Static strength and High and Low-Cycle Fatigue at room temperature 1/2

Transcription

1 Task 6 - Safety Review and Licensing On the Job Training on Stress Analysis Static strength and High and Low-Cycle Fatigue at room temperature 1/2 Davide Mazzini Ciro Santus Pisa (Italy) June 15 July 14, 2015

2 Prof. Ciro Santus Teaching Fundamental of Machine Design (Bachelor, Mechanical Engineering) Computer-Aided Engineering, FE (Master, Mechanical Engineering) Research Fatigue of Materials and Structures Contact Mechanics Dynamics 2

3 My latest paper Eng. Fr. Mechanics, Elsevier Flange leakage pressure deduced from a Weight Function application Validations: -FE - Exper. 3

4 Other paper Eng. Fr. Mechanics, Elsevier Analytical/ Numerical procedure to calculate the Stress Intensity Factors for Rolling Contact Fatigue FE validation 4

5 Table of content Class VI.a.1 Content Static strength of metals, Ductile/ Brittle - Tensile test - Plastic collapse vs. Brittle fracture notched components Fatigue of metals - Stress/ Strain approaches - Low/ High Cycle Fatigue - Fatigue notch sensitivity 5

6 Books Books on Material mechanical properties W. D. Callister, D. G. Rethwisch. Fundamentals of Materials Science and Engineering An Integrated Approach. Wiley N. E. Dowling. Mechanical Behavior of Materials. Prentice Hall Books specifically on Fatigue S. Suresh. Fatigue of Materials. Cambridge University Press H. E. Boyer. Atlas of Fatigue Curves. ASM International and many many others 6

7 Metals Most usual metal crystal structures FCC Face Centered Cubic BCC Body Centered Cubic 7

8 Metals Dislocation mechanics The dislocation mobility is the basic for Metals ductility 8

9 Dislocation Mechanics Dislocation interactions Other dislocation previousy accumulated work hardening Other defect alloy composition Grain boundaries heat treatment 9

10 Mechanical tests on materials Static, quasi-static, or monotonic tests Tensile tests Hardness tests Fracture Toughness tests Charpy tests and others 10

11 Tensile test Specifications Uniform section of the specimen Imposed constant (low) Strain rate up to fracture Measurements: Load Cell and Extensometer Displacement Material properties tested Bulk strength without any gradient (unnotched specimen) Ductility up to fracture 11

12 Tensile test ASTM Standard E8/E8M 11 Definition of the test, specimen sizes, recommendations, etc. 12

13 Tensile test ASTM Standard E8/E8M 11 Specimen: - Flat specimen - Round specimen 13

14 Tensile test ASTM Standard E8/E8M 11 Specimen: - Flat specimen Initialsection and lenght: 2 A0 D, L0 G 4 - Round specimen Most used 14

15 Tensile test F A 0 S U Necking Post necking Elastic-plastic, post yield S Y S F Final Fracture Linear elastic behavior 0.2% F L L 0 15

16 Tensile Test definitions F Load as measured by theload cell L Elongation as measured by the extensometer 0 0 Y U F F F A L L Engineering stress Engineering strain E (before yield) Young's modulus S, S, S Yield, Ultimate, Fracture strength values Elongation at Fracture(usually in %) 16

17 Tensile Test definitions Yield point Conventional Yield (at 0.2% offset) Yield point Line parallel to the elastic 0.2% Mild/ high-carbon steel, C 0.2% And all the other metals Low-carbon steel, C % 17

18 Tensile Test True curve Engineering/ True curve, Engineering, True F Ais thecurrent area A L L dl +...= L L L L 0 0 Before necking: (1 ) ln(1 ) 18

19 Tensile Test True curve After necking A Ais no more uniform, the test reduces to a portion of thespecimen 19

20 Tensile Test True curve True curve Stress/ Strain at final fracture At least at fracture F F 0 SF A F ln A A 0 AF F 0 F 0 f is known: Instead of, Reduction of Area % RA100 A A A A Af (measured after fracture) 20

21 Example AISI , Engineering 1000 S Y S U Stress, MPa E exp. data 0.2% Yield line 0.2% Yield Strength Ultimate Tensile Strength Fracture Strain, % S F, F 21

22 Example AISI , True, F F Stress, MPa Linear interpolation from Necking point to Fracture point Engineering True Strain, % 22

23 Homework Write a MATLAB script to find both Engineering and True curve and find the Stress and elongation parameters 23

24 YouTube video 24

25 Why does the Necking happen? S U is not a strength parameter, Necking is a point of instability onset F A Positive df d da A dt dt dt Negative Chain model of the tensile specimen Weakest link It goes into Necking Atneckingd F /dt 0: d da A dt dt After necking d A/ dis t predominant until fracture thus d F / dt 0 The other links experience unloading before reaching their necking condition, so necking does not extend to the stronger links 25

26 Necking on the entire specimen Other materials (not metal) may have necking distributed on the entire specimen Atneckingd F /dt 0: d da A dt dt After necking d A/ dt is predominant thus the load drops, but d before fracture, becomes dt predominant again so necking extends to the entire specimn e 26

27 Steel - Different mechanical properties Tempering after quenching at different temperatures (Es. AISI 4340) 27

28 Different mechanical properties Hardness tests Resistance to the penetration / scratch 28

29 Different mechanical properties 29

30 Different mechanical properties Hardness tests Differences with respect to the Tensile test: Compressive rather than Tensile Plastic deformation and No fracture Multiaxial (stress) instead of Uniaxial Small surface portion of material instead of bulk material Result dependent on the Standard definition of load and indenter size Nevertheless a linear relationship is remarkably accurate (only for steels): S 3.45HB U 30

31 Ductile - Brittle Metals can be (broadly) distinguished into: - Ductile, elongation at fracture > 5% - Brittle, elongation at fracture < 5% Usually brittle metals do not reach the Necking Stress, MPa Example: Quenched steel S F, F Strain, % 31

32 Ductile - Brittle Different criteria for Ductile/ Brittle metals - Ductile: - Plastic collapse - Ductility exhaustion - Brittle: - Fracture 32

33 Notched geometry Stress Concentration Force flux Central hole in a plate Stress concentrates at the notch apex either a circle or any other concave shape 33

34 Notched geometry Stress Concentration Factor Central hole in a plate Nominalstress:,, (force/area) n 0 Maximum stress: max (peak value) SCF: K t max 34

35 Notched geometry Stress Concentration Factor Central hole in a plate K t max 35

36 Notched geometry Stress Concentration Factor Many tables and graph for several cases 36

37 Ductile metal Plastic collapse Different stages of the load F a b c d Elastic perfectly plastically Model time Plasticity onset Plastic collapse 37

38 Ductile metal Plastic collapse F AS Y At plastic collapse the ultimate force does not depend on the Stress Concentration Factor 38

39 Ductile metal Ductility exhaustion The fracture could happen before the Plastic Collapse, if the strain reaches the (true) elongation at fracture Fracture for ductility exhaustion max Plasticity zone spreading out F max F? How to calculate? 39

40 Ductile metal The Neuber s rule (1946) Any kind of (radiused) notch, el el, After imposing equal the (triangular) areas it follows: el el KS t KS t E 2 ( KS t ) E S nominalstress 40

41 Ductile metal The Neuber s rule (1946) Any material model, such as Elastic perfectly plastically S Y Neuber s hyperbola ( KS t ) E 2 41

42 Ductile metal Plastic collapse/ Neuber s rule example Steel Fe360-S235 S Y t 235 MPa E 205GPa RA% 50% K 5.0(any shape) Byincreasing the load, what happens first: Plastic collapse or Ductility exhaustion? 42

43 Plastic collapse/ Neuber s rule example Steel Fe360-S235 S Y t 235 MPa E 205GPa RA% 50% K 5.0(any shape) F 1 ln RA% /100 Y Ductile metal Assuming to have plastixc collapse first: S Neuber: max max K t E 2 43

44 Ductile metal Plastic collapse/ Neuber s rule example Steel Fe360-S235 then, assuming elastic prefectly S Y t 235 MPa plastic material model: E 205GPa RA% 50% K 5.0(any shape) max S Y finally, can besolved: max max 2 KS t Y max E being F plastic collapse happens first 44

45 Plastic collapse/ Neuber s rule example Steel Fe360-S235 S Y t 235 MPa E 205GPa RA% 50% K Y 5.0(any shape) 2.Which is the(minimum) K ductilityexhaustion first? F t Ductile metal Homework: 1.What if a different steel is considered: S 1700 MPa and 0.08 to have 45

46 Brittle metal The maximum stress just induces fracture Fracture: K S max t F 2500 The SCF has a direct effect on fracture. Ductile metals are usually preferred than Brittle No more margin due to ductility Stress, MPa S F, F Strain, % 46

47 Different levels of stress concentration severity Ductile/ Brittle metal Ductile, blunt notch Plastic collapse Kt Ductile, sharp notch Plastic Collapse or Ductility exhaustion Kt Ductile, Crack notch How to predict the strength? r r 0 Kt Brittle, blunt notch Fracture Kt Brittle, sharp notch Fracture Kt Brittle, Crack notch How to predict the strength? Kt 47