Endurance Strength Pg 274

Transcription

1 [Pg / 8] Fatigue Analysis Pg 257 The Units used as standard: in, kip, kpsi, sec, hp in, kip, kpsi, sec/min, hp Endurance Strength Pg 274 Fatigue failure occurs when a machine element is sujected to fluctuating load. The inherent strength of the material weaken at every cycle until eventually the structure is overcome y the applied cyclic load. To determine the strength of material under fatigue loading, specimens are sujected to repeated loading of specified magnitude and counted to destruction. The most widely used is the R. R. Moore machine fatigue test. Aove: Moores' Fatigue Test machine Below: SN diagrams from Moores' experiment

2 [Pg 2 / 8] # S-N DIAGRAM: Endurance (fatigue) strength against numer of cycles of Moore's steel specimen. See Fig 6-0 Pg 266 # Below: SN graph of other metals under fatigue load.

3 [Pg 3 / 8] Endurance Infinite Life Endurance Limit ' = 0.5S ut if S ut 400MPa (See Eqn 6-8 pg 274) NB: Endurance limits found only in steel and titanium Endurance Limit Modifying Factors Pg 278 Surface factor, k a as ut = Eg: If surface is machined: k a = 4.5S ut Size factor for round and rotating shaft, k =.24d 0.07 if 2.79 d 5mm k =.5d 0.57 if 5 < d 254mm Load factor, k c = ==> ending load k c = 0.85 (for ending and axial load comined) Temperature factor, k d, Reliaility factor, k e, Misc factor, k f = Endurance Limits, = k a k k c k d k e k f '

4 [Pg 4 / 8] CYCLIC LOADINGS Pg 292 Static Load is applied slowly without shock and is held at constant value. Repeated and Reversed Reversed: when a load-carrying component is sujected to certain level of tensile load followed y a same level of compressive load. Repeated: when loading is repeated many thousand times. σ max - maximum stress acting on the specimen σ min - minimum stress acting on the specimen τ max - maximum shear stress acting on the specimen τ min - minimum shear stress acting on the specimen K f - stress concentration factor mean stress acting on the specimen σ max + σ min σ m = K f 2 alternating stress acting on the specimen σ max σ min σ a = K f 2

5 [Pg 5 / 8] STRESS CONCENTRATION Pg 287 K t theoritical stress concentration factor Pg 05 See Tale A-5 to A-6 K f q = notch sensitivities. (concentration factor are less severe for some materials). K t See Fig 6-20, 6-2 and eqn & For Cast Iron: q = 0.2 ( ) K f = + q K t actual stress concentration factor (reduced value of Kt due to different material type ie different notch sensitivities) σ t = K f σ n SC stress (at Stress Concentration region) Sample Prolem Given : P = 5kN Cross section area : A n = ( 25mm) ( 25mm) = 625 mm 2 P Normal stress (without notch), σ n = = Pa Stress concentration occurs at notch : See pg 003 Fig A-3-3 : A n r d 2.5mm = = 0. 25mm w d 30mm = =.2 K t = mm S ut = 400MPa r f = 2mm q = 0.73 ( ) K f = + q K t = Cross section area at notch region : A t = ( 25mm) ( 25mm 5mm) = 500 mm 2 P Actual stress at notch : σ t = K f = MPa A t

6 [Pg 6 / 8] Fatigue Failure Criterion Pg 297 Langer's eqn (for early cycle yielding) : σ a S y + σ m S y = [6-48] η Modified Goodman equation: σ a + σ m S ut = [6-45] η Gerer equation: ησ a 2 ησ m + = [6-46] S ut Sodererg equation: σ a + σ m S y = [6-44] η If η =.0 then the stress (σ m,σ a ) lies on the Langer line or the other fatigue curves. Any points lower than the curves are safe i.e. η >.0. To ensure the materials do not yield at the first cycle loading, the Langer's equation must e applied against oth stresses σ m, σ a. If the material is considered safe y Langer, further analysis must done using any of the Fatigue equations as can e explained y the figure elow. The Sodererg lines is an exception to the aove ecause it does need to e accompanied y Langer's test.

7 [Pg 7 / 8] Fatigue Finite Life Pg 276 Method : To find the finite life, we need the equation S f = an x Total numer. of cycles, N x < If S ut < 490MPa then f = 0.9 If 490 S ut 400MPa get f from Fig 6-8 pg 277 ( ) 2 fs ut a = = log fs ut 3 σ a if σ m = 0 then N x = a If σ m 0 then do the following steps: Apply modified Goodman equation: Use the equation derived from S f σ a S f σ m + = to get S f S ut S f = an x that is, N x = a

8 [Pg 8 / 8] Stress Concentration Factor at Finite Life K 3 = K f ( ) Sut ( ) ( ) Sut K 3 3 log K N = N x K f K f K 3 From the figure aove, when the mean stress is compressive, failure occurs when σ a = In a complete setup, the figure elow shows the safe area for Goodman Fatigue life.