东南大学：《建筑力学 Architectural Mechanics》课程教学课件（英文讲稿）A22 Cyclic Loading and Fatigue

Cyclic Loading and Fatiguemi@ser.e.cn

Cyclic Loading and Fatigue mi@seu.edu.cn

Contents·CyclicStressandFatigue（周变应力与疲劳）·CharacteristicsofFatigueFailure（疲劳失效特征）·TechniqueTermsInvolved inCyclic Loading（周变荷载指标）·ClassificationofCyclicLoading（周变荷载分类）·Stress-lifeDiagram（应力寿命图）·FactorsAffectFatigueStrength（疲劳强度的影响因素）·AllowableStress ScopeofEqualAmplitudeFatigue（常幅疲劳问题的许用应力范围）·FatigueStrengthCondition（疲劳强度条件）2

• Cyclic Stress and Fatigue（周变应力与疲劳） • Characteristics of Fatigue Failure（疲劳失效特征） • Technique Terms Involved in Cyclic Loading（周变荷载指标） • Classification of Cyclic Loading（周变荷载分类） • Stress-life Diagram（应力寿命图） • Factors Affect Fatigue Strength（疲劳强度的影响因素） • Allowable Stress Scope of Equal Amplitude Fatigue（常幅疲劳问 题的许用应力范围） • Fatigue Strength Condition（疲劳强度条件） 2 Contents

Cyclic Stress and Fatigue: Cyclic Stress: stresses varying periodically with time: Fatigue Failure: failure of structural members under theapplication of cyclic stresses typically with magnitude far less thanyield stress.: Examples: (a) coupling gears; (b) eccentric motors; (c) train wheelaxes.3

• Cyclic Stress: stresses varying periodically with time. Cyclic Stress and Fatigue • Fatigue Failure: failure of structural members under the application of cyclic stresses typically with magnitude far less than yield stress. • Examples: (a) coupling gears; (b) eccentric motors; (c) train wheel axes. 3

Characteristics of Fatigue Failure. Fatigue failure stress << ultimatestrength / yield stress: Fatigue failure typically occurs aftermany cycles of stress application: Fatigue failure experiences threestages: crack initiation & propagation.and eventual fracture: Fatigue failure happens in the form ofbrittle fractureRough zoneFatigue origin.Fracture surface is composed of aSmooth zonerough zone and a smooth zone2

Smooth zone Rough zone Characteristics of Fatigue Failure • Fatigue failure stress << ultimate strength / yield stress • Fatigue failure typically occurs after many cycles of stress application • Fatigue failure experiences three stages: crack initiation & propagation, and eventual fracture • Fatigue failure happens in the form of brittle fracture • Fracture surface is composed of a rough zone and a smooth zone Fatigue origin 4

Technique Terms Involved in Cyclic Loading. Maximum Stress: omaxT: Minimum Stress: 00minomar+0max0.min·Average Stress: ,20a0maxmin: Stress Amplitude: .2. Stress Scope: △o =0.Omaxmin0min· Cycle Characteristics:0max5

t σ o T  m  min  a  a  max • Maximum Stress: • Stress Scope:  max  min • Minimum Stress:       max min • Average Stress: min max 2 m      • Stress Amplitude: max min 2 a      Technique Terms Involved in Cyclic Loading • Cycle Characteristics: min max r    5

Classification of Cyclic Loading: Symmetric Cycling: equal but opposite maximum and minimumstress9,=αmaxma0110Omin0=0.maminamaxUnsymmetricCycling0=o.+a,mamax00=0mamin0min0max6

• Symmetric Cycling: equal but opposite maximum and minimum stress • Unsymmetric Cycling min max r 1         a max min   m   0    max m a      min m a   min max r    t σ o  min  a max  a  Classification of Cyclic Loading 6

Classification of Cyclic Loading· Pulse Cycling0min =0=α2maxmaxWOmax0maxr=0a.0.ma20Or:0=0mina00=80minmaxmaxam2O? Static (Constant) Stress=Omin=OmO max2maxOOmin=0r=100.a7

• Pulse Cycling   max max  • Or: min   0 max a m 2      r  0 max   0   min max  min a m 2      r   • Static (Constant) Stress    max min m   a   0 r 1 σ o  a  max σ o  a  max  min 7 Classification of Cyclic Loading

Stress-life (S-N) Diagram? Fatigue properties areshown on o-N diagrams0max (MPa). A member may fail due tofatigue at stress levels750significantly below theultimate strength if650subjected to many loading550cycles..When the stress is reduced106104105107Nbelow the endurance limit(c,), fatigue failures do notoccur for any number ofcycles

• Fatigue properties are shown on σ-N diagrams. • When the stress is reduced below the endurance limit (σr ), fatigue failures do not occur for any number of cycles. • A member may fail due to fatigue at stress levels significantly below the ultimate strength if subjected to many loading cycles. Stress-life (S-N) Diagram 750 650 550 4 10 6 10 5 10 7 10 N  max MPa 8

Factors Affect Fatigue Strength? Stress Concentration Surface Roughness Surface Strength9

• Stress Concentration • Surface Roughness • Surface Strength Factors Affect Fatigue Strength 9

Allowable Stress Scope for Equal-amplitude Fatigue2.60 (400)3-4·Equal-amplitude:2.48(300)2.30(200)△α =20。=0max类别= const.-02.18(150)min1ON212.00 (100)B=3: Experimental data shows:101.90(80)1.78 (60)Aα=Omax -0min =(a/N)/B1.70(50)1.60(40)5.005.305.706.006.306.70=[40]=(c/n)vB(10%）（2×105）（5×10）（10°）(2×10%(5×10°)IgN表6-1我数·值构件和连接类别/234C1940×1012861 ×11p12.18×10"2325V10″B4433构件和连接类别5678c096×100.41×10121.47×10/20.65-10a3333· Fatigue strength condition: [△o|≤ n,△α10

Allowable Stress Scope for Equal-amplitude Fatigue       1 max min 1 a N C N              • Fatigue strength condition:   . f      n 10 • Equal-amplitude: max min 2 const.          a • Experimental data shows: