CREEP OF POLYTETRAFLUOROETHYLENE UNDER VARIOUS LOADING CONDITIONS

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Introduction. One of the directions of the deve- lopment of engineer durability calculations of struc- tural elements theory is consideration of their rheo- nomous properties in order to describe the processes of long-term deforming and destruction. From the one hand, for calculating creep and long-term durability of structural elements it is necessary to use the equa- tion of mechanical states which describes complica- ted deformation processes. From the other hand, kinematic equation of damages should be used in deformation type. The materials show rheonomous and hereditary features in deformation processes as well as in long-term destruction. Despite of the fact that there are a lot of theoretical and experimental re- searches, the question of choosing adequate descrip- tion method of deformational processes for different classes of polymer materials under non-stationary loading and complex stress cannot be finally solved, especially in the most complex thermomechanical loadings [1-7]. The requirements of practical ap- plicability for the resulting mechanical state equation in some cases of cyclic loading makes us to make a compromise in accuracy while describing complex deformation processes. The task is to reduce this com- promise to the logical minimum. The development of cyclic creep model provides new opportunities for experimental research task for- mulation, makes experiment purposeful and allows to choose test program for checking the theory. Research targets. Studies of creep of partially crystal polymer and composite materials on polymer base remain topical. The influence of complex static and cyclic stress state and non-stationary loading con- ditions on deformation process mostly remains unclear. Research targets are: 1. According to the short-term monotonic loading tests data, to make up an equation of mechanical states in terms of real stresses and deformations under comp- lex stress state for direct and reverse creep for three modifications of tetrafluoroethylene. 2. To research and to describe creep of the same materials under non-stationary static and cyclic sta- tionary and non-stationary loading 3. To make a conclusion about the possibility of formularization of destruction deformation criteria for studied materials. Materials and testing method with predeter- mined intensity of real stresses. The samples were made of pipe blanks of polytetrafluoroethylene F-4, F-4D by turning on the lathe tool and part of F-4D blanks were annealed; F-4D0 blanks were heated until 80 °C with the following cooling in the heating stove. The degree of materials’ crystallinity was detected by German - Weidinger’s method and it is: 30% for F-4, 45% for F-4D, 38% for inner surface of F-4D0, 25% for outer surface of F-4D0. The densities of these materials are: for F-4 - 2.25 g/sm2, for F-4D and for F-4D0 - 2.23 g/sm2. The samples were thin-walled tubes with the wall thickness t0 = 1.0 mm in working part and the length of working part lp = 120 mm. The outer diameter (D0) of F-4 and F-4D working parts is 23.5 mm, for F-4D0 - 26 mm. The wall thickness fluctuations along the working part did not exceed 0.05 mm. The fluctua- tions of working parts lengths were within ± 1 mm and the fluctuations of outer diameter - within ± 0.1 mm. The samples were fixed in special sealing caps. Sample tests were held on equipment [25; 26], which allow to study mechanical properties of materials under biaxial stress state with static and cyclic loading. Lateral sample deformation was measured on the base l0 = 50 mm by optical system with the value of division 0.01 mm. Transverse deformation was mea- sured by arrow indicator. Temperature was 22 ± 1 °C. The intensity of real stress values for tubular sample under flat stress state with static loading was obtained by formula: . (1) Under cyclic loading the intensity of maximum stress value per cycle was obtained by formula: (2) Real stress components (axial σ and tangential σ ) were measured with considering current values of outer diameter (D) and thickness of the wall (t). The thickness of the wall was measured from the con- dition of constant value. The ratio between main stress components n = σ /σ was established by choice of equipment plunger pair [25]. The delay time of equipment adjustment was not exceed 2 minutes, besides the fluctuations of stress intensity were not exceed 5% from set value of stress intensity σ or σ and fluctuations n were not exceed 6%. Obtained experimental data under short time loading and creep with static loading are presented in the form of deformation curves in coordinates σ - ε and creep curves in coordinates ε - τ. The intensity of real (logarithmic) stresses were ob- tained by formula: . (3) Real deformation components ε , ε , ε were ob- tained by following dependences, considering current sample dimensions D, t and current base l (the sam- ple length): ε = ln ; ε = ln ; ε = ln . (4) Lode’s parameter for stresses is calculating: μ = 2 - 1μ = 2 - 1, (5) where σ and σ - the main stresses. Tests results. Polytetrafluoroethylene deforma- tion under short time loading. Short time loading PTFE deformation tests were held under linear and flat stress states with various ratios of axial and tangential stresses (n = σ /σ ) in conditions of pro- portional loading. For PTFE there is an influence of stress state type on deformation curve, besides the material shows the highest rigidity when the ratio σ /σ is close to equiaxial tension and the lowest - when it is under linear stress state. The variation of the loading speed from 0.03 MPa/sec. to 0.3 MPa/sec. influences on the deformation curves insignificantly. The law of immediate deformation was studied by tests on the fast sample unloading from the fixed level of stress intensity under various types of stress state. Nonlinear dependences of instantly elastic deformation from stress intensities for studied fluoroplastics are presented in an article [26]. According to the results of the measurements, the transverse deformation coefficient values under axial tension are vary from 0.3 to 0.48. For the selection of the law of instant plastic deformation (the term is conditional) the data of the tests on the multiple loading with the speed dσi/dt = 0.1-0.3 MPa/sec., with the registration of the σi and εi levels and further instant sample unloa- ding was used. After exposure of at least one hour, permanent (instant elastic) deformations were mea- sured. The dependence of instant plastic fluoroplas- tics deformations from the stress intensity is presen- ted in the article [27]. Instant plastic deformations of fluoroplastics depend on the type of the stress state. Direct and reverse creep under static loading. Direct creep is the increase of deformations in time under permanent real stresses (i.e. under constantly decreasing loads) (fig. 1-3). Complete deformation is the sum of four components: instant elastic, instant plastic, viscoplastic, viscoelastic [7-13]. To study visco- elastic creep deformation the tests on reverse creep (fig. 4-6) were held (returning after loading). Fig. 1. Rheonomic F-4D0 creep dependence (n = 0.5) under various intensities of real stresses : o - experimental curves; Δ - calculated curves Fig. 2. Rheonomic F-4D0 creep dependence (n = 1.15) under various intensities of real stresses : o - experimental curves; Δ - calculated curves Fig. 3. Rheonomic F-4D creep dependence (n = 0.5) under various intensities of real stresses : o - experimental curves; Δ - calculated curves Fig. 4. Reverse F-4 creep curves (n = 0.5) under various intensities of real stresses : o - experimental curves; Δ - calculated curves Fig. 5. Reverse F-4D creep curves (n = 0.5) under various intensities of real stresses : o - experimental curves; Δ - calculated curves Fig. 6. Reverse F-4D0 creep curves (n = 0.5) under various intensities of real stresses : o - experimental curves; Δ - calculated curves As a result, the complete equation of mechanical states in stress and deformation intensities (σi, εi) under stationary loading was obtained, besides the condition of deformation speeds and stress deviators similarity is observed [27]: θ + Table 1 Constant equations of mechanical states Parameters Studied materials F-4 F-4D F-4D0 E0, MPa 800 900 615 σ∗∗, MPa 27.5 28.5 22.5 v 0.48/0.50 0.48/0.50 0.48/0.50 ϒ 1·10-2 1·10-2 1·10-2 α 0.05 0.20 0.25 β 0.03 0.06 0.08 m 2.80 1.65 2.20 σ∗, MPa 10 10 10 a 1 1 1 b 0.1 0.1 0.6 c 0.30 0.08 0.26 n 3.2 3.7 2.8 A1 5.5·10-2 11·10-4 9.5·10-4 A2 1.7·10-2 1.8·10-4 1.8·10-4 μ1, sec. 110 110 85 μ2, sec. 2475 3200 3000 d 1 1 1 l 0.3 0.3 0.5 δ 1.05 1.18 1.17 k 3.95 1.89 4.00 A3 7·10-6 14·10-6 26·10-6 æ, sec. 14.0·10-3 14.1·10-3 1.5·10-3 Non-stationary static loading modes of studying materials. Non-stationary static loading modes are presented on the fig. 7-10. Here also the dependen- ces of real deformations from time are shown. Accor- ding to the comparison of experimental and calcula- ted data, generally, the calculation reproduces the creep process under complex loading mode with satisfacto- ry accuracy. The experiment showed, that the diffe- rences are mostly connected with insufficient accuracy in approximation of functions + . To describe viscoelastic component of the complete deformation in this function, it is necessary to take more than two exponents. One of the additional ex- ponents has to have the relaxation time in the fol- lowing interval: 10·103 sec. ≤ μ ≤ 15·103 sec. Fig. 7. Non-stationary static loading mode and creep curves F-4D (n = 0.5): o - experimental curves; Δ - calculated curves Fig. 8. Disproportional static loading mode and creep curves F-4D: o - experimental curves; Δ - calculated curves Fig. 9. Non-stationary static loading mode and creep curves F-4 (n = 0.5): o - experimental curves; Δ - calculated curves Fig. 10. Non-stationary static loading mode and creep curves F-4 (n = 0.5): o - experimental curves; Δ - calculated curves Creep under cyclic loading with various frequ- encies. Fluoroplastics F-4, F-4D, F-4D0 creep under cyclic loading with the frequencies 2.4 Hz, 5.0 Hz and 10.0 Hz were tested in the conditions of maxi- mum per cycle intensity constancy with the cycle asym- metric coefficient τ = σ - σ = 0.5 and tempe- rature 22 ± 1 °C (fig. 14-16). The form of the cycle is sinusoidal. To compare creep complete deformati- ons under static and cyclic loadings, isochronous de- pendences were made σ - ε and σ - ε while obtaining the creep time t = 5·103 sec. (fig. 11-13). Fig 11. Creep curves F-4 (n = 2.8) under cyclic loading with the frequency of 10 Hz Fig. 12. Creep curves F-4D0 (n = 1.15) under cyclic loading with the frequency of 5 Hz Fig. 13. Creep curves F-4 (n = 1.25) under cyclic loading with the frequency of 10 Hz Fig. 14. The maximum stress intensity dependence from the maximum deformation intensity F-4 with ∗ = . (n = 1.25): ● - f = 0; Δ - f = 10 Hz Fig. 15. The maximum stress intensity dependence from the maximum deformation intensity F-4D with ∗ = . (n = 1.25): ● - f = 0; □ - f = 2.5 Hz; o - f = 5 Hz; Δ - f = 10 Hz; ∇ - f = 5 Hz with n = 0.88 Fig. 16. The maximum stress intensity dependence from the maximum deformation intensity F-4D with ∗ = . (n = ∞): ● - f = 0; ◊ - f = 0 Hz; ♦ - f = 1.2 Hz; Δ - f = 10 Hz; ∇ - f = 5 Hz with n = 2.8 Thus, experimental points of the same material and type of stress state under frequencies of 2.5 and 5.0 Hz do not completely match to the experimental ones under stationary static loading. It is also notice- able that the material rigidity tends to increase under cyclic loading in comparison with static one, if the maximum variable stress intensity during the cycle equals to the intensity of permanent stresses under stationary loading. Besides, in comparison with static loading and frequencies of 2.5 Hz and 5.0 Hz, under frequencies of 10 Hz there is a significant rigidity increase. The most valuable increase of the material rigidity is when n = σx / σθ is close to n = ∞ (linear tension), i.e. under conditions, when under static loa- ding there is the most intensive development of visco- plasic deformations. The examples of the creep curves under cyclic loa- ding are presented on the fig. 11-13, 17, 18. The na- ture of the curves differs from one for the static loa- ding. Let us apply for cyclic loading the same equa- tion as for various cases of static loading from the previous section. The instant elastic and instant plas- tic intensity deformation components are calculated from the maximum stresses per cycle and viscoelastic component is calculated directly by substitution of a variable σ values in the equation: ε = ( - μ ) (τ - Δ)θ. (7) ∗ The calculation of the first three complete defor- mation components does not occur logical issues, but the calculation of viscoplastic component is not so obvious. After drafting series of attempts, the following empirical dependence for that component under cyclic loading was suggested: ε ( ∗) - 1 + + θ + æτ, (8) where λ - is an empirical coefficient (for F-4 λ = 0.58, for F-4D λ = 0.65, for F-4D0 λ = 0.5). The calculated according to this equation creep curves are presented on the fig. 20, 21. Fig. 17. Creep curves F-4D (n = 1.25) under cyclic loading with the frequency of 10 Hz: ● - experimental curves; Δ - calculated curves Fig. 18. Creep curves F-4D (n = 1.25) under cyclic loading with the frequency of 2.5 Hz: ● - experimental curves; Δ - calculated curves Moreover, there was made an attempt to use that empirical dependency also for creep deformation presentation under non-stationary modes of cyclic loading as a several cycle blocks with variable values of σ [30]. Discussions. Ultimate deformation of fluoro- plastics under static and cyclic loading. First of all, studying of ultimate deformation is important from an opportunity of formulation some deformation de- struction criteria for polymer materials [7]. Experi- mental data about ultimate material deformation al- lows to estimate objectively admissible creep defor- mation of structural elements. For the fluoroplastics in wide range of n there is no ultimate deformation con- stancy [30]. In whole series of non-stationary loading cases the current deformations εi (εimax) already reach the ultimate value zone on the first loading steps (fig. 19). That also attests against deformation destruction criteria. Fig. 19. Creep curves and loading mode (n = 1.25) of cyclic loading with the frequency of 5 Hz The study of PTFE F-4 sample failure mode is interesting. Under static loading with mostly tensile axial stress the destruction occurs along the transver- sal section of the tubular sample without visible loca- lization of viscoplastic deformation (with the main- taining the assigned real stress considering the defor- mation changes). Under biaxial stress state, when n = 1.25, in the destruction place pores occurs, which means that the material is strongly loosened. Some- times pores occurs in samples under axial tension. Probably, the loosening precedes the sample disrup- tion along the plane of transverse section. Under cy- clic loading the same material loosening occurs and only in some cases when n = 1.25 the failure mode differs from described. Under that conditions before the pores appearance a small bubble occurs on the surface of the damaged sample. Experimental results can be used for estimation of structural elements rigidity. Conclusion. Creep deformation of fluoroplastics (F-4, F-4D, F-4D0) under stationary and non-statio- nary loading is satisfactory described by the equation of mechanical states, which considers instant elastic, viscoelastic, instant plastic and viscoplastic deforma- tion components with the use of the volume constan- cy condition and the condition of stress and defor- mation deviators similarity. Also that deformations can be described with addition of special parameters, which are functions of the stress deviator form. The speed of creep under cyclic loading with the constant sign of real stress intensities is lower, than the one under the same static loading when the inten- sity of permanent stresses σi equals to the intensity of the maximum variable stresses σimax. Frequency changing from 2.5 to 10 Hz does not cause any signi- ficant changing of polytetrafluoroethylene deforma- tion properties, except the case of uniaxial tension with the frequency of 10 Hz, when the increase of the material rigidity occurs, in comparison with other frequencies and n = σx / σθ values during the expe- riment. An application of the mechanical states equati- on, based on results of statistical test results, to the cyclic loading mode gives quite lower results of designed deformation creep values. Thus, an empirical amend- ment was suggested to that equation of mechanical states. For fluoroplastics in quite wide range n there is no constancy in ultimate deformations. The current deformations already reach the ultimate value zone on the first stages of loading, however, destruction does not occur. That also attests against deformation criteria of failure.

About the authors

L I Ogorodov

Peter the Great Saint-Petersburg Polytechnic University

Author for correspondence.
Email: L.ogorodov@mail.ru
Associate Professor, Candidate of Technician Sciences, Hydraulic and Strength Department, Peter the Great Saint-Petersburg Polytechnic University. Scientific interests: polymer and composite materials, material resistance, creep, material ageing, material durability, long-term fracture 29 Polytechnicheskaya St., St. Petersburg, 195251, Russia

I P Nickolaeva

Peter the Great Saint-Petersburg Polytechnic University

Email: inna4i4n@mail.ru
Associate Professor, Candidate of Technician Sciences, Hydraulic and Strength Department, Peter the Great Saint-Petersburg Polytechnic University. Scientific interests: polymer and composite materials, material resistance, creep, material durability 29 Polytechnicheskaya St., St. Petersburg, 195251, Russia

E L Yakovleva

Peter the Great Saint-Petersburg Polytechnic University

Email: helena47@mail.ru
Associate Professor, Candidate of Technician Sciences, Hydraulic and Strength Department, Peter the Great Saint-Petersburg Polytechnic University. Scientific interests: polymer and composite materials, material resistance, creep, material ageing, material durability, long-term fracture 29 Polytechnicheskaya St., St. Petersburg, 195251, Russia

O V Fominykh

Peter the Great Saint-Petersburg Polytechnic University

Email: luola94@mail.ru
Master’s Degree Student, Construction Mechanics and Structures Department, Peter the Great Saint-Petersburg Polytechnic University. Scientific interests: polymer and composite materials, material resistance, creep, material ageing, material durability, long-term fracture 29 Polytechnicheskaya St., St. Petersburg, 195251, Russia

References