is the indentation depth at the beginning of the dwell period.
Hereby, the m value for Stage a was assessed from the recorded data of the first 20 s, and the fit of Stage b included data between 30 and 200 s. The data of the transient region between 20 and 30 s was discarded.
Here, k = 1.3806488 × 10−23 m2 kg s−2 K−1 is the Boltzmann constant and c* is the constraint factor, which describes the relation between hardness and flow stress (2.8 for a Berkovich indenter tip at constant 8 % representative strain) .
The UFP Cu is obtained by selective dissolution. The resulting structure in axial direction is shown in Fig. 1. The ligament diameter is ∼200 nm, as determined from image analysis. While the ligaments at the sample surface could be identified with sufficient precision by digital image analysis, the pores could not be tracked with good accuracy due to the strong contrast variations below the foam surface (see Fig. 1b). Starting from a composite having comparable grain size for Fe and Cu, respectively, one might expect that the pore diameter is of comparable dimension to the ligaments. Moreover, ligament widths and pore sizes are not perfectly homogenous throughout the entire specimen. This is related to the manufacturing process involving shear in only one axis and not in multiple axis. The relative density of this foam structure is 53 ± 1.5 % from analyzing SEM images, and supported by EDX investigations showing ~ 3 % Fe remaining in the foam.
Young’s modulus and hardness
To access the change of hardness H and Young’s modulus E over temperature, DC measurements were performed with a constant strain rate. The data points marked as red squares in Fig. 2 visualize the correlation between Young’s modulus, which was obtained from the reduced modulus, and temperature. The values for 22 °C in the non-oxidized state are indicated by the label “Start.” First, an increase of the Young’s modulus from 17 ± 3.5 GPa to 26.8 ± 3 GPa was observed up to 100 °C, which was followed by a decrease in modulus down to 22.2 ± 2.2 GPa at 200 °C and 16.7 ± 2.1 GPa at 300 °C. The data points marked as black circles in Fig. 2 show the change of hardness over temperature. A strong increase of the hardness from 220 ± 60 MPa at 22 °C up to ~ 950 ± 300 MPa at 50 °C was observed, which stayed constant at 100 and 200 °C. At 300 °C, a hardness drop from 940 ± 140 MPa to 300 ± 60 MPa was observed. The values of the RT hardness after the high temperature experiments at 22 °C are in both graphs close indicated as “End.” The sample after high temperature indentation shows an enormous increase of around 500 % in hardness and 200 % in Young’s modulus compared to the original 22 °C experiments.
Strain rate sensitivity
The existence of additional strengthening from supersaturated Fe in the Cu ligaments .
The Gibson and Ashby equation is predominantly valid for homogenous foam structures and lower relative densities .
The assumed near zero Poisson’s ratio is not fully valid for relative densities >35 % such as in the present UFP Cu .
The used yield strength for bulk Cu with ~ 200 nm grain size is just an estimation, the structure size in the UFP Cu varies from ~ 100–300 nm.
Even a thin oxide layer can cause a pileup of dislocations and, therefore, strongly influence the material properties.
For a further discussion, we assume that the Ashby and Gibson Eq. (5) describes the mechanical properties of the UFP Cu well . Then, the experimentally determined value of 220 MPa for the yield strength of the UFP Cu would require that the yield strength of the foam ligaments is in the order of 1.9 GPa. This interpretation suggests that the yield strength of the ligaments in the UFP Cu approaches the theoretical strength of Cu (>6 GPa ), as it was already achieved for nanoporous Au foams by Biener et al. .
Here, E C is the Young’s modulus of the composite, E * of the UFP Cu and E 0 of the oxide, while ν * and ν 0 are the particular fractions of the UFP Cu and oxide. This equation is derived from the composite theory for the Young’s modulus according to fiber-reinforced composites, whereby the load direction is perpendicular to the fiber direction .
This allows an estimation of the hardness values, but for estimating the Young’s modulus a detailed knowledge of the oxide composition after different oxidation times and temperatures is necessary. Literature reviews exist regarding the oxidation temperature and time, and the resulting ratios of different copper oxides [42, 43, 44, 45, 46]. Not only the thickness of the grown oxide is crucial, but also the type of oxide after different oxidation temperatures plays a major role.
Figure 6b shows the results of the model for obtaining hardness and Young’s modulus values depending on the relative amount of oxide in the plastic zone. The prediction for the hardness is quite accurate due to the nearly identical hardness of the oxides. A precise estimation of the Young’s modulus is not possible, since the ratio of different oxides is unknown. A change in the ratio of the oxides between 10 and 50 % as used here was also reported by Lenglet et al. .
Strain rate sensitivity
The increasing strain rate sensitivity over temperature from 0.03 to 0.1–0.2, shown in Fig. 7, can be explained by thermally activated climb-controlled annihilation of lattice dislocations in the Cu ligaments, which favorably takes place at high angle grain boundaries [49, 50]. The large fraction of high angle grain boundaries is a consequence of the HPT process. The high misorientation and amount of high angle grain boundaries enhances climbing controlled processes, even at low temperatures. At elevated temperature (100–300 °C) a similar behavior was found for equal channel angular pressing (ECAP) UFG Al by Vevecka-Priftaj et al.  and for ECAP UFG Cu by Bach et al.  (Fig. 7).
The obtained activation volume for the UFP Cu at 22 °C does not correlate with the values of bulk UFG Cu with the same structure size. The activation volume for non-oxidized UFP Cu is in the order of 250–850 b 3 when taking the upper and lower boundary for the hardness to yield strength conversion into account. This activation volume indicates a dominant deformation behavior governed by interaction between lattice and forest dislocations, which is typical for CG Cu (~ 1000 b 3). Lower values of ~ 100 b 3 were observed for UFG Cu  and UFG Al . The obtained activation volume for the oxidized sample is within the same order of magnitude, namely 50–150 b 3 (Fig. 4). Hereby, giving the activation volume in units of b 3 of Cu is feasible due to the nearly same Burgers vector for the 1/2·(110) dislocation in Cu (b = 0.255 nm ) and the 1/2·(100) dislocation in Cu2O (b = 0.213 nm ). In general, after oxidation the density of the UFP Cu increases and an oxide layer grows, while the measured activation volume significantly drops from 250–850 to 20–100 b 3 (Fig. 4). Polycrystalline copper oxides do not extensively plastically deform in a temperature range from 22 °C up to 300 °C at atmospheric pressure [52, 53]. Thus, the reason for the drop in activation volume is that the oxide layer on top of the Cu ligaments traps dislocations inside the Cu ligaments and thereby strongly reduces the activation volume of the foam, as schematically shown in Fig. 6c. Dislocations are not able to glide from the Cu phase into the ceramic phase due to differences of the crystal structure, and the free path for dislocations to move inside the plastic zone is thus reduced. Additionally, stress is induced close to the Cu–CuO interface in the copper phase by the effect of epitaxial strains due to relatively high difference in the Pilling–Bedworth ratio (oxide–metal volume ratio), which hinders dislocation movement close to the interface. Contrarily in the case of the non-oxidized Cu ligaments shown in Fig. 6c, the dislocation mobility is not influenced by surface oxides and the dislocations can exit to the surface. Both, the CL and DC measurements show a sudden decrease of A immediately after first oxidation occurred (Fig. 4). After this first drop the activation volume up to 300 °C approximately remains on the same level of 50–150 b 3, comparable to UFG bulk Cu where grain boundaries hinder the dislocation movement.
In conclusion, nanoindentation experiments between room temperature and 300 °C were successfully conducted on UFP Cu. During testing at elevated temperatures, an oxidation of the copper occurred. Increasing hardness and Young’s modulus were observed with increasing indentation temperature, which is related to the oxidation of the copper foam. A model was developed taking into account the mechanical properties and growing rates of the copper oxides, which allows an explanation of the measured mechanical properties in dependence on the proceeding oxidation. The oxidation did not significantly affect the rate dependent properties of the UFP Cu since the oxide mostly deforms elastically. The strain rate sensitivity of 0.03 at RT is in the range of UFG bulk copper [21, 35]. Furthermore, an increase of the strain rate sensitivity from 0.03 at RT to 0.1–0.2 at 300 °C was observed, which can be linked to more pronounced thermally activated grain boundary processes at elevated temperatures [50, 51]. The activation volume was strongly influenced by the oxidation due to a change in deformation mechanism. Hereby, the oxide layer on top of the ligaments hindered dislocations to exit to the surface and dislocations were piled-up at the oxide-metal interface.
The financial support by the Austrian “Marshall-Plan Scholarships” and the Montanuniversität Leoben (MK, MMP) as well as the “Zukunftsfond Steiermark” (PN 6019-Nanofatigue) (VM, DK) are gratefully acknowledged. Parts of this work were funded by the Austrian Science Fund (FWF) via the international Project I 1020-N20.
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