Mechanical Properties of
Polvethvlene J
J
R . H, CAREY, E. F. SCRIJLZ, . ~ N DG. J. DIENES Bakelite Dicision, Union Carbide and Carbon Corporation, Bound Brook,
A
study of the fundamental and practical mechanical properties of various molecular weight polyethylene resins b y means of tensile stress-strain and torsional torquedeflection curves is described. By combining these two techniques, the stiffness properties have been evaluated with good accuracy over an unusually wide range of temperatures. Other mechanical properties, such as stress and strain a t the “elastic limit,” and energy of strain can also be evaluated quantitatively on the basis of these data. Analysis of the stress-strain cur) os, appropriate to certain temperature ranges, has been made. In the -30’ to +25” C. range, the stress-strain curves are continuously curved and are best described by an exponential-type function which permits the determination of an initial tangent modu~us. Below -30’ C. a inore conventional elastic behavior is observable arid a tangent modulus may be evaluated graphically. Similarfy, a modulus is calculable from the initial straight line portion of the torsional torque-deflection curves. I t i s shown that, over a com-
yield equivalent moduli. The log modulus-temperature curves for different molecular weight resins show the wellknown inverted S-shape with the curves being flat and extended when compared with vinyl or rubber elastomers. ’These curves coincide a t low temperature--i.e., they are independent of molecular weight. As the temperature is increased the curves fan out; the higher molecular weight materials being characterized by higher moduli. An “elastic limit” has been defined as the point on the stressstrain curve where the tangent modulus is 50% of the initial modulus. The corresponding area under the curve is the strain energy. A fundamental relation independent o f temperature and molecular weight, consistent w i t h the general exponential nature of the curves, can be stated: The product of the initial modulus and the strain a t the elastic limit are proportional to the stress a t the elastic limit. On the basis of this principle a unified picture o f most of the mechanical properties has been attained.
point is obtainable. In order to study the elastic propertias it is necessary, therefore, to oktain stress-strain curves at high magnification and to work out a proper method of analysis of thwe curves. In addition to the elastic modulus a considerable :mount of further information about .the mechanical properties i i derivable from such stress-sti ain curves. This paper deals primarily with the study of polyethylene stress-strain curves below the yield point obtained at high magnification. At very low temperatures a modified torsional technique, which permits the determination of torque-deflection curves, has been found convenient. These studies, which are an integral part of the stiffness-temperature investigation, are nluo included.
HE stiffness-temperature propertie* of polyethylene can be
1 Present address, North American Aviation Corporation, Los Angeles, Calif,
J.
mon temperature range, torsional and tensile techniques
T
determined approximately by the torsion method of Cliash and Berg (6, 6) in the -60” to $22’ C. temperature range. This method is inadequate, howevei, when it is desired to investigate the dependence of the mechanical properties on such variables LLS the molecular weight or concentration of various fillers. The degree of reproducibility is usually not sufficient t o observe rather fine but real differences. It was also found that the theoretical equation relating the torque and the torsional deflection is not obeyed well by mmples of different thicknesses. The need for a more suitable method of determining the mechanical properties of polyethylene resins and compounds was definitely indicated. It was felt that the difficulties w t h the torsion test are probably due to the nature of the stress-strain curves. Exploratory experiments showed that even the initial portion of the polyethylene stress-strain curve is highly curved. Accordingly, Clash and Berg’s single point measurement would not compare equivalent points whenever the shape of stress-strain curve changes owing to changes in temperature, molecular weight, 01 composition. Since the strain level depends on the thickness in a torsional specimen, it is also understandable that, because of the high curvature in the stress-strain curves, the torsional modulus is a function of the t h i c k n e ~ . It was decided, therefore, to investigate in detail the stressstrain properties of polyethylenes, over a wide temperature range with the goal in mind that both fundamental and practical information were sought. The over-all shape of the polyethylene stress-strain curve, as obtained at low magnification, is well known (4). A typical curve is shown in Figure 1 for a Bakelite polyethylene resin compound. While such a curve ahows the yield point and the cold-drawing properties rather well, the initial part of the curve is so compressed on the strain axis that no reliable measure of the elastic properties below the yield
iV.
KXFEHIIMEWTAL TECIZYIQUESm u MErIxoI) OF AVALYSIS
Stress-Strain Curves in Tension. EXPERIMENTAL TECHLoad-elongation curves of injection-molded specimens of polyethylene were obtained with Baldwin-Southwark universal testing machines equipped with 0. S. Peters microformer rworders and extensometers ( T y p e PS-7). The tensile specimens conformed to American Society for Testing Materials’ Designation D 638-44T. The tests a t 25‘ C. were made in a constmt temperature room herd at 25“ C. and 50% relative humidity on a machine having a load scale range of 0 to 120 pounds. The low temperature tests m r e made in a constant temperature cabinet inserted between the crossheads of a testing machine having a load scale range of 0 to 600 pounds. Satisfactory operation of the extensometer a t low temperatures was obtaiiied by thoroughly cleaning all surfaces with acetone and allowing them to dry. No lubricants were used. Elongation magnifications of 20 and 40 were used depending upon the stiffness and the temperature. Both magnifications were used at room temperature and found to give identical results. Speed of testing was controlled by means of a Peters ram pacing diive. Three testingrates, 0.01,0.1, and 0 4 inch ppr ~ ~ Q uwcre B, NIQUES.
842
,
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1950
ui
:: 0 8 E
' 04
o
'
6
0.P
O
O
2
3
4
5
STRAIN, IN./IN
Figure 1. Typical Low Magnification Stress-Strain Curve for a Bakelite Polyethylene Compound
~
in tension is calculable by the well-accepted technique of drawing in the initial slope. The procedure is illustrated by the dotted line in Figure 2. Young's modulus calculated this way n-ill be referred to as the initial tangent modulus. The coefficient of variation was 3.5%. A large part of this error is a result of the unavoidable difficulties in graphically determining the tangent. This technique of evaluation wax found to be satisfactory from -60" to about -30" C., and was used for all the tensile stressstrain data in this temperature range. Above -30" C., as already pointed out in connection with the stress-strain curve illustrated in Figure 3, a straight line portion is no longer observable. It is evident that an extrapoletiom technique is necessary in order to obtain an initial modulus value comparable to the tangent modulus used a t low temperatures. The nature of the stress-strain curve suggests an exponential' behavior. By numerically differentiating the stress-strain curve and plotting the logarithm of the slope against the strain a linear relation was obtained. This is illustrated by a typical example in Figure 4 for the stress-strain data represented by the k r v e of Figure 3. The straight line is well-defined. Denoting by E the slope of the stress-strain curve at any strain, which is t h e tangent modulus at this strain, the straight line of Figure 4 mean& that the following equation holds:
E investigated at 25", -2", and -41" C. An appreciable change in [nodulus was observed with testing speed; the modulus increased with increasing speeds. The magnitude of this effect was about a 15 to 20% change in modulus for a tenfold change in speed. For this investigation, testing speed was standardized at 0.1 inch per minute. The continuously recorded load-elongation curves were transformed into stress-strain curves by means of point by point computations. All stresses were calculated as load per original cross-sectional areas. Injection and compression molded specimens exhibited no appreciable differences in the low strain region investigated. The low temperature data presented later show the equivalence of the two types of specimens. Cursory investigation at 25" C. supported this conclusion. s.4TCRE O F STRESS-STRAIN CURVES AT HIGHAND L O W T N \ I PERATURES. In Figure 1 a typical low magnification stress-strain curve of polyethylene I S shown (obtained at a testing rate of 1.0 inch per minute). Although curves of the scale shown in Figure 1 are very useful, the region between 0 and 20% strain, the elmtic region which is of prime importance in many practical applications, can only be studied by using slow straining rates and high strain magnification Two typical high magnification stressstrain rurves are shown in Figures 2 and 3. The curves are dirert copies, in terms of stress and strain, of the continuous load-elongation curve charted by the recorder. Because of limited extensometer travel this technique cannot be used above a strain of about 20%, and a detailed record of the complete stress-strain curve is unobtainable. Special techniques will have to be worked out for studying in detail the yielding phenomenon, for example. This investigation deals only with the initial povtion of the stress-strain curve. The effects of temperature are qualitatively indicated by a comparison of Figures 2 and 3. Near room temperature, the curve is exponential and shows no well-defined yield point. At lower temperatures, however, in addition to an increase in the stress at any given strain, there is a change in the shape of the curve. Instead of being exponential the initial portion of the stress-strain curve is quite linear and extends to high stresses. The "knee" of the curve is sharper and a well-defined yield point is observable at about 7% strain. DETERMINATION OF THE MODULUS.As Figure 2 and the above discussion show, the stress-strain curve for polyethylene a t low temperature is characterized by an initial straight line portion. At these temperatures, therefore, the elastic modulus
a43
(11
=
vi U w v)
STRhIN, IN./IN.
Figure 2.
0
Stress-Strain Curve for D-55 Polyethylene at -57" C. (0.10 Inch/Min.)
002
004
(106
008
010
STRAIN, IN I IN
Figure 3.
012
014
.
016
018
Stress-Strain Curve for D-55 Polyethylene at t25" C.
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
844
' L I
I
I
I
\.
r s I
I
I
!
I
Y
Figure 4. T a n g e n t RBodulm cs. Strain for ID-55 Polyethylene at 25" C.
+
Vol. 42, No. 5
10%. In the temperature range betn-een -30" and 25" C., the strain corresponding to 50% modulus may be easily found from thc log E versus e curves (Figure 4). The area under the stress-strain curve from 0 to ~ g . is~ the . energy of strain, although n-ha,t portion of this energy is elast,ic cannot be determined from stress-strain curves alone. This area, denot,ed by W , was evaluated by graphical integration with a precision of about 10%. Because of the nonlinearity of t,hr stress-strain curves and the arbitrary definition of the apparent elast,ic limit this quantity is analogous but' not necessarily equiv;llent to elast,icresilience. Torsional Torque-Deflection Curves. I t is impractical to work at t'ernperatures below -60" C. with as complicated an inst'runient as a univei,sal testing machine and its accessorier;. Because of this, the torsional technique may be modified to give modulus measurements comparable to those obtained from the tensile stress-strain curves. Since the stress-strain curve is linear at low strains in the low temperature range the initial slope of a torque-deflection curve is expected to be const'ant and a rnmwi'e of the shear modulus.
EXPERIMENTAL TECHNIQUES. In the original Clash and Berg
(5) technique a single deflection reading is taken 5 seconds after tile application of a constant torque. This technique was modified
or ffe
log E = log Eo - 2.3 where Eo
tangent modulus at strait1 = Q-i.e., is the initial tangent modulus e = strain a = constant, characterist,ic of tlic material and teniperature of test 1
The constant, a, is evident.ly a measure of t,he curvature in the stress-strain curve and can be used as an index of the curvature in this temperature range. E@,the modulus extrapolated to zero st,rain, is B quantity entirely analogous to the initial tangent modulus used in the lontemperature range, Reproducibility has bcrri found to be good, witli the coefficient of variation between 1.5 to 2.5%, depending on Ihe compound and the test temperature. This method of evaluation was used for all the tensile stress-strain data in the -30" t.o +25" C. region where both Eo and CY have bceri determined. The form of Equation 1is suggested by t,he behavior of a simple viscoelwtic model-namely, a bIaxwell element-when subjected to a constant rate of straining ( 1 ) . According to theorv, however, CY should depend on the rate of straining while Eo should he independent of it. Over the range of straining rates available, t,he data show the opposite. Therefore, for the present, Equation 1 is to be considered only an empirical equat.ion describing the stress-strain as obtained under the conditions of measurements used. APPAREST ELASTIC LIMITASD SmaiN ENERGY.From a strcssstrain curve it is possible to extract more information than the value of the initial tangent modulus. There are no st'andard methods of analysis, however, for the wide variety of curvatures one encounters in polyethylene at various temperatures (see Figures 2 and 3). Keverthelesa, it is desirable to have some memure of what may be termed an elastic limit and the corresponding strain energy. Johnson's method of determining the apparent elastic limit seemed to answer most of the requirements. In this method (10) a secant modulus corresponding to 50% of the tangent modulus is drawn as shown by the line OB in Figure 3. Then a line, AB', is drawn parallel t o OB and tangent to the stress-strain curve. The point of tangency is defined as the apparent elastic limit and the corresponding strain and stress will be denoted by 6E.L.and 8E.L. (Figure 3). It is realized that' these definitions are quite arbit,rary; nevertheless, they are useful and the quantities 'are easily evalaated over the complete temperature range and can be determined with an accuracy of about
by taking a series of 5-second deflection readings at increasing applied loading torques. It, is realized that the torquc-deflection curve obtained this way is not equivalent to a stres3-strain curve obtained at a given rate of straining or stressing since the specimen is returned to a state of zero twist bekeen readings. At Ion. temperatures and Fvithin the elastic range, however, the initial linear portion is expected t o be a good measure of the shear modulus.
DEGREES OF ANGULAR TWIST
Figure 5 . Torque-Deflection Curve for D-45 l'nlyethylene at -50" C.
To facilitate testing at very low tempwatures, minor modificatiFns have been introduced in the original Clash and Berg technique. I t was found advantageous to increase the specimen span length to 3 inches and to employ specimens of about 0.050 inch in thickness in order to obtain higher sensitivit,y of the deflection readings. Frequent bearing freezing at lorn t,eiriperatures necessitated the installation of heavy duty heating collars with a variable temperature control both below and above the lower bearing of the t'orsion shaft. Liquefied Freon 12 was etnployed as an immersion liquid with liquid nitrogen as a coolant. The specimens were die cut from compression molded plaques as ill the original Clash and Berg method. DmERRIINATIOri O F THE h ~ O D l J L U SI N THE -125' to -25"
