Design Agains Fatigue - part Fatigue Endurance Prediction Milan Rika [email protected] 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 Computational work P r e - p r o je c t phase D e s ig n

phase P ro to ty p e v e r ific a t io n R eal s e r v ic e DATABASE Experimental work Strains and stress calculations Fatigue curves Finding of critical places Loading spectra 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 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 ttle fracture and fatigue damage of large structures CTU in Prague, Faculty of Mechanical Engineering DAF Page 6 ttle 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, Rp0.2)

Smooth and Notched Round Bar Laboratory Tensile Specimens CTU in Prague, Faculty of Mechanical Engineering DAF Page 9 aterial behavior under static and cyclic loading Engineering stress (Lagrange stress) S = F / A0, Engineering strain of measured specimen leght e = (l - l0) / l0 True stress (Cauchy stress) = F / A f l l0 A F l S 1 e S 0 S S 1 A A l0 l 0 l l0 l ln 1 e ln ln 1 l0 l0 Rm

Aproximation of the true stress-strain diagram True (logaritmic) strain = ln(l / l0). 800 800 700 700 600 600 True Skuten tah. stress-strain diagram diagram 500 , S [MPa] force recomputation at the instantaneous section 400 500 400 Engineering Konvenn tah.

stress-strain diagram diagram 300 Re 300 200 K pn 200 100 100 f 0 0 0 0.2 0.4 0.6 , e [1] 0.8

1 0 0.002 0.004 K - monotonic strength hardening koeff. n - monotonic strength hardening exponent p - plastic strain , e [1] CTU in Prague, Faculty of Mechanical Engineering DAF Page 10 Stress-Life Analysis: Constant Amplitude Loading Stress Amplitude, Sa Mean Stress, Sm Stress Range, SS 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 [MPa]

Aproximation of the cyclic stress-strain curve 300 n a K ap 200 a 100 [1] 0 -0.01 -0.005 0 0.005 0.01 -100 a ae ap a a E K 1 n -200 -300

ap a ae K n E (tension) - cyclic strain hardening koeff. - cyclic strain hardening exponent - Youngs modulus of elasticity CTU in Prague, Faculty of Mechanical Engineering DAF Page 14 Changing of Cyclic Material Behavior cyclic hardening softening c Relaxation b t

Creep d e t Softening static t t t t

t t A Memory deformation curves: Hardening a C C 0 D t D

E C 0 A B B 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 uasistatic and Fatigue Design, Fatigue categories 1. Quasi-static strength (N<102 cycles) 2. Low-cycle fatigue (102

fatigue of material fatigue of elements fatigue of structural parts fatigue of structures C CTU in Prague, Faculty of Mechanical Engineering Strength Permanent Fatigue 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 1A 2 10 A Micro-crack Formation 1 Atomic Distance CTU in Prague, Faculty of Mechanical Engineering Macro-crack Creation 2 10 1 mm Macro-crack

Growth 2 10 mm Grain Size of Austenite DAF Page 20 Initiation Slip bands Quasibrittle 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, Whler curve ) 1000 a [MPa] structural steel Fatigue limit 100 1,E+04 1,E+05 1,E+06 1,E+07 N [1] 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, Whler curve ) 1000 1000

aa [MPa] [MPa] alloy steel 100 100 1,E+04 1,E+04 1,E+05 1,E+05 1,E+06 1,E+06 1,E+07 1,E+07 N [1] [1] CTU in Prague, Faculty of Mechanical Engineering DAF Page 25 proximation of the Fatigue Stress-Life Curves (S-N) Aproximation aw N C 1000 [MPa] ocel

Alloyslitinov Steel ocel konstrukn Structural Steel dural 2024 T3 Dural 2024 T4 Basquin a f 2 N a f fatigue strength coefficient amplituda napt Stress Amplitude 1/ w 100 1.E+04 b b 1 fatigue strength exponent 1 1

C f b 2 w 1.E+05 1.E+06 poet kmit N [1] Load Cycles 1 b 1.E+07 CTU in Prague, Faculty of Mechanical Engineering DAF Page 26 Strain-Life Curve (-N), Manson-Coffins curve Aproximation 1 amplituda pom. deformace Strain Amplitude a [1] f '

0.1 f b c 2 N f 2 N E a ae ap c f fatigue ductility coefficient 1 c 0.01 f ' /E 0.001 a b 1 general tangent method ae 2 a 3,5 ap 0.0001 1.E+00 fatigue ductility exponent

1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Rm 0 ,12 N f E N 0,6 1.E+07 plkmit 2N [1] Numberpoet of Half-Cycles CTU in Prague, Faculty of Mechanical Engineering DAF Page 27 0,6 Hysteresis loop

[MPa] Aproximation of the cyclic stress-strain curve 300 n a K ap 200 a 100 [1] 0 -0.01 -0.005 0 0.005 0.01 -100 a ae ap 1 n a a

E K -200 -300 ap a ae K n E (tension) - cyclic strain hardening koeff. - cyclic strain hardening exponent - Youngs modulus of elasticity CTU in Prague, Faculty of Mechanical Engineering DAF Page 28 Relations Between Coefficients a ae ap a f 2 N 1 n K cyclic strain hardening koeff.

n cyclic strain hardening exponent a a E K f fatigue strength coefficient b b a ae ap f 2 N b f 2 N c E fatigue strength exponent f fatigue ductility coefficient c fatigue ductility exponent 6 material parameters, 4 independent: K , n, f , b, f , c a f 2 N K f 2 N b n c b

n cn CTU in Prague, Faculty of Mechanical Engineering K f n f DAF Page 29 lations 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

n 1. Example 1: Approximation of a stress amplitude is a K ap . Derive equation for the total strain amplitude of a hysteresis loop a ae ap ? b 2. Example 2: Approximation of the fatigue curve is aw N C or a f 2 N . Derive relations between parameters C , , f b, w. 3. Example 3: There are 6 material fatigue parameters K , n , f , b, f , c , only are 4 independent. Derive relations between these parameters. 4. Example 4: There is special number of cycles ( N t ) in the Strain-life curve, where ae ap . Derive equation to calculate this number N t . CTU in Prague, Faculty of Mechanical Engineering DAF Page 33