Design Agains Fatigue part Fatigue Endurance Prediction Milan

Design Agains Fatigue - part Fatigue Endurance Prediction Milan Růžička milan. ruzicka@fs. cvut. cz

Contents 1. Introduction: Life Prediction loop, limit states 2. Static and cyclic tests of materials 3. Categorization of Material Fatigue 4. Philosophy of Structure Design 5. Material Behaviors under Static and Cyclic Loading 6. Phases of Fatigue Process 7. Fatigue Curves 8. Stress State in Notches 9. Notch factor 10. Another Influences on Fatigue Strength Value 11. Influence of Mean Stress 12. Analysis of dynamic loading 13. Damage Accumulation 14. Fatigue Life Prediction Methods CTU in Prague, Faculty of Mechanical Engineering DAF Page 2

Fatigue life prediction loop Strains and stress calculations Finding of critical places Fatigue life prediction Fatigue life verification and recalculation Service loading and critical places verification CTU in Prague, Faculty of Mechanical Engineering DAF Page 3

CAX- analysis CAD model MISES VALUE +3. 67 E+00 +8. 67 E+01 +1. 70 E+02 +2. 83 E+02 +3. 36 E+02 +4. 19 E+02 +5. 02 E+02 +5. 85 E+02 +6. 68 E+02 +7. 51 E+02 +8. 34 E+02 +9. 17 E+02 +1. 00 E+03 +1. 63 E+03 FEM analysis 2 3 1 Elastic, Plastic Creep Analysis of Fatigue Damage Analysis of limit state CTU in Prague, Faculty of Mechanical Engineering DAF Page 4

Limit states 1. L. S. of Strength • • Static Strength (Ductile Fracture) Plasticity, Plast. Adaptation Stability, Buckling Brittle Fracture Creep (Creep Fracture) Low-, High-Cycle Fatigue Temperature Shock Fatigue + Creep Interaction 2. L. S. of Functional Capability • • • Elastic and Plastic Deformation Impact Damage Dynamic Response Wearing Corrosion CTU in Prague, Faculty of Mechanical Engineering DAF Page 5

Brittle fracture and fatigue damage of large structures CTU in Prague, Faculty of Mechanical Engineering DAF Page 6

Brittle fracture and fatigue damage of large structures Takona bridge The Latchford Bridge Failure (2003 ) CTU in Prague, Faculty of Mechanical Engineering DAF Page 7

Static and cyclic tests of materials Ultimate Strength, Su (Rm) Yield Strength, Sy (Re, Rp 0. 2) Smooth and Notched Round Bar Laboratory Tensile Specimens CTU in Prague, Faculty of Mechanical Engineering DAF Page 9

Material behavior under static and cyclic loading Engineering stress (Lagrange stress) S = F / A 0, Engineering strain of measured specimen leght e = (l - l 0) / l 0 force recomputation at the instantaneous section True stress (Cauchy stress) = F / A True (logaritmic) strain = ln(l / l 0). True stress-strain diagram Aproximation of the true stress-strain diagram Engineering stress-strain diagram K - monotonic strength hardening koeff. n - monotonic strength hardening exponent p - plastic strain CTU in Prague, Faculty of Mechanical Engineering DAF Page 10

Stress-Life Analysis: Constant Amplitude Loading Stress Amplitude, Sa Mean Stress, Sm Stress Range, ΔS Two types of fatigue loadings regimes stress amplitude loading control - soft loading strain amplitude loading control - hard loading. Source: http: //fatiguecalculator. com CTU in Prague, Faculty of Mechanical Engineering DAF Page 11

Different mean stress CTU in Prague, Faculty of Mechanical Engineering DAF Page 12

Cyclic stress-strain curve saturated hysteresis loops cyclic stress-strain curve The materials deformation during a fatigue test is measured in the form of a hysteresis loop. After some initial transient behavior the material stabilizes and the same hysteresis loop is obtained for every loading cycle. Each strain range tested will have a corresponding stress range that is measured. The cyclic stress strain curve is a plot of all of this data CTU in Prague, Faculty of Mechanical Engineering DAF Page 13

Hysteresis loop Aproximation of the cyclic stress-strain curve K’ n’ E CTU in Prague, Faculty of Mechanical Engineering - cyclic strain hardening koeff. - cyclic strain hardening exponent - Young’s modulus of elasticity (tension) DAF Page 14

static hardening softening Creep Relaxation Softening cyclic Memory deformation curves: Hardening Changing of Cyclic Material Behavior CTU in Prague, Faculty of Mechanical Engineering DAF Page 15

Fatigue Testing Machines http: //www. kuleuven. ac. be CTU in Prague, Faculty of Mechanical Engineering DAF Page 16

Fatigue Testing Machines CTU in Prague, Faculty of Mechanical Engineering DAF Page 17

Stress- Life Curves www. tu-berlin. de www. ncode. com CTU in Prague, Faculty of Mechanical Engineering DAF Page 18

Quasistatic and Fatigue Design, Fatigue categories 1. Quasi-static strength (N<102 cycles) 2. Low-cycle fatigue (102<N<5· 105 cycles) Rm 3. High –cycle fatigue (5· 105< N<2· 106 cycles) Quasi-static Strength Low-cycle Fatigue High-cycle Fatigue range Re • fatigue of material • fatigue of elements • fatigue of structural parts • fatigue of structures C CTU in Prague, Faculty of Mechanical Engineering Strength Permanent Fatigue categories Lifetime Unlimited Limited DAF Page 19

Phases of a Fatigue Process • Phase of cyclic behaviors changing, there is change of metal structure in all of volume. Generally it takes only few percentages of specimen life. • Phase of fatigue crack nucleation, includes local changes in surface layers of material caused by dislocation effect. • Phase of crack propagation, includes stage of micro-crack growing in major crack and further crack growth. • Phase of final fracture, involving highspeed quasi-brittle crack of residual section when fracture toughness is exceeded or ductile crack at yield and strength limit exceeding. Glissile Dislocation ° 1 A Micro-crack Formation 2 ° 10 A 1 m Atomic Distance CTU in Prague, Faculty of Mechanical Engineering Macro-crack Creation 10 m 2 1 mm Macro-crack Growth 2 10 mm Grain Size of Austenite DAF Page 20

Initiation Slip bands Quasi-brittle Fracture Fatigue Crack growth Fatigue Crack Nucleation Intruses CTU in Prague, Faculty of Mechanical Engineering DAF Page 21

Fracture surfaces CTU in Prague, Faculty of Mechanical Engineering DAF Page 22

Fatigue Design methods COMPONENT FATIGUE BEHAVIOR CRITERIA OF FATIGUE DESIGN PERMANENT STRENGHT (UNLIMITED FATIGUE LIFE) FATIGUE STRENGHT (LIMITED FATIGUE LIFE) SAFE-LIFE STRUCTURE FAIL-SAFE STRUCTURE DAMAGE-TOLERANCE STRUCTURE SLOW CRACK GROWTHSTRUCTURE CTU in Prague, Faculty of Mechanical Engineering DAF Page 23

S-N curve (stress-life curve, Wöhler curve ) Fatigue limit • stress amplitude loading control - soft loading • R=const. , or Sm=const. • Enduramce limit, Fatigue limit SFL • Probability of fracture P [%] CTU in Prague, Faculty of Mechanical Engineering DAF Page 24

S-N curve (stress-life curve, Wöhler curve ) CTU in Prague, Faculty of Mechanical Engineering DAF Page 25

Aproximation of the Fatigue Stress-Life Curves (S-N) Aproximation Basquin Stress Amplitude Alloy Steel Structural Steel Dural 2024 T 4 Load Cycles CTU in Prague, Faculty of Mechanical Engineering DAF Page 26

Strain-Life Curve (e-N), Manson-Coffin‘s curve Strain Amplitude Aproximation general tangent method Number of Half-Cycles CTU in Prague, Faculty of Mechanical Engineering DAF Page 27

Hysteresis loop Aproximation of the cyclic stress-strain curve K’ n’ E CTU in Prague, Faculty of Mechanical Engineering - cyclic strain hardening koeff. - cyclic strain hardening exponent - Young’s modulus of elasticity (tension) DAF Page 28

Relations Between Coefficients K’ cyclic strain hardening koeff. n’ cyclic strain hardening exponent 6 material parameters, 4 independent: CTU in Prague, Faculty of Mechanical Engineering DAF Page 29

Relations between the strength and the fatigue limit http: //fatiguecalculator. com STEELS: Sf in tension 0, 35 Rm in bending = 0, 43 Rm in torssion 0, 25 Rm. CTU in Prague, Faculty of Mechanical Engineering DAF Page 30

Example http: //fatiguecalculator. com CTU in Prague, Faculty of Mechanical Engineering DAF Page 31

Questions and problems I 1. What is difference between static design and fatigue design of structures? 2. What are typical attributes for low cycle fatigue and for high cycle fatigue? 3. Draw a hysteresis loop and describe on it elastic and plastic part of strain. 4. Specify phases of damage and fatigue progress in metals. 5. What is main difference between safe-life and fail-safe design philosophy? 6. What are main attributes of the damage tolerance design philosophy? 7. Define the fatigue limit of a given material 8. What type of fatigue curve describes high cycle fatigue primary? Draw this curve. 9. What type of fatigue curve describes low cycle fatigue? Draw this curve. 10. Could be fatigue limit higher as yield strength? 11. How many percent of ultimate strength could you predict the fatigue limit of carbon steel? CTU in Prague, Faculty of Mechanical Engineering DAF Page 32

Questions and problems I CTU in Prague, Faculty of Mechanical Engineering DAF Page 33