MATEC Web of Conferences 2, 08002 (2014) DOI: 10.1051/matecconf/ 2014120 8002 C Owned by the authors, published by EDP Sciences, 2014 Prediction for multiaxial fatigue strength with small defects Keiji Yanase 1,2* and Masahiro Endo1,2 Department of Mechanical Engineering, Fukuoka University, Fukuoka City, Fukuoka, Japan Institute of Materials Science and Engineering, Fukuoka University, Fukuoka City, Fukuoka, Japan Abstract As an extension of previous studies, this paper further examine the applicability and characteristics of the predictive method, in particular, for the case of proportional loading The predictive method is based on the area -parameter model and Endo’s biaxial fatigue failure criterion The present study manifests that the critical plane is normal to the direction of maximum principal stress, and the fatigue strength is dictated by both the maximum and minimum principal stresses Introduction In recent decades, the ability to assess the effect of small defects, inclusions and inhomogeneities on the uniaxial fatigue strength has been improved rapidly [1] However, the structural components in service are often subjected to multiaxial fatigue loading (e.g., combined axial and torsional loading in a shaft) Therefore, it is of practical merit to propose a predictive model that can connect the fatigue strength under multiaxial loading with that under uniaxial loading According the previous studies by the authors, the multiaxial fatigue strength in the presence of small surface defect can be predicted by the following equation [2-4]: max ^6w (T )` Vw 1.43( HV 120) (1) ( area max )1/6 where, in the case of proportional loading: ¦w (T ) (cos2 T N sin T ) V (1 N )sin T W (2) In Eq (2), V and W signify the stress amplitudes by axial and torsional loadings, respectively, and a parameter N (= -0.18) accounts for the effect of stress biaxility Figure illustrates the procedures to predict the fatigue strength In essence, Eq (1) can be classified as the critical plane approach Results and Discussions Based on a necessary condition to find the fatigue strength (Fig 1), the critical angle, T calculated as: * cri, is Corresponding author: kyanase@fukuoka-u.ac.jp This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20141208002 MATEC Web of Conferences 䢵䢷䢲 䢵䢷䢲 䢵䢲䢲 䢵䢲䢲 V (Failure Curve) V (Failure Curve) w w 䢴䢷䢲 䢴䢷䢲 with V = 156 MPa , V (MPa) w w with W = 100 MPa w with W = 20 MPa w 䢳䢷䢲 䢳䢲䢲 䢳䢲䢲 䢷䢲 䢷䢲 T 䢲 䢯䢸䢲 with W = 150 MPa 䢴䢲䢲 w with V = 20 MPa 䢳䢷䢲 w w w w , V (MPa) w with V = 100 MPa 䢴䢲䢲 䢯䢶䢲 䢯䢴䢲 䢲 䢴䢲 T cri 䢶䢲 Angle, T (degree) 䢸䢲 䢺䢲 䢳䢲䢲 䢲 䢯䢸䢲 䢳䢴䢲 䢯䢶䢲 䢯䢴䢲 䢲 䢴䢲 cri 䢶䢲 Angle, T (degree) 䢸䢲 䢺䢲 䢳䢲䢲 䢳䢴䢲 (a) Prediction for normal stress amplitude, V0 (b) Prediction for shear stress amplitude, W0 Figure Schematic illustration to find the fatigue strength w ¦ w (T ) wT T § 2W · tan ă â V0 Tcri o Tcri (3) In practice, Tcri in Eq (3) represents the principal stress direction Further, by substituting Eq (3) into Eq (1), the following equation can be obtained: (1 N ) V0 Vw Đ V0 à âVw ĐW à (1 N ) ă âVw Nă (4) By using the experimental data, the predictive capability of Eq (4) is examined in Fig As shown, a reasonable accuracy is observed Moreover, by using the maximum and minimum principal stresses, V n (normal to critical plane㸧 and V p (parallel to critical plane), Eq (4) leads to the following equation: V nw V p à 1.43( HV 120) Đ ă1 N u Vn ( area max )1/ â (5) Eq (5) coincides with a phenomenological equation proposed by Yanase and Endo [5] As manifested by Eqs (3) and (5), the orientation of critical plane is independent of N but the fatigue strength is affected by N 䢳䢰䢴 䢳䢰䢳 +10% 䢳 References 䢢 S35C SCM435 High tension brass 䢲䢰䢻 08002-p.2 Eq.(4) 䢲䢰䢺 -10% w 䢲䢰䢹 䢲䢰䢸 V /V Y Murakami, Metal fatigue: Effects of small defects and nonmetallic inclusions, Elsevier (2002) M Endo, I Ishimoto, Int J Fatigue 28, pp 592-597 (2006) K Yanase, ASTM Materials Performance and Characterization 2(1), DOI: 10.1520/MPC20130013 (2013) M Endo, K Yanase, Theoretical and Applied Fracture Mech 69, pp.34-43 (2014) K Yanase, M Endo, Engng Fract Mech., (submitted) 䢲䢰䢷 䢲䢰䢶 䢲䢰䢵 䢲䢰䢴 䢲䢰䢳 䢲䢢 䢲 䢲䢰䢳 䢲䢰䢴 䢲䢰䢵 䢲䢰䢶 䢲䢰䢷 䢲䢰䢸 W /V 䢲䢰䢹 w 䢲䢰䢺 䢲䢰䢻 䢳䢰䢲 䢳䢰䢳 Figure Predictions with Eq (4) 䢳䢰䢴 ... Curve) w w 䢴䢷䢲 䢴䢷䢲 with V = 156 MPa , V (MPa) w w with W = 100 MPa w with W = 20 MPa w 䢳䢷䢲 䢳䢲䢲 䢳䢲䢲 䢷䢲 䢷䢲 T 䢲 䢯䢸䢲 with W = 150 MPa 䢴䢲䢲 w with V = 20 MPa 䢳䢷䢲 w w w w , V (MPa) w with V = 100 MPa... (degree) 䢸䢲 䢺䢲 䢳䢲䢲 䢳䢴䢲 (a) Prediction for normal stress amplitude, V0 (b) Prediction for shear stress amplitude, W0 Figure Schematic illustration to find the fatigue strength w Ư w (T ) wT T Đ... Murakami, Metal fatigue: Effects of small defects and nonmetallic inclusions, Elsevier (2002) M Endo, I Ishimoto, Int J Fatigue 28, pp 592-597 (2006) K Yanase, ASTM Materials Performance and Characterization