平均应力修正 |
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可使用平均应力修正来说明非零平均应力的影响。 一般情况下，可通过完全反转的循环载荷的标准试验得到疲劳曲线。然而，真实的疲劳载荷不能完全反转，法向平均应力对部件的疲劳性能有显著影响。就疲劳强度而言，拉伸法向平均应力是有害的，而压缩法向平均应力是有益的。可使用平均应力修正来说明非零平均应力的影响。 根据材料、应力状态、环境和应变振幅的不同，疲劳寿命通常取决于沿剪切面或拉伸面出现的微裂纹生长。临界平面平均应力修正方法结合了支配这两类裂纹生长的主要参数。由于可能的失效模式不同（以剪切或拉伸为主），不能指望使用单一的平均应力修正方法来关联所有材料在所有生命周期中的试验数据。关于多轴疲劳寿命估算的最佳方法，目前还没有达成共识。对于基于应力的平均应力修正方法，拉伸裂纹可使用 Goodman 和 FKM 模型。剪切裂纹可使用 Findley 模型。对于基于应变的平均应力修正法，拉伸裂纹可使用 Morrow 模型和 Smith-Watson-Topper 模型。剪切裂纹可使用 Brown-Miller 模型和 Fatemi-Socie 模型。如果定义了多个模型，SimSolid会从所有可用的损害值中选择造成最大损害的模型。 Goodman 模型可使用 Goodman 模型评估临界平面上拉伸裂纹生长造成的损害。 (1) S e = S a 1− S m S U ↵ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGtbWaaSbaaSqaaiaadwgaaeqaaO Gaeyypa0ZaaSaaaeaacaWGtbWaaSbaaSqaaiaadggaaeqaaaGcbaWa aeWaaeaacaaIXaGaeyOeI0YaaSaaaeaacaWGtbWaaSbaaSqaaiaad2 gaaeqaaaGcbaGaam4uamaaBaaaleaacaWGvbaabeaaaaaakiaawIca caGLPaaaaaGaeyyTH8laaa@4004@ 其中： S m MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGtbWaaSbaaSqaaiaad2gaaeqaaa aa@33AE@ 是平均应力，公式为 S m = S m a x + S m i n / 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGtbWaaSbaaSqaaiaad2gaaeqaaO Gaeyypa0ZaaSGbaeaadaqadaqaaiaadofadaWgaaWcbaGaamyBaiaa dggacaWG4baabeaakiabgUcaRiaadofadaWgaaWcbaGaamyBaiaadM gacaWGUbaabeaaaOGaayjkaiaawMcaaaqaaiaaikdaaaaaaa@3FBE@ S a MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGtbWaaSbaaSqaaiaadggaaeqaaa aa@33A2@ 是应力振幅 S e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGtbWaaSbaaSqaaiaadwgaaeqaaa aa@33A6@ 是平均应力校正后的应力振幅 S u MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGtbWaaSbaaSqaaiaadwhaaeqaaa aa@33B6@ 是极限振幅Goodman 模型总是以加速疲劳失效的方式来处理正平均应力修正，而忽略负平均应力。这种方法提供了压缩平均应力的保守结果。 Haigh 图表描述了在给定的失效循环次数下，应力振幅和平均应力的不同组合。 Figure 1. Goodman Haigh 图表 Findley 模型 Findley 准则通常适用于有限寿命疲劳的情况。每个平面的方程如下：(2) Δ τ 2 + k σ n = τ f * ( N f ) b MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq qHuoarcqaHepaDaeaacaaIYaaaaiabgUcaRiaadUgacqaHdpWCdaWg aaWcbaGaamOBaaqabaGccqGH9aqpcqaHepaDdaqhaaWcbaGaamOzaa qaaiaacQcaaaGccaGGOaGaamOtamaaBaaaleaacaWGMbaabeaakiaa cMcadaahaaWcbeqaaiaadkgaaaaaaa@47A4@ 其中： τ f * MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aa0 baaSqaaiaadAgaaeaacaGGQaaaaaaa@397E@ 是由剪切疲劳强度系数 τ f ' MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aa0 baaSqaaiaadAgaaeaacaGGNaaaaaaa@397C@ 计算得出，使用： (3) τ f * = 1 + k 2 τ f ' MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aa0 baaSqaaiaadAgaaeaacaGGQaaaaOGaeyypa0ZaaOaaaeaacaaIXaGa ey4kaSIaam4AamaaCaaaleqabaGaaGOmaaaaaeqaaOGaeqiXdq3aa0 baaSqaaiaadAgaaeaacaGGNaaaaaaa@41A7@ 修正因子 1 + k 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaaca aIXaGaey4kaSIaam4AamaaCaaaleqabaGaaGOmaaaaaeqaaaaa@397A@ 通常的设定值约为 1.04。 Note: τ f * MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aa0 baaSqaaiaadAgaaeaacaGGQaaaaaaa@397E@ 必须根据振幅来定义。如果 τ f ' MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aa0 baaSqaaiaadAgaaeaacaGGNaaaaaaa@397C@ 不是由用户来定义，则 SimSolid 使用以下公式进行计算：(4)(30) τ f ' = C f * 0.5 * S R I 1 − b ± b 2 − 4 a c 2 a W h e r e , C f = 2 1 + k 1 + k 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHep aDdaqhaaWcbaGaamOzaaqaaiaacEcaaaGccqGH9aqpcaWGdbGaamOz aiaacQcacaaIWaGaaiOlaiaaiwdacaGGQaGaam4uaiaadkfacaWGjb GaaGymamaalaaabaGaeyOeI0IaamOyaiabgglaXoaakaaabaGaamOy amaaCaaaleqabaGaaGOmaaaakiabgkHiTiaaisdacaWGHbGaam4yaa WcbeaaaOqaaiaaikdacaWGHbaaaaqaaiaadEfacaWGObGaamyzaiaa dkhacaWGLbGaaiilaaqaaiaadoeacaWGMbGaeyypa0ZaaSaaaeaaca aIYaaabaGaaGymaiabgUcaRmaalaaabaGaam4AaaqaamaakaaabaGa aGymaiabgUcaRiaadUgadaahaaWcbeqaaiaaikdaaaaabeaaaaaaaa aaaa@5CDE@ 常数 k 由实验得出，即执行涉及两种或两种以上应力状态的疲劳试验。对于延性材料，k 通常在 0.2 和 0.3 之间变化。 FKM据 FKM 准则，根据应力比 (R=SMIN/Smax) 值将 Haigh 图表分为四个区域。然后使用修正后的值选择损害和寿命计算阶段的 SN 曲线。 下面的 FKM 方程说明了修正应力振幅的计算过程 ( S e A MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacaWGLbaabaGaamyqaaaaaaa@38A9@ )。损害计算中使用的实际应力值是修正的应力振幅（即 2 ⋅ S e A MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabgw SixlaadofadaqhaaWcbaGaamyzaaqaaiaadgeaaaaaaa@3BAF@ ）。这些公式适用于所输入的 SN 曲线。 区域 1 (R>1.0)： S e A = S a 1 − M MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacaWGLbaabaGaamyqaaaakiabg2da9iaadofadaWgaaWcbaGa amyyaaqabaGcdaqadaqaaiaaigdacqGHsislcaWGnbaacaGLOaGaay zkaaaaaa@3FB0@ 区域 2 (-∞≤R≤0.0)： S e A = S a + M * S m MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa aaleaacaWGLbaabaGaamyqaaaakiabg2da9iaadofadaWgaaWcbaGa amyyaaqabaGccqGHRaWkcaWGnbGaaiOkaiaadofadaWgaaWcbaGaam yBaaqabaaaaa@4005@ 区域 3 (0.0 |
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