Creep

Plastic materials subjected to a constant stress can deform continuously with time and the behavior under different conditions such as temperature. This continuous deformation with time is called creep or cold flow. In some applications the permissible creep deformations are critical, in others of no significance. But the existence of creep necessitates information on the creep deformations that may occur during the expected life of the product. Materials such as plastic, RP, zinc, and tin creep at room temperature. Aluminum and magnesium alloys start to creep at around 300°F. Steels above 650°F must be checked for creep.

There are three typical stages. The initial strain takes place almost immediately, consisting of the elastic strain plus a plastic strain near its end, if the deformation extends beyond the yield point. This initial action in the first stage shows a decreasing rate of elongation that can be called strain hardening (as in metals). The action most important to the designer's working area concerns the second stage that is at a minimum strain rate and remains rather constant. In the third stage a rapid increase in the creep rate occurs with severe specimen necking/ thickness reduction and ultimately rupture. It is important for the designer to work in the second stage and not enter the third stage. Thus, after plotting the creep vs. time data of a 1,000 h test, the second stage can be extrapolated out to the number of hours of desired product life.

These test specimens may be loaded in tension or flexure (with some in compression) in a constant temperature environment. With the load kept constant, deflection or strain is recorded at regular intervals of hours, days, weeks, months, or years. Generally, results are obtained at different stress levels.

In conducting a conventional creep test, curves of strain as a function of time are obtained for groups of specimens; each specimen in one group is subjected to a different constant stress, while all of the specimens in the group are tested at one temperature. In this manner families of curves are obtained. Important are the several methods that have been proposed for the interpretation of such data.

The rate of viscoelastic creep and stress relaxadon at a given temperature may vary significandy from one TP to another because of differences in the chemical structure and shape of the plastic molecules (Chapter 1). These differences affect the way the plastic molecules interact with each other. Viscoelastic creep and stress relaxadon tests are generally conducted up to 1,000 hours. Time-temperature super-positioning is often used to extrapolate this 1,000 hours of data to approximately 100,000 hours (= 12 years). Basically with TPs subjected to heat there is an increase in the rate of creep and stress relaxation. The TSs and particularly reinforced thermosets (RTSs) remains relatively unaffected until a high temperature is encountered.

Usually the strain readings of a creep test can be more accessible if they are presented as a creep modulus that equals stress divided by strain. In the viscoelastic plastic, the strain condnues to increase with time while the stress level remains constant. Result is an appearance of a changing modulus. This creep modulus also called the apparent modulus or viscous modulus when graphed on log-log paper, is a straight line and lends itself to extrapolation for longer periods of time.

Plastic viscoelastic nature reacts to a constant creep load over a long period of time by an ever-increasing strain. With the stress being constant, while the strain is increasing, result is a decreasing modulus. This apparent modulus and the data for it are collected from test observations for the purpose of predicting long-term behavior of plastics subjected to a constant stress at selected temperatures.

The creep test method of loading and material constituents influences creep data. Increasing the load on a part increases its creep rate. Particulate fillers provide better creep resistance than unfilled plastics but are less effective than fibrous reinforcements. Additives influence data such as the effect of a flame-retardant additive on the flexural modulus provides an indication of its effect on long-time creep. Increasing the level of reinforcement in a composite increases its resistance to creep. Glass-tiber-reinforced amorphous TP RPs generally has greater creep resistance than glass fiber-reinforced crystalline TP RPs containing die same amount of glass fiber. Carbon-fiber reinforcement is more effective in resisting creep than glass-fiber reinforcement.

Figure 3.8 Mechanical Maxwell model

Elastic spring

Elastic spring

Weight

Weight

For the designer there is generally a less-pronounced curvature when creep and relaxadon data are plotted log-log. Predictions can be made on creep behavior based on creep and relaxation data. This usual approach makes it easier to extrapolate, particularly with creep modulus and creep-rupture data.

To relate the viscoelastic behavior of plastics with an S-S curve the popular Maxwell model is used, this mechanical model is shown in Fig. 3.8. This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis that can be related to plastic's non-Newtonian flow behavior. It consists of a spring [simulating modulus of elasticity (H)] in series with a dashpot of coefficient of viscosity (77). It is an isostress model (with stress 5), the strain (e) being the sum of the individual strains in the spring and dashpot.

Based on this mechanical loading system a differential representation of linear viscoelasticity is produced as:

When a load is applied to the system the spring will deform. The dashpot will remain stationary under the applied load, but if the same load continues to be applied, the viscous fluid in the dashpot will slowly leak past the piston, causing the dashpot to move. Its movement corresponds to the strain or deformation of the plastic material.

When the stress is removed, the dashpot will not return to its original position, as the spring will return to its original position. The result is a viscoelastic material behavior as having dual actions where one is of an elastic material (spring), and the other like the viscous liquid in the deldt = ("\IE) dS/dt + (8/r¡)

dashpot. The properties of the elastic phase is independent of time, but the properties of the viscous phase are very much a function of time, temperature, and stress (load). A thinner fluid resulting from increased temperature under a higher pressure (stress) will have a higher rate of leakage around the piston of the dashpot during the time period. A greater creep occurs at this higher temperature that caused higher stress levels and strain.

The Maxwell model relates to a viscoelastic plastic's S-S curve. The viscoelasticity of the plastic causes an initial deformation at a specific load and temperature. It is followed by a continuous increase in strain under identical test conditions until the product is either dimensionally out of tolerance or fails in rupture as a result of excessive deformation.

Test data using the apparent creep modulus approach is used as a method for expressing creep. It is a convenient method of expressing creep because it takes into account initial strain for an applied stress plus the deformation or strain that occurs with time. Because parts tend to deform in time at a decreasing rate, the acceptable strain based on service life of the part must be determined. The shorter the duration of load, the higher the apparent modulus and the higher the allowable stress.

When plotted against time, they provide a simplified means of predicting creep at various stress levels. It takes into account the initial strain for an applied stress plus the amount of deformation or strain that occurs over time. Fig. 3.9 shows curves of deformation versus time. Beyond a certain point, creep is small and may safely be neglected for many applications.

; Apparent creep modulus vs. log time with increased load (Courtesy of Mobay/Bayer)

LOG TIME ->

The acceptable strain based on the desired service life of a product can be determined since they deform under load in time at a decreasing rate. Short duration results in the higher apparent modulus and in turn a higher allowable stress. The apparent modulus is most easily explained with an example. The apparent modulus Ea is calculated in a very simplified approach as:

Ea= Stress/Initial strain + Creep (3-2)

As long as the stress level is below the elasdc limit of the material, its E can be obtained from the usual equation:

If a compressive stress of 10,000 psi (69 MPa) is used, the result is a strain of 0.015 in ./in. (0.038 cm/cm) for FEP plastic at 63°F (17°C). Thus:

If this stress level remains for 200 hours, the total strain will be the sum of the initial strain plus the strain due to time. This total strain can be obtained from a creep-data curve. With a total deformation under a tension load for 200 hours of 0.02 in./in., the result is:

An E can then be determined for one year. Extrapolating from the straight-line creep-data curve gives a deformation of 0.025 in./in. the E becomes:

Different attempts have been used to create meaningful formulas for the apparent modulus change with respect to time. However the factors in the formulas that would fit all conditions are more complicated to use than presenting test data in a graph form and using it as the means for predicting the strain (elongation) at some distant point in time. Log-log test data usually form a straight line and lend themselves to easy extrapolation by the designer. The slope of the straight line depends on the material being tested such as its rigidity and temperature of heat deflection with the amount of stress in relation to tensile strength.

Long term behavior of plastics involves plastic exposure to conditions that include continuous stresses, environment, excessive heat, abrasion, and/or continuous contact with liquids. Tests such as those outlined by ASTM D 2990 that describe in detail the specimen preparations and testing procedure are intended to produce consistency in observations and records by various manufacturers, so that they can be correlated to provide meaningful information to product designers. The procedure under this heading is intended as a recommendadon for uniformity of making setup conditions for the test, as well as recording the resulting data. The reason for this move is the dme consuming nature of the test (many years' duration), which does not lend itself to routine testing. The test specimen can be round, square, or rectangular and manufactured in any suitable manner meeting certain dimensions. The test is conducted under controlled temperature and atmospheric conditions.

The requirements for consistent results are oudined in detail as far as accuracy of time interval, of readings, etc., in the procedure. Each report of test results should indicate the exact grade of material and its supplier, the specimen's method of manufacture, its original dimensions, type of test (tension, compression, or flexure), temperature of test, stress level, and interval of readings. When a load is initially applied to a specimen, there is an instantaneous strain or elongation. Subsequent to this, there is the time-dependent part of the strain (creep), which results from the continuation of the constant stress at a constant temperature. In terms of design, creep means changing dimensions and deterioration of product strength when the product is subjected to a steady load over a prolonged period of time.

All the mechanical properties described in tests for the conventional data sheet properties represented values of short-term application of forccs. In most cases, the data obtained from such tests are used for comparative evaluation or as controlling specifications for quality determination of materials along with short-duration and intermittent-use design requirements. The visualization of the reaction to a load by the dual component interpretation of a material is valuable to the understanding of the creep process, but meaningless for design purposes. For this reason, the designer is interested in actual deformation or part failure over a specific time span. The time segment of the creep test is common to all materials, strains are recorded until the specimen ruptures or the specimen is no longer useful because of yielding. In either case, a point of failure of the test specimen has been reached, this means making observations of the amount of strain at certain time intervals which will make it possible to construct curves that could be extrapolated to longer time periods. The initial readings are 1, 2, 3, 5, 7, 10, and 20 h, followed by readings every 24 h up to 500 h and then readings every 48 h up to 1,000 h.

The strain readings of a creep test can be more convenient to a designer if they are presented as a creep modulus. In a viscoelastic material, strain continues to increase with time while the stress level remains constant.

Since the modulus equals stress divided by strain, there is the appearance of a changing modulus.

The method of obtaining creep data and their presentation have been described; however, their application is limited to the exact same material, temperature use, stress level, atmospheric conditions, and type of test (tensile, compression, flexure) with a tolerance of ±10%. Only rarely do product requirement conditions coincide with those of the test or, for that matter, are creep data available for all grades of material. In those cases a creep test of relatively short duration such as 1,000 h can be instigated, and the information can be extrapolated to the long-term needs. It should be noted that reinforced thermoplastics and thermosets display much higher resistance to creep (Chapter 4).

The stress-strain-time data can be plotted as creep curves of strain vs. log time (Fig. 3.10 top view). Different methods are also used to meet specific design requirements. Examples of methods include creep curves at constant times to yield isochronous stress versus strain curves or at a constant strain, giving isometric stress versus log-time curves, as shown in the bottom views in Fig. 3.10.

To date the expected operating life of most plastic products designed to

Figure 3 10 Examples of different formatted creep vs. log time curves (Courtesy of Mobay/Bayer)

Figure 3 10 Examples of different formatted creep vs. log time curves (Courtesy of Mobay/Bayer)

Increasing Stress

Increasing Stress

ISOMETRIC STRESS ISOCHRONOUS STRESS

VS LOG TIME

VS STRAIN

ISOMETRIC STRESS ISOCHRONOUS STRESS

VS LOG TIME

VS STRAIN

Log time

Strain

Log time

Strain withstand creep is usually at least ten to twenty years. Available data at the time of designing will not be available so one uses available creep test-data based on at least 1,000 hours that is the recommended time specified in the ASTM standard. These long-time data have been developed and put to use in designs for over a half-century in designing plastic materials. An example is the engineering design and fabrication of the first all-plastic airplane.

Creep information is not as readily available as that from short-term property data sheets. From a designer's viewpoint, it is important to have creep data available for products subjected to a constant load for prolonged periods of time. The cost of performing or obtaining the test in comparison with other expenditures related to product design would be insignificant when considering the element of safety and confidence it would provide. Furthermore, the proving of product performance could be carried out with a higher degree of favorable expectations as far as plastic material is concerned. Progressive material manufacturers can be expected to supply the needed creep and stress-strain data under specified use conditions when requested by the designer; but, if that is not the case, other means should be utilized to obtain required information.

In conclusion regarding this subject, it can be stated that creep data and a stress-strain diagram indicate whether plain plastic properties can lead to practical product dimensions or whether a RP has to be substituted to keep the design within the desired proportions. For long-term product use under continuous load, plastic materials have to be considered with much greater care than would be the case with metals.

Preparing the important creep rupture data for the designer is similar to that for creep except that higher stresses are used and the time is measured to failure. It is not necessary to record strain. The data are plotted as the log stress vs. log time to failure. In creep-rupture tests it is the material's behavior just prior to the rupture that is of primary interest. In these tests a number of samples are subjected to different levels of constant stress, with the time to failure being determined for each stress level.

The overall behavior is the time-dependent strain at which crazing, stress whitening, and rupture decreases with a decreasing level of sustained stress. The time to develop these defects increases with a decreasing stress level.

Thermoplastic fiber RPs display a degree of creep, and creep rupture compared to RPs with thermoset plastics. TS plastic RPs reinforced with carbon and boron is very resistant to deformation (creep) and failure (creep rupture) under sustained stadc load when they are loaded in a fiber-dominated direction. The creep and creep rupture behavior of aramid fiber is not as good but still rather high. Creep and creep rupture with RPs has to take into consideration the stresses in matrixdominated directions. That is fiber oriented directional properties influence the data.

In service products may be subjected to a complex pattern of loading and unloading cycles that is represented by stress relaxation. This variability of intermittent loading can cause design problems in that it would clearly not be feasible to obtain experimental data to cover all possible loading situations, yet to design on the basis of constant loading at maximum stress would not make efficient use of materials or be economical. In such cases it is useful to have methods for predicting the extent of the accumulated strain that will be recovered during the no load periods after cyclic loading.

Tests have been conducted that provide useful stress relaxation data. Plastic products with excessive fixed strains imposed on them for extended periods of time could fail. Data is required in applications such as press fits, bolted assemblies, and some plastic springs. In time, with the strain kept constant the stress level will decrease, from the same internal molecular movement that produces creep. This gradual decay in stress at a constant strain (stress-relaxation) becomes important in these type applications in order to retain preloaded conditions in bolts and springs where there is concern for retaining the load.

The amount of relaxation can be measured by applying a fixed strain to a sample and then measuring the load with time. The resulting data can be presented as a series of curves. A relaxation modulus similar to the creep modulus can also be derived from the relaxation data, it has been shown that using the creep modulus calculated from creep curves can approximate the decrease in load from stress relaxation. From a practical standpoint, creep measurements are generally considered more important than stress-relaxation tests and are also easier to conduct.

The TPs are temperature dependent, especially in the region of the plastics' glass transition temperature (Tg). Many unreinforced amorphous types of plastics at temperatures well below the Tg have a tensile modulus of elasticity of about 3 x 1010 dynes/cm2 [300 Pa (0.04 psi)] at the beginning of a stress-relaxation test. The modulus decreases gradually with time, but it may take years for the stress to decrease to a value near zero. Crystalline plastics broaden the distribution of the relaxation times and extend the relaxation stress to much longer periods. This pattern holds true at both the higher and low extremes of crystallinity. With some plastics, their degree of crystallinity can change during the course of a stress-relaxation test.

Stress-relaxadon test data has been generated for the designer. Plasdc is deformed by a fixed amount and the stress required maintaining this deformation is measured over a period of time. The maximum stress occurs as soon as the deformation takes place and decreases gradually with time from this value.

Creep data in designing products has been used for over a century; particularly since the 1940s. Unfortunately there is never enough data especially with the new plastics that are produced. However, relationships of the old and new are made successfully with a minor amount of testing.

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