Değişik yükleme durumlarında polipropilen gerilme gevşemesine bağlı olarak viskoelastik davranışının incelenmesi
Başlık çevirisi mevcut değil.
- Tez No: 75594
- Danışmanlar: PROF. DR. SELMA AKKURT
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Makine Mühendisliği Ana Bilim Dalı
- Bilim Dalı: İmalat Bilim Dalı
- Sayfa Sayısı: 153
Özet
Çevrimli önyüklemeden önce sonra polipropilenin viskoelastik davranışı gerilme gevşemesi testleriyle üçüncü bölümde incelenmiştir. Gevşeme testleri, kapalı döngü, elektrohidrolik servokontrollu test makinası yardımıyla basit tek eksenli çekme ve çevrimli ön yüklemeden sonra uygulanmıştır. Deneysel veriler, lineer viskoelastik model kullanılarak teorik sonuçlarla karşılaştırılmıştır. Hesaplanan sonuçlar, deneysel olanlarla birbirine uymaktadır. Aynı bölümde polipropilenin hesaplanan gerilme-şekil değiştirme eğrileri, bir denge gerilmesi ve viskozite fonksiyonu içeren bir fazla yük teorisine bağlı bir oluşum teorisinden çıkarılmıştır. Hesaplanan sonuçlar deneysel olanları tutmaktadır. Fazla yük teorisi sonuç olarak polipropilenin lineer olmayan viskoelastik plastik davranışını açıklamaktadır. Dördüncü bölümde, polipropilende çevrimli önyüklemeden sonra çevrimli deformasyon ve. gerilme gevşemesi incelenmiştir. Çevrimli deformasyon testleri, düz ve tavlanmış polipropilen örneklere uygulanmıştır. Pervane şeklindeki histeriz çevriminin şekli geniş sferulitli düz polipropilenin karakteristiğidir. Tavlanmış örnekler için gevşeme testlerinde gerilme düşüşü, aynı şekil değiştirmede düz örnekler için olanınkinden daha küçüktür. Gerilme düşüşü davranışı, sferulit yapısının farklılığını gösterir. Gerilme gevşemesi davranışı, morfolojiye, testlerin yapılışına ve şekil değiştirme aralığına bağlıdır. Beşinci bölümde izotaktik polipropilen örneklerin, dört farklı sıcaklık kademesinde, dört şekil değiştirme hızında basit çekme testlerinden sonra gerilme gevşemesi oluşumları incelenmiştir. Aktivasyon enerjisinin değeri, zaman-sıcaklık süperpozisyon prensibi yardımıyla belirlenmiştir. Hesaplanan, gerilme-şekil değiştirme ve gerilme gevşemesi eğrileri, fazla yük teorisine dayalı oluşum denkleminden çıkarılmıştır. Fazla yük teorisinde sıcaklığa bağlı viskozite ve aktivasyon enerjisinden bahsedilmektedir. Hesaplanan- sonuçlar, ileri sürülen oluşum denkleminden ve verilerin karşılaştırılmasından elde edilmiştir. Fazla yük modeline dayalı ileri sürülen oluşum denklemleri, polipropilen örneklerin viskoelastik-plastik davranışını açıklamaktadır.
Özet (Çeviri)
The classical theory of elasticity deals with mechanical properties of elastic solids, for which, in accordance with Hooke's law, stress is always directly proportional to strain in small deformations but independent of the rate of strain. The. classical theory of hydrodynamics deals with properties of viscous liquids, for which, in accordance with Newton's law, the stress is always directly proportional to rate of strain but independent of the strain itself. These categories are idealizations, however, although the behavior of many solids approaches Hooke's law for infinitesimal strains, and that of many liquids approaches Newton's law for infinitesimal rates of strain, under other conditions deviations are observed. Two types of deviations may be distinguished. First, when finite strains are imposed on solids (especially these soft enough to be deformed substantially without breaking) the stress-strain relations are murch more complicated (non-Hookean); similarly, in steady flow with finite strain rates, many fluids (especially polimeric solutions and melts) exhibit marked deviations from Newton's law (non-Newtonian flow). The dividing line between“infinitesimal”and“finite”depends, of course, on the level of precision under consideration and“finite”depends, of course, on the level of precision under consideration and it varies greatly from one material to another. Second, even if both strain and rate of strain are infinitesimal, a system may exhibit behavior which combines liquid like and solid like characterictics. For example, a body which is not quite solid does not maintain a constant deformation under constant stress but goes on slowly deforming with time, or creeps. When such a body is constrained at constant deformation, the stress required to hold it diminishes gradually, or relaxes. On the other hand, a body which is not quite liquid may, while flowing under constant stress, store some of the energy input, instead of dissipating it all as heat; and it may recover part of its deformation when the stress is removed (elastic recoil). When such bodies are subjected to sinusoidally oscillating stress, the strain is neither exactly in phase with the stress (as it would be for a perfectly elastic solid) nor 90° out of phase (as it would be for a perfectly viscous liquid) but is somewhere in between. Some of the energy input is stored and recovered in each cycle, and some is dissipated as heat. Materials whose behavior exhibits such characteristics are called viscoelastic. If both strain and rate of strain are infinitesimal, we have linear viscoelastic behavior; then, in a given experiment the ratio of stress to strain is a function of time (or frequency) alone, and not of stress magnitude.The relations between stress, strain and their time dependences are in general described by a“constitutive equation”. If strains and/or rates of strain are finite, the constitutive equation may be quite complicated. If they are infinitesimal, however, corresponding to linear viscoelastic behavior, the constitutive equation is relatively simple. In many of the materials of interest in classical physics, as well as of pratical importance in engineering, viscoelastic anomalies are negligible or of minor significance. Though the foundations of the phenomena logical theory of linear viscoelasticity were inspired by creep and relaxation experiments on fibers of metal and glass and the dissipation of energy in sinusoidally oscillating deformations has provided valuable information about the structure of metals, the deviations from perfect elasticity here are small. In polimeric systems, by contrast, mechanical behavior is dominated by viscoelastic phenomena which are often truly spectacular. The prominence of viscoelasticity in polymers is not unexpected when one considers the complicated molecular adjustments which must underlie any macroscopic mechanical deformation. In deformation of a hard solid such as diamond, sodium chloride, or crystalline zinc, atoms are displaced from equilibrium positions in fields of force which are quite local in character; from knowledge of the interatomic potentials, elastic constants can be calculated. Other mechanical phenomena reflect structural imperfections involving distances discontinuously larger than atomic dimensions. In an ordinary liquid, viscous flow reflects the change with time, under stress, of the distribution of molecules surrounding a given molecule; here, too, the relevant forces and processes of readjustment are quite local in character, and from knowledge of them the viscosity can |n principle be calculated. In a polymer, on the other hand, each flexible threadlike molecule pervades an average volume much greater than atomic dimensions and is continually changing the shape of its contour as it wriggles and writhes with its thermal energy. To characterize the various configurations or contour shapes which it assumes, it is necessary to consider (qualitatively speaking) gross long-range contour relationships, somewhat more local relationships seen with a more detailed scale, and so on, eventually including the orientation of bonds in the chain backbone with respect to each other on a scale of atomic dimensions. Rearrangements on a local scale (kinks) are relatively rapid, o a long- range scale(convolutions) very slow. Under stress, a new assortment of configurations is obtained; the response to the local aspects of the new distribution is rapid, the response to the long-range aspects is slow, and all told there is a very wide and continuous range of time scale covering the response of such a system to external stress. Every polymeric system has a glass-transition temperature below which the writhing thermal motions essentially cease. Here, long-range convolutional readjustments are severely restricted; there is still a wide range of response rates to external stress, but different in nature. From measurements of viscoelastic properties of polymers, information can be obtained about the nature and the rates of the configurational rearrangements, and the disposition and interrelations. From the standpoint of the physical chemist, thisprovides a field of inquiry with unique features of interest. Investigation of viscoelastic properties of polymers has also been greatly stimulated, of course, by the practical importance of mechanical behavior in the processing and utilization of rubbers, plastics, and fibers. As a result, a very high proportion of all studies on viscoelasticity in the past there decades has been devoted to the viscoelasticity of polymers. The principal purpose of this article is to relate the viscoelasticity of polymers to molecular structure and modes of molecular motion, and to describe the dependence of viscoelastic properties on molecular weight, molecular-weight distribution, temperature, concentration, chemical structure, and other variables. However, it is necessary first to provide a phenomenological background with definitions of strain and stress and their interrelations in a medium regarded as a continuum. In a stress- relaxation test, the specimen is deformed a fixed amount, and the stress required to maintain this deformation is measured for a period of time. The maximum stress occurs as soon as the deformation takes place, and the stress decreases gradually with time from this maximum value. From the practical standpoint, creep measurements are generally considered more important than stress relaxation measurement, and since creep measurements are so easily made, stress-relaxation tests have been neglected by engineers and research workers who evaluate the behavior of high polymeric materials. However, scientists who are interested in the theory of viscoelastic materials and in the relation of properties to molecular structure have concentrated more on stress relaxation than on creep measurements. Stress-relaxation date are generally more easily interpreted in terms of viscoelastic theory than are creep data. Stress- relaxation data, are however also of interest in a number of practical applications such as the determination of the stress holding a metal insert in some fabricated plastic pieces or the evaluation of antioxidants in polymers Many types of instruments have been used to measure stress relaxation. Relatively simple instruments may be used with rubbers and low modulus polymers, but it is a much more difficult task to build an accurate instrument for rigid polymers. The apparatus must "be very rigid, otherwise the deformation of the apparatus may be comparable to that of the polymer. Also, the transducer used to measure the stress must be capable of operating with very little deformation. For instance, a rigid polymer one inch long might be stretched only 0.001 inch in a stress-measuring device should not deform more than 10 microinches unless its deformation is compensated for in some manner. A modified balance may be used with rubbery materials. One end of the test specimen is attached to the pan of a balance while the other end is attached to a stretching device. The. length of the stretched specimen is held constant by changing the load on the balance. The changing load can be calculated as a stress on the specimen; this stress when plotted as a function of time gives the stress- relaxation curve. More elaborate instruments use strain gages or differential transformers in connection with electronic recorders to give a permanent and continuous record ofthe stress as a function of time. The stress is measured by a strain gage attached to a cantilever beam spring. When a stress is applied to the specimen, the beam is bent a slight amount. The deflection of the beam is in turn transmitted to the strain gage, thus changing its resistance and its electrical output; the electrical voltage is fed into the recorder to give a trace proportional to stress (or force) versus time. The elongation is applied to the specimen by quickly pulling down on the lower rod. The elongation stop allows one to impose any fixed elongation to the specimen. The elongation is held constant by tightening the lower set screw. The viscoelastic behavior of polypropylene before and after cyclic preloading was investigated by stress relaxation tests in chapter 3. The relaxation tests were performed after a simple uniaxial tension (number of cycles N=0) and after the cyclic preloading (N=0) by use of a closed loop, electrohydraulic, servocontrolled testing machine. The tests were conducted under different sets of strain rate, number of cycles, and strain amplitude. The experimental data were compared with theoretical results analyzed by use of a linear viskoelastic model. The three-element model consists of a Maxwell unit and a Hookean spring in parallel. The calculated results agree well with the experimental ones; in particular, in the relaxation tests after the cyclic preloadings (N=50), the calculated results agree very well with the experimental ones at both the predetermined strain rates of 1000 ju/s and 10000 /j/s, at a strain amplitude of ± 5%. It can be seen that the linear viscoelastic model explains the viscoelastic characteristics of polypropylene despite the solution of the constitutive equation constructed by the simple there- element model. Stress -relaxation behavior is studied in polypropylene samples subjected to different cyclic preloadings and to simple tension in chapter 3, too. The relaxation tests are performed under different sets of strain amplitude number of cycles and strain rate, using a closed-loop, electrohydraulic, servocontrolled testing machine. The calculated stress-strain arves are determined from a constitutive equation based on overstress theory in which an equilibrium stress and a viscosity function are treated. The calculated results agree well with the experimental ones. It is concluded that the overstress theory explains the nonlinear viscoelastic-plastic behavior of polypropylene. Cyclic deformation and stress relaxation after cyclic preloading in polypropylene were investigated by using on electrohydraulic, servocontralled testing machine in chapter 4. The cyclic deformation tests were performed under various sets of strain rate, number of cycles, and strain amplitude in the as-received sample and a quenched sample. The distinctive shape of the hysteresis loop, termed a propeller-like shape, is characteristic of the as-received polypropylene with large spherulites, in marked contrast to the behavior of metals. The curves at strain amplitudes from ± 1,5 % to ± 5 % indicate a propeller - like shape ; these loops change into the steady state response as the number of cycles (N) is increased up to N=30 to 50. The drop of stress in relaxation test for the quenched samples is smaller than that for the as-received samples at the same strain levels. This stress drop behavior reflects the difference of spherulite structure. The stress relaxation behavior defends on the morphology, the predetermined strain amplitude and the process of the tests.Samples of isotactic polypropylene (PP) were subjected to stress-relaxation experiments after simple tensile tests at four strain rates and at different levels of temperature in chapter 5. The relaxation moduli were determined in the range of temperature between 20 and 80°C with a relaxation period of 1200 s duration. The activation energy value of the shift factor was determined using the time temperature superposition principle. The calculated stress-strain curves and stress-relaxation curves were obtained from constitutive equations based on on overstress theory in which the temperature dependence of viscosity was amenable to an Arrhenius type equation. The quasi-equilibrium stress depends on both the current strain and the temperature. The calculated results were obtained by the proposed constitutive equation and compared with the data. The proposed constitutive equations based on the overstress model explain well the viscoelastic-plastic behavior of polypropylene samples.
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