Design Agains Fatigue - part Fatigue Endurance Prediction Design Agains Fatigue - part Fatigue Endurance Prediction Milan Růžička

CTU in Prague, Faculty of Mechanical Engineering DAF Page 2 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 3 Fatigue life prediction loop Finding of critical places Strains and stress calculations Fatigue life verification and recalculation Service loading and critical places verification Fatigue life prediction

CTU in Prague, Faculty of Mechanical Engineering DAF Page 4 CAX- analysis Elastic, Plastic Creep Analysis of Fatigue Damage MISES VALUE E E E E E E E E E E E E E E Analysis of limit state CAD model FEM analysis

CTU in Prague, Faculty of Mechanical Engineering DAF Page 5 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 6 Brittle fracture and fatigue damage of large structures

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 9 Static and cyclic tests of materials Smooth and Notched Round Bar Laboratory Tensile Specimens Ultimate Strength, S u (R m ) Yield Strength, S y (R e, R p0.2 )

CTU in Prague, Faculty of Mechanical Engineering DAF Page 10 Material behavior under static and cyclic loading K - monotonic strength hardening koeff. n - monotonic strength hardening exponent  p - plastic strain 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 Engineering stress-strain diagram Aproximation of the true stress-strain diagram

CTU in Prague, Faculty of Mechanical Engineering DAF Page 11 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:

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 13 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 14 Hysteresis loop K’ - cyclic strain hardening koeff. n’- cyclic strain hardening exponent E- Young’s modulus of elasticity (tension) Aproximation of the cyclic stress-strain curve

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 16 Fatigue Testing Machines

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 18 Stress- Life Curves

CTU in Prague, Faculty of Mechanical Engineering DAF Page 19 Quasistatic and Fatigue Design, Fatigue categories R m range R e  C Quasi-static Strength Low-cycle Fatigue High-cycle Fatigue Lifetime Limited Unlimited Strength Permanent Fatigue 1.Quasi-static strength (N<10 2 cycles) 2.Low-cycle fatigue (10 2 <N<5·10 5 cycles) 3.High –cycle fatigue (5·10 5 < N<2·10 6 cycles) Fatigue categories fatigue of material fatigue of elements fatigue of structural parts fatigue of structures

CTU in Prague, Faculty of Mechanical Engineering DAF Page 20 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 high- speed quasi-brittle crack of residual section when fracture toughness is exceeded or ductile crack at yield and strength limit exceeding. 1 A  10 2 A  1  2  1 mm10 2 mm Atomic Distance Grain Size of Austenite Micro-crack Formation Glissile Dislocation Macro-crack Creation Macro-crack Growth

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

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 23 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 GROWTH- STRUCTURE

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

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 26 Aproximation of the Fatigue Stress-Life Curves (S-N) Alloy Steel Structural Steel Dural 2024 T4 Load Cycles Stress Amplitude Aproximation Basquin

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

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

CTU in Prague, Faculty of Mechanical Engineering DAF Page 29 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 30 Relations between the strength and the fatigue limit STEELS: S f in tension  0,35 Rm in bending = 0,43 Rm in torssion  0,25 Rm.

CTU in Prague, Faculty of Mechanical Engineering DAF Page 31 Example

CTU in Prague, Faculty of Mechanical Engineering DAF Page 32 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 33 Questions and problems I.