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Concentration factors S x Shape Factor or Stress Concentration Factor of an Elastic Stress Relative Stress Gradient G Kt 1 y x S x 0 y CTU in Prague, Faculty of Mechanical Engineering DAF Page 1 Concentration factors R4 2 1 11 1 5 10 20 http://mechanika.fs.cvut.cz/calculator.php CTU in Prague, Faculty of Mechanical Engineering DAF Page 2 Concentration factors https://www.efatigue.com/constantamplitude/stressconcentration/ CTU in Prague, Faculty of Mechanical Engineering DAF Page 3 Fatigue notch factor Stress amplitude [MPa] Fatigue notch factor 600 FL Kf FL, N smooth 500 notched 400 Theoretically, if material has high notch sensitivity q 300 Kt K f FL 200 FL,N 100 0 1,E+03 q 1 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 Number of cycles [1] CTU in Prague, Faculty of Mechanical Engineering DAF Page 4 Fatigue notch factor, Kf 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, 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. K f 1 Kt 1 q Notch radius CTU in Prague, Faculty of Mechanical Engineering DAF Page 5 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. Loading Type Axial Bending Torsion kL 0.9 1.0 0.57 CTU in Prague, Faculty of Mechanical Engineering DAF Page 6 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 7 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 8 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 kS D FL d 10 FL D Vexp d V exp m S x y CTU in Prague, Faculty of Mechanical Engineering DAF Page 9 Fatigue limit modifiing factors Surface treatment factor, kT CTU in Prague, Faculty of Mechanical Engineering DAF Page 10 Fatigue limit of a real part Estimation of the fatigue limit of a real part FL, N FL kL kSF kS kT Kf CTU in Prague, Faculty of Mechanical Engineering DAF Page 11 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 1000 a [MPa] alloy steel 100 1.E+04 1.E+05 1.E+06 1.E+07 N [1] n 1. FL, N a CTU in Prague, Faculty of Mechanical Engineering 1. DAF 1. 1. Page 12 Example – Fatigue safe factor calculation Problem description: Railway axle Material: alloy steel 24CrMo4, ASTM 4130 A Point A of the potential crack initiation Experimental strain amplitude measurement (in the point A): a,max 312 microstrain CTU in Prague, Faculty of Mechanical Engineering DAF Page 13 Example – continuation http://fatiguecalculator.com a f 2N 1570 2N b FL 1570 2 107 CTU in Prague, Faculty of Mechanical Engineering 0,076 0,076 437.5 DAF MPa Page 14 Example – continuation http://fatiguecalculator.com Kt 2.09 CTU in Prague, Faculty of Mechanical Engineering DAF Page 15 Example – continuation FEM Calculation – CTU Prague Wheel Braking disc Axle Kt 1.95 CTU in Prague, Faculty of Mechanical Engineering DAF Page 16 Example – continuation Kt 1.95 Stress amplitude [MPa] K f 1 Kt 1 q 1 2.0 1 0.83 1.83 600 smooth 500 notched 400 300 FL 200 FL,N 100 0 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 Number of cycles [1] 15 CTU in Prague, Faculty of Mechanical Engineering DAF Page 17 Example – continuation Fatigue Limit Estimation of the fatigue limit of a real part FL, N FL, N FL kL kSF kS kT factor k value loading kL 1.00 surface finish kSF 0.67 size factor kS 0.70 size factor kT 1.00 Kf 437.5 1.00 0.67 0.70 1.00 112.1 1.83 MPa CTU in Prague, Faculty of Mechanical Engineering DAF Page 18 Example – continuation Fatigue loading Estimation of the nominal stress amplitude A Experimental strain amplitude measurement (in the point A): a,max 512 microstrain a E 206850 0.000312 64.5 CTU in Prague, Faculty of Mechanical Engineering MPa DAF Page 19 Example – continuation Safety factor Estimation of the safety factor nFL FL, N 112.1 A Stress amplitude [MPa] a 64.5 MPa MPa 600 smooth nFL 500 notched 400 FL, N 112.1 1.74 a 64.5 300 FL 200 FL,N 100 0 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 Number of cycles [1] CTU in Prague, Faculty of Mechanical Engineering DAF Page 20 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 ks ? Shaft with higher or smaller diameter? CTU in Prague, Faculty of Mechanical Engineering DAF Page 21 Questions and problems II Example: Estimate the fatigue limit and the safety factor of the part on the Fig. 1. under harmonic loading. The material of the part is steel 4130 bar Su= 778 see http://fatiguecalculator.com/cgi-bin/StressShowMatProp.pl MPa Fig. 1 Other inputs: D= 50 d= 30 r= 5 F= 40 q= 0,8 R= -1 n L= ? N FL 2,00E+06 Ra= 12,5 mm mm mm kN 1 outer diameter inner diameter notch radius maximum loading force notch sensitivity of the steel stress ratio fatigue life safety factor number of fatigue limit cycles surface roughness CTU in Prague, Faculty of Mechanical Engineering Solution shape factor notch factor fatigue limit safety factor DAF Kt= Kf= sFL= nF= 1,71 1,57 7,95E+01 1,40E+00 Page 22