Model for the Demonstration of Elastic and Plastic Properties G. GOWFINGER and C. B. WENDELL, JR. Godfrey L. Cabot, Inc., Boston, Massachusetts
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T IS customary to describe the mechanical behavior of high polymers, such as rubber or fibers, in terns of a system of springs and dashpots. The springs represent the elastic component or components of the e a terial, and the dashpots the flow. In combination with the springs the dashpots represent the retarded elastic effect shown by many high polymers. Such a model is convenient and helpful in visualizing the form andmeaning of the differential equations describing the stressstrain relationships of these materials. However, it is difficult to construct a dexonstration =ode1 of any versatility &ployiug actual springs and dashpots
removed the piston moves back into equilibrium position. The dashpot can be replaced by a capillary through which a viscous fluid is forced by the pressure differential created by the movement of the piston. On this basis a model was built consisting of an allglass syringe (S),a two-way stopcock (11),a one-way stopcock (I),and a glass container of about 5-cc. volume ( V z ) . With this model it is possible to demonstrate three combinations of the spring-dashpot system; namely, (a) instantaneous elastic deformation, (b) re-
C
m
time
Figure B
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FIGURE 2.-TIME-ELONOATIONCURVESAND THE CORRESPONDING
MECHANICAL MODELS
The curves are obtained when: FIGURE1.-MODEL
FOR
THE
DEMONSTRATION OF ELASTIC AND PLASTIC PROPERTIES
A B C
Stopcock I
Closed Closed Open
Stopcock II
connecting syringe ( S ) with tube ( T ) connecting syringe ( S ) with capillary (C) connecting syringe ( S ) with capillary (C)
By taking advantage of the gas laws i t is easy to re- tarded elastic deformation, and ( 6 ) plastic flow. Figure place the spring with a cylinder and piston in which air 1 shows the instrument. On the bottom a 2-cc. allis expanded by pulling on the piston. When the force is glass syringe (S)can he seen which is connected through 434
the single lead of a two-way stopcock ( I n to a vessel placed above. One of the connections (C) from this stopcock is a capillary about 10 cm. long and 0.7 to 1.0 mm. in diameter which is connected to the bottom of the vessel ( V 2 ) The other arm of the two-way stopcock is connected through a tube (T) which leads through a ring seal to the top of the vessel (V,). Above the end of the tube (V,) a one-way stopcock ( I ) connects the container with the atmosphere. Volume V2is filled to within a few mm. of the top of the tube VI with medium viscosity lubricating oil. When stopcock I is closed and stopcock 11is put in a position in which the syringe is connected to the tube T and hence to volume V,, the syringe connects with a gas volume. By attaching a weight to the bottom of the syringe this moves downward, creating an underpressure in the completely closed volume, and the downward movement stops when the atmospheric pressure balances the weight attached to the piston. This process takes place quite rapidly and creates the illusion of instantaneous elastic response and hence corresponds to the spring. When stopcock II is in a position to connect the syringe with the capillary C and stopcock I is still closed, then the oil placed in volume Vz has to flow through this capillary to permit the piston to move downward and create the underpressure required to balance the attached weight. The velocity of the movement of the piston, of course, depends on the size of the
capillary, the volume of oil which has to he displaced, and the viscosity of the oil. If the dimensions are as mentioned above and a medium to low viscosity oil is used, equilibrium will be reached in about one minute, which is a sufficientlength of time to take measurements for plotting the curve, nevertheless short enough for convenient demonstration purposes. On the removal of the weight the piston moves back according to a curve which is the reciprocal of the expansion curve. Finally, when stopcock II is in the position to connect the syringe with the capillary and stopcock I is open, the piston moves under the weight attached to it as a model of plastic flow. The slope of the time-elongation curve thus obtained is the same as the initial slope of the curve representing retarded elastic deformation. In Figure 2 the mechanical models cotresponding to these three possibilities are shown and with each is given the pattern of curve which can be obtained when plotting the position of the syringe versus time. A similar model was built with two three-way stopcocks and by putting volume V2in a slightly different position five combinations of springs and dashpots could he demonstrated. By providing a variety of capillaries and independent volumes interconnected with a sufficientnumber of stopcocks any model could, of course, be built. However, these more intricate models are hardly suited for simple classroom demonstration.
