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  • 1. Materiali per l’IngegneriaM.Ferraris1“true” engineering curvenecking Formation of poresPores coalescenceCrack propagationhttp://web.umr.edu/~be120/lessons/intro/tension/testing_st/fracture.gif
  • 2. Materiali per l’IngegneriaM.Ferraris2
  • 3. Materiali per l’IngegneriaM.Ferraris3
  • 4. Materiali per l’IngegneriaM.Ferraris4
  • 5. Metallic samplesfor tensile test
  • 6. Yield strength(σs, σy, σ0,2)(σs, σP(0,2))Yield strength or proportionallimit (Rp0,2)Yield Strength (YS, Sy),“Yield Strength (offset = 0.2 %)”
  • 7. Upper and lower yieldstrength(ReL)Upper Yield Strength (UYS)and Lower Yield Strength(LYS)
  • 8. (σMAX)(R, Rm)(Rm)Tensile Strength (TS, Su,UTS)
  • 9. elongation %(At)Maximum elongation (Elmax)10000⋅−lll
  • 10. Typical stress-strain curvesfailuretensile strengthupper yield pointlower yield pointσystrainstressmaterial creeps (extensionwithout increased stress) orsample ‘necks’elasticregionplasticregionyield elongation ultimate elongationultimate strengthmaterial mayfollow either pathwww.matcoinc.com/images/sem1a.jpg
  • 11. http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/Tensile.htm
  • 12. Materiali per l’IngegneriaM.Ferraris12COMPRESSION TEST
  • 13. Materiali per l’IngegneriaM.Ferraris13Bending or flexural test
  • 14. Materiali per l’IngegneriaM.Ferraris14THREE POINT BENDING TEST
  • 15. Materiali per l’IngegneriaM.Ferraris153 and 4 point bending
  • 16. Materiali per l’IngegneriaM.Ferraris16Asymmetric 4 point bending for ceramic joinedmaterialsFleFeFeFiFiFliMfTT = Fle - lile + li
  • 17. Materiali per l’IngegneriaM.Ferraris17BENDING TEST on Al2O3and glassσ (MPa)ε
  • 18. Materiali per l’IngegneriaM.Ferraris18Flexural strength of ceramics
  • 19. Materiali per l’IngegneriaM.Ferraris19TEST:• Draw ε versus t (strain vs time) when a material isloaded at σ = constant, in the elastic field
  • 20. Materiali per l’IngegneriaM.Ferraris20TEST• Draw ε versus t (strainvs time) when a materialis loaded at σ =constant, in the elasticfield
  • 21. Materiali per l’IngegneriaM.Ferraris21TEST• Draw ε versus t (strainvs time) when a materialis loaded at σ =constant, in the elasticfield
  • 22. Materiali per l’IngegneriaM.Ferraris22CREEPPlastic deformation even if stress is in the elasticfieldfractureElastic deformationCreep ICreep IIICreep II
  • 23. Materiali per l’IngegneriaM.Ferraris23CREEPConstant load in the elastic field gang ive to aplastic deformation, progressive to fracture.•Thermally activated processMetals T> 0,3-0,4Tfus (K)Ceramics T> 0,6-0,7 TfusAmorphous materials T> Tgtests: a constant load is applied at a given T,strain is recorded versus time.
  • 24. Materiali per l’IngegneriaM.Ferraris24CREEP I:cold working higher than anenaling.CREEP II:constant strain: balance between cold working andannealingCREEP III:micro-cavity and other macro-defects at the grainboundaries: fracture of the sample
  • 25. Materiali per l’IngegneriaM.Ferraris25Creep II : steady statenCRnss ATRECdtdϑϑεε ⋅=⋅−⋅⋅== expC= costant depending on materialsϑ = applied stressn = coefficient depending on materials 3 < n < 8ECR = activation EnergyR= perfect gas constantT = test Temperature
  • 26. Materiali per l’IngegneriaM.Ferraris26CREEP curves when increasing T or applied stressεCurve trendwhen increasingapplied stress ortest Temperature
  • 27. Materiali per l’IngegneriaM.Ferraris27°Ccreep curves for a borosilicate glassat 200 and 420 °C, from 18 to 36 MPa)
  • 28. Creep dCreep degradation of Steelsegradation of Steels forforPipelinesPipelines100 000 h100 000 hInitial stateInitial stateZ. L. Kowalewski - IPPT, Poland
  • 29. CreepCreep development in 13HMFdevelopment in 13HMF SteelSteel forforPipelinesPipelines0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0T im e [ h ]051 01 52 02 53 03 54 0Creepstrain[%]A s - r e c e iv e dE x p lo it e d144 000 h144 000 hInitial stateInitial state0 0 . 1 0 . 2 0 . 3S t r a in01 0 02 0 03 0 04 0 05 0 06 0 0Stress[MPa]Z. L. Kowalewski - IPPT, Poland
  • 30. 360 h 550 h 988 hMicroscopic view of specimens (40HNMA Steel)after creep tests up to:Z. L. Kowalewski - IPPT, PolandZbigniew L. KowalewskiE-mail: zkowalew@ippt.gov.pl
  • 31. Materiali per l’IngegneriaM.Ferraris31How to increase creep resistance?• High melting T and E materials• Large grains or mono-crystals (small grainsincrease grain motion at the grain boundaries)• Solid sotutions• Precipitates• Second phases (composites)
  • 32. Materiali per l’IngegneriaM.Ferraris32TEST:• Apply a tensile stress to a material in the elasticfield.• Repeat the test several times.• Is it possible to have the material failure ?
  • 33. Materiali per l’IngegneriaM.Ferraris33TEST:• Apply a tensile stress to a material in the elasticfield.• Repeat the test several times.• Is it possible to have the material failure ?• If yes, draw a graph with the applied stress (σ)versus the number of cycles (n) necessary toobtain the material failure
  • 34. Materiali per l’IngegneriaM.Ferraris34S-N curves: stress (S) vs number of cycles(N) to obtain failureNS Fe, Ti, steelsAl, CuDispersion rangeFatigue limit
  • 35. Materiali per l’IngegneriaM.Ferraris35Fatigue• Failure of materials due to cyclic loading.• Main reason of mechanical failure of materials• Failure happens at stress lower than σR or σY• Catastrophic failure of materials (also for ductilematerials !)• Fatigue tests: materials are cyclically loaded at differentstresses up to failure.• Fatigue limit: when cyclically loaded below this limit,materials do not fail
  • 36. Materiali per l’IngegneriaM.Ferraris36Fatigue testNumber of cycles(N)sample Load NLoad N
  • 37. Materiali per l’IngegneriaM.Ferraris37S-N curveσa=σmax−σmin2S=NS σmax , σmin : appliedstresses during testsFracture zoneSafe zone
  • 38. Materiali per l’IngegneriaM.Ferraris38Materials and Fatigue• Between 35-65% of their tensile strength most ofmetals fail because of fatigue (e.g. Fe, Ti alloys,intrinsical fatigue limit)• Other metals fail in any case after a given limit (e.g. Al,no intrinsical fatigue limit)• Fatigue resistence: stress necessary to fracture thematerial after a given number of cycles at this stress• Fatigue life: number of cycles necessary to fracturethe materials at a given load.
  • 39. Materiali per l’IngegneriaM.Ferraris39Fatigue: fracture surfaceStarting point (surface defect)StartingpointFatigue surface,smoothCatastrophic failure,rough surface
  • 40. Materiali per l’IngegneriaM.Ferraris40Fatigue: fracture surfaceFatigue surface, smoothCatastrophic brittle failure,also on ductile materials,rough surface
  • 41. Materiali per l’IngegneriaM.Ferraris41Frattura a fatica• Ogni processo di frattura a fatica comprende laformazione e la propagazione di cricche– I materiali duttili (metalli, alcuni polimeri) possonocontrastare entro certi limiti la propagazione di unacricca, poi cedono comunque per frattura fragile– I materiali fragili non sono in grado e vanno incontroa fratture fragili, catastrofiche (ceramici, vetri)
  • 42. Materiali per l’IngegneriaM.Ferraris42Ductile and brittle fracture• Ductile fracture: high plastic deformation at thecrack tip, slow crack propagation• Brittle fracture: no (or low) plastic deformation at thecrack tip, quick crack propagation, catastrophicfailure)Al steel
  • 43. Materiali per l’IngegneriaM.Ferraris43Mystery failures - de HavillandComet• G-ALYY was leased from B.O.A.C. to South African Airways. Flight SA201 was on its way from London to Johannesburg. After afuel stop in Rome the plane took-off, but only 36 minutes later the radio-contact was interrupted in the area of Stromboli. January1954.• The next morning remains were found in the sea. Since the sea was at this place as deep as 1000 meters, no parts of the aircraft couldbe inspected. Only four days after the crash the Comet flights were again suspended, one of the reasons being the similarities to theYP crash. G-ALYY had only performed 2704 flighthours. A very intensive flight test program was performed in order to find outthe reason of the YY and YP crashes, with no special conclusion.• Only after a very long expensive investigations, which included the assembly of the remains of the crashed YP and the underwaterstress test of the YU Comet which came from B.O.A.C. Finally the fuselage of YU broke up on a sharp edge of the forward escape-hatch. After that this rupture was repaired the tests were restarted, but only shortly afterwards the fuselage broke up. This time therupture started at the upper edge of a window and was three meters long.• The YP and YY crashes were due to metal fatigue, which took place because of the crystalline changes in the fuselage skin. Theywere amplified by the high speed and altitude the Comets were operated. The metal fatigue resulted in ruptures of the fuselage, thishad as a consequence a terrible decompression at 33Kft, tearing up the plane with all known consequences.http://www.geocities.com/CapeCanaveral/Lab/8803/comet.htmhttp://www.baaa-acro.com/Photos-2/G-ALYP.jpg
  • 44. Materiali per l’IngegneriaM.Ferraris44
  • 45. Materiali per l’IngegneriaM.Ferraris45Stress intensity factor]21[210 +=tmaρσσ• Macro-defects (pores, cracks) inall materials act as stressconcentration factors• True stress on the material at thetip of the crack (σ m) is higher thanthe nominal stress (σ o)ρt = radius of the cracka = length of a crack on thesurface• Critical Defects (Griffith Theory,Fracture mechanics, see )• Without defects, tensile strengthwould be close to the theoreticalvalues (as it is for monocrystallinematerials or small brittle materials)
  • 46. Materiali per l’IngegneriaM.Ferraris46Crack propagationRole of :ρt = radius of the cracka = length of a crack on the surface– If plastic deformation is possible, ρt can increaseand decrease σ m– If plastic deformation is not possible, there iscatastrophic failure.– Griffith Theory quantify what above with math........]21[210 +=tmaρσσ
  • 47. Materiali per l’IngegneriaM.Ferraris47• Stress intensity factor for long cracks withsmall radiusσm=2σ0aρt12Callisterσo= nominal stressσm= stress on materialK=σm/σo = stress intensityfactor, K=2(a/ρ)1/2
  • 48. Materiali per l’IngegneriaM.Ferraris48• During crack propagation surface elastic energy γs isreleased• Griffith Theory: criterion for crack propagation (energybalance)σc = (2 E γs / π a)1/2(brittle materials)σc = (2 E (γp + γs )/ π a)1/2(ductile, plastic material= surface plastic energy =γp)σc = critical stress, crack propagation for σ> σcCrack propagation and criticalparameters
  • 49. Materiali per l’IngegneriaM.Ferraris49σc = (2 E (γp + γs )/ π a)1/2Gc = 2 (γp + γs )Gc = σ2π a/ Ecrack propagates when:σ2π a/ E > Gc (Griffith theory)K stress intensity factor (MPa m1/2)K = (GcE)1/2=Y σ (π a)1/2For materials containing macroscopicdefects, crack propagation occurs when σ >σ cY adimentional parameter (depends on sampleand crack geometry)Fracture toughnessKc = Y σc (π a)1/2(MPa m1/2)KIc = Y σc (π a)1/2FracturethoughnessCrack propagation and critical parameters
  • 50. Materiali per l’IngegneriaM.Ferraris50KIC criticalparameters(defect length andstress)above which there isfailure (all materials)KIc = Y σc (π a)1/2(ASTM E 399)
  • 51. Materiali per l’IngegneriaM.Ferraris51
  • 52. Materiali per l’IngegneriaM.Ferraris52
  • 53. Materiali per l’IngegneriaM.Ferraris53
  • 54. Materiali per l’IngegneriaM.Ferraris54
  • 55. Materiali per l’IngegneriaM.Ferraris55How to increase materials fatigueresistance?• Surface strengtheningmethods• Coatings• Suitable mechanical design• Fatigue and fracturemechanics to model andpredict components life !(seeThermal fatigue, corrosion, …)
  • 56. Materiali per l’IngegneriaM.Ferraris56Ni based super-alloyFatigue inducedintergranular crackLight (optical)microscopy
  • 57. Materiali per l’IngegneriaM.Ferraris57HARDNESS• Material resistance to surface compressionApplied loadIndenterSample
  • 58. Materiali per l’IngegneriaM.Ferraris58Vickers Hardness, HV
  • 59. Materiali per l’IngegneriaM.Ferraris59Brinell HardnessHB= P/(πDh) = carico/area improntaVickers HardnessHV= 1.854P/L2indenterSamplesurface
  • 60. Materiali per l’IngegneriaM.Ferraris60RockwellHardness measurepenetration depth
  • 61. Materiali per l’IngegneriaM.Ferraris61example: 60 HR30W= superficial Rockwell hardness =60 scale30W
  • 62. Materiali per l’IngegneriaM.Ferraris62Example: 80 HRB= Rockwell hardness = 80 scale BValues lower than 20 or higher than 100 are not acceptable
  • 63. Materiali per l’IngegneriaM.Ferraris63Correlation hardness/tensile propertiesSteel TS: about= 3.45 HBbrassCast ironsteel
  • 64. Materiali per l’IngegneriaM.Ferraris64
  • 65. Materiali per l’IngegneriaM.Ferraris65Hardnessprofile
  • 66. Materiali per l’IngegneriaM.Ferraris66StressResilience modulus (Ur)Ur = ∫ σ dε (between ε0 andεy) (ELASTIC FIELD)σ=E ε εy= σy / EUr = ½ σy εy = ½ σy2/Estrain
  • 67. Materiali per l’IngegneriaM.Ferraris67Toughness and fracture toughness• Toughness = energy absorbed up to fracture = area of σ/ε curveup to fracture ) (J / m3)• Fracture toughness = fracture resistance in presence of notchesStressstrainBrittle, fragile, low ∫ σ dεDuctile, tough, plastic…..large ∫ σ dε
  • 68. Materiali per l’IngegneriaM.Ferraris68Charpy test:Measure of theenergy necessaryto fracture anotched sample(impact of ahammer)Starting positionhammerscalefinal positionsampleRuler
  • 69. Materiali per l’IngegneriaM.Ferraris69Absorbed impact energy vs temperature for several steels: ductile tobrittle transitionAbsorbedimpactenergyRole of C and Fe3C on dislocation motion and ductile to brittle transition
  • 70. Fracture surfaces after Charpy test (V-notched) at given TDuctile to brittle transition
  • 71. Materiali per l’IngegneriaM.Ferraris71Effect of ductile to brittle transition...• 4 °C• steel
  • 73. Materiali per l’IngegneriaM.Ferraris73Ex: Cu, Al, Ag, AuEx: Fe, W, CrEx: Mg, Ti, ZnHEXAGONALBCC FCC
  • 74. Materiali per l’IngegneriaM.Ferraris74CHARPY tests onsteel at different Tat room T(2.22 J/mm2)at -200 °C(0.04 J/mm2)
  • 75. Materiali per l’IngegneriaM.Ferraris75Charpy test on steels withsame composition butdifferent thermaltreatments:0,89 J/mm2C40 steelannealed0,07 J/mm2C40 steel quenched
  • 76. Materiali per l’IngegneriaM.Ferraris76DUCTILITY TESToofSTRAINlll )(100%−⋅= ooneckingAAA f )(100%−⋅=
  • 77. Materiali per l’IngegneriaM.Ferraris77
  • 78. Materiali per l’IngegneriaM.Ferraris78T1T2T3T4T1<T2<T3<T4
  • 79. Stress/strain curves for iron vs TemperatureStressStrain
  • 80. Materiali per l’IngegneriaM.Ferraris80Stress/strain curves vs TemperatureFepolymers