off-axis tensile properties and fracture in a unidirectional graphite/polyimide composite (celion...

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Off-Axis Tensile Properties and Fracture in a Unidirectional Graphite/Polyimide Composite (Celion 6000/PMR 15) JEFFREY HARPER', J. DANIEL WHITTENBERGER, and FRANCES I. HURWITZ NASA Lewis Research Center Cleveland, OH 44135 Tensile properties of unidirectional Celion 6000 graphite/ PMR 15 polyimide composites prepared by hot molding and cold molding processes were measured at room temperature and 316"C, the upper use temperature of the polyimide resin, at both 45 and 90" to the fiber axis. The resulting fractures were characterized by scanning electron microscopy and ma- terialographic techniques. Variation in tensile properties with processing history occurred in the elastic modulus and strain to failure for specimens loaded at 90" at 316"C, and in the fracture stress, and hence the in-plane shear stress, for those loaded at 45" at room temperature. Significant plastic defor- mation was observed in the 45" orientation at 316°C for ma- terial produced by both processing methods. In general, frac- ture occurred by both failure within the matrix and at the fiber- matrix interface;the degree of interfacial failure increased with temperature. Secondary cracking below the primary fracture surface also was observed. INTRODUCTION N u m e r o u s structural aerospace applications of graphite/polyimide composites involve exposure of these materials to temperatures of up to 316°C (600°F). Tensile testing of graphite fiber reinforced polyimide composites at their upper use tempera- ture has, until recently, been limited by the diffi- culties associated with gripping the specimen at elevated temperature (1, 2). For this reason, there is a sparsity of tensile property data (strength, elas- tic modulus, and strain to failure) for these compos- ites at elevated temperature despite their need in prediction and analysis of mechanical behavior. The data that do appear are based on flexural tests and are calculated from elastic beam theory. However, as the temperature is increased, plastic deformation of the material can occur, resulting in a shifting of the neutral axis and change in the mode of failure from primarily tensile to a mixture of compression and shear. The occurrence of plastic deformation violates the basic assumption of linear beam theory that all deformation is elastic, thus invalidating the test. Recently, Whittenberger and Hurwitz (3) re- ported on the development of a gripping system for direct tensile testing of polymeric composites at elevated temperatures. As an initial test of the spec- imen gripping system, tensile properties of uniaxial 0" fiber orientation Celion 6000 graphite/PMR 15 Present address, Standard Oil Company of Ohio, Cleveland, OH POLYMER COMPOSITES, JULY, 1984, Yo/. 5, No. 3 polyimide composites were measured at both room temperature and 316"C, since the high strength in the fiber direction poses the most severe test of the gripping method. This paper extends the prior work to a study of tensile behavior in Celion 6000/PMR 15 composites at 45 and 90" to the fiber axis. The PMR 15 resin (4, 5) is the product of the in- situ reaction of three monomer components on the reinforcing fibers: 4,4'-methylene dianiline (MDA), the dimethyl ester of 3,3',4,4'-benzophenonetetra- carboxylic acid (BTDE) and the monomethyl ester of S-norbornene-2,3-dicarboxylic acid (NE) to form end-capped imide prepolymers. NE (nadimide) endgroups serve as the site of a thermally induced addition reaction to form a thermoset whose cross- linked structure is proposed to vary with processing history (6). Tensile properties and modes of fracture of uni- directional Celion 6000/PMR 15 composites tested at 45 and 90" to the fiber axis at 316°C are com- pared with those at room temperature. Differences in tensile behavior with variation in processing his- tory also are discussed. EXPERIMENTAL PROCEDURES Eight ply unidirectional Celion 6000/PMR 15 panels, 76 by 203 mm by nominally 1.5 mm thick and containing approximately SO v/o fiber were fabricated with fiber axis at 45 and 90" to the longitudinal laminate axis as described in Ref 3. The fiber lot used (HTA 7-9431) had a longitudinal strain to failure of 1.2 percent as determined by 179

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Off-Axis Tensile Properties and Fracture in a Unidirectional Graphite/Polyimide Composite

(Celion 6000/PMR 15)

JEFFREY HARPER', J. DANIEL WHITTENBERGER, and FRANCES I. HURWITZ

NASA Lewis Research Center Cleveland, OH 44135

Tensile properties of unidirectional Celion 6000 graphite/ PMR 15 polyimide composites prepared by hot molding and cold molding processes were measured at room temperature and 316"C, the upper use temperature of the polyimide resin, at both 45 and 90" to the fiber axis. The resulting fractures were characterized by scanning electron microscopy and ma- terialographic techniques. Variation in tensile properties with processing history occurred in the elastic modulus and strain to failure for specimens loaded at 90" at 316"C, and in the fracture stress, and hence the in-plane shear stress, for those loaded at 45" at room temperature. Significant plastic defor- mation was observed in the 45" orientation at 316°C for ma- terial produced by both processing methods. In general, frac- ture occurred by both failure within the matrix and at the fiber- matrix interface; the degree of interfacial failure increased with temperature. Secondary cracking below the primary fracture surface also was observed.

INTRODUCTION

N u m e r o u s structural aerospace applications of graphite/polyimide composites involve exposure of these materials to temperatures of up to 316°C (600°F). Tensile testing of graphite fiber reinforced polyimide composites at their upper use tempera- ture has, until recently, been limited by the diffi- culties associated with gripping the specimen at elevated temperature (1, 2). For this reason, there is a sparsity of tensile property data (strength, elas- tic modulus, and strain to failure) for these compos- ites at elevated temperature despite their need in prediction and analysis of mechanical behavior. The data that do appear are based on flexural tests and are calculated from elastic beam theory. However, as the temperature is increased, plastic deformation of the material can occur, resulting in a shifting of the neutral axis and change in the mode of failure from primarily tensile to a mixture of compression and shear. The occurrence of plastic deformation violates the basic assumption of linear beam theory that all deformation is elastic, thus invalidating the test.

Recently, Whittenberger and Hurwitz (3) re- ported on the development of a gripping system for direct tensile testing of polymeric composites at elevated temperatures. As an initial test of the spec- imen gripping system, tensile properties of uniaxial 0" fiber orientation Celion 6000 graphite/PMR 15

Present address, Standard Oil Company of Ohio, Cleveland, OH

POLYMER COMPOSITES, JULY, 1984, Yo/. 5, No. 3

polyimide composites were measured at both room temperature and 316"C, since the high strength in the fiber direction poses the most severe test of the gripping method. This paper extends the prior work to a study of tensile behavior in Celion 6000/PMR 15 composites at 45 and 90" to the fiber axis.

The PMR 15 resin (4, 5 ) is the product of the in- situ reaction of three monomer components on the reinforcing fibers: 4,4'-methylene dianiline (MDA), the dimethyl ester of 3,3',4,4'-benzophenonetetra- carboxylic acid (BTDE) and the monomethyl ester of S-norbornene-2,3-dicarboxylic acid (NE) to form end-capped imide prepolymers. NE (nadimide) endgroups serve as the site of a thermally induced addition reaction to form a thermoset whose cross- linked structure is proposed to vary with processing history (6).

Tensile properties and modes of fracture of uni- directional Celion 6000/PMR 15 composites tested at 45 and 90" to the fiber axis at 316°C are com- pared with those at room temperature. Differences in tensile behavior with variation in processing his- tory also are discussed.

EXPERIMENTAL PROCEDURES Eight ply unidirectional Celion 6000/PMR 15

panels, 76 by 203 mm by nominally 1.5 mm thick and containing approximately SO v/o fiber were fabricated with fiber axis at 45 and 90" to the longitudinal laminate axis as described in Ref 3. The fiber lot used (HTA 7-9431) had a longitudinal strain to failure of 1.2 percent as determined by

179

Jeffrey Harper, 3. Daniel Whittenberger, and Frances 1. Hurwitz

the manufacturer. (Newer lots of Celion 6000 have a higher strain capability.) Two molding cycles were used:

(1) Cold mold: The staged prepreg was placed into a cold matched metal die and inserted into a press preheated to 316°C;

(2) Hot mold: The staged prepreg was placed into a mold preheated to 232°C and inserted into a press preheated to the same temperature. In both molding procedures, contact pressure was applied until the temperature of the mold (as mea- sured by a thermocouple inserted in the rail) reached 232"C, at which time 3.45MPa molding pressure was applied. The temperature was in- creased to 316°C at an average rate of 4"C/min, and both pressure and temperature were main- tained for 2 h. The heater was turned off, and the laminate removed from the press when the temper- ature had cooled to 232°C. All composites were then postcured in a convection air oven at 316°C for 16 h.

Panels were examined for gross defects by ultra- sonic C-scan. Standard materialographic techniques were used to determine microporosity and uniform- ity of composite structure.

All tensile tests utilized specimens nominally 200 mm long by 9.5 mm wide, having unidirectional fibers at either 45 or 90" to the longitudinal speci- men axis. Straight-sided, untabbed specimens were roughened in the grip region and held in compres- sion by six bolts, as described in Re$ 3. Because of the relatively low strength of the composites in the 45 and 90" directions as compared with the 0" direction, bolt torques of only 2.8 and 5.1 Nm (25 and 45 in-lb) were employed at room temperature and 316"C, respectively, as compared with the 10.8 and 18.2 Nm (95 and 160 in-lb) torques required for specimens tested in the 0" direction at the same temperatures. Testing was conducted at nominal strain rates of 8 x 10-6s-' in the 45" material and 4 x 10-6s-1 in the transverse specimens. Strain was measured optically with a cathetometer, and stress- strain curves calculated from the load-time and elongation-time data (3). Testing was carried out at both room temperature and 316°C. A minimum of three specimens were tested for each combination of temperature, layup, and processing history.

Standard materialographic procedures were used to examine cross sections of selected test specimens for microcracking and fiber-matrix separation. In addition, fracture surfaces were cleaned ultrasoni- cally with ethanol, sputter coated with 10 nm of gold, and examined by scanning electron micros- copy.

RESULTS Ultrasonic scans of each panel and optical mi-

croscopy of polished cross sections indicated that both hot and cold mold processing methods pro- duced void free laminates. Panels ranged in thick- ness from 1.33 to 1.68 mm; volume fraction fiber (Vf), as determined from sample thickness (7), ranged from .46 to .57. The thickness of any one panel varied by approximately 0.1 mm from one

side of the panel to the other. There was no signifi- cant difference in thickness or fiber volume fraction with processing method. Both hot and cold-molded Celion 6000/PMR 15 composites possess a non- uniform fiber distribution with many fiber-free re- gions, as evidenced by optical microscopy of pol- ished cross sections (Fig. 1).

Representative stress-strain plots for laminates tested at 316°C are shown in Fig. 2. In transverse tension (90" fiber orientation), stress-strain curves were linear to failure (Fig. 2a) . However, in mate- rial tested at 45" to the fiber axis, significant plastic deformation generally was evident (Fig. 2b). By contrast, material tested at room temperature at either 90 or 45" to the fiber axis exhibited linear elastic deformation to fracture. In all cases, elastic moduli were calculated from the linear portion of the stress-strain curves by linear regression tech- niques; regression coefficients were 2.95.

Fracture stress, aij, strain to failure, cij, and elastic modulus, Eij for hot and cold-molded laminates tested at room temperature and 316°C and loaded at 45 and 90" to the fiber axis are summarized in Table 1 . Notation follows the convention shown in Fig. 3, with the 1 axis parallel to the fiber direction. In the 45" orientation, shear stress in the 12 plane, 712, is calculated from the relationship 712 = For completeness, tensile properties of specimens tested with the load direction coincident with the fiber axis (3) as well as shear moduli (Glz) measured in forced torsion with the twist axis coincident with the fiber axis (8) for laminates fabricated by both molding procedures and tested at both room tem- perature and 316°C also are included in Table 1.

Several general trends in properties were noted: (1) Under similar test conditions, the strain to fail- ure and fracture stress of the materials tested at 45" are greater than those at 90"; however, the elastic moduli are similar in both directions. (2) All shear and tensile properties in the 45 and 90" directions are temperature dependent, whereas the tensile properties at 0" orientation are temperature inde- pendent. (3) In transverse tension, the strain to failure is larger at room temperature than it is at 316°C.

Statistical comparison of tensile data obtained for hot and cold-molded laminates using a t-test shows

'

:

Fig. 1 . Typical cross section of (a) cold molded and (b) hot molded Celion 6OOO/PMR 15 laminates.

180 POLYMER COMPOSITES, JULV, 1984, Vol. 5, No. 3

Tensile Properties of Unidirectional Celion 6000 GraphitelPMR 15

10

5 .

that significant variation (at the 95 percent confi- dence level) in tensile properties with processing history occurs (1) in transverse tension at elevated temperature in the elastic modulus E 2 2 and strain to failure 622; (2) at 45" loading in the room tem- perature fracture stress, uxr and hence in the in- plane shear stress, 712; and (3) in the shear moduli, Glz, at both test temperatures.

In samples fractures at 45" to the fiber axis, total

'

l5 r

4o

HOT MOLDED 316' C -45" ORIENTATION

L - 7.5x 10-6 s-1 - EF 1.52 pt

COLD MOLDED 316' C -9G" ORIENTATION

- 2 . 5 ~ 1 6 ~ s-l

GAUGE LENGTH = 38.1 mm

LE - 2.8 GPa

strain to failure at 316°C is similar to that at room temperature. However, plastic deformation equal to approximately one-fourth the total strain was observed in both hot and cold molded laminates tested at elevated temperature. For those materials which exhibited plasticity, the proportional limit occurred at approximately 0.7 percent strain; elas- tic deformation at fracture averaged 1.0 percent, and the plastic strain at failure was nominally 0.35 percent.

Typical transverse tensile fractures are shown in Figs. 4 and 5. At room temperature (Fig. 4 ) failure occurred within the matrix as well as at the fiber- matrix interface. N o longitudinal fiber splitting is observed; however, a number of fibers are fractured transverse to their axes. Both cold and hot molded materials exhibit primarily brittle fracture; both show evidence of matrix shearing. A limited amount of microplastic matrix deformation can be seen (Fig. 4b); however, the occurrence of localized heating on sputter coating cannot be ruled out as a contrib- uting factor in this observation.

At 316"C, both cold and hot-molded laminates (Fig. 5a and b ) again exhibit a mixture of matrix, interfacial, and transverse fiber fracture. Compari- son with room temperature fractures (Fig. 4 ) shows that more fiber pullout occurs at elevated temper- ature on both halves of the fracture surface, with a slight increase in microplastic deformation: how- ever, the overall appearance remains primarily one

4

(a) (bl Fig. 3. lllustration of nomenclature convention for orthogonal axes of a unidirectional composite. ( a ) General case and (b ) laminate tested at 45" to thefiber axis.

Table 1. Tensile and Shear Properties of Unidirectional Celion 6000/PMR 15 Composites at Room Temperature and 316OC. All Values Represent a Minimum of Three Determinations Except as Otherwise Noted. Standard Deviations are Given in Parentheses.

Molding Process ~

property Load direction relative to fiber axis Hot Cold

25OC 31 6OC 25OC 31 6°C

- 123.0 (6.8) 121.2 (4.6) 1 1 8.1 (5.5) - 1.20 (.12) l.l6(.07) 1.14(.08)

Gi2 (GPaY Twist about fiber axis 5.11 (.21)' 3.54 (.08)' 4.21 (.20)' 2.88 (.17)' 47.8 (8.1) 16.0 (3.0)

€22 (GPa) 7.59 (.65) 4.06 (.70)' 7.74 (.94) 2.86 (51) ' c22 (%I .71 (.04) .37 (.08)' .64 (.16) 5 6 (.07)' a, (MPa) 45O 103.2(16.2)' 41.5 (6.7) 79.9 (0.4)' 34.7 (4.0) Ex (GPa) 7.28 (1.65) 4.17 (.88) 8.114 3.88 (.36) 6 ("4 1.43 (.40) 1.35 (.13) .974 l.l8(.42) 712 (MPaI3 51.6 (8.1r 20.8 (3.4) 40.0 (0.2)' 17.3 (2.0)

nil (MPa)' 0" - 1440 (63.0) 1388 (92.0) 1336 (91 .O) Ell (GPa)' 611 ("4'

(MPa) goo 53.8 (1.7) 14.8 (3.3)

* Indicates statistical ditterence between hot and cold molded material. 'FnwnRrd.3. * Fnwn M. 9. 'Cakulatd fmm the relationship TI* = 0.m 'Single determination.

POLVMERCOMPOSITES, JULY, 1984, V d . 5, No. 3 181

Jeffrey Harper, J . Daniel Whittenberger, and Frances 1. Hurwitz

Fig. 4 . Fracture su7face of composites tested at 90" to the fiber axis, ambient temperature. (a ) - (b ) Cold molded and ( c ) hot molded material.

of brittle failure. Some matrix shear also is ob- served.

Typical fracture surfaces of materials tested in the 45" direction are presented in Figs. 6 and 7. At room temperature a combination of matrix crack- ing, matrix shear, interfacial failure and transverse fiber breakage are observed (Fig. 6 ) . Shear is seen to have occurred in more than one direction on the same surface, as indicated in Fig. 6u. No major differences are noted between fractures in hot and cold molded composites. Variation in the width of matrix rich regions occurs in both materials (com- pare resin rich areas depicted in transverse section,

Fig. 5. Fracture surface of composites tested at g o " , 316°C. (a ) Cold and ( b ) hot molded material.

shown in Fig. I). Most matrix shearing takes place in the wider resin-rich zones (Fig. 6).

At 316°C fracture in both hot and cold molded materials is characterized by pullout of fiber bun- dles parallel to the load direction (Fig. 7u and c ) . Enlargement of the areas (Fig. 7b and d) shows failure to be primarily interfacial, as evidenced by the pullout of clean fibers. Some matrix tensile fracture and transverse fiber breakage also occurs. Matrix shear is evidenced to a much lesser extent than at room temperature.

Examination of polished materialographic cross sections (thickness-gage length planes) reveals little if any difference between the two molding cycles. Fiber orientation, however, is important; fiber pull- out is much more evident in the 45" orientation (Fig. 8b) than in the transverse direction (Fig. 8u). The microstructure at the fracture surfaces does not vary with test temperature. Secondary damage below the surface is found at both 45 and 90" orientations, and is more evident at elevated tem- peratures. A typical example of secondary cracking is shown in Fig. 8c, where interfacial failure can be seen to be an important part of crack formation.

DISCUSSION In composites, ply strength is weakest transverse

to the fiber direction. The transverse composite modulus ( E z z ) in general is slightly higher than that of the matrix modulus (Em), as the fibers limit matrix

182 POLYMER COMPOSITES, JULY, 7984, Val. 5, No. 3

Tensile Properties of Unidirectional Celion 6000 GraphitelPMR 15

Fig. 6. Fracture surface of composites tested at 45" to thefiber axis, room temperature.

deformation (9); for this same reason the composite strain is less than the strain capability of the matrix alone. The result is a reduction in composite trans- verse strength relative to that of the matrix material by itself. The transverse Young's modulus and strain to failure in glass reinforced epoxy and polyester composites have been shown to depend on fiber volume fraction, Vf (1 0); increasing Vf corresponds with decreased transverse failure strain and higher transverse modulus. In this study Vf ranged from 0.51 to 0.S6 for the cold molded material, and from 0.52 to 0..57 for hot molded samples. Regression analysis showed no correlation between € 2 2 or Ezz and Vf over the narrow range of volume fractions represented here, nor could the difference in E2z between hot and cold molded material at 316°C be attributed to differences in Vf between the hot and cold molded laminates.

Previous studies (6) of hot and cold mold proc- essing have shown that hot molded Celion 6000/ PMR 1 S has a 25 percent higher shear modulus ( G ) than do cold molded composites with the same fiber, matrix stoichiometry and fiber volume frac- tion, suggesting a major influence of thermal history on matrix and/or interface structure. Additionally, in microstructural and weight loss evaluation of

Fig. 7. Fracture surface of composites tested at 45" to the fiber axis, 316°C. (a) - (b) Cold molded and (c)-(d) hot molded laminates.

samples exposed in a convection air oven at 316°C (1 l), hot molded laminates exhibited a greater re- sistance to thermo-oxidative degradation than did

POLYMER COMPOSITES, JULY, 1984, Vd. 5, No. 3 183

Jeffrey Harper, J . Daniel Whittenberger, and Frances 1. Hurwitz

Fig. 8. Polished thickness-gage length plane sections of hot molded composites fractured at ( a ) go", room temperature, (b) 45", room temperature and (c) 45", 316°C.

those processed by the more conventional cold mold procedure. Taken together with the tensile and shear data in this study, it would appear that matrix and perhaps interfacial properties are influ- enced significantly by thermal processing history. Both processes yield matrices which appear to be capable of some microplastic deformation; however the hot molded material has the higher transverse modulus at elevated temperature, and correspond- ingly smaller transverse strain to failure (Table I ) . At 316"C, strain to failure is less than at room temperature for both processing methods, and the

degree of fiber pullout is increased, indicative of an increase in failure at the fiber-matrix interface as contrasted with the greater degree of the intra- matrix failure at room temperature.

In the 4.5" samples tested at room temperature the mode of failure is primarily matrix shear, with hot molded laminates exhibiting higher shear strength than cold molded material. At 316"C, fail- ure occurs partially by pullout of fiber bundles into the load direction followed by tensile rupture of those fibers. Fracture is, for the most part, interfa- cial, with secondary cracking occurring below the primary fracture surface. The occurrence of plastic deformation, roughly equal to one-fourth the total strain, supports our initial contention that applica- tion of elastic beam theory in flexure testing of graphite fiber/PMR 15 composites, particularly at elevated temperature, is invalid. The presence of plastic behavior is consistent with the previous (9) observation of plasticity in interlaminar shear spec- imens tested at 316°C. No significant difference with molding cycle is seen. On the basis of the fracture analysis presented here, however, the in- terfacial and matrix influences have not been clearly resolved.

SUMMARY OF RESULTS Characterization of the tensile behavior of hot

and cold molded Celion 6000/PMR 15 laminates at both room temperature and 316°C showed that:

(1) In transverse tension, the fracture stress at room temperature was approximately three times that at 316°C. Tensile behavior was elastic to frac- ture at b,oth test temperatures. At elevated temper- ature modulus and strain to failure varied with processing history; the hot-molded material ex- hibited a higher strain to failure and lower modulus than its cold-molded counterpart. Composite be- havior reflected both matrix and fiber-matrix inter- facial properties. Fiber pullout increased at 316°C relative to that observed at room temperature. Sec- ondary cracking below the primary fracture surface was evident, principally at elevated temperature.

(2) At 4.5" to the fiber axis fractures showed evidence of significant matrix shearing at ambient temperature. The room temperature shear strength was 2 to 2% times that at 316°C. At room temper- ature, the cold-molded material had the higher shear strength; at elevated temperature, no differ- ence in shear strength with processing was ob- served. At 316°C both hot and cold molded lami- nates showed evidence of plastic deformation. Frac- ture at elevated temperature was primarily by fiber pullout. Secondary cracking below the primary fracture surface was seen, particularly at 31 6°C. Fracture stress was 2 to 3 times that measured at 90" to the fiber axis.

ACKNOWLEDGMENTS One of the authors (J. H.) wishes to acknowledge

support of this work by the NASA Lewis Coopera- tive Training Program in conjunction with the Uni- versity of Cincinnati.

184 POLYMER COMPOSITES, JULY, 1984, Vof. 5, No. 3

Tensile Properties of Unidirectional Celion 6000 GraphitelPMR 15

REFERENCES

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2. M. Sittig, ed. “Carbon and Graphite Fibers”, pp. 384-385, Noyes Data Corp., New Jersey (1980).

3. J. D. Whittenberger and F. I. Hurwitz, Polym. Comp., 3,75 (1982).

4. T. T. Serafini, P. Delvigs, and G. R. Lightsey,]. A w l . Polym. Sci., 16,905 (1972).

5. T. T. Serafini, in International Conference on Composite Materials, Vol. 1, E. Scala, ed., pp. 202-220, AIME, New

York (1976). (Also NASA-TM-X-71682, 1975.) 6. F. I. Hurwitz Polym Comp., 3, 152 (1982). 7. J. D. Whittenberger, F. I. Hurwitz, J. J. Ricca, and R. M.

Jurta, J . Muter. Sci. Lett., 1, 249 (1982). 8. B. W. Rosen J . Comp. Mater., 6,552 (1972). 9. B. D. Agarwal and L. J. Broutman, “Analysis and Perform-

ance of Fiber Composites”, pp. 34-42, Wiley, New York (1980).

10. J. Bailey and A. Parvizi,]. Muter. Sci., 16, 649 (1981). 11. F. I. Hurwitz and J. D. Whittenberger, in “Technology

Transfer”, Proceedings of the 13th National SAMPE Tech. Conf., pp. 477-486, SOC. Advancement Mater. Process Eng., Azusa, CA (1981).

POLYMER COMPOS/lES, JULY, 1984, V d . 5, No. 3 185