Computa(onal Fa(gue Design of Structures A. ConstanHnescu Laboratoire de Mécanique des Solides CNRS UMR 7649 Ecole Polytechnique Universita’ di Pavia, 2014 1 Teamwork Financial Support Eric Charkaluk Ky Dang Van, Habibou Maitournam LaeHHa Verger – PSA Peugéot – Citroen SébasHen Amiable – Airbus Mohamed Ferjani Gwaenael Huelou -‐ LMS Armel Mbiakop – LMS Kostas Danas – LMS Raphael Guerchais – LMS Giulia Scalet –Universita’ di Pavia CostanHno Menna – Universita’ di Napoli Universita’ di Pavia, 2014 2 FaHgue of structures: a piece of history Versailles accident 1842 “I have this day to announce to you one of the most frigh4ul events that has occurred in modern 6mes. … The train of the le: bank was unusually long; … from 1500 to 1800 passengers. On arriving between Meudon and Bellevue the axle tree of the first engine broke. … The second engine … passed over it, and the boiler burst … The carriages arrived of course, and passed over the wreck, when six of them were … instantly ignited. Three were totally consumed, … without the possibility of escape to the unhappy inmates, who were locked up … The number of killed is variously es6mated (between 40 and 80).” ‘The Times’, May 11, 1842 Universita’ di Pavia, 2014 3 FaHgue of structures: a piece of history Versailles accident 1842 William John Macquorn Rankine (1820 – 1872) He showed that the axles had failed by progressive growth of a bri`le crack from a shoulder or other stress concentraHon source on the shaa, such as a keyway. “...the fractures appear to have commenced with a smooth, regularly-‐formed, minute fissure, extending all round the neck of the journal, and penetra6ng on an average to a depth of half an inch. … un6l the thickness of sound iron in the center became insufficient to support the shocks to which it was exposed”. Universita’ di Pavia, 2014 4 FaHgue of structures: a piece of history August Wohler (1819 – 1914) Defined a criHcal value of stress below which failure will not occur Universita’ di Pavia, 2014 5 Wohler curve Wohler’s Remarks • Rupture at stress levels lower than the elasHc limit if the stress is repeated a sufficient number of Hmes • Stress range rather than maximum stress determines the number of cycles • There appears to be a limiHng stress range which may be applied indefinitely without failure • For increasing maximum stress, the lifeHme decreases Universita’ di Pavia, 2014 6 ComputaHonal FaHgue Design of Structures Ques(ons • FaHgue: crack iniHaHon or crack propagaHon • FaHgue and consHtuHve behaviour Universita’ di Pavia, 2014 7 FaHgue domains and principal concepts Concepts • MulHscale Problem • Damage and PlasHcity • Energy DissipaHon Universita’ di Pavia, 2014 8 ComputaHonal FaHgue Design n Industry dependent l Series large / small l Known / unkown clients l Materials l InspecHon ? Virtual CAD model Mechanical analysis Shakedown state elastoplasHc computaHon Fa(gue Analysis Life(me DV criterion Universita’ di Pavia, 2014 9 Outline • Material Observa(ons Metals • High Cycle FaHgue DVK criterium examples • Low Cycle FaHgue dissipated energy examples • Recent modeling • Conclusions & PerspecHves Universita’ di Pavia, 2014 10 Metals – polycrystaline grain structure SEM observaHons: surfaces, boundaries, grain orientaHon Cartographie d’orientation cristallographique 111 Universita’ di Pavia, 2014 101 IPF [001] m=0 ,4 l = 41° 4 B4 (1 11) [101] 001 11 DeformaHon mechanism: glide Tension Zn monocristal Compression Al monocristal Universita’ di Pavia, 2014 12 Defects • Defects in atomic structure: 10^13 par cm3 • Carpet folds Universita’ di Pavia, 2014 13 PSB – Persistent Slip Bands [Ahmed, 2001] Sangid IJF 2013 [Ahmed, 2001 Universita’ di Pavia, 2014 14 PSB intrusion and extrusion [Ma et Laird, 1989] Universita’ di Pavia, 2014 15 Crack IniHaHon and propagaHon Microscopic crack: IniHaHon on PBS Microscopic crack: IniHaHon on extrusion [Cottrell et Hull, 1957] Universita’ di Pavia, 2014 16 Outline • Material ObservaHons Metals • High Cycle Fa(gue DVK criterium examples • Low Cycle FaHgue dissipated energy examples • Recent modeling • Conclusions & PerspecHves Universita’ di Pavia, 2014 17 High Cycle FaHgue Universita’ di Pavia, 2014 18 Dang Van FaHgue criterion Homogeneisation of the REV Meso-Macro stress relation REV Universita’ di Pavia, 2014 19 Crystal PlasHcity • Plan de glissement denses – CFC : 12 systèmes – 4 plans denses – 3 directions invariantes par plan [Cottrell, 1953] Universita’ di Pavia, 2014 20 Dang Van faHgue criterion Plastic strain only on one active slip system normal and tangential shear load on the slip system Dang Van criterion: Infinite lifetime if and only if Shakedown interpretation Universita’ di Pavia, 2014 21 Dang Van faHgue criterion Dang Van – Papadopoulos criterion: Infinite lifetime if and only if Shakedown interpretation: Melan's theorem Universita’ di Pavia, 2014 22 ComputaHona FaHgue Design n Industry dependent l Series large / small l Known / unkown clients l Materials l InspecHon ? Virtual CAD model Mechanical analysis Shakedown state Fa(gue Analysis Life(me Universita’ di Pavia, 2014 23 Case study: connectors of drillstrings FaHgue induced by cyclic loadings (Spanos et al., 2003): Ø alternated bending in dog-‐leg Ø alternated bending induced by buckling Ø malfuncHonings induced by vibraHons vibration au niveau vibraHons sinduced du contact roche/outil by contact rock/drill bit Common locaHons of failures : vibrati on s au vibraHons induced by niveau du contact puits/garni tu contact wellbore/drillstring Ø tool-‐joints No tools dedicated to the predic(ons Ø die marks done by gripping system of the fa(gue life of drillstrings Universita’ di Pavia, 2014 24 Case study: connectors of drillstrings Difficulties: l Notch l Finite lifetime Ferjani Averbuch Constantinescu (2010) 25 Universita’ di Pavia, 2014 Case studies: turbine blades Universita’ di Pavia, 2014 Damage vs. Computed Dang Van criticality Wackers, Arrieta, Constantinescu, Maitournam, ASME 2010 26 Outline • Material ObservaHons • High Cycle FaHgue DVK criterium examples • Low Cycle FaHgue dissipated energy examples • Recent modeling • Conclusions & PerspecHves Universita’ di Pavia, 2014 27 Low Cycle FaHgue Universita’ di Pavia, 2014 28 Orowan – crystall plasHcity 1934 Disloca(on as a physical concept in Taylor, Polanyi and Orowan . n DislocaHons solved the gross discrepancy between the plasHc strength of crystals that could be expected from sliding along crystal planes and the actually observed, much lower strength of single crystals. n confirmed much later, in the mid-‐50s, with electron microscopy n Key role of crystal dislocaHons in defining plasHc strength of single-‐ and polycrystalline materials is common knowledge n cyclic material behaviour Universita’ di Pavia, 2014 30 Cyclic Material behavior: Skelton et al. 9Cr1Mo 316L Universita’ di Pavia, 2014 31 ComputaHonal FaHgue Design Virtual CAD model Mechanical analysis Shakedown state elastoviscoplasHc Fa(gue Analysis Life(me dissipated energy / per cycle Universita’ di Pavia, 2014 32 Case study: exhaust manifold Outline • Material ObservaHons • High Cycle FaHgue DVK criterium examples • Low Cycle FaHgue dissipated energy examples • Recent modeling • Conclusions & PerspecHves Universita’ di Pavia, 2014 34 TMF lifeHme of cylinderheads Courtesy PSA Peugéot-‐Citroen Mean Stress Effect Criterion R² LCF R² TMF W 0.87 0.89 WΔ𝜎 0.86 0.87 W𝜎max 0.92 0.88 W𝜎H 0.93 0.9 [Int.J.FaHgue 2012] [FFEMS 2012] ECF’20 Trondheim, Norway 2014 35 Microstructural observaHon INRIA Lyon team at ESRF [Limodin et al. 2013] PorosiHes -‐ Voids • Scales: 10-‐6 -‐10-‐3 m • Shapes: ellipHcity 0.2 – 1 ECF’20 36 ProbablisHc daHgue criterion Defect growth as a Paris Law Probability Failure Universita’ di Pavia 2014 37 ObjecHve Numerical study • Understand microstructural evolution under macroscopic cyclic loading Universita’ di Pavia 2014 38 Literature: monotonic loading Tvergaard at al.[2012] Gurson type models Leblond & Gologanu [2004] Gurson [1977] Tvergaard [1984++] Hutchinson[1985] Leblond & Gologanu, … [1993] ; Benzerga and Besson [2001] Monchiet et al. [2006] Madou and Leblond [2013] Composite Comparison models Ponte Castaneda [1991] Michel & Suquet[1992] Numerical models McMecking [1990] Worswick [1990] Danas & Ponte Castaneda [2012] Universita’ di Pavia 2014 39 Literature: cyclic loading Monchiet et al. [2008]-‐ applicaHons to Dang Van type HCF faHgue criteria Numerical models with axial symetry Devaux et al. [1997] Besson & Guilleler-‐Neel [2003] Rabold Kuna [2005] ECF’20 40 Numerical experiments • 3D periodic unit cell • different iniHal porosity • ellipHcal void shapes • Finite strains • Matrix Material: • elastoplasHc matrix • nonlinear isotropic hardening ECF’20 41 Numerical Experiments Loading • triaxiality control • Cyclic loading: 50-‐100 cycles ECF’20 42 Results: Small versus finite strains EvoluHon of aspect raHo during cycling See also Leblond et al. [xx] or Cazacu O. et al. [2014]. ECF’20 43 Results: void shape evoluHon spherically constrained shape free shape ECF’20 44 FaHgue of structures ECF’20 45 Results: influence iniHal void shape Universita’ di Pavia 2014 46 Results: influence of kinemaHc hardening ECF’20 47 Outline • Material ObservaHons • High Cycle FaHgue DVK criterium examples • Low Cycle FaHgue dissipated energy examples • Recent modeling • Conclusions & Perspec(ves Universita’ di Pavia, 2014 48 ComputaHonal FaHgue Design of Structures Conclusions -‐ effect of microstructure -‐ influence of complex stress/strain paths -‐ difficult to determine a damage parameter ECF’20 49 ComputaHonal FaHgue Design of Structures Perspec(ves -‐ improve material plasHcity and faHgue models -‐ towards micro structures Jiang et al. Nature Materials 2013 ECF’20 50 References ECF’20 51 References ECF’20 52 References Universita’ di Pavia, 2014 53
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