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Epoxy-copper composites with gradation of filler content
Composites Part B 127 (2017) 36e43
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Epoxy-copper composites with gradation of filler content zef Stabik*, Agnieszka Dybowska Jo Silesian University of Technology, Department of Mechanical Engineering, ul. Konarskiego 18A, 44-100 Gliwice, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 March 2017 Received in revised form 25 May 2017 Accepted 18 June 2017 Available online 20 June 2017
The goal of this work was to study the structure and electrical properties of functional polymeric graded materials with epoxy resin matrix and copper powder as a filler. Gradation of the filler content and in this way gradation of electrical properties was obtained using centrifugal casting technology. Filler particles distribution in the matrix was controlled by changing casting parameters. Rotational velocity influenced particles distribution and electrical resistivity distribution the most significantly. Performed experiments showed that it is possible to control the structure of graded composites and in this way the gradation of electrical properties. Elaborated polymeric graded materials may be applied in many industrial fields where products with low surface electrical resistivity on one surface and high electrical resistivity in the rest of the volume are needed. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Polymer-matrix composites Particle reinforcement Electrical properties Electron microscopy
1. Introduction In many industrial application desirable are materials that possess different properties in the outer layer and in the rest of the volume. Usually coatings and laminates are proposed in these cases. In such solutions two difficult to solve problems arise. First, very good adhesion is needed at the interface between different materials and the second, stresses concentrate at the interfaces between layers. Both problems can be diminished in great extend if composites properties change gradually from the surface into the inner volume. Such materials range to the wide class of Functionally Gradient Materials (FGMs). Because of different meaning of “gradient” in mathematics and in the materials science, the term “Functionally Graded Materials” is used now as more adequate [1,2]. The progress in knowledge about FGMs is giving new inspirations for scientists to prepare advanced materials with specific functions and properties changing without definite interfaces [3e8]. In the case of polymers as matrixes such systems are called Polymeric Graded Materials (PGMs). Till now there are known many methods allowing to produce functionally graded materials such as: powder metallurgy (PM), self-propagating high temperature synthesis (SHS), in situ polymerisation, corona discharge, UV irradiation, gravity and centrifugal casting, physical vapour deposition (PVD), chemical vapour
* Corresponding author. Institute of Theoretical and Applied Mechanics, Silesian University of Technology, Konarskiego 18a Street, 44-100 Gliwice, Poland. E-mail address: [email protected] (J. Stabik). http://dx.doi.org/10.1016/j.compositesb.2017.06.025 1359-8368/© 2017 Elsevier Ltd. All rights reserved.
deposition (CVD), spark plasma sintering (SPS) and other less popular [8e19]. One of the effective methods that could be successfully applied in production of PGMs is the centrifugal casting of liquid polymer filled with solid particles. During this process, owing to application of the centrifugal force, spatial gradual distribution of filler particles in the matrix and gradation of properties is possible to achieve. It is not quite modern technology, but very effective and possible to realize in industry without high investments. There are modern methods that enable to control properties more precisely but it is very difficult, in many cases even impossible, to obtain axisymmetric products with radial gradation of properties. These methods are also more time consuming. Very sophisticated and expensive equipment, not available in the market, is needed to manufacture such products. The basic problem which appears in centrifugal casting technology is to control filler particles motion to obtain their defined radial distribution. Finding manners to control gradation of particles distribution is necessary to influence many properties such as hardness, coefficient of friction, wear resistance, thermal and electrical properties etc. [20e23]. In the case of centrifugal casting, filler particles are arranged gradually along radial direction as a result of forces action on solid particles and liquid matrix but is also influenced by different densities of components, differences in size and shape of particles and also by viscosity of polymeric matrix [20,24e27]. The main purpose of this study was to find relations between centrifugal casting conditions and structure and electrical properties of graded epoxy matrix composites filled with electro
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37
conducting solid particles. To determine the most important factors influencing particles arrangement in centrifugal field of forces a short theoretical analysis of particle motion in the fluid is needed.
ReP ¼
2. Filler particle motion during centrifugal casting
and DP e diameter of the particle, m e dynamic viscosity of the fluid. Together with eq. (3) it gives Stokes' equation for drag force
Stokes' theory [28e31] describes the movement of a single spherical particle in Newtonian liquid under the influence of gravitational, centrifugal, buoyant, and viscous forces. When particle of mass ‘m’ is moving in fluid under the action of external force ‘FE’ two additional forces arise, buoyant force ‘FB’ and drag force ‘FD’. Particle velocity ‘v’ is determined according to forces balance:
m
dv ¼ FE FB FD dt
(1)
where dv ¼ aE is acceleration due to FE action. dt According to Archimedes' law, buoyant force is equal:
rF rP
FB ¼ m,aE ,
(2)
where rF and rP are fluid and particle densities, respectively. The densities difference is one of factors which can be applied to influence filler gradation during centrifugal casting. The drag force is equal [30]:
A FD ¼ CD ,v2 ,rF , P 2
(3)
where CD is drag coefficient and AP is area of particle's projection on plane perpendicular to flow direction. By substituting eqs. (2) and (3) into eq. (1) and dividing by ‘m’, we have:
dv r C ,v2 ,AP ,rF ¼ aE , 1 F D dt rP 2m
(4)
In centrifugal casting, when the axis of rotation is horizontal, summary displacement due to gravity action may be neglected and the only external force effectively acting is centrifugal force. Thus acceleration due to the external force equals aE ¼ r,u2 (r - radial position of the particle, u e angular velocity) and eq. (4) may be rewritten
dv r C ,v2 ,AP ,rF ¼ r,u2 , 1 F D dt rP 2m
(6)
Analytical solutions for equilibrium velocity are possible only with many simplifying assumption [30,31]. The main problem is to evaluate the drag coefficient value,C. D, which depends on many factors such as Reynolds' number of the particle, ReP, particle size and shape and other. Known Stokes' law applies to individual spherical particle moving in Newtonian fluid with Reynolds number less than 1,0 [30]:
24 CD ¼ ReP where:
(8)
m
FD ¼ 3p,m,v,DP
(9)
For the centrifugal casting case equilibrium velocity is equal
ve ¼
u2 ,r,ðrP rF Þ,DP 2 18m
(10)
Equilibrium velocity is mainly influenced by rotational velocity, particle diameter, densities difference, fluid viscosity and radial position of the particle. For given filler particles type and geometry and for given mould dimensions, rotational velocity and fluid viscosity are the main parameters which can be applied to affect filler particle motion during rotational casting. These two parameters were used as controlling factors in presented experimental programme. During PGMs' formation many additional factors have to be taken into account such as particles interactions, particle size and shape distributions, viscosity changes due to polymerization process, rheological properties of Non-Newtonian matrix, convectional and counter flows and many other [32]. Numerical simulations were performed to search influence of mentioned factors on motion of particles in sedimentation and centrifugal processes [33,34]. In recent years numerical procedures have also been proposed to describe particle motion in polymerizing fluids under centrifugal forces action [32,35]. But even the most developed numerical procedures are also based on simplifying assumptions, mainly concerning rheological properties of polymer and size and shape distributions of filler particles. Taking into account mentioned limitations of theoretical and numerical solutions and in order to prepare experimental data for comparative purposes and theoretical studies, in the present work an experimental programme was proposed to control radial particles distribution by changing centrifugal casting parameters of epoxy-copper composites. 3. Experimental part 3.1. Materials
(5)
The drag force increases together with increasing velocity and in a short time constant velocity is reached. The equilibrium velocity, ve, may be calculated using eq. (5)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r,ðrP rF Þ,m Ve ¼ u, CD ,AP ,rP ,rF
v,DP ,rF
(7)
Epoxy resin ‘Epidian 6’ cured with 12 pph by weight of triethylenetetramine ‘Z1’ (‘‘Organika-Sarzyna’’ Chemical Plant S.A. in Nowa Sarzyna e Poland) was used as composite matrix. Relatively low viscosity of this system enabled filling without diluent. Powdered copper ‘A-53SS’ (Chemical Enterprise STANCHEM sp.j. Poland) was added as filler. Cooper particles were chosen because of high electrical conductivity and almost spherical shape. Main characteristics of materials, given by suppliers, are presented in Table 1. Fig. 1 presents microscopic image of cooper particles. Applied filler is characterized by narrow particles size distribution (Fig. 2). Particle size analysis was carried out using the MASTERSIZER 2000 (Malvern Instruments Ltd.). 3.2. Procedure and specimens preparation Rotational velocity was changed to influence centrifugal force. The time elapsing between curing agent addition and mixture pouring into the mould, in the following text called ‘holding time’, was applied to effect mixture viscosity. Because the goal of the research was to elaborate functional materials with electrical
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J. Stabik, A. Dybowska / Composites Part B 127 (2017) 36e43 Table 1 Main properties of epoxy resin, hardener and cooper powder. Epoxy resin ‘Epidian 6’ Density (20 C) [g/cm3] Viscosity (25 C) [mPa$s] Epoxy number [mol/100 gg] Boiling point [ C]
1,17 10000÷15000 0,51÷0,54 >200
Triethylenetetraamine curing agent ‘Z1’ Form Density (25 C) [g/cm3] Viscosity (25 C) [mPa$s] Amine value [mg KOH/g]
colourless liquid 0,98 20÷30 min. 1100
Cooper powder ‘A-53SS’ Cu content [% by weight] Density (25 C) [g/cm3] Surface resistivity (25 C) [U] Electric conductivity [s/m]
99.58 8.933 1.7$108 59.6$106 Fig. 2. Particle size distribution of A-53SS cooper powder.
Eight experimental systems were prepared. Rotational velocity and holding time were changed according to scheme presented in Table 2. Two samples were prepared for every system, one to determine electrical resistivity gradation and the other to determine filler distribution in radial direction. The holding time was chosen in a range enabling initial viscosity variation but allowing also easy mixture casting. 3.3. Determination of particles distribution in radial direction
Fig. 1. SEM image of copper powder A-53SS particles.
properties gradation, copper particles were applied to modify electrical properties. The structure and gradation of electrical resistivity of produced PGMs were determined. Compounds with constant initial copper powder content, equal 10% vol., were first prepared. Homogenous compounds with this initial filler content were next converted into graded materials in centrifugal casting process. Specimens were prepared and cured at temperature 20 C in the following steps. First, copper particles were 15 min thoroughly mixed with epoxy resin at 300 rpm using high speed rotational mixer. Next, curing agent was added followed by 5 min intensive mixing of the composition with the same velocity. After defined holding time the mixture was poured into the mould and subjected to rotation around horizontal axis in laboratory stand of our own construction [16,36]. During holding time the compound was slowly mixed (30 rpm) to avoid filler sedimentation. Rotational velocities greater than needed to overcome gravitational forces were chosen. For 25 mm minimum inner radius of specimen this velocity was 189 rpm. The limits of rotational velocity (211 rpm and 422 rpm) were determined in preliminary tests taking into account equipment possibilities and obtained results. Rotation was maintained for 2 h to preliminary cure epoxy resin. Afterwards additional amount of epoxy resin mixed with curing agent but without copper powder was poured into the mould and cured in centrifugal casting process. Additional inner layer was applied to enable future maintenance in turning lathe. Samples with length L ¼ 158 mm and outer diameter D ¼ 77 mm were prepared. After demoulding specimens were post-cured in 24 h at 20 C.
Before structure observations, specimens were cut perpendicularly to their axis and polished. More details concerning samples preparation are given in Ref. [36]. Five rings were prepared out of every specimen. Exemplary photographs of prepared cross-sections are shown in Fig. 3. Particles distribution was observed using light microscope LEICA MEF4A. Subsequent images with the same magnification were combined together to form panoramic image (Fig. 4). Panoramic images were analysed using computer software system MultiScan Base 13.01. Particles equivalent diameter was defined as diameter of the ball with the same cross-section area as measured cross-section area of a given particle. Particles content was defined as summary area taken by cross section of particles ski and others divided by total area of analysed region. J. Chrapon [37] proved that such simplified method of filler content determination gives values very near to the volumetric content, especially in the case of spherical particles. Figs. 1 and 4 prove that applied cooper particles were almost spherical. 3.4. Measurement of electrical surface resistivity First, surface resistance, Rs, was determined. Rs was defined as the ratio of applied DC voltage,U, to the measured current, Is, Table 2 Parameters of centrifugal casting. Specimen code
Holding time [min]
Rotational velocity [rpm]
1 2 3 4 5 6 7 8
0 4 8 12 16 20 0 0
300 300 300 300 300 300 211 422
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Fig. 3. Cross-sections of specimens cast without holding time and at different rotational velocities [a) 211 rpm, b) 300 rpm, c) 422 rpm ] and with constant rotational velocity (300 rpm) and different holding time [d) 4 min, e) 12 min, f) 20 min].
Fig. 4. Examples of panoramic images of the outer layers of specimens cast at different rotational velocities: a) 211 rpm, b) 300 rpm, c) 422 rpm.
flowing between two strip copper electrodes. The electrodes were 20 mm wide and 20 mm thick. The gap between the electrodes was 7 mm. To secure good electrical contact between electrodes and the surface of the sample an additional band clamps were used. Measurements were performed every 30 mm along the sample. The scheme of measuring electrodes arrangement on the sample's surface is presented in Fig. 5. Surface resistance measurements
Fig. 5. Test piece and arrangement of electrodes for surface resistivity measurements.
were performed according to IEC 60093 and PN-88/E-04405 standards using MIC-2500 m (Sonel S.A - Poland) [38,39]. After surface resistance measurement outer layer of the specimen was removed by grinding and polishing. Then, surface resistance measurement was repeated. This procedure was continued until the measured value of resistance was higher than the maximum of the meter range. Removed layers had thicknesses in the range 0,2e0,4 mm depending on grinding process possibilities. For each layer five
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surface resistance measurements were made and mean values were calculated. Surface resistivity, rS , were calculated values according to the following formula [39]:
rS ¼
RS ,B g
(11)
where B is the effective length of measuring electrode, g e width of the gap between electrodes. 4. Results and discussion 4.1. Copper particles distribution Because of large number of numeric and graphic results, only observed regularities and relationships are presented here. Exemplary macroscopic photographs of samples cross-sections (Fig. 3) show that centrifugal casting is an effective way to produce functional graded materials. Analysis of these photographs confirms that it is possible to influence particle content gradation in radial direction by changing rotation velocity and holding time. Images show that more effective factor controlling the concentration gradation is rotational velocity. It is in accordance with theoretical considerations summarized in eq. (10). Second order relationship between particle radial velocity and rotational velocity is predicted by Stokes' theory whereas viscosity of the fluid affects radial velocity inversely proportionally. It was possible to control viscosity of epoxy matrix only in qualitative manner by changing holding time. Mixing resin with hardener initialize curing process. Viscosity changes non-linearly with the curing time. Two simultaneous processes take place: crosslinking of macromolecules leading to viscosity increase and heat generation due to exothermic reaction and thus temperature increase leading to viscosity decrease. In the case of graded composites additional factor affecting viscosity in curing process is variability of filler content. The higher is the filler content the lower is the exothermic effect and the higher is thermal conductivity [40]. Additionally, interactions between filler and matrix have impact on thermal properties and curing process [41]. Resultant ‘viscosity-curing time’ dependence is very complex and hardly to predict [42,43]. Qualitatively it was observed that viscosity increased with the holding time. To describe quantitatively particles distribution in radial direction, panoramic photographs were analysed with computer software help. Two different particle distribution characteristics in dependence on the distance from the outer surface were prepared: average equivalent diameter of the particles, and particles content. Radial distributions of average particles diameter for different rotational velocities are shown in Figs. 6e8. In all cases the biggest particles were concentrated near outer surface of the samples. It is in accordance with Stokes' theory because bigger particles reach higher radial velocities. It is also generally observed tendency that sedimentation process leads to particles segregation. This is widely applied in particle size measurement procedures [44]. The higher was rotational velocity the steeper and narrower profile was achieved. The higher rotational velocity and thus higher centrifugal forces caused higher velocities of radial movement of solid particles. Sedimentation process took place in shorter time and closer packing of particles near the outer surface of samples was achieved. Many additional factors effecting cooper particles movement in epoxy matrix, mentioned in the earlier theoretical considerations, caused that observed distributions are not very smooth. Initial solid particles distribution in the fluid, interactions and collisions of particles during flow, Brownian movement of the fluid, differences in viscosity due to non-uniform curing are the main factors and
Fig. 6. Average value of particle diameter depending on distance from the surface e specimen cast at 211 rpm.
Fig. 7. Average value of particle diameter depending on distance from the surface e specimen cast at 300 rpm.
Fig. 8. Average value of particle diameter depending on distance from the surface e specimen cast at 422 rpm.
processes of random character influencing final particles distribution in ready composite. Apart from this the shape of distribution of mean particle diameter is in general in accordance with Stokes' theory predictions. More important for presented research is filler concentration
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profile in the composite (Figs. 9e11) because it determines electrical properties. Concentration distributions are more regular and smooth. Concentration gradations are also in accordance with Stokes' theory predictions. Solid lines presented in Figs. 9e11 were determined using least squares method. Exponential relationships in the form y ¼ A þ B,expðC,xÞ were applied to fit the data. Exponential models were accepted taking into account solid particles distributions predicted by theoretical considerations and observed in experimental researches [45,46]. The obtained coefficient of determination (adjusted R-squared) in the range 0,92e0,77 indicates a good fit of mathematical models to experimental data. In the statistics point of view, proposed mathematical model explains well the variability of the analyzed factor. Results presented in Fig. 11 have to be shortly explained. Probably the highest rotational velocity caused that big particles in very short time moved to the outer layer of the composite. Small particles were blocked and were not able to penetrate into this layer. Deeper layers where particles with different diameters were packed exhibited higher volume content of the filler. It is well known that particles with wide diameter distribution can be packed closer than with the narrow size distribution.
41
parts with low electrical resistivity on the outer surface and insulating properties in the rest of the volume. This kind of products are needed for many applications, especially in explosive atmospheres for example in mining and chemical industry. Because of this, apart from the structure, electrical properties were searched. Cured, unfilled epoxy resins exhibit electrical surface resistivity about 0.8e12 $1016 U [47]. Addition of copper particles with very high electrical conductivity to epoxy matrix caused in all cases essential decrease of surface resistivity on the outer surface of the samples. Observed changes of electrical resistivity for other electroconductive fillers, eg. carbon particles, are not so pronounced [48]. Due to the procedure described in 3.4. Dependences of surface resistivity on radial distance from the outer surface were elaborated. Fig. 12 and Fig. 13 show the influence of rotational velocity on electrical resistivity. Achieved gradation of electrical properties reflected gradation of cooper particles concentration. General and expected tendency was noticed that the higher was copper particles concentration the lower was electrical resistivity. There was no direct proportionality between these two characteristics because surface resistance is not proportional to the filler content [49,50].
4.2. Electrical resistivity In the practical point of view prepared PGMs were planned for
Fig. 11. Relation between particles content and distance from the surface e specimen cast at 422 rpm.
Fig. 9. Relation between particles content and distance from the surface e specimen cast at 211 rpm.
Fig. 10. Relation between particles content and distance from the surface e specimen cast at 300 rpm.
Fig. 12. Relation between surface resistivity and distance from the surface for different rotational velocities.
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Fig. 13. Dependence of surface resistivity on rotational velocity.
Usually above defined concentration significant decrease of resistivity is observed. The minimum content of the filler giving pronounced transition from high to low electrical resistivity is called ‘percolation threshold’ [50,51]. It depends on many factors like filler shape and size distribution, structure and filler-matrix interactions. Results show that in outer layers percolation threshold was exceeded in all cases. Observed influence of rotational velocity on electrical resistivity was alike as its influence on particle concentration. The same type of relationships were observed. The best fitting of experimental models to measured values of resistivity data were achieved when exponential models were applied (Figs. 12 and 13). The models presented together with the graphs may be applied in the practice to predict surface
resistivity of these type of PGMs in future applications. For other PGMs systems presented methodology may be applied. If only surface properties are essential the procedure may be simplified by excluding from the procedure the analysis of samples structure. Relationships between surface electrical resistivity gradation and the time elapsing between compound preparation and pouring into the mould (holding time) are presented in Fig. 14. Differences in surface resistivity due to the changes of holding time are less pronounced. It is in accordance with results achieved for particles distribution research. Also results relating holding time and electrical resistivity may be described very well by using exponential experimental models. In practical point of view it is very important that electrical resistivity values on the outer surface were small enough to avoid electrical charge accumulation and surface static electrification. At the same time in the deeper layers surface electrical resistivity was of the same range as observed for pure epoxy resin and typical for polymeric electrical insulators. In accordance with the experimentally confirmed practice [52,53] and with requirements of the EN 13463-1 standard [54], the electrostatic charge accumulation is eliminated when the surface resistivity is lower or equal to 109 U and is significantly reduced when the surface resistivity is lower than 1011 U. All of the elaborated PGMs may be classified as electrostatic safe. Many of searched composites exhibited surface resistivity lower than 106 U. 5. Conclusions The centrifugal casting method enable to manufacture polymeric epoxy-cooper composite materials characterized by radial gradation of particles content and in this way with radial gradation of electrical resistivity. These materials may be classified as PGMs because they can be designed and then manufactured with functionally changing properties. It is possible to affect particle concentration and electrical resistivity gradation by changing centrifugal casting parameters. More pronounced influence on both gradations have rotational velocity than time elapsing between compound preparation and its pouring into the mould. Achieved results are in accordance with theoretical considerations based on Stokes' theory. Elaborated PGMs exhibit electrical resistivity allowing to avoid static electricity danger. Acknowledgments This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References
Fig. 14. Dependence of surface resistivity on holding time for specimens centrifuged at 300 rpm.
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Epoxy-copper composites with gradation of filler content zef Stabik*, Agnieszka Dybowska Jo Silesian University of Technology, Department of Mechanical Engineering, ul. Konarskiego 18A, 44-100 Gliwice, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 March 2017 Received in revised form 25 May 2017 Accepted 18 June 2017 Available online 20 June 2017
The goal of this work was to study the structure and electrical properties of functional polymeric graded materials with epoxy resin matrix and copper powder as a filler. Gradation of the filler content and in this way gradation of electrical properties was obtained using centrifugal casting technology. Filler particles distribution in the matrix was controlled by changing casting parameters. Rotational velocity influenced particles distribution and electrical resistivity distribution the most significantly. Performed experiments showed that it is possible to control the structure of graded composites and in this way the gradation of electrical properties. Elaborated polymeric graded materials may be applied in many industrial fields where products with low surface electrical resistivity on one surface and high electrical resistivity in the rest of the volume are needed. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Polymer-matrix composites Particle reinforcement Electrical properties Electron microscopy
1. Introduction In many industrial application desirable are materials that possess different properties in the outer layer and in the rest of the volume. Usually coatings and laminates are proposed in these cases. In such solutions two difficult to solve problems arise. First, very good adhesion is needed at the interface between different materials and the second, stresses concentrate at the interfaces between layers. Both problems can be diminished in great extend if composites properties change gradually from the surface into the inner volume. Such materials range to the wide class of Functionally Gradient Materials (FGMs). Because of different meaning of “gradient” in mathematics and in the materials science, the term “Functionally Graded Materials” is used now as more adequate [1,2]. The progress in knowledge about FGMs is giving new inspirations for scientists to prepare advanced materials with specific functions and properties changing without definite interfaces [3e8]. In the case of polymers as matrixes such systems are called Polymeric Graded Materials (PGMs). Till now there are known many methods allowing to produce functionally graded materials such as: powder metallurgy (PM), self-propagating high temperature synthesis (SHS), in situ polymerisation, corona discharge, UV irradiation, gravity and centrifugal casting, physical vapour deposition (PVD), chemical vapour
* Corresponding author. Institute of Theoretical and Applied Mechanics, Silesian University of Technology, Konarskiego 18a Street, 44-100 Gliwice, Poland. E-mail address: [email protected] (J. Stabik). http://dx.doi.org/10.1016/j.compositesb.2017.06.025 1359-8368/© 2017 Elsevier Ltd. All rights reserved.
deposition (CVD), spark plasma sintering (SPS) and other less popular [8e19]. One of the effective methods that could be successfully applied in production of PGMs is the centrifugal casting of liquid polymer filled with solid particles. During this process, owing to application of the centrifugal force, spatial gradual distribution of filler particles in the matrix and gradation of properties is possible to achieve. It is not quite modern technology, but very effective and possible to realize in industry without high investments. There are modern methods that enable to control properties more precisely but it is very difficult, in many cases even impossible, to obtain axisymmetric products with radial gradation of properties. These methods are also more time consuming. Very sophisticated and expensive equipment, not available in the market, is needed to manufacture such products. The basic problem which appears in centrifugal casting technology is to control filler particles motion to obtain their defined radial distribution. Finding manners to control gradation of particles distribution is necessary to influence many properties such as hardness, coefficient of friction, wear resistance, thermal and electrical properties etc. [20e23]. In the case of centrifugal casting, filler particles are arranged gradually along radial direction as a result of forces action on solid particles and liquid matrix but is also influenced by different densities of components, differences in size and shape of particles and also by viscosity of polymeric matrix [20,24e27]. The main purpose of this study was to find relations between centrifugal casting conditions and structure and electrical properties of graded epoxy matrix composites filled with electro
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conducting solid particles. To determine the most important factors influencing particles arrangement in centrifugal field of forces a short theoretical analysis of particle motion in the fluid is needed.
ReP ¼
2. Filler particle motion during centrifugal casting
and DP e diameter of the particle, m e dynamic viscosity of the fluid. Together with eq. (3) it gives Stokes' equation for drag force
Stokes' theory [28e31] describes the movement of a single spherical particle in Newtonian liquid under the influence of gravitational, centrifugal, buoyant, and viscous forces. When particle of mass ‘m’ is moving in fluid under the action of external force ‘FE’ two additional forces arise, buoyant force ‘FB’ and drag force ‘FD’. Particle velocity ‘v’ is determined according to forces balance:
m
dv ¼ FE FB FD dt
(1)
where dv ¼ aE is acceleration due to FE action. dt According to Archimedes' law, buoyant force is equal:
rF rP
FB ¼ m,aE ,
(2)
where rF and rP are fluid and particle densities, respectively. The densities difference is one of factors which can be applied to influence filler gradation during centrifugal casting. The drag force is equal [30]:
A FD ¼ CD ,v2 ,rF , P 2
(3)
where CD is drag coefficient and AP is area of particle's projection on plane perpendicular to flow direction. By substituting eqs. (2) and (3) into eq. (1) and dividing by ‘m’, we have:
dv r C ,v2 ,AP ,rF ¼ aE , 1 F D dt rP 2m
(4)
In centrifugal casting, when the axis of rotation is horizontal, summary displacement due to gravity action may be neglected and the only external force effectively acting is centrifugal force. Thus acceleration due to the external force equals aE ¼ r,u2 (r - radial position of the particle, u e angular velocity) and eq. (4) may be rewritten
dv r C ,v2 ,AP ,rF ¼ r,u2 , 1 F D dt rP 2m
(6)
Analytical solutions for equilibrium velocity are possible only with many simplifying assumption [30,31]. The main problem is to evaluate the drag coefficient value,C. D, which depends on many factors such as Reynolds' number of the particle, ReP, particle size and shape and other. Known Stokes' law applies to individual spherical particle moving in Newtonian fluid with Reynolds number less than 1,0 [30]:
24 CD ¼ ReP where:
(8)
m
FD ¼ 3p,m,v,DP
(9)
For the centrifugal casting case equilibrium velocity is equal
ve ¼
u2 ,r,ðrP rF Þ,DP 2 18m
(10)
Equilibrium velocity is mainly influenced by rotational velocity, particle diameter, densities difference, fluid viscosity and radial position of the particle. For given filler particles type and geometry and for given mould dimensions, rotational velocity and fluid viscosity are the main parameters which can be applied to affect filler particle motion during rotational casting. These two parameters were used as controlling factors in presented experimental programme. During PGMs' formation many additional factors have to be taken into account such as particles interactions, particle size and shape distributions, viscosity changes due to polymerization process, rheological properties of Non-Newtonian matrix, convectional and counter flows and many other [32]. Numerical simulations were performed to search influence of mentioned factors on motion of particles in sedimentation and centrifugal processes [33,34]. In recent years numerical procedures have also been proposed to describe particle motion in polymerizing fluids under centrifugal forces action [32,35]. But even the most developed numerical procedures are also based on simplifying assumptions, mainly concerning rheological properties of polymer and size and shape distributions of filler particles. Taking into account mentioned limitations of theoretical and numerical solutions and in order to prepare experimental data for comparative purposes and theoretical studies, in the present work an experimental programme was proposed to control radial particles distribution by changing centrifugal casting parameters of epoxy-copper composites. 3. Experimental part 3.1. Materials
(5)
The drag force increases together with increasing velocity and in a short time constant velocity is reached. The equilibrium velocity, ve, may be calculated using eq. (5)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r,ðrP rF Þ,m Ve ¼ u, CD ,AP ,rP ,rF
v,DP ,rF
(7)
Epoxy resin ‘Epidian 6’ cured with 12 pph by weight of triethylenetetramine ‘Z1’ (‘‘Organika-Sarzyna’’ Chemical Plant S.A. in Nowa Sarzyna e Poland) was used as composite matrix. Relatively low viscosity of this system enabled filling without diluent. Powdered copper ‘A-53SS’ (Chemical Enterprise STANCHEM sp.j. Poland) was added as filler. Cooper particles were chosen because of high electrical conductivity and almost spherical shape. Main characteristics of materials, given by suppliers, are presented in Table 1. Fig. 1 presents microscopic image of cooper particles. Applied filler is characterized by narrow particles size distribution (Fig. 2). Particle size analysis was carried out using the MASTERSIZER 2000 (Malvern Instruments Ltd.). 3.2. Procedure and specimens preparation Rotational velocity was changed to influence centrifugal force. The time elapsing between curing agent addition and mixture pouring into the mould, in the following text called ‘holding time’, was applied to effect mixture viscosity. Because the goal of the research was to elaborate functional materials with electrical
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J. Stabik, A. Dybowska / Composites Part B 127 (2017) 36e43 Table 1 Main properties of epoxy resin, hardener and cooper powder. Epoxy resin ‘Epidian 6’ Density (20 C) [g/cm3] Viscosity (25 C) [mPa$s] Epoxy number [mol/100 gg] Boiling point [ C]
1,17 10000÷15000 0,51÷0,54 >200
Triethylenetetraamine curing agent ‘Z1’ Form Density (25 C) [g/cm3] Viscosity (25 C) [mPa$s] Amine value [mg KOH/g]
colourless liquid 0,98 20÷30 min. 1100
Cooper powder ‘A-53SS’ Cu content [% by weight] Density (25 C) [g/cm3] Surface resistivity (25 C) [U] Electric conductivity [s/m]
99.58 8.933 1.7$108 59.6$106 Fig. 2. Particle size distribution of A-53SS cooper powder.
Eight experimental systems were prepared. Rotational velocity and holding time were changed according to scheme presented in Table 2. Two samples were prepared for every system, one to determine electrical resistivity gradation and the other to determine filler distribution in radial direction. The holding time was chosen in a range enabling initial viscosity variation but allowing also easy mixture casting. 3.3. Determination of particles distribution in radial direction
Fig. 1. SEM image of copper powder A-53SS particles.
properties gradation, copper particles were applied to modify electrical properties. The structure and gradation of electrical resistivity of produced PGMs were determined. Compounds with constant initial copper powder content, equal 10% vol., were first prepared. Homogenous compounds with this initial filler content were next converted into graded materials in centrifugal casting process. Specimens were prepared and cured at temperature 20 C in the following steps. First, copper particles were 15 min thoroughly mixed with epoxy resin at 300 rpm using high speed rotational mixer. Next, curing agent was added followed by 5 min intensive mixing of the composition with the same velocity. After defined holding time the mixture was poured into the mould and subjected to rotation around horizontal axis in laboratory stand of our own construction [16,36]. During holding time the compound was slowly mixed (30 rpm) to avoid filler sedimentation. Rotational velocities greater than needed to overcome gravitational forces were chosen. For 25 mm minimum inner radius of specimen this velocity was 189 rpm. The limits of rotational velocity (211 rpm and 422 rpm) were determined in preliminary tests taking into account equipment possibilities and obtained results. Rotation was maintained for 2 h to preliminary cure epoxy resin. Afterwards additional amount of epoxy resin mixed with curing agent but without copper powder was poured into the mould and cured in centrifugal casting process. Additional inner layer was applied to enable future maintenance in turning lathe. Samples with length L ¼ 158 mm and outer diameter D ¼ 77 mm were prepared. After demoulding specimens were post-cured in 24 h at 20 C.
Before structure observations, specimens were cut perpendicularly to their axis and polished. More details concerning samples preparation are given in Ref. [36]. Five rings were prepared out of every specimen. Exemplary photographs of prepared cross-sections are shown in Fig. 3. Particles distribution was observed using light microscope LEICA MEF4A. Subsequent images with the same magnification were combined together to form panoramic image (Fig. 4). Panoramic images were analysed using computer software system MultiScan Base 13.01. Particles equivalent diameter was defined as diameter of the ball with the same cross-section area as measured cross-section area of a given particle. Particles content was defined as summary area taken by cross section of particles ski and others divided by total area of analysed region. J. Chrapon [37] proved that such simplified method of filler content determination gives values very near to the volumetric content, especially in the case of spherical particles. Figs. 1 and 4 prove that applied cooper particles were almost spherical. 3.4. Measurement of electrical surface resistivity First, surface resistance, Rs, was determined. Rs was defined as the ratio of applied DC voltage,U, to the measured current, Is, Table 2 Parameters of centrifugal casting. Specimen code
Holding time [min]
Rotational velocity [rpm]
1 2 3 4 5 6 7 8
0 4 8 12 16 20 0 0
300 300 300 300 300 300 211 422
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Fig. 3. Cross-sections of specimens cast without holding time and at different rotational velocities [a) 211 rpm, b) 300 rpm, c) 422 rpm ] and with constant rotational velocity (300 rpm) and different holding time [d) 4 min, e) 12 min, f) 20 min].
Fig. 4. Examples of panoramic images of the outer layers of specimens cast at different rotational velocities: a) 211 rpm, b) 300 rpm, c) 422 rpm.
flowing between two strip copper electrodes. The electrodes were 20 mm wide and 20 mm thick. The gap between the electrodes was 7 mm. To secure good electrical contact between electrodes and the surface of the sample an additional band clamps were used. Measurements were performed every 30 mm along the sample. The scheme of measuring electrodes arrangement on the sample's surface is presented in Fig. 5. Surface resistance measurements
Fig. 5. Test piece and arrangement of electrodes for surface resistivity measurements.
were performed according to IEC 60093 and PN-88/E-04405 standards using MIC-2500 m (Sonel S.A - Poland) [38,39]. After surface resistance measurement outer layer of the specimen was removed by grinding and polishing. Then, surface resistance measurement was repeated. This procedure was continued until the measured value of resistance was higher than the maximum of the meter range. Removed layers had thicknesses in the range 0,2e0,4 mm depending on grinding process possibilities. For each layer five
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surface resistance measurements were made and mean values were calculated. Surface resistivity, rS , were calculated values according to the following formula [39]:
rS ¼
RS ,B g
(11)
where B is the effective length of measuring electrode, g e width of the gap between electrodes. 4. Results and discussion 4.1. Copper particles distribution Because of large number of numeric and graphic results, only observed regularities and relationships are presented here. Exemplary macroscopic photographs of samples cross-sections (Fig. 3) show that centrifugal casting is an effective way to produce functional graded materials. Analysis of these photographs confirms that it is possible to influence particle content gradation in radial direction by changing rotation velocity and holding time. Images show that more effective factor controlling the concentration gradation is rotational velocity. It is in accordance with theoretical considerations summarized in eq. (10). Second order relationship between particle radial velocity and rotational velocity is predicted by Stokes' theory whereas viscosity of the fluid affects radial velocity inversely proportionally. It was possible to control viscosity of epoxy matrix only in qualitative manner by changing holding time. Mixing resin with hardener initialize curing process. Viscosity changes non-linearly with the curing time. Two simultaneous processes take place: crosslinking of macromolecules leading to viscosity increase and heat generation due to exothermic reaction and thus temperature increase leading to viscosity decrease. In the case of graded composites additional factor affecting viscosity in curing process is variability of filler content. The higher is the filler content the lower is the exothermic effect and the higher is thermal conductivity [40]. Additionally, interactions between filler and matrix have impact on thermal properties and curing process [41]. Resultant ‘viscosity-curing time’ dependence is very complex and hardly to predict [42,43]. Qualitatively it was observed that viscosity increased with the holding time. To describe quantitatively particles distribution in radial direction, panoramic photographs were analysed with computer software help. Two different particle distribution characteristics in dependence on the distance from the outer surface were prepared: average equivalent diameter of the particles, and particles content. Radial distributions of average particles diameter for different rotational velocities are shown in Figs. 6e8. In all cases the biggest particles were concentrated near outer surface of the samples. It is in accordance with Stokes' theory because bigger particles reach higher radial velocities. It is also generally observed tendency that sedimentation process leads to particles segregation. This is widely applied in particle size measurement procedures [44]. The higher was rotational velocity the steeper and narrower profile was achieved. The higher rotational velocity and thus higher centrifugal forces caused higher velocities of radial movement of solid particles. Sedimentation process took place in shorter time and closer packing of particles near the outer surface of samples was achieved. Many additional factors effecting cooper particles movement in epoxy matrix, mentioned in the earlier theoretical considerations, caused that observed distributions are not very smooth. Initial solid particles distribution in the fluid, interactions and collisions of particles during flow, Brownian movement of the fluid, differences in viscosity due to non-uniform curing are the main factors and
Fig. 6. Average value of particle diameter depending on distance from the surface e specimen cast at 211 rpm.
Fig. 7. Average value of particle diameter depending on distance from the surface e specimen cast at 300 rpm.
Fig. 8. Average value of particle diameter depending on distance from the surface e specimen cast at 422 rpm.
processes of random character influencing final particles distribution in ready composite. Apart from this the shape of distribution of mean particle diameter is in general in accordance with Stokes' theory predictions. More important for presented research is filler concentration
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profile in the composite (Figs. 9e11) because it determines electrical properties. Concentration distributions are more regular and smooth. Concentration gradations are also in accordance with Stokes' theory predictions. Solid lines presented in Figs. 9e11 were determined using least squares method. Exponential relationships in the form y ¼ A þ B,expðC,xÞ were applied to fit the data. Exponential models were accepted taking into account solid particles distributions predicted by theoretical considerations and observed in experimental researches [45,46]. The obtained coefficient of determination (adjusted R-squared) in the range 0,92e0,77 indicates a good fit of mathematical models to experimental data. In the statistics point of view, proposed mathematical model explains well the variability of the analyzed factor. Results presented in Fig. 11 have to be shortly explained. Probably the highest rotational velocity caused that big particles in very short time moved to the outer layer of the composite. Small particles were blocked and were not able to penetrate into this layer. Deeper layers where particles with different diameters were packed exhibited higher volume content of the filler. It is well known that particles with wide diameter distribution can be packed closer than with the narrow size distribution.
41
parts with low electrical resistivity on the outer surface and insulating properties in the rest of the volume. This kind of products are needed for many applications, especially in explosive atmospheres for example in mining and chemical industry. Because of this, apart from the structure, electrical properties were searched. Cured, unfilled epoxy resins exhibit electrical surface resistivity about 0.8e12 $1016 U [47]. Addition of copper particles with very high electrical conductivity to epoxy matrix caused in all cases essential decrease of surface resistivity on the outer surface of the samples. Observed changes of electrical resistivity for other electroconductive fillers, eg. carbon particles, are not so pronounced [48]. Due to the procedure described in 3.4. Dependences of surface resistivity on radial distance from the outer surface were elaborated. Fig. 12 and Fig. 13 show the influence of rotational velocity on electrical resistivity. Achieved gradation of electrical properties reflected gradation of cooper particles concentration. General and expected tendency was noticed that the higher was copper particles concentration the lower was electrical resistivity. There was no direct proportionality between these two characteristics because surface resistance is not proportional to the filler content [49,50].
4.2. Electrical resistivity In the practical point of view prepared PGMs were planned for
Fig. 11. Relation between particles content and distance from the surface e specimen cast at 422 rpm.
Fig. 9. Relation between particles content and distance from the surface e specimen cast at 211 rpm.
Fig. 10. Relation between particles content and distance from the surface e specimen cast at 300 rpm.
Fig. 12. Relation between surface resistivity and distance from the surface for different rotational velocities.
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Fig. 13. Dependence of surface resistivity on rotational velocity.
Usually above defined concentration significant decrease of resistivity is observed. The minimum content of the filler giving pronounced transition from high to low electrical resistivity is called ‘percolation threshold’ [50,51]. It depends on many factors like filler shape and size distribution, structure and filler-matrix interactions. Results show that in outer layers percolation threshold was exceeded in all cases. Observed influence of rotational velocity on electrical resistivity was alike as its influence on particle concentration. The same type of relationships were observed. The best fitting of experimental models to measured values of resistivity data were achieved when exponential models were applied (Figs. 12 and 13). The models presented together with the graphs may be applied in the practice to predict surface
resistivity of these type of PGMs in future applications. For other PGMs systems presented methodology may be applied. If only surface properties are essential the procedure may be simplified by excluding from the procedure the analysis of samples structure. Relationships between surface electrical resistivity gradation and the time elapsing between compound preparation and pouring into the mould (holding time) are presented in Fig. 14. Differences in surface resistivity due to the changes of holding time are less pronounced. It is in accordance with results achieved for particles distribution research. Also results relating holding time and electrical resistivity may be described very well by using exponential experimental models. In practical point of view it is very important that electrical resistivity values on the outer surface were small enough to avoid electrical charge accumulation and surface static electrification. At the same time in the deeper layers surface electrical resistivity was of the same range as observed for pure epoxy resin and typical for polymeric electrical insulators. In accordance with the experimentally confirmed practice [52,53] and with requirements of the EN 13463-1 standard [54], the electrostatic charge accumulation is eliminated when the surface resistivity is lower or equal to 109 U and is significantly reduced when the surface resistivity is lower than 1011 U. All of the elaborated PGMs may be classified as electrostatic safe. Many of searched composites exhibited surface resistivity lower than 106 U. 5. Conclusions The centrifugal casting method enable to manufacture polymeric epoxy-cooper composite materials characterized by radial gradation of particles content and in this way with radial gradation of electrical resistivity. These materials may be classified as PGMs because they can be designed and then manufactured with functionally changing properties. It is possible to affect particle concentration and electrical resistivity gradation by changing centrifugal casting parameters. More pronounced influence on both gradations have rotational velocity than time elapsing between compound preparation and its pouring into the mould. Achieved results are in accordance with theoretical considerations based on Stokes' theory. Elaborated PGMs exhibit electrical resistivity allowing to avoid static electricity danger. Acknowledgments This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References
Fig. 14. Dependence of surface resistivity on holding time for specimens centrifuged at 300 rpm.
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