Microsoft Word - numero_38_art_39 T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 289 Focussed on Multiaxial Fatigue and Fracture Fatigue strength of SS400 steel under non-proportional loading T. Morishita, T. Takaoka Graduate School of Science and Engineering, Ritsumeikan University, Japan gr0202xp@ed.ritsumei.ac.jp, rm0033px@ed.ritsumei.ac.jp T. Itoh College of Science and Engineering, Ritsumeikan University, Japan itohtaka@fc.ritsumei.ac.jp ABSTRACT. This study discusses fatigue properties of low carbon steel, type SS400 steel, under non-proportional loading. Multiaxial fatigue tests under proportional and non-proportional loading conditions with various stress amplitudes were carried out using a hollow cylinder specimen at room temperature. In the test, three types of stress paths were employed. They are a push-pull, a reversed torsion and a circle loading. The circle loading is a cyclic loading combined the push-pull and the reversed torsion loading in which axial and shear stress waveforms have 90 degrees phase differences. From the obtained test results, poor evaluations of failure life under non-proportional loading are indicated when the life is correlated by the equivalent strain range based on von Mises Δεeq and the non-proportional strain range ΔεNP. A modified strain parameter is presented which can evaluate the failure life in high and low strain levels under non-proportional loading. KEYWORDS. Fatigue; Multiaxial stress; Non-proportional loading; Life evaluation; Carbon steel. Citation: Morishita, T., Takaoka, T., Itoh, T., Fatigue strength of SS400 steel under non- proportional loading; Frattura ed Integrità Strutturale; 38 (2016) 289-295. Received: 30.07.2016 Accepted: 31.08.2016 Published: 01.10.2016 Copyright: © 2016 This is an open access article under the terms of the CC-BY 4.0; which permits unrestricted use; distribution; and reproduction in any medium; provided the original author and source are credited. INTRODUCTION on-proportional loading of which directions of principal stress and principal strain are changed in a cycle occurs in various structures such as machinery for construction and transportation. In studies of multiaxial fatigue under non-proportional loading conditions; it has been reported that failure life is reduced accompanying with an additional hardening depending on both strain path and material [1-12]. Itoh et al. have carried out series of multiaxial low cycle fatigue (LCF) tests under non-proportional loading conditions to examine properties of cyclic deformation and failure life [10-12]. They presented a strain parameter for life evaluation under non-proportional loading; a non- proportional strain range ΔεNP; which includes a non-proportional factor taking into account the effect of loading path N T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 290 and a material constant related to the additional hardening due to non-proportional loading [4;10-12]. However; there is few studies discussing failure life in high cycle region and fatigue strength under non-proportional loading [13;14]. In order to ensure reliability and safety of machinery; evaluating models for non-proportional loading including the high cycle region is required. In this study; multiaxial fatigue tests under proportional and non-proportional loading conditions were carried out in the low stress level to discuss fatigue strength. For evaluation of failure life in the high cycle region; an applicability of equivalent stress and strain ranges based on von Mises and ΔεNP is discussed and ΔεNP is also modified to be suitable strain range for life evaluation. TEST MATERIAL AND EXPERIMENTAL PROCEDURE aterial tested was rolled steel for general structure; type SS400 steel (A283 GRADE D for ASTM; St 44-2 for DIN). A hollow cylinder specimen with 12mm outer-diameter; 9mm inner-diameter in a gauge part is used. An electrical servo controlled hydraulic fatigue testing machine for push-pull and reversed torsion loadings of which maximum push-pull loading and torque are ±50 kN and ±500 N·m was employed as testing machine. Load controlled fatigue tests were carried out at room temperature. Stress paths were a push-pull; a reversed torsion (rev. torsion) and a circle loading. Fig. 1 shows the stress paths and the stress waveforms. The push-pull and the rev. torsion loading tests are proportional loading tests in which principal directions of stress and strain are fixed. The circle loading test is non-proportional loading test in which axial stress and shear stress have 90 degrees sinusoidal out-of-phase difference. In the circle loading test; axial and shear stress ranges are the same value based on von Mises; Δσ= 3 Δτ. Number of cycles to failure (failure life) Nf was determined as the cycle at which a crack occurred on the surface of test specimen. The crack size is big enough to be checked by looking and this test is controlled by loading. Therefore; Nf can be considered as the cycle at which test specimen ruptured. (a) Stress path (b) Stress waveform Figure 1: Stress path and stress waveform. EXPERIMENTAL RESULTS AND DISCUSSION Evaluation of Failure Life with Equivalent Stress and Strain ig. 2 shows a correlation of failure life with an equivalent stress amplitude based on von Mises Δσeq/2. Failure life can be correlated by a unique line independent of loading path in the stress region over the fatigue strength σw. In the load controlled test; failure life in the circle loading test tends to be longer than those in the push-pull and rev. torsion loading tests. The strain range in the circle loading test becomes smaller in comparison with that in the push-pull loading test at the same stress range because of additional hardening caused by non-proportional loading. In addition; it is known that failure life in the circle loading test is smaller than that in the push-pull loading test at same strain range due to M F T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 291 non-proportional loading. In this stress level and the material of SS400; a relative good agreement of data correlations may be resulted from that the additional hardening is balanced with the reduction in failure life. Fatigue strength in the circle loading test σwCI (150MPa) is lower than that in others σwPP (175MPa). Fig. 3 shows observations of specimen surface in the push-pull and the circle loading tests at stress amplitude level around the fatigue strengths; Δσeq/2=200; 175 and 150MPa. The observed location was set at the sufficient distances from a main crack which contributes directly to Nf. In the push-pull loading test; the roughness caused by local plastic deformation can be observed clearly on the specimen surface only at Δσeq/2=200MPa. In the circle loading test; on the other hand; the remarkable roughness can be observed at Δσeq/2=200 and 175MPa in comparison with those in the push-pull loading test at each equivalent stress amplitude; which may be resulted from the increase in the number of activated slip systems due to the rotation of principal direction of stress under non-proportional loading. The roughness leads to more chance of initiation of microcracks and the earlier crack initiation. Consequently; the surface roughness causes reduction of the fatigue strength in the circle loading test. Fig. 4 is the failure life correlated by an equivalent total strain range based on von Mises Δεeq. The strain ranges used are those at the cycle of 0.5Nf in experiments. In this figure; the bold solid line is drawn by a universal slope curve [16] based on the experimental data in the push-pull loading test. The universal slope curve is given by 6.0 f 12.0  BNAN -feq (1) where the coefficients A and B are equated as 3.5σB/E and εf0.6 according to the definition of the universal slope method. E; σB and εf are Yong’s modulus; a tensile strength and an elongation; respectively. In this study; A is put as the mechanical properties obtained from the tensile test but B is defined to fit the universal slope curve to the data of the push-pull loading test. In LCF region; failure life in the rev. torsion loading test is underestimated and conversely that in the circle loading test is overestimated out of the factor of 2 band. The same tendency of failure life was shown in the previous study of strain controlled multiaxial LCF test [11]; therefore it suggests that the failure life and the non- proportionality are not affected by the difference in the test control of strain or stress for the tested material. In the high cycle fatigue region; with decrease in strain range; failure life in the circle loading test approaches to that in the push-pull loading test. This trend indicates that the effect of non-proportional loading on failure life is decreased in the lower strain level; which will be mentioned in next. 103 104 105 106 107 100 150 200 250 300 350 Number of cycles to failure Nf, cycles E q u iv al en t st re ss a m p li tu de , M P a   eq 2 MPa175σ PPw  MPa145σ CIw  Push-pull Rev.torsion Circle Figure 2: Correlation of Nf with equivalent stress amplitude based on von Mises. T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 292 Equivalent stress amplitude Δσeq/2, MPa 200 175 150 P u sh -p u ll C ir cl e 20 μm 20 μm 20 μm 20 μm 20 μm 20 μm Axial direction Figure 3: Observation of specimen surface after fatigue tests at Δσeq/2=200MPa; 175MPa and 150MPa. Factor of 2 Method of universal slope curve 103 104 105 106 107 0.1 0.5 1 Number of cycles to failure Nf, cycles E qu iv al en t st ra in r an g e   e q , % 2.0 1.0 Push-pull Rev.torsion Circle Figure 4: Correlation of Nf with Δεeq. Applicability of Non-proportional Strain Range for Life Evaluation Itoh et al. have reported that the large reduction in failure life has a close relation with the strain path and the material [4;6;7;10;11] and they also proposed the non-proportional strain range ΔεNP for life evaluation defined as eqNP )1(  fNP (2) T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 293 where Δεeq is the maximum principal strain range under non-proportional loading which can be calculated by ε and γ. α and fNP are the material constant and the non-proportional factor; respectively. The former is the parameter related to the additional hardening due to non-proportional loading and the latter is the parameter expressing the intensity of non- proportional loading. The value of α is the ratio to fit Nf in the circle loading test to that in the push-pull loading test at the same Δεeq. In this study; the value of α for SS400 is put α = 0.59. fNP is defined as st L f d)( 2 C IR1 pathaxIm NP     ee (3) where εI(t) is the maximum absolute value of principle strain at time t and εImax is the maximum value of εI(t) in a cycle. e1 and eR are unit vectors for εImax and εI(t); ds the infinitesimal trajectory of the strain path. Lpath is the whole strain path length during a cycle and “×” denotes vector product. The integral measures the rotation of the maximum principal strain direction and the integration of strain amplitude after the rotation. Therefore; fNP totally evaluates the severity of non- proportional loading in a cycle. Fig. 5 (a) shows failure life correlated by ΔεNP. A relative good correlation can be seen in the LCF region but the failure life in the high cycle fatigue region tends to be underestimated. Fig. 5 (b) is a comparison of the failure life in evaluation Nfeva and experiment Nfexp; where Nfeva is evaluated from the life curve in the push-pull loading test and the following equation NP ff eq f BNAN     1 6.012.0 (4) Fig. 5 (b) also shows conservative estimation of failure life in the high cycle fatigue region. In the figure; data which did not reach to failure are omitted. The cause of the underestimation of Nfeva in high cycle fatigue region is considered from that Eq. (4) does not take into account the effect of non-proportional loading on life being weak under elastic deformation. Actually; additional hardening becomes smaller in the lower stress and strain levels. In order to modify non- proportional strain range; the effect of non-proportionality depending on strain level is discussed in next section. Factor of 2 Method of universal slope curve 103 104 105 106 107 0.1 0.5 1 Number of cycles to failure Nf, cycles N o n p ro p or ti on al s tr ai n r an g e   N P , % 2.0 1.0 Push-pull Rev.torsion Circle N o n -p ro p o rt io n al s tr ai n r an g e   N P , % 102 103 104 105 106 107 102 103 104 105 106 107 Failure life in experiment Nf exp , cycles F ai lu re l if e in e v al u at io n N fe v a , cy cl es Push-pull Rev.torsion Circle exp f eva f NN  Factor of 2 Push-pull Rev.torsion Circle (a) Correlation of Nf with ΔεNP (b) Comparison of Nfeva and Nfexp Figure 5: Evaluation of failure life by non-proportional strain range. Modified Non-proportional Strain Range Fig. 6 shows correlations of Nf with elastic and plastic strain ranges (Δεeeq and Δεpeq). Δεeeq in the circle loading test is defined as Δεeeq=ANf0.12 based on elastic part of universal slope curve [16] and Δεpeq is defined as Δεpeq=Δεeq  Δεeeq; where Δεeq is the strain range obtained by test results. In Fig. 6; the bold lines show the relationships of ΔεeeqNf and T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 294 ΔεpeqNf; the thin line shows the relationship of ΔεpeqNf assuming Δεpeq to be BNf 0.6/(1+α fNP). The relationships of ΔεpeqNf are drawn by separate lines in the proportional loading and the non-proportional loading. This results show that the elastic deformation behaviour may be independent on the non-proportional loading becomes of the smaller chance of interaction of slip systems due to non-proportional loading [2;3;6;12]. In order to estimate the effect of non-proportional loading in the lower stress/strain level; the modified equation is presented as NP . 12.0 + 1 f BN AN     f feq (5) Fig. 7 shows comparison between Nfeva* and Nfexp. Nfeva* is evaluated by the modified non-proportional strain range defined in Eq. (5). In Fig. 7; almost of the data are replotted within the factor of 2 band and the correlation becomes better in comparison with that in Fig. 5 (b). Therefore the modified non-proportional strain range becomes a suitable parameter for life evaluation in the high and the low strain levels under non-proportional loading. However; the definition of α still needs more discussion with additional experimental results in future studies. 102 103 104 105 106 107 0.01 0.05 0.1 0.5 1 Number of cycles to failure Nf, cycles S tr ai n r an g e  e eq ,  p eq , % Push-pull (Elastic strain) Push-pull (Plastic strain) Rev. torsion (Elastic strain) Rev. torsion (Plastic strain) Circle (Elastic strain) Circle (Plastic strain) 12.0 f e eq  AN 6.0 f p eq  BN NP 6.0 fp eq 1 f BN    2 Figure 6: Correlations of Nf by Δεeeq and Δεpeq. 102 103 104 105 106 107 102 103 104 105 106 107 Failure life in experiment Nf exp , cycles F ai lu re l if e in e va lu at io n N fe va * , c y cl es exp f *eva f NN  Factor of 2 Push-pull Rev.torsion Circle Figure 7: Comparison of Nfeva* and Nfexp. T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 295 CONCLUSIONS (1) The failure life in proportional and non-proportional loading tests can be correlated by a unique life curve in the stress region over the fatigue strength. (2) The fatigue strength in the circle loading test is lower than that in the push-pull and the rev. torsion loading tests. In the circle loading test; the remarkable roughness can be observed in comparison with those in the push-pull loading test at each equivalent stress range. The surface roughness leads to earlier crack initiations and reducing fatigue strength. (3) In the circle loading test; non-proportional strain range tends to overestimate failure life in the high cycle fatigue region because the effect of non-proportional loading becomes weak. (4) The modified non-proportional strain range is the suitable strain parameter for life evaluation independent on strain path and strain level. 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[16] Manson, S.S., Halford, G.R., Practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage, International Journal of Fracture, 17 (1981) 169-172. << /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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