1. CTU in Prague, Faculty of Mechanical Engineering DAF Page 1 Concentration factors Shape Factor or Stress Concentration Factor of an Elastic Stress Relative Stress Gradient

2. CTU in Prague, Faculty of Mechanical Engineering DAF Page 2 http://mechanika.fs.cvut.cz/calculator.php Concentration factors 1515 22 R 4 20 10  1 11

3. CTU in Prague, Faculty of Mechanical Engineering DAF Page 3 Concentration factors https://www.efatigue.com/constantamplitude/stressconcentration/

4. CTU in Prague, Faculty of Mechanical Engineering DAF Page 4 Fatigue notch factor Theoretically, if material has high notch sensitivity q Fatigue notch factor

5. CTU in Prague, Faculty of Mechanical Engineering DAF Page 5 Fatigue notch factor, K f and notch sensitivity factor, q Experiments have shown that the effect of notches is less than that the estimated effect according a traditional stress concentration factor, K t. The fatigue notch factor, K f, can be described as the effective stress concentration in fatigue. This effect is dealt with using a notch sensitivity factor, q. Notch radius

6. CTU in Prague, Faculty of Mechanical Engineering DAF Page 6 Fatigue limit modifiing factors Loading factor, k L Historically, fatigue limits have been determined from simple bending tests where there is a stress gradient in the test specimen. A specimen loaded in tension will have a lower fatigue limit than one loaded in bending. An empirical correction factor, called the loading factor, is used to make an allowance for this effect.

7. CTU in Prague, Faculty of Mechanical Engineering DAF Page 7 Fatigue limit modifiing factors Surface finish factor, k SF Fatigue limits are determined from small polished laboratory specimens. A surface finish correction is made to estimate the fatigue limit of the part with the actual surface finish k SF

8. CTU in Prague, Faculty of Mechanical Engineering DAF Page 8 Fatigue limit modifiing factors Size factor, k S Experimentally, larger parts have lower fatigue limits than smaller parts. Since the materials data is obtained from small specimens, a correction factor, called the size factor, is used for larger diameters.

9. CTU in Prague, Faculty of Mechanical Engineering DAF Page 9 Fatigue limit modifiing factors Size factor, k S For non-circular sections an effective diameter is computed. The effective diameter is obtained by equating the volume of material subjected to 95% of the maximum stress to a round bar in bending with the same highly stressed volume

10. CTU in Prague, Faculty of Mechanical Engineering DAF Page 10 Fatigue limit modifiing factors Surface treatment factor, k T

11. CTU in Prague, Faculty of Mechanical Engineering DAF Page 11 Fatigue limit of a real part Estimation of the fatigue limit of a real part

12. 1.CTU in Prague, Faculty of Mechanical Engineering 1.DAF1. 1.Page 12 Safety factor of unlimited fatigue life (permanent strength) 1.Alternating stress (R=-1) operational loading stress amplitude  a fatigue limit of the real part in the critical cross section area  FL,N

13. CTU in Prague, Faculty of Mechanical Engineering DAF Page 13 Example – Fatigue safe factor calculation Railway axle Material: alloy steel 24CrMo4, ASTM 4130 Point A of the potential crack initiation Experimental strain amplitude measurement (in the point A): Problem description: A

14. CTU in Prague, Faculty of Mechanical Engineering DAF Page 14 Example – continuation http://fatiguecalculator.com

15. CTU in Prague, Faculty of Mechanical Engineering DAF Page 15 Example – continuation http://fatiguecalculator.com

16. CTU in Prague, Faculty of Mechanical Engineering DAF Page 16 Example – continuation FEM Calculation – CTU Prague Wheel Braking disc Axle

17. CTU in Prague, Faculty of Mechanical Engineering DAF Page 17 Example – continuation 15

18. CTU in Prague, Faculty of Mechanical Engineering DAF Page 18 Fatigue Limit Estimation of the fatigue limit of a real part factorkvalue loadingkLkL 1.00 surface finishk SF 0.67 size factorkSkS 0.70 size factorkT1.00 Example – continuation

19. CTU in Prague, Faculty of Mechanical Engineering DAF Page 19 Estimation of the nominal stress amplitude Experimental strain amplitude measurement (in the point A): A Fatigue loading Example – continuation

20. CTU in Prague, Faculty of Mechanical Engineering DAF Page 20 Safety factor Estimation of the safety factor n FL A Example – continuation

21. CTU in Prague, Faculty of Mechanical Engineering DAF Page 21 Questions and problems II. 1.What is difference between the shape factor and the notch factor? Write their definition equations. 2.Define the notch sensitivity factor of material and write equation for it (as a function of shape and notch factor). 3.Depends the stress concentration factor of metals on a material parameters? And what about of the notch factor? 4.What is the typical value of the stress concentration factor at a large tensile loaded plate with a round hole in the middle? Is the notch factor of such plate lower or higher as the shape factor? 5.Is the fatigue limit of a real part the same as the fatigue limit of a basic material? What other factors could be taken in the account by an expression of such fatigue limit? 6.What dimension of a shaft has higher the size factor k s ? Shaft with higher or smaller diameter?

22. CTU in Prague, Faculty of Mechanical Engineering DAF Page 22 Questions and problems II. Example: