1Evolution of the design philosophy1950 Irwin: G definitionLINEAR ELASTIC FRACTURE MECHANICS1960 Rice:J integral definitonELASTO-PLASTIC FRACTURE MECHANICSParis: fatigue crack propagationDAMAGE TOLERANT APPROACH2Linear-elastic fracture mechanics limit validity3Linear-elastic fracture mechanics limit validityPlastic zone where the stress values are not knownThe plastic zone must be lower than the K-dominant zone 4YPlane strainMFLEKIcStress planeBab ahKsn, , , , 2 5224, , snKh a b a MFLEaeff - Keff MFEPJIcNOP/PcolKIcStable crack growthbhNO41ToughnessmMaterialToughnessKIc[MPa ]Yieldingstresssn[MPa]Failurestressr [Mpa]Failure strainf[%]ReductionareaZ [%]SteelsAISI 1144 66 540 840 5 7ASTM A470-8 60 620 780 17 45ASTM A517-F 187 760 830 20 6630CrMo2AISI 4130110 1090 1150 14 49ASTM A538-C 123 1310 1350 12 54ASTM A538fuso sotto vuoto176 1290 1345 15 66Aluminium alloys2014-T651 24 415 485 13 -2024-T351 34 325 470 20 -2219-T37. 41 315 395 11 -6061-T651 34 275 310 12 -7075-T651 29 505 570 11 -42ToughnessmmMaterial KIc[MPa ]Material KIc[MPa]Polymers CeramicsABS 3,0 Soda-lime glass 0,76Acrylic 1,8 Magnesia, MgO 2,9Epoxy 0,6 AluminaAl2O34,0PC 2,2 Al2O3, 15% ZrO210,0PVC 2,4 SiliconcarbideSiC 3,7PVC rubber mod. 3,35 SiliconnitrideSi3Ni45,644where:E'=E plane stressplane strainIf there are all the three loading modes: is the tangential elasticity coefficient.K=KIc'2EKG =) 1 ('2 =EE 2 ' '2 2 2III II IKEKEKG + + =' E2KRIc=5Elasto plastic fracture mechanicsLinear-elasticNon linear-elastic6LBWE= U2cricca senza elemento22BaE= U2cricca)2(2aE+ LWE B1= U2 2BEadadU22=EaG2 2 =G versus stressesU=Uelement without crack+UcrackIf the plate is loaded by a uniform stress :Griffith showed that the strain energy due to the crack is proportional to the energy of a circle (of radius a) corresponding value before the crack initiation:BB7Elasto plastic fracture mechanicsGaE= 2 2G=2a2=HIf the plastic zone is largeJ=JRHa=JR t e ptnE K= += +1When the behaviour is not linear elastic:E8Elasto plastic fracture mechanicsJel+Jp=JR tmE K= +H aEH aKJmm R 2 1+ =+dUdaaE= 2 2elasticplastic14Elasto plastic fracture mechanicsJel