Stress scale factor and critical plane models under multiaxial proportional loading histories Manuel de Freitas a,⇑ , Luis Reis a , Marco Antonio Meggiolaro b , Jaime Tupiassú Pinho de Castro b a IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal b Pontifical Catholic University of Rio de Janeiro, PUC-Rio, Rua Marquês de São Vicente 225, Rio de Janeiro, RJ 22451-900, Brazil article info Article history: Received 15 September 2016 Received in revised form 16 December 2016 Accepted 17 December 2016 Available online 24 December 2016 Keywords: Multiaxial fatigue Damage calculation Stress scale factor Critical-plane approach abstract It has been experimentally proven that the shear stress level needed to cause fatigue failure is lower than the axial one. This fact has led to consider a Stress Scale Factor (SSF) between shear and axial stress to reduce different applied stresses to the same shear stress space or principal stress space, consequently facilitating the yielding analysis or fatigue damage evaluations. Most of multiaxial fatigue models use an SSF, and materials can be classified as shear sensitive (low SSF values) or tensile sensitive (large SSF values), depending on the main fatigue microcrack initiation process under multiaxial loadings. The use of SSF is quite common in many multiaxial fatigue criteria based on the critical plane approach. Such criteria adopt a SSF value assumed constant for a given material, sometimes varying with the fatigue life (in cycles) but not with the SAR (Stress Amplitude Ratio), the stress amplitude level, or the loading path shape. In this work, in-phase proportional tension- torsion tests related to 42CrMo4 steel specimens for several values of SAR are presented. The SSF approach is then compared with critical-plane models, based on their predicted fatigue lives and the observed ones for the studied tension-torsion histories. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Experimentally, it has been proven that the shear stress level needed to cause fatigue failure is lower than the axial one and several references can be found in the literature related to this material behavior [1,2]. This fact has led to consider a Stress Scale Factor (SSF) between shear and axial stress in order to reduce different applied stresses to the same shear stress space or principal stress space to facilitate the yielding analysis or fatigue damage evaluations. In this way, most of multi- axial fatigue models use a stress scale factor to consider the fatigue damage contributions from the axial and shear stress components regarding the material strength degradation. Materials can be classified as shear or tensile sensitive, depending on the main fatigue microcrack initiation process under multiaxial loadings [2]. Initiating microcracks under multiaxial loading are usually sub-divided into shear or tensile types. The dominant fatigue mechanism in so-called shear-sensitive materials is Mode II and microcracks nucleate along a shear plane where the range of the shear components is maximum, with the normal components only playing a secondary role. However, other materials such as 304 stainless steel under certain load histories, and cast irons [1], may initiate fatigue cracks in plane of maximum tensile strain or stress ranges, in this case, even if the microcrack nucleates in shear, its so- http://dx.doi.org/10.1016/j.engfracmech.2016.12.016 0013-7944/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: mfreitas@dem.ist.utl.pt (M. de Freitas), luis.g.reis@ist.utl.pt (L. Reis), meggi@puc-rio.br (M.A. Meggiolaro), jtcastro@puc-rio.br (J.T.P. de Castro). Engineering Fracture Mechanics 174 (2017) 104–116 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech