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The effect of particulate agglomeration and the residual stress state on the modulus of filled resin Part 1. Modulus of untreated graded sand-filled composite
The effect of particulate agglomeration and the residual stress state on the modulus of filled resin Part 1. Modulus of untreated graded sand-filled composite S. AHMED and F. R. JONES (University of Sheffield, UK) An untreated graded sand-filled polyester resin has been found to exhibit a higher modulus than previously reported for a particulate composite. A discontinuity in the stress-strain curve, which was dependent upon the volume fraction of sand, was observed. A residual stress mechanism is proposed to explain these results and the behaviour of the composite at different curing temperatures. Fractography demonstrated the presence of trans-granular and inter-granular fractures. The former confirmed the presence of a strong matrix-particle interface bond even though the latter could only be explained by the expected poor 'chemical' adhesion in the absence of a coupling agent. These apparent contrasting results are considered to arise from the presence of residual compressive stresses around agglomerates of irregularly shaped particles. Key words: residual stress mechanism; stress-strain curve; particulate agglomeration; graded sand-filled polyester resin; fractography; matrix-particle interface
The reinforcement of a polymer matrix by a particulate second phase is very complex. The particles appear to restrict the mobility and the deformability of the matrix by introducing mechanical restraints. The degree of restraint is dependent upon the shape, size and spacing of the particles, the nature of polymeric matrix and the interracial bond. Several groups of researchers have studied the dependence of particle volume fraction on modulus of a composite. 1-11 The theories which have been developed to explain the variation between the modulus of the filled composite and volume fraction do not normally take into account the effect of particle size, packing density, and the distribution of the particles throughout the composite. Vollenberg and Heikens 8 recently reported that the Young's modulus can be a function of particle size at the same volume fraction. Furthermore a number of theories have been proposed to explain the elastic behaviour of particulate
composites. Because of the filler rigidity all of these analytical solutions are less accurate for higher modular ratio of filler to the matrix. An additional drawback common to all these estimates is their failure to allow for any lateral effect which is especially important at high volume fractions of rigid filler. 1 In this paper a transition in Young's modulus from a law of mixtures lower bound to upper bound with volume fraction, for a graded sand-filled polyester resin is reported and a hypothesis developed to explain the results.
EXPERIMENTAL The resin selected for this study was Crystic 272 (Scott-Bader & Co Ltd) an isophthalic unsaturated polyester resin which was cured using 2 phr of 50% methyl ethyl ketone peroxide solution (catalyst M) and 1 phr of cobalt naphthenate solution. At this
0010-4361/88/070277-06 $3.00©1988 Butterworth & Co (Publishers) Ltd COMPOSITES. VOLUME 19. NUMBER4. JULY 1988
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concentration, the resin has a gel time of approximately 20 min. Sand fillers were supplied by Stanton & Staveley Ltd in three grades, coarse, medium and fine. Sieve analysis showed that >94% of particles were in the range of 0.6-1.18 mm, >95% from 600 to 300 ~tm, and >88% from 300 to 150 ~tm for the coarse, medium and fine grades respectively. The ratio of resin:catalyst: accelerator:filler was 65:1.3:0.65 :x parts by weight where x varied in increments of 30 g, from 30 g to 140 g (10 g of each grade of sand). A two-stage casting technique was developed to maintain the sand particles in suspension. Firstly the activated resin was poured into a mould and then half of the premixed sand mixture was sprinkled by hand onto the surface just prior to gelation. Once the first layer of sand and resin had set, the second layer was cast in the same way by taking the same amount of activated resin and the remaining half of the sand mixture. The mould was then left open to the atmosphere at room temperature for at least 24 h prior to post-curing. The thickness after casting depended upon the volume fraction of sand. The volume fraction of sand was determined by burning off the matrix, from weighed samples 20 x 20 mm in dimension, which were taken from each of the tested specimens. To calculate the volume fraction of sand Vs, the density of sand was taken to be 2.65 g cm -3.
RESULTS Two typical stress-strain curves are shown in Fig. 1. Curve 1 for a composite of low volume fraction of sand has an initially linear reponse which becomes progressively non-linear above strains of 0.05%. The curvature (curve 1, Fig. 1) results from the dewetting of isolated particles. The same phenomenon was observed in model 0°/sand/0° unidirectional glass fibre laminate where the detailed micromechanics can be studied. 12 Curve 2 shows the reproducible discontinuity which is observed for composites of high volume fraction which is in contrast to the progressive change in slope for the low volume fraction composite. This discontinuity cannot be the result of a viscoelastic response in the matrix since the stress-strain curve for the unfilled polyester resin (Fig. 2) has only limited non-linearity. Nor can it be a function of the testing technique since it was highly reproducible. Furthermore, at similar volume fractions of particles, neither glass bead, coarse sand or fine sand-filled resin composites exhibited the same effect. 13 In addition, as shown in Fig. 1, the effect is not observed at low volume fractions of graded sand. Thus the discontinuous form of the stress strain curves in Figs 1 and 2 must be associated with the microstructure of the composite. Similar observations have also been reported elsewhere. 7 20
Tensile test specimens 200 x 20 mm were cut from the cold cured cast plates using a water cooled rotating diamond wheel. Aluminium alloy (HS15) end tags 30 x 21 × 1.5 mm, were bonded to all tensile test specimens with cold curing Araldite adhesive (Ciba-Geigy plc) prior to post curing. The following post curing schedules were used: 4 h at 120°C and 15 h at 50°C under 5 kPa pressure in an air circulating oven with temperature controlled to + I°C. The specimens were allowed to cool down inside the oven for approximately 10 h prior to testing.
18 16 lq
1
12
2
8 6 q 2 0
0.02
0.1
TENSILE TESTING Tensile tests were performed on a Mayes SM200 machine which was calibrated to BS 1610. The cross head speed was 0.5 mm min-1. Electrical resistance strain gauges, 90 mm in length, were bonded onto the smooth surface of the specimen with the recommended cyanoacrylate adhesive, to monitor the strain along the length of the specimen. The preliminary testing was carried out with an extensometer but because a discontinuity was recorded the experiments were rerun using a different tensile testing machine and extensometer located in the Department of Mechanical Engineering. The same result was observed. One possible consideration, slippage of the extensometer, was examined using 10 mm electrical resistance strain gauges, but the same effect was observed. A further possibility of localised heterogenity was circumvented by using 90 mm gauges. The stress on the specimen was calculated from the applied load and the original average cross-sectional area of the specimen, which was measured at five different locations along the length of the specimen. The modulus was obtained from the linear portion of the stress-strain curve. 278
0.2
Strain (~o)
Fig. 1 Typical stress-strain curves for sand-filled resin sample cured at 120°C. Curve l - l o w Vs (=12%), curve 2-high Vs (=27%). Curve 2 is displaced along E-axis for presentation 20
18 16 3
~
4
2 0
0.02
0.06
0.1 0.1q 0.18 0.2 Strain (~) Fig. 2 S t r e s s - s t r a i n curves f o r unfilled resin(4) and filled resin o f v o l u m e fraction of sand 26.2%, 17.5%, 13.3% (curves 1,2 and 3 respectively) showing reproducible discontinuity and its shift t o higher values of strain with increasing v o l u m e fraction of resin m a t r i x
C O M P O S I T E S . JULY 1988
The strain at which the discontinuity occurs was determined by extending the linear portion of the curves. It was found to decrease with increasing volume fraction of sand as shown in Fig. 2. Unloading the specimens which have been stressed to just above the discontinuity produced a small degree of hysteresis and a low permanent set. On reloading, the discontinuity reappeared at a slightly lower value of strain but the gradient remained essentially the same, indicating that no significant dewetting or other irreversible process
2°I 18
16 14
g
8 6 4 2
0
0.02 0.04 0.06 0.08
0
0.02 0.04 0.06 0.08
had occurred at the discontinuity. Furthermore by annealing at 80°C for 90 min, the discontinuity in the unstressed 120°C cured specimen was still present but occurred at a slightly lower value of strain (Fig. 3). Fig. 4 shows the particle distribution in low and high volume fraction sand-filled resin; the microstructures in the two cases are different, at low Vs the particles are isolated by the matrix but at high Vs, particle agglomeration can be seen. The fracture surface of a high Vs composite was also characterized by the presence of fractured sand particles as shown in Fig. 5. The effect of Vs on the modulus of a series of composites prepared at different post-cure temperatures is shown in Figs. 6-8. The striking observation is that the modulus tends to a higher value as the V, increased and that a higher post cure temperature resulted in a larger modulus. Thus the presence of a discontinuity in the stress-strain curves appears to occur simultaneously with a transition to a high modulus state and that this transition occurs at a lower V, at higher post-curing temperatures. A discontinuity in the stress-strain curves for glass-bead filled composite was also observed by Nicolais et al. 7 but they where unable to suggest a plausible mechanism. Previous research 14 had indicated that the resin had a thermal expansion coefficient which was highly temperature sensitive and
Strain {~) Fig. 3 The effect of annealing at 80°C (curve 2 and 4) on the stress-strain curves for sand-filled resin post-cured at 120°C. Vs=25.4% and Vs=27.0% for curves 1 and 2 and 3 and 4 respectively
Fig. 5 Fractograph showing particle pull-out and fractured sand particles in a composite (Vs=29%) post-cured at 120°C 30
2o Z~Z~ .
lO
2 I
I
I
I
I
0.1 0.2 Volume fraction of sand (%)
Fig. 4 (a) Optical micrograph of polished section of a low volume fraction sand-filled resin (I/,=6%) showing particle distribution (X 20); (b) a high volume fraction sand-filled resin (Vs=29%) showing agglomeration of particles(X 25)
C O M P O S I T E S . JULY 1988
I 0.3
Fig. 6 Comparison of theoretical and experimental moduli of sand-filled composite cured at 20°C (Em=3.314 GPa, E,=72.4 GPa). Curves 1 and 2 are Law of Mixtures 11 upper and lower bound are curves 3 and 4, Paul's 15 upper and lower bounds, respectively
279
responsible for the induction of large restraint strains in laminated fibre composites and that the same phenomenon could operate on the microscale in these composites is considered below.
DISCUSSION The effect of particle volume fraction on the low strain tensile moduli, for samples cured at 20°C, 50°C and 120°C are given in Figs. 6-8 together with the law of mixture approximation and the equations of Paul 15 who considered a cubic particle array surrounded by a cube of matrix. The upper bound for the latter assumes a uniform applied stress at the boundary of the cube and is given by: 1 + ( m - 1 ) V s 2/3 1 + (m-l)
(Vs/3-Vs)/
Ec = Em
(1)
Where m is modulus ratio Es/Em. The lower bound is found by using same model and is for uniform displacement at the boundary. It is given by Equation (2) where E~ and Em are moduli of the composite, matrix and V~ is the volume fraction of sand respectively: 30
20
I
Fig. 7
I
I
I
I
0.1 0.2 Volume fraction of sand (%}
0
I
0.3
Comparison of theoretical and experimental moduli of cured at 50°C for 15 h (Em=3.345 GPa).
sand-filled composite See Fig. 6 for key
30 1
?~
20
/x
I
I
0.1
I
3
I
0.2
I
I
0.3
Volume fraction of sand (96) Fig. 8
Comparison of theoretical and experimental moduli of sand-filled composite cured at 120°C for 4 h (Era=3.9 GPa). See Fig. 6 for key
280
Ec = Em
1 + m / ( m - 1 ) - Vs %
(2)
The bounds given by Equations (1) and (2) are given in Figs. 6-8 (curves 3 and 4) where it is seen that they poorly represent the experimental results. Better theoretical predictions have been obtained from the Law of mixtures equations n for the limiting conditions of uniform stress and uniform strain. For a non-bonded particle it is considered that both particle and matrix can carry equal stress. The lower bound for Ec is therefore given by: Ec =
EmEs E Y m + EmVs
(3)
In the case of strong bond between the components, an upper bound is obtained from consideration of strain uniformity: Ec = EsVs + EmVm
(4)
These bounds are given as curves i and 2 in Figs. 6-8. The experimental points for the composite cured at 20°C for 90 days lie between these bounds. At a low particle volume fraction the experimental points lie close to the lower bound and approach the higher bound as Vs increases. A similar trend can be observed for composites cured at 50°C, and 120°C except that the results are displaced to lower volume fraction. The tendency of the modulus to deviate most from the lower bound at high volume fractions has been observed by several authors. 1-3 Young2, for example, suggested that this resulted from an interaction between the particles. In this system a hybrid mixture of particles containing semi angular sand particles of sizes ranging from 150 ~tm to 1.18 mm has been used. There is a tendency at low volume fractions, for the sand particles to agglomerate giving rise to poor dispersion because of irregular size and shapes. But at high volume fractions the particles are highly agglomerated. Thus there is a transition from a dispersion of isolated particles into a mixture of interwoven phases. Filler agglomeration results in the transfer of stress by particle to particle bearing rather than by a shear mechanism. The agglomeration also causes immobility of the matrix between the dispersed phase. If this were the only reinforcing mechanism the composites would have a modulus which is independent of curing temperature. However, the experimental moduli for the composites post-cured at 120°C are closer to the upper bound law of mixtures for strain compatibility than those prepared at lower teperatures. It would appear therefore that a good interracial bond is formed which enables the load to be transferred between the resin and the sand particles. Since these sand particles have not been treated with adhesion promoters, a physical rather than chemical adhesion mechanism must operate. This is confirmed by the absence of resin fillets on the particles within a fracture surface as shown in Fig. 9. The presence of particle pull-out and debonding typical of a poor interracial bond, can also be observed. However, another feature of the fracture surfaces of these composites is the presence of cloven sand particles COMPOSITES. JULY 1988
The distribution of stress around an inclusion in a resin matrix in terms of the modulus ratio and expansion coefficients has been discussed elsewhere. 17-19
Fig. 9 Fracture surface showing particle pull-out and river lines in surrounding resin
(Figs. 5 and 10) which can only be understood in terms of good adhesion between the sand and resin. These apparently contrasting observations can only be explained if the particles remain bonded until one particle fractures. When this occurs, localized changes in the stress state cause debonding of the adjacent particles. In which case the adhesion of the sand to the resin must result from a restraint shrinkage mechanism which develops during cooling from the post-curing temperature. In earlier experiments with continuous fibre composites, it was observed that curing stresses which can result from shrinkage during polymerization, are small and can be annealed-out during post-curing. 16 The adhesion between the matrix and the particles in the post-cured composites is postulated to result from the generation of residual thermal compressive stresses, within the agglomerated particles. Particle agglomeration causes local variations in stiffness and expansion coefficient which are responsible for a restrained local volume shrinkage of the matrix. The magnitude of the residual stresses which result, will be greater for a larger volume fraction of matrix, thereby explaining the decrease in the applied strain at the discontinuity with volume fraction of sand particles.
With a fumarate isophthalic polyester resin which can be cured at room tempeature to a matrix having essentially similar mechanical properties to the postcured resin, 2° it is possible to test these ideas, since at a lower curing temperature the thermal restraint strains will result in a poorer bond between the resin and the particles. The results in Fig. 7 demonstrate that at 50°C the composite has a lower modulus. For cold cured composites, an even lower modulus at the same volume fraction has been observed (Fig. 6). Thus the magnitude of the stresses which develop during curing, depends upon the stress-free temperature and/or post-cure temperature whichever is the lower, and the interparticulate spacing. For the room temperature cured composite the residual stresses arise through curing shrinkage which although small cannot be ignored. Since the micromechanics of this material will also be a function of the geometrical packing of the particles it will be necessary to differentiate between these effects. The work is therefore being extended to spherical particles where geometrical factors are minimized. CONCL USlONS The experimental moduli for untreated graded sandfilled polyester resin have been found to be higher than previously published. At the same volume fraction the modulus of samples post-cured at 50°C and 120°C are progressively higher than that for a cold-cured composite. The transition from a low modulus state to a high modulus state with volume fraction is considered to result from agglomeration of sand particles and the presence of an anisotropic residual stress which leads to an apparent improvement of interfacial bond strength with post-curing temperature. Thus the compressive thermal stresses which form within the agglomerates increase the load bearing capacity of the composite. The discontinuity in the stress-strain curves for high volume fraction composites which has been observed, is considered to result from the disruption of the agglomerates and the release of these compressive stresses. Consequently the fracture surfaces show evidence of crack pinning with failure occurring by a combination of particle pull-out, trans-granular and inter-granular fractures. Thus the poorly chemically bonded sand particles, act as well bonded particles within the agglomerates where the thermal compressive stresses are high. ACKNOWLEDGEMENTS
The authors wish to thank the Government of Pakistan for financial assistance (to S.A.). We also thank Scott-Bader and Co. Ltd. for polyester resin and Stavely plc for sand fillers. REFERENCE Fig. 10 Fractograph showing broken sand particle lacking adhered resin fragments
COMPOSITES . JULY 1988
1 Ishai, O. and Cohen, L.J. Int J Mech Sci 9 (1967)p 539 2 Young,R.J. and Beaumont, P.M.R. J Mater Sci 12 (1977)p 684
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3 Spanoudakis, J. and Young, R.J J Mater Sci 19 (1984) p 473 4 ibid 19 (1984) p 487
5 Dekkers, M.E.J. and Heikens, D. JAppl Polym Sci 28 (1983) p 3809 6 Young, R.J. Proc lnt Conf"Fillers 86" (Plastics and Rubber Institute, London, 1986) Paper 13 7 Nicolais, L., Narkis, M. and Lavengood, R.E. 'Composite Material Testing and Design' ASTM STP 497 (American Society for Testing and Materials, 1972) p 575 8 Vollenberg, P.H.Th. and Heikens, D. Proc lnt Conf"Fillers 86" (Plastics and Rubber Institute, London, 1986) Paper 14 9 Moloney, A.C., Kansch, H.H., Kaiser, T. and Beer, H. Proc Int Conf"Fillers 86" (Plastics and Rubber Institute, London, 1986) Paper 17 10 ibid J Mater Sci 22 (1987) p 381 11 Broutman, L.J. and Krock, R.H. 'Modern Composite Materials' (Addison Wesley, Massachusetts, 1967) 12 Ahmed, S. and Jones, F.R. Proc 3rd Int ConfFibre Reinforced Composites '88, Extending the limits (Plastics and Rubber Institute, Liverpool, UK, March 1988) Paper 16
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13 Ahmed, S. and Jones, F.R. in preparation 14 Mulheron, M. Jones, F.R. and Bailey, J.E. Comput Sci Technol 25 (1986) p 119 15 Paul, B. Trans Metal Soc AM1E 218 (1960) p 36 16 Garrett, K.W. and Bailey, J.E. J Mater Sci 12 (1977) p 157 17 Koufopoulous, T. and Theocaris, P.S. J Composite Mater 3 (1969) p 308 18 Parkis, V.J. and Durelli, A.J. JAppl Mech 32 (1965) p 504 19 Daniel, I.M. and Durelli, A.J. Experimental Mech 2 (1962) p 240 20 Jones, F.R., Wheatley, A.R. and Bailey, J.E. in 'Composite Structures' edited by I.H Marshall (Applied Science London, 1981) pp 415-419
A U THORS T h e a u t h o r s a r e with t h e S c h o o l o f M a t e r i a l s , U n i v e r s i t y o f Sheffield, N o r t h u m b e r l a n d R o a d , S h e f f i e l d S10 2 T Z , U K . E n q u i r i e s s h o u l d b e d i r e c t e d to Dr Jones.
C O M P O S I T E S . J U L Y 1988
The reinforcement of a polymer matrix by a particulate second phase is very complex. The particles appear to restrict the mobility and the deformability of the matrix by introducing mechanical restraints. The degree of restraint is dependent upon the shape, size and spacing of the particles, the nature of polymeric matrix and the interracial bond. Several groups of researchers have studied the dependence of particle volume fraction on modulus of a composite. 1-11 The theories which have been developed to explain the variation between the modulus of the filled composite and volume fraction do not normally take into account the effect of particle size, packing density, and the distribution of the particles throughout the composite. Vollenberg and Heikens 8 recently reported that the Young's modulus can be a function of particle size at the same volume fraction. Furthermore a number of theories have been proposed to explain the elastic behaviour of particulate
composites. Because of the filler rigidity all of these analytical solutions are less accurate for higher modular ratio of filler to the matrix. An additional drawback common to all these estimates is their failure to allow for any lateral effect which is especially important at high volume fractions of rigid filler. 1 In this paper a transition in Young's modulus from a law of mixtures lower bound to upper bound with volume fraction, for a graded sand-filled polyester resin is reported and a hypothesis developed to explain the results.
EXPERIMENTAL The resin selected for this study was Crystic 272 (Scott-Bader & Co Ltd) an isophthalic unsaturated polyester resin which was cured using 2 phr of 50% methyl ethyl ketone peroxide solution (catalyst M) and 1 phr of cobalt naphthenate solution. At this
0010-4361/88/070277-06 $3.00©1988 Butterworth & Co (Publishers) Ltd COMPOSITES. VOLUME 19. NUMBER4. JULY 1988
277
concentration, the resin has a gel time of approximately 20 min. Sand fillers were supplied by Stanton & Staveley Ltd in three grades, coarse, medium and fine. Sieve analysis showed that >94% of particles were in the range of 0.6-1.18 mm, >95% from 600 to 300 ~tm, and >88% from 300 to 150 ~tm for the coarse, medium and fine grades respectively. The ratio of resin:catalyst: accelerator:filler was 65:1.3:0.65 :x parts by weight where x varied in increments of 30 g, from 30 g to 140 g (10 g of each grade of sand). A two-stage casting technique was developed to maintain the sand particles in suspension. Firstly the activated resin was poured into a mould and then half of the premixed sand mixture was sprinkled by hand onto the surface just prior to gelation. Once the first layer of sand and resin had set, the second layer was cast in the same way by taking the same amount of activated resin and the remaining half of the sand mixture. The mould was then left open to the atmosphere at room temperature for at least 24 h prior to post-curing. The thickness after casting depended upon the volume fraction of sand. The volume fraction of sand was determined by burning off the matrix, from weighed samples 20 x 20 mm in dimension, which were taken from each of the tested specimens. To calculate the volume fraction of sand Vs, the density of sand was taken to be 2.65 g cm -3.
RESULTS Two typical stress-strain curves are shown in Fig. 1. Curve 1 for a composite of low volume fraction of sand has an initially linear reponse which becomes progressively non-linear above strains of 0.05%. The curvature (curve 1, Fig. 1) results from the dewetting of isolated particles. The same phenomenon was observed in model 0°/sand/0° unidirectional glass fibre laminate where the detailed micromechanics can be studied. 12 Curve 2 shows the reproducible discontinuity which is observed for composites of high volume fraction which is in contrast to the progressive change in slope for the low volume fraction composite. This discontinuity cannot be the result of a viscoelastic response in the matrix since the stress-strain curve for the unfilled polyester resin (Fig. 2) has only limited non-linearity. Nor can it be a function of the testing technique since it was highly reproducible. Furthermore, at similar volume fractions of particles, neither glass bead, coarse sand or fine sand-filled resin composites exhibited the same effect. 13 In addition, as shown in Fig. 1, the effect is not observed at low volume fractions of graded sand. Thus the discontinuous form of the stress strain curves in Figs 1 and 2 must be associated with the microstructure of the composite. Similar observations have also been reported elsewhere. 7 20
Tensile test specimens 200 x 20 mm were cut from the cold cured cast plates using a water cooled rotating diamond wheel. Aluminium alloy (HS15) end tags 30 x 21 × 1.5 mm, were bonded to all tensile test specimens with cold curing Araldite adhesive (Ciba-Geigy plc) prior to post curing. The following post curing schedules were used: 4 h at 120°C and 15 h at 50°C under 5 kPa pressure in an air circulating oven with temperature controlled to + I°C. The specimens were allowed to cool down inside the oven for approximately 10 h prior to testing.
18 16 lq
1
12
2
8 6 q 2 0
0.02
0.1
TENSILE TESTING Tensile tests were performed on a Mayes SM200 machine which was calibrated to BS 1610. The cross head speed was 0.5 mm min-1. Electrical resistance strain gauges, 90 mm in length, were bonded onto the smooth surface of the specimen with the recommended cyanoacrylate adhesive, to monitor the strain along the length of the specimen. The preliminary testing was carried out with an extensometer but because a discontinuity was recorded the experiments were rerun using a different tensile testing machine and extensometer located in the Department of Mechanical Engineering. The same result was observed. One possible consideration, slippage of the extensometer, was examined using 10 mm electrical resistance strain gauges, but the same effect was observed. A further possibility of localised heterogenity was circumvented by using 90 mm gauges. The stress on the specimen was calculated from the applied load and the original average cross-sectional area of the specimen, which was measured at five different locations along the length of the specimen. The modulus was obtained from the linear portion of the stress-strain curve. 278
0.2
Strain (~o)
Fig. 1 Typical stress-strain curves for sand-filled resin sample cured at 120°C. Curve l - l o w Vs (=12%), curve 2-high Vs (=27%). Curve 2 is displaced along E-axis for presentation 20
18 16 3
~
4
2 0
0.02
0.06
0.1 0.1q 0.18 0.2 Strain (~) Fig. 2 S t r e s s - s t r a i n curves f o r unfilled resin(4) and filled resin o f v o l u m e fraction of sand 26.2%, 17.5%, 13.3% (curves 1,2 and 3 respectively) showing reproducible discontinuity and its shift t o higher values of strain with increasing v o l u m e fraction of resin m a t r i x
C O M P O S I T E S . JULY 1988
The strain at which the discontinuity occurs was determined by extending the linear portion of the curves. It was found to decrease with increasing volume fraction of sand as shown in Fig. 2. Unloading the specimens which have been stressed to just above the discontinuity produced a small degree of hysteresis and a low permanent set. On reloading, the discontinuity reappeared at a slightly lower value of strain but the gradient remained essentially the same, indicating that no significant dewetting or other irreversible process
2°I 18
16 14
g
8 6 4 2
0
0.02 0.04 0.06 0.08
0
0.02 0.04 0.06 0.08
had occurred at the discontinuity. Furthermore by annealing at 80°C for 90 min, the discontinuity in the unstressed 120°C cured specimen was still present but occurred at a slightly lower value of strain (Fig. 3). Fig. 4 shows the particle distribution in low and high volume fraction sand-filled resin; the microstructures in the two cases are different, at low Vs the particles are isolated by the matrix but at high Vs, particle agglomeration can be seen. The fracture surface of a high Vs composite was also characterized by the presence of fractured sand particles as shown in Fig. 5. The effect of Vs on the modulus of a series of composites prepared at different post-cure temperatures is shown in Figs. 6-8. The striking observation is that the modulus tends to a higher value as the V, increased and that a higher post cure temperature resulted in a larger modulus. Thus the presence of a discontinuity in the stress-strain curves appears to occur simultaneously with a transition to a high modulus state and that this transition occurs at a lower V, at higher post-curing temperatures. A discontinuity in the stress-strain curves for glass-bead filled composite was also observed by Nicolais et al. 7 but they where unable to suggest a plausible mechanism. Previous research 14 had indicated that the resin had a thermal expansion coefficient which was highly temperature sensitive and
Strain {~) Fig. 3 The effect of annealing at 80°C (curve 2 and 4) on the stress-strain curves for sand-filled resin post-cured at 120°C. Vs=25.4% and Vs=27.0% for curves 1 and 2 and 3 and 4 respectively
Fig. 5 Fractograph showing particle pull-out and fractured sand particles in a composite (Vs=29%) post-cured at 120°C 30
2o Z~Z~ .
lO
2 I
I
I
I
I
0.1 0.2 Volume fraction of sand (%)
Fig. 4 (a) Optical micrograph of polished section of a low volume fraction sand-filled resin (I/,=6%) showing particle distribution (X 20); (b) a high volume fraction sand-filled resin (Vs=29%) showing agglomeration of particles(X 25)
C O M P O S I T E S . JULY 1988
I 0.3
Fig. 6 Comparison of theoretical and experimental moduli of sand-filled composite cured at 20°C (Em=3.314 GPa, E,=72.4 GPa). Curves 1 and 2 are Law of Mixtures 11 upper and lower bound are curves 3 and 4, Paul's 15 upper and lower bounds, respectively
279
responsible for the induction of large restraint strains in laminated fibre composites and that the same phenomenon could operate on the microscale in these composites is considered below.
DISCUSSION The effect of particle volume fraction on the low strain tensile moduli, for samples cured at 20°C, 50°C and 120°C are given in Figs. 6-8 together with the law of mixture approximation and the equations of Paul 15 who considered a cubic particle array surrounded by a cube of matrix. The upper bound for the latter assumes a uniform applied stress at the boundary of the cube and is given by: 1 + ( m - 1 ) V s 2/3 1 + (m-l)
(Vs/3-Vs)/
Ec = Em
(1)
Where m is modulus ratio Es/Em. The lower bound is found by using same model and is for uniform displacement at the boundary. It is given by Equation (2) where E~ and Em are moduli of the composite, matrix and V~ is the volume fraction of sand respectively: 30
20
I
Fig. 7
I
I
I
I
0.1 0.2 Volume fraction of sand (%}
0
I
0.3
Comparison of theoretical and experimental moduli of cured at 50°C for 15 h (Em=3.345 GPa).
sand-filled composite See Fig. 6 for key
30 1
?~
20
/x
I
I
0.1
I
3
I
0.2
I
I
0.3
Volume fraction of sand (96) Fig. 8
Comparison of theoretical and experimental moduli of sand-filled composite cured at 120°C for 4 h (Era=3.9 GPa). See Fig. 6 for key
280
Ec = Em
1 + m / ( m - 1 ) - Vs %
(2)
The bounds given by Equations (1) and (2) are given in Figs. 6-8 (curves 3 and 4) where it is seen that they poorly represent the experimental results. Better theoretical predictions have been obtained from the Law of mixtures equations n for the limiting conditions of uniform stress and uniform strain. For a non-bonded particle it is considered that both particle and matrix can carry equal stress. The lower bound for Ec is therefore given by: Ec =
EmEs E Y m + EmVs
(3)
In the case of strong bond between the components, an upper bound is obtained from consideration of strain uniformity: Ec = EsVs + EmVm
(4)
These bounds are given as curves i and 2 in Figs. 6-8. The experimental points for the composite cured at 20°C for 90 days lie between these bounds. At a low particle volume fraction the experimental points lie close to the lower bound and approach the higher bound as Vs increases. A similar trend can be observed for composites cured at 50°C, and 120°C except that the results are displaced to lower volume fraction. The tendency of the modulus to deviate most from the lower bound at high volume fractions has been observed by several authors. 1-3 Young2, for example, suggested that this resulted from an interaction between the particles. In this system a hybrid mixture of particles containing semi angular sand particles of sizes ranging from 150 ~tm to 1.18 mm has been used. There is a tendency at low volume fractions, for the sand particles to agglomerate giving rise to poor dispersion because of irregular size and shapes. But at high volume fractions the particles are highly agglomerated. Thus there is a transition from a dispersion of isolated particles into a mixture of interwoven phases. Filler agglomeration results in the transfer of stress by particle to particle bearing rather than by a shear mechanism. The agglomeration also causes immobility of the matrix between the dispersed phase. If this were the only reinforcing mechanism the composites would have a modulus which is independent of curing temperature. However, the experimental moduli for the composites post-cured at 120°C are closer to the upper bound law of mixtures for strain compatibility than those prepared at lower teperatures. It would appear therefore that a good interracial bond is formed which enables the load to be transferred between the resin and the sand particles. Since these sand particles have not been treated with adhesion promoters, a physical rather than chemical adhesion mechanism must operate. This is confirmed by the absence of resin fillets on the particles within a fracture surface as shown in Fig. 9. The presence of particle pull-out and debonding typical of a poor interracial bond, can also be observed. However, another feature of the fracture surfaces of these composites is the presence of cloven sand particles COMPOSITES. JULY 1988
The distribution of stress around an inclusion in a resin matrix in terms of the modulus ratio and expansion coefficients has been discussed elsewhere. 17-19
Fig. 9 Fracture surface showing particle pull-out and river lines in surrounding resin
(Figs. 5 and 10) which can only be understood in terms of good adhesion between the sand and resin. These apparently contrasting observations can only be explained if the particles remain bonded until one particle fractures. When this occurs, localized changes in the stress state cause debonding of the adjacent particles. In which case the adhesion of the sand to the resin must result from a restraint shrinkage mechanism which develops during cooling from the post-curing temperature. In earlier experiments with continuous fibre composites, it was observed that curing stresses which can result from shrinkage during polymerization, are small and can be annealed-out during post-curing. 16 The adhesion between the matrix and the particles in the post-cured composites is postulated to result from the generation of residual thermal compressive stresses, within the agglomerated particles. Particle agglomeration causes local variations in stiffness and expansion coefficient which are responsible for a restrained local volume shrinkage of the matrix. The magnitude of the residual stresses which result, will be greater for a larger volume fraction of matrix, thereby explaining the decrease in the applied strain at the discontinuity with volume fraction of sand particles.
With a fumarate isophthalic polyester resin which can be cured at room tempeature to a matrix having essentially similar mechanical properties to the postcured resin, 2° it is possible to test these ideas, since at a lower curing temperature the thermal restraint strains will result in a poorer bond between the resin and the particles. The results in Fig. 7 demonstrate that at 50°C the composite has a lower modulus. For cold cured composites, an even lower modulus at the same volume fraction has been observed (Fig. 6). Thus the magnitude of the stresses which develop during curing, depends upon the stress-free temperature and/or post-cure temperature whichever is the lower, and the interparticulate spacing. For the room temperature cured composite the residual stresses arise through curing shrinkage which although small cannot be ignored. Since the micromechanics of this material will also be a function of the geometrical packing of the particles it will be necessary to differentiate between these effects. The work is therefore being extended to spherical particles where geometrical factors are minimized. CONCL USlONS The experimental moduli for untreated graded sandfilled polyester resin have been found to be higher than previously published. At the same volume fraction the modulus of samples post-cured at 50°C and 120°C are progressively higher than that for a cold-cured composite. The transition from a low modulus state to a high modulus state with volume fraction is considered to result from agglomeration of sand particles and the presence of an anisotropic residual stress which leads to an apparent improvement of interfacial bond strength with post-curing temperature. Thus the compressive thermal stresses which form within the agglomerates increase the load bearing capacity of the composite. The discontinuity in the stress-strain curves for high volume fraction composites which has been observed, is considered to result from the disruption of the agglomerates and the release of these compressive stresses. Consequently the fracture surfaces show evidence of crack pinning with failure occurring by a combination of particle pull-out, trans-granular and inter-granular fractures. Thus the poorly chemically bonded sand particles, act as well bonded particles within the agglomerates where the thermal compressive stresses are high. ACKNOWLEDGEMENTS
The authors wish to thank the Government of Pakistan for financial assistance (to S.A.). We also thank Scott-Bader and Co. Ltd. for polyester resin and Stavely plc for sand fillers. REFERENCE Fig. 10 Fractograph showing broken sand particle lacking adhered resin fragments
COMPOSITES . JULY 1988
1 Ishai, O. and Cohen, L.J. Int J Mech Sci 9 (1967)p 539 2 Young,R.J. and Beaumont, P.M.R. J Mater Sci 12 (1977)p 684
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3 Spanoudakis, J. and Young, R.J J Mater Sci 19 (1984) p 473 4 ibid 19 (1984) p 487
5 Dekkers, M.E.J. and Heikens, D. JAppl Polym Sci 28 (1983) p 3809 6 Young, R.J. Proc lnt Conf"Fillers 86" (Plastics and Rubber Institute, London, 1986) Paper 13 7 Nicolais, L., Narkis, M. and Lavengood, R.E. 'Composite Material Testing and Design' ASTM STP 497 (American Society for Testing and Materials, 1972) p 575 8 Vollenberg, P.H.Th. and Heikens, D. Proc lnt Conf"Fillers 86" (Plastics and Rubber Institute, London, 1986) Paper 14 9 Moloney, A.C., Kansch, H.H., Kaiser, T. and Beer, H. Proc Int Conf"Fillers 86" (Plastics and Rubber Institute, London, 1986) Paper 17 10 ibid J Mater Sci 22 (1987) p 381 11 Broutman, L.J. and Krock, R.H. 'Modern Composite Materials' (Addison Wesley, Massachusetts, 1967) 12 Ahmed, S. and Jones, F.R. Proc 3rd Int ConfFibre Reinforced Composites '88, Extending the limits (Plastics and Rubber Institute, Liverpool, UK, March 1988) Paper 16
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13 Ahmed, S. and Jones, F.R. in preparation 14 Mulheron, M. Jones, F.R. and Bailey, J.E. Comput Sci Technol 25 (1986) p 119 15 Paul, B. Trans Metal Soc AM1E 218 (1960) p 36 16 Garrett, K.W. and Bailey, J.E. J Mater Sci 12 (1977) p 157 17 Koufopoulous, T. and Theocaris, P.S. J Composite Mater 3 (1969) p 308 18 Parkis, V.J. and Durelli, A.J. JAppl Mech 32 (1965) p 504 19 Daniel, I.M. and Durelli, A.J. Experimental Mech 2 (1962) p 240 20 Jones, F.R., Wheatley, A.R. and Bailey, J.E. in 'Composite Structures' edited by I.H Marshall (Applied Science London, 1981) pp 415-419
A U THORS T h e a u t h o r s a r e with t h e S c h o o l o f M a t e r i a l s , U n i v e r s i t y o f Sheffield, N o r t h u m b e r l a n d R o a d , S h e f f i e l d S10 2 T Z , U K . E n q u i r i e s s h o u l d b e d i r e c t e d to Dr Jones.
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