The paper contains the results of fatigue tests of 10HNAP steel under nonproportional
bending with torsion. The circular smooth specimens were tested. The tests were
carried out at the fatigue test stands MZGS-200PL and MZGS-200L. The best results of
experimental and calculation lives consistence for the considered materials was obtained
using the criterion of maximum shear stresses in the critical plane and the Palmgren-Miner
hypothesis of damage accumulation

Macha, E.

Marciniak, Z.

Rozumek, D.

Electronic archive of Ternopil National Ivan Puluj Technical University

Section 2     ENVIRONMENTAL (CORROSIVE MEDIUM, TEMPERATURE,  LOADING   WAVEFORM,    ETC.)     EFFECTS   ON THE FATIGUE CRACK PROPAGATION  283COMPARISON OF THE CALCULATED AND EXPERIMENTAL FATIGUE LIVES UNDER NON-PROPORTIONAL BENDING  WITH TORSION OF 10HNAP STEEL  Z. Marciniak , D. Rozumek, E. Macha  Opole University of Technology, ul. Mikołajczyka 5, 45-271 Opole, Poland  Abstract The paper contains the results of fatigue tests of 10HNAP steel under non-proportional bending with torsion. The circular smooth specimens were tested. The tests were carried out at the fatigue test stands MZGS-200PL and MZGS-200L. The best results of experimental and calculation lives consistence for the considered materials was obtained using the criterion of maximum shear stresses in the critical plane and the Palmgren-Miner hypothesis of damage accumulation.  1. Introduction  Non-proportional loadings very often occur while service of machine elements [1]. In literature we can find many various fatigue failure criteria for description of material tests under multiaxial loading. Test results are described with stress [2], strain [3] and energy [4] criteria. The well known and often applied criteria were proposed by Gough and Pollard [5], McDiarmid [6], Papadopoulos [7], Brown and Miller [3], Macha [2]. Nishihara and Kawamoto [8] published the test results for four materials: two steels, cast iron and duralumin. Specimens were subjected to cyclic bending with torsion with different phase displacements between stresses and different ratios of stress amplitudes. In [9], Liu and Zenner were engaged in tests of non-proportional loading; they applied the criterion of shear stress intensity. Under bending with torsion they found that increase of the phase displacement between loadings from 0 to π/2 caused 20% drop of the strength limit for trapezoid-shaped loading, and 15% increase of the strength limit for triangular loadings.  The aim of this paper is comparison of the calculated and experimental fatigue lives obtained under proportional and non-proportional bending with torsion for 10HNAP steel.  2. Experiment  10HNAP steel was subjected to fatigue tests. The material is a low-alloy constructional steel. It is a general-purpose steel of higher resistance to atmospheric corrosion. Chemical composition and some mechanical properties of 10HNAP steel are presented in Tables 1 and 2.   Table 1. Chemical composition of  10HNAP steel in %  C Mn Si P S Cr Ni Cu Fe 0.11 0.52 0.26 0.098 0.016 0.65 0.35 0.26 Bal.  Table 2. Monotonic and fatigue mechanical properties of  10HNAP steel σY MPa σU MPa σaf MPa N0 cycles E GPa ν 418 566 300 3.1347·106 215 0.29  Specimens of round sections were tested (see Fig. 1) They were cut from the sheets 16 mm in thickness according to the rolling direction.    XIII Internation Colloquium  "MECHANICAL FATIGUE OF METALS"  284 Fig. 1. Shape and dimensions of a specimen   The specimen surface was grinded and polished. Two diameters of the specimens were applied: d = 7.5 mm for variable-amplitude loading, and d = 8 mm for polyharmonic loading. The tests were realized at Opole University of Technology, at two fatigue tests stands:   MZGS-200L (variable-amplitude loading) under frequency 20 Hz, and MZGS-200PL (polyharmonic loading); the dominating frequency  was 29 Hz [10]. Fig. 2 shows the applied 30-second stress paths, registered during the tests. Figs. 2a and 2b show variable-amplitude stress paths registered under λσ = 1, and in Fig. 2c one can see polyharmonic stress paths for  λσ = 0.5.  (a)  (b)  (c)  Fig. 2. Stress paths (a) proportional (variable-amplitude), (b) non-proportional  (variable-amplitude), and (c) non-proportional  (polyharmonic)  2.1. Procedure for fatigue life assessment  Fatigue life of the specimens was calculated according to the algorithm shown in Fig. 3. In the block 1 of the algorithm 820 s loading histories were registered during polyharmonic tests, and for variable-amplitude tests more than 2000 s loading histories were measured. Stresses were calculated using the elastic model of the material. In the block 2, the critical plane position was determined with the damage accumulation method The equivalent stress histories were calculated for the established position of the plane with the maximum damage degree (the block 3).    Section 2     ENVIRONMENTAL (CORROSIVE MEDIUM, TEMPERATURE,  LOADING   WAVEFORM,    ETC.)     EFFECTS   ON THE FATIGUE CRACK PROPAGATION  285  Fig. 3. A general algorithm of fatigue life calculations for materials under multiaxial service loading   The equivalent stress history  σeq(t) was calculated according to the following criteria  [2]: - criterion of the maximum shear stresses on the critical plane    )2cos()t(2)2sin()t()t( xyxeq α⋅τ+α⋅σ=σ ,    (1)  where α - the angle determining the critical plane position.  - criterion of the maximum normal stresses on the critical plane    )2sin()t()(cos)t()t( xy2xeq ατ−α⋅σ=σ      (2)  - criterion of the maximum normal and shear stresses on the maximum shearing plane   ατ+ασ−++ατ−α⋅σ−=σ)2cos()t()2sin()t(21B))2sin()t()(cos)t()(B2()t(xyxxy2xeq,   (3) where:  )N()N(Bf1f1−−τσ=       (4)  is the ratio of fatigue strength limits under bending and torsion for a number of cycles   Nf = 105, assumed according to Sanetra [11]. Next, cycles and half-cycles were counted with the rain flow algorithm, and a damage degree S(T0) was calculated with use of the Palmgren-Miner hypothesis of damage accumulation  [12, 13]:  ( )σ⋅<σ∑=σ⋅≥σσσ=,afor;0k1iafor;mNnTPMSafai,eqafai,eqai,eqaf0i0   (5) where σeq,ai – amplitude of the equivalent stress,  XIII Internation Colloquium  "MECHANICAL FATIGUE OF METALS"  286m – coefficient  of  the Wöhler curve slope under bending, σaf – fatigue limit under bending, N0 – number of cycles corresponding to the fatigue limit  σaf, ni – number of cycle with amplitude σeq,ai determined from the stress history σeq(t) at observation time  T0, a – coefficient including amplitudes below the fatigue limit while fatigue damage accumulation ( a = 0.5 was assumed), k – number of intervals in the amplitude histogram.  Calculations were also done with hypotheses by Serensen – Kogayev [14] and Corten – Dolan [15], where significant differences between calculations and experimental results were observed. In order to neglect influence of the stress gradient, fatigue characteristics for alternating bending were used for calculations.  Fatigue life  Tcal was calculated according to the following equation:  )T(STT0PM0cal = ,      (6)  where T0 – observation time.  3. The test results and their analysis  The tests were realized under combined bending with torsion for two ratios of nominal stresses, λσ = 0.5 and 1, and for different cross-correlation coefficients,  rστ = 0, 0.5 and 1, under variable-amplitude histories [10]. The coefficient of loading irregularity for bending and torsion was  I = 1. The  MATLAB program was used for generation of random signals; next the signals were subjected to digital filtration by a narrow-band filter. The dominating loading frequency was 20 Hz. The periods of loading repetition were equal to 2000 seconds. Fatigue tests of specimens made of 10HNAP steel were tested under nine loading combinations (see Table 3). The mean experimental lives under different ratios of nominal stresses  λσ  and cross-correlation coefficients  rστ for both tested steels were compared in Fig. 4. From the comparison of experimental data it appears that the correlation coefficient  rστ, stresses σmax and the ratio of stresses λσ strongly influence the fatigue life. In 10HNAP steel, under non-proportional stresses for  λσ = 1 the mean experimental life is 1.8 times greater, and for λσ = 0.5 it is 5.2 times greater in relation to proportional stresses. Polyharmonic tests were performed for thirteen combinations of non-proportional bending with torsion under the constant cross-correlation coefficient rστ = 0.16 and different ratios of maximum stresses (Table 4).   Table 3. Nominal stresses under variable-amplitude bending with torsion in  10HNAP steel at the stand  MZGS-200L Combination of loading σmax MPa τmax MPa λσ =maxmaxστ Standard deviation  σµ (MPa) Standard deviation  τµ (MPa) Correlation coefficient   rστ KWL1 212 212 1.0 53.43 53.43 0 KWL2 212 212 1.0 53.43 53.43 1 KWL3 301 150 0.5 75.86 37.80 1 KWL4 342 171 0.5 86.19 43.09 0 KWL5 342 171 0.5 86.19 43.09 1 KWL6 212 212 1.0 53.43 53.43    0.5 KWL7 320 160 0.5 80.65 40.32    0.5 KWL8 384 192 0.5 109.75 55.24 0 KWL9 320 160 0.5 80.65 40.32 1  Section 2     ENVIRONMENTAL (CORROSIVE MEDIUM, TEMPERATURE,  LOADING   WAVEFORM,    ETC.)     EFFECTS   ON THE FATIGUE CRACK PROPAGATION  287 Fig. 4. Comparison of mean fatigue lives depending on different parameters of the stress state  Table 4. Nominal stresses under polyharmonic bending with torsion in 10HNAP steel at the stand MZGS-200PL Combination of loading  σmax MPa τmax MPa λσ=maxmaxστ  Standard deviation σµ (MPa) Standard deviation  τµ (MPa) K01 475 90 0.189 183.76 31.41 K02 475 130 0.274 185.32 47.74 K03 475 170 0.358 185.33 60.78 K04 475 210 0.442 182.51 74.04 K05 420 90 0.214 170.38 31.85 K06 420 130 0.309 159.20 49.65 K07 420 170 0.405 170.38 62.14 K08 420 210 0.500 168.25 82.08 K09 330 130 0.394 137.52 49.23 K10 330 170 0.515 133.96 62.14 K11 330 210 0.636 134.62 83.17 K12 250 170 0.68 96.25 57.55 K13 250 210 0.84 91.00 79.83  Power spectral density was characterized by four frequency peaks with the dominating peak 29 Hz. The coefficient of loading irregularity was I = 0.99 for bending and I = 0.97 for torsion. While testing, 820 s histories of bending and torsional moments were registered. They were applied for stress calculations in a linear-elastic range.    After calculations and considerations with the above methods it was found that the best life estimation was obtained according to the criterion of maximum shear stresses on the critical plane and the Palmgren-Miner hypothesis of damage accumulation. The comparison of the calculation and experimental results were presented in Fig. 5. From these figures it appears that:   (i) under variable-amplitude stress histories  (Fig. 5a): - for 10HNAP steel, 77 % of the results of fatigue life estimations are included into the scatter band with coefficient 2, and  100 % - into the scatter band with coefficient 3. (ii) under polyharmonic stress histories (Fig. 5b): - for 10HNAP steel,  73 % of the results of fatigue life estimation are included into the scatter band with coefficient 2, and 97% - into the scatter band with coefficient 3.    XIII Internation Colloquium  "MECHANICAL FATIGUE OF METALS"  288  a) b) Fig. 5. Comparison of the calculated lives Tcal with experimental ones Texp for: a) variable-amplitude loading and  b) polyharmonic loading   The results of life estimation according to the criterion of maximum normal stresses on the critical plane for variable-amplitude loading came out the scatter band with coefficient 3 and then the calculation life was overestimated. In the case of polymarmonic loading, 64 % of  10HNAP steel were included into the scatter band with coefficient 3. It can be found that according to the criterion of maximum normal and shear stresses on the plane of maximum shearing (variable-amplitude loading), 90 % of the results for 10HNAP steel are included into the scatter band with coefficient 3. In the case of polyharmonic loading, 97 % of 10HNAP steel were included into the scatter band with coefficient 3.    4. Conclusions  Basing on the calculated and experimental fatigue lives for the tested material, we can formulate the following conclusions:   1) The best agreement between the calculated and experimental results for variable-amplitude and polyharmonic loading was obtained according to the criterion of maximum shear stresses on the critical plane and the Palmgren-Miner damage accumulation hypothesis.  2) The considered criteria of maximum normal and shear stresses or normal stresses on the critical plane with use of the Palmgren-Miner damage accumulation hypothesis showed the overestimated calculation lives, exceeding the assumed scatter band with coefficient 3.  3) Application of damage cumulation hypotheses by Serensen-Kogayev and Corten-Dolan for all the considered criteria was not successful – significant divergence was observed.   References 1. Stephens R.I., Fatemi A., Stephens R.R., Fuchs H.O.: Metal Fatigue in Engineering, Second Edition, John Wiley & Sons, Inc., 2001, ps 472 2. Macha E.: Generalization of fatigue fracture criteria for multiaxial sinusoidal loadings in the range of random loadings, Biaxial and Multiaxial Fatigue, EGF 3, Eds M.W. Brown and K.J. Miller, Mechanical Engineering Publications, London 1989, pp. 425-436 3. Brown M.W., Miller K.J.: Two decades of progress in the assessment of multiaxial low-cycle fatigue life, in: Low-Cycle Fatigue and Life Prediction, Amzallag C., Leis B., Rabbe P., Eds ASTM STP 770, Philadelphia, 1982, pp. 482-499 4. Łagoda T., Macha E. & Niesłony A.: Comparison of the rain flow algorithm and the spectral method for fatigue life determination under uniaxial and multiaxial random loading, Journal of ASTM International, Vol. 1, No. 8, 2004, pp. 544-556 5. Gough H.J., Pollard H.V.: The effect of specimen form on the resistance of metals to combined alternating stresses, Proc. of the Institution of Mechanical Engineers, Vol. 135, 1935, pp. 549-573 Section 2     ENVIRONMENTAL (CORROSIVE MEDIUM, TEMPERATURE,  LOADING   WAVEFORM,    ETC.)     EFFECTS   ON THE FATIGUE CRACK PROPAGATION  2896. McDiarmid D. L.: Fatigue behaviour under out-of-phase bending and torsion, The Aeronautical Journal of the Royal Aeronautical Society, March 1981, pp. 118-122 7. Papadopoulos I.V.: A new criterion of fatigue strength for out-of-phase bending and torsion of hard metals, Int. J. Fatigue, Vol. 16, 1994, pp. 377-384  8. Nishihara T., Kawamoto M.: The Strength of Metals under Combined Alternating Bending and Torsion with Phase Difference, Memoirs of the College of Engineering, Kyoto Imperial University, Vol. XI, No. 5, 1945, pp. 85-112  9. Liu J., Zenner H.: The fatigue limit of ductile metals under multiaxial loading, Biaxial/Multiaxial Fatigue and Fracture, ESIS 31, Eds A. Carpinteri, M. de Freitas and A. Spagnoli, Elsevier, London 2003, pp. 147-164  10. Marciniak Z.: Fatigue life of structural steels under non-proportional bending with torsion, Doctoral thesis, Opole University of Technology, 2005, p. 149 (in Polish) 11. Sanetra C.: Untersuchungen zum Festigkeitsverhalten bei mehrachsiger Randombeanspruchung unter Biegung und Torsion, Disseration, Technischen Universität Clausthal, Clausthal-Zellerfeld, 1991, s. 151 12. Palmgren A.: Die Labensdauer von Kugellagern, VDI-Z, Vol. 68, 1924, ss. 339-341 13. Miner M. A.: Cumulative damage in fatigue, Journal of Applied Mechanics Vol. 12, 1945 14. Serensen S.V., Kogayev V.P., Shnejderovich R.M.: Permissible loading and strength calculations of machine components, Third Edn., Mashinostroenie, Moskva 1975, 488 ps (in Russian)  15. Corten H. T., Dolan T. J.: Cumulative fatigue damage, Proc. of Int. Conf. on Fatigue of Metals, The Institution of Mechanical Engineers and ASME, London, New York 1956, pp. 235-246   

Comparison of the calculated and experimental fatigue lives under non-proportional bending with torsion of 10hnap steel

http://elartu.tntu.edu.ua/bitstream/123456789/16799/2/Conf_2006_Marciniak_Z-Comparison_of_the_calculated_283-289.pdf

Comparison of the calculated and experimental fatigue lives under non-proportional bending with torsion of 10hnap steel

Abstract

Similar works

Full text

Available Versions

Electronic archive of Ternopil National Ivan Puluj Technical University