Chapter 10 Elastic and Elastic-Plastic Contact

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Transcript of Chapter 10 Elastic and Elastic-Plastic Contact

Chapter 10Elastic and Elastic-Plastic Contact254413 Introduction to Contact MechanicsAssistant Professor Thongchai FongsamootrMechanical Engineering Department, Chiangmai University 10.1 Introduction elastic elastic-plastic contact 5,6,7,9 10.2 Geometrical Similarity circle of contact d/ 10.2.1 Geometrical Similarity contact circle d/ Geometrical similarity 10.2 Geometrical Similarity geometrical similarity indentations a/R mean contact pressure geometrical similarity geometrical similarity mean contact pressure a/R 10.3 Indenter types10.3.1 Conical, pyramidal and spherical indenters Vickers = 68o = 22o contact circle a 10.3.1 375 . 0 sin Ra 10.3 Indenter types10.3.1 Conical, pyramidal and spherical indenters h = 65o A = 24.5h2 70.3o 10.3.22 2tan 4h A 10.3 Indenter types10.3.1 Conical, pyramidal and spherical indenters Rahs22 tan sin RaRa tanahRa vRaahah v s 2v s h h21 10.3 Indenter types10.3.1 Conical, pyramidal and spherical indenters 6.2.3 c uz P1/2 uz P2/3 mean contact pressure cone sphere 10.3 Indenter types10.3.1 Conical, pyramidal and spherical indenters mean contact pressure Hardness 3 mean contact pressure vickers 10.3 Indenter types10.3.2 Sharp and blunt indenters 2 sharp indenter Vickers indenter > 70o Vickers indenter = 68o 10.3 Indenter types10.3.2 Sharp and blunt indenters elastic rigid-plastic Cone Punch and Sphere blunt indenters Cones and pyramid sharp indenters 10.4 Elastic-Plastic contact10.4.1 Elastic recovery elastic material 1 10.4.1(a) 3 = 0 max = 1/2 Tresca 1-3 = Y 1 = Y 10.4.1(b) elastic part R 1 elastic-plastic stress field ep 10.4 Elastic-Plastic contact10.4.1 Elastic recovery 1 R residual stress R R = YRelaxation elastic strain 10.4.1(d) elastic recovery s1 Full load elastic-plastic stress fields 10.4 Elastic-Plastic contact10.4.1 Elastic recovery fully-loaded unloaded 10.4.2(a) Unloading plastic zone full load unloading elastic recovery 10.4 Elastic-Plastic contact10.4.1 Elastic recovery Elastic contact elastic-plastic total elastic displacement uz r uz r rigid Full load 10.4 Elastic-Plastic contact10.4.1 Elastic recovery unloading Full load Hirst and Howse elastic-plastic loading pre-stress Hirst and Howse elastic recovery = 75% 10.4 Elastic-Plastic contact10.4.1 Elastic recovery Unloading sR Y Elastic recovery reloading elastic-plastic deformation 10.4.3 10.4 Elastic-Plastic contact10.4.2 Compliance flat punch uz 10.4.3 P uz ( )aPEuz21 2 10.4 Elastic-Plastic contact10.4.2 Compliance Loading Unloading AC full load ACF Elastic-plastic ABD Unloading DG DA ABD Energy dissipated ADG 10.4 Elastic-Plastic contact10.4.2 Compliance ADG ABD flat punch Field and Swain Compliance elastic elastic-plastic 10.4.5 P uz|r=0 loading unloading 10.4 Elastic-Plastic contact10.4.2 Compliance elastic contact load-point 6.2.1i load load unloading (assuming no reverse plasticity) 3213* 4 REP RPE223* 43]]]

10.4 Elastic-Plastic contact10.4.2 Compliance unloading E* unloading curve unloading zero load elastic unloading ( 2)221* 4 R EddP 10.4 Elastic-Plastic contact10.4.2 Compliance 10.4.2 rigid ht full load Pt hr P=0 hs Ps reloading hr ht 10.4 Elastic-Plastic contact10.4.2 Compliance3231321* 43t r t PREh h]]]]

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.|sttstsrPPhPPhh 10.4 Elastic-Plastic contact10.4.2 Compliance elastic reloading contact circle total elastic penetration contact circle full load /2 contact circle hp 2+ p t h h222r tr ttt ph hh hhh h+ 10.4 Elastic-Plastic contact10.4.2 Compliance contact circle [ ] 2122 p p h Rh a 10.4 Elastic-Plastic contact10.4.3 The elastic-plastic contact surface 6 2 non-rigid indenter R perfectly rigid indenter R+ FEM 10.4.6 elastic-plastic 10.4 Elastic-Plastic contact10.4.3 The elastic-plastic contact surface 10.4.1 FEM WC indenter elastic-plastic glass-ceramic P=1000 N R = 3.18 mm 10.5 Internal friction and plasticity slip Slippage internal frictionJaeger and Cook slip 10.5.1 coefficient of internal sliding friction 10.5 Internal friction and plasticity = 45o =max N = m 2-D 2 cosmax+ m N 2 sinmax 2 3 1max 2 3 1 +m( ) o m S + max2121( ) ( ) oS 2 1 1 21232121 ]]]

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+ 10.5 Internal friction and plasticity Tresca =0 So = Y/2 slide = 45o 90o 0 shear fracture max shear stress max compressive stress 10.5.1 10.5.4 Couloumb Jager and Cook 12 tan 10.5 Internal friction and plasticity 3 = 0 1 Co compressive strength 10.5.3b 1 3 10.5.6 1 3 Couloumb( )]]]

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