Ind. Eng. Chem. Prod. Res. Dev. 1984, 23, 81-85
81
Bowen, R. L. J . Dent. Res. 1985, 4 4 , 690. Bowen, R. L. Pedletr. Dent. 1982 4(1), 10. Bowen, R. L.; Cobb, E. N.; Rapson, J. E. J . Dent. Res. 198211, 61(9), 1070. Bowen, R. L.; Cobb. E. N.; Setz, L. E. Dsntfstry 82 1982b, 2(4). 11. Bowen, R. L.; Cobb, E. N. J . Am. Dent. Assoc. 1983. Cartledge, G. H. J . Am. Chem. Soc. 1941, 63, 906. Ingram, D. J. .; kdgson, W. G.; Parker. C. A.; Rees, W. T. Nature (London) 1855, 176, 1227. Oster, G.; Yang, N . I . Chem. Rev. 1968. 68, 143. Parker, C. A. Fmc. R . Soc. London 1953. 220, 104. Parker, C. A. Trans. Farahy Soc. 1954, 50, 1213. Parker, C. A.; Hatchard, C. 0. J . phvs. Chem. 1959, 63, 22. Porter, G. B.; Doering, J. G. W.; Karanka, S. J . Am. Chem. SOC. 1962, 84, 4027.
at room temperature. The broken surfaces are shown in Figures 3 and 4. Conclusions From the foregoing evidence, the sequential application of the three active agents to a dentin surface initiates polymerization by a free-radical mechanism (the methacrylate groups of N T W M A and PMDM would probably not polymerize by ionic mechanisms under these conditions). A more detailed understanding of the mechanisms by which this polymerization occurs will allow a broadening of the scope of materials and conditions that are potentially available, and will increase the probability that these in vitro methods will be transferred to industrial and clinical utility. Assays of biological safety, which have commenced, must precede clinical trials. Registry No. Fe2(C20A)3, 2944-66-3; NTG-GMA, 83418-59-1; PMDM, 83418-60-4. Literature Cited
Received for review July 25, 1983 Accepted October 11, 1983 This investigation was supported, in part, by Research Grant DE05129-05A1 to the American Dental Association Health Foundation from the National Institutes of Health-National Institute of Dental Research, and is part of the dental research program conducted by the National Bureau of Standards in cooperation with the American Dental Association Health Foundation.
Book of ASTM Standards, Part 27; American Society for Testing and Materials: Philadelphia, PA, 1964; p 212.
Flexural Properties of Glass Fiber Reinforced Rigid Polyurethane Foam Klyotake Morlmoto' and Toshlo Surukl Nisshin Spinning Go., Ltd. Nishiarai Laboratoty, 1-18- 1, Nishiarai Sakaecho, AdachLku, Tokyo 123, Japan
Ryutoku Yobomlya Department of Industrial Ghemktry. Ghiba Institute of Technology, 2- 17- 1, Tsudsnuma. krashino-Shi, Chid 275, Japan
The flexural properties of rigid polyurethane foams (PUF) and glass fiber reinforced rigid polyurethane foams (FRU) with different expansion ratios were investigated by the bending test. Both the flexural modulus and the flexural strength increased and the temperature dependencies decreased when the longer fiber was used to reinforce the polyvethane foam. The increased apparent density of the matrix also accelerated these tendencies. The reinforcing effect of glass fiber was analyzed quantitatively from the fiber efficiencyfactor, k,, with the simple rule of mixture expressed in the following equation: E, = E,V, k,€,V,. It was concluded that the actual values of interlaminar shear strength obtained by a short beam method agreed well with the theoretical values.
+
Introduction Rigid polyurethane foam (PUF) is used for thermal insulation in various fields (Saunders et al., 1964) such as systems of refrigerated transportation including refrigerators and freezers, plants such as piping and tanks, ships and vehicles, and buildings due to excellent thermal insulating characteristics. Recently, relatively low-expanded, high-density PUF reinforced with glass fibers have been used for structural material. The molding techniques and uses of reinforced reaction injection molding (R-RIM), for example, an injection molding of PUF solution preliminarily blended with milled glass fiber, have been rapidly developed and the characteristics have been reported (Schulte et al., 1979; Sistak, 1979). However, the physical properties of PUF reinforced with milled glass fiber have not been substantially improved except for the modulus of elasticity, impact resistance, and dimensional stability (Brownbill, 1980). 0196-432118411223-0081$01.50/0
Meanwhile, PUF reinforced with long fiber has not been commercialized successfully owing to its difficult moldability, although the flexural and tensile characteristics are expected to be remarkably improved (McDonell Douglas Corp., 1969; Ogawa et al., 1980). In this paper, the flexural characteristics of rigid polyurethane foam reinforced uniformly and oriented randomly in a plane with glass fiber (FRU) are investigated for samples in which the volume content of glass fiber is constant and the expansion ratio of matrix varies with the length of glass fiber.
Experimental Section Materials. Molding of FRU. (a) FRU-L. A sheet of glass fiber continuous strand mat (Asahi Fiber Glass Co., LM.;CSM no. 8600-600,600g/m2) was placed in a metallic open mold of a rectangular shape having an inside area of 1000 X 1000 mm and a depth of 50 mm. 0
1984 American Chemical Society
82
Ind. Eng. Chem. Rod. Res. Dev., Vol. 23, No. 1, 1984
Table I. Matrix (PUF) Formulation component composition
A
B
structure
parts by wt
polyoxypropylated pentaerythritol (equiv 140, HD-402; Sanyo Kasei Co., Ltd.)
100
triethylenediamine (catalyst) (Dabco; Air Products and Chemicals Inc.)
0.3
silicon surfactant (SH-193; Tore Silicon Co., Ltd.)
2.0
polyme thylene-pol yphen ylene-polyisocyanate (equiv 140, crude MDI 44V-20; SBU Co., Ltd.)
103 NiO C'
C
Fron-11 (blowing agent) (Asahi Glass Co., Ltd.)
0 - 25
Cl-C-F Ll
isocyanate index (NCOIOH) rate of foaming (at 20 "C) The whole PUF solution, prepared by the mixing prescribed amount of liquids A, B, and C shown in Table I with a hand-mixer, was quickly poured into the mold and the contents were pressed down to 3 mm thickness with a top plate just fitting the mold. This was left to stand for 30 min. During molding, the temperature of the mold was kept at about 40 OC. (b) FRU-M. The prescribed amount of 13 mm length chopped strands (Fuji Fiber Glass Co., Ltd.; FES no. 130730) was mixed with the isocyanate component (liquids B and C) and thoroughly dispersed before the addition of the poly01 component (liquid A). The following operations were carried out according to the procedure of (a) without glass fiber continuous strand mat. (e) FRU-S. The prescribed amount of 3 mm length chopped strands (Fuji Fiber Glass Co., Ltd.; FES no. 30730) was added instead of 13 mm length according to the procedure of (b). The FRU samples for the determination of interlaminar shear strength were prepared by molding boards of 200 X 200 X 15 mm size, according to the above-mentioned procedure. Molding of PUF. PUF was prepared by mixing liquids A, B, and C according to the above-mentioned procedure without any glass fiber. The compounding formulation, density, glass fiber content, expansion ratio of matrix, and flexural properties at room temperature (25 "C) are listed for each sample in Table 11. Bending Test. The bending test was conducted according to JIS K-6911 with a Shimadzu Autograph DSS-2OOO. The sample size was 80 X 25 X 3 mm, at a cross head speed of 5 mm/min and bending span length of 50 mm. Determination of Interlaminar Shear Strength. The interlaminar shear strength was determined by use of a test specimen 25 mm wide and 15 mm thick according to the 3-point-bending test by the short beam method (Christiansen et al., 1974). The interlaminar shear stress, 7 , is given by 3 P 7 = -(1) 4 bd where P is the load, b is the width, and d is the thickness
1.03 cream time 100 s rise time 240 s
'
Jt
I
AL-
"C
I I , ,
1
C
L
I
F
Figure 1. Flexural moduli of FRU and PUF vs. temperature.
of the test specimen. The tensile and compressive stresses acting on the outer layers of the test specimen, a, is given by 3 P a = - -(L/d) 2 bd then the following equation is obtained from (1)and (2). a = 2~(L/d)
(3)
When 7 is constant in eq 3, a is proportional to L l d . Therefore, 7 represents the slope of a straight line crossing the origin of a coordinate consisting of L l d on the abscissa and of a on the ordinate. In the experiment, L l d could not be lessened below 1.5. Only when the line accurately crossed the origin was the interlaminar shear strength calculated. Observation of Fracture Cross Section. The nature of the fracture cross section caused by bending was observed by a scanning electron microscope (Akashi: MSM4). Results and Discussion Reinforcing Effect of Fibers upon the Flexural Modulus. Flexural moduli of FRU reinforced with different lengths of glass fiber and expansion ratios are shown against temperature in Figure 1 with those of PUF. It reveals that the longer the glass fiber of reinforcement (FRU-S < FRU-M < FRU-L), the greater is the flexural modulus and the smaller is the dependence of the flexural modulus upon temperature. In other words, as the fiber length is increased, the reinforcing effect is increased and the stiffness is improved. A simple rule of mixture is found
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23,No. 1, 1984 83 FRU-L
0.2 0.1 -0
0.6
0 8 9,"
1.0
,
1.2
0.6
0.8
A p p a r e n t dsns>t.y
1.0 Of
1.2
0.6
foam matr,x
0.8
1 g/"
1.0
1.2
2.
0.2
)
Figure 2. Relation between &E and the apparent density of foam matrix.
c L
3.1
e
to quantitatively evaluate the reinforcing effect of the glass fiber as follows (Hayashi, 1971, pp 27-41) E , = E,V, + kEEfVf (4) where E,, E,, and Ef are the flexural moduli of composite, matrix (PUF),and reinforcement (glassfiber), respectively, V, and Vf are volume fractions of matrix and reinforcement, respectively, and kE is the fiber efficiency factor. The fiber efficiency factor, ItE, depends upon fiber length, degree of orientation, and Ef/E,, and it ranges for 0 to 1. When Ef/Emis small, and the longer fiber is so perfectly orientated as to be an ideal composite, the value of kE approaches 1. kE of each FRU sample was calculated when the flexural modulus, Et, of glass strand was constant (Ef = 7100 kg/mm2) (Hayashi, 1971, pp 82-87), in the temperature range of 25 to 100 "C,and flexural modulus of matrix, E,, was obtained from the experimental value of PUF for comparison. Figure 2 shows the relation between kE and the apparent density of the matrix. It reveals that the higher the apparent density, the greater is kE of every sample, and the longer the fiber, the greater is kE. Moreover, it is found that the higher the temperature, the lower is kE, approaching zero especially in FRU-S reinforced with short fibers. The maximum value of kE of FRU-L is approximately 0.55 (flexural modulus of matrix is 300 kg/mm2 or more). The fiber efficiency factor of nonorientated long fibers is 3/8 according to Krenchel (Holliday, 1966). His value is smaller than that of FRU-L reinforced with continuous fibers, nearing the maximum value, 0.35, of FRU-M reinforced with fibers of 13 mm length. Nielsen et al. (1968) also calculated the fiber-efficiency factor, kE, of composites reinforced, at random in a plane, with fibers which are longer than critical fiber length by the following equation
( E O )= E m V m + k&fVf
(5)
where (EO) is Young's modulus for the case of random orientation of fibers in a plane, given by
where V , and Vf are the volume fractions of matrix and fibers, respectively. Figure 3 shows the relation between kE obtained by this experiment or kE of the above-mentioned Nielsen's calculated value and the flexural modulus of matrix, E,, or ratio of moduli, Ef/E,. Nielsen's value of kE is 0.30 at Vf = 0.09 and Ef/E, = 25.7 (marked 0 in Figure 3). Under the same conditions, the experimental results of kE for FRU-L, FRU-M, and FRU-S are 0.51,0.29, and 0.28, respectively. They, except FRU-L, agree well with Nielsen's value. The experimental curve for FRU-M agrees relatively well with that of Nielsen's calculated curve, while the curve for FRU-S is lower than Nielsen's curve, especially at lower elasticity of matrix. It means that the
1 0c
276 300
??C
I
1
100
tc 6C
30
A0
25.-
Figure 3. Dependences of k~ on the flexural modulus of foam matrix. FRU-8
FRU-M
FRU-L
PUF
UPUF-3
25
50
75
100 25
50
75
100 2 5
Temperature
(
5C 7 5
133
25
50
75
100
C j
Figure 4. Flexural strengths of FRU and PUF vs. temperature.
I
0.3
1
FRU-L
FRU-M
0.2
scr" 0.1
0 0.6
0.8
1.3
1.2
0.6
2.3
1.0
Pm , R p o a r e n t d e n s i t y o f
1.2
0.6
foam matrlx
9.81.0
:
g/cm?
1.2 )
Figure 5. Relation between k, and the apparent density of foam matrix.
shorter the fiber, the more is the fiber efficiency factor apt to be affected by the flexural modulus of matrix. Flexural Breaking and Adhesion between Matrix and Fiber. Flexural strengths of FRU and PUF are shown in Figure 4. The results show that the flexural strength increases in the following order: PUF < FRU-S < FRU-M < FRU-L. The longer the fiber, the lower is the dependence on temperature. The following rule of mixture is used to illustrate the trend of flexural strength U, = u,V, + k,ufVf (6) where uo u,, and uf are flexural strengths of composite, matrix, and fiber, respectively, V, and Vf are volume fractions of matrix and fiber, respectively, and k, is the fiber efficiency factor. In this calculation the value of uf was assumed to be constant (285 kg/mm2) (Hood, 1963) in the temperature range of 25 to 100 "C. The relation between k , calculated from eq 6 and the apparent density of the matrix, p,, is shown in Figure 5. It reveals that the
84
Ind. Eng. Chem. Rod. Res. De".. Vol. 23. No. 1. 1984
I
e e m m
c m o m
e e o m m m m m
-300
3-00
3.400.4000
"-!a??
-!9??
,
'
'F
1?mui?cq??
A a Figure 6. Cross sections of fractured samples for bending test.
Table 111. Interlaminar Shear Strenflh of FRU at 2 5 "C interlaminar shear strength fiber density, r(obsd), rb(calcd), sample no. kgh" clcm' k a h " of FRU leneth. I . mm
s-1' s-2'
3 t
5-3'
f
S-A' .
t 13 t
M-1' M-2' M-3' M-4' L-1' L-2'
m o o -
oe-o Wmem
0
0 - c (D
0000
mwom
3 N N
o o w m m3mm
m o c w m m m o
0
0
r-
W
-9e-N
0 - c -
0000
o3 N o m m NN
O N ~ O ( D W N ~ -
b m 3 3 N 3 . 4
00000000
m w e
. u
M C
I
0000 0000
0000 00000000 0000 00000000~ N ~ N ( DW ~ N W w m ~ w m c m w
mNN.4
m N N 3
O N N d C O N N 3
t
continuous
L-3'
t t
L4'
f
1.88 1.51 0.98 0.50 2.58 1.98 1.12 0.55 3.30 2.15 1.51 0.79
M C
1.23 1.20 0.91 0.66 1.71 1.62 1.40 1.14
-
fiber efficiency factor, k,, is dependent on both the expansion ratio of the matrix (apparent density of the matrix) and the temperature. Since the dependences of ko on the expansion ratio and on the temperature are great in FRU-L, though the reinforcing effect of fiber on composites is the highest, it is necessary to pay attention to design FRU-L as a structural member. Although the nature of flexural breaking of FRU varies with the types of samples and the temperature, they were divided into the following three types: (a) the test piece was completely broken into two parts; (b) cracks were observed on the pulling part; and (c) buckling occurred on the compression part. The nature of breaking changed according to the order of (a) (b) (c) as the temperature increased. Scanning electron micrographs of the fractured surface are shown in Figures 6A and B. This behavior was similar to that provided by Beaumont et al. (1972) and Takesima et al. (1977) as follows. Cracks occur on the superficial layer first and then peeling takes place from the cracked surface along the fibers by the difference of the adhesion between matrix and fiber, followed by cutting of the fibers (Figure 6A) or by falling off of the fibers from the matrix (Figure 6B) at the place where the peeling occurred. The interlaminar shear strength of each sample is listed in Table 111. Although the interlaminar shear strength was not so clearly observed in high density (1.2 g/cm3 or more) samples, the lower the apparent density, the smaller was the interlaminar shear strength in general. The interfacial shear strength, theoretically calculated according to Takeshima et al. (1977), was compared with the experimental data. The breaking mechanism is considered in that a crack occurs on the matrix portion followed hy peeling at the interface between fiber and matrix
- -
w + c c l I I I
o3 N o m m N N
t
1.25 1.07 0.81 0.50 1.30 1.10 0.85 0.54 1.32 1.12 0.88 0.59
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 1, 1984
and then the fiber falls off from the resin because the fiber is cut by the part that peeled off. Stress, uo, acting on the fiber when peeling takes place at the interface, is expressed in the following equation, regardless of friction at the interface (Takaku et al., 1973) no = 27b/(Y (7) a = [2Gm(1- K)/Ef In (ro/rf)]l/z
(8)
where G, is the modulus of shear elasticity of the matrix, K is a parameter representing slippage of the surface (Yamaki, 1976), Ef is the modulus of the fiber, 2r0 is the distance between fibers, rf is the radius of fiber, and 7 b is the interfacial shear strength. Assuming that the peeling length of fiber on which a stress, uo, acts increases as the peeling progresses at the interface and the fiber is cut at the weakest spot, the length of falling-off-fiber is obtained as follows. First the strength distribution, P(u), of minute length, Ax, of fiber is assumed to be a normal distribution; P(u)is expressed in the equation 1
(9)
where a is the average strength of fiber and 8 is the standard deviation. When t is substituted for the term of (a - a)/& the distribution of t is as follows
Here regarding to = (ao- @/8,the cutting probability of a fiber having Ax length is expressed in the equation S = f o P o ( t )dt -0I
The average length of falling-off-fibers (I,) obtained by the equation
1, = Ax/s
is, therefore, (12)
Since the strength of the minute length, Ax, of fiber is impossible to measure, the strength of fiber having Ax length is obtained from the strength distribution of fibers having nAx length. The strength distribution, g(a), of fibers having nAx length is obtained by the equation
The distribution o f t of fibers having nAx length is expressed in the equation
85
(16)
8=W2O
Getting a and 8 from eq 15 and 16 and tofrom eq 10 and 11, a. is obtained from the equation uo = a to2. When the value obtained in the above way is substituted for uo in eq 7, the interfacial shear strength, 7b, can be obtained. The results of calculations are shown in Table 111, assuming that a,, = 285, 2, = 40, 80 = 0.308, and f = -4.096 for FRU-M, and a,, = 290, Zex = 35, Bo = 0.359, and f = -3.290 for FRU-S. These results of FRU-M and FRU-S agree well with the experimental data in the apparent density ranges of 0.8 to 1.0, while they differ in higher and lower apparent density ranges. Although the reason for the above phenomena is not clear, it is considered to be so because the effect acting among the cells in the matrix foam is great and also the sample of high expansion ratio is of sandwich structure which has the inner layer with relatively lower density than that of outer skin layer. Conclusions The flexural properties of rigid polyurethane foam (PUF) and glass fiber reinforced rigid polyurethane foam (FRU) were carried out by the bending test. Both the flexural modulus and the flexural strength increased and their temperature dependences decreased when the longer fiber was used to reinforce the polyurethane foam. The increased apparent density of matrix also accelerated these tendencies at constant volume fractions of glass fiber. The fiber efficiency factors for flexural modulus, kE,were 0.55 for continuous fiber, 0.29 for 13 mm length fiber, and 0.28 for 3 mm length fiber at Ef/Em= 25.7. Acknowledgment This work has been supported by Nishiarai Chemical Laboratory in Nisshin Spinning Co., Ltd. The authors acknowledge the great help and advice from Mr. K. Kimura, Director of Chemical Division of the company, and they also wish to express their thanks to Professor A. Nakajima of Kyoto University for his continued advice and helpful discussions. Literature Cited
+
Beaumont, P. W. R.; Harris, B. J . Meter. Scl. 1072, 7, 1265-1279. Brownbill, D. Mod. Plest. Int. Oct 1080, 41-43. Christlansen, A. W.; Liiiey, J.; Shortail, J. B. Flbre Scl. Techno/. 1974, 7, 1-13. Hayashi, T. “Fukug6 Zakyb Kbgaku (Composite Material Technology)”; Nikkagiren Publications: Tokyo, 1971; pp 27-44. Hayashi, T. “Fukug6 Zakyb KOgaku (Composite Material Technology)”; Nikkagiren Publications: Tokyo, 1971; pp 82-87. Hoillday. L., Ed. “Composite Materials”; Elsevier Publishing Co.: London, 1966; pp 165-171. Hood, J. C. “A Quality Assurance Test for Tensile Strength of Glass Fiber Strands, Yarns, and Rovings”, 18th Annual Technical Conference, 1963. Reinforced Plastics Dlvlslon, the Society of the Plastics Industry, Inc. Section 9-E. McDonneil Douglas Corp. Mod. Plest. Nov 1060, 66-67. Nieisen, L. E.; Chen, P. E. J . Meter. JMLSA June 1068, 352-358. Ogawa, F.; Morimoto, T. Int. Prog. ðenes, 1980. 2 , 85-89. Seunders, J. H.; Frisch, K. C. “Polyurethans: Chemistry and Technology, Part 11. Technology”; Interscience Publishers: New York, 1964; pp 268-298. Schuite, K. W.; Boden, H.; Seel, K.; Weber, C. Eur. J . Cell. Plsst. 1970, 2(2), 61-67. Sistak, B. J. Plest. Des. Process. 1079, 7$(10), 20-26. Takaku, A.; ArrMge, R. 0. C. J . phys. D : Appl. phys. 1973, 6, 2038-2047. Takeshlma, M.;Yamaki. J. Kobunshi Ronbunshu 1977, 34(5). 367-375. Yamaki, J. J . Phys. D : Appl. Phys. 1976, 7, 115-131.
.
The shape of go@)for various n, the average of t, f, and the standard deviation, Eo, under the distribution of go@) can be obtained from eq 14. From the average strength, a,,, of fibers having nAx length and the standard deviation, Z,, obtained by the experiment, the shape of g(u), 8,and a, is acquired by the equations a = aex- fZ,,/Zo (15)
Received for review March 8, 1983 Revised manuscript received August 30, 1983 Accepted September 27, 1983
