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Effects of macroscopic defects on the damping behavior of CuAlMn shape memory alloy
Journal of Alloys and Compounds 425 (2006) 200–205
Effects of macroscopic defects on the damping behavior of CuAlMn shape memory alloy Q.Z. Wang, F.S. Han ∗ , J. Wu, G.L. Hao, Z.Y. Gao Key Laboratory of Material Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, Anhui 230031, China Received 28 December 2005; received in revised form 20 January 2006; accepted 24 January 2006 Available online 23 March 2006
Abstract Two types of macroscopic defects, graphite particulates and pores with millimeter dimensions, were introduced into the Cu–11.9Al–2.5Mn (wt.%) shape memory alloy, and the damping behaviors of the resultant composites were investigated. It is found that the damping capacity of the porous and the composite was greatly elevated particularly at relatively low temperatures. The higher the volume fraction or the smaller the size of the macroscopic defects, the higher the damping capacity of the composites. However, the graphite particulates showed more significant damping enhancement than the pores because of the combined effects of the matrix, dislocations and the particulates themselves. © 2006 Elsevier B.V. All rights reserved. Keywords: Shape memory alloys; Damping; Composite; Porous alloys; Internal friction
1. Introduction High damping capacity has been one of the most important properties of materials used in engineering structures where undesirable noise and vibration are to be passively attenuated. Among the prevalent high damping metallic materials, shape memory alloys (SMAs) could be one of the most promising candidates due to their high damping capacity arising from the reversible martensitic phase transformation (MT) and the stress induced reorientation of martensite variants [1,2]. It is generally accepted that micro-structural defects play a dominant role in the damping response of materials [3–6]. From this fundamental concept, a variety of high damping metals and metal matrix composites (MMCs) have been developed, leading to accelerated develop and application of high damping metals. These materials, however, can still in part meet the needs of the engineering societies due to limited damping capacity as well as other shortcomings. It has been disclosed in our previous studies that the reinforcements in a composite can be either particulates or pores in macroscopic dimensions and high proportion if damping enhancement is required [7,8]. The damping capac-
∗
Corresponding author. Tel.: +86 551 5591435; fax: +86 551 5591434. E-mail address: [email protected] (F.S. Han).
0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.01.062
ity of alloys, with either high or low intrinsic damping, can be substantially improved through this macroscopic MMC route, typically from several times to an order higher than that of the parent materials. This enhancement originates from the increase in the damping source, overlapping and interaction of different damping mechanisms. It is therefore rationalized that the damping behavior of SMA can also be tailored in this way, allowing increased damping together with decreased density. The resultant material can find use in a number of industrial areas, including lightweight structures and energy absorption apparatus, etc. For the composites with macroscopic reinforcements, the essential matters of concern would be what damping mechanisms will be operative and how the macroscopic defects influence the distribution, movement and interaction of microscopic defects in the materials [9]. Obviously, these matters can be very different in different alloy families and reinforcements. Under the condition of SMAs based composites, incorporation of the second phase (particulates or pores) is expected to generate additional energy dissipation sources through the new phase, the matrix/reinforcement interface and the disturbance on the nucleation and growth of the martensite during the MT, the motion of the martensite interfaces or the domain walls. Clarification of these issues is undoubtedly essential for development of high damping SMAs based composites and is thus the focus of the present study.
Q.Z. Wang et al. / Journal of Alloys and Compounds 425 (2006) 200–205
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Two kinds of reinforcements, graphite particulates and pores, are utilized in the present study, where the pores are regarded as a special phase. They have contrast mechanical properties and should impose very different effect on the inherent damping mechanisms of the SMA. It is expected that the results will be helpful for better understanding the effects of macroscopic defects on the damping behavior of the CuAlMn SMA and useful for developing novel high damping materials. 2. Experimental procedure 2.1. Specimen preparation An air pressure infiltration process was employed to fabricate either the composite specimens using a Cu–11.9Al–2.5Mn (wt.%) SMA and graphite particulates (Gr), or porous specimens using the same SMA and water-soluble salt particulates. The graphite or the salt particulates with a chosen size were weighed using an electronic balance with an accuracy of 0.01 g and uniaxially pressed into a steel die with an inner diameter of 70 mm under an appropriate pressure. The porous compact was then preheated to 900 ◦ C and infiltrated with the SMA melt under one atmosphere pressure, resulting in a composite either composed of Gr or salt particulates. After the melt solidified, the specimens containing the salt particulates were washed with water to remove the salt, leaving the porous structures. Fig. 1 shows the typical structures of the porous SMA and the composite specimens. The distributions of both the pores and graphite particulates are apparently uniform over the matrix. All the specimens used for comparison were cut from the same ingot using an electric sparking machine to guarantee the identity of the microstructures. Before the damping measurements, all the specimens were subjected to a homogenization treatment by keeping at 900 ◦ C for 900 s followed by water quenching.
2.2. Volume fraction of the reinforcements The specimen density was determined from its weight and physical dimensions, from which the volume fraction of the reinforcement was calculated by the following equation: Vf = 1 −
ρr ρb
(1)
with Vf as the volume fraction of reinforcement; ρr as the density of the composite and ρb as the density of the bulk specimens, respectively.
Fig. 1. Typical structures of (a) the porous SMA and (b) the composite.
2.3. Damping measurements Internal friction (IF), Q−1 , was used to characterize the damping property of the specimens and was measured using a computer controlled automatic inverted torsion pendulum by forced vibration. This apparatus basically consists of an inverted torsion pendulum, a temperature programmer and a photoelectron transformer. The whole measurement is controlled by an IBM × PC586 computer and an 8087 processor and the data can be processed in real time. The range of the maximum excitation strain amplitude is 10−6 to 10−4 . The resolution in the IF measurements is 1 × 10−4 . The details of the apparatus can be found in Ref. [8].
3. Results and analysis 3.1. Typical damping behavior of the bulk CuAlMn SMA Fig. 2 shows the typical IF as a function of temperature for the bulk CuAlMn SMA in a heating and cooling cycle. Two IF peaks are found at the both curves and they appear at around 150◦ C (termed P1) and 325 ◦ C (termed P2) during heating, while they arise at around 130 ◦ C (termed P1 ) and 215 ◦ C (termed P2 ) during cooling. Combination of these features with the result of
Fig. 2. Typical IF behavior of the bulk CuAlMn alloy measured in a heating/cooling cycle at a heating/cooling rate of 6 ◦ C/min at 1.0 Hz.
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Fig. 3. Differential scanning calorimetry (DSC) results for the bulk, porous and composite measured at a heating/cooling rate of 10 ◦ C/min.
differential scanning calorimetry (DSC) shown in Fig. 3 highlights that, as has been demonstrated in [10], P1 and P1 arise from the fining and coarsening process of twins, while P2 and P2 are due to the reverse and forward MT, respectively. 3.2. Effect of macroscopic pores on the damping capacity of the CuAlMn SMA Fig. 4 illustrates the comparison of the IF against temperature between the bulk and the porous specimens with varied porosities and pore sizes. It is seen that the IF background was significantly elevated in the porous specimens, i.e. the overall damping capacity is enhanced. For instance, compared with the bulk alloy that has an average IF value of 0.006 at ambient temperature, the porous alloy with a porosity of 69% shows an average IF of about 0.0115, nearly two times higher than that
Fig. 4. Effect of porosity and pore size on the IF of the porous CuAlMn alloy measured at a heating rate of 6 ◦ C/min at 1.0 Hz.
of the bulk alloy. The enhancement becomes more pronounced as the porosity increases or the pore size decreases, suggesting that the pores may play an important role in the IF of the porous alloy. As mentioned above, the pores can be regarded as a special reinforcement with a near zero modulus. It is the difference in the elastic modulus and thermal expansion coefficient between the matrix and pore that causes inhomogeneous stress and strain distribution around pores during the fabrication of the porous CuAlMn alloy. This state will be intensified in the IF measurement due to the disturbance of applied cyclic stress. Atoms and vacancies are forced to move and redistributed within the distorted regions. This response is hysteretic and inevitably causes energy dissipation [11]. The dissipation of elastic energy in porous materials has been rationalized in terms of a mechanism known as mode conversion and stress concentration around pores [12,13], that is, in the IF measurements, the stress state may change from the normal into the shear at the boundaries of macroscopic pores. An inhomogeneous stress field, which is simultaneous with the stress mode conversation, is built up around pores [14], making the pores dilate and distort. The pores’ dilatation and distortion are accompanied by dislocation generation and motion to relax the residual thermal stress and stress concentration, giving rise to additional dissipation of elastic energy [12]. It is well known that the damping originated from the dislocation mechanism should be strain amplitude dependent [15]. The damping of the porous specimens does show the obvious strain amplitude dependence, giving a strong evidence for its dislocation nature, as shown in Fig. 5. Thus, the macroscopic pores may be high-energy dissipation resource. This leads to the higher the porosity, or the smaller the pores in the same porosity, the higher the damping capacity of the porous materials. Nevertheless, the changes in the matrix microstructures of the porous specimens should not be neglected. During the infiltration and subsequent solidification, the salt particulates played a constraint role in the martensite nucleation and growth and thus were favorable for the refinement of the matensite, as demonstrated by Fig. 6. This refined martensite structure obvi-
Fig. 5. Dependence of IF on the strain amplitude for the porous and composite.
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Fig. 6. Microstructures of the (a) bulk, (b) porous, and (c) composite.
ous contributed to the elevation of the IF background in terms of the damping mechanism in SMAs. 3.3. Effect of macroscopic graphite particulates on the damping capacity of CuAlMn SMA Fig. 7 shows the effect of the macroscopic graphite particulates on the damping capacity of the CuAlMn SMA. The damping enhancement is more pronounced in the composite than in the porous alloy. For example, the composite with 74% reinforcement shows an average IF value of about 0.028 at ambient temperature, nearly four times higher than that of the bulk alloy. Similar to the porous alloy, the higher the volume fraction or the smaller the graphite particulate size, the higher the damping capacity. For particulates reinforced MMC, the damping mechanisms have been extensively investigated and can be described by the extended rule of mixture [16], that is ψc = ψm Vm + ψp Vp + ψi Vi
(2)
Fig. 7. Effect of volume fraction and diameter of the graphite particulates on the IF of the composite measured at a heating rate of 6 ◦ C/min at 0.5 Hz.
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where Ψ c , Ψ m and Ψ p represent the damping capacity of the composite, matrix and particulates, respectively; Vm and Vp denote the volume fraction of the matrix and particulates, respectively; Ψ i Vi represents the contribution of the matrix/reinforcement interface to the overall damping of the composite. This relationship indicates that the overall damping capacity of a composite is not only correlated to the individual constituent but also to the interface. It is known from Fig. 7 that, at ambient temperature, the average IF value of the graphite is about 0.016 and that of the bulk CuAlMn alloy is 0.006. Thus the contribution of the matrix and reinforcement to the overall damping of the composite containing 74% reinforcement is only 0.013, less than half of the overall damping capacity, i.e. 0.028, as shown in Fig. 7. It follows that the interface damping should be predominant among all the three damping origins. It has been confirmed that the particulates reinforced MMCs prepared by infiltration process basically possess weakly bonded reinforcement/matrix interfaces and on the other hand, the interfacial bonding is likely weak due to the layered structure in the graphite particulates [17,18]. The effect of weakly bonded interfaces on the overall damping of particulates reinforced composites has been well documented by interface slip model [19,20], in which the interface damping is proposed to arise from the frictional energy loss between the particulates and the matrix. Similar to the porous CuAlMn alloy, the matrix microstructure of the composite has been modified by the graphite particulates. There will be increased dislocations around the graphite particulates [21] and the martensites will be refined, as is shown in Fig. 6(c). Accordingly, the damping resulted from the motions of dislocations and martensite variants is elevated. 3.4. Effect of heating rate on the IF of the porous and the composite It has been known that three mechanisms contribute to the overall damping of a SMA, i.e. two stationary contributions related to the phase transition and each phase, respectively, and one transient contribution proportional to (dT/dt)/f, where dT/dt is the temperature change rate and f is the frequency [22]. Figs. 8 (a) and (b) illustrate that the two IF peaks do contain the contribution of the transient damping because the heights decreased with decreasing the heating rate, whilst the IF backgrounds kept almost unchanged at varied temperature change rates, demonstrating that the tailoring in the microstructures is the main reason for the enhanced damping capacity in the porous and the composite specimens indeed. 4. Discussion It is obvious that the damping of the present graphite particulates reinforced composite consists of the contributions of dislocation, interface, matrix and the graphite particulates, while that of the porous alloy only contains the dislocation damping and the matrix damping. Even if the contributions of the latter two damping mechanisms are comparable to those of
Fig. 8. Effect of heating rate on the IF of the (a) porous and (b) the composite.
the composite, the absence of the matrix/reinforcement interfacial friction and the high damping phase of graphite is obviously unfavorable to the damping enhancement in the porous alloy. It is seen from Figs. 4 and 7 that, although the IF backgrounds of the porous and composite specimens were higher than that of the bulk alloy, the P2 peak arising from the reverse MT decreased in the both alloys. This can be due to the occurrence of the complicated dislocation configuration or the carbonide during the fabricating of the specimens. In addition, part of the dislocations generated in the parent phase can be inherited by the martensite as immobile non-basal stacking faults [20,23,24] during the forward MT. All those factors tend to hinder the phase interface sliding and the growth of new phase during the MT. Moreover, the porous and composite specimens are in a very complicated and inhomogeneous stress and strain state, which state can be further intensified in IF measurements due to the disturbance of the applied stress. The crystal lattices can be distorted in the regions adjacent to the pores or graphite particulates, leading to partially destroyed coherency between
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the martensite and the parent phases during the MT [25,26]. All these factors should be responsible for the decreased P2 peak. It can be inferred that all those defects incorporated during the fabrication of the specimens will also hinder the sliding of the twins boundaries, resulting in the decrease of the low-temperature peak arising from the fining of the twins. 5. Conclusions Graphite particulates reinforced and porous Cu–11.9Al– 2.5Mn (wt.%) SMA specimens were fabricated and used to examine the effects of macroscopic defects on the damping behavior of SMA. Two IF peaks were found at the IFtemperature spectra of the specimens, in which the hightemperature peak was related to the reverse MT while the lowtemperature one to the fining process of the twins. Compared with the bulk alloy, the porous and composite specimens showed the enhanced IF backgrounds but decreased IF peaks. The damping enhancement became more pronounced with increasing the volume fraction or decreasing the size of the macroscopic defects. It is proposed that the damping of the composite consists of the contributions of dislocations, interfaces apart from those of the matrix and the graphite particulates, while the damping of the porous specimens only consists of the dislocation damping and the matrix damping. These differences in damping source should be responsible for the different damping capacities in the porous and the composite. Introduced defects and the complicated defect configuration in the porous and the composite tend to hinder the phase interface sliding and the growth of new phase during the MT, and distorted crystal lattices can destroy the coherency between the martensite/austenite phases. All these factors can result in the decrease of the high-temperature IF peak.
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References [1] J.V. Humbeeck, J. Alloys Comp. 355 (2003) 58. [2] J.S. Juan, M.L. N´o, J. Alloys Comp. 355 (2003) 65. [3] M. Vogelsang, R. Arsenadet, R. Fisher, Metall. Mater. Trans. A 17 (1986) 379. [4] T. Christman, S. Suresh, Acta Metall. Mater. 36 (1988) 1691. [5] D.C. Dunand, A. Mortensen, Acta Metall. Mater. 39 (1991) 1405. [6] F.S. Shieu, S.L. Sass, Acta Metall. Mater. 39 (1991) 539. [7] F.S. Han, Z.G. Zhu, J. Mater. Sci. 34 (1999) 291. [8] F.S. Han, Z.G. Zhu, C.S. Liu, J.C. Gao, Metall. Mater. Trans. A 30 (1999) 771. [9] J.N. Wei, Z.B. Li, F.S. Han, Phys. Stat. Sol. (a) 191 (2002) 125. [10] Q.Z. Wang, F.S. Han, Q. Wang, Phys. Stat. Sol. (a) 201 (2004) 2910. [11] T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Netherlands, Dordrecht, 1987, p. 97. [12] J. Zhang, M.N. Gungor, E.J. Lavernia, J. Mater. Sci. 28 (1993) 1515. [13] J. Banhart, J. Baumeister, M. Weber, Mater. Sci. Eng. A 205 (1996) 221. [14] C.S. Liu, Z.G. Zhu, F.S. Han, J. Banhart, Phil. Mag. A 78 (1998) 1329. [15] S. Kustov, J. Pons, E. Cesari, M. Morin, J.V. Humbeeck, Mater. Sci. Eng. A 373 (2004) 328. [16] A. Wolfenden, J.M. Wolla, Metal Matrix Composites Theory and Experiment TX, Teax A&M University, College Station, 1990. [17] K.A. Tsoi, R. Stalmans, J. Schrooten, Acta Metall. Mater. 50 (2002) 3535. [18] J.N. Wei, H.F. Cheng, Y.F. Zhang, F.S. Han, Z.C. Zhou, J.P. Shui, Mater. Sci. Eng. A 325 (2002) 444. [19] D.J. Nelson, J.W. Hancock, J. Mater. Sci. 13 (1978) 2429. [20] N.N.K. Shore, A. Ghosh, B.D. Agarwal, J. Reinforced Plast. Compos. 1 (1982) 353. [21] Q.Z. Wang, F.S. Han, J. Wu, G.L. Hao, Mater. Sci. Eng. A 408 (2005) 247. [22] J.E. Bidaux, R. Schaller, W. Benoit, Acta Metall. 37 (1989) 803. [23] C.L. Francisco, A. Antoni, T. Vicenc, A. Manfred, Phil. Mag. A 61 (1990) 159. [24] X. Duan, W.M. Stobbs, Script. Metall. 23 (1989) 441. [25] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic, New York, 1972. [26] J. Yang, Y.H. Wu, Shape Semory Alloys and Their Applications, USTC, Hefei, 1993, p. 124.
Effects of macroscopic defects on the damping behavior of CuAlMn shape memory alloy Q.Z. Wang, F.S. Han ∗ , J. Wu, G.L. Hao, Z.Y. Gao Key Laboratory of Material Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, Anhui 230031, China Received 28 December 2005; received in revised form 20 January 2006; accepted 24 January 2006 Available online 23 March 2006
Abstract Two types of macroscopic defects, graphite particulates and pores with millimeter dimensions, were introduced into the Cu–11.9Al–2.5Mn (wt.%) shape memory alloy, and the damping behaviors of the resultant composites were investigated. It is found that the damping capacity of the porous and the composite was greatly elevated particularly at relatively low temperatures. The higher the volume fraction or the smaller the size of the macroscopic defects, the higher the damping capacity of the composites. However, the graphite particulates showed more significant damping enhancement than the pores because of the combined effects of the matrix, dislocations and the particulates themselves. © 2006 Elsevier B.V. All rights reserved. Keywords: Shape memory alloys; Damping; Composite; Porous alloys; Internal friction
1. Introduction High damping capacity has been one of the most important properties of materials used in engineering structures where undesirable noise and vibration are to be passively attenuated. Among the prevalent high damping metallic materials, shape memory alloys (SMAs) could be one of the most promising candidates due to their high damping capacity arising from the reversible martensitic phase transformation (MT) and the stress induced reorientation of martensite variants [1,2]. It is generally accepted that micro-structural defects play a dominant role in the damping response of materials [3–6]. From this fundamental concept, a variety of high damping metals and metal matrix composites (MMCs) have been developed, leading to accelerated develop and application of high damping metals. These materials, however, can still in part meet the needs of the engineering societies due to limited damping capacity as well as other shortcomings. It has been disclosed in our previous studies that the reinforcements in a composite can be either particulates or pores in macroscopic dimensions and high proportion if damping enhancement is required [7,8]. The damping capac-
∗
Corresponding author. Tel.: +86 551 5591435; fax: +86 551 5591434. E-mail address: [email protected] (F.S. Han).
0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.01.062
ity of alloys, with either high or low intrinsic damping, can be substantially improved through this macroscopic MMC route, typically from several times to an order higher than that of the parent materials. This enhancement originates from the increase in the damping source, overlapping and interaction of different damping mechanisms. It is therefore rationalized that the damping behavior of SMA can also be tailored in this way, allowing increased damping together with decreased density. The resultant material can find use in a number of industrial areas, including lightweight structures and energy absorption apparatus, etc. For the composites with macroscopic reinforcements, the essential matters of concern would be what damping mechanisms will be operative and how the macroscopic defects influence the distribution, movement and interaction of microscopic defects in the materials [9]. Obviously, these matters can be very different in different alloy families and reinforcements. Under the condition of SMAs based composites, incorporation of the second phase (particulates or pores) is expected to generate additional energy dissipation sources through the new phase, the matrix/reinforcement interface and the disturbance on the nucleation and growth of the martensite during the MT, the motion of the martensite interfaces or the domain walls. Clarification of these issues is undoubtedly essential for development of high damping SMAs based composites and is thus the focus of the present study.
Q.Z. Wang et al. / Journal of Alloys and Compounds 425 (2006) 200–205
201
Two kinds of reinforcements, graphite particulates and pores, are utilized in the present study, where the pores are regarded as a special phase. They have contrast mechanical properties and should impose very different effect on the inherent damping mechanisms of the SMA. It is expected that the results will be helpful for better understanding the effects of macroscopic defects on the damping behavior of the CuAlMn SMA and useful for developing novel high damping materials. 2. Experimental procedure 2.1. Specimen preparation An air pressure infiltration process was employed to fabricate either the composite specimens using a Cu–11.9Al–2.5Mn (wt.%) SMA and graphite particulates (Gr), or porous specimens using the same SMA and water-soluble salt particulates. The graphite or the salt particulates with a chosen size were weighed using an electronic balance with an accuracy of 0.01 g and uniaxially pressed into a steel die with an inner diameter of 70 mm under an appropriate pressure. The porous compact was then preheated to 900 ◦ C and infiltrated with the SMA melt under one atmosphere pressure, resulting in a composite either composed of Gr or salt particulates. After the melt solidified, the specimens containing the salt particulates were washed with water to remove the salt, leaving the porous structures. Fig. 1 shows the typical structures of the porous SMA and the composite specimens. The distributions of both the pores and graphite particulates are apparently uniform over the matrix. All the specimens used for comparison were cut from the same ingot using an electric sparking machine to guarantee the identity of the microstructures. Before the damping measurements, all the specimens were subjected to a homogenization treatment by keeping at 900 ◦ C for 900 s followed by water quenching.
2.2. Volume fraction of the reinforcements The specimen density was determined from its weight and physical dimensions, from which the volume fraction of the reinforcement was calculated by the following equation: Vf = 1 −
ρr ρb
(1)
with Vf as the volume fraction of reinforcement; ρr as the density of the composite and ρb as the density of the bulk specimens, respectively.
Fig. 1. Typical structures of (a) the porous SMA and (b) the composite.
2.3. Damping measurements Internal friction (IF), Q−1 , was used to characterize the damping property of the specimens and was measured using a computer controlled automatic inverted torsion pendulum by forced vibration. This apparatus basically consists of an inverted torsion pendulum, a temperature programmer and a photoelectron transformer. The whole measurement is controlled by an IBM × PC586 computer and an 8087 processor and the data can be processed in real time. The range of the maximum excitation strain amplitude is 10−6 to 10−4 . The resolution in the IF measurements is 1 × 10−4 . The details of the apparatus can be found in Ref. [8].
3. Results and analysis 3.1. Typical damping behavior of the bulk CuAlMn SMA Fig. 2 shows the typical IF as a function of temperature for the bulk CuAlMn SMA in a heating and cooling cycle. Two IF peaks are found at the both curves and they appear at around 150◦ C (termed P1) and 325 ◦ C (termed P2) during heating, while they arise at around 130 ◦ C (termed P1 ) and 215 ◦ C (termed P2 ) during cooling. Combination of these features with the result of
Fig. 2. Typical IF behavior of the bulk CuAlMn alloy measured in a heating/cooling cycle at a heating/cooling rate of 6 ◦ C/min at 1.0 Hz.
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Fig. 3. Differential scanning calorimetry (DSC) results for the bulk, porous and composite measured at a heating/cooling rate of 10 ◦ C/min.
differential scanning calorimetry (DSC) shown in Fig. 3 highlights that, as has been demonstrated in [10], P1 and P1 arise from the fining and coarsening process of twins, while P2 and P2 are due to the reverse and forward MT, respectively. 3.2. Effect of macroscopic pores on the damping capacity of the CuAlMn SMA Fig. 4 illustrates the comparison of the IF against temperature between the bulk and the porous specimens with varied porosities and pore sizes. It is seen that the IF background was significantly elevated in the porous specimens, i.e. the overall damping capacity is enhanced. For instance, compared with the bulk alloy that has an average IF value of 0.006 at ambient temperature, the porous alloy with a porosity of 69% shows an average IF of about 0.0115, nearly two times higher than that
Fig. 4. Effect of porosity and pore size on the IF of the porous CuAlMn alloy measured at a heating rate of 6 ◦ C/min at 1.0 Hz.
of the bulk alloy. The enhancement becomes more pronounced as the porosity increases or the pore size decreases, suggesting that the pores may play an important role in the IF of the porous alloy. As mentioned above, the pores can be regarded as a special reinforcement with a near zero modulus. It is the difference in the elastic modulus and thermal expansion coefficient between the matrix and pore that causes inhomogeneous stress and strain distribution around pores during the fabrication of the porous CuAlMn alloy. This state will be intensified in the IF measurement due to the disturbance of applied cyclic stress. Atoms and vacancies are forced to move and redistributed within the distorted regions. This response is hysteretic and inevitably causes energy dissipation [11]. The dissipation of elastic energy in porous materials has been rationalized in terms of a mechanism known as mode conversion and stress concentration around pores [12,13], that is, in the IF measurements, the stress state may change from the normal into the shear at the boundaries of macroscopic pores. An inhomogeneous stress field, which is simultaneous with the stress mode conversation, is built up around pores [14], making the pores dilate and distort. The pores’ dilatation and distortion are accompanied by dislocation generation and motion to relax the residual thermal stress and stress concentration, giving rise to additional dissipation of elastic energy [12]. It is well known that the damping originated from the dislocation mechanism should be strain amplitude dependent [15]. The damping of the porous specimens does show the obvious strain amplitude dependence, giving a strong evidence for its dislocation nature, as shown in Fig. 5. Thus, the macroscopic pores may be high-energy dissipation resource. This leads to the higher the porosity, or the smaller the pores in the same porosity, the higher the damping capacity of the porous materials. Nevertheless, the changes in the matrix microstructures of the porous specimens should not be neglected. During the infiltration and subsequent solidification, the salt particulates played a constraint role in the martensite nucleation and growth and thus were favorable for the refinement of the matensite, as demonstrated by Fig. 6. This refined martensite structure obvi-
Fig. 5. Dependence of IF on the strain amplitude for the porous and composite.
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Fig. 6. Microstructures of the (a) bulk, (b) porous, and (c) composite.
ous contributed to the elevation of the IF background in terms of the damping mechanism in SMAs. 3.3. Effect of macroscopic graphite particulates on the damping capacity of CuAlMn SMA Fig. 7 shows the effect of the macroscopic graphite particulates on the damping capacity of the CuAlMn SMA. The damping enhancement is more pronounced in the composite than in the porous alloy. For example, the composite with 74% reinforcement shows an average IF value of about 0.028 at ambient temperature, nearly four times higher than that of the bulk alloy. Similar to the porous alloy, the higher the volume fraction or the smaller the graphite particulate size, the higher the damping capacity. For particulates reinforced MMC, the damping mechanisms have been extensively investigated and can be described by the extended rule of mixture [16], that is ψc = ψm Vm + ψp Vp + ψi Vi
(2)
Fig. 7. Effect of volume fraction and diameter of the graphite particulates on the IF of the composite measured at a heating rate of 6 ◦ C/min at 0.5 Hz.
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where Ψ c , Ψ m and Ψ p represent the damping capacity of the composite, matrix and particulates, respectively; Vm and Vp denote the volume fraction of the matrix and particulates, respectively; Ψ i Vi represents the contribution of the matrix/reinforcement interface to the overall damping of the composite. This relationship indicates that the overall damping capacity of a composite is not only correlated to the individual constituent but also to the interface. It is known from Fig. 7 that, at ambient temperature, the average IF value of the graphite is about 0.016 and that of the bulk CuAlMn alloy is 0.006. Thus the contribution of the matrix and reinforcement to the overall damping of the composite containing 74% reinforcement is only 0.013, less than half of the overall damping capacity, i.e. 0.028, as shown in Fig. 7. It follows that the interface damping should be predominant among all the three damping origins. It has been confirmed that the particulates reinforced MMCs prepared by infiltration process basically possess weakly bonded reinforcement/matrix interfaces and on the other hand, the interfacial bonding is likely weak due to the layered structure in the graphite particulates [17,18]. The effect of weakly bonded interfaces on the overall damping of particulates reinforced composites has been well documented by interface slip model [19,20], in which the interface damping is proposed to arise from the frictional energy loss between the particulates and the matrix. Similar to the porous CuAlMn alloy, the matrix microstructure of the composite has been modified by the graphite particulates. There will be increased dislocations around the graphite particulates [21] and the martensites will be refined, as is shown in Fig. 6(c). Accordingly, the damping resulted from the motions of dislocations and martensite variants is elevated. 3.4. Effect of heating rate on the IF of the porous and the composite It has been known that three mechanisms contribute to the overall damping of a SMA, i.e. two stationary contributions related to the phase transition and each phase, respectively, and one transient contribution proportional to (dT/dt)/f, where dT/dt is the temperature change rate and f is the frequency [22]. Figs. 8 (a) and (b) illustrate that the two IF peaks do contain the contribution of the transient damping because the heights decreased with decreasing the heating rate, whilst the IF backgrounds kept almost unchanged at varied temperature change rates, demonstrating that the tailoring in the microstructures is the main reason for the enhanced damping capacity in the porous and the composite specimens indeed. 4. Discussion It is obvious that the damping of the present graphite particulates reinforced composite consists of the contributions of dislocation, interface, matrix and the graphite particulates, while that of the porous alloy only contains the dislocation damping and the matrix damping. Even if the contributions of the latter two damping mechanisms are comparable to those of
Fig. 8. Effect of heating rate on the IF of the (a) porous and (b) the composite.
the composite, the absence of the matrix/reinforcement interfacial friction and the high damping phase of graphite is obviously unfavorable to the damping enhancement in the porous alloy. It is seen from Figs. 4 and 7 that, although the IF backgrounds of the porous and composite specimens were higher than that of the bulk alloy, the P2 peak arising from the reverse MT decreased in the both alloys. This can be due to the occurrence of the complicated dislocation configuration or the carbonide during the fabricating of the specimens. In addition, part of the dislocations generated in the parent phase can be inherited by the martensite as immobile non-basal stacking faults [20,23,24] during the forward MT. All those factors tend to hinder the phase interface sliding and the growth of new phase during the MT. Moreover, the porous and composite specimens are in a very complicated and inhomogeneous stress and strain state, which state can be further intensified in IF measurements due to the disturbance of the applied stress. The crystal lattices can be distorted in the regions adjacent to the pores or graphite particulates, leading to partially destroyed coherency between
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the martensite and the parent phases during the MT [25,26]. All these factors should be responsible for the decreased P2 peak. It can be inferred that all those defects incorporated during the fabrication of the specimens will also hinder the sliding of the twins boundaries, resulting in the decrease of the low-temperature peak arising from the fining of the twins. 5. Conclusions Graphite particulates reinforced and porous Cu–11.9Al– 2.5Mn (wt.%) SMA specimens were fabricated and used to examine the effects of macroscopic defects on the damping behavior of SMA. Two IF peaks were found at the IFtemperature spectra of the specimens, in which the hightemperature peak was related to the reverse MT while the lowtemperature one to the fining process of the twins. Compared with the bulk alloy, the porous and composite specimens showed the enhanced IF backgrounds but decreased IF peaks. The damping enhancement became more pronounced with increasing the volume fraction or decreasing the size of the macroscopic defects. It is proposed that the damping of the composite consists of the contributions of dislocations, interfaces apart from those of the matrix and the graphite particulates, while the damping of the porous specimens only consists of the dislocation damping and the matrix damping. These differences in damping source should be responsible for the different damping capacities in the porous and the composite. Introduced defects and the complicated defect configuration in the porous and the composite tend to hinder the phase interface sliding and the growth of new phase during the MT, and distorted crystal lattices can destroy the coherency between the martensite/austenite phases. All these factors can result in the decrease of the high-temperature IF peak.
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