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Anisotropic compressive properties of porous copper produced by unidirectional solidification
Materials Science and Engineering A340 (2003) 258 /264 www.elsevier.com/locate/msea
Anisotropic compressive properties of porous copper produced by unidirectional solidification S.K. Hyun *, H. Nakajima The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan Received 5 November 2001; received in revised form 18 March 2002
Abstract Porous copper whose long cylindrical pores are aligned in one direction has been fabricated by unidirectional solidification of the melt in a mixture gas of hydrogen and argon. The compressive yield strength of the porous copper with the cylindrical pores orientated parallel to the compression direction decreases linearly with increasing porosity. For the porous copper whose pore axes are perpendicular to the compressive direction, the compressive yield strength slightly decreases in the porosity range up to 30% and then decreases significantly with increasing porosity. The compressive stress /strain curves depend on the compressive direction with respect to the pore direction, which are due to the stress concentration around the pores and the buckling of the copper between the pores. From two different types of stress /strain curve, the energy absorption capacity of the porous copper with the pores parallel to the compressive direction is higher than that perpendicular to the compressive direction at a given porosity. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Porous copper; Unidirectional solidification; Compressive strength; Yield strength; Buckling
1. Introduction Over the past few decades, ‘metals containing a number of voids (pores)’ have been studied and interest is growing in development for applications materialized not only by utilizing the inherent low density but also by utilizing the pores themselves and the large specific surface area [1 /4]. Although the porosity for conventional application generally ranges from 15 to 98%, two expressions to name these metals are widely distinguished according to the porosity level. One is ‘porous metals’, which are normally sintered by metallic powders to porosity in the range from 15 to 75%. These porous metals provide specialized products for applications such as filtration, fluid flow control, self-lubricating bearing, battery electrodes, etc. Another one is called ‘metal (or metallic) foams’, which are defined as the high
* Corresponding author. Tel.: /81-6-6879-8435; fax: /81-6-68798439 E-mail address: hyun23@saken (S.K. Hyun).
porosity ranges from 80 to 98%, and provide a distinct advantage over solid metals for energy absorption, sound absorption, vibration suppression, thermal management, etc. However, these metals have similar characteristic on pore geometry, which is almost spherical, and there are serious weak points for application since the spherical pores deteriorate mechanical properties such as tensile strength and ductility. Recently, a new type of porous metals whose long cylindrical pores are aligned in one direction has been fabricated by unidirectional solidification method at a pressurized hydrogen or nitrogen gas with argon gas [5 / 15]. These porous metals should be distinguished from the conventional porous metals whose pores are almost isotropic and spherical. Hereafter, we designate these porous metals with elongated pores lotus-structured porous metals, because they look like lotus roots. The tensile properties of the lotus-structured porous copper whose pores are aligned in one direction are superior to that of conventional porous metals [16,17]. Thus, such long pore-aligned porous metals are expected as a new category of engineering materials.
0921-5093/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 1 8 1 - 8
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Table 1 Chemical composition of copper (mass ppm)
Fig. 1. Schematic drawing of the fabrication apparatus for lotusstructured porous copper: (a) before; and (b) after unidirectional solidification.
Compressive properties of foam metals have been extensively investigated. In the strain /stress curves, there is a plateau regime, where the stress remains nearly constant with increasing strain [1,2]. Energy absorption is closely related with this region. On the other hand, Simone and Gibson [18] investigated compressive properties of porous copper fabricated by unidirectional solidification, but no investigation on anisotropy for uniaxial compressive properties was carried out. From this point of view, the present work was undertaken to investigate the uniaxial compressive properties of lotus-structured copper with elongated cylindrical pores orientation parallel and perpendicular to the compressive direction to discuss the anisotropy of the compressive strength.
2. Experimental procedures
Ag
S
As
Sb
Bi
Pb
Se
Te
Fe
10
3
B1
B1
B1
B1
B1
B1
B1
mm in length) with water-cooled copper plate, as illustrated in Fig. 1. High purity copper was melted in the crucible by radio-frequency heating under high-pressure mixture gas of hydrogen and argon. Chemical analysis of the copper is compiled in Table 1. The purities of hydrogen and argon gases used for these experiments were 99.999%. The temperature of the molten copper in the crucible was monitored by a W-5Re/W-26Re thermocouple and was set to be 1473 K. This thermocouple is able to measure correctly the temperature in the hydrogen atmosphere. In order to make hydrogen dissolve and diffuse uniformly in the molten copper the pressurized condition was maintained for l.8 ks. Thus, hydrogen was dissolved into the molten copper to the equilibrium concentration according to the Sieverts’ law in the hydrogen atmosphere. The pressures of hydrogen and argon during melting and solidification were changed in order to produce the various specimens with different porosity as shown in Table 2. Then, the stopper stick was pulled out and then the molten copper was poured down into the mold whose bottom plate was cooled down with water-circulated through a chiller. The lateral side was made of aluminacoated stainless steel tube, which is suitable for heatinsulating material in order to be solidified in one direction from the bottom to top. During solidification, hydrogen in the melt is rejected at the solid /liquid interface due to the solubility gap of hydrogen between in the liquid and in the solid as shown in Fig. 2 and forms cylindrical pores that are aligned parallel to the solidification direction. The ingots obtained were 100 mm in diameter and maximum 150 mm in height, and contained various levels of porosity that was controlled by the total and partial pressures of hydrogen and argon during melting and solidification as shown in Table 2. Typical cross-section of ingot the porous copper is shown in Fig. 3.
2.1. Materials 2.2. Compressive testing The specimens of the lotus-structured porous copper were fabricated by the vacuum-assisted and pressurized casting apparatus, which consists of a graphite crucible (110 mm in outside diameter, 90 mm in inside diameter, and 170 mm in length) with a hole (20 mm in diameter) on the bottom of the crucible, a stopper stick for preventing the melt flow through the hole, an induction heating coil and a mold (100 mm in diameter and 150
Cylindrical specimens for the compression tests with 10 mm in diameter and 20 mm in height were cut from the ingots by using a spark-erosion wire cutting machine (Model A320D, Sodick Co.). Fig. 4 shows the cylindrical specimens with different porosity for the compression tests. It can be seen that the specimens with higher porosity consist of larger pores than those with lower
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Table 2 Pressure condition during melting and solidification, and porosity No.
Total pressure of mixture gas (MPa)
Partial pressure of hydrogen (MPa)
Partial pressure of argon (MPa)
Porosity (%)
1 2 3 4
0.4 1.1 0.3 0.12
0.0 0.4 0.3 0.12
0.4 0.7 0.0 0.0
0.0 30.4 48.4 59.5
Fig. 2. Temperature dependence of hydrogen solubility in a metal. Fig. 5. Compressive yield strength of lotus-structured porous copper in the direction parallel and perpendicular to pore axis.
porosity. Little damage is introduced in the specimens even in the case of high porosity during the sparkerosion cutting. In the first type of specimens, the ingots were cut so that the compressive direction was parallel to the direction of the pore axes, and in the second type, perpendicular to the pore axes. The porosity is evaluated from the following expression: Fig. 3. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity (PH /0.12 MPa and PAr /0.0 MPa). 2
Porosity 1
Fig. 4. Optical micrographs of specimens for compressive test. Upper part: lotus-structured porous copper with cylindrical pores parallel to the lateral axis. Lower parts: lotus-structured porous copper with cylindrical pores perpendicular to the lateral axis.
Apparent density of porous copper : (1) Denstiy of non-porous copper
The apparent density of the individual specimen was calculated from a measurement of its weight and volume for each configuration. Compression tests were performed on the specimens in an Instron Universal Testing Machine (Model 4482, Instron Corp., Canton, MA, USA) at room temperature. The crosshead speed was 1 mm min 1. The strains were calculated from the actuator displacement and the initial specimen length, taking into account the displacements within the testing machine. The yield strength was evaluated from the stress /strain curve by the 0.2% offset method. The deformation behaviors were observed using optical microscope by interrupting the compression tests at strains of 30, 50 and 80%.
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Fig. 6. Formation of barrier to dislocation movement in the region of stress concentration.
3. Results and discussion 3.1. Compressive yield strength The compressive tests were performed on lotusstructured porous copper with different pore orientations and porosities. The yield strengths of specimens with cylindrical pore orientation parallel and perpendicular to the compressive direction are plotted against the porosity in Fig. 5. The values of yield strength of the porous copper with the cylindrical pores parallel to the compressive direction agree well with the data reported by Simone and Gibson [18]; besides, the compressive yield strength is similar tendency to the tensile yield strength of previous tensile test [17]. However, the values of the compressive yield strength of non-porous copper measured in present work are about one half of the values of the tensile yield strength of non-porous copper [17]. Similar difference in the yield strength was also observed in the results by Simone and Gibson [18]. Such difference may not be attributed to the impurity content and the morphology of the texture of the specimens. The reason is not clear at present. Further investigations are necessary to elucidate the difference. The data points for the yield strengths of the porous copper with the pores parallel to the compressive direction lie each on a straight line which passes through the point of 0 MPa at the porosity of 100%; the specific yield strength does not change by the pore existence. This fact indicates that pores aligned parallel to the compression direction cause little stress concentration in the specimens. Simple rule of mixtures of empty pores and solid body can be applied to these specimens. In the case of the specimens with pores perpendicular to the compression direction, the compressive yield strength slightly decreases until 30% porosity and then decreases significantly with increasing porosity. Although it is difficult to explain perfectly the reason for this, we suggest the following mechanism. As seen in Fig. 6, if a pore is placed in the plate for compressive loading, the stress concentrates at the edge of the pore.
Fig. 7. Compressive stress /strain curves of lotus-structured porous copper.
Therefore, the strength level of this region is higher than that of matrix. Before the stress level reaches the yield strength, at first plastic deformation locally occurs in the region of stress concentration. Plastic hardening is accompanied by plastic deformation and thus, this region becomes barrier such as Cottrell /Lomer locks [19,20] against moving dislocations in the matrix until the cross slip makes progress. Consequently, the yield strength of this specimen will not rapidly decrease with porosity at low porosity levels.
3.2. Flow stress characteristics Compressive stress /strain curves for the lotus-structured porous copper specimens with different porosities and compressive direction are shown in Fig. 7. The slope of the stress /strain curves decreases with increasing porosity and depends on compressive direction with respect to the pore direction at a given porosity. At low strain level, the stress of the specimen with pores parallel to the compressive direction is higher than that of specimen with the pores perpendicular to the compressive direction. However, this appearance is reversed with increasing strain. For understanding this behavior, we consider two reasonable possibilities as follows. First, while the stress concentration occurs around the pores in the specimen with pores perpendicular to the compressive direction, there is little stress concentration around pores in the specimen with the cylindrical pore parallel to the compressive direction. The stress concentration is important factor for determination on the strength of porous metals [17,21], which the strength decreases with stress concentration. For this reason, the pores perpendicular to the compressive direction are easily deformed at lower stress.
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Fig. 10. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity in the direction parallel to pore axis after compression test: (a) o /0; and (b) o /50%. Fig. 8. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity in the direction parallel to pore axis after compression test: (a) o /0; (b) o /30; (c) o /50; and (d) o /80%.
Fig. 11. Volume fraction of pores plotted against strain in the specimen with 59.5% porosity.
Fig. 9. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity in the direction perpendicular to pore axis after compression test: (a) o /0; (b) o /30; (c) o /50 and (d) o /80%.
Next, different types of deformation such as buckling occur in the specimens depending on compressive direction with the pore axis. Buckling in a specimen may result from loading misalignment and the specimen can be deformed at lower stresses. The macrographs of the lotus-structured porous copper with 59.5% porosity compressed 0, 30, 50 and 80% in the direction parallel and perpendicular to the pore axis are shown in Figs. 8 and 9, respectively.
Fig. 12. Compressive stress /strain curves of lotus-structured porous copper with 59.5% porosity.
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curves may be attributed to the stress concentration, the buckling and the volume fraction of pores.
3.3. Energy absorption
Fig. 13. Schematic compressive stress /strain curves of lotus-structured porous copper.
Schematic stress /strain curve of the lotus-structured porous copper is shown in Fig. 13. The curve exhibits the three regions: (I) elastic region characterized by elastic modulus; (II) stress plateau region characterized by a shallow slope corresponding to the plastic yielding, buckling and bending of cell ligaments; and (III) densification region characterized by a relatively steep slope. From the compression test data, the energy absorption during the compression can be calculated by integrating the area under the stress /strain curve [1]:
Table 3 Densification strain and absorption energy of lotus-structured porous copper Porosity (%)
Apparent density (Mg m 3)
Compressive direction with pore Densification strain, o D axis (%)
Stress (MPa)
Absorbed energy per volume (MJ m 3)
30.4
6.25
Parallel Perpendicular
48.4 29.8
234 144
70.8 25.7
48.4
4.64
Parallel Perpendicular
51.2 33.8
159 70.5
47.1 14.4
59.5
3.57
Parallel Perpendicular
46.3 33.0
91.5 36.1
27.8 7.2
In the parallel case, two types of buckling are observed in specimen during compression. One is the macro-buckling observed outside of specimens as shown in Fig. 8(c). Another is the micro-buckling observed around the pores. Fig. 10 shows the microstructure around the pores before and after 50% height reduction, in which the copper ligaments between pores after compression is buckled like zigzag. However, in the perpendicular case, macro-buckling is not observed outside of specimens during compression, while micro-buckling is found inside of specimens. Furthermore, as shown in Fig. 11, the volume fraction of pores after 50% compression in the perpendicular case is lower than that in the parallel case. Also, the slope of stress /strain curve in the perpendicular case is rapidly increased at 50% compressive strain as shown in Fig. 12. It can be explained that the pores in the perpendicular case is easily crushed during compression due to the stress concentration around the pores. Consequently, anisotropy of the slope of stress /strain
o
W
g s(o) do;
(2)
0
where W is the absorbed energy per unit volume and o is the strain. Table 3 compiles the absorbed energy up to densification strain, which is defined as the strain corresponding to the end of the stress plateau of lotus-structured porous copper. The stress and the absorbed energy at densification strain decrease with increasing porosity. At a given porosity the absorbed energy of the specimen in the parallel case is higher than that of the specimen in the perpendicular case, because the lotus-structured porous copper with pores parallel to the compressive direction has higher strength and ductility than that with pores perpendicular to the compressive direction. It can be seen that the energy absorption capacity of lotusstructured porous copper with the pores parallel to the
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compressive direction is higher than that perpendicular to the compressive direction at a given porosity.
tion to Dr. K. Murakami and Dr T. Ikeda of Osaka University for stimulating discussion.
4. Conclusions References The lotus-structured porous copper having long aligned pores was fabricated via melt-route process and their anisotropic compressive properties were studied. The results obtained are as follows. (1) Compressive properties of the lotus-structured porous copper depend on the porosity and on the orientation of the pore axis relative to the compressive direction. (2) The slope of stress /strain curve decreases with increasing the porosity and depends on compressive direction with respect to the pore direction. At low strain level, the stress of the specimen with pores perpendicular to the compressive direction is lower than that of specimen with the pores parallel to the compressive direction. However, this tendency is reversed with increasing strain. The anisotropy of the slope of stress /strain curves may be attributed to various types of buckling. (3) The absorbed energy of the specimen with pores parallel to the compressive direction is higher than that of the specimen in the perpendicular to the compressive direction at a given porosity.
Acknowledgements The present work was supported by Grant-in-Aid for Scientific Research A (No. 09355025) and for University and Society Collaboration (No. 11792022) of the Ministry of Education, Culture, Sports, Science and Technology. The authors wish to express their apprecia-
[1] L.J. Gibson, M.F. Ashby, Cellular Solids, 2nd ed., Cambridge University Press, UK, 1997. [2] M.F. Ashby, A. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson, H.N.G. Wadley, Metal Foams, Butterworth-Heinemann Ltd, USA, 2000. [3] J. Banhart, Jom 52 (2000) 22. [4] M. Eisenmann, ASM Handbook, v. 7 Powder Metal Technologies and Applications, ASM Internationals, Material Park, USA, 1998, p. 1031. [5] L.V. Boiko, V.I. Shapovalov, E.A. Chernykh, Metallurgiya 346 (1991) 78. [6] H. Nakajima, Mater. Integration 12 (1999) 37. [7] H. Nakajima, Prod. Tech. 51 (1999) 60. [8] H. Nakajima, Boundary 15 (1999) 9. [9] H. Nakajima, Funct. Mater. 20 (2000) 27. [10] H. Nakajima, J. High Temp. Mater. 26 (2000) 95. [11] H. Nakajima, Bull. Iron Steel Inst. Jpn. 6 (2001) 33. [12] H. Nakajima, S.K. Hyun, K. Ohashi, K. Ota, K. Murakami, Colloids Surf. A 179 (2001) 209. [13] H. Nakajima, Mater. Trans. 42 (2001) 1827. [14] S. Yamamura, Y. Shiota, K. Murakami, H. Nakajima, Mater. Sci. Eng. A 318 (2001) 137. [15] S.K. Hyun, H. Nakajima, in: J. Banhart, M. Ashby, N. Fleck (Eds.), Cellular Metals and Metal Foaming Technology, Verlag MIT Publishing. [16] S.K. Hyun, Y. Shiota, K. Murakami, H. Nakajima, in: M. Koiwa, K. Otsuka, T. Miyazaki (Eds.), Proc. Int. Conf. on Solid / Solid Phase Transformations’ 99 (JIMIC-3), Japan Inst. Metals, Kyoto, 1999, p. 341. [17] S.K. Hyun, K. Murakami, H. Nakajima, Mater. Sci. Eng. A 299 (2001) 241. [18] A.E. Simone, L.J. Gibson, J. Mater. Sci. 32 (1997) 451. [19] A.H. Cottrell, Philos. Mag. 43 (1952) 645. [20] W.M. Lomer, Philos. Mag. 42 (1951) 1327. [21] A.R. Boccaccini, G. Ondracek, E. Mombello, J. Mater. Sci. Lett. 14 (1995) 534.
Anisotropic compressive properties of porous copper produced by unidirectional solidification S.K. Hyun *, H. Nakajima The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan Received 5 November 2001; received in revised form 18 March 2002
Abstract Porous copper whose long cylindrical pores are aligned in one direction has been fabricated by unidirectional solidification of the melt in a mixture gas of hydrogen and argon. The compressive yield strength of the porous copper with the cylindrical pores orientated parallel to the compression direction decreases linearly with increasing porosity. For the porous copper whose pore axes are perpendicular to the compressive direction, the compressive yield strength slightly decreases in the porosity range up to 30% and then decreases significantly with increasing porosity. The compressive stress /strain curves depend on the compressive direction with respect to the pore direction, which are due to the stress concentration around the pores and the buckling of the copper between the pores. From two different types of stress /strain curve, the energy absorption capacity of the porous copper with the pores parallel to the compressive direction is higher than that perpendicular to the compressive direction at a given porosity. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Porous copper; Unidirectional solidification; Compressive strength; Yield strength; Buckling
1. Introduction Over the past few decades, ‘metals containing a number of voids (pores)’ have been studied and interest is growing in development for applications materialized not only by utilizing the inherent low density but also by utilizing the pores themselves and the large specific surface area [1 /4]. Although the porosity for conventional application generally ranges from 15 to 98%, two expressions to name these metals are widely distinguished according to the porosity level. One is ‘porous metals’, which are normally sintered by metallic powders to porosity in the range from 15 to 75%. These porous metals provide specialized products for applications such as filtration, fluid flow control, self-lubricating bearing, battery electrodes, etc. Another one is called ‘metal (or metallic) foams’, which are defined as the high
* Corresponding author. Tel.: /81-6-6879-8435; fax: /81-6-68798439 E-mail address: hyun23@saken (S.K. Hyun).
porosity ranges from 80 to 98%, and provide a distinct advantage over solid metals for energy absorption, sound absorption, vibration suppression, thermal management, etc. However, these metals have similar characteristic on pore geometry, which is almost spherical, and there are serious weak points for application since the spherical pores deteriorate mechanical properties such as tensile strength and ductility. Recently, a new type of porous metals whose long cylindrical pores are aligned in one direction has been fabricated by unidirectional solidification method at a pressurized hydrogen or nitrogen gas with argon gas [5 / 15]. These porous metals should be distinguished from the conventional porous metals whose pores are almost isotropic and spherical. Hereafter, we designate these porous metals with elongated pores lotus-structured porous metals, because they look like lotus roots. The tensile properties of the lotus-structured porous copper whose pores are aligned in one direction are superior to that of conventional porous metals [16,17]. Thus, such long pore-aligned porous metals are expected as a new category of engineering materials.
0921-5093/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 1 8 1 - 8
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Table 1 Chemical composition of copper (mass ppm)
Fig. 1. Schematic drawing of the fabrication apparatus for lotusstructured porous copper: (a) before; and (b) after unidirectional solidification.
Compressive properties of foam metals have been extensively investigated. In the strain /stress curves, there is a plateau regime, where the stress remains nearly constant with increasing strain [1,2]. Energy absorption is closely related with this region. On the other hand, Simone and Gibson [18] investigated compressive properties of porous copper fabricated by unidirectional solidification, but no investigation on anisotropy for uniaxial compressive properties was carried out. From this point of view, the present work was undertaken to investigate the uniaxial compressive properties of lotus-structured copper with elongated cylindrical pores orientation parallel and perpendicular to the compressive direction to discuss the anisotropy of the compressive strength.
2. Experimental procedures
Ag
S
As
Sb
Bi
Pb
Se
Te
Fe
10
3
B1
B1
B1
B1
B1
B1
B1
mm in length) with water-cooled copper plate, as illustrated in Fig. 1. High purity copper was melted in the crucible by radio-frequency heating under high-pressure mixture gas of hydrogen and argon. Chemical analysis of the copper is compiled in Table 1. The purities of hydrogen and argon gases used for these experiments were 99.999%. The temperature of the molten copper in the crucible was monitored by a W-5Re/W-26Re thermocouple and was set to be 1473 K. This thermocouple is able to measure correctly the temperature in the hydrogen atmosphere. In order to make hydrogen dissolve and diffuse uniformly in the molten copper the pressurized condition was maintained for l.8 ks. Thus, hydrogen was dissolved into the molten copper to the equilibrium concentration according to the Sieverts’ law in the hydrogen atmosphere. The pressures of hydrogen and argon during melting and solidification were changed in order to produce the various specimens with different porosity as shown in Table 2. Then, the stopper stick was pulled out and then the molten copper was poured down into the mold whose bottom plate was cooled down with water-circulated through a chiller. The lateral side was made of aluminacoated stainless steel tube, which is suitable for heatinsulating material in order to be solidified in one direction from the bottom to top. During solidification, hydrogen in the melt is rejected at the solid /liquid interface due to the solubility gap of hydrogen between in the liquid and in the solid as shown in Fig. 2 and forms cylindrical pores that are aligned parallel to the solidification direction. The ingots obtained were 100 mm in diameter and maximum 150 mm in height, and contained various levels of porosity that was controlled by the total and partial pressures of hydrogen and argon during melting and solidification as shown in Table 2. Typical cross-section of ingot the porous copper is shown in Fig. 3.
2.1. Materials 2.2. Compressive testing The specimens of the lotus-structured porous copper were fabricated by the vacuum-assisted and pressurized casting apparatus, which consists of a graphite crucible (110 mm in outside diameter, 90 mm in inside diameter, and 170 mm in length) with a hole (20 mm in diameter) on the bottom of the crucible, a stopper stick for preventing the melt flow through the hole, an induction heating coil and a mold (100 mm in diameter and 150
Cylindrical specimens for the compression tests with 10 mm in diameter and 20 mm in height were cut from the ingots by using a spark-erosion wire cutting machine (Model A320D, Sodick Co.). Fig. 4 shows the cylindrical specimens with different porosity for the compression tests. It can be seen that the specimens with higher porosity consist of larger pores than those with lower
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260
Table 2 Pressure condition during melting and solidification, and porosity No.
Total pressure of mixture gas (MPa)
Partial pressure of hydrogen (MPa)
Partial pressure of argon (MPa)
Porosity (%)
1 2 3 4
0.4 1.1 0.3 0.12
0.0 0.4 0.3 0.12
0.4 0.7 0.0 0.0
0.0 30.4 48.4 59.5
Fig. 2. Temperature dependence of hydrogen solubility in a metal. Fig. 5. Compressive yield strength of lotus-structured porous copper in the direction parallel and perpendicular to pore axis.
porosity. Little damage is introduced in the specimens even in the case of high porosity during the sparkerosion cutting. In the first type of specimens, the ingots were cut so that the compressive direction was parallel to the direction of the pore axes, and in the second type, perpendicular to the pore axes. The porosity is evaluated from the following expression: Fig. 3. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity (PH /0.12 MPa and PAr /0.0 MPa). 2
Porosity 1
Fig. 4. Optical micrographs of specimens for compressive test. Upper part: lotus-structured porous copper with cylindrical pores parallel to the lateral axis. Lower parts: lotus-structured porous copper with cylindrical pores perpendicular to the lateral axis.
Apparent density of porous copper : (1) Denstiy of non-porous copper
The apparent density of the individual specimen was calculated from a measurement of its weight and volume for each configuration. Compression tests were performed on the specimens in an Instron Universal Testing Machine (Model 4482, Instron Corp., Canton, MA, USA) at room temperature. The crosshead speed was 1 mm min 1. The strains were calculated from the actuator displacement and the initial specimen length, taking into account the displacements within the testing machine. The yield strength was evaluated from the stress /strain curve by the 0.2% offset method. The deformation behaviors were observed using optical microscope by interrupting the compression tests at strains of 30, 50 and 80%.
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Fig. 6. Formation of barrier to dislocation movement in the region of stress concentration.
3. Results and discussion 3.1. Compressive yield strength The compressive tests were performed on lotusstructured porous copper with different pore orientations and porosities. The yield strengths of specimens with cylindrical pore orientation parallel and perpendicular to the compressive direction are plotted against the porosity in Fig. 5. The values of yield strength of the porous copper with the cylindrical pores parallel to the compressive direction agree well with the data reported by Simone and Gibson [18]; besides, the compressive yield strength is similar tendency to the tensile yield strength of previous tensile test [17]. However, the values of the compressive yield strength of non-porous copper measured in present work are about one half of the values of the tensile yield strength of non-porous copper [17]. Similar difference in the yield strength was also observed in the results by Simone and Gibson [18]. Such difference may not be attributed to the impurity content and the morphology of the texture of the specimens. The reason is not clear at present. Further investigations are necessary to elucidate the difference. The data points for the yield strengths of the porous copper with the pores parallel to the compressive direction lie each on a straight line which passes through the point of 0 MPa at the porosity of 100%; the specific yield strength does not change by the pore existence. This fact indicates that pores aligned parallel to the compression direction cause little stress concentration in the specimens. Simple rule of mixtures of empty pores and solid body can be applied to these specimens. In the case of the specimens with pores perpendicular to the compression direction, the compressive yield strength slightly decreases until 30% porosity and then decreases significantly with increasing porosity. Although it is difficult to explain perfectly the reason for this, we suggest the following mechanism. As seen in Fig. 6, if a pore is placed in the plate for compressive loading, the stress concentrates at the edge of the pore.
Fig. 7. Compressive stress /strain curves of lotus-structured porous copper.
Therefore, the strength level of this region is higher than that of matrix. Before the stress level reaches the yield strength, at first plastic deformation locally occurs in the region of stress concentration. Plastic hardening is accompanied by plastic deformation and thus, this region becomes barrier such as Cottrell /Lomer locks [19,20] against moving dislocations in the matrix until the cross slip makes progress. Consequently, the yield strength of this specimen will not rapidly decrease with porosity at low porosity levels.
3.2. Flow stress characteristics Compressive stress /strain curves for the lotus-structured porous copper specimens with different porosities and compressive direction are shown in Fig. 7. The slope of the stress /strain curves decreases with increasing porosity and depends on compressive direction with respect to the pore direction at a given porosity. At low strain level, the stress of the specimen with pores parallel to the compressive direction is higher than that of specimen with the pores perpendicular to the compressive direction. However, this appearance is reversed with increasing strain. For understanding this behavior, we consider two reasonable possibilities as follows. First, while the stress concentration occurs around the pores in the specimen with pores perpendicular to the compressive direction, there is little stress concentration around pores in the specimen with the cylindrical pore parallel to the compressive direction. The stress concentration is important factor for determination on the strength of porous metals [17,21], which the strength decreases with stress concentration. For this reason, the pores perpendicular to the compressive direction are easily deformed at lower stress.
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Fig. 10. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity in the direction parallel to pore axis after compression test: (a) o /0; and (b) o /50%. Fig. 8. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity in the direction parallel to pore axis after compression test: (a) o /0; (b) o /30; (c) o /50; and (d) o /80%.
Fig. 11. Volume fraction of pores plotted against strain in the specimen with 59.5% porosity.
Fig. 9. Optical micrograph of cross-section of lotus-structured porous copper with 59.5% porosity in the direction perpendicular to pore axis after compression test: (a) o /0; (b) o /30; (c) o /50 and (d) o /80%.
Next, different types of deformation such as buckling occur in the specimens depending on compressive direction with the pore axis. Buckling in a specimen may result from loading misalignment and the specimen can be deformed at lower stresses. The macrographs of the lotus-structured porous copper with 59.5% porosity compressed 0, 30, 50 and 80% in the direction parallel and perpendicular to the pore axis are shown in Figs. 8 and 9, respectively.
Fig. 12. Compressive stress /strain curves of lotus-structured porous copper with 59.5% porosity.
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curves may be attributed to the stress concentration, the buckling and the volume fraction of pores.
3.3. Energy absorption
Fig. 13. Schematic compressive stress /strain curves of lotus-structured porous copper.
Schematic stress /strain curve of the lotus-structured porous copper is shown in Fig. 13. The curve exhibits the three regions: (I) elastic region characterized by elastic modulus; (II) stress plateau region characterized by a shallow slope corresponding to the plastic yielding, buckling and bending of cell ligaments; and (III) densification region characterized by a relatively steep slope. From the compression test data, the energy absorption during the compression can be calculated by integrating the area under the stress /strain curve [1]:
Table 3 Densification strain and absorption energy of lotus-structured porous copper Porosity (%)
Apparent density (Mg m 3)
Compressive direction with pore Densification strain, o D axis (%)
Stress (MPa)
Absorbed energy per volume (MJ m 3)
30.4
6.25
Parallel Perpendicular
48.4 29.8
234 144
70.8 25.7
48.4
4.64
Parallel Perpendicular
51.2 33.8
159 70.5
47.1 14.4
59.5
3.57
Parallel Perpendicular
46.3 33.0
91.5 36.1
27.8 7.2
In the parallel case, two types of buckling are observed in specimen during compression. One is the macro-buckling observed outside of specimens as shown in Fig. 8(c). Another is the micro-buckling observed around the pores. Fig. 10 shows the microstructure around the pores before and after 50% height reduction, in which the copper ligaments between pores after compression is buckled like zigzag. However, in the perpendicular case, macro-buckling is not observed outside of specimens during compression, while micro-buckling is found inside of specimens. Furthermore, as shown in Fig. 11, the volume fraction of pores after 50% compression in the perpendicular case is lower than that in the parallel case. Also, the slope of stress /strain curve in the perpendicular case is rapidly increased at 50% compressive strain as shown in Fig. 12. It can be explained that the pores in the perpendicular case is easily crushed during compression due to the stress concentration around the pores. Consequently, anisotropy of the slope of stress /strain
o
W
g s(o) do;
(2)
0
where W is the absorbed energy per unit volume and o is the strain. Table 3 compiles the absorbed energy up to densification strain, which is defined as the strain corresponding to the end of the stress plateau of lotus-structured porous copper. The stress and the absorbed energy at densification strain decrease with increasing porosity. At a given porosity the absorbed energy of the specimen in the parallel case is higher than that of the specimen in the perpendicular case, because the lotus-structured porous copper with pores parallel to the compressive direction has higher strength and ductility than that with pores perpendicular to the compressive direction. It can be seen that the energy absorption capacity of lotusstructured porous copper with the pores parallel to the
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compressive direction is higher than that perpendicular to the compressive direction at a given porosity.
tion to Dr. K. Murakami and Dr T. Ikeda of Osaka University for stimulating discussion.
4. Conclusions References The lotus-structured porous copper having long aligned pores was fabricated via melt-route process and their anisotropic compressive properties were studied. The results obtained are as follows. (1) Compressive properties of the lotus-structured porous copper depend on the porosity and on the orientation of the pore axis relative to the compressive direction. (2) The slope of stress /strain curve decreases with increasing the porosity and depends on compressive direction with respect to the pore direction. At low strain level, the stress of the specimen with pores perpendicular to the compressive direction is lower than that of specimen with the pores parallel to the compressive direction. However, this tendency is reversed with increasing strain. The anisotropy of the slope of stress /strain curves may be attributed to various types of buckling. (3) The absorbed energy of the specimen with pores parallel to the compressive direction is higher than that of the specimen in the perpendicular to the compressive direction at a given porosity.
Acknowledgements The present work was supported by Grant-in-Aid for Scientific Research A (No. 09355025) and for University and Society Collaboration (No. 11792022) of the Ministry of Education, Culture, Sports, Science and Technology. The authors wish to express their apprecia-
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