Issue 33

Y. Wang et alii, Frattura ed Integrità Strutturale, 33 (2015) 345-356; DOI: 10.3221/IGF-ESIS.33.38 355 linear cumulative damage rule for different materials tested under VA multiaxial fatigue loading. The critical plane was determined by using the  -MVM. (2) The MVM is an efficient and valid method to determine the orientation of the critical plane when it is used to evaluate fatigue damage under complex variable amplitude multiaxial fatigue loading. (3) Since the controlling parameter of the MMCCM is just the shear strain resolved along the direction of maximum variance of the resolved shear strain, when the MMCCM is used to estimate fatigue damage under variable amplitude multiaxial fatigue loading, cycles can directly be counted by using rainflow method. A CKNOWLEDGEMENTS his work is partly supported by Jiangsu Oversea Research & Training Program for University Prominent Young & Middle-aged teachers and Aviation Science Funds of China (No. 2013ZA52008). R EFERENCES [1] Findley, W.N., Modified theory of fatigue failure under combined stress, In: Proc of the society of experimental stress analysis, 14 (1956) 35-46. [2] Brown, M.W., Miller, K.J., A theory for fatigue under multiaxial stress-strain conditions, In: Proc institution of mechanical engineering, 187 (1973) 745-56. [3] Wang, C.H., Brown, M.W., A path-independant parameter for fatigue under proportional and non-proportional loading, Fatigue of Engineering Materials and Structures, 16 (1993)1285–1293. [4] Fatemi, A., Socie, D.F., A critical plane approach to multiaxial fatigue damage including out-of-phase loading, Fatigue Fract Eng Mater Struct, 11 (1988) 149-65. [5] Marciniak, Z., Rozumek, D., Macha, E., Verification of fatigue critical plane position according to variance and damage accumulation methods under multiaxial loading, Int J Fatigue, 58 (2014) 84-93. [6] Bedkowski, W., Macha, E., Ohnami, M., Sakane, M., Fracture plane of cruciform specimen in biaxial low cycle fatigue-estimate by variance method and experimental verification, Trans ASME J Eng Mater Technol, 117 (1995) 183–90. [7] Carpinteri, A., Macha, E., Brighenti, R., Spagnoli, A., Expected principal stress directions under multiaxial random loading Part I: Theoretical aspects of the weight function method, Int J Fatigue, 21(1999) 83–88. [8] Carpinteri, A., Macha, E., Brighenti, R., Spagnoli, A., Expected principal stress directions under multiaxial random loading Part II: numericalsimulation and experimentally assessment through the weight functionmethod, Int. J. Fatigue, 21(1999): 89–96. [9] Susmel, L., A simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, Int. J. Fatigue, 32 (2010) 1875-1883. [10] Susmel, L., Tovo, R., Estimating fatigue damage under variable amplitude multiaxial fatigue loading, Fatigue & Fracture of Engineering Materials & Structures, 34 (2011) 1053-1077. [11] Matsuishi, M., Endo, T., Fatigue of Metals Subjected to Varying Mar. Stress, Presented at Japan Society of Mechanical Engineers, Fukuoka, Japan, (1968). [12] Shamsaei, N., Fatemi, A., Socie, D.F., Multiaxial fatigue evaluation using discriminating strain paths. Int. J. Fatigue, 33 (2011) 597-609. [13] Bannantine, J.A., Socie, D.F., Multiaxial fatigue life estimation technique, In: Mitchel M, Landgraf R, editors. ASTM symposium on advances in fatigue lifetime predictive techniques, ASTM STP 1122 (1991) 249–75. [14] Wang, C.H., Brown, M.W., Life prediction techniques for variable amplitude multiaxial fatigue – part I: theories, J. Eng. Mater. Technol. 118 (1996) 367–70. [15] Papadopoulos, I.V., Critical plane approaches in high-cycle fatigue: on the definition of the amplitude and mean value of the shear stress acting on the critical plane, Fatigue Fract. Eng. Mater. Struct., 21 (1998) 269-285. [16] Susmel, L., Tovo, R., Benasciutti, D., A novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading, Fatigue & Fracture of Engineering Materials & Structures, 32 (2009) 441-459. [17] Susmel, L., Taylor, D., A critical distance/plane method to estimate finite life of notched components under variable T