Biaxial multiaxial fatigue and fracture

Biaxial1 Fracture 1- BIAXIAL/MULTIAXIAL FATIGUE AND FRACTURE I R 45 M Other titles in the ESlS Series EGF EGF EGF EGF EGF EGF EGF EGFIESIS ESIS/EGF ESlS I O ESIS I I ESlS 12 ESlS 13 ESlS 14 ESlS 15 ESIS 16 ESlS 17 ESIS 18 ESIS 19 ESlS 20 ESlS 21 ESIS 22 ESlS 23 ESlS 24 ESlS 25 ESIS 26 ESIS 27 ESIS 28 ESIS 29 ESlS 30 The Behaviour of Short Fatigue Cracks Edited by K.J Miller and E.R de 10s Rios The Fmcture Mechanics of Welds Edited by J.G Blauel and K.-H Schwalbe Biaxial and Multiaxial Fatigue Edited by M.W Brown and K.J Miller The Assessment ofCracked Components h-v Fracture Mechanics Edited by L.H Larsson Yielding, Damage, and Failure OfAnisotmpic So1id.s Edited by J.F! Boehler High Temperature Fracture Mechanisms and Mechanics Edited by P Bensussan and J.P Mascarell Environment Assisted Fatigue Edited by P Scott and R.A Cottis Fracture Mechanics Verification by Large Scale Testing Edited by K Kussmaul Dcfect Assessment in Components Fundamentals and Applications Edited by J.G Blauel and K.-H Schwalbe Fatigue under Biaxial and Multiaxial Loading Edited by K Kussmaul, D.L McDiarmid and D.F Socie Mechanics and Mechanisms of’ Damage in Composites and Multi-Materials Edited by D Baptiste High Temperature Structural Design Edited by L.H Larsson Short Fatigue Cracks Edited by K.J Miller and E.R de 10s Rios Mixed-Mode Fatigue and Fracture Edited by H.P Rossmanith and K.J Miller Behaviour of Defect.s at High Rmpemtures Edited by R.A Ainsworth and R.P Skelton Fatigue Design Edited by J Solin, G Marquis, A Siljander and S Sipila Mis-Matching of Welds Edited by K.-H Schwalbe and M KoCak Fretting Fatigue Edited by R.B Waterhouse and T.C Lindley Impnct of Dynamic Fracture of Polymers and Composites Edited by J.G Williams and A Pavan Evaluating Material Properties by Dynamic Testing Edited by E van Walle Multiaxial Fatigue & Design Edited by A Pineau, G Gailletaud and T.C Lindley Fatigue Design of Components ISBN 008-0433 18-9 Edited by G Marquis and J Solin Futigue Design and Reliability ISBN 008-043329-4 Edited by G Marquis and J Solin Minimum Reinforcement in Concrete Member.s ISBN 008-043022-8 Edited by Albert0 Carpinteri Multiaxial Fatigue and Fracture lSBN 008-043336-7 Edited by E Macha, W Bqdkowski and T aagoda Fracture Mechanics: Applications and Challenges ISBN 008-043699-4 Edited by M Fuentes, M Elices, A Martin-Meizoso and J.M Martinez-Esnaola Fracture of Po[vmer.s, Composites andddhesives ISBN 008-0437 10-9 Edited by J.G Williams and A Pavan Fracture Mechanics Testing Method.s,fiirPo1ymer.s Adhesives and Comjmsites ISBN 008-043689-7 Edited by D.R Moore, A Pavan and J.G Williams Temperature-Fatigue Inteemction ISBN 008-043982-9 Edited by L Remy and J Petit From Charp.v to Present Impuct Te.sting ISBN 008-043970-5 Edited by D FranCois and A Pineau For information on how to order titles 1-21, please contact MEP Ltd Northgate Avenue Bury St Edmonds, Suffolk, IP32 6BW, UK Titles 22-29 can be ordered from Elsevier (http://www.elsevier.com) BIAXIALMULTIAXIAL FATIGUE AND FRACTURE Editors: Andrea Carpinteri Manuel de Freitas Andrea Spagnoli ESIS Publication 31 This volume contains 25 peer-reviewed papers selected from those presented at the 6thInternational Conference on BiaxialMultiaxial Fatigue and Fracture held in Lisbon, Portugal, 25-28 June 2001 The meeting was organised by the Instituto Superior Tecnico and sponsored by the Portuguese Ministerio da Ciencia e da Tecnologia and by the European Structural Integrity Society x SIS 2003 Elsevier Amsterdam - Boston - London - New York - Oxford - Paris San Diego - San Francisco - Singapore - Sydney - Tokyo ELSEVIER SCIENCE Ltd The Boulevard Langford Lane Kidlington, Oxford 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EIsevier Internet Homepage http:/hPww.elsevier.com Consult the Elsevier homepage for full catalogue information on all books journals and electronic products and services Elsevier Titles of Related Interest CARPINTERI Minimum Reinforcement in Concrete Members ISBN: W8-043022-8 MURAKAMI Metal Fatigue Effects of Small Defects and Nonmetallic Inclusions ISBN: W8-044064-9 FRANPIS and PINEAU From Charpy to prescot Impact Testing ISBN 008043970-5 RAVICHANDRAN ETAL Small Fatigue Crack Mechpnics Mechanisms C Applicatims ISBN: 008443011-2 NENTES ETAL Fracture Mechanics: Applicationsand Challenges ReMY and PmlT ISBN 008-043699-4 Temperature-FatigueInteraction ISBN: 008-043982-9 JONES Failure Analysis Care Studies 11 ISBN WR-043959-4 TANAKA C DULIKRAVICH Inverse Problems in Engineering Mechanics 11 ISBN: W8-043693-5 MACHA €TAL Muluaxial Fatigue and Fracture ISBN: 008-043336-7 UOMOTO Non-DestructiveTesting in Civil Engineaing ISBN: w8-0437174 MARQUIS C SOLIN Fatigue Design of Components VOYlADJISETAL Damage Mechanics in hgineering Materials ISBN: 008-043318-9 ISBN: 008-043322-7 MARQUIS & SOLIN Fatigue Design and Reliability VOYIADJIS & KATTAN Advances in Damage Mechanics:Metals and Metal Matrix Composites ISBN: 008-043329-4 ISBN W8-043601.3 MOORE E T A L Fracture Mechanics Testing Methods for Polymers Adhesives and Composites ISBN: 008043689-7 WILLIAMS & PAVAN Fracture of Polymers,Compositesand Adhesives ISBN: 008-043710-9 Related Journals Free specimen copy gladly sent on request Elsevier Ltd, The Boulevard, Langford Lane Kidlington, Oxford, OX5 IGB, UK Acta Metallurgicaet Materialia Cement and Concrete Research Composite Structures Computers and Structures Corrosion Science Engineering Failure Analysis Engineering Fracture Mechanics European Journal of Mechanics A & B InternationalJournal of Fatigue InternationalJournal of Impact Engineering InternationalJournal of Mechanical Sciences InternationalJournal of Non-Linear Mechanii:S InternationalJournal of Plasticity International Journal of Pressure Vessels & Piping InternationalJoumal of Solids and Structures Journal of Applied Mathematicsand Mechanics Joumal of Construction Steel Research Journal of the Mechanics and Physics of Solids Materials Research Bulletin Mechanics of Materials Mechanics Research Communications NDTBrE International Scripta Metallurgicaet Materialia Theoretical and Applied Fracture Mechanics Tribology International Wear To Contact the Publisher Elsevier Science welcomes enquiries concerning publishing proposals: books, journal special issues, conference proceedings, etc All formats and media can be considered Should you have a publishing proposal you wish to discuss, please contact, without obligation, the publisher responsible for Elsevier's mechanics and structural integrity publishing pmpmme: Dean Eastbury Senior Publishing Editor, Materials Science &Engineering Elsevier Ltd Phone: The Boulevard, Langford Lane Kidlington, Oxford Fax: OX5 IGB, UK E.mail: +44 1865 843580 +44 1865 843920 d.eastbury@elsevier.com General enquiries, including placing orders, should be directed to Elsevier's Regional Sales Offices -please access the Elsevier homepage for full contact details (homepage details at the top of this page) vii CONTENTS Preface xi Multiaxial Fatigue of Welded Structures Assessment of Welded Structures by a Structural Multiaxial Fatigue Approach K Dung Van,A Bignonnet and J L Fayard Evaluation of Fatigue of Fillet Welded Joints in Vehicle ComponentsUnder Multiaxial Service Loads G Savaidis, A Savaidis, R Schliebner and M Vormwald Multiaxial Fatigue Assessment of Welded Structures by Local Approach F Labesse-Jied, B Lebrun, E Petitpas and J.-L Robert Micro-Crack Growth Behavior in Weldments of a Nickel-Base Superalloy Under Biaxial Low-Cycle Fatigue at High Temperature N Zsobe and S Sakurai 23 43 63 High Cycle Multiaxial Fatigue Multiaxial Fatigue Life Estimations for 6082-T6 Cylindrical Specimens Under In-Phase and Out-of-Phase Biaxial Loadings L Susrnel and N Petrone Long-Life Multiaxial Fatigue of a Nodular Graphite Cast Iron G.B Marquis and P Karjalainen-Roikonen The Influence of Static Mean Stresses Applied Normal to the Maximum Shear Planes in Multiaxial Fatigue R.P Kaufman and T Topper 83 105 123 Non-Proportional and Variable-Amplitude Loading Fatigue Limit of Ductile Metals Under Multiaxial Loading J Liu and H Zenner 147 Sequenced Axial and Torsional Cumulative Fatigue: Low Amplitude Followed by High Amplitude Loading P Bonacuse and S Kalluri 165 Estimation of the Fatigue Life of High Strength Steel Under Variable-Amplitude Tension with Torsion: Use of the Energy Parameter in the Critical Plane T Lagoda, E Macha, A Niesiony and F Morel 183 Geomehy Yariation and Life Estimates of Biaxial Fatigue Specimens 493 where: The material cyclic values were taken from Table Two strain paths were chosen for the life prediction analysis, as is shown in Fig 5b The first path was at a direction e= O', aligned with the slot axis and at a plane that intersected the surface at y = 45' The second path was at e= 45' to the slot direction and again at a plane intersecting the surface at y= 45' In Figs 6a and 6b, the life predictions using the subsurface damage model and employing the two strain paths described above are compared to the experimental results and to a life prediction carried out using a simpler, hot-spot approach [ll] that searches for the highest value of the maximum shear strain along the subsurface path The solid diagonal line in Fig corresponds to a perfect correlation between experimental and predicted fatigue life, while the dashed line corresponds to a factor of two on life Estimated life was obtained by summation of the subsurface damage up to a radial distance of lmm in Fig 6a and O S m m in Fig 6b In general, the predicted lives shown in Fig are within a factor of two on life for all the tests data, independent of the path or the subsurface distance used It can also be seen that the hot-spot approach yields a more conservative life estimate, while the predictions using the subsurface damage model are non-conservative in all cases In general, the summation of the damage of up to a lmm subsurface distance predicted shorter lives compared with the summation of damage at subsurface distance of up to 0.5mm It should also be noticed that although a different strain variation was simulated for the two paths investigated (Figs 5b and 5c) it does not appear to influence much the predicted lives in Fig This is further discussed later DISCUSSION Life prediction analysis In Fig the life prediction results using the subsurface model are compared to the experimental and the hot-spot lives using the same simulated surface maximum shear strain In consistency with Fig 6, it is shown that the hot-spot approach predicts the shortest lives while the deeper path, up to a lmm subsurface strain, yields the shortest lives Fig also demonstrates that the predicted life using the subsurface damage model is currently sensitive to the chosen subsurface distance In the past, the hot-spot approach assumed that the crack propagation direction coincides with the maximum shear strain direction, which is at 45' to the slot axis However, this was not observed in the testing of the rhombic specimens as is depicted schematically in Fig It can be seen that for the specimens subjected to the higher load amplitude levels of 20kN and 17.5kN (Specimens A and B) the crack has initiated and propagated in the e= O direction However, at the intermediate load level of 15kN (Specimen C), the crack initiates in the e= ' G.SHATIL AND h? ERSOY 494 7 log(experimenta1life) log(experimenta1life) Fig Life prediction of the rhombic plate specimens using a subsurface shear strain damage analysis and two different strain paths, where the damage summations are carried out up to: (a) p = lmm; and ( b ) p= 0.5mm Geometry Variation and Life Estimates of Biaxial Fatigue Specimens 495 direction and then deviates to the 8= 45' direction as it continues to propagate Furthermore, for the specimens subjected to the lowest load levels of 12.5kN and lOkN (Specimens D and E), the crack initiates and propagates in the 8= 0" direction only This pattern of crack direction is in good agreement with the subsurface strain model predictions as is shown in Fig The predicted lives for Specimens D and E in the 8= 0' direction are shorter than those predicted in the 8= 45' direction Crack Initiation To ensure that cracks initiate and propagate at the center of the specimens, three types of stress raiser geometries were considered: slot, spherical, and drill notches The local refined FEA mesh for the three notch types is shown in Fig As mentioned earlier the slot was made by Electro-Discharge Machining (EDM) The spherical notch was machined by using a ball nose cutter tool and indenting the tool to a depth of mm A through hole was machined by using a lmm fine drili tool These notch types were tried during the optimization of the anticlastic bending specimen geometry in order to investigate the stress and strain distribution near the crack The FEA simulation indicated that, for the symmetry of the biaxial stresses, the sphere was the most suitable notch type 0.014 0*)02 r , I I A l=l.Omm L T - x=o.5mm - -I I Log (Life) Fig Predicted and experimental lives for the same surface strains However, in the testing of specimens having a spherical type of notch, it was difficult to detect initiation and, instead of one major crack, a group of small shallow cracks appeared Specimens tested using the drilled hole resulted in failure in the specimen's comers It was therefore decided to proceed with testing using the EDM slot although it created a stress concentration near the slot comers which was more complex to model 496 G.SHATIL AND N ERSOY Fig Experimental crack growth direction (a) specimens A and B; (b) specimen C; and (c) specimens D and E Fig FEA mesh models for the three anticlastic specimen notch geometries used in the development stage; (a) slot; (b) sphere; and (c) through hole Further development of the subsurface fatigue model The subsurface fatigue model developed in [6] has assumed that the initiation of fatigue cracks and the localized damage in ductile materials are associated with the formation of persistent slip bands on a critical plane In particular, it is assumed that if, for example, the Brown-Miller model for case B cracks or the Lohr-Ellison model is used for the fatigue damage, the critical plane is in a direction through the component thickness and usually aligned at 45’ to the surface It is therefore argued that, although the surface strain dominates fatigue crack initiation, fatigue life is also associated with a secondary effect due to what may be called the ‘subsurface process zone’ This secondary effect is strongly dependent on the geometry of the critical area and could be represented by using values of multiaxial strain parameters, obtained from the surface into the material’s thickness from FEA analysis by using a particular critical path illustrated in Fig In the following, the subsurface model is further developed from the analysis of a critical subsurface path to the use of a critical subsurface plane The critical plane model is based on the same principles previously used to modify the surface life in the subsurface path model However, while in the critical path model the subsurface strain increments were used to accumulate the damage, in the subsurface plane model a fraction of the subsurface damage is calculated locally for reference points on the critical plane This is conducted by using the strain at these points to calculate a corresponding fatigue life and damage, Di =l/A! The total fatigue damage is then simply averaged and summed up over the total number of the reference points: Geometry Variation and Lije Estimates of Biaxial Fatigue Specimens 497 D=- C" ( l - w i D wiG )Di n+l where n is the number of reference points on a particular plane instead of the number of increments used in Eq (1) Additionally, the damage fraction at each reference point is modified to account for the reference point depth and the local strain gradient using two weighted functions, wD and wG, respectively These functions use a similar linear relation to that used with the previous critical subsurface path (Eqs and 3): w.D =l-hi H (7) where hi is the distance of the i-th reference point to the surface, H i s a global dimension such as arbitrary depth, total thickness or diameter of the component A&eq,i is the maximum value of a multiaxial strain parameter range obtained on the intersection of the critical subsurface plane with the surface It should be noted that, when no strain gradient exists in the critical plane, the value of the weight function W: is zero and therefore the damage contribution from each point is equal regardless of its distance from the surface This critical subsurface plane model was used to predict the life to failure of the anticlastic bending tests from two subsurface planes shown in Fig 10 Both planes were at an angles p i n g i n g from '0 to 90°, one plane aligned at 8= '0 and the other at 8= 45' In the analysis, the maximum shear strain parameter was used for the life calculation by employing FEA nodal results as reference points However, instead of having a 'cut off' depth, the damage was only calculated from reference points that contain a strain range value that has a corresponding life shorter than lo7 cycles to failure in the material strain-life curve, Eq (5) Table Prediction of life of anticlastic specimens using critical subsurface plane model Specimen Load (+/-)kN A B C D E 20.0 17.5 15.0 12.5 10.0 Experimental life 6000 5170 16524 347971 1010350 Critical subsurface Critical subsurface plane 8=45' plane B= ' 4299 16801 137456 1775810 18020600 2901 6197 11871 57553 381463 The predicted cycles to failure from the critical subsurface plane analyses are compared to the experimental life in Table The life predictions from the subsurface plane that is at 8= 0" to the slot face (Fig 10) are within a factor of two on the experimental life for the higher loads, G.SHATIL AND N ERSOY 498 while predictions using points on this plane are conservative for applied load of less then 12.5kN The lives predicted using the subsurface plane that is at 8= 45Oto the slot face are very non-conservative which may indicate that this is not the critical fatigue damage subsurface plane in the case of the anticlastic specimens Although no other planes have been investigated in this work, it should be noticed that according to Eqs and the critical subsurface plane is that with the highest value of surface strain and with the lowest averaged strain gradient In the limit case, when subsurface strain gradient does not exist, the subsurface model predicted life is similar to the hot spot or surface strain predictions