Progress Report No. 1:
A report of work carried out during the
period lst October, 1967 to 31st March, 196

Dootson, M.

English

1. General Progress
In the six months from April to September 1968 the task of primary
importance has been to design lateral extensometers and to improve the
longitudinal extensometer and consequently enable reproducable measurements
of the deformations undergone by creep specimens to be made … [cont.]

CERES Research Repository (Cranfield Univ.)

CoA Memo. No. 162 September2 1968 THE COLLEGE OF AERONAUTICS DEPARTMENT OF MATERIALS The time-dependent mechanical properties of fibre reinforced polymers - by - M. Dootson, B.Sc. (Eng.) Progress Report No. 2 A report of work carried out during the period 1st April to 30th September, 1963. Contents Page No. 1. General Progress 	 1 2. Apparatus Development 	 1 2.1 Longitudinal extensometer 	 1 2.2 Lateral extensometer 	 2 2.3 Specimen production 	 3 2.4 Alterations to the tensile creep testing machine 3. Experimental results  3.1 Young's Modulus of 1 E1 -glass fibres 	 4 3.2 Creep compliance of unreinforced resin 	 5 3.3 100 second creep compliance of the uniaxially reinforced resin 	 6 References 	 7 Figures 1. General Progress In the six months from April to September 1968 the task of primary importance has been to design lateral extensometers and to improve the longitudinal extensometer and ccnsequently enable reproducable measurements of the deformations undergone by creep specimens to be made. Resulting from experience gained in testing using the existing tensile creep testing machine, slight alterations are being made to the five further machines now in production. So that specimens of unreinforced resin can be made, sheets of resin of constant thickness are required. A mould has been designed and manufactured in which these sheets of resin are produced. To find the Young's modulus of the 1 E1 -glass fibres used for the reinforcement of the composite materials, a minor series of tests has been conducted using an Instron testing machine. As the creep tests conducted during the past six months have used extensometers that have not been fully developed, the results obtained from them have been designated as preliminary. These results have been used to indicate the loading conditions required for the main series of creep tests. The computation associated with the theoretical work reported in Progress Report No. 1 (March 1968) has been completed and the fThished work with examples of its use has been recently published (August 1968). Consequently no theoretical work is contained in this report. The results from the preliminary creep tests on unreinforced resin and 100 second isochronous tests on the uniaxially reinforced system have been used to examine the accuracy of the theoretical predictions. 2. Apparatus Development 2.1 Longitudinal Extensometer In the previous progress report (March 1968) the design of a longitudinal extensometer is described. This extensometer is clamped to the specimen at each end of the gauge length by means of two silver steel rods. Trials of this extensometer on I.C.I. Darvic unplasticised P.V.C. showed that at low stress levels the extensometer gave results for 100 second creep coinciding with the values quoted by Turner (December 1964). It should be mentioned here that a small 12 volt A.C. vibrator has been developed which is used to prevent any stick-slip of the transducers on all extensometers. At high stress levels however it was found that the extensions being recorded were larger than Turner's results. It was thought that this was probably due to premature yielding in the region of the extensometer clamps, indicatin-,  stress concentrations in the specimen in this region. To confirm that stress concentrations do in fact exist in this area,further 100 second creep tests were conducted on a rubber modified polystyrene. This material was chosen 2 because it is very prone to crazing which can easily be observed. The crazing mechanism is very stress dependent and consequently if the stress is chosen judiciously very little crazing is observed at the average stress in the specimen but at the increased stress in the region of a stress concentration the crazing is very marked. By loading a specimen with its extensometer attached at this stress level the stress concentrations can be readily observed around the grips of the extensometer. To eliminate these stress concentrations it has been necessary to redesign the means of clamping the extensometer to the specimen. Figure 1 shows the details of one of these clamps. Stuck to either side of the specimen using Araldite glue are cylindrical aluminium pads, 1/8  inch in diameter and .05 inch thick, located in position by a jig. The screws, by which the extensometer is clamped to these pads, have their ends machined to give a very fine point protruding from a flat surface. When the screws are tightened up the points pierce the aluminium pads and prevent slipping, and the hard shoulders, in contact with the surfaces of the pads, nrevent any possible twisting of the extensometers. Figure 2 shows a general view of the extensometer and it can be seen to be of the direct reading type, using a Sogenique linear displacement differential capacitance transducer as its sensitive element. Further 100 second creep tests on rubber modified polystyrene using this type of extensometer failed to indicate any stress concentrations related to this method of clamping. The accuracy and reproducability of this extensometer were checked by testing further samples of 'Daryl& P.V.C. in creep. The 100 second ieochronous stress-strain curve obtained agreed with Turner's results to within 3% up to a stress of 4 x 106  dynes/me which is equivalent to a strain of 1.6% in this material. This accuracy is considered to be satis-factory, taking the variation from sample to sample into account. 2.2 Lateral Extensometer A lateral extensometer is required to measure the lateral creep contraction associated with the longitudinal creep. The first extensometer that was designed for this purpose is shown in Figure 3. In principle it is very simple as it consists of two probes in contact with the sides of the specimen with a linear displacement transducer measuring their relative movement. The spring incorporated in the transducer is adequately strong to keep the probes in contact with the specimen. The main problem associated with the use of this extensometer is that as the specimen creeps longitudinally it moves through the probes of the extensometer. Consequently if the specimen is not exactly parallel sided the transducer will record the change of width of the specimen,as well as its lateral contraction. Using the routing technique to produce samples the width is constant to within t.002 cm, but as the transducer measures with a sensitivity of .00001 cm. this represents a large error. Tests using tY.s extensometer indicate that the errors involved are normally small but that large errors can occur. To enable this extensometer to be used with a guarantee of accuracy it is therefore necessary that the specimens should be ground in the 3 locality of extensometer probes to ensure a parallel section. As this -would be a time consuming process it was decided to try an alternative method first. The second extensometer is designed to measure the contraction over a fixed gauge length. Because the gauge length is small (of the order of 3/4 inch) the pads stuck to the surface of the specimen must be small to keep end effects to a minimum. Figure 4 shows the extensometer designed to measure changes of this gauge length. This consists of two arms, each fixed to a pair of the brass pads and able to rotate freely about conical holes machined in the centre of each pad. These arms rest on rollers suspended between ball races to enable the arms to move without friction. The relative movement of the two arms is measured by a transducer. As the specimen creeps the arms rotate about the brass pads so as to remain in contact with the rollers. The slight geometrical error introduced by the two arms rotating about different centres has been calculated to be small enough to be ignored even at relatively large strains. This extensometer has been tested on 'Darvic' P.V.C. and consistent reproducable results have been obtained for the creep contraction ratio at 100 seconds. Very little data has been published for the creep contraction ratio of P.V.C. and what data is available is widely divergent but the value obtained lies within the range of values. Further tests using this extensometer but using specimens of less thickness have shown that some errors can still be incurred due to flexibility of the samples. Attempts have been made to measure the creep contraction ratio of the specimen through its thickness by measuring the relative movements of the two faces. The variations of the thickness of the specimen are however too large to make this feasible without grinding the two surfaces in the locality of the probes. 2.3 Specimen production In order to be able 	 produce samples of unreinforced resin it is necessary to make sheets of resin of constant thickness. Figure 5 shows the mould that has been designed to make these sheets in. It consists of two pieces of 3/B inch plate glass, 1 ft. square, bolted together around three sides of their circumference and held a constant distant apart by a polythene spacer around these same sides. To prevent any leakage from the mould, the polythene spacer is smeared with petroleum jelly before insertion. The glass plates are coated with a wax polish to act as a release agent for the resin. Around the edges of the glass plates are steel angle supports to prevent any bending. To facilitate the pouring of resin into the mould, the top edges of the glass plates are bevelled inwards. Resin is poured with the mould in the vertical plane and it has been found that the air bubbles in the resin have adequate time to rise to the free surface. Many sheets of uniaxially reinforced resin have been produced using the filament winding machine. It has been found that the critical process for controlling the volume fraction of the glass of the composite is not the variable rot ers of the filament winding machine, as has been expected, but the large rubber rollers through which the composite is drawn to remove air bubbles. The minimum pressure that must be applied to the composite to remove all the air bubbles has been found to remove resin as well and a volume fraction for the glass of much less than 0.40 cannot be obtained in consequence. Using the equipment at present available it is difficult to raise the pressure exerted by the rollers high enough to make any significant increase in the percentage of glass present in the final composite. As a consequence, the volume fraction of glass present in all the composites manufactured to date has been of the order of 0.4. 2.4 Alterations to creep-rig In the original design for the creep rig all the main bearings were specified as being roller bearings as these have a high static load capacity. These have no automatic method of location and it has been found to be inconvenient to need to centralise the system for each test. Consequently in the five new machines currently being produced, double ball races, having an adequate static load capacity and a suitable locat ng mechanism, will be used. During the preliminary 100 second tests on the uniaxially reinforced system it was found that on some tests on the 0° system that loads were applied to the specimen up to the design limit of the machine. At these loads the specimen pulled out of the jaws. To prevent this, the inside faces of the jaws have been lined with fine grade carborundum paper allowing the specimen to be gripped adequately. To facilitate the manufacturing procedure of the jaws the design has been altered slightly. Now the jaw faces are clamped to the specimen outside the machine and the specimen and jaws are loaded into the machine by passing a 1/2 diameter pin through each pair of jaws. The only attendant problem with this design is the cutting of an accurate 1/2  inch diameter hole on the centreline of a sample of glass reinforced resin. It is hoped to overcome this problem by trepanning using the -13.5 inch hole, used to locai-e the router template, to centralise the lip inch hole. 3. Experimental Results 3.1 Young's Modulus of 'E'-glass fibres The manufacturers of 'E'-glass fibres quote their Young's Modulus as being the same as that of the bulk glass from whch they are drawn. It was decided to test the practicallity of measuring the modulus of the fibres themselves, and if it should prove practical to check the value of modulus obtained with the values quoted by manufacturers. The first problem encountered was to measure the diameter of individual fibres to an accuracy consistent with the required accuracy of the modulus. The 'E'-glass, as it is obtained from the manufacturers, is in the form of a -5- roving consisting of twelve strands of 204 fibres. As the diameter of the individual fibres is of the order of .001 cm a single fibre must be removed very carefully from the roving. This fibre was then stuck to a glass slide and viewed through a microscope with one thousand times magnification using transmitted light. The measuring graticule, used with the microscope was graduated into 1 mm. divisions. Consequently to obtain a 1% accuracy of measurement it was necessary to estimate to 1/10 division. It being difficult to focus clearly on the centre plane of the fibre this estimation was not easy. After the diameter of each fibre had been measured it was gripped in the matron testing machine prior to loading. The grips used were rubber faced and designed specially for use with fibres. The load scale used for the tests was 0-10 gms and the cross head speeds chosen lay between 0.05 and 0.5 in/min. The extension of the fibre was measured as being equal to the cross head movement of the machine initially, but it was found that there was considerable contribution from the extension of the gripping system. This was allowed for in later tests by using fibres of lengths varying from one to twelve inches and thus being able to calculate the contribution of the grip's. The value of the Young's modulus obtained in this way for these 'El -glass fibres was 6.55x 1011 dynesicm2 with a scatter of ±5%. This compares with the values of the modulus of the bulk glass quoted by the manufacturers varying from 6.90:: 1011 dynes/cm2. Whether this difference is due to inaccuracies in the measuring system or to a change in the properties of the glass when it changes from its bulk form to fibres is not yet known. 3.2 Creep compliance of unreinforced resin Several tensile creep tests have been made on samples of unreinforced Araldite MY 753 with HY 951 hardener to measure the creep compliance and the creep contraction ratio to enable some preliminary predictions to be made as to the behaviour of the uniaxially reinforced composite. Two difficulties have been encountered during this series of experiments. The first has been that the lateral extensometers that have been in use have been in a state of development and the results obtained have not been completely reliable. The second has been that the sheets of resin have become warped during the curing process as the shelves inthe oven used were not perfectly flat. These problems have now been rectified btt the results shown here may contain inaccuracies. Figure 6 shows the creep compliances of the two straightest samples that were tested. The first sample was tested for 5000 seconds, as this was only intended as a preliminary test, while the second sample was tested for 100,000 seconds which will be the normal duration of future creep tests. The variation between these curves is due to the first sample being less straight than the second. Other samples tested where the bend in the gauge length was more obvious gave considerably higher compliances as would be expected. 6 On the basis of some 100 second creep tests it was decided that the initial creep contraction ratio was 0.37 although this value could be in error. With no information to the contrary it was decided to assume that the Poisson'; ratio of this resin behaved in accordance with Turner's (1966) approximation that the bulk modulus is independent of time. The results of the preliminary creep test have been analysed using a computer program developed by the author while at the Civil Engineering Department of the University of Southampton. This program calculates the optimum finite retardation time spectrum of the resin from its creep results by a linear regression technique. In Figure 7 is the six element spectrum calculated to describe the three decades of creep curve analysed. The accuracy of this 	 is such that the sum of the square of the errors is 5 x 10_ 29 (cm2/dyne)2 which represents an average error of O.O.6% 3.3 100 second creep compliance of the uniaxially reinforced resin In order to enable a preliminary comparison between theoretical and experimental results to be made, a set of 100 second creep tests were conducted on specimens cut from a uniaxially reinforced sheet of resin at various angles to the fibre axis. It is hoped that while the values of the 100 second creep contraction ratio were measured using the first type of lateral extensometer described, and in consequence may not be very accurate, that they should indicate the correct trend. Figure 8 shows the predicted variation with angle of the 100 second compliance of the uniaxially reinforced system used here compared with the experimentally obtained values. The prediction is based on the preliminary results of the creep compliance of the resin and the assumption that the volume fraction of the glass is 40%. The volume fraction of the individual specimens were measured by first weighing the gauge length of each specimen and then burning off the resin content in an oven at 680°C for 15 minutes. The weight of the glass left was then recorded and the volume fractions of the two phases calculated assuming that the specific gravity of the resin was 1.18 and the specific gravity of the 1 E1 -glass was 2.55. The volume fractions of the specimens varied between the limits of 37% and 42%. There is good agreement between the experimental and predicted results with the predicted results being slightly high. This is due to the pre-liminary creep sample being slightly bent. Figure 9 shows the predicted variation of the 100 second creep contraction ratio with angle for the uniaxially reinforced resin with a volume fraction of glass of 40%. The experimental results with which these predictions are compared show a similar but less noticeable trend. 7 References 1. Dootson, M. The time-dependent mechanical properties of fibre reinforced polymers. Progress Report Yo. 1. CoA Memo. No. 150, March, 1968. The use of a single composite element to describe the creep properties of fibre reinforced composites. CoA Note Mat. No. 23, August 1968. 2. Dootson, M. 3. 	 Turner, S. 	 Creep in thermoplastics. Unplasticised PVC. Brit. Plast., December 1964. Turner, S. 	 The foundations of possible engineering design methods for plastics. Trans. J. Plastics Inst., p. 127, July 1966. FIGURE I LONGITUDINAL EXTENSOF2TER CLAMP FIGURE 2 LONGITUDDTAL EXTENSOMETER FIGURE 3 SURFACE MEASURING LATERAL EXTENSOI'ETER FIGT,TRE 4 MMIF.uld.) LATERAL EXTENSOMETER FIGURE 5 MOULD FOR T.DIREINFORCF0 RESIN 1.0 	 L 160 	 16100 10000 	 100000 00  0 4 0 0  4 0 0 4- 0  4, 0 0 0 0 + PRELIMINARY 5000 SEC. CREEP TEST ( USED FOR SPECTRUM & PREDICTIONS ). 0 100.000 SEC. CREEP TEST 0 cp 0 0 0 3.0 - 2.0 ;NE , SECS FlaIPE 6 	 CREEP OOMPL ANCE OF UNREINFORCED !O070 MY 753 4'0  ,i'0 2 0 10 	 34.82 	 121.3 	 422.2 	 1470 	 5120 , secs FIGURE 7 	 SIX ELEMENT FINITE RETARDATION TIME SPECTRUM OF 100°/s MY 753, BASED ON 5000 SEC. CREEP TEST. So W 3.199 x 10-11 2 - 1 5 1.0 05 0 	 15 	 30 	 45 	 60 	 75 	 90 6° Rai 	 B `,ARiAT1ON OF y HE 1C0 SEC. CREEP COMPLIANCE OF UNIAXIALLY RE INFORCEID MY 753 WITH ANGLE. Vf = 0.40, CV Rs' 0.. L! • 2 0.5 30 	 75 	 95 Go 	  FIGURE 9 VARIATION OF THE 100 SEC. CREEP CONTRACTION RATIO OF UNMIALLY REINFORCED MY 753 WITH ANGLE. Vf = 0.40. 

The time-dependent mechanical properties of fibre reinforced polymers

1. General Progress
The six months from April to September 1969 have been spent mainly
in consolidating the work of the previous eighteen months.
Firstly, due to major servicing problems, it became necessary to
redesign the resin impregnating head of the filament winding machine.
By the removal of all moving parts from the vicinity. of the resin, these
servicing problems have been completely overcome. Using the redesigned
machine many sheets of high quality glass reinforced epoxy resin have
been produced.
A sophisticated version of the spring mounted lateral extensometer
described in Progress Report No. 3 has been designed and tested. Six
of these have now been produced and are now in service yielding satisfactory
results.
The majority of the period has been spent in setting up the tensile
creep testing machines. This has been necessitated by the discovery that
errors of up to 10% in creep compliance have been obtained through misalignments
of the loading linkages of the order of .01 inch.
All the apparatus is now functioning correctly and more creep results
for uni- and bi-directionally reinforced specimens are being obtained.
Included in these current creep results are not only values for creep
compliances but also for the creep contraction of these specimens

CoA Memo. No. 202 September, 1969 THE COUgGE OF AERONAUTICS DEPARTMENT OF MATERIALS The time-dependent mechanical properties of fibre reinforced polymers by - M. Dootson, B.Sc.(Eng.) Progress Report No. 4 A Report of work carried out during the period 1st April to 30th September, 1969 Contents Page No. 1. General Progress 	 1 2. Apparatus development 	 1 2.1 Lateral extensometer 	 1 2.2 Filament winding machine 	 2 3. Experimental Results 	 3 4. Remarks 	 4 4.1 Packing order 	 4 4.2 Future programme 	 4 Figures 1. General Progress The six months from April to September 1969 have been spent mainly in consolidating the work of the previous eighteen months. Firstly, due to major servicing problems, it became necessary to redesign the resin impregnating head of the filament winding machine. By the removal of all moving parts from the vicinity. of the resin, these servicing problems have been completely overcome. Using the redesigned machine many sheets of high quality glass reinforced epoxy resin have been produced. A sophisticated version of the spring mounted lateral extensometer described in Progress Report No. 3 has been designed and tested. Six of these have now been produced and are now in service yielding satisfactory results. The majority of the period has been spent in setting up the tensile creep testing machines. This has been necessitated by the discovery that errors of up to 10% in creep compliance have been obtained through mis-alignments of the loading linkages of the order of .01 inch. All the apparatus is now functioning correctly and more creep results for uni- and bi-directionally reinforced specimens are being obtained. Included in these current creep results are not only values for creep compliances but also for the creep contraction of these specimens. 2. Apparatus development 2.1 Lateral extensometer In Progress Report No. 3 it was suggested that the optimum form of lateral extensometer was such that it could be mounted onto the specimen by spring pressure. A simple model of an extensometer of this type was tested and shown tc work satisfactorily.  Figure 1 shows the sophisticated version of this simple model that has been designed, tested and brought into general use. The general principle of operation of the extensometer is shown in Figure la.. The extensaaeter is held onto the specimen by the two spring loaded plungers. The spring pressure can be adjusted such that the extensometer will not slip on the specimen and none of the points of contact of the extensometer on the specimen are depressed into the surface. The transducer remains in contact with the surface of the specimen during contraction and measures the magnitude of this phenomenon. In order to ensure that the transducer is in contact with the centre of the specimen and that the extensometer is unable to twist on the specimen, a specimen centralising device has been included on the extensometer. This is shown in Figure lb. It consists simply of two plates, each with three protuberances on the surface, mounted on a left and right hand threaded rod passing through the base plate of the extensometer. The 2 threaded rod is rotated until the protuberances are all lightly in contact with the surface of the specimen. In this position the specimen is centralised in the extensometer. This form of extensometer appears to cause no form of stress concentration in the specimen as test results have been of the correct magnitude. Also the output from the transducer appears to follow the movement of the specimen very well with little or no evidence of any stick-slip. 2.2 Filament widning machine The original filament winding machine,, described in Progress Report No. 1, has worked satisfactorily and has produced good quality laminated. Cleaning the resin impregnating head after each winding, however, was found to be a very dirty job. On some occasions when the resin gelled before the winding was finished, due to a build up of exotherm, it was found necessary to remake any moving parts that had been submersed in resin. These were clearly unsatisfactory occurences and in consequence a new resin impregnating head, of the design Shawn in Figure 2, has been made. This has no moving parts submersed in the resin and is thus much easier to clean and service. The only changes that have been made from the original machine have been with the impregnating head. A light aluminium structure, connected to the driving thread, supports the impregnating head above the mandrel. The head consists of an inverted bottomless polythene bottle, which contains the resin, onto which is screwed an adjustable nozzle. This nozzle prodUces a rectangular orifice 1/8 inch long which can be adjusted to any width between 0 and 0.04 inch. In Figure 2b, section 4.4 shows a cross-section through the centre of the nozzle. Two 1/8 inch thick mild steel plates, shaped to give a tapering hole, can be seen. The right hand plate is fixed in position while the one on the left can be adjusted to vary the gap between the plates. The left hand plate has a slot cut through it from the bottom edge to a hole near the top. This leaves a thin piece of metal at the top edge which acts in a similar manner to a hinge. By screwing a set screw with a conical end into this slot, in the position marked by the left hand solid spot, the gap between the two plates is decreased. To open the gap again a second conically ended set screw is screwed into the conical hole, marked by the right hand solid spot, after the first has been unscrewed. To ensure that the adjustable plate does not stick in position it slides between two thin P.T.F.E. gaskets. It has been found that accurate control of the quantity of resin passing through the nozzle can be obtained. A better quality of laiinate is produced using this new system than previously. This is probably due to the relative lack of air entrainment in the resin which in turn is due to the lack of moving parts. 3. Epxerimental Results Because of the drive to get all apparatus working correctly by this time, only a few experimental results have been obtained. Firstly, the results shown in Figure 3 for a set of unidirectionally reinforced specimens were obtained before the lateral extensometers were completed. Thede values of creep compliance follow the familiar pattern for unidirectional specimens that has already been shown. The 0° results show very little time dependence while the high angle results creep markedly. The 75° results are again higher than the 90°. No comparison has yet been made between these experimental results and theoretical predictions. Figure 4 shows some creep compliance results for a set of bidirectionally reinforced specimens with of = .48, x = .39, y = .61. Again, these results were obtained before the lateral extensometers were completed and so there are no values of the creep contraction ratio for these specimens. Also at the time of these tests the creep apparatus had not been accurately aligned and some errors are possible in the magnitude of the compliances. The first results that have been obtained with all the apparatus in correct working order are shown in Figures 5 and 6. These figures show the creep compliances and creep contraction ratios for samples cut at various angles from the bidirectionally reinforced sheet B2. This has an average volume fraction of glass of 0.51 and contains 66% of this glass in the surface layers in the x-direction and the remaining 31f% of glass in the central layer in the y-direction. The usual bi-directional trend can be seen with the samples in the x and y directions having low compliances and samples at intermediate angles having higher compliances and larger time  dependence. The creep contraction ratios in Figure 6 are of particular interest as they are the first that have been obtained on this contract. Two main points of interest should be noted from this Figure. Firstly that the ratios are small at 0° and 90° (in the order of 0.1) and larger at intermediate angles (up to 0.45) and secondly that while the ratios increase with time at intermediate angles, they appear to decrease at 0° and 90°. In the case of the 0° results not only was 1112 found to decrease with time but also was the contraction strain, e12. This seems a most unusual occurence and it will be of interest to see whether this can be predicted from theoretical considerations. To show the variation of the compliance and contraction ratio with angle for these specimens, Figure 7 and 8 show these functions, taken at 100 seconds, plotted agrAnst angle. 4. Remarks 4.1 Packing order Theoretical predictions for the mechanical properties of fibre reinforced plastics, other than uni-directionally reinforced, yield bounds rather than an exact sc4ution. These bounds represent uniform strain and uniform stress assumptions. It is possible that, depenaing on the packing order of the layers of a multi-directional laminate, the mechanical properties may vary within these extremes. In order to check whether this thought is of any consequence, a batch of laminates has been produced in which pairs of laminates have the same values of x and y and similar values of of with the only difference being in the packing order. Tests on specimens cut from these laminates should produce valuable information on the effects, if any, of packing order on creep compliance and creep contraction ratio. 4.2 Future programme During the next six months it is hoped to produce sufficient creep data for glass reinforced plastics to enable some conclusive comparisons to be made between theoretical predictions and actual behaviour for these materials. It would be interesting to follow these tests with a further selection using a different ratio for the moduli between the phases. If a different technology is required to manufacture these materials it would be useful to study this in the near future. L A SECTION B -B SECTION A-A r C SPECIMEN CENTRALISERS FIGURE 1 TRANSDUCER \ 0 \ BASE PLATE SPECIMEN SPRING LOADED PLUNGER a) LATERAL EXTENSOMETER L.H. AND R.H. THREADED ROD GUIDE RODS SECTION C-C b) SPECIMEN CENTRALISING DEVICE.  FIGURE. 2 POLYTHENE BOTTLE GLASS FIBRE SCREW-ON ADJUSTABLE NOZZLE DRIVING THREAD 1 1 	 \ 1 1 1 1 STABILISERS MANDREL a) MODIFIED RESIN IMPREGNATING HEAD  b) SCREW-ON ADJUSTABLE NOZZLE  B P.T.F.E GASKETS . L A SECTION B-B SECTION A-A 105 10 2 	 10 3 TIME, SECS 104 O oo O -In  (0,10-12  C M 2 /dyne  - 10 3 	 104 	 10 5 TIME, SECS -In  (t)  10-12  cm2/dyne  00 0 0 0 0 0 0 0 0 ta" A a A A 	 A A A 4 A A 	 AA 10 2 FIGURE 3 	 VARIATION OF CREEP COMPLIANCE WITH TIME. Vf ..51, X 7. 1 Y = 0. FIGURE 4 VARIATION OF CREEP COMPLIANCE WITH TIME, Vf u -4 8, X=-39, Y=•61 x 0 °  o 22.5° A 90°  0' 9 	 0 	 0 A A 4 A A A A * 0 • 0 A ® a A -o NE 6 CI A 	 A e A A a 0° t 16° o 45° 0 67° '1 	 90° 9 0 0 K 	 9 	 9 	 9  cr3 9 o 	 r0 '03  O 0r + 	 .1 A 	 4 	 4 	 .A °A II A 104 	 105 FIGURE 5 12 VARIATION OF CREEP COMPLIANCE WITH TIME. Vf 7, • 51, X: •66, Y •34 0 °  + 16° 45°  X 67° • 90°  0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0I 	  10   10 2 	 10 3 	10 	10 5  TIME, SECS FIGURE 6 	 VARIATION OF CREEP CONTRACTION RATIO WITH TIME Vf •51, X ='66, Y=.34 TIME , SECS - ill  (1 00),  10-12cm2/dyne  30 	 60 	 90 0 FIGURE 7 VARIATION OF 100 SEC CREEP COMPLIANCE WITH ANGLE Vf 	 X=•66, Y.-34 30 	 60 	90 FIGURE 8 VARIATION OF 100 SECOND CREEP CONTRACTION RATIO 	 WITH ANGLE Vf = •51, X=•66, V= •34 

1. General Progress
In the six months from October, 1968 to March, 1969 the work has
been divided into two main sections. The first of these has been the
collection of tensile creep data both for the unreinforced resin and for
the uni- and bi-directionally reinforced composites. The second section
has been the continued quest for a successful lateral extensometer.
In Progress Report No. 2 it was reported that five creep machines were
in production. These have now been installed and are all functioning
satisfactorily. Longitudinal extensometers of the type described in
Progress Report No. 2 have been manufactured for use on these rigs.
Comparisons have been made2between the experimental creep results of
the composites described in this report and theoretical predictions based
on the Elemental model.3'4 Good agreement was shown to exist between
the experiment and theory

3 IL Iio! !h 	 1 71 CoA Memo. No. 183    March, 1969 THE COLTEGE OF AERONAUTICS DEPARTMENT OF MATERIALS The time-dependent mechanical properties of fibre reinforced polymers - by - M. Dootson, B.Sc. (Eng.) Progress Report No. 3 A report of work carried out during the period 1st October, 1968 to 30th March, 1969. Contents Page No. 1. General Progress 	 1 2. Lateral Extensometer 	 1 3. Experimental Results 	 2 3.1 Unreinforced MY753 	2 3.2 Uni-directionally reinforced MY753 	 2 3.3 Bi-directionally reinforced MY753 	 4 4. Theoretical Discussion 	 4 References 	 5 Figures 	 6 1. General Progress In the six months from October, 1968 to March, 1969 the work has been divided into two main sections. The first of these has been the collection of tensile creep data both for the unreinforced resin and for the uni- and bi-directionally reinforced composites. The second section has been the continued quest for a successful lateral extensometer. In Progress Report No. 2 it was reported that five creep machines were in production. These have now been installed and are all functioning satisfactorily. Longitudinal extensometers of the type described in Progress Report No. 2 have been manufactured for use on these rigs. Comparisons have been made2between the experimental creep results of the composites described in this report and theoretical predictions based on the Elemental model.3'4 Good agreement was shown to exist between the experiment and theory. 2. Lateral Extensometer In Progress Report No. 21two types of lateral extensometer were described. The first was mounted on the creep machine itself and measured the change of width of the specimen by means of the probes which were kept in contact with the surface of the specimen. This was unsuccessful as it also measured any nonparallelism of the sides of the specimen. An attempt to counteract this was made by the design of a second extensometer which, while its weight was carried by the creep machine, was attached to the specimen at fixed gauge points. This was more successful than the first but it was shown to be susceptible to very small sideways movements of the specimen relative to the machine. To remove this error it became necessary to design an extensometer that was mounted directly on the specimen. Figure 1 shows the first attempt at solving this problem. It consists of two clamps, each with four point mounting, screwed into small aluminium pads that had been glued to the specimen. The transducer measures the relative movement of the two clamps. Tests showed that the presence of this extensometer did not affect the longitudinal creep compliance of specimens, and it was consequently hoped that this indicated that the axial stress distribution of the specimen had not been disturbed. Measurements of the creep contraction ratio using this extensometer were very consistent but unfortunately they were consistently smaller than expected. This is presumably due to a change in stress distribution caused by clamping a rigid body to a flexible specimen. In view of these three attempts to produce a successful lateral exten-someter the necessary qualifications for success would appear to be:- 2 - i) Measurements must be taken at one place on the specimen. ii) The extensometer must be mounted directly on the specimen. iii) The method of mounting the extensometer on the specimen must not interfere with the axial stress pattern in the specimen. The only apparent solution to this problem is to spring load an extensometer on to the specimen. A simple extensometer which operates on this principle has been built and is shown in Figure 2. Using this, some 100 second results have been obtained for the creep contraction of the MY 753 resin. These results, shawn in Figure 6,can be seen to compare very well with those measured on this material by Darlington using his creep contraction measuring equipment. 3. Experimental Results All creep results that have been reported in previous Progress Reports were considered to be preliminary but here the longitudinal creep measurements have all been made using fully developed apparatus. The creep contraction results that are included here are still only of a preliminary nature. 3.1 Unreinforced MY 753 To determine the stress-strain behaviour of the resin fully it is necessary to know:- i) The variation of the creep compliance with time and stress. ii) The variation of the creep contraction ratio with time and stress. iii) The extent of inter-batch variation. The first of these requires the measurement of longitudinal creep over a specified time period at several stress levels. As it is necessary to remove any effects due to inter-batch variations, the specimens to be tested must be produced from one sheet. The creep tests that have been performed were carried out on a set of five specimens at stresses up to 2.5 x 105  dynes/cm2  for a duration of. between 105 and 106 seconds. The individual stress levels were chosen such that the region of linearity of stress-strain behaviour should be clearly delineated. In Figure 3 the results of this series of creep tests are shown. At the lower stress levels, the compliances can be seen to be superimposed, indicating the linearity of the resin at these stresses. Above a stress of 6.1. x 107  dynes/cm2  the curves begin to diverge as the resin becomes non-linear. The upper curve in Figure 6, which shows the 100 second stress-strain behaviour of the resin, shows the onset of non-linearity clearly. It is important that the creep tests on the composite materials are carried out at a stress level such that the resin is in the linear region. This stress level is equivalent to a strain at 100 seconds 3 of not more than 0.2%. To ensure that even in the regions of stress concentrations no non-linearity is observed the 100 second strain is normally kept down to 0.1%. In Figure 3, the continuous line shows the creep compliance in the linear region. This line was calculated as being the best fit of the low stress data by the ICT 1905 computer using a linear regression technique., The discontinuous retardation time spectrum associated with this linear region creep compliance is shown in Figure 4. Due to inexactitudes in the weighing of the two components of the resin during manufacture of specimens, a certain amount of variation in the properties of the resin occurs. This is obviously minimised by taking care at all stages of manufacture, but some variations still occur. Figure 5 shows a typical set of low stress compliances for samples cut from different sheets of MY 753 resin. The variation in properties is in the order of ± 5%. This variation is sufficiently large to make it necessary to manufacture a control specimen of resin with each batch of composite material produced rather than use an average description of the resin. To complete the description of the resin, creep contraction results are required. As the lateral extensometer is not yet fully reliable, these results were obtained by Darlington using his creep contraction extensometers. The 100 second results that he obtained are shown in Figure 6 in conjunction with the associated values of the longitudinal strain. From these results the creep contraction ratio at 100 seconds has been calculated to be 0.388. In the development of the spring loaded lateral extensometer, results were obtained for the 100 second creep contraction of the MY 753. These are compared with Darlington's results in Figure 6 and, while only of a preliminary nature, agree very well with the accurately obtained values. 3.2 Uni-directionally reinforced MY 753 Figures 7, 8, 9 show a selection of creep data obtained for uni-directionally reinforced MY 753. In order that the properties of the resin remained linear, these tests were conducted such that the 100 second strain was of the order of 0.1%. The results have been grouped according to volume fraction to give a picture of the variation of the creep compliance with angle unclouded by other variations. In Progress Report No. 2 the variation of the 100 second creep compliance of this system was predicted and compared with experimental results. Here again the same trend of results with angle is obtained with higher compliances obtained at 60° to the fibre axis than at 90°. All three figures show the same trend but the most descriptive is Figure 7. It can be seen that at low angles to the fibre axis there is very little creep while at higher angles the time dependent extension is a considerable proportion of the whole. A comparison between these results and theoretical predictions based on the Elemental model has been made2and the agreement was shown to be good, apart from what was described as an apparent error in the measurement of the volume fraction of the fibres. It has since been shown that in fact no errors are introduced from this source. The upper curve in Figure 5 corresponds with the low stress curve in Figure 3 and was in fact used to describe the resin properties for the purposes of the theoretical predictions. This is some 5% above the mean value of the four curves in Figure 5 and would in fact account for part of the observed discrepancy between the theoretical and experimental results for the composite. 3.3 Bidirectionally reinforced MY753 ------ Figure 10 shows the creep compliance results of the only bidirectional samples that have been tested to date. These have approximately the same number of fibres in each of two orthogonal directions. One of the samples was cut at 0° to one of the orthogonal directions and the other at 45°. The general shape of the creep curves is much the same as those for the uni-directional specimens. Here however, as predicted, there is a larger creep compliance in the 0° direction, and the 45° sample behaves in the same manner as a unidirection sample cut at this angle. 	 45° is, in this bidirectional case, the angle at which maximum compliance and creep rate are obtained. Comparison between these results and theoretical predictions again show a good agreement, with the same magnitude of discrepancy as for the unidirectional case. 4. Theoretical Dsicussion In section 3.2 it is described how there is a small discrepancy between the experimental and theoretical results for the creep compliance. This is only partly due to the variation in the properties of the resin and always results in a predicted compliance that is greater than the actual measurements. On a careful search through the foundations of the theoretical model a possible source of this error has been found. In HashinI ssoriginal paper in which he discusses the elastic constants of a unidirectional composite in which the fibres are randomly distributed, it appears that the random distribution that he proposes is of a specific type. This is such that each fibre is surrounded by a cylinder of resin, the diameter of which bears a constant ratio to the diameter of the fibre. In order that there shall be no voids in the composite it is therefore necessary that the diameter of the fibres is graded down to an infinitesimal size. This model type of random distribution is not the same as that found in real composites where the fibre diameter is constant and the distribution random in a general sense. In a later paper when discussing the possible limits within which the properties of a unidirectional composite, composed of two cylindrical phases of arbitrary phase geometry, must lie, Hashin shows that his specific random case corresponds with the upper bound of compliance for these composites. Any variation from Hashin's random case must therefore produce a lower compliance. References 4. Hashin, Z. 5. Hashin, Z. The time-dependent mechanical properties of fibre reinforced polymers. Progress Report No. 2. CoA Memo. No. 162, September, 1968. The creep behaviour of fibre reinforced plastics. Paper 5, P.I. Conference on 'Engineering Properties' of Plastics', 6-8 January, 1969. 1. Dootson, M. 2. Dootson„ M. 3. Dootson, M. 4. Dootson, M. The use of a describe the reinforced c CoA Note Mat o simple composite element to creep properties of fibre mposites. . 23, August, 1968. A method of analysis of the time dependent stress/ strain relationship in fibre-reinforced plastics. Paper 13, Institute of Physics Conference on 'Stresses in Composite Materials', 25-27 September, 1968. The elastic moduli of fiber-reinforced materials. J. Appl. Mechs., Trans. A.S.M.E., 31, 223. June, 1964. On Elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry. J. Mech. Phys. Solids, 13,119 1965. FIGURE 1. Direct mounted lateral extensometer FRONT FACE REMOVED FIGURE 2. Spring loaded lateral extensometer 100 1 100000 	 1000000 t secs — 1000 	 10000 STRESS 107dynes/c me q 3.154 0 CREEP COMPLIANCE OF MY753 50 0; CD 6.427 10.053 13197 26.394 4.5 4.0 3.5 3.0 FIG 3 DISCONTINUOUS RETARDATION TIME SPECTRUM FOR MY753 So= 3.097x 10-"cm2 dyne E ro E 6 (6'  - ------ ----- — 41'     4 5 	 6 7 8  10 =-.* FIG 4 10 100 	 1000 	 10000 	 100000 TIME , SECONDS FIGURE 5 CREEP COMPLIANCE OF MY753 AT LOW STRESSES. 10 FIGURE 6 LONGITUDINAL AND LATERAL 100 SECOND STRAINS OF MY 753 o DOOTSON + DARLINGTON 1.0 0.5 10 	 20 CT, 107 dynes / c m 2 S TRAiN 30 50 L0 30  20 FIGURE 9 TENSILE CREEP COMPLIANCE OF UNIDIRECTIONALLY REINFORCED MY753 Vf =0.50 1. .02 FIGURE 7 TENSILE CREEP COMPLIANCE OF UNIDIRECTIONALLY REINFORCED MY 753 Vf :0.37 .01 20 	 20 5 15' 10 100 100 1000 10000 100000 TIME, SECONDS TIME, SECONDS -4.- 75° 15 15° x 	 ti UPo E 10 0° 0 1000 	 10000 	 000000 	 10 90°  1000 	 10000 	 100000 0) E 10 TIME, SECONDS 10 100 	 1000 	10000 	 100000 TIME , SECONDS 15 OS. FIGURE 8 TENSILE CREEP COMPLIANCE OF UNIDIRECTIONALLY REINFORCED MY 753 Vf = 0.43 ± .01 FIGURE 10 TENSILE CREEP COMPLIANCE OF BIDIRECTIONALLY REINFORCED MY 753 Vf = 0 .45 ±.03 , X = .515, Y=-485 

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The time-dependent mechanical properties of fibre reinforced polymers

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