PSI - Issue 82

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2026) 000–000

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 82 (2026) 112–118

© 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers Abstract The continuum mechanics fatigue model operates on state variables that are continuous in time, unlike cycle-counting-based methods that rely on deconstructing stress histories into a set of distinct cycles. This way, the continuum-based approach provides a modeling framework that, in principle, can handle arbitrary stress histories. Despite its successful application for a wide range of problems, the current formulations cannot fully capture the complexities of out-of-phase loading. The present work investigates this issue in further detail by considering cyclic stress histories induced by combinations of bending and torsion with various phase differences for infinite fatigue lifetimes. For mild steel, hard steel and duraluminum subjected to certain combinations of shear stress and normal stress with phase differences of 90 degrees, the model will overestimate the fatigue limit for some stress combinations. For a brittle cast iron, the observed fatigue limits are well captured when applying a generalized format that takes into account the effect of the shear stress fatigue limit. © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers Keywords: Continuum mechanics fatigue model; high-cycle fatigue, multiaxial, out-of-phase 1. Introduction The continuum mechanics fatigue model by Ottosen et al. (2008) has received attention in the research community as an appealing approach to multiaxial high-cycle fatigue modeling. Unlike traditional fatigue models, which rely on 8th International Conference on Structural Integrity and Durability (ICSID2025) Continuum mechanics fatigue model: Fatigue limits for out-of phase combinations of normal and shear stress Sigbjørn Tveit a, *, Niels Saabye Ottosen b , Aase Reyes a a Department of Built Environment, Oslo Metropolitan University, Post box 4, St. Olavs plass, 0130 Oslo, Norway b Division of Solid Mechanics, Lund University, Box 118, 22100 Lund, Sweden

* Corresponding author. Tel.: +47 672 36 668. E-mail address: sigbjorn.tveit@oslomet.no

2452-3216 © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers 10.1016/j.prostr.2026.04.018