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Enhanced damping of a magnesium alloy by addition of copper
Journal of Alloys and Compounds 352 (2003) 106–110
L
www.elsevier.com / locate / jallcom
Enhanced damping of a magnesium alloy by addition of copper Narasimalu Srikanth, Calvin He Gaofeng, Manoj Gupta* Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore Received 28 August 2002; accepted 3 October 2002
Abstract A new idea of using a stiffer metallic element, such as copper, to enhance the damping of AZ91 magnesium alloy is successfully attempted. The study focuses on the relationship between the damping capability of the composite with the weight percentage of copper added to the matrix. Results of this study show that addition of about 8.1, 15.5 and 20.6 wt.% of copper increases the overall damping capacity of the AZ91 matrix by 64%, 78% and 107%, respectively. Particular emphasis is placed on rationalizing the increase in damping in terms of the increase in dislocation density and presence of plastic zone at the matrix–particulate interface. 2002 Elsevier Science B.V. All rights reserved. Keywords: Alloys; Composite materials; Mechanical properties
1. Introduction Stiffer materials with high damping property are actively sought for dynamic mechanical systems such as in spacecrafts, semiconductor equipment and robotics. Magnesiumbased formulations are one such category of materials that has the capability to exhibit such properties especially when it is unified with stiffer phase particulates [1]. In related studies, it has been shown that the addition of ceramic particulates to the magnesium matrix assists in improving damping properties of the magnesium matrix [2]. The results of the literature search, however, reveal that no attempt is made to investigate the effect of stiffer metallic phase addition on the damping behavior of magnesium alloys. Accordingly, the primary objective of this investigation was to investigate the energy dissipation of a magnesium alloy containing variable amounts of copper.
2. Materials and processes The hybrid composite samples were prepared using the disintegrated deposition method (DMD) and the matrix used was AZ91 magnesium alloy [2]. The processing
*Corresponding author. Tel.: 165-6874-6358; fax: 165-6779-1459. E-mail address: [email protected] (M. Gupta).
parameters were controlled so as to allow only partial reaction of copper with the metallic melt. Three composite rods with 8.1, 15.5 and 20.6 equivalent of copper in weight percentage were extruded. Scanning electron microscopy and X-ray diffraction studies were conducted to establish the presence of copper and Cu-rich phases. The results of microstructural characterization of the MMC specimens obtained using image analysis and the density measurements are listed in Table 1. Fig. 1 shows a typical SEM micrograph which illustrates the microstructural characteristics of AZ91-8.1 Cu sample. The coefficient of thermal expansion was determined on the extruded composite samples using a thermal–mechanical analyzer and the results are shown in Table 1.
3. Damping measurement method The impact-based ‘free–free’ or ‘suspended’ beam method was performed based on the ASTM C1259-98 standard [3]. Description of the experimental set-up is given in Ref. [4]. The receptance frequency response function (FRF) ‘a (v )’, which is the ratio between displacement response to the applied impact force, was plotted as a Nyquist plot corresponding to the resonance condition [5]. Using least squares technique, a circle was fit and based on a hysterically damped vibrating system the circle diameter can be shown to be inversely dependent on the damping coefficient. Fig. 2 shows typical circle fit plots
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01131-3
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110
107
Table 1 Results of the microstructural characterization Cu weight (%)
Cu volume (%)
Density (g / cm 3 )
Cu particulate size (mm)
Cu particulate aspect ratio
Experimental mean CTE (10 26 / 8C)
0.0 8.1 15.5 20.6
0.0 1.75 3.59 4.99
1.82 2.00 2.11 2.29
– 1.560.6 1.260.4 1.060.2
– 1.560.3 1.560.3 1.460.2
30.648 28.157 27.857 24.942
of the monolithic sample and the samples containing 8.1, 15.5 and 20.6 wt.% of Cu. The exact location and determination of the natural frequency and the corresponding damping factor ‘hfree ’ was calculated using a frequency spacing technique [5]. Fig. 3 shows the typical circle plot from which two points are selected for damping loss factor calculation, denoted as point a and b corresponding to frequencies va and vb , respectively, which are lesser and greater than the natural frequency vn , respectively. Thus, the damping factor hfree can be expressed using the angles shown in Fig. 3, as follows [5]:
v 2a 2 v 2b 1 ]]]]]]. hfree 5 ]]] tan (Dua ) 1 tan (Dub ) v 2r
(1)
4. Results and discussion The suspended beam experimental method was found to be highly repeatable and was nondestructive. The circle-fit approach was found to be efficient in determining the damping factor from the suspended beam’s FRF data. Using this approach, the damping factor of AZ91 magnesium alloy was found to be 0.008660.0005 which can be favorably compared with the damping measurements of Housh et al. which was found to be 0.0079 at low strain amplitude [6].
Fig. 1. SEM micrograph showing the microstructural characteristics of AZ91-8.1 Cu sample.
Uniform distribution of Cu particulates and its intermetallic phases in the metal matrix was seen in all the composite samples. Thus an isotropic material behavior can be expected in all the composite samples, from a global perspective. Close inspection of the Cu particulate at high magnification illustrated good Cu–Mg interfacial bonding in all the three composites investigated in the present study. Table 2 lists the damping factor of the monolithic sample and the three AZ91-Cu samples. Comparison shows that addition of Cu in the AZ91 matrix increases the overall damping capacity and this damping improvement increases with Cu weight percentage. The overall damping capacity of the metal matrix composite is directly related to the damping capacity of each of its constituents. Based on the damping studies of Thirumalai et al. [7] Cu has a lower loss factor of the order of 0.0015 as compared to AZ91 Mg alloy, which has an order of 0.0086, based on the present work. Hence it can be expected that addition of Cu in the AZ91 matrix would result in the decrease in damping capacity of the composite. Thus, the damping improvement observed from the experiment results has to be attributed primarily to the interface between reinforcement and the metallic matrix. In metallic materials the damping capacity arises due to intrinsic dissipation of strain energy due to mechanisms at the crystal level. The most significant role comes from point defect relaxation, microplasticity, dislocation motion, grain boundary sliding, inclusion-matrix friction, magnetoelastic effects, and elastothermodynamic effects [8,9]. Particulate reinforced metal matrix composites have additional mechanisms apart from the regular damping mechanisms in the metallic matrix due to a high residual stress in the matrix and due to high dislocation density at the particulate / matrix interface, which improve their damping capacity [10]. The high residual stresses and the dislocation density are caused due to large difference in the coefficient of thermal expansion between the phases (such as the CTE for Cu is 17 ppm / 8C [2], and for Mg it is 30.6 ppm / 8C, refer to Table 1). In addition, transformation of Cu to Mg–Cu intermetallics can enhance this residual stress and dislocation density since the coefficient of thermal expansion of intermetallics can be expected to be much lower than the parent metals. This will increase the overall CTE mismatch when compared to a pure Cu condition. To obtain a lower bound of this increase in
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110
108
Fig. 2. Circle-fit plot of FRF data of: (a) pure AZ91 sample, (b) the AZ91-8.1 Cu sample, (c) the AZ91-15.5 Cu sample and (d) the AZ91-20.6 Cu sample.
dislocation density and residual stress at the matrix–particulate interface, the particulate can be considered as a pure Cu condition, as described in the following paragraphs. Based on the works of Dunand and Mortensen [11], the high residual stresses result as an annular plastic zone of radius Cs around a spherical particle of radius r s as follows:
S
Da E DT Cs 5 r s ]]] (1 2 n )sy
D
mum alternating shear stress amplitude, s and ´ are the corresponding stress and strain, respectively, acting on the specimen. Thus it is clear from Eq. (3) that the damping depends directly on the strain amplitude and the volume fraction of the plastic zone, which directly depends on reinforcement volume fraction. Also, it is clear that the interaction of plastic zones is expected to be more when
(2)
where Da is the difference between the CTEs of Mg and Cu, DT is the temperature difference which is around 327 8C, E and n are the matrix elastic modulus and Poisson’s ratio, sy is the matrix yield stress and r s is the particulate radius. Based on mechanical spectroscopic studies of Carreno-Morelli et al., the damping due to the plastic zone is as follows [12]: fzp Gc r s d´ tan f ¯ ]]]] ps 2o
(3)
where fzp is the plastic zone volume fraction, Gc is the shear modulus of the composite sample, so is the maxi-
Fig. 3. Use of the natural frequency and two data points to derive the damping factor.
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110
109
Table 2 Results of theoretical predictions of microstructural characteristics and of experimental damping measurement Cu weight (%)
Interparticle spacing (mm)
Estimated plastic zone radius (mm)
Estimated dislocation density (m 22 )
Exp. damping loss factor hfree
Increase in damping a (%)
0.0 8.1 15.5 20.6
– 13.33 7.36 5.13
– 0.37 0.77 1.07
– 2.12E112 5.76E112 9.53E112
0.0086 0.0141 0.0153 0.0178
– 64 78 107
a
When compared to that of the monolithic sample.
the plastic zone is larger with smaller inter-particulate distance. Table 2 lists the plastic zone radius and the inter-particulate distance for the composite samples based on the model of Nardone and Prewo described as follows [13]:
F G
lt l5 ] Vf
0.5
(4)
where l is the inter-particulate spacing, t, l and Vf are the thickness, length and volume fraction of the reinforcement, respectively. This also suggests that the presence of clusters can also influence the overall damping capacity due to interaction of the plastic zones. Another major source of damping can be expected due to the high dislocation density rth at the particle–matrix interface, which are listed in Table 2. These were computed using the prismatic dislocation-punching model of Arsenault and Shi expressed as follows [14]: B Da DT Vf rth 5 ]]]] bt(1 2Vf )
(5)
where B is a geometric constant (equals 12 for equiaxed particulates), b is the Burgers vector which is around 0.3 nm [15], and t is the smallest dimension of the reinforcement. According to the Granato–Lucke dislocation model the dislocation behaves like an elastic string pinned between both sides due to any hard particulates such as precipitates, reinforcement particulate or antiplane dislocations and under a low strain amplitude (below 10 24 ) type cyclic load it bows, which introduces increased relative atomic movement in a crystalline lattice thus interfering with homogenous deformation of the bulk material [8,16]. In the present experimental set-up the strain magnitude induced in the specimen is of the order of 10 26 and hence the frequencydependent dislocation damping is applicable and is as follows [8]: Q
21 f
a o BLL 4 v 2 ¯ ]]] p 2 Cb 2
(6)
where a o is a numerical factor of order 1, B is the damping constant, v is the operating frequency, L is the effective dislocation loop length which depends on the pinning distance, C is the dislocation line tension (¯0.5 Gb 2 ), G is
the shear modulus, b is Burgers vector and L is the total dislocation density. Thus increased density of dislocation due to presence of Cu and its intermetallics in the AZ91 Mg alloy matrix contributes to increased dislocation-based damping characteristics in the MMC. Experiment results in Table 2 show an increase in damping factor when the particulate weight percentage increases which confirms this hypothesis. Other damping mechanisms such as grain boundary sliding and elasto-thermodynamic damping can be seen to be insignificant in the present experimental study due to room temperature operation conditions, sample dimensions and frequency magnitude [17,18]. Thus, from the above discussions, it is encouraging to note that addition of stiffer metallic phase in the form of particulates in a metallic matrix increases damping reasonably. Presently, further numerical work is in progress to understand the effect of reinforcing a stiffer metallic phase on the overall damping characteristics of a ductile metallic matrix. In addition, similar work is in progress on other composite formulations to further strengthen the feasibility of this approach.
5. Conclusions 1. The free–free beam type flexural resonance method can successfully be used with circle-fit approach to measure the damping characteristics of the Mg–Cu composites. 2. Addition of Cu particulates in a metal matrix enhances energy dissipation due to the various intrinsic damping mechanisms acting in parallel. 3. Experiment results show that damping of AZ91 Mg alloy increases with an increase in Cu weight percentage. This can be explained due to increase in dislocation density and plastic zone radius.
References [1] M. Gupta, M.O. Lai, D. Saravanaranganathan, J. Mater. Sci. 35 (2000) 2155–2161. [2] N. Srikanth, M. Gupta, Mater. Res. Bull. 37 (2002) 1149–1162. [3] ASTM C1259-98: dynamic Young’s modulus, shear modulus, and Poisson’s ratio for advanced ceramics by impulse excitation of
110
[4] [5] [6]
[7]
[8]
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110 vibration, in: Annual Book of ASTM Standards, American Society for Testing and Materials, Philadelphia, 1998, pp. 1–10. N. Srikanth, D. Saravanaranganathan, M. Gupta, Mater. Sci. Technol. 16 (2000) 309–314. D.J. Ewins, Modal Testing: Theory and Practice, Research Studies Press, Wiley, New York, 1984. S.E. Housh, B. Mikucki, A. Stevenson, in: 10th Edition, ASM Metals Handbook, Vol. 2, ASM International, Metals Park, OH, 1990, pp. 455–479. R. Thirumalai, R. Gibson, in: R.B. Bhagat (Ed.), Damping of Multiphase Inorganic Materials, ASM International, Metals Park, OH, 1993, pp. 37–46. R.D. Batist, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Characterization of Materials part II, Materials Science and Technology— A Comprehensive Treatment, Vol. 2b, VCH, New York, 1994, pp. 161–214.
[9] J.E. Bishop, V.K. Kinra, Metall. Mater. Trans. A 26A (1995) 2773–2783. [10] R.B. Bhagat, M.F. Amateau, E.C. Smith, Int. J. Powder Metall. 25 (1986) 311–316. [11] D. Dunand, A. Mortensen, Mater. Sci. Eng. A135 (1991) 179–184. [12] E. Carreno-Morelli, S.E. Urreta, R. Schaller, Acta Mater. 48 (2000) 4725–4733. [13] V.C. Nardone, K.W. Prewo, Scripta Metall. 20 (1986) 43–47. [14] R.J. Arsenault, N. Shi, Mater. Sci. Eng. 81 (1986) 175–181. [15] H.J. Frost, M.F. Ashby, in: Deformation-Mechanism Maps: the Plasticity and Creep of Metals and Ceramics, Pergamon Press, Oxford, 1982, p. 90. [16] A. Granato, K. Lucke, J. Appl. Phys. 27 (1956) 583–593. ˆ Phys. Rev. 71 (1947) 533–546. [17] T.S. Ke, [18] E.J. Lavernia, R.J. Perez, J. Zhang, Metall. Mater. Trans. A 26A (1995) 2803–2818.
L
www.elsevier.com / locate / jallcom
Enhanced damping of a magnesium alloy by addition of copper Narasimalu Srikanth, Calvin He Gaofeng, Manoj Gupta* Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore Received 28 August 2002; accepted 3 October 2002
Abstract A new idea of using a stiffer metallic element, such as copper, to enhance the damping of AZ91 magnesium alloy is successfully attempted. The study focuses on the relationship between the damping capability of the composite with the weight percentage of copper added to the matrix. Results of this study show that addition of about 8.1, 15.5 and 20.6 wt.% of copper increases the overall damping capacity of the AZ91 matrix by 64%, 78% and 107%, respectively. Particular emphasis is placed on rationalizing the increase in damping in terms of the increase in dislocation density and presence of plastic zone at the matrix–particulate interface. 2002 Elsevier Science B.V. All rights reserved. Keywords: Alloys; Composite materials; Mechanical properties
1. Introduction Stiffer materials with high damping property are actively sought for dynamic mechanical systems such as in spacecrafts, semiconductor equipment and robotics. Magnesiumbased formulations are one such category of materials that has the capability to exhibit such properties especially when it is unified with stiffer phase particulates [1]. In related studies, it has been shown that the addition of ceramic particulates to the magnesium matrix assists in improving damping properties of the magnesium matrix [2]. The results of the literature search, however, reveal that no attempt is made to investigate the effect of stiffer metallic phase addition on the damping behavior of magnesium alloys. Accordingly, the primary objective of this investigation was to investigate the energy dissipation of a magnesium alloy containing variable amounts of copper.
2. Materials and processes The hybrid composite samples were prepared using the disintegrated deposition method (DMD) and the matrix used was AZ91 magnesium alloy [2]. The processing
*Corresponding author. Tel.: 165-6874-6358; fax: 165-6779-1459. E-mail address: [email protected] (M. Gupta).
parameters were controlled so as to allow only partial reaction of copper with the metallic melt. Three composite rods with 8.1, 15.5 and 20.6 equivalent of copper in weight percentage were extruded. Scanning electron microscopy and X-ray diffraction studies were conducted to establish the presence of copper and Cu-rich phases. The results of microstructural characterization of the MMC specimens obtained using image analysis and the density measurements are listed in Table 1. Fig. 1 shows a typical SEM micrograph which illustrates the microstructural characteristics of AZ91-8.1 Cu sample. The coefficient of thermal expansion was determined on the extruded composite samples using a thermal–mechanical analyzer and the results are shown in Table 1.
3. Damping measurement method The impact-based ‘free–free’ or ‘suspended’ beam method was performed based on the ASTM C1259-98 standard [3]. Description of the experimental set-up is given in Ref. [4]. The receptance frequency response function (FRF) ‘a (v )’, which is the ratio between displacement response to the applied impact force, was plotted as a Nyquist plot corresponding to the resonance condition [5]. Using least squares technique, a circle was fit and based on a hysterically damped vibrating system the circle diameter can be shown to be inversely dependent on the damping coefficient. Fig. 2 shows typical circle fit plots
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01131-3
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110
107
Table 1 Results of the microstructural characterization Cu weight (%)
Cu volume (%)
Density (g / cm 3 )
Cu particulate size (mm)
Cu particulate aspect ratio
Experimental mean CTE (10 26 / 8C)
0.0 8.1 15.5 20.6
0.0 1.75 3.59 4.99
1.82 2.00 2.11 2.29
– 1.560.6 1.260.4 1.060.2
– 1.560.3 1.560.3 1.460.2
30.648 28.157 27.857 24.942
of the monolithic sample and the samples containing 8.1, 15.5 and 20.6 wt.% of Cu. The exact location and determination of the natural frequency and the corresponding damping factor ‘hfree ’ was calculated using a frequency spacing technique [5]. Fig. 3 shows the typical circle plot from which two points are selected for damping loss factor calculation, denoted as point a and b corresponding to frequencies va and vb , respectively, which are lesser and greater than the natural frequency vn , respectively. Thus, the damping factor hfree can be expressed using the angles shown in Fig. 3, as follows [5]:
v 2a 2 v 2b 1 ]]]]]]. hfree 5 ]]] tan (Dua ) 1 tan (Dub ) v 2r
(1)
4. Results and discussion The suspended beam experimental method was found to be highly repeatable and was nondestructive. The circle-fit approach was found to be efficient in determining the damping factor from the suspended beam’s FRF data. Using this approach, the damping factor of AZ91 magnesium alloy was found to be 0.008660.0005 which can be favorably compared with the damping measurements of Housh et al. which was found to be 0.0079 at low strain amplitude [6].
Fig. 1. SEM micrograph showing the microstructural characteristics of AZ91-8.1 Cu sample.
Uniform distribution of Cu particulates and its intermetallic phases in the metal matrix was seen in all the composite samples. Thus an isotropic material behavior can be expected in all the composite samples, from a global perspective. Close inspection of the Cu particulate at high magnification illustrated good Cu–Mg interfacial bonding in all the three composites investigated in the present study. Table 2 lists the damping factor of the monolithic sample and the three AZ91-Cu samples. Comparison shows that addition of Cu in the AZ91 matrix increases the overall damping capacity and this damping improvement increases with Cu weight percentage. The overall damping capacity of the metal matrix composite is directly related to the damping capacity of each of its constituents. Based on the damping studies of Thirumalai et al. [7] Cu has a lower loss factor of the order of 0.0015 as compared to AZ91 Mg alloy, which has an order of 0.0086, based on the present work. Hence it can be expected that addition of Cu in the AZ91 matrix would result in the decrease in damping capacity of the composite. Thus, the damping improvement observed from the experiment results has to be attributed primarily to the interface between reinforcement and the metallic matrix. In metallic materials the damping capacity arises due to intrinsic dissipation of strain energy due to mechanisms at the crystal level. The most significant role comes from point defect relaxation, microplasticity, dislocation motion, grain boundary sliding, inclusion-matrix friction, magnetoelastic effects, and elastothermodynamic effects [8,9]. Particulate reinforced metal matrix composites have additional mechanisms apart from the regular damping mechanisms in the metallic matrix due to a high residual stress in the matrix and due to high dislocation density at the particulate / matrix interface, which improve their damping capacity [10]. The high residual stresses and the dislocation density are caused due to large difference in the coefficient of thermal expansion between the phases (such as the CTE for Cu is 17 ppm / 8C [2], and for Mg it is 30.6 ppm / 8C, refer to Table 1). In addition, transformation of Cu to Mg–Cu intermetallics can enhance this residual stress and dislocation density since the coefficient of thermal expansion of intermetallics can be expected to be much lower than the parent metals. This will increase the overall CTE mismatch when compared to a pure Cu condition. To obtain a lower bound of this increase in
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110
108
Fig. 2. Circle-fit plot of FRF data of: (a) pure AZ91 sample, (b) the AZ91-8.1 Cu sample, (c) the AZ91-15.5 Cu sample and (d) the AZ91-20.6 Cu sample.
dislocation density and residual stress at the matrix–particulate interface, the particulate can be considered as a pure Cu condition, as described in the following paragraphs. Based on the works of Dunand and Mortensen [11], the high residual stresses result as an annular plastic zone of radius Cs around a spherical particle of radius r s as follows:
S
Da E DT Cs 5 r s ]]] (1 2 n )sy
D
mum alternating shear stress amplitude, s and ´ are the corresponding stress and strain, respectively, acting on the specimen. Thus it is clear from Eq. (3) that the damping depends directly on the strain amplitude and the volume fraction of the plastic zone, which directly depends on reinforcement volume fraction. Also, it is clear that the interaction of plastic zones is expected to be more when
(2)
where Da is the difference between the CTEs of Mg and Cu, DT is the temperature difference which is around 327 8C, E and n are the matrix elastic modulus and Poisson’s ratio, sy is the matrix yield stress and r s is the particulate radius. Based on mechanical spectroscopic studies of Carreno-Morelli et al., the damping due to the plastic zone is as follows [12]: fzp Gc r s d´ tan f ¯ ]]]] ps 2o
(3)
where fzp is the plastic zone volume fraction, Gc is the shear modulus of the composite sample, so is the maxi-
Fig. 3. Use of the natural frequency and two data points to derive the damping factor.
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110
109
Table 2 Results of theoretical predictions of microstructural characteristics and of experimental damping measurement Cu weight (%)
Interparticle spacing (mm)
Estimated plastic zone radius (mm)
Estimated dislocation density (m 22 )
Exp. damping loss factor hfree
Increase in damping a (%)
0.0 8.1 15.5 20.6
– 13.33 7.36 5.13
– 0.37 0.77 1.07
– 2.12E112 5.76E112 9.53E112
0.0086 0.0141 0.0153 0.0178
– 64 78 107
a
When compared to that of the monolithic sample.
the plastic zone is larger with smaller inter-particulate distance. Table 2 lists the plastic zone radius and the inter-particulate distance for the composite samples based on the model of Nardone and Prewo described as follows [13]:
F G
lt l5 ] Vf
0.5
(4)
where l is the inter-particulate spacing, t, l and Vf are the thickness, length and volume fraction of the reinforcement, respectively. This also suggests that the presence of clusters can also influence the overall damping capacity due to interaction of the plastic zones. Another major source of damping can be expected due to the high dislocation density rth at the particle–matrix interface, which are listed in Table 2. These were computed using the prismatic dislocation-punching model of Arsenault and Shi expressed as follows [14]: B Da DT Vf rth 5 ]]]] bt(1 2Vf )
(5)
where B is a geometric constant (equals 12 for equiaxed particulates), b is the Burgers vector which is around 0.3 nm [15], and t is the smallest dimension of the reinforcement. According to the Granato–Lucke dislocation model the dislocation behaves like an elastic string pinned between both sides due to any hard particulates such as precipitates, reinforcement particulate or antiplane dislocations and under a low strain amplitude (below 10 24 ) type cyclic load it bows, which introduces increased relative atomic movement in a crystalline lattice thus interfering with homogenous deformation of the bulk material [8,16]. In the present experimental set-up the strain magnitude induced in the specimen is of the order of 10 26 and hence the frequencydependent dislocation damping is applicable and is as follows [8]: Q
21 f
a o BLL 4 v 2 ¯ ]]] p 2 Cb 2
(6)
where a o is a numerical factor of order 1, B is the damping constant, v is the operating frequency, L is the effective dislocation loop length which depends on the pinning distance, C is the dislocation line tension (¯0.5 Gb 2 ), G is
the shear modulus, b is Burgers vector and L is the total dislocation density. Thus increased density of dislocation due to presence of Cu and its intermetallics in the AZ91 Mg alloy matrix contributes to increased dislocation-based damping characteristics in the MMC. Experiment results in Table 2 show an increase in damping factor when the particulate weight percentage increases which confirms this hypothesis. Other damping mechanisms such as grain boundary sliding and elasto-thermodynamic damping can be seen to be insignificant in the present experimental study due to room temperature operation conditions, sample dimensions and frequency magnitude [17,18]. Thus, from the above discussions, it is encouraging to note that addition of stiffer metallic phase in the form of particulates in a metallic matrix increases damping reasonably. Presently, further numerical work is in progress to understand the effect of reinforcing a stiffer metallic phase on the overall damping characteristics of a ductile metallic matrix. In addition, similar work is in progress on other composite formulations to further strengthen the feasibility of this approach.
5. Conclusions 1. The free–free beam type flexural resonance method can successfully be used with circle-fit approach to measure the damping characteristics of the Mg–Cu composites. 2. Addition of Cu particulates in a metal matrix enhances energy dissipation due to the various intrinsic damping mechanisms acting in parallel. 3. Experiment results show that damping of AZ91 Mg alloy increases with an increase in Cu weight percentage. This can be explained due to increase in dislocation density and plastic zone radius.
References [1] M. Gupta, M.O. Lai, D. Saravanaranganathan, J. Mater. Sci. 35 (2000) 2155–2161. [2] N. Srikanth, M. Gupta, Mater. Res. Bull. 37 (2002) 1149–1162. [3] ASTM C1259-98: dynamic Young’s modulus, shear modulus, and Poisson’s ratio for advanced ceramics by impulse excitation of
110
[4] [5] [6]
[7]
[8]
N. Srikanth et al. / Journal of Alloys and Compounds 352 (2003) 106–110 vibration, in: Annual Book of ASTM Standards, American Society for Testing and Materials, Philadelphia, 1998, pp. 1–10. N. Srikanth, D. Saravanaranganathan, M. Gupta, Mater. Sci. Technol. 16 (2000) 309–314. D.J. Ewins, Modal Testing: Theory and Practice, Research Studies Press, Wiley, New York, 1984. S.E. Housh, B. Mikucki, A. Stevenson, in: 10th Edition, ASM Metals Handbook, Vol. 2, ASM International, Metals Park, OH, 1990, pp. 455–479. R. Thirumalai, R. Gibson, in: R.B. Bhagat (Ed.), Damping of Multiphase Inorganic Materials, ASM International, Metals Park, OH, 1993, pp. 37–46. R.D. Batist, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Characterization of Materials part II, Materials Science and Technology— A Comprehensive Treatment, Vol. 2b, VCH, New York, 1994, pp. 161–214.
[9] J.E. Bishop, V.K. Kinra, Metall. Mater. Trans. A 26A (1995) 2773–2783. [10] R.B. Bhagat, M.F. Amateau, E.C. Smith, Int. J. Powder Metall. 25 (1986) 311–316. [11] D. Dunand, A. Mortensen, Mater. Sci. Eng. A135 (1991) 179–184. [12] E. Carreno-Morelli, S.E. Urreta, R. Schaller, Acta Mater. 48 (2000) 4725–4733. [13] V.C. Nardone, K.W. Prewo, Scripta Metall. 20 (1986) 43–47. [14] R.J. Arsenault, N. Shi, Mater. Sci. Eng. 81 (1986) 175–181. [15] H.J. Frost, M.F. Ashby, in: Deformation-Mechanism Maps: the Plasticity and Creep of Metals and Ceramics, Pergamon Press, Oxford, 1982, p. 90. [16] A. Granato, K. Lucke, J. Appl. Phys. 27 (1956) 583–593. ˆ Phys. Rev. 71 (1947) 533–546. [17] T.S. Ke, [18] E.J. Lavernia, R.J. Perez, J. Zhang, Metall. Mater. Trans. A 26A (1995) 2803–2818.