PSI - Issue 31

N.D. Bibbo et al. / Procedia Structural Integrity 31 (2021) 75–79 N. D. Bibbo et al. / Structural Integrity Procedia 00 (2019) 000–000

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multiaxial fatigue has been under development, dating back to Gough and Pollard (1935). Since then, many multiaxial fatigue criteria have been proposed, some of which are widely used in the industry today. There is still much research activity in this area, as multiaxial fatigue is still not fully understood and multiaxial fatigue criteria can give very unpredictable results. Probably the most popular methods are the so called “critical plane methods”. These are commonly based on the observation that for ductile materials fatigue initiation occurs on a specific material plane that is subjected to the largest shear stresses; however they can also be based on planes of maximum damage or damage can be integrated across all planes. The method thus requires the assessment of a number of material planes, in order to find the critical plane subjected to the largest damage. The first of these methods is the Findley method, Findley (1956). Due to its maturity and its wide use in the industry, this method is tested against a more recent critical plane method known as the Modified Wöhler Curve Approach, Susmel et. al. (2011). One of the most common areas for fatigue to occur are in the vicinity of a welded joint. The reason for this is three fold. One being that welded joints are one of the most common fastening methods due to simplicity, versatility and cost. The second being that the welding process itself is chaotic in nature which leads to irregularities and defects in the weld geometry. The last being that, very often welds are located very close to geometric stress concentrators or the weld itself also commonly acts as a stress concentrator itself. Due to the irregularities present in a weld, it is next to impossible to predict the material behavior and geometry at a weld. Several methods have been developed that can help predict the weld stresses, such as the nominal, hotspot and notch stress approaches, more on these can be found in, Hobbacher (2016). In this article, the notch stress method is analyzed, primarily due to its suitability for use with critical plane methods. In order to assess the Findley and MWCM criterions and the notch stress method, the methods are applied to welded joint test specimens that have undergone fatigue testing. The welded test specimens and the results of fatigue testing are found in the following literature; Bäckström (2003), Siljander et. al. (1991), Sonsino (1995), Witt et. al. (1997), Amstutz et. al. (2001) and Yousefi et. al. (2001). A similar and more extensive study was performed by, Pedersen (2016), with the same test specimens. 2. Findley criterion The Findley criterion is the first damage criterion implementing the critical plane method and originates to the fifties, Findley (1956). Despite its age and the development of many newer critical plane methods, the Findley method is still widely used today. The original formulation of the Findley criterion can be seen in Eqn. 1. The Findley damage parameter is accumulated based on shear stress amplitude and the maximum occurring normal stress over the load time history. is a material parameter defined from fatigue experimentation and can be derived knowing two of the following four parameters fatigue parameters; � – fully reversed uniaxial bending limit, � – fully reversed torsion limit, � – purely pulsating uniaxial bending limit or � – purely pulsating torsion limit. The equations necessary to calculate can be found in, Bruun et. al. (2015). ��� �1� A more useful representation can be formulated to a uniaxial equivalent stress as seen in Eqn. 2 and is taken from, Bruun et. al. (2015). A uniaxial equivalent stress can be used for evaluation against the uniaxial normal stress SN curve. �� ��� 1 2 � �1 � � �2� 3. Modified Wöhler Curve Method The modified Wöhler Curve Method (MWCM) is a multi-axial fatigue criterion that, like Findley, assumes that the damage primarily occurs due to cyclic shear stress, Susmel (2014). In its original proposition, the maximum damage plane is selected by assessing all planes of interest for the maximum variance of the given planes shear stress time history. In this article, the critical plane is selected based on the maximum damage principle, that is, the MWCM method is applied to all assessed planes. The plane with the highest calculated damage sum is assumed to be the