IDENTIFICATION OF FATIGUE FRACTURE PLANE POSITIONS WITH THE EXPECTED PRINCIPAL STRESS DIRECTION Aleksander KAROLCZUK Ewald MACHA Technical University of Opole Department of Mechanics and Machine Design International Conference on FATIGUE CRACK PATHS (FCP 2003) Parma, September, 2003

2 Plan of presentation Introduction Experimental data Weight function method Averaging procedure and weight functions Calculated and experimental results Conclusions

3 Introduction Fatigue fracture planes treated as critical planes can be used in multiaxial fatigue criteria to calculate fatigue life Biaxial stress state Reduction Stress state in critical plane

4 Maximum principal stress direction  1 Introduction Averaged direction of maximum principal stress  1 Averaged directions of principal stresses  1,  2,  3 Are they related to fatigue fracture plane position?

5 Experimental data Loading: r  Random bending, torsion and combined bending with torsion for three values of the cross correlation coefficient r  Different ratio of maximum torsional stress to maximum bending stress  =  max /  max Material: 18G2A steel Fig. 1. Specimen geometry  =  max /  max  =  max /  max rrrr r  and Tab.1. Cross correlation coefficients r  and ratio of maximum stresses  =  max /  max

6 Experimental data Fig. 2. The part of loading history Bending Torsion

7 Fig. 3. Histograms BendingTorsion Experimental data

8 Fig. 4. Spectrum BendingTorsion Experimental data

9 Measurement methodology of experimental slope of fatigue crack line Magnification: 60 times Area: 1,8 mm x 1,8 mm Resolution: 167x167 pixels on 1 mm 2 Fig.5. Experimental slope  exp of fatigue crack line Experimental data

10 Experimental data Fig.6. Photos of fatigue crack lines for pure torsion mm mm  exp = 41.7 o  exp = 42.1 o  exp = 42.4 o  exp = 45.8 o  exp = 46.0 o

mm mm  exp = 28.0 o  exp = 32.0 o  exp = 30.4 o  exp = 34.6 o  exp = 31.1 o Fig.7. Photos of fatigue crack lines for r  = –0,01 i  =0,97 Experimental data

12 Experimental data Tab.2. Average values of experimental angles

13 Weight function method The mean directions of the principal stress axes may be described by the weighted mean Euler angles: Where: - is the summation of the weights (2) (1) Principal stress directions are described by three Eulers angles:  (t),  (t),  (t)

14 Weight functions Weight 1 No weighted averaged process Weight 2 Based on the maximum principal stress  1 (t k ) Where: m  - the parameter of the Wöhler curve  af - fatigue limit c- constant (c = 0.5) (4) (3)

15 Weight 3 Based on the parameter of normal strain energy density W n (5) Where: - fatigue limit (6) (7) Weight functions

16 (8) Where: - fatigue limit (9) (10) Weight functions Weight 4 Based on the parameter of shear strain energy density W ns

17 Fig. 8. Absolute values of difference between experimental and calculated values of fatigue crack lines angles using the weight function method Calculated and experimental results

18 Calculated and experimental results Fig. 9. Absolute values of difference between experimental and calculated values of fatigue crack lines angles using the weight function method

19 1.Under random torsion and combined bending with torsion for stress ratio  = 0.97 and near to zero correlation between normal and shear stresses r  = -0.01, two fatigue crack directions have been observed from which one of them is dominated. 2.The cross correlation coefficient between bending and torsion r  has great influence on the fatigue fracture plane position The position of fatigue fracture plane can be successfully established with use of suitable weight functions based on stress or energy parameters For most of the loading the calculated fatigue fracture plane positions with use of the weight functions W 2 and W 3 agree with experimental ones very well. Conclusions