12 Multi-mode Model and Calculation Method for Fatigue Damage …
169
2. Brown, M., Miller, K.J.: A theory for fatigue under multiaxial stress-strain conditions. Inst.
Mech. Eng. 187, 745–756 (1973)
3. Fatemi, A., Socie, D.F.: A critical plane approach to multiaxial damage including out-of-phase
loading. Fatigue Fract. Eng. Mater. Struct. 11(3), 149–156 (1988)
4. Smith, R.N., Watson, P., Topper, T.H.: A stress-strain parameter for the fatigue of metals. J.
Mater. 5(4), 767–778 (1970)
5. Sines, G.: Behaviour of metals under complex static and alternating stresses. In: Sines, G.,
Waisman, J.L. (eds.) Metal Fatigue, pp. 145–169. McGraw-Hill, New York (1959)
6. Crossland, B.: Effect of large hydrostatic pressures on torsional fatigue strength of an alloy
steel. In: Proceedings of International Conference on Fatigue of Metals, pp. 138–149. London
(1956)
7. Findley, W.: A theory for the effect of mean stress on fatigue of metals under combined torsion
and axial load or bending. J. Eng. Ind. 301–306 (1959)
8. Morel, F.: A critical plane approach for life prediction of high cycle fatigue under multiaxial
variable amplitude loading. Int. J. Fatigue 22(2), 101–119 (2000)
9. Matake, T.: An explanation on fatigue limit under combined stress. Bull. JSME 20, 257–263
(1977)
10. McDiarmid, D.L.: A shear stress based critical-plane criterion of multiaxial fatigue failure for
design and life prediction. Fatigue Fract. Eng. Mater. Struct. 17, 1475–1484 (1999)
11. Papadopoulos, I.V.: Long life fatigue under multiaxial loading. Int. J. Fatigue 23, 839–849
(2001)
12. Carpinteri, A., Spagnoli, A., Vantadori, S.: Multiaxial assessment using a simplified critical
plane based criterion. Int. J. Fatigue 33, 969–976 (2011)
13. Susmel, L., Taylor, D.: A critical distance/plane method to estimate finite life of notched
components under variable amplitude uniaxial/multiaxial fatigue loading. Int. J. Fatigue 38,
7–24 (2012)
14. Suman, S., Kallmeyer, A., Smith, J.: Development of a multiaxial fatigue damage parameter
and life prediction methodology for non-proportional loading. Frattura ed Integrità Strutturale
38, 224–230 (2016)
15. Meggiolaro, M.A., Miranda, A.C., de Castro, J.: Comparison among fatigue life prediction methods and stress-strain models under multiaxial loading. In: Proceedings of 19th
International Congress of Mechanical Engineering, Brasilia, DF, pp. 1–10 (2007)
16. Wang, Y.-Y., Yao, W.-X.: Evaluation and comparison of several multiaxial fatigue criteria. Int.
J. Fatigue 26, 17–25 (2004)
17. Karolczuk, A., Macha, E.: A review of critical plane orientations in multiaxial fatigue failure
criteria of metallic materials. Int. J. Fatigue 134, 267–304 (2016)
18. Karolczuk, A., Papuga, J., Palin-Luc, T.: Progress in fatigue life calculation by implementing
life-dependent material parameters in multiaxial fatigue criteria. Int. J. Fatigue 134 (2020)
19. Bourago, N.G., Zhuravlev, A.B., Nikitin, I.S.: Models of multiaxial fatigue fracture and service
life estimation of structural elements. Mech. Solids 46(6), 828–838 (2011)
20. Paris, P.C., Erdogan, F.A.: Critical analysis of crack propagation laws. J. Basic Eng. 85, 528–533
(1963)
21. Forman, R.G., Kearney, V.E., Engle, R.M.: Numerical analysis of crack propagation in a cyclicloaded structure. Trans. ASME J Basic Eng. 89(3), 459–464 (1967)
22. Collins, J.A.: Failure of Materials in Mechanical Design: Analysis, Prediction. Prevention.
Wiley, NY (1993)
23. Bathias, C., Paris, C.P.: Gigacycle Fatigue in Mechanical Practice. Dekker, NY (2004)
24. Kachanov, L.M.: On the time of destruction under creep conditions. Izv. AN SSSR OTN 8,
26–31 (in Russian) (1958)
25. Rabotnov, J.N.: On the mechanism of long-term destruction. Voprosi prochnosti materialov i
konstrukcij. AN SSSR OTN, 5–7 (in Russian) (1959)
26. Murakami, S.: Continuum Damage Mechanics. A Continuum Mechanics Approach to the
Analysis of Damage and Fracture. Springer, Dordrecht (2012)
169
2. Brown, M., Miller, K.J.: A theory for fatigue under multiaxial stress-strain conditions. Inst.
Mech. Eng. 187, 745–756 (1973)
3. Fatemi, A., Socie, D.F.: A critical plane approach to multiaxial damage including out-of-phase
loading. Fatigue Fract. Eng. Mater. Struct. 11(3), 149–156 (1988)
4. Smith, R.N., Watson, P., Topper, T.H.: A stress-strain parameter for the fatigue of metals. J.
Mater. 5(4), 767–778 (1970)
5. Sines, G.: Behaviour of metals under complex static and alternating stresses. In: Sines, G.,
Waisman, J.L. (eds.) Metal Fatigue, pp. 145–169. McGraw-Hill, New York (1959)
6. Crossland, B.: Effect of large hydrostatic pressures on torsional fatigue strength of an alloy
steel. In: Proceedings of International Conference on Fatigue of Metals, pp. 138–149. London
(1956)
7. Findley, W.: A theory for the effect of mean stress on fatigue of metals under combined torsion
and axial load or bending. J. Eng. Ind. 301–306 (1959)
8. Morel, F.: A critical plane approach for life prediction of high cycle fatigue under multiaxial
variable amplitude loading. Int. J. Fatigue 22(2), 101–119 (2000)
9. Matake, T.: An explanation on fatigue limit under combined stress. Bull. JSME 20, 257–263
(1977)
10. McDiarmid, D.L.: A shear stress based critical-plane criterion of multiaxial fatigue failure for
design and life prediction. Fatigue Fract. Eng. Mater. Struct. 17, 1475–1484 (1999)
11. Papadopoulos, I.V.: Long life fatigue under multiaxial loading. Int. J. Fatigue 23, 839–849
(2001)
12. Carpinteri, A., Spagnoli, A., Vantadori, S.: Multiaxial assessment using a simplified critical
plane based criterion. Int. J. Fatigue 33, 969–976 (2011)
13. Susmel, L., Taylor, D.: A critical distance/plane method to estimate finite life of notched
components under variable amplitude uniaxial/multiaxial fatigue loading. Int. J. Fatigue 38,
7–24 (2012)
14. Suman, S., Kallmeyer, A., Smith, J.: Development of a multiaxial fatigue damage parameter
and life prediction methodology for non-proportional loading. Frattura ed Integrità Strutturale
38, 224–230 (2016)
15. Meggiolaro, M.A., Miranda, A.C., de Castro, J.: Comparison among fatigue life prediction methods and stress-strain models under multiaxial loading. In: Proceedings of 19th
International Congress of Mechanical Engineering, Brasilia, DF, pp. 1–10 (2007)
16. Wang, Y.-Y., Yao, W.-X.: Evaluation and comparison of several multiaxial fatigue criteria. Int.
J. Fatigue 26, 17–25 (2004)
17. Karolczuk, A., Macha, E.: A review of critical plane orientations in multiaxial fatigue failure
criteria of metallic materials. Int. J. Fatigue 134, 267–304 (2016)
18. Karolczuk, A., Papuga, J., Palin-Luc, T.: Progress in fatigue life calculation by implementing
life-dependent material parameters in multiaxial fatigue criteria. Int. J. Fatigue 134 (2020)
19. Bourago, N.G., Zhuravlev, A.B., Nikitin, I.S.: Models of multiaxial fatigue fracture and service
life estimation of structural elements. Mech. Solids 46(6), 828–838 (2011)
20. Paris, P.C., Erdogan, F.A.: Critical analysis of crack propagation laws. J. Basic Eng. 85, 528–533
(1963)
21. Forman, R.G., Kearney, V.E., Engle, R.M.: Numerical analysis of crack propagation in a cyclicloaded structure. Trans. ASME J Basic Eng. 89(3), 459–464 (1967)
22. Collins, J.A.: Failure of Materials in Mechanical Design: Analysis, Prediction. Prevention.
Wiley, NY (1993)
23. Bathias, C., Paris, C.P.: Gigacycle Fatigue in Mechanical Practice. Dekker, NY (2004)
24. Kachanov, L.M.: On the time of destruction under creep conditions. Izv. AN SSSR OTN 8,
26–31 (in Russian) (1958)
25. Rabotnov, J.N.: On the mechanism of long-term destruction. Voprosi prochnosti materialov i
konstrukcij. AN SSSR OTN, 5–7 (in Russian) (1959)
26. Murakami, S.: Continuum Damage Mechanics. A Continuum Mechanics Approach to the
Analysis of Damage and Fracture. Springer, Dordrecht (2012)