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. R 4. 2. 111. 15. 10. 20. CTU in Prague, Faculty of Mechanical Engineering. DAF. Page 2.
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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
R 4
2
111
15
10
20
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 2
Concentration factors
http://mechanika.fs.cvut.cz/calculator.php
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 3
Concentration factors
https://www.efatigue.com/constantamplitude/stressconcentration/
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 4
Fatigue notch factor
Fatigue notch factor
Theoretically,
if material has high notch sensitivity q
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 5
Fatigue notch factor, Kf and notch sensitivity factor, q
Experiments have shown that the effect of notches is less than that the estimated effect accordinga traditional stress concentration factor, Kt.
The fatigue notch factor, Kf, can be described as the effective stress concentration in fatigue.
This effect is dealt with using a notch sensitivity factor, q.
Notch radius
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 6
Fatigue limit modifiing factors
Loading factor, kL
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.
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 7
Fatigue limit modifiing factors
Surface finish factor, kSF
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
kSF
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 8
Fatigue limit modifiing factors
Size factor, kS
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.
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 9
Fatigue limit modifiing factors
Size factor, kS
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
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 10
Fatigue limit modifiing factors
Surface treatment factor, kT
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
Safety factor of unlimited fatigue life (permanent strength)
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 13
Example – Fatigue safe factor calculation
Problem description:
Railway axle
Material: alloy steel 24CrMo4, ASTM 4130
Point A of the potential crack initiation
Experimental strain amplitude measurement (in the point A):
A
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 14
http://fatiguecalculator.com
Example – continuation
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 15
http://fatiguecalculator.com
Example – continuation
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 16
FEM Calculation – CTU Prague
Example – continuation
Wheel
Braking disc
Axle
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 17
Example – continuation
15
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 18
Fatigue Limit
Example – continuation
Estimation of the fatigue limit of a real part
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 19
Fatigue loading
Example – continuation
Estimation of the nominal stress amplitude
A
Experimental strain amplitude measurement (in the point A):
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 20
Safety factor
Example – continuation
Estimation of the safety factor nFL
A
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 21
Questions and problems II
.
CTU in Prague, Faculty of Mechanical Engineering
DAF
Page 22
Questions and problems II
Example:
.