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Studies of the microhardness of glass fibre reinforced polymer (GFRP)
Polymer Testing
11(1992)225-231
~,~
Studies on the Microhardness of Glass Fibre Reinforced Polymer ( G F R P ) V. Dubey, R. Bajpai, P. Parashar & S. C. Datt* Department of Postgraduate Studies and Research in Physics, Rani Durgavati University, Jabalpur 482001, India (Received 18 October 1991; accepted 12 December 1991)
A BSTRA CT The Vickers microhardness test has been carried out on GFRP specimens at different loads ranging from 5 to 160g. The Vickers hardness number (Ho)-load behaviour has been explained on the basis of strain hardening phenomena. This reveals that the value of H~ is greater at small stresses and it becomes independent of load beyond ll0g. In this range the value of the logarithmic index, n, is 2. The non-linear behaviour of microhardness with load has three different values of logarithmic index. Further, the dependence of load on Ho in GFRP specimens has been explained on the basis of Newtonian resistance pressure as proposed by Hays and Kendall.
1 INTRODUCTION Industrial innovations, improved energy planning, sky rocketing costs and uncertain availability of various metals and their alloys, have created a greater interest in polymer composites. Glass fibre reinforced polymer is one of the important composites whose mechanical behaviour depends on the chemical nature of filler and matrix material. In this composite glass fibrous fillers contribute high tensile strength, high modulus and the disadvantage of brittleness while the polymeric matrix provides the properties such as toughness, low strength, high thermal expansivity and low thermal stability in both the physical and chemical sense. Vickers microhardness testing has been utilized by Gonzales et * To whom correspondence should be addressed. 225 Polymer Testing 0142-9418/92/$05.00 © 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
226
v. Dubey et al.
al.l-a to detect thermal degradation and crystallinity changes in rigid polymers. Datt et al. 4 have studied the microhardness of a n u m b e r of
polymeric materials and their blends by the Vickers method. Harding and Welsh, 5 Mittal and Gupta 6 and Taya and Chen T have studied some of the mechanical properties of glass fibre reinforced composites such as stiffness, tensile modulus and strength, but no observations have been reported regarding their microhardness. Hence the authors were motivated to investigate the Vickers hardness of G F R P specimens in the microhardness range.
2 EXPERIMENTAL PROCEDURE Commercially available G F R P sheet of thickness 1 m m was used in the present investigation. Specimens of size 1 cm 2 were cut from this sheet. The specimen was fixed on a plane glass plate with quickfix in such a way that the surface to be indented was perfectly horizontal. The plate was then fixed on the stage of the microscope so as to avoid any displacement of the specimen during the indentation. The indentations were carried out with a m h p 160 microhardness tester with a Vickers diamond pyramidal indenter having a square base and pyramidal angle of 136°. The indenter was attached to a Carl Zeiss NU2 universal research microscope. The applied load was varied from 5 to 160 g and was applied very slowly and at a steady rate. The time of indentation was kept at 30 s in each case. The diameters of the indentations were measured using a micrometer eyepiece with an objective of magnification 2 5 x . The mean value of the diameter was used for calculating the hardness number. For each value of load, at least five indentations were made and the average Vickers hardness number, Hv, was calculated from the following relation: Hv -
1.854 x L d2 ( k g / m m 2)
where L is load in kg and d is the diameter of indentation in mm.
3 RESULTS AND DISCUSSION Various results of microhardness studies carried out on G F R P specimens are discussed in the following sections.
Studies on the microhardness o f GFRP
227
f
14 12
i
6 4 i
L
I
I
20
40
60
80
I
I
100 120 Load ( g )
i
I
140
160
Fig. l. Variation of Hv with load. 3.1 Variation of H~ with load Figure 1 illustrates the variation of the Vickers hardness number, Hv, with load from 5 to 160 g. Initially, the microhardness increases with load but later it attains the intermediate saturation value of 14-1 k g / m m 2 at 80 g. It again starts increasing at 95 g and acquires a final saturation value of 1 5 k g / m m 2 at l l 0 g . Finally, it becomes independent of load as no change is observed in the value of Hv. The increase in Hv, as the load increases, can be explained on the basis of strain' hardening p h e n o m e n a in polymeric materials. 8 As the load increases the specimen is subjected to greater and greater strain hardening, and consequently an increase in Hv is observed. It has been found that the rate of increase of H~ is greater between 10 and 20 g as compared to that between 20 and 80 g. As the load increases beyond 20 g, the indenter gradually comes into contact with epoxy (polymer matrix) and glass fibres, and the strain hardening process increases at a slower rate. Beyond a load of 80 g and upto a load of 95 g, the change in Hv is almost negligible. The value of Hv further increases beyond the load of 95 g and tends to reach a saturation value at 110 g as no change in the value of Hv is observed between 110 and 160g. Finally, Hv becomes constant and independent of load. This saturation value of Hv beyond l l 0 g may be due to p e r m a n e n t deformation caused by chain-chain slipping in the polymer matrix. Van der Waals' and relatively high molecular forces between individual macromolecules, and the presence of glass fibres in the matrix of the polymer contribute to the strength of GFRP. Thus it is observed that in G F R P specimens there is a sharp increase in H~ values at low loads and then this rate of increase in Hv values decreases gradually and finally tends to become constant at a load of 110 g. It can be concluded that the rate of strain
V. Dubey et al.
228
hardening is large at low loads and this effect decreases as the load is increased.
3.2 Logarithmic index The load dependent nature of the microhardness of materials can be determined by Meyer's Law, L = ad", where a is a constant, L is load, d is the length of the diagonal and n is the logarithmic index. The plot of log L versus log d is shown in Fig. 2. It is interesting to note that this plot consists of four distinct regions which means that the value of n is not the same throughout the range of load. The values of n obtained from the slopes of four distinct regions are 3.23, 2.33, 2.24 and 2.0, respectively. These values of n indicate that the matrix polymer in G F R P belongs to the category of soft material. 9'1° It is evident from Meyer's law that Hv increases continuously with load when n > 2. It can also be observed from Fig. 1 that Hv increases continuously with increasing load as n is greater than 2 for the entire range of load. n approaches 2 in the range of 110-160 g at which Hv becomes independent of load. Thus in the regions of which Hv increases with load, n has a value greater than 2 and in the region in which Hv is independent of load, n has a value equal to 2. Hence, the logarithmic index n is the measure of rate of strain hardening.
2"2
D
2"0 - -
C
1.8
..a
1.6
1"4
--
A
B
1-2
1,0
0"8 O I,
I
I
I
I
2"7
2"8
2"9
3"0
3"1
I 32
tog d
Fig. 2.
Variation of log L with log d.
229
Studies on the microhardness o f G F R P
3.3 Analysis of microhardness The behaviour of microhardness is non-linear up to a load of 110 g. Therefore, the small stress behaviour can be attributed to Newtonian resistance pressure. Kick cited in Ref. 11 has proposed an analysis of the results on hardness according to which the relation between load L and diagonal d of the impression is represented by an equation of the form, L=K,d" (1) where K1 is a standard hardness and n a constant. His analysis, however, has not received wide acceptance on account of the fact that n usually has a value less than 2 and also has in some cases two values, one for the high and another for the low load region. In our case, there are four values of n, viz. 3-23, 2-33, 2.24 and 2-00. It is also evident that the hardness becomes independent of load in the region where n = 2. But the successive layers of the specimen are different in their load-dependent nature. Therefore, we have three values of n for three successive regions below the surface. We can overcome this difficulty by assuming that there are three values of Newtonian resistance pressure of the specimen for its three successive regions. Newtonian resistance pressure, W, is the minimum applied load needed to produce an indentation, since it allows no plastic deformation. Hence considering the specimen resistance pressure to be equal to W, Kick's equation can be modified to L - W = Kzd 2 (2)
140
120 - -
•
n = 3.23
10C
=
8C
6O
40
20
4
6
8
10
12
14
d2
Fig. 3.
Variation of d" with d 2.
16
18
230
V. Dubey et al. 2"1 Ic
17
15 1" 0
LJ i-i ~0~ 0'7 05 0.2
Fig. 4.
1
1
1
2-7
28
2"9
1
I
3"1 3'0 log d
I
I
3"2
3"3
Variation of log d with log (L - W).
where K2 is a constant. The factor W now allows the limiting case to prevail where microhardness is not marked by dependence on the load and the logarithmic index n assumes a value equal to 2. From eqns (1) and (2), we may write Newtonian resistance pressure W as W = K , d " - K2d 2
(3)
Using the above equations, we have plotted d" versus d 2 in Fig. 3 for obtaining the three values of W. The values obtained of Newtonian resistance pressure for successive regions are 2, 5-76 and 3.81g, respectively. Figure 4 shows the plot of log d versus log (L - W). This plot is a straight line and from its slope we obtain the value of n = 2. Hence the Hv-load behaviour in G F R P can also be explained on the basis of Newtonian resistance pressure as proposed by Hays and Kendall 12 and Parashar. 13
REFERENCES 1. Gonzalez, A., Martin, B., Munoz, M. & de Saja, J. A., Polymer Testing, 6 (1986) 361. 2. Gonzalez, A., Martin-Gil, J. & de Saja, J. A., J. Appl. Poly. Sci., 31 (1986) 717. 3. Gonzalez, A., Pastor, J. M., de Saja, J. A. & Perez, A., Die Angewandte Makromoleculare Chemie, 130 (1985) 201. 4. Datt, S. C., Keller, J. M., Parasher, P. & Bajpai, R., Makromol. Chem., Macromol. Syrup., 20/21 (1988) 465-74.
Studies on the microhardness of GFRP
5. 6. 7. 8. 9. 10. 11.
231
Harding, J. & Welsh, L. M., J. Mater. Sci., 18 (1983) 1810-26. Mittal, R. K. & Gupta, V. B., J. Mater. Sci., 17 (1982) 3179-88. Taya, M. &Chen, T. W., J. Mater. Sci., 17 (1982) 2801-8. Bajpai, R. & Datt, S. C., Indian J. Pure Appl. Phys., 24 (1986) 254-5. Onitsch, E. M., Mikroskopie, 2 (1947) 131. Hanneman, H., Metallurgia Manchr., 2,3 (1941) 135. Kotru, P. N., Raina, K. K. & Kachroo, S. K., J. Mater. Sci., 19 (1984) 2582-92. 12. Hays, C. & Kendall, E. G., Metallograph, 6 (1973) 275. 13. Parashar, P., Mechanical properties of some polymers. PhD thesis, University of Jabalpur, 1986, pp. 98, 100.
11(1992)225-231
~,~
Studies on the Microhardness of Glass Fibre Reinforced Polymer ( G F R P ) V. Dubey, R. Bajpai, P. Parashar & S. C. Datt* Department of Postgraduate Studies and Research in Physics, Rani Durgavati University, Jabalpur 482001, India (Received 18 October 1991; accepted 12 December 1991)
A BSTRA CT The Vickers microhardness test has been carried out on GFRP specimens at different loads ranging from 5 to 160g. The Vickers hardness number (Ho)-load behaviour has been explained on the basis of strain hardening phenomena. This reveals that the value of H~ is greater at small stresses and it becomes independent of load beyond ll0g. In this range the value of the logarithmic index, n, is 2. The non-linear behaviour of microhardness with load has three different values of logarithmic index. Further, the dependence of load on Ho in GFRP specimens has been explained on the basis of Newtonian resistance pressure as proposed by Hays and Kendall.
1 INTRODUCTION Industrial innovations, improved energy planning, sky rocketing costs and uncertain availability of various metals and their alloys, have created a greater interest in polymer composites. Glass fibre reinforced polymer is one of the important composites whose mechanical behaviour depends on the chemical nature of filler and matrix material. In this composite glass fibrous fillers contribute high tensile strength, high modulus and the disadvantage of brittleness while the polymeric matrix provides the properties such as toughness, low strength, high thermal expansivity and low thermal stability in both the physical and chemical sense. Vickers microhardness testing has been utilized by Gonzales et * To whom correspondence should be addressed. 225 Polymer Testing 0142-9418/92/$05.00 © 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
226
v. Dubey et al.
al.l-a to detect thermal degradation and crystallinity changes in rigid polymers. Datt et al. 4 have studied the microhardness of a n u m b e r of
polymeric materials and their blends by the Vickers method. Harding and Welsh, 5 Mittal and Gupta 6 and Taya and Chen T have studied some of the mechanical properties of glass fibre reinforced composites such as stiffness, tensile modulus and strength, but no observations have been reported regarding their microhardness. Hence the authors were motivated to investigate the Vickers hardness of G F R P specimens in the microhardness range.
2 EXPERIMENTAL PROCEDURE Commercially available G F R P sheet of thickness 1 m m was used in the present investigation. Specimens of size 1 cm 2 were cut from this sheet. The specimen was fixed on a plane glass plate with quickfix in such a way that the surface to be indented was perfectly horizontal. The plate was then fixed on the stage of the microscope so as to avoid any displacement of the specimen during the indentation. The indentations were carried out with a m h p 160 microhardness tester with a Vickers diamond pyramidal indenter having a square base and pyramidal angle of 136°. The indenter was attached to a Carl Zeiss NU2 universal research microscope. The applied load was varied from 5 to 160 g and was applied very slowly and at a steady rate. The time of indentation was kept at 30 s in each case. The diameters of the indentations were measured using a micrometer eyepiece with an objective of magnification 2 5 x . The mean value of the diameter was used for calculating the hardness number. For each value of load, at least five indentations were made and the average Vickers hardness number, Hv, was calculated from the following relation: Hv -
1.854 x L d2 ( k g / m m 2)
where L is load in kg and d is the diameter of indentation in mm.
3 RESULTS AND DISCUSSION Various results of microhardness studies carried out on G F R P specimens are discussed in the following sections.
Studies on the microhardness o f GFRP
227
f
14 12
i
6 4 i
L
I
I
20
40
60
80
I
I
100 120 Load ( g )
i
I
140
160
Fig. l. Variation of Hv with load. 3.1 Variation of H~ with load Figure 1 illustrates the variation of the Vickers hardness number, Hv, with load from 5 to 160 g. Initially, the microhardness increases with load but later it attains the intermediate saturation value of 14-1 k g / m m 2 at 80 g. It again starts increasing at 95 g and acquires a final saturation value of 1 5 k g / m m 2 at l l 0 g . Finally, it becomes independent of load as no change is observed in the value of Hv. The increase in Hv, as the load increases, can be explained on the basis of strain' hardening p h e n o m e n a in polymeric materials. 8 As the load increases the specimen is subjected to greater and greater strain hardening, and consequently an increase in Hv is observed. It has been found that the rate of increase of H~ is greater between 10 and 20 g as compared to that between 20 and 80 g. As the load increases beyond 20 g, the indenter gradually comes into contact with epoxy (polymer matrix) and glass fibres, and the strain hardening process increases at a slower rate. Beyond a load of 80 g and upto a load of 95 g, the change in Hv is almost negligible. The value of Hv further increases beyond the load of 95 g and tends to reach a saturation value at 110 g as no change in the value of Hv is observed between 110 and 160g. Finally, Hv becomes constant and independent of load. This saturation value of Hv beyond l l 0 g may be due to p e r m a n e n t deformation caused by chain-chain slipping in the polymer matrix. Van der Waals' and relatively high molecular forces between individual macromolecules, and the presence of glass fibres in the matrix of the polymer contribute to the strength of GFRP. Thus it is observed that in G F R P specimens there is a sharp increase in H~ values at low loads and then this rate of increase in Hv values decreases gradually and finally tends to become constant at a load of 110 g. It can be concluded that the rate of strain
V. Dubey et al.
228
hardening is large at low loads and this effect decreases as the load is increased.
3.2 Logarithmic index The load dependent nature of the microhardness of materials can be determined by Meyer's Law, L = ad", where a is a constant, L is load, d is the length of the diagonal and n is the logarithmic index. The plot of log L versus log d is shown in Fig. 2. It is interesting to note that this plot consists of four distinct regions which means that the value of n is not the same throughout the range of load. The values of n obtained from the slopes of four distinct regions are 3.23, 2.33, 2.24 and 2.0, respectively. These values of n indicate that the matrix polymer in G F R P belongs to the category of soft material. 9'1° It is evident from Meyer's law that Hv increases continuously with load when n > 2. It can also be observed from Fig. 1 that Hv increases continuously with increasing load as n is greater than 2 for the entire range of load. n approaches 2 in the range of 110-160 g at which Hv becomes independent of load. Thus in the regions of which Hv increases with load, n has a value greater than 2 and in the region in which Hv is independent of load, n has a value equal to 2. Hence, the logarithmic index n is the measure of rate of strain hardening.
2"2
D
2"0 - -
C
1.8
..a
1.6
1"4
--
A
B
1-2
1,0
0"8 O I,
I
I
I
I
2"7
2"8
2"9
3"0
3"1
I 32
tog d
Fig. 2.
Variation of log L with log d.
229
Studies on the microhardness o f G F R P
3.3 Analysis of microhardness The behaviour of microhardness is non-linear up to a load of 110 g. Therefore, the small stress behaviour can be attributed to Newtonian resistance pressure. Kick cited in Ref. 11 has proposed an analysis of the results on hardness according to which the relation between load L and diagonal d of the impression is represented by an equation of the form, L=K,d" (1) where K1 is a standard hardness and n a constant. His analysis, however, has not received wide acceptance on account of the fact that n usually has a value less than 2 and also has in some cases two values, one for the high and another for the low load region. In our case, there are four values of n, viz. 3-23, 2-33, 2.24 and 2-00. It is also evident that the hardness becomes independent of load in the region where n = 2. But the successive layers of the specimen are different in their load-dependent nature. Therefore, we have three values of n for three successive regions below the surface. We can overcome this difficulty by assuming that there are three values of Newtonian resistance pressure of the specimen for its three successive regions. Newtonian resistance pressure, W, is the minimum applied load needed to produce an indentation, since it allows no plastic deformation. Hence considering the specimen resistance pressure to be equal to W, Kick's equation can be modified to L - W = Kzd 2 (2)
140
120 - -
•
n = 3.23
10C
=
8C
6O
40
20
4
6
8
10
12
14
d2
Fig. 3.
Variation of d" with d 2.
16
18
230
V. Dubey et al. 2"1 Ic
17
15 1" 0
LJ i-i ~0~ 0'7 05 0.2
Fig. 4.
1
1
1
2-7
28
2"9
1
I
3"1 3'0 log d
I
I
3"2
3"3
Variation of log d with log (L - W).
where K2 is a constant. The factor W now allows the limiting case to prevail where microhardness is not marked by dependence on the load and the logarithmic index n assumes a value equal to 2. From eqns (1) and (2), we may write Newtonian resistance pressure W as W = K , d " - K2d 2
(3)
Using the above equations, we have plotted d" versus d 2 in Fig. 3 for obtaining the three values of W. The values obtained of Newtonian resistance pressure for successive regions are 2, 5-76 and 3.81g, respectively. Figure 4 shows the plot of log d versus log (L - W). This plot is a straight line and from its slope we obtain the value of n = 2. Hence the Hv-load behaviour in G F R P can also be explained on the basis of Newtonian resistance pressure as proposed by Hays and Kendall 12 and Parashar. 13
REFERENCES 1. Gonzalez, A., Martin, B., Munoz, M. & de Saja, J. A., Polymer Testing, 6 (1986) 361. 2. Gonzalez, A., Martin-Gil, J. & de Saja, J. A., J. Appl. Poly. Sci., 31 (1986) 717. 3. Gonzalez, A., Pastor, J. M., de Saja, J. A. & Perez, A., Die Angewandte Makromoleculare Chemie, 130 (1985) 201. 4. Datt, S. C., Keller, J. M., Parasher, P. & Bajpai, R., Makromol. Chem., Macromol. Syrup., 20/21 (1988) 465-74.
Studies on the microhardness of GFRP
5. 6. 7. 8. 9. 10. 11.
231
Harding, J. & Welsh, L. M., J. Mater. Sci., 18 (1983) 1810-26. Mittal, R. K. & Gupta, V. B., J. Mater. Sci., 17 (1982) 3179-88. Taya, M. &Chen, T. W., J. Mater. Sci., 17 (1982) 2801-8. Bajpai, R. & Datt, S. C., Indian J. Pure Appl. Phys., 24 (1986) 254-5. Onitsch, E. M., Mikroskopie, 2 (1947) 131. Hanneman, H., Metallurgia Manchr., 2,3 (1941) 135. Kotru, P. N., Raina, K. K. & Kachroo, S. K., J. Mater. Sci., 19 (1984) 2582-92. 12. Hays, C. & Kendall, E. G., Metallograph, 6 (1973) 275. 13. Parashar, P., Mechanical properties of some polymers. PhD thesis, University of Jabalpur, 1986, pp. 98, 100.