CHAPTER 11 FATIGUE,CREEP AND FRACTURE Summary Fatigue loading is generally defined by the following parameters stress range,o,=20a mean stress,om =(omax +omin) alternating stress amplitude,a=(omax-omin) When the mean stress is not zero stress ratio,R=Omin Omax The fatigue strength oN for N cycles under zero mean stress is related to that oa under a condition of mean stress om by the following alternative formulae: Oa ON[1-(om/ors)](Goodman) Oa =oN[1-(am/OTs)2](Geber) da ON[1-(om/oy)](Soderberg) where ors tensile strength and oy=yield strength of the material concerned.Applying a factor of safety F to the Soderberg relationship gives =-(%。,P】 Theoretical elastic stress concentration factor for elliptical crack of major and minor axes A and B is K,=1+2A/B The relationship between any given number of cycles n at one particular stress level to that required to break the component at the same stress level N is termed the"stress ratio" (n/N).Miner's law then states that for cumulative damage actions at various stress levels: ++ n1 n3 +…+etc.=1 The Coffin-Manson law relating the plastic strain range Asp to the number of cycles to failure N is: △ep=K(Nf)b 443CHAPTER 11 FATIGUE, CREEP AND FRACTURE Summary Fatigue loading is generally defined by the following parameters stress range, a, = 2a, mean stress, a,,, = Z(a,,,ax + a,,,,,) alternating stress amplitude, a, = (arna - ami,) 1 When the mean stress is not zero amin amax stress ratio, R, = - The fatigue strength CN for N cycles under zero mean stress is related to that a, under a condition of mean stress am by the following alternative formulae: a, = a~[1 - (am/a~s)] a, = a~[l - (am/a~~)2] a, = a~[l - (am/ay)] (Goodman) (Geber) (Soderberg) where CTTS = tensile strength and ay = yield strength of the material concerned. Applying a factor of safety F to the Soderberg relationship gives a, = “N [l- (31 am F) F Theoretical elastic stress concentration factor for elliptical crack of major and minor axes A ahd B is Kt = 1 + 2A/B The relationship between any given number of cycles n at one particular stress level to that required to break the component at the same stress level N is termed the “stress ratio” (n/N). Miner’s law then states that for cumulative damage actions at various stress levels: nl n2 n3 -+-+-+... + etc. = 1 N1 N2 N3 The Coffin-Manson law relating the plastic strain range failure Nf is: to the number of cycles to AS, = K(Nf)-b or -b AE~ = (%) 443