Microsoft Word - numero_37_art_32 Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 241 Focussed on Multiaxial Fatigue and Fracture Estimation of fatigue lifetime for selected metallic materials under multiaxial variable amplitude loading Yingyu Wang Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China yywang@nuaa.edu.cn Luca Susmel Department of Civil and Structural Engineering, the University of Sheffield, Sheffield S1 3JD, UK l.susmel@sheffield.ac.uk ABSTRACT. This paper initially investigates the accuracy of two methods, i.e., the Maximum Variance Method (MVM) and the Maximum Damage Method (MDM), in predicting the orientation of the crack initiation plane in three different metallic materials subjected to multiaxial variable amplitude loading. According to the validation exercise being performed, the use of both the MVM and the MDM resulted in a satisfactory level of accuracy for selected three metals. Subsequently, three procedures to estimate the fatigue lifetime of metals undergoing multiaxial variable amplitude loading were assessed quantitatively. Procedure A was based on the MDM applied along with Fatemi-Socie’s (FS) criterion, Bannantine-Socie’s (BS) cycle counting method and Miner’s linear rule. Procedure B was based on the MVM, FS criterion, BS cycle counting method and Miner’s linear rule. Procedure C involved the MVM, the Modified Manson Coffin Curve Method (MMCCM), the classical rainflow cycle counting method and Miner’s linear rule. The results show that the usage of these three design procedures resulted in satisfactory predictions for the materials being considered, with estimates falling within an error band of three. KEYWORDS. Multiaxial fatigue; Variable amplitude loading; Critical plane; Life prediction. INTRODUCTION ince the beginning of the last century, devising a sound method to estimate the fatigue lifetime of a component subjected to variable amplitude (VA) multiaxial loading has been the goal of numerous experimental/theoretical investigations. There are four aspects that need to be considered to estimate fatigue lifetime under multiaxial variable amplitude fatigue loading, i.e., the cyclic stress-strain model, the cycle counting method, the damage model and the damage accumulation model. [1] In addition, also the following aspects should be considered under multiaxial variable amplitude load histories: determining the orientation of the critical plane and calculating the amplitude and mean value of the stress/strain components relative to the critical plane. [2] S Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 242 Fatigue criteria based on the concept of the critical plane are generally considered to be more accurate for multiaxial fatigue life estimation [1]. As far the low/medium cycle fatigue regime is concerned, the most successful criteria are seen to be those proposed by Smith, Watson and Topper [3], Brown & Miller [4, 5], Fatemi & Socie [6], and Susmel [7, 8]. As to the determination of the orientation of the critical plane, the MVM and the MDM are widely discussed in Refs [9- 11]. The MVM assumes that the damage in any material plane can be related to the variance of the stress/strain signal in that plane. The plane on which the variance of the resolved shear stain/stress reaches its maximum value is defined as the critical plane. The MDM postulates that the critical plane is that material plane which experiences the maximum extent of fatigue damage. The rainflow cycle counting method [12] has been most widely and successfully used under uniaxial loading. Among the methods dealing with VA multiaxial loading histories, Bannantine and Socie’s (BS) method [13] and Wang and Brown’s method [14, 15] deserve to be mentioned explicitly. Formalising an appropriate damage accumulation model is another tricky problem to be addressed properly in order to estimate fatigue damage under VA multiaxial loading [16,17]. Miner’s linear damage rule [18] is still the most used rule. In this paper, the accuracy of the MVM and the MDM in predicting the orientation of the critical plane is assessed. The accuracy of three procedures suitable for estimating multiaxial fatigue lifetime of metallic materials is checked against experimental data taken from the literature. The considered design procedures are as follows: (a) Procedure A: FS criterion applied with MDM, BS cycle counting method and Miner’s linear rule; (b) Procedure B: FS criterion applied with MVM, BS cycle counting method and Miner’s linear rule; (c) Procedure C: MMCCM applied with MVM, rainflow counting method and Miner’s linear rule. FATIGUE CRITERIA FS criterion atemi and Socie [6] proposed a shear-strain based multiaxial fatigue criterion that can be expressed as follows:     00 cff b f f y maxn, N2N2 G k1 2                (1) where /2 is the shear stain amplitude relative to the critical plane, n,max is the maximum normal stress, k is a material constant, andy is the material yield strength. MMCCM criterion The MMCCM [7, 8] postulates that the degree of multiaxiality and non-proportionality of the stress state at the critical location can be quantified through the following stress ratio: a maxn, a n,an,m       (2) wherea denotes the shear stress amplitude relative to the critical plane, n,m and n,a are the mean value and the amplitude of the stress normal to the critical plane, respectively, and n,max is the maximal normal stress relative the critical plane. For a given value ofthe profile of the corresponding modified Manson–Coffin curve can be described by using the following general relationship:          cff b f f a N2)('N2 G )(' (3) where ’f(), b(), ’f(), and c() are fatigue constants that can be determined from the fully-reversed uniaxial and torsional fatigue curves [7, 8]. F Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 243 BS CYCLE COUNTING METHOD annantine and Socie [13] have proposed a method based on the critical plane concept and the rainflow cycle counting method. This method makes use of a major channel and some auxiliary channels. For those materials whose fatigue breakage is shear governed, the major channel is the shear strain history. For those materials characterised by a Mode I dominated cracking behaviour, the major channel is the normal strain history. The rainflow cycle counting method is used to post-process the master channel. The normal stress signal is the auxiliary channel for FS criterion. The schematic of BS cycle counting method is shown in Fig.1. Figure 1: Schematic of BS cycle counting method. EXPERIMENTAL EVALUATIONS number of experimental data were selected from the technical literature [19, 20] to check the accuracy of the considered procedures in estimating multiaxial fatigue lifetime. The summary of the static and fatigue properties of the investigated materials are reported in Tabs. 1 and 2. When the material constants listed in Tabs. 1 and 2 were not directly available in the original sources, they were estimated as follows [1]: 3 ' ' ff   ; ff '3'  ; bb0  ; cc0  The required stress component was calculated from the strain load histories being provided by using the model proposed by Jiang and Sehitoglu [21, 22]. The hardening effect under non-proportional loading was taken into account by making the following assumption [1]: K25.1'K NP  ; 'n'n NP  Material Ref. E (GPa) G (GPa) y (MPa) k in FS S45C [19] 186 70.6 496 1 1050 QT steel [20] 203 81 1009 0.6 304L stainless steel [20] 195 77 208 0.15 Table 1: Static properties of the investigated materials B A Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 244 Material Ref. K' (MPa) n' 'f 'f (MPa) b c 'f 'f (MPa) b0 c0 S45C [19] 1215 0.217 0.359 923 -0.099 -0.519 0.198 685 -0.12 -0.36 1050 QT steel [20] 1558 0.123 2.01 1346 -0.062 -0.725 3.48 777 -0.062 -0.725 304L stainless steel [20] 2841 0.371 0.122 1287 -0.145 -0.394 0.211 743 -0.145 -0.394 Table 2: Fatigue properties of the investigated materials  /√3  /√3  /√3  /√3  /√3 Path AV Path TV Path PV Path AT Path E1  /√3  /√3  /√3  /√3    /√3   Path E2 Path R01 Path R02 Path FR Path PI Figure 2: Investigated loading paths The investigated loading paths are shown in Fig. 2. The stress and strain associated with any material plane can be obtained by coordinate transformation. Figure 3: Comparison of observed and predicted orientation of crital plane by the MVM Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 245 Figure 4: Comparison of observed and predicted orientation of crital plane by the MDM. Critical plane orientation The predicted orientation of the critical plane versus experimental orientation of Stage I crack plane for S45C steel, 1050 QT steel and 304L steel is reported in Figs 3 and 4. As it can be seen from these figures, the predictions made through the MVM and the MDM are characterised by the same level of accuracy, with 90% of the data falling within an error band of 20%. Figure 5: Comparison of observed and predicted fatigue lives by Procedure A. Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 246 Figure 6: Comparison of observed and predicted fatigue lives by Procedure B Figure 7: Comparison of observed and predicted fatigue lives by Procedure C Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 247 Fatigue lifetime prediction The predicted versus experimental fatigue lifetime diagram determined via Procedure A is reported in Fig. 5. The predicted vs experimental fatigue lifetime diagram obtained through Procedure B is reported in Fig. 6. Finally, Fig. 7 shows the predicted vs experimental fatigue lifetime diagram determined using Procedure C. As it can be seen from Figs. 5, 6 and 7, all the data fall within an error scatter band of 3. CONCLUSIONS 1. Both the MVM and the MDM can predict the orientation of the critical plane satisfactorily. The MVM is more efficient from a computation point of view. 2. Satisfactory fatigue lifetime predictions are obtained by using Procedure A, B and C. 3. The MVM can be applied with FS criterion successfully to predict fatigue lifetime for metallic materials undergoing VA multiaxial fatigue loading. ACKNOWLEGEMENTS he Aviation Science Funds of China (No.: 2013ZA52008) and the National Natural Science Foundation of China (No.: 10702027) are acknowledged for supporting the present research work. REFERENCES [1] Socie, D.F., Marquis, G.B., Multiaxial Fatigue, SAE, Warrendale, PA. (2000). [2] Wang, Y., Susmel, L.,Critical plane approach to multiaxial variable amplitude fatigue loading, Fracture and Structural Integrity, 33(2015) 345-356. [3] Smith, K.N., Watson, P., Topper, T.H., A stress-strain function for the fatigue of metals, J. Mater., 5(1970) 767-776. [4] [2] Brown M.W., Miller K.J., A theory for fatigue under multiaxial stress-strain conditions, In: Proc institution of mechanical engineering, 187 (1973)745-56. [5] Kandile, F.A., Brown, M.W., Miller, K.J., Biaxial low-cycle fatigue fracture of 316 stainless steel at elevated temperature, Met. Soc. Lond., 280 (1982) 203-210. [6] Fatemi A., Socie D.F., A critical plane approach to multiaxial fatigue damage including out-of-phase loading, Fatigue Fract Eng Mater Struct, 11 (1988) 149-65. [7] Susmel L., Meneghetti G., Atzori B., A simple and efficient reformulation of the classical Manson-Coffin curve to predict lifetime under multiaxial fatigue loading-Part I: plain materials, Journal of Engineering Materials and Technology, 131 (2009) 021009-1-021009-9. [8] Wang, Y., Susmel, L., The modified Manson-Coffin Curve Method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading, Int. J. Fatigue, 83(2016) 135-149. [9] Marciniak, Z., Rozumek, D., Macha, E., Verification of fatigue critical plane position according to variance and damage accumulation methods under multiaxial loading, Int. J. 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[22] Jiang Y., Sehitoglu H., Modeling of cyclic racheting plasticity, Part II: comparison of model simulations with experiments, Journal of Applied Mechanics, 63 (1996) 726–733. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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