## Static stress

The mechanical properties of plastics enable them to perform in a wide variety of end uses and environments, often at lower cost than other design materials such as metal or wood. This section reviews the static property aspects that relate to short term loads.

As reviewed thermoplastics (TPs) being viscoelastic respond to induced stress by two mechanisms: viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied mechanical energy as frictional heat and results in permanent material deformation. Elastic deformation stores the applied mechanical energy as completely recoverable material deformation. The extent to which one or the other of these mechanisms dominates the overall response of the material is determined by the temperature and by the duration and magnitude of the stress or strain. The higher the temperature, the most freedom of movement of the individual plastic molecules that comprise the TP and the more easily viscous flow can occur with lower mechanical performances.

With the longer duration of material stress or strain, the more time for viscous flow to occur that results in the likelihood of viscous flow and significant permanent deformation. As an example when a TP product is loaded or deformed beyond a certain point, it yields and immediate or eventually fails. Conversely, as the temperature or the duration or magnitude of material stress or strain decreases, viscous flow becomes less likely and less significant as a contributor to the overall response of the material; and the essentially instantaneous elastic deformation mechanism becomes predominant.

Changing the temperature or the strain rate of a TP may have a considerable effect on its observed stress-strain behavior. At lower temperatures or higher strain rates, the stress-strain curve of a TP may exhibit a steeper initial slope and a higher yield stress. In the extreme, the stress-strain curve may show the minor deviation from initial linearity and the lower failure strain characteristic of a britde material.

At higher temperatures or lower strain rates, the stress-strain curve of the same material may exhibit a more gradual initial slope and a lower yield stress, as well as the drastic deviation from initial linearity and the higher failure strain characteristic of a ductile material.

There are a number of different modes of stress-strain that must be taken into account by the designer. They include tensile stress-strain, flexural stress-strain, compression stress-strain, and shear stress-strain.

### Tensile Stress-Strain

In obtaining tensile stress-strain (S-S) engineering data, as well as other data, the rate of testing direcdy influence results. The test rate or the speed at which the movable cross-member of a testing machine moves in relation to the fixed cross-member influences the property of material. The speed of such tests is typically reported in cm/min. (in./min.). An increase in strain rate typically results in an increase yield point and ultimate strength.

An extensively used and important performance of any material in mechanical engineering is its tensile stress-strain curve (ASTM D 638). It is obtained by measuring the continuous elongation (strain) in a test sample as it is stretched by an increasing pull (stress) resulting in a stress-strain (S-S) curve. Several useful qualities include the tensile strength, modulus (modulus of elasticity) or stiffness (initial straight-line slope of the curve following Hooke's law and reported as Young's modulus), yield stress, and the length of the elongation at the break point.

Stress is defined as the force on a material divided by die cross sectional area over which it initially acts (engineering stress). When stress is calculated on the actual cross section at the time of the observed failure instead of the original cross sectional area it is called true stress. The engineering stress is reported and used practically all the time.

Strain is defined as the deformation of a material divided by a corresponding original cross section dimensions. The units of strain are meter per meter (m/m) or inch per inch (in./in.). Since strain is often regarded as dimensionless, strain measurements are typically expressed as a percentage.

Tensile strength is the maximum tensile stress sustained by a specimen during a tension test. When a maximum stress occurs at its yield point it is designated as tensile strength at yield. When the maximum stress occurs at a break, it is its tensile strength at break. In practice these differences are frequentiy ignored.

The ultimate tensile strength is usually measured in megapascals (MPa) or pounds per square inch (psi). Tensile strength for plastics range from under 20 MPa (3000 psi) to 75 MPa (11,000 psi) or just above, to more than 350 MPa (50,000 psi) for reinforced thermoset plastics (RTPs).

The area under the stress-strain curve is usually proportional to the energy required to break the specimen that in turn can be related to the toughness of a plastic. There are types, particularly among the many fiber-reinforced TSs, that are very hard, strong, and tough, even though their area under the stress-strain curve is extremely small.

Tensile elongation is the stretch that a material will exhibit before break or deformation. It is usually identified as a percentage. There are plastics that elongate (stretch) very little before break, while others such as elastomers have extensive elongation.

On a stress-strain curve there can be a location at which an increase in strain occurs without any increase in stress. This represents the yield point that is also called yield strength or tensile strength at yield. Some materials may not have a yield point. Yield strength can in such cases be established by choosing a stress level beyond the material's elastic limit. The yield strength is generally established by constructing a line to the curve where stress and strain is proportional at a specific offset strain, usually at 0.2%. Per ASTM testing the stress at the point of intersection of the line with the stress-strain curve is its yield strength at 0.2% offset.

Another important stress-strain identification is the proportional limit. It is the greatest stress at which the plastic is capable of sustaining an applied load without deviating from the straight line of an S-S curve.

The elastic limit identifies a material at its greatest stress at which it is capable of sustaining an applied load without any permanent strain remaining, once stress is completely released.

With rigid plastics the modulus that is the initial tangent to the S-S curve does not change significantiy with the strain rate. The softer TPs, such as general purpose polyolefins, the initial modulus is independent of the strain rate. The significant time-dependent effects associated with such materials, and the practical difficulties of obtaining a true initial tangent modulus near the origin of a nonlinear S-S curve, render it difficult to resolve the true elastic modulus of the softer TPs in respect to actual data.

The observed effect of increasing strain is to increase the slope of the early portions of the S-S curve, which differs from that at the origin. The elastic modulus and strength of both the rigid and the softer plastics each decrease with an increase in temperature. Even though the effects of a change in temperature are similar to those resulting from a change in the strain rate, the effects of temperature are much greater.

### Modulus of Elasticity

Many unreinforced and reinforced plastics have a definite tensile modulus of elasticity where deformation is direcdy proportional to their loads below the proportional limits. Since stress is proportional to load and strain to deformation, stress is proportional to strain. Fig. 2.4 shows this relationship. The top curve is where the S-S straight line identifies a modulus and a secant modulus based at a specific strain rate at point C' that could be the usual 1% strain. Bottom curve secant moduli of different plastics are based on a 85% of the initial tangent modulus.

There are unreinforced commodities TPs that have no straight region on the S-S curve or the straight region of this curve is too difficult to locate. The secant modulus is used. It is the ratio of stress to the corresponding strain at any specific point on the S-S curve. It is the line from the initial S-S curve to a selected point C on the stress-strain curve based on an angle such as 85% or a vertical line such as at the usual 1% strain.

Hooke's Law highlights that the straight line of proportionality is calculated as a constant that is called the modulus of elasticity (E). It is

Figure 2.4 Examples of tangent moduli and secant moduli

Figure 2.4 Examples of tangent moduli and secant moduli

the straight-line slope of the initial portion of the stress-strain curve: Stress/Strain = Constant (2-9)

The modulus of elasticity is also called Young's modulus, elastic modulus, or just modulus. E was defined by Thomas Young in 1807 although others used the concept that included the Roman Empire and Chinese-BC. It is expressed in terms such as MPa or GPa (psi or Msi). A plastic with a proportional limit and not loaded past its proportional limit will return to its original shape once the load is removed.

With certain plastics, particularly high performance RPs, there can be two or three moduli. Their stress-strain curve starts with a straight line that results in its highest E, followed by another straight line with a lower S, and so forth. To be conservative providing a high safety factor the lowest E is used in a design, however the highest E is used in certain designs where experience has proved success.

Standard ASTM D 638 states that it is correct to apply the term modulus of elasticity to describe the stiffness or rigidity of a plastic where its S-S characteristics depend on such factors as the stress or strain rate, the temperature, and its previous history as a specimen. However, D 638 still suggests that the modulus of elasticity can be a useful measure of the S-S relationship, if its arbitrary nature and dependence on load duration, temperature, and other factors are taken into account.

Interesting straight-line correlations exist of the tensile modulus of elasticity to specific gravity of different materials (Fig. 2.5). In this figure, the modulus/specific gravity of reinforced plastics with its high performing fibers (graphite, aramid, carbon, etc.) continues to increase in the upward direction.

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