A new stress-based multiaxial high-cycle fatigue damage criterion

A new stress-based high-cycle fatigue damage criterion for multiaxial load cases, D = αDσβDτγ is presented. This criterion is based on a critical plane approach that the damage parameter is a function of normal stress amplitude and shear stress amplitude on critical plane of maximum shear stress ran...

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Опубліковано в: :	Functional Materials
Дата:	2018
Автори:	Xin Li, Jianwei Yang, Dechen Yao
Формат:	Стаття
Мова:	English
Опубліковано:	НТК «Інститут монокристалів» НАН України 2018
Теми:	Methods and devices
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Цитувати:	A new stress-based multiaxial high-cycle fatigue damage criterion / Xin Li, Jianwei Yang, Dechen Yao // Functional Materials. — 2018. — Т. 25, № 2. — С. 406-411. — Бібліогр.: 18 назв. — англ.

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spelling	Xin Li Jianwei Yang Dechen Yao 2019-06-19T16:17:25Z 2019-06-19T16:17:25Z 2018 A new stress-based multiaxial high-cycle fatigue damage criterion / Xin Li, Jianwei Yang, Dechen Yao // Functional Materials. — 2018. — Т. 25, № 2. — С. 406-411. — Бібліогр.: 18 назв. — англ. 1027-5495 DOI:https://doi.org/10.15407/fm25.02.406 https://nasplib.isofts.kiev.ua/handle/123456789/157131 A new stress-based high-cycle fatigue damage criterion for multiaxial load cases, D = αDσβDτγ is presented. This criterion is based on a critical plane approach that the damage parameter is a function of normal stress amplitude and shear stress amplitude on critical plane of maximum shear stress range. The coefficient α, β and γ in the damage function are material parameters. Tensions with torsion test data are required to ascertain these coefficients. This criterion matches the test results well and shows accurate predictions of fatigue failure life compared to some present methods. en НТК «Інститут монокристалів» НАН України Functional Materials Methods and devices A new stress-based multiaxial high-cycle fatigue damage criterion Article published earlier
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	A new stress-based multiaxial high-cycle fatigue damage criterion
spellingShingle	A new stress-based multiaxial high-cycle fatigue damage criterion Xin Li Jianwei Yang Dechen Yao Methods and devices
title_short	A new stress-based multiaxial high-cycle fatigue damage criterion
title_full	A new stress-based multiaxial high-cycle fatigue damage criterion
title_fullStr	A new stress-based multiaxial high-cycle fatigue damage criterion
title_full_unstemmed	A new stress-based multiaxial high-cycle fatigue damage criterion
title_sort	new stress-based multiaxial high-cycle fatigue damage criterion
author	Xin Li Jianwei Yang Dechen Yao
author_facet	Xin Li Jianwei Yang Dechen Yao
topic	Methods and devices
topic_facet	Methods and devices
publishDate	2018
language	English
container_title	Functional Materials
publisher	НТК «Інститут монокристалів» НАН України
format	Article
description	A new stress-based high-cycle fatigue damage criterion for multiaxial load cases, D = αDσβDτγ is presented. This criterion is based on a critical plane approach that the damage parameter is a function of normal stress amplitude and shear stress amplitude on critical plane of maximum shear stress range. The coefficient α, β and γ in the damage function are material parameters. Tensions with torsion test data are required to ascertain these coefficients. This criterion matches the test results well and shows accurate predictions of fatigue failure life compared to some present methods.
issn	1027-5495
url	https://nasplib.isofts.kiev.ua/handle/123456789/157131
citation_txt	A new stress-based multiaxial high-cycle fatigue damage criterion / Xin Li, Jianwei Yang, Dechen Yao // Functional Materials. — 2018. — Т. 25, № 2. — С. 406-411. — Бібліогр.: 18 назв. — англ.
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first_indexed	2025-11-25T20:40:42Z
last_indexed	2025-11-25T20:40:42Z
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fulltext	406 Functional materials, 25, 2, 2018 ISSN 1027-5495. Functional Materials, 25, No.2 (2018), p. 406-411 doi:https://doi.org/10.15407/fm25.02.406 © 2018 — STC “Institute for Single Crystals” A new stress-based multiaxial high-cycle fatigue damage criterion Xin Li1, Jianwei Yang2, Dechen Yao2 1 School of Mechanical-electronic and Automobile Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China 2 Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles, School of Machine-electricity and Automobile Engineering, Beijing University of Civil Engineering and Architecture Received February 2, 2018 A new stress-based high-cycle fatigue damage criterion for multiaxial load cases, D = aDσ bDτ g is presented. This criterion is based on a critical plane approach that the damage parameter is a function of normal stress amplitude and shear stress amplitude on critical plane of maximum shear stress range. The coefficient a, b and g in the damage function are material parameters. Tensions with torsion test data are required to ascertain these coefficients. This criterion match- es the test results well and shows accurate predictions of fatigue failure life compared to some present methods. Keywords: Multiaxial high-cycle fatigue; critical plane; stress-based fatigue analysis. Предложен новый критерий определения повреждения материалов за счет напряжений, возникающих при многоциклической нагрузке D = aDσ bDτ g. Этот критерий основан на приближении, что параметр повреждения является функцией нормальной амплитуды напряжения и амплитуды сдвигового напряжения. Коэффициенты a, b и g в функции повреждения являются экспериментальными параметрами. Для определения этих коэффициентов используется напряженность, возникающая при испытаниях на кручение. Этот критерий хорошо соответствует результатам испытаний и показывает более точные прогнозы усталостных отказов по сравнению с некоторыми существующими современными методами. Новий метод визначення втоми матеріалів, заснований на багатоціклічному навантаженні. Xin Li, Jianwei Yangb, Dechen Yaoc Запропоновано новий критерій визначення пошкодження матеріалів за рахунок напружень, що виникають при багатоциклічному навантаженні D = aDσ bDτ g. Цей критерій заснований на наближенні, що параметр пошкодження є функцією нормальної амплітуди напруги і амплітуди сдвигової напруги. Коефіцієнти a, b і g у функції ушкодження є експериментальними параметрами. Для визначення цих коефіцієнтів використовується напруженість, що виникає при випробуваннях на крутіння. Цей критерій добре відповідає результатам випробувань і показує більш точні прогнози втомних відмов у порівнянні з деякими існуючими сучасними методами. 1. Introduction Almost every mechanical component is sub- jected to multiaxial loadings. How to predict the life of these mechanical parts is a key fac- tor for designers. Early fatigue researchers use equivalent stress, such as Von Mises criterion or Tresca criterion, to put forward their fatigue life prediction criterions, which are essentially extension of static yield criteria [1]. The aim of these methods is reducing the multiaxial stress components to an equivalent uniaxial stress, Functional materials, 25, 2 2018 407 Xin Li et al. / A new stress-based multiaxial ... expecting to transfor the multiaxial fatigue to a simple uniaxial fatigue problem. However, a difficulty of this type of procedure is defini- tion of a mean stress, whose meaning is unclear within multiaxial stress conditions. In present, it is believed that the critical plane method is an efficient way of fatigue life prediction, for it has a clearer physical meaning than other fatigue life prediction methods. Many critical plane methods have been proposed to assist in the mechanical design [2]. A typical criti- cal plane criterion is proposed by Findley [3]. He uses a linear combination of normal stress and shear stress in the critical plane as a mean stress. A similar concept depends on the test of proportional combination of cyclic bending and torsion was proposed by Stulen and Cummings [4]. McDiarmid [5] pointed out that the impor- tant factors of high cycle fatigue (HCF) are the maximum shear stress range and the normal stress in the critical plane of the maximum shear stress amplitude. Rashed et al. [6] pro- pose a stress-strain criterion in consideration of the nonproportional multiaxial loading con- dition. Chen et al [7]. discuss the applicability of several mutliaxial fatigue damage criterions under variable amplitude loading. Another class of fatigue criterion is the energy based parameters, which also use the critical plane concept. Smith et al. [8] proposed Smith-Watson-Topper (SWT) criterion which is well-known and widely accepted. Chu et al. [9] proposed a criterion that extends the SWT criterion to include a shear term. Liu [10] used a virtual energy method for shear and normal facture. Glinka et al. [11] proposed a criterion based on the summation of the product of nor- mal stress and strain ranges, and that of shear stress and strain ranges on the critical shear plane. In this paper, a stress-based fatigue damage criterion for multiaxial fatigue is proposed. Ex- periment data of three metals [12-14] were used to estimate the criterion, with the lives ranging from 8.5×103 to 1.3×106 cycles, and two classi- cal critical plane criterions are used to compare with this criterion. The results show that the new criterion correlates with the experimen- tal results very well and effects for multiaxial high-cycle fatigue cases. 2. The establish of the stress-based high cycle multiaxial fatigue damage criterion A load-based criterion for damage to multi- axis fatigue cycles is established. The new fa- tigue damage criterion is based on four con- cepts as follows: Concept 1: Multiaxial fatigue damage occurred on the plane of maximum shear stress range, which is defined as the criti- cal plane. Critical plane method is developed on the basis of phenomenological observations of fatigue crack development. The critical plane approach receives the most attention because of its good correlation with test data and its ex- plicit physical meaning. Metal fatigue experi- ments show that the cracks generally propa- gate along the plane of maximum shear stress range15. In this paper, the critical plane is de- fined as the plane which suffers the maximum shear stress range. Concept 2: The maximum shear stress amplitude and the normal stress ampli- tude on the critical plane are the two main factors contribute to the fatigue damage. The critical plane method generally uses com- bination of shear stress and normal stress or stress amplitudes on the critical plane as dam- age parameters for HCF [16,17]. The shear stress induces dislocation movement along slip line, while the normal stress opens the crack, reduces friction between the crack surfaces and accelerates the propagation of the crack [18]. In the new fatigue damage criterion, the dam- age parameters are shear stress amplitude and normal stress amplitude. Concept 3: In uniaxial conditions (ten- sion or torsion), the stress and fatigue cir- cle follow the Basquin function. Under mac- roscopically elastic uniaxial loading conditions, fatigue life can be described in terms of a S-N (or Wöhler) curve which associates the stress amplitude with the life (described in the num- ber of cycles to failure) of a experimental speci- men or a engineering component. Generally, the relationship between the stress amplitude and the fatigue life can be described using an exponential equation. The mostly used equa- tion is known as Basquin function as follows: S S Nf f n = ( )' 2 (1) Where S is the uniaxial stress amplitude, Nf is the number cycles to fatigue, S’ f and n are mate- rial parameters. For tension or torsion fatigue test, Basquin function can be described as σ σ τ τ a f f b a f f c N N = ( ) = ( ) ' ' 2 2 (2) Where σa is the normal stress amplitude, σf ’ is fatigue strength coefficient, b is fatigue strength exponent, τa is shear stress amplitude, τf ’ is shear fatigue strength coefficient, c is shear fatigue strength exponent. 408 Functional materials, 25, 2, 2018 Xin Li et al. / A new stress-based multiaxial ... Concept 4: The total fatigue damage is a function of the damage caused by normal stress amplitude and shear stress ampli- tude on the critical plane. Based on concept 2, we can assume that the total damage in one cycle is a function of the damages caused by normal stress and shear stress on the critical plane. That is to say D f D D= ( )σ τ, (3) Where D is the total damage of one cycle, D=1/ Nf , Dσ is the damage caused by normal stress amplitude on the critical plane, Dτ is the dam- age caused by shear stress amplitude on the critical plane. The fatigue damage caused by normal stress and shear stress can be converted from Equa- tion (2) D Dn a f b a f c σ τ σ σ τ τ = æ è ççççç ö ø ÷÷÷÷÷ = æ è ççççç ö ø ÷÷÷÷÷ - - , ' ' , 1 1 (4) Where σn,a is the amplitude of the normal stress on the critical plane, τa is the amplitude of the shear stress on the critical plane. With the analysis of the test data of differ- ent metals, we define the form of the damage function as follows D D D= α σ β τ γ (5) Where α, β and γ are coefficients of material. Substituted Equation (4) in Equation (5), the damage function of the new fatigue damage criterion is D n a a n a f b a f c σ τ α σ σ τ τ β γ , , ' ' ,( ) æ è çççç ö ø ÷÷÷÷ æ è çççç ö ø ÷÷÷÷ = - - (6) The fatigue life is reciprocal of the damage. 3. Criterion assessment Material test data. Combined axial load or bending and torsion experimental data taken from the published literature [12-14] were used in order to assessment the new fatigue damage criterion. The test materials conclude SM45C structural steel, 6082-T6 and 7075-T651 alumi- num alloys. The tensile performances of these metals are listed in Table 1, the bending and torsion experimental data are listed in Table 2. The test load can be described as follows σ σ σ ω τ τ τ ω ϕ x x m x a xy xy m xy a t t t t ( ) = + ( ) ( ) = + +( ) , , , , sin sin (7) The material coefficients used in the fatigue damage criterion are listed in Table 3. The contrastive criterions. Two critical plane criterions proposed by Findly [3] and Mc- Diarmid [5] are compared with the new crite- rion. Findly proposed a linear combination of nor- mal stress and shear stress in the critical plane for a given number of cycles to failure τ σ τa n f f c k N+ = ( )' 2 (8) Table 1 Tensile performance of metals Metal type SM45C steel 6082-T6 AL 7075-T651 AL Young modulus (GPa) 208.6 69.4 71.7 Yield stress (MPa) 418 301 501 Tensile strength (MPa) 731 343 561 Fig.1 The comparison of observed lives and the new criterion prediction lives. Fig.2 The prediction lives comparison of differ- ent criterions for SM45C steel. Functional materials, 25, 2 2018 409 Xin Li et al. / A new stress-based multiaxial ... Where k is a material coefficient. The critical plane is defined as the plane experience the maximum value of fatigue damage. This crite- rion was effective for proportional combination of bending and torsion condition. McDiarmid noticed that the important pa- rameters of loading in HCF are the maximum Table 2 The bending and torsion loading parameters and observed lives Nf exp . Prediction lives NFD from Findly, NMD from McDiarmid and NNEW from the new criterion No. σx,a (MPa) σx,m (MPa) τxy,a (MPa) τxy,m (MPa) φ (°) Nf exp (cycles) NFD (cycles) NMD (cycles) NNEW (cycles) SM45C steel bearing-torsion 1 390 0 151 0 0 8500 3894 12203 8465 2 349 0 148 0 0 24000 18723 56609 22622 3 325 0 153 0 0 32000 34589 100033 35283 4 372 0 93 0 0 38000 75341 268707 39016 5 309 0 134 0 0 100000 172938 518088 84512 6082-T6 aluminum alloy bearing-torsion 6 70 -3 118 0 0 71255 32493 33992 69769 7 71 -1 117 1 1 78730 34065 35670 74325 8 59 -1 100 1 -7 230750 121693 127282 356997 9 53 -1 83 1 -2 1018775 497186 521716 2071817 10 52 -2 82 0 2 1289550 551221 578247 2350208 11 147 -2 106 1 -4 31000 17275 18860 41134 12 151 -4 104 0 -3 64090 17510 19165 42524 13 163 -2 81 0 -5 124460 38276 42627 125552 14 147 1 90 -1 -8 132215 37471 41279 113714 15 146 -3 76 -1 -6 232370 77265 85848 294717 16 118 -3 82 1 -5 315795 119040 130226 454012 17 119 1 72 -1 0 694062 211765 233434 973212 7075-T651 aluminum alloy bearing-torsion 18 127.2 0 170.5 0 0 59194 20360 62695 55842 19 166.1 0 110.4 0 0 136646 143785 460252 182242 20 201.3 0 130 0 0 45500 35333 115236 29302 21 153.5 0 100.3 0 0 662627 287777 931454 440128 22 137.4 0 79.7 0 0 1018000 1093868 3819905 2280773 23 205.8 0 137.5 0 0 35804 25825 82384 20037 24 147.5 0 86.9 0 0 225000 589466 2038538 1037802 25 203.8 0 136.3 0 0 12708 27784 88576 22032 Fig.4 The prediction lives comparison of differ- ent criterions for 7075-T651 aluminum alloy. Fig.3 The prediction lives comparison of differ- ent criterions for 6082-T6 aluminum alloy 410 Functional materials, 25, 2, 2018 Xin Li et al. / A new stress-based multiaxial ... shear stress range and the normal stress on the critical plane. The critical plane is defined as the plane of maximum shear stress range. The criterion is τ τ σ σ τa u n f f c N+( ) = ( )-1 2 2,max ' (9) Where τ-1 is fatigue limit of torsion, σu is ulti- mate strength, σn,max is the maximum normal stress on the critical plane. The particular parameters of these criteri- ons are listed in Table 4. Some parameters (k in Findly criterion, α, β and γ in the new criterion) are obtained from fitting of the bending-torsion test data. 4. Results and discussion The comparison of the observed lives and new criterion prediction lives of different mate- rials are showed in Fig.1. Fig.2 to Fig.4 demon- strate the new criterion prediction lives in com- parison with Findly criterion and McDiarmid Table 3 Material coefficients used in the fatigue damage criterion σf’ (MPa) b τf’ (MPa) c SM45C steel 1024.3 –0.0946 441.44 –0.0511 6082-T6 Al 1053.1 –0.1426 470.27 –0.1258 7075-T651 Al 1072.6 –0.1246 760.33 –0.1264 Table 4 Parameters of these Findely criterion, McDiarmid criterion and the New criterion Material Findly criterion McDiarmid criterion New criterion k τ–1 (MPa) σu (MPa) a b g SM45C steel 0.219 197.2 731 3.789 0.326 0.409 6082-T6 Al 0.12 68.2 343 9.295 0.0138 1.225 7075-T651 Al 0.377 109.9 561 74.346 0.427 0.905 Fig.5 Error indexes of different criterions for SM45C steel. criterion prediction lives for the three materials respectively. In all figures, the central diagonal line presents the perfect agreement between the observed lives and the prediction lives. For Fig.2 to Fig.4, the dashed lines represent factor 2 and factor 3 bandwidths. Fig.1 proves that the new criterion matches the test result well. Fig.2 to Fig.4 show that for different materials, the new criterion’s predic- tion result is the best among the three crite- rions. Generally, most prediction life points of Findly criterion are in factor 3 band, while some prediction life points of McDiarmid cri- terion are out of factor 3 band. For 6082-T6 aluminum alloy, these two criterions perform almost the same. For a quantitative judgment of the predic- tion quality of the new criterion and the com- parison of different criterions, an error index is introduced as follows I N N N f pre f = - ´ ln ln ln % exp exp 100 (10) Fig.6 Error indexes of different criterions for 6082-T6 aluminum alloy. Functional materials, 25, 2 2018 411 Xin Li et al. / A new stress-based multiaxial ... The comparisons of different criterions for the three materials are shown in Fig.5 to Fig.7 respectively. For SM45C steel, the error (ab- solute value) of the new criterion is less than 1.5%, while the maximum errors (absolute value) of Findly and McDiarmid are up to 8.6% and 18.5% respectively; for 6082-T6 aluminum alloy, the error (absolute value) of the new cri- terion is less than 5.2%, while the maximum errors (absolute value) of Findly and McDiar- mid are up to 11.7% and 10.9% respectively; for 7075-T651 aluminum alloy, the error (absolute value) of the new criterion is less than 12.4%, while the maximum errors (absolute value) of Findly and McDiarmid are up to 9.7% and 20.5% respectively. Generally the prediction er- ror of the new criterion is less than Findly cri- terion and McDiarmid criterion. But for 7075- T651 aluminum alloy, the maximum error of Findly criterion is less than the new criterion. The prediction result of McDiarmid criterion is the worst among the three criterions. 3. Conclusion A new concept is introduced to formulate the new fatigue damage criterion. This new cri- terion fits the test data of different materials perfectly; most of the prediction lives points are in factor 2 band; the error analysis shows that the error of the new criterion generally with- in the range of ±5%. It is more accurate than Findly criterion and McDiarmid criterion. This research provides a new thinking for high-cycle fatigue life prediction. Fig.7 Error indexes of different criterions for 7075-T651 aluminum alloy. Acknowledgement Project funded by China Postdoctoral Sci- ence Foundation (2016M591060) and Beijing Postdoctoral Research Foundation (2016ZZ-79) are gratefully acknowledged. Reference 1. Y.S. Garud. J Test Eval, 9, 165, 1981. 2. A. Karolczuk, E. Macha, Int J Fract, 134, 267, 2005. 3. W.N. Findly, J Eng Ind, 9, 301, 1959 4. F.B.Stulen, H.N. Cummings Proceedings of the ASTM, 54, 822, 1954. 5. D.L.McDiarmid, Fatigue under out-of-phase biax- ial stresses of different frequencies. In: Miller K.J. and Brown M.W .(eds) Mutliaxial fatigue ASTM STP 853. Philadelphia: ASTM, 1985, pp. 606- 621. 6. G. Rashed, R. Ghajar,,G., J Mech. Sci. Techn., 21, 1153 2007. 7. H. Chen, D.G. Shang, Y.J. Tian, et al. J Mech. Sci. Techn., 26, 3439, 2012. 8. R.N. Smith, P. Watson, T.H.Topper,. J Mater, 5, 767, 1970. 9. C.C. Chu, F.A.Conle, J.F.Bonnen, Mutliaxial stress-strain modeling and fatigue life predic- tion of SAE axle shafts. In: McDowell D,L, and Ellis R. (eds) Advances in multiaxial fatigue ASTM STP 1191. Philadelphia: ASTM, 1993, pp. 37-54. 10. R.C.Liu, A method based on a virtual strain-en- ergy parameters for multiaxial fatigue. In: Mc- Dowell, DL and Ellis R (eds) Advances in mul- tiaxial fatigue ASTM STP 1191. Philadelphia: ASTM, 1993, pp. 67-84.. 11. G. Glinka, G.Shen, A.Plumtree, Fatigue Fract Eng Mater Struct,, 18, 37, 1995. 12. S.B. Lee, A criterion for fully reversed out-of –phase torsion and bending. In: Miller KJ and Brown MW (eds) Mutiaxial fatigue ASTM STP 853. Philadelphia: ASTM, 1985, pp. 553-568. 13. L. Susmel, N. Petrone, Multiaxial fatigue life es- timations for 6082-T6 cylindrical specimens un- der in-phase and out-of-phase biaxial loadings In: Carpinteri A et al. (eds), Biaxial/multiaxial fatigue and fracture. Oxford: Elsevier, 2002, pp. 83-104. 14. T. Zhao, Y. Jiang Y,. Int J Fatigue, 30, 834, 2008. 15. G. Marquis, D. Society, Fatigue Fract Engng Mater Struct , 23, 293, 2000. 16. T. Matake, Bull Jpn Soc Mech Eng, 20, 257, 2000. 17. D.L. McDiarmid, Fatigue Fract Engng Mater Struct ,14, 429, 1991. 18. D. Socie, Critical plane approaches for multiaxi- al fatigue damage assessment. In: McDowell D.L and Ellis R. (eds) Advances in multiaxial fatigue ASTM STP 191. Philadelphia: ASTM, 1993, pp. 7-36.

A new stress-based multiaxial high-cycle fatigue damage criterion

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