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It is common use to call the time dependent ratio of tensile stress to strain the relaxation modulus, E, and to present the results of the experiments in the form of E as a function of time. This quantity should be distinguished, however, from the tensile modulus E as determined in elastic deformations, because stress relaxation does not occur upon deformation of an ideal rubber.

The stress-relaxation behaviour of polymers is extremely temperature-dependent, especially in the region of the glass temperature. For amorphous polymers the constant n may vary between 0. If the behaviour over a longer time period must be described, a number of equations of this type can be superposed, each with a different relaxation time. This is due to the volume retardation phenomenon, which, as mentioned before, is a decrease of free volume.

This volume retardation hinders to an increasing degree the movements of parts of the polymer chains and thus causes the relaxation times to increase with ageing. For a material that experienced a temperature quench only shortly ago, the volume retardation is still relatively fast, so that the relaxation times are relatively large. In the course of time the relaxation times increase, and consequently the stress relaxation will proceed slower.

An illustrative example is shown in Fig. From McLoughlin, and Tobolsky From Struik , Courtesy of the author and of Elsevier Science Publishers. Creep elasto-plasticity Dimensional stability is one of the most important properties of solid materials, but few materials are perfect in this respect. Creep is the time-dependent relative deformation under a constant force tension, shear or compression. Hence, creep is a function of time and stress. For small stresses the strain is linear, which means that the strain increases linearly with the applied stress. For higher stresses creep becomes non-linear.

As long as creep is linear, time-dependence and stress-dependence are separable; this is not possible at higher stresses. A simple check for separability of the variables is that curves of log strain vs. From bottom to top 10, 20, 30, 40, 50 and 60 MPa. The stress-dependence and time dependence are separable at stresses below about 35 MPa and inseparable at stresses above about 35 MPa.

As the amount of deformation increases, viscous phenomena become increasingly important. At a given moment the specimen may show yielding, i. The results of creep experiments are usually expressed in the quantity creep compliance, the time-dependent quotient of strain and stress. Creep properties are very much dependent upon temperature. Well below the glass transition point very little creep will take place, even after long periods of time.

As the temperature is raised, the rate of creep increases. In the glass-transition region the creep properties become extremely temperature-dependent. In many polymers the creep rate goes through a maximum near the glass-transition point. For n the same reasoning is valid as for the stress relaxation. The simple relaxation and retardation phenomena described by Eqs.

The reaction rate constant corresponds with the reciprocal relaxation or retardation time. In reality, these phenomena show even more correspondence with a system of simultaneous chemical reactions. Of course the reciprocals of the various compliances are equal to the elastic moduli presented in Fig. He studied nearly all aspects of this field, but paid special and careful attention on tensile and torsional creep.

An example of his careful measurements are creep measurements on poly vinyl chloride. Creep measurements in general suffer from ageing processes during long time creep, just as was mentioned for stress relaxation, because the creep retardation times increase approximately proportional to the ageing time te. In order to distinguish between creep with constant time constants retardation times and ageing, PVC samples were quenched from 90 C i. During those measurements the retardation times may be considered to be constant. Results are shown in Fig.

The creep rate decreases with increasing ageing time due to decrease of free volume, but the curves are parallel and superposition by almost horizontal shifts is possible, in order to obtain one master curve. Master curves obtained at different temperatures could also be superposed by almost horizontal shifts to obtain one super master curve see Fig. There, the effect of creep measurements where measuring time exceeds the ageing time, also becomes clear: creep turns out to be less fast, because during the measurements the volume retardation is continuing in the way described before, thereby causing the free volume to decrease.

Both the shortly aged and long-aged curves in Fig. The different curves were measured for various values of time te elapsed after the quench. The master curve gives the result of a superposition by shifts that were almost horizontal; the arrow indicates the shifting direction. The crosses refer to another sample quenched in the same way, but only measured for creep at a te of 1 day.

The master curve at 20 C was obtained by time—temperature superposition compare Section The origin of the phenomenon of ageing lies in the fact that glasses are not in thermodynamic equilibrium; their volume and entropy are too large, hence there is a tendency to volume reduction volume retardation. Decreases of rates of stress relaxation and creep are consequences of this phenomenon. Ageing does not affect secondary thermodynamic transitions; so the range of ageing falls between Tg and the first secondary transition Tb.

Propositions 1—4 are schematically illustrated by Figs. Physical ageing is important from a practical point of view. Application of polymeric materials is even based on ageing: without progressive stiffening, due to physical ageing, polymeric materials would not be able to resist mechanical loads during long periods of time.

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All polymers age in the same way, their relaxation times increasing proportionally to the ageing time. Proposition 6 is illustrated by Fig. Tg is the glass transition temperature, Tb the temperature of the highest secondary transition, and n the specific volume. By means of horizontal and vertical shifting the curves of all materials can be superimposed. Proposition 7 is illustrated by Fig.

Physical ageing persists for very long periods; at temperatures well below Tg — 25 K it may persist for hundreds of years. PVC 1. The master curves for the different materials were superimposed by horizontal and vertical shifts. S t Stress level high low t1 te log t FIG. For high stresses, the straight line region sets in at t1 9. Proposition 9 is illustrated by Fig. The long-term behaviour of polymers is fundamentally different from the short time behaviour; the first cannot be explained from the latter, if the ageing time is neglected.

Proposition 10 is illustrated by Fig. In other words it is completely rejuvenated. Ageing therefore is a thermoreversible process to which one and the same sample can be subjected an arbitrary number of times. It has just to be retreated each time to the same temperature above Tg. Struik also — showed that his concept of physical ageing and its affects on the mechanical behaviour can be extended to semi-crystalline polymers; the only additional assumption needed is that in semi-crystalline polymers the glass transition is broadened and extended towards the high temperature side.

Struik showed furthermore that for amorphous and semi-crystalline polymers the ageing effect after complicated thermal histories is strikingly similar. Filled rubbers behave in the same way as semi-crystalline materials. Leaderman was the first to suggest that in viscoelastic materials time and temperature are equivalent to the extent that data at one temperature can be superimposed upon data taken at a different temperature, merely by shifting curves. Williams et al. This superposition is frequently used because the time scale or frequency scale of the viscoelastic behaviour of polymers from the glass transition to the flow region covers 10 to 15 decades, depending on the molecular weight of the polymer.

There are no instruments available to cover this range. Time temperature superposition is the remedy. These curves were corrected reduced for density and temperature. An arbitrary temperature To K 25 C was selected as the reference temperature. This reduction is of course not necessary for tan d. The amount each reduced modulus has to be shifted along the logarithmic time axis in making the master curve, the so-called shift factor, aT, is a function of temperature. The determination of log aT is quite difficult in the pseudo-rubbery region, where the curves are rather flat.

As will be shown later, the same values of the shift factor are obtained by plotting G0 o and G00 o versus log o. In the pseudo-rubbery region the curves for storage modulus are also rather flat, but the loss modulus goes through a minimum and accordingly the values of the shift factor are easier to determine. The reference temperature of the master curve is 25 C.

From Eisele , as reconstructed from Castiff and Tobolsky , In general, different values are experimentally g g found for different polymers see Table This WLF equation enables us to calculate the time frequency change at constant temperature, which — as far as the dynamic-mechanical behaviour is concerned — is equivalent to a certain temperature change at constant time frequency. This has been stated, for instance, by Rusch and Beck Most data from Ferry The TPSP for amorphous polymers above Tg The rates of relaxation and retardation processes above the glass temperature are strongly dependent on the viscosity and thus on the fraction of free volume present.

Because the viscosity not only depends on temperature but also on static pressure the glass transition temperature increases approximately 1 C per 20 bar of pressure it is not surprising that pressure also affects the viscoelastic processes. A qualitatively relation analogous to Eq. These data together with others at different temperatures are combined with reduced variables in Fig.

The treatment appears to be very succesful. From Fillers and Tschoegl Courtesy The American Institute of Physics. Mechanical Properties of Solid Polymers Example For polyisobutylene Tg is K. If we take for the WLF constants not the universal values of The values of We again apply Eq.

Combination of Eq. The shift factor is also the relative time shortening needed to simulate at a higher temperature a property measured at the reference temperature; it is the time lengthening to simulate at a lower temperature a property measured at the reference temperature. Solution Eq. Interrelations between different viscoelastic functions of the same material For a given material the viscoelastic properties — the relaxation behaviour for solid materials — can be determined by a number of different techniques.

The results obtained by each technique are expressed in the form of a characteristic function. In tensile deformation these functions are: a. Stress relaxation: The relaxation modulus as a function of time: E t b. Creep: The retardation compliance as a function of time: S t c. Periodic deformation: The components of the dynamic modulus or the dynamic compliance as functions of the frequencies E0 o and E00 o or S0 o and S00 o It will often be desirable to convert the results of one type of experiment into the characteristic quantities of another type.

Unfortunately, there are no rigorous rules for these conversions.

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The problem may be approached in two ways. In the first place, exact interrelations can be derived from the theory of linear viscoelasticity. This method has two disadvantages. The theory of linear viscoelasticity is applicable to rather small deformations only. The exact relations are not very suitable for numerical calculations, because the moduli or compliances must be known for zero to infinite times and the dynamic moduli or compliances from zero to infinite frequencies.

In practice, the exact interrelations will thus seldom be applicable. For a survey of these relationships the reader is referred to the monographs of Ferry and Schwarzl Schwarzl studied the errors to be expected in the application of this type of equations, starting from the theory of linear viscoelasticity. His results are given schematically in Fig. For non-linear viscoelastic behaviour, the exactitude of the approximate equations cannot be predicted. As it is impossible to mention all the approximate relationships that have been proposed in the literature; just to show, only a few examples will be given.

The applicability, however, decreases with an increasing amount of information required. Deformation properties The strength properties of solids are most simply illustrated by the stress—strain diagram, which describes the behaviour of homogeneous brittle and ductile specimens of uniform cross section subjected to uniaxial tension see Fig. Within the linear region the strain is proportional to the stress and the deformation is reversible. If the material fails and ruptures at a certain tension and a certain small elongation it is called brittle.

If permanent or plastic deformation sets in after elastic deformation at some critical stress, the material is called ductile. Between these two temperatures the behaviour — brittle or ductile — is mainly determined by the combination of temperature and rate of deformation. During the deformation of ductile polymers there is often an increase in stress with deformation; this is known as work-hardening.

If at some point the stress is removed, the material recovers along a path nearly parallel to the linear region; the sample then shows a permanent plastic deformation. There is a basic difference between rupture above the glass transition temperature where the polymer backbones have an opportunity to change their configurations before the material fails and well below Tg where the backbone configurations are essentially immobilised within the period of observation: brittle materials. Ultimate strength The observed brittle strength is generally very variable, but is always 10— times smaller than the theoretical value.

Only some very fine fibres e. Mechanical Properties of Solid Polymers prepared which have tensile strengths approaching the theoretical value. The multiplication factor can easily be of the order of 10— But even if the crack-tip tends to zero the material still possesses certain strength, so that there must be an extra effect to explain the facts. Griffith gave the answer to this problem by showing that for a crack to grow, it is not sufficient for the stresses at the crack-tip to exceed the theoretical strength; in addition sufficient elastic energy must be released to provide the extra surface energy that a growing crack demands.

This will be discussed in more detail in Sect. Ultimate strength of ductile materials If a material does not appreciably work-harden after yielding, in tension, its yield stress will be very nearly the maximum stress the material can support before it pulls apart, i. Tabor showed that the yield stress of a material is proportional to the indentation hardness see Chap. If a material shows work-hardening, as in many crystalline polymers due to orientation during the plastic deformation , the ultimate strength if calculated on the basis of original cross section will of course be higher than the yield stress.

Transition from ductility to brittleness, and vice versa As we have seen, mobility of the molecules is one of the sources of ductility. However, if the mobility is obstructed by some barrier, an internal crack may form, and initiate crack propagation. In this way a ductile solid may become brittle. On the other hand a brittle solid may be made ductile by applying hydrostatic pressure. Let us consider a brittle solid, which fails at a tensile stress s.

If the critical shear stress is less than this, the material will flow in a ductile manner before the tensile stress is large enough to produce brittle failure. Phenomena like this are well known. At great depths rocks can flow although they are normally very brittle. Even quartz can flow plastically under sufficiently high hydrostatic pressure. Well-known yield criteria are the Tresca criterion and the Von Mises criterion.

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Discussion of this subject falls beyond the scope of this book, but a clear description is presented in, e. If stresses increase above a certain value yield will occur. For metals this critical value is almost independent of pressure, whereas for polymers it is strongly dependent on pressure. An example is shown in Fig. In indentation hardness experiments, plastic indentation can often be made in relatively brittle materials. Hardness values thus obtained are a measure of the plastic properties of the brittle solid!

Another effect, which greatly influences the type of rupture, is orientation. If a polymer is heated just above the glass transition temperature, stretched several hundred percent in one direction and cooled to room temperature while under stress, the polymer chains will be trapped in a non-random distribution of conformations: more orientation parallel to the stretching direction. The material becomes markedly anisotropic and will be considerably stronger in the direction of orientation and weaker in the transverse direction. The area under the stress—strain curve energy per unit volume , a rough measure of toughness, may be 20 times as large for a properly oriented specimen of the same material.

If crystallisation and orientation go together, the strength can be further improved. The strongest polymeric materials synthetic fibres are oriented crystalline polymers. Crazing Crazing is a form of non-catastrophic failure that may occur in glassy polymers, giving rise to irreversible deformation. Crazes scatter light and are readily visible to the unaided eye as whitened planes perpendicular to the direction of stress. The molecular chains in a craze are aligned parallel to the direction of stress; they are drawn into a lacework of oriented threads or sheets, separated from each other by a maze of interconnected voids.

This leads to visual impairment and enhanced permeability. Craze formation is now considered to be a mode of plastic deformation peculiar to glassy polymers or to glassy regions in a polymer that is competitive with shear ductility. Thus, when subject to a tensile stress, high-molecular-mass glassy polymers can exhibit three main types of response: a.

They can extend uniformly b. They can extend in a necking mode c. They can craze — and finally break It seems reasonable to assume that crazing is a process which can occur quite naturally in any orientation hardening material, which exhibits plastic instability at moderate strains and in which the yield stress is much higher than the stress required for the nucleation of voids cavitations. It is interesting to remark that like most mechanical parameters the crazing stress exhibits viscoelastic characteristics, decreasing with increasing temperature and with decreasing strain rate which is an indication that it is better to speak of a crazing strain.

The mechanical properties of solid polymers

We come back to the discussion of crazes in Sect. Numerical values Table The data on the tensile strength are graphically reproduced in Fig. Flexural strength 0. Table The strength ratios of polymers are compared with those of other materials in Table The following empirical equation provides a good estimate see Fig.

Finally there is a rough relationship between the maximum elongation and the Poisson ratio of polymers. The correlation is illustrated in Fig. Rate dependence of ultimate strength When the rate of elongation is increased, the tensile strength and the modulus also increase; the elongation to break generally decreases except in rubbers. Normally an increase of the speed of testing is similar to a decrease of the temperature of testing. To lightly cross-linked rubbers even the time—temperature equivalence principle can be applied. The rate dependence will not surprise in view of the viscoelastic nature and the influence of the Poisson ratio on the ultimate properties.

The value of v is thus a function of the rate of measurement.

Class 11 Physics - Mechanical Properties of Solids - Stress, Strain and Hooke's Law

This fact is illustrated by data of Warfield and Barnet and Schuyer see page Introduction Stress—strain behaviour of poly methyl methacrylate is shown in Fig. At low temperatures the polymer behaves brittle at this rate of deformation and at high temperatures ductile. Curve a shows rubberlike behaviour of a cross-linked thermoplastic above Tg.

According to Andrews Above this temperature the stress—strain curves show a maximum after which the stress decreases. This maximum in the curve is called the yield point, with corresponding yield stress sy and yield strain ey. Ductile deformation increases fast with increasing temperature: the fracture deformation ef of some percents at brittle fracture can increase to several hundreds of percents at ductile fracture.

The brittle temperature is dependent on the rate of deformation, not only for plastic materials but also for metals, as is shown in Fig. Hence, a material can behave ductile in a tensile tester whereas it behaves brittle at the same temperature in an impact tester, in particular in the presence of a notch. In this respect the fracture energy per unit volume, i.

According to Vincent According to Warburton-Hall and Hazell In practice the difference between brittle fracture and ductile fracture is that broken pieces that were obtained by brittle fracture can in principle be glued together; this is not possible with broken pieces obtained by ductile fracture.

Yield behaviour Yield point In ductile materials the maximum in the stress—strain curve is the yield point. Two definitions of yield points are in use see Fig. There are in practice three possibilities for stretch behaviour, as shown in Fig. Influences of the yielding process The yielding process is influenced by several parameters, e.

Compare F Copper at C. From Bauwens-Crowet et al. It is for PMMA much higher 5. Apparently the activation volume is quite small for PMMA. The lines appear to be parallel and their mutual distance can be described by a WLF equation. This behaviour shows that the yielding process is a viscoelastic phenomenon.

Results for pressures from 0. It appears that — Both the yield stress and the yield deformation increase with increasing pressure — The initial Young modulus also increases with increasing pressure: from 0. The filled circles connect all fracture points in a fracture envelope. From Rabinowitz et al. The Eyring model for yield The flow model of Eyring provides a basis to correlate the effects of temperature and strain rate on flow stress.

The idea is that a segment of a polymer molecule must pass over an energy barrier in moving from the one position to another in the solid. This leads to a relationship between the strain rate and the yield stress see, e. McCrum et al. This is in agreement with results for polycarbonate, presented in Fig. The slopes of those parallel curves, with temperature as a parameter, are equal to 2. Solution From Fig. According to Table According to McCrum et al.

Results for Eq. Brittle fracture, crazing For brittle materials the stress—strain curves are almost linear up to the fracture point and the fracture strain is small, of the order of a few percentages. At 10 C the fracture strain increases, which points to a transition to ductile behaviour. Hence, the brittle temperature is the temperature where the brittle and ductile curves cross each other. There are several parameters that affect the brittleness and the brittle—ductile transition temperature, such as molecular weight, presence of cross-links, crystallinity and the presence of notches.

A schematic way, following Fig. Below Tb the brittle stress is smaller than the yield stress, so that the material fails in a brittle way. Above Tb the yield stress is smaller than the brittle stress, so that the material fails in a ductile way. The reason for the decreasing brittle strength is that a low molecular weight polymer has more chain ends, thus more inhomogeneities, where fracture can find its way. The result is that the brittle curve in Fig. On the other hand, the yield stress will be increased Mechanical Properties of Solid Polymers considerably and accordingly the brittle temperature will increase.

The material becomes more brittle. It is worthwhile mentioning that at high cross-link densities also the brittle strength will decrease. Consequently the brittle temperature will increase with increasing crystallinity: the material becomes more brittle. Such a notch will of course in principle not affect the brittle temperature, but it does affect the distribution of the applied force in the sample.

Accordingly, the yield stress curve will be increased and consequently the brittle temperature will apparently be shifted to higher values. As an example, in Table It is well-known that sy increases fast upon temperature decrease close to the glass transition or close to the b-transition. If sy increases fast upon a temperature decrease in the neighbourhood of Tg, as is often the case for amorphous polymers like PS and PIB, then the brittle temperature Tb lies closely to Tg. If crystallinity is present so that the glass transition covers a broad temperature region, or if there is a secondary transition far away form Tg, then sy will increase slowly upon a temperature decrease and only in the region of Tb, hence far away from Tg, sy will increase fast.

Accordingly Tb will be considerably lower. Fatigue failure A material that is subjected to cyclic application of stresses may fail after a large number of load cycles without nearly reaching the maximum failure stress of direct loading. The effect of such cyclic stresses is to initiate microscopic cracks at centres of stress concentration within the material or on the surface, and subsequently to enable these cracks to propagate, leading to eventual failure.

For high stress amplitudes less cycles are needed for failure than for low stress amplitudes. This limiting stress is called the fatigue limit or durability or endurance limit. This is an important property for materials that are subject or frequently changing stresses, like, e.

Creep failure Fracture by creep is the phenomenon that fracture takes place only some time after applying a constant load. The time needed for fracture of the material is shorter for higher loads. An outstanding example of creep fracture is shown in Fig. Here results are presented of measurements at different temperatures on high density polyethylene HDPE tubes that are subjected to internal biaxial stresses Van der Vegt, The various curves consist of two straight lines: the upper ones for ductile fracture and the lower ones for brittle fracture.

The positions of the bends in the various curves form a straight line. Accordingly, long-term behaviour at room temperature may be obtained by extrapolation of short-term measurements at high temperatures. In order to explain this apparently anomalous behaviour ductile fracture at shorter times than brittle fracture the curves shown in Fig. Due to the time temperature superposition increasing temperature and longer times are qualitatively identical.

At the highest stresses region A the applied stress will cause brittle fracture already after a short time, with broken pieces that can be glued together. At lower stresses region B more time is needed for failure and the material fails in a ductile way. At still lower stresses region C and longer times again brittle fracture appears, but now by the formation of brittle micro-voids. According to Van der Vegt Crazes and cracks Crazing is a phenomenon that frequently precedes fracture in many glassy polymers and that occurs in regions of high hydrostatic tensions.

It leads to the formation of interpenetrating micro-voids and small fibrils, as schematically presented in Fig. Crazing occurs mostly in brittle polymers like polystyrene and poly methyl methacrylate and is typified by a whitening of the crazed region, due to differences in refractive index, and thus by light scattering from the fibrils. If the applied load is sufficient, the polymer bridges elongate and FIG. Polymer bridges connect opposite surfaces. In cracks the space is completely empty, so that cracks are different from crazes that they are not able to support a load.

Another difference between crazes and cracks is that crazes may disappear upon unloading and rejuvenating the sample above the glass transition temperature. This is not possible with cracks see also Chap. Fracture mechanics According to Williams the tensile stress st at the tip of a crack see Fig. Failure occurs where the stress concentration is highest, i. It shows that the stress increases for longer a increases and sharper r decreases cracks. For thin elliptical cracks, e.

Of course cracks are in general not elliptical, but it shows the enormous amplification of the average stress at the crack tip. Hence the equation has to be modified and in general use is made of the classical analysis of Griffith Elastic energy is released by putting a sharp crack of length 2a into a thin plate, but energy is also needed to form two new surfaces. The work done per unit area of crack surface is GC. The factor 2 arises because of the formation of two new surfaces.

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This is caused by viscoelastic energy: for the formation of polymer cracks not only two new surfaces are formed but the majority of energy is needed to pull apart polymer molecules microscopically it is shown that a crack has not a very smooth surface, but a surface with many coiled polymer molecules that are pulled apart. The dependence of U on the crack length is shown in Fig. This figure resembles the formation of critical nuclei in crystallisation processes see Chap. For crack half-lengths smaller than 2acr the crack is stable under the applied stress; for half-lengths larger than 2acr the crack will grow under the applied stress s.

Accordingly, the fracture tensile stress, i. From Eq. The equations above are valid for thin, wide sheets, i. If this condition is not obeyed, KIC becomes dependent on the width of the sheet, so that, in contrast with GIC, the stress intensity factor KIC is not a material property.

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The equations above are valid for plane—stress situations, i. For thicker sheets plain—strain conditions occur at the crack tip. According to Eqs. Experimentally, however, the difference is much bigger. Solution a Substitution in Eq. Ultimate stress—strain properties of amorphous elastomers Lightly cross-linked elastomers follow a simple pattern of ultimate behaviour. Smith has shown that the ultimate properties of this class of polymers follow a time— temperature equivalence principle just as the viscoelastic response to small non-destructive stresses does.

Curves of stress divided by absolute temperature versus log time-to-break at various temperatures can be made to coincide by introducing the temperature-dependent shift factor aT. Application of the same shift factor causes the curves of the elongation at the break ebr versus the logarithm of time-to-break at various temperatures to coincide. A direct consequence is that all tensile strengths divided by absolute temperature , when plotted against elongation at break, fall on a common failure envelope, independent of the temperature of testing.

Crystallisation accompanying stretching invalidates the simple time—temperature equivalence principle. Moreover, investigations of Smith, and Landel and Fedors , proved that the failure envelope is independent of the path, so that the same envelope is generated in stress relaxation, creep and constant-rate experiments. As such it serves a very useful failure criterion. Landel and Fedors showed that a further generalisation is obtained if the data are reduced to ne, i. The latter is related to the modulus by Properties of Polymers 7. It is valid for polybutadiene, polyisobutylene, silicon and fluorocarbon elastomers and for epoxy resins.

At higher temperatures these polymers follow a common response curve, at lower temperatures they diverge due to their different Tg-temperatures, their different chain flexibilities and their different degrees of cross-linking. For glassy and semi-crystalline polymers the number of investigations is restricted and no generalisations have been found. Other mechanical properties of polymers The other mechanical properties of polymers have the typical character of product properties: they are not only dependent on the intrinsic nature of the material but also on the environmental conditions, in other words, they are systemic quantities.

They will be treated separately in Chap. In amorphous polymers this is simply a rearrangement of the randomly coiled chain molecules molecular orientation. In crystalline polymers the phenomenon is more complex. Crystallites may be reoriented or even completely rearranged and oriented recrystallisation may be induced by the stresses applied. The rearrangements in the crystalline material may be read from the X-ray diffraction patterns. Nearly all polymeric objects have some orientation; during the forming shaping of the specimen the molecules are oriented by viscous flow and part of this orientation is frozen in as the object cools down.

But this kind of orientation is negligible compared with the stress-imposed orientation applied in drawing or stretching processes. Orientation is generally accomplished by deforming a polymer at or above its glass transition point. Fixation of the orientation takes place if the stretched polymer is cooled to below its glass transition temperature before the molecules have had a chance to return to this random orientation. By heating above the Tg the oriented polymer will tend to retract: in amorphous polymers the retractive force is even a direct measure of the degree of orientation obtained.

Orientation has a pronounced effect on the physical properties of polymers. Oriented polymers have properties, which vary in different directions, i. Uniaxial orientation is accomplished by stretching a thread, strip or bar in one direction. Usually this process is carried out at a temperature just above the glass transition point. The polymer chains tend to line up parallel to the direction of stretching, although in reality only a small fraction of the chain segments becomes perfectly oriented.

Uniaxial orientation is of the utmost importance in the production of man-made fibres since it provides the desired mechanical properties like modulus and strength. In addition, it is only by stretching or drawing that the spun filaments become dimensionally stable and lose their tendency to creep — at least at room temperature. The filaments as spun possess a very low orientation unless spinning is performed at extreme velocities. Normally a separate drawing step is required to produce the orientation necessary for optimum physical properties.

In practice a drawing machine consists of two sets of rolls, the second running faster depending on the stretch ratio, which is usually about four. As mentioned already, the effects of orientation on the physical properties are considerable. They result in increased tensile strength and stiffness with increasing orientation. Of course, with increasing orientation the anisotropy of properties increases too. Oriented fibres are strong in the direction of their long axis, but relatively weak perpendicular to it. If the orientation process in semi-crystalline fibres is carried out well below the melting point Tm , the thread does not become thinner gradually, but rather suddenly, over a short distance: the neck.

The so-called draw ratio L is the ratio of the length of the drawn to that of the undrawn filament; it is about 4—5 for many polymers, but may be as high as 40 for linear polyolefins and as low as 2 in the case of regenerated cellulose. The degree of crystallinity does not change much during drawing if one starts from a specimen with a developed crystallinity before drawing ; if on the other hand, the crystallinity of the undrawn filament is not, or only moderately, developed, crystallinity can be greatly induced by drawing.

The drawing energy involved is dissipated as heat, which causes a rise of temperature and a reduction of the viscosity. As the polymer thread reaches its yield-stress, it becomes mechanically unstable and a neck is formed. Mechanical Properties of Solid Polymers During the drawing process the crystallites tend to break up into microlamellae and finally into still smaller units, possibly by unfolding or despiralizing of chains. Spherulites present tend to remain intact during the first stages of drawing and often elongate into ellipsoids. Rupture of the filament may occur at spherulite boundaries; therefore it is a disadvantage if the undrawn thread contains spherulites.

After a first stage of reversible deformation of spherulites, a second phase may occur in which the spherulites are disrupted and separate helices of chains in the case of polyamides become permanently arranged parallel at the fibre axis. At extreme orientations the helices themselves are straightened. Measurement of the orientation Orientation can be measured by a number of methods Birefringence or double refraction This is often the easiest method Stein and Tobolsky, ; De Varies, and Andrews, Birefringence is made up of contributions from the amorphous and crystalline regions.

The increase in birefringence occurring in crystalline polymers by orientation is due to the increase in mean orientation of the polarisable molecular chain segments. In crystalline regions the segments contribute more to the overall birefringence than in less ordered regions. Also the average orientation of the crystalline regions behaving as structural units may be notably different from the mean overall orientation. X-ray diffraction in crystalline polymers Unoriented crystalline polymers show X-ray diffraction patterns, which resemble powder diagrams of low-molecular crystals, characterised by diffraction rings rather than by spots.

As a result of orientation the rings contract into arcs and spots. From the azimuthal distribution of the intensity in the arcs the degree of orientation of the crystalline regions can be calculated Kratky, Infrared dichroism In oriented samples the amount of absorption of polarised infrared radiation may vary greatly when the direction of the plane of polarisation is changed.

If stretching vibrations of definite structural groups involve changes in dipole moment that are perpendicular to the chain axis, the corresponding absorption bands are strong for polarised radiation vibrating perpendicular to the chain axis and weak for that vibrating along the axis.

Sometimes separate absorptions can be found for crystalline and amorphous regions; in such a case the dichroism of this band gives information about orientation in both regions. This relation has a broad theoretical validity. Mechanical properties of yarns filaments, fibres The mechanical properties of fibres and yarns are quite complex and have been the subject of much experimental work.

A stressed fibre is a very complicated viscoelastic system in which a number of irreversible processes, connected with plasticity, can take place. Typical stress—strain curves are shown in Fig. In addition Fig. In comparison Fig. B Stress—strain curves of woollike fibres Heckert, Eo is the limiting tangential slope in the stress—strain diagram for strain tending to zero.

Mechanical Properties of Solid Polymers 1. From Northolt and Baltussen The very wide range of the numerical values of the mechanical properties is evident. The modulus of organic polymer fibres varies between 1 and GPa. The tenacities or tensile strengths may even vary from about 0. Notwithstanding this great variety of mechanical properties the deformation curves of fibres of linear polymers in the glassy state show a great similarity. All curves consist of a nearly straight section up to the yield strain between 0.

Also the sonic modulus versus strain curves of these fibres are very similar see Fig. Apart from a small shoulder below the yield point for the medium- or low-oriented fibres, the sonic modulus is an increasing, almost linear function of the strain. Important properties of several high-performance fibres are listed in Table Empirical relations for partly oriented yarns Many years ago De Vries discovered two important relations, when he was studying the orientation in drawing viscose-rayon yarns: one for the relationship between draw ratio and modulus, the other for the stress—strain correlation in drawn yarns.

The differences in initial moduli per polymer are due to differences in orientation angles. CL is a constant having the value of approximately 8 GPa for viscose-rayon yarn. The same applies for nylon yarns. For yarns with helical molecular chains silk, hair, isot. Native cellulose cotton is added to the series for comparison. The organic fibres are tested as such; averages of 10 filament measurements 10 cm gauge are given for the tensile data. Measured in unidirectional composite test bars, three-point bending test, onset of deflection for the organic-fibre-reinforced composites; catastrophic failure for the carbon composites.

M5 composites proved to be able to carry much higher loads than the load at onset of deflection and to absorb more energy at high compressive strains in a mode analogous to the flow behaviour in steel being damaged. Percentage of oxygen in the atmosphere that will sustain burning of the material see Chap.

Empirical relation between compliance and birefringence Very interesting are the classic results obtained by Northolt in investigating a stretch series of polyester PET tire yarns. Poly ethylene terephthalate used to be an extremely useful polymer for studying mechanical properties of fibres, since it may be spun as an isotropic filament and can be stretched to a very wide range of yarns of increasing degrees of orientation. Experimental data of the dynamic compliance and the birefringence of this stretch series are given in Fig. January 5, - Published on Amazon. Verified Purchase. It wasn't great, but it was a required book for the class I took, so I suppose it was everything I needed.

That's about all I can say.

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I actually barely read anything in the class. August 15, - Published on Amazon. Not a good book and it is unfortunate that the title overlaps with the most outstanding book without the word "introduction" in it. I definitely recommend the other book over this. Go to Amazon. Discover the best of shopping and entertainment with Amazon Prime. Prime members enjoy FREE Delivery on millions of eligible domestic and international items, in addition to exclusive access to movies, TV shows, and more.

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