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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.

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Ctu in prague faculty of mechanical engineering

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


Ctu in prague faculty of mechanical engineering

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

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

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

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

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

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

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

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

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

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


Ctu in prague faculty of mechanical engineering

  • CTU in Prague, Faculty of Mechanical Engineering

  • DAF

  • Page 12

Safety factor of unlimited fatigue life (permanent strength)

  • Alternating stress (R=-1)

  • operational loading stress amplitude sa

  • fatigue limit of the real part in the critical cross section area sFL,N


Ctu in prague faculty of mechanical engineering

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

CTU in Prague, Faculty of Mechanical Engineering

DAF

Page 14

http://fatiguecalculator.com

Example – continuation


Ctu in prague faculty of mechanical engineering

CTU in Prague, Faculty of Mechanical Engineering

DAF

Page 15

http://fatiguecalculator.com

Example – continuation


Ctu in prague faculty of mechanical engineering

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

CTU in Prague, Faculty of Mechanical Engineering

DAF

Page 17

Example – continuation

15


Ctu in prague faculty of mechanical engineering

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

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

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

CTU in Prague, Faculty of Mechanical Engineering

DAF

Page 21

Questions and problems II

  • What is difference between the shape factor and the notch factor? Write their definition equations.

  • Define the notch sensitivity factor of material and write equation for it (as a function of shape and notch factor).

  • Depends the stress concentration factor of metals on a material parameters? And what about of the notch factor?

  • 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?

  • 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?

  • What dimension of a shaft has higher the size factor ks ? Shaft with higher or smaller diameter?

.


Ctu in prague faculty of mechanical engineering

CTU in Prague, Faculty of Mechanical Engineering

DAF

Page 22

Questions and problems II

Example:

.


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