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ENERGY MODELS OF FATIGUE LIFE OF STEELS AND AN ALUMINIUM ALLOY UNDER NONPROPORTIONAL LOADING

The Seventh International Conference on Biaxial/Multiaxial Fatigue and fracture Berlin, June 28 – July 1, 2004. ENERGY MODELS OF FATIGUE LIFE OF STEELS AND AN ALUMINIUM ALLOY UNDER NONPROPORTIONAL LOADING. Takamoto ITOH 1 Aleksander KAROLCZUK 2 Cyprian LACHOWICZ 2 Ewald MACHA 2.

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ENERGY MODELS OF FATIGUE LIFE OF STEELS AND AN ALUMINIUM ALLOY UNDER NONPROPORTIONAL LOADING

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  1. The Seventh International Conference on Biaxial/Multiaxial Fatigue and fracture Berlin, June 28 – July 1, 2004 ENERGY MODELS OF FATIGUE LIFE OF STEELS AND AN ALUMINIUM ALLOY UNDER NONPROPORTIONAL LOADING Takamoto ITOH1 Aleksander KAROLCZUK2 Cyprian LACHOWICZ2 Ewald MACHA2 1 Fukui University, Department of Mechanical Engineering 2Technical University of Opole, Department of Mechanics and Machine Design

  2. Plan of presentation • Introduction • The energy parameters • Fatigue tests • Calculated and experimental results • Conclusions

  3. Transformation Introduction The concept of the critical plane (Stanfield 1935)

  4. -Smith-Watson-Topper criterion (1970), (uniaxial stress state) (1) -Socie modification (1987), (in the plane of max{1}) (2) -Nitta–Ogatta-Kuwabara criterion (1988) - Mode I (3) - Mode II Introduction Energy criteria

  5. -Glinka and et al. criterion (1994), (in the plane of max. ns) (5) -Pan and et al. modification (1999) (6) -Liu criterion (1993), (in the plane of max. product ) - Mode I (4) - Mode II Introduction

  6. - Lagoda-Machacriterion (1998) • Lagoda and Macha formulated a generalised criterion of normal Wn(t) and shear strain energy density Wns(t) in the critical plane. • Main assumption: • Fatigue crack is formed by the part of strain energy density which corresponds to work of normal stress σn(t) on normal strain n(t) - Wn(t) and work of shear stress ns(t) on shear strain occurring in sdirection in the critical plane with normal n - Wns(t) (7) Introduction

  7. Introduction where the strain energy density parameter is (8) • The main aims of this work are: • Verification of the energy criterion of multiaxial fatigue proposed by Lagoda and Macha for low-cycle non-proportional loading • The analyze of the history of energy parameters in the critical plane

  8. Maximum shear strain energy density Maximum normal strain energy density The criterion of normal strain energy density (C1) The criterion of shear strain energy density (C2) The criterion of normal and shear strain energy density (C3) The criterion of normal and shearstrain energy density (C4) The energy parameters Four particular versions of the generalized criterion of normal and shear strain energy density are proposed: (9) or (10) THE CRITICAL PLANE

  9. generally: for =0, = 1 (11) in the plane of in uniaxial tension-compression tests right side of equation (11) is (12) Fatigue effort under multiaxial state Eq. (11) must be equivalent to fatigue effort under uniaxial state Eq. (12), thus (13) Fatigue life is computed from energy characteristic obtained from uniaxial tests Eq. (12) (14) The energy parameters THE CRITERION OF MAXIMUM NORMAL STRAIN ENERGY DENSITY IN THE CRITICAL PLANE (C1)

  10. generally: for =1, = 0 (15) in the plane of in uniaxial tension-compression tests right side of equation (15) is (16) The energy parameters THE CRITERION OF MAXIMUM SHEAR STRAIN ENERGY DENSITY IN THE CRITICAL PLANE (C2)

  11. (17) Tension-compression fatigue tests Mohr’s circles for stress and strain state

  12. (18) Fatigue life is computed from energy characteristic obtained from uniaxial tests Eq. (13) (19) The energy parameters Fatigue effort under multiaxial state Eq. (15) must be equivalent to fatigue effort under uniaxial state Eq. (17), thus,

  13. generally: for 1, = 1 (20) in the plane of in uniaxial tension-compression tests right side of equation (20) is (21) Fatigue effort under multiaxial state Eq. (20) must be equivalent to fatigue effort under uniaxial state Eq. (21), thus (22) The energy parameters THE CRITERION OF MAXIMUM SHEARAND NORMAL STRAIN ENERGY DENSITY IN THE CRITICAL PLANE (C3)

  14. Thus, the equivalent parameter is: (24) Fatigue life is computed from energy characteristic obtained from uniaxial tests (25) The energy parameters The coefficient  should be chosen to obtain the best correlation between uniaxial and multiaxialfatigue tests. For simplicity the coefficient  is chosen as: (23)

  15. generally: for 1, = 1 (26) in the plane of in uniaxial tension-compression tests right side of equation (26) is (27) The energy parameters THE CRITERION OF MAXIMUM SHEARAND NORMAL STRAIN ENERGY DENSITY IN THE CRITICAL PLANE (C4)

  16. (28) Tension-compression fatigue tests Mohr’s circles for stress and strain state

  17. The energy parameters Fatigue effort under multiaxial state Eq. (26) must be equivalent to fatigue effort under uniaxial state Eq. (28), thus, (29)

  18. Thus, the equivalent parameter is: (31) Fatigue life is computed from energy characteristic obtained from uniaxial tests (32) The energy parameters The coefficient  should be chosen to obtain the best correlation between uniaxial and multiaxialfatigue tests. For simplicity of Eq. 29 the coefficient  is chosen as: (30)

  19. Fatigue life: The energy parameters, summary The equivalent parameters are: C1: in the plane of C2: in the plane of C3: in the plane of C4: in the plane of

  20. Fatigue tests Materials: SUS304 steel Al 6061 aluminum alloy Specimens: cylindrical thin-walled Loading: combined tension-compression and torsion under controlled strain Tests were performed under 14 different strain paths Strain paths

  21. Wn, MJ/m3 Not taken into account Not taken into account Wns, MJ/m3 Fatigue tests Histories of energy parameters SUS 304 Case 13 Strain path

  22. Not taken into account Wns, MJ/m3 Fatigue tests Histories of energy parameters Al 6061 Case 12 Strain path

  23. 3(2Nf) (2Nf)/3 Calculated and experimental results C1: Amplitudes of strain energy density Weq,q according to criterion C1 against the energy fatigue characteristic for SUS 304

  24. Calculated and experimental results C2: Amplitudes of strain energy density Weq,q according to criterion C2 against the energy fatigue characteristic for SUS 304

  25. Calculated and experimental results C3: Amplitudes of strain energy density Weq,q according to criterion C3 against the energy fatigue characteristic for SUS 304

  26. Calculated and experimental results C4: Amplitudes of strain energy density Weq,q according to criterion C4 against the energy fatigue characteristic for SUS 304

  27. Calculated and experimental results C1: C2: C3: C4: Amplitudes of strain energy density Weq,q according to criteriaC1-C4 against the energy fatigue characteristic for SUS 304

  28. Calculated and experimental results C1: Amplitudes of strain energy density Weq,q according to criterion C1 against the energy fatigue characteristic for Al 6061

  29. Calculated and experimental results C2: Amplitudes of strain energy density Weq,q according to criterion C2 against the energy fatigue characteristic for Al 6061

  30. Calculated and experimental results C3: Amplitudes of strain energy density Weq,q according to criterion C3 against the energy fatigue characteristic for Al 6061

  31. Calculated and experimental results C4: Amplitudes of strain energy density Weq,q according to criterion C4 against the energy fatigue characteristic for Al 6061

  32. Calculated and experimental results C1: C2: C3: C4: Amplitudes of strain energy density Weq,q according to criteria C1-C4 against the energy fatigue characteristic for Al 6061

  33. Calculated and experimental results C1: in the plane of Comparison of the calculated Ncaland experimental lives Nexp

  34. Calculated and experimental results C2: in the plane of Comparison of the calculated Ncaland experimental lives Nexp

  35. Calculated and experimental results C3: in the plane of Comparison of the calculated Ncaland experimental lives Nexp

  36. Calculated and experimental results C4: in the plane of Comparison of the calculated Ncaland experimental lives Nexp

  37. C1: C2: C4: C3: Calculated and experimental results Histograms of scatter coefficients

  38. Conclusions • For 6061 Al aluminum alloy, the best relation between the experimental life and the energy parameter was obtained according to the criterion C2 of shear strain energy density in the critical plane. • For SUS 304 steel, the best relation between the experimental life and the energy parameter was obtained according to the criterion C3 of normal and shear strain energy density in the critical plane • In general, the criterion C2 of shear strain energy density in the critical plane can be applied for both materials • For unstable materials and regimes the uniaxial fatigue tests should be carried out under energy control system to obtained the fatigue energy characteristic (Wa-2Nf) used in criteria based on energy parameters

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