西安石油大学：《过程设备设计基础 Basic Theory and Design of Process Equipments》课程教学资源（电子课件）第四章 压力容器设计 Design of Pressure Vessel 4.5 疲劳分析（Fatigue Analysis）

第四章 压力容器设计 CHAPTER IV Design of Pressure Vessel 4.5疲劳分析(Fatigue Analysis) 1

1 4.5
 Fatigue Analysis
 CHAPTER Design of Pressure Vessel

过程设备设计 4.1概述 4.2设计准则 4.5.1概述 4.3常规设计 4.5.2低循环疲劳曲线 4.5.3压力容器的疲劳设计 4.4分析设计 4.5.4影响疲劳寿命的其它 因素 4.5疲劳分析 4.6压力容器设计技术进展 2

2 4.1
4.2  4.3  4.4  4.5  4.6  4.5.1
4.5.2  4.5.3  4.5.4  !"


4.5.1 Introduction 过程设备设计 4.5 Fatigue Analysis 教学重点: 压力容器的疲劳设计。 教学难点: 低循环疲劳曲线

3 4.5.1 Introduction
 4.5 Fatigue Analysis
   
 

4.5.1 Introduction 过程设备设计 4.5 Fatigue Analysis 4.5.1 Introduction Causes for the increase of fatigue failure of pressure vessels: I (1) Increase of fatigue loadings; (2) Use of high strength materials Characteristics of fatigue failure: (1) No obvious plastic deformation; (2) Low stress level )Originating from the high stressed zone

4 4.5.1 Introduction
 4.5 Fatigue Analysis 4.5.1 Introduction Causes for the increase of fatigue failure of pressure vessels: (1) Increase of fatigue loadings; (2) Use of high strength materials Characteristics of fatigue failure: (1) No obvious plastic deformation; (2) Low stress level; (3) Originating from the high stressed zone

4.5.1 Introduction 过程设备设计 Parameters to describe fatigue loading: maximum stress minimum stress o max min mean stress alternating stress amplitud o a stress ratio R nax Imin max O+0 R max min max R=-1 or Om=0 complete reversed fatigue; R=0 or 0 pulsative fatigue; mIn R=+1 or min static load

5 4.5.1 Introduction
 Parameters to describe fatigue loading: maximum stress σ max minimum stress σ min mean stress σ m alternating stress amplitudeσ a stress ratio R ( ) 21 σ m = σ max + σ min ( ) 21 σ a = σ max −σ min σ max = σ m + σ a min max R = σ /σ R = −1 or σ m = 0 complete reversed fatigue
R=0 or σ min = 0 pulsative fatigue
R=+1 or σ min = σ max static load.

4.5.1 Introduction 过程设备设计 High cycle fatigue: N>10 Low cycle fatigue: N=102-105 102 10310410510510710 Cycle number M Fig4-62 Stress cyclic curve Fig4-6. High cycle fatigue curve

6 4.5.1 Introduction
 High cycle fatigue: N>105; Low cycle fatigue : N=102~105 8 Fig.4-63 High cycle fatigue curve σa σ t σa σmσm ax σm i n S t r e s s a mp l i t u d e σa 103 104 105 106 107 10 σ−1 103 102 Cycle number N Fig.4-62 Stress cyclic curve

4.5.2 Low cycle fatigue curve 过程设备设计 4.5.2 Low cycle fatigue curve Calculated curve for low cycle fatigue S=-EE (4-92) NE=O (4-93) P 100 where C ef=1100-v where e is the true strain at fracture and y is the percentage reduction in area

7 4.5.2 Low cycle fatigue curve
 4.5.2 Low cycle fatigue curve Calculated curve for low cycle fatigue S E t ε 21 =
4-92 Nε p = C
4-93 where C f ε21 = ψ ε − = 100100 ln f where f ε is the true strain at fracture and ψ is the percentage reduction in area.

4.5.2 Low cycle fatigue curve 过程设备设计 100 (4-94) 2100-y 8.=E.+E S ea ee +-ee ee s=-Ee to (4-95) P E 100 n O 4√N100 E 100 n + 4√N100-y (4-96)

8 4.5.2 Low cycle fatigue curve
 −ψ = 100 100 ln 2 1 C
4-94 t p e ε = ε + ε E t E p E e S ε ε ε 21 21 21 = = + a E e σ ε 21 = S E p σ a = ε + 21
4-95 S E N = a − + 4 100 100 ln ψ σ S E N = − + − 4 100 100 1 ln ψ σ
4-96

4.5.2 Low cycle fatigue curve 过程设备设计 Experimental curve Calculated curve Design curve 103 10 10 10 10 Cycle number N Fig 4-64 Low cycle fatigue curves

9 4.5.2 Low cycle fatigue curve
 Cycle number N 10 102 103 104 105 106 102 103 104 105 S t r e s s a m p l i t u d e S a Experimental curve Calculated curve Design curve   4-64 Low cycle fatigue curves

4.5.2 Low cvcle fatigue curve 过程设备设计 Effect of mean stress on fatigue life Typical loading for pressure vessels(pulsative fatigue): 0 mIn Goodman equation E 、O b B (4-97) Fig. 4-65 Effect of mean stress: Goodman line

10 4.5.2 Low cycle fatigue curve
 2 σ max σ m = Effect of mean stress on fatigue life Typical loading for pressure vessels (pulsative fatigue): σ min = 0 Goodman equation: 1 1 + = − b a m σ σ σ σ
4-97 E a σ s σ b σ m σ O D B A −1 σ σs C Fig. 4-65 Effect of mean stress: Goodman line