1.9 Dynamic loading: τ ty : torsion yield stress (torsion) τ sy : shear yield stress (shear) In the last lectures only static loadings are considered

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1 1.9 Dynaic loading: In the last lectures only static loadings are considered A static loading is: or the load does not change the load change per tie N Unit is 10 /sec 2 Load case Ι: static load (case I acc. to Aug. Bach) Liit stress for this case are: P0,2 : yield stress of aterial (tension) by : bending yield stress (bending) τ ty : torsion yield stress (torsion) τ sy : shear yield stress (shear) LEC-DT-1_05.doc Seite 1 von 12

2 Fluctuating / swell loading: load case ΙΙ a) fluctuating / fully released pure swell loading b) fluctuating not released Fully released, pure swell loading: sign of stress is not changed during cycle Liit stress for this case are: : tension swell strength : bending swell strength τ : torsion swell strength tsw bsw tsw Case ΙΙΙ : reversing loading a) fully reversed stress b) non zero reversed stress eversing loading or alternating loading is a very frequent kind of loading: Fully reversing loading: the sign of stress is changing during each cycle LEC-DT-1_05.doc Seite 2 von 12

3 Most applied testing device for alternating (bending) stresses to evaluate the fatigue strength of aterials is the rotary bending test achine. otating shaft with bending oent: rotary bending = reversing bending A rotating section with applied bending oent undergoes fully reversed loading fro tension to copression during 1 revolution. Liit stress for this case are: : Tension / copression reversing strength < P0,2 : reversing bending strength τ : reversing torsion shear strength t b t The load, which a aterial can hold for a very long tie (for ever) under these loading conditions (case Ι, ΙΙ, ΙΙΙ) is the fatigue strength or endurance strength (Dauerfestigkeit) LEC-DT-1_05.doc Seite 3 von 12

4 Cyclic stresses: Cyclic stresses with non zero ean stress Definitions for cyclic stresses: Mean stress: = ax + 2 Stress range: = ax Stress aplitude: a a ax = = 2 2 Stress ratio: S or κ S = ax κ Aplitude ratio: A a A a ( ax ) ( ax ) ( ax ) ( ax ) 0,5i a 1 = = = = 0,5i S S 1 load cycle: when the sae load characteristic starts again: LEC-DT-1_05.doc Seite 4 von 12

5 Most used patterns of cyclic stresses: Load case Ι: static loading S = 1 ; ax = = = const ; a = 0 A = 0 a Load case ΙΙ: fluctuating / swell loading a) Coon case: 1> S 0 b) eleased tension / swell tension loading: = 0 ; S = 0 ; Aa = 1 ; = 2 ax eleased copression / swell copression loading: ax = 0 ; S = ; Aa = 1 ; = 2 Load case ΙΙΙ: coplete reversing loading: = 0 ax = ax ; S = 1 ; Aa = ; = 0 = = a Coon case: 0 reversing loading 0> 1 ; = 0 ; 1 A S a LEC-DT-1_05.doc Seite 5 von 12

6 First fatigue tests by August Wöhler ( 1864 ) eason: Fractures of rail road wagon axles, even when loaded far away fro any liits Materials show a liited nuber of load cycles under certain stress levels Fracture of a shaft with fatigue fracture area (Dauerbruchfläche) and spontanous fracture area (Gewaltbruchfläche) and arks (astlinien). esults of fatigue tests are shown in so called Wöhler-diagras: Fatigue strength vs. cycles to failure (so called Wöhler curve), a) for ferrous alloys: steels and alloyed cast steels Fatigue stress ratio is : S / S / S f = ; S f = fatigue strength ; S ut = f Steel are considered fatigue resistant if at a certain load (stress) ore than cycles are conducted without a failure. UT 10i 10 6 LEC-DT-1_05.doc Seite 6 von 12

7 Steels show a clear endurance liit: a) short cycle fatigue b) ediu cycle fatigue c) long cycle fatigue, endurance strength Fatigue strength for: b) aluiu alloys, no exact or distinct endurance liit Endurance liit as a function of tensile strength of aterials: 1000 psi = MPa ; 300 kpsi = MPa LEC-DT-1_05.doc Seite 7 von 12

8 Epirical relations for endurance liit S e for steels : S 0,5i For bending e S 0,45i For axial loading (tension, copression) e S 0,29i For torsion e Approxiate endurance liits S e for various aterials Cycles Magnesiu alloys n = 10 8 S 0,35i Copper alloys n = ,25i < S < 0,5i e e Nickel alloys n = ,35i < S < 0,65i e The agnitude of alternating stress depends of the ean stress level for cyclic stresses: Alternating stress ratio as a function of ean stress ratio for axial loaded cast iron. All of these fatigue stresses/endurance strengths for the different load cases ust be detered by special fatigue tests and the ean stress level are influencing the results. To evaluate all data for a aterial is a difficult and tie consug task. LEC-DT-1_05.doc Seite 8 von 12

9 The data are tabulated in data lists for aterials: Fro this data we get a new set of liit stresses for aterials: Load cases: I = static loading, II = released fluctuating (swell) loading, III = dynaic reversing loading Liit stresses according to the load cases: I static loading: = tensile yield strength (0, 2% strain), τ τ P0,2 Cf BF TF SF TCS = copression flow stress, = bending flow stress, = torsion flow stress, = shear flow stress, II = released fluctuating (swell) loading: τ BS TS TC B T = tension, copression swell strength, III = dynaic reversing loading: τ = bending swell strength, = torsion swell strength = tension, copression reversing strength, = bending reversing strength, = torsion reversing strength LEC-DT-1_05.doc Seite 9 von 12

10 The cobination of fatigue strength of a aterial for different load cases together with different ean stresses a shown in the Sith-Goodan diagras: x = s = κ : stress ratio ; I, II, III load cases acc. to Aug. Bach: - III: full reversing loading - II : full released swell loading - I : static loading LEC-DT-1_05.doc Seite 10 von 12

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