3. Principal Physical Test Methods
3.3 Elastic Modulus
Elastic modulus is the ratio of stress to strain, measured within the range where deforma- tion is reversible and proportional to the stress. Young’s modulus is the ratio of the tensile (or compressive) stress to the extension (or compression) strain, i.e.,
E = (F/a)/(e/L) (3.1)
= FL/ae
where F/a is the ratio of the tensile (or compressive) force to the initial cross-sectional area and e/L is the ratio of the length increase (or decrease) to the initial length. For materials subjected to shear deformation (i.e., relative displacement of two parallel to them), the shear or rigidity modulus, G, applies. This is represented by Figure 3.3.
G = shear stress/shear strain (3.2)
= (force/area of one face)/(displacement/distance between faces)
It is less than Young’s modulus, being related to the latter; thus, E/2G = (1 + Poission’s ratio);
for rubber, Poisson’s ratio for small strains is 0.5 and G is thus about one-third of E.
Elastic modulus (Young’s or shear) has the same dimensions as stress and is listed in kgf/mm2 ormPa; for fibers it can be expressed in gf/denier. Poisson’s ratio is lateral strain divided by longitudinal strain in a material subjected to stress; thus, in a stretched ten- sile test piece it equals (the proportional decrease in width or thickness)/(the proportional increase in length).
The value of Young’s modulus indicates the resistance of a material to reversible longi- tudinal deformation. It can be considered as the theoretical stress required to double the length of a specimen, but this is not realized in practice because either the material breaks short (e.g., glass, most materials and hard plastics), or the stress/strain relationship is not linear. For most plastics materials, Young’s modulus is less than 1/10 that of metals, while for rubbers it is only 1/10,000 or less; some fibers, however, have a modulus approach- ing that of metals. For materials in the rubber-like (high-elastic) state, elastic modulus increases with an increase in the degree of crosslinking. Young’s modulus can be derived from measurements of extension under load or of the bending of a rod or beam or of defor- mation under compressive load. The strain should be kept small so as to maintain a linear stress-strain relationship. This applies particularly to compression, where the linear range is especially small if the shape factor (ratio of cross-sectional dimensions to height) is large, and if the end faces of the test piece cannot slip freely over the compressing surfaces (the test piece then “barrels” and in shear gives a bigger linear range), so that measurements of
1 2
h
l
3 4 4'
l
3' 1' 2'
h N
(a) (b)
(c) FIGURE 3.3
Typical shear specimen.
shear modulus are often advantageous. The measurement of complex modulus is also use- ful, because it can be analyzed into an in-phase or storage modulus and an out-of-phase or loss modulus, corresponding respectively to components of the stress in phase and 90 degree out of phase with the applied strain; the out-of-phase modulus determines the energy loss in cyclic deformations. The ratio of out-of-phase modulus to in-phase modulus is the loss tangent (tan δ, δ being the loss angle). A related quantity is the internal fric- tion, equal to the out-of-phase modulus divided by the angular frequency of the deforma- tion cycles. Both the in-phase and out-of-phase moduli, especially the latter, increase with an increasing rate of deformation. Hence, modulus measured at high deformation rates, notably under “dynamic” conditions (e.g., impact vibration, rapidly repeated deformation cycles), is higher than the “static” modulus measured under equilibrium conditions or by slow deformation.
Bulk modulus is the ratio of the change in external pressure to the change in column for reversible conditions, and it indicates the resistance of a substance to volume compression.
It is high in organic polymers; materials appear in about the same order as for Young’s modulus, but the values are higher, sometimes greatly so. Thus, the bulk modulus for soft rubbers is similar to that for water and the less compressible organic liquids (i.e., initially 200 kgf/mm2, as compared with Young’s modulus 0.2 kgf/mm2). The rubber technologist’s
“modulus” is the stress (calculated on the initial cross section) at a stated elongation, usu- ally a multiple of 100%. It is not a modulus in the strict sense and is better called “stress at X% elongation,” or simply “X% stress value.”
Hardness as measured on vulcanized rubber is essentially a function of elastic modulus.
The preparation of test pieces is as follows:
• A test piece of proper dimension must be prepared prior to each test.
• Direct molding can be possible from a mixed compound.
• Specimens are needed to be cut, sliced, or buffed from the finished products.
3.3.1 Effect of Mixing and Molding
Processing variables can affect to a great extent the results obtained on the final product;
different physical tests are carried out in order to detect the results of these variables, such as state of cure and level of dispersion.
Mixing is carried out in open two-roll mills and/or internal mixers, like Banbury or Intermix types following the standard methods.
The conditions and time of storage between mixing and vulcanization can affect the properties; hence it is necessary to store the material in a dark and dry atmosphere. The preferred conditioning time is 24 h.
To get a better idea from the laboratory test results with the full-sized factory equipment, the tightest possible control on equipment, times, temperatures, and procedures is necessary.
3.3.2 Effect of Cutting/Die Cut from Sheet
The accuracy of the final test result depends considerably on the accuracy with which the test piece was prepared. The first requirement is that the test piece should be dimension- ally accurate.
It is essential that cutters be sharp and free from nicks or unevenness in the cutting edge as that can produce flaws in the test piece resulting in premature failure. Blunt knives lower tensile strength on ring test pieces by 5-10%.
It is normal to restrict stamping to sheets no thicker than 4 mm as the “dishing” effect becomes more severe as the thickness increases.
Rotary cutters can be used to produce discs or rings from thin sheets and are necessary for sheets above about 4 mm thick to prevent distortion.
A lubricant that has no effect on the rubber can be applied during cutting the sample, particularly when using a rotating cutter.
3.3.3 Test Pieces from Finished Products
It is desirable to test wherever possible on the actual finished product rather than on spe- cially prepared test pieces that may have been produced under rather different conditions.
To obtain a test piece from a finished product, it is necessary to cut a large block and then reduce the thickness and remove irregularities by using the buffing/slitting machine.
Some examples of test pieces are shown in Figure 3.4.
The particular disadvantage of buffing is that heat is generated which may cause signifi- cant degradation of the rubber surface. The effect of buffing on tensile properties (drop) on soft rubbers is 10-15%, whereas for a tire tread type the drop is about 5-10%.
A discussion of all the test methods available to the rubber compounder is not intended.
Here we discuss only a few of the most common tests, their significance, and equipment used, considering the limited operating budget available to small/medium-scale manufac- turers. Table 3.1 presents processability test information, and Table 3.2 presents informa- tion for vulcanizate testing. The samples are cured at optimum cure time determined from a rheometer (see Figure 3.5).
3.4 Some Special Features of General Physical Tests