PSI - Issue 21

Emre Kurt et al. / Procedia Structural Integrity 21 (2019) 21–30

22 2

Author name / StructuralIntegrity Procedia 00 (2019) 000 – 000

1. Introduction Fatigue cracks, one of the main reasons of structural damage encountered in the industry, are very important for design and performance of modern structural materials. Many studies related to fracture and crack propagation problems in the literature are focused on cracked structures exposed to pure mode-I loads acting perpendicular to the crack plane and two-dimensional mixed mode-I/II loads, in which crack propagates in the plane. However, many practical engineering applications, structures and machine parts containing cracks are often subjected to combinations of modes I-II and III loads, so-called mixed mode-I/II/III loads, such that they exert three-dimensional mixed mode stress field around the crack front, for which mode-I analysis approaches are not sufficient. As a consequence, mixed mode loading occurs and crack can propagate in a non-planar manner depending on the geometry, loading and boundary conditions. Accurate and precise prediction of crack propagation surface and life of materials under mixed mode-I/II/III loading conditions is more complicated and difficult due to three-dimensional nature and its complexity arising from the existing coupled mode effects along the crack front (Yaren et al. (2019). Studies performed for thorough clarification of fracture mechanism of structures containing cracks under mixed mode-I/II/III loadings are relatively new and limited in the literature and have mainly focused on simpler geometries such as plate and cylindrical type specimens (Hyde and Aksogan (1994), Davidson and Sediles (2011), Citarella et al. (2014); (2015), Hannemann et al. (2017)). Different specific loading fixtures enabling any combinations of modes I, II and III, have been introduced in order to perform fracture and fatigue tests using conventional axial test machine (Richard and Kuna (1990), Schirmeisen and Richard (2009), Karpour and Zarrabi (2010), Richard et al. (2014), Richard and Eberlein (2016), Richard et al. (2017), Zeinedini (2018)). Ratios of the three fundamental fracture modes in terms of stress intensity factors (SIFs) directly relate to different mode mixity levels and determine the characteristics of crack surface profile under fatigue loads. Since intricate interaction of fracture modes under mixed mode loading affects not only the equivalent stress intensity factor range but also the shape of the crack front and crack path, three dimensional SIFs must be calculated accurately. For cracked structures subjected to mixed mode loading, modified Paris law (Eq. 1 ) along with equivalent SIF (Δ K eq ) range is used for fatigue crack growth and life prediction. Various criteria have been proposed for prediction of crack propagation profile under general multi-axial loading. Pook (1985), Richard et al. (2001) and Schollmann et al. (2001) developed three-dimensional (3D) criteria for the prediction of crack kinking and twisting angles and equivalent SIF. Irwin (1957), Tanaka (1974), Sih (1974) and Kikuchi et al. (2012) also developed equations to obtain equivalent SIF. In this study, three-dimensional fatigue crack propagation analyses are performed for two applications; an inclined penny shaped crack in a large body under tensile load (Ren and Guan (2017)) and multiple semi-elliptical surface cracks in a dog bone shaped specimen under tensile load (Shu et al. (2017)). Fatigue crack growth surfaces and lives obtained from the analyses are presented. FRAC3D solver, which is part of Fracture and Crack Propagation Analysis System (FCPAS) is used to compute three-dimensional mixed mode SIFs. FRAC3D is a general-purpose standalone finite element-based program (Ayhan and Nied (1998); (2002)) employing enriched crack tip elements to compute SIFs. Enriched finite elements do not require special mesh near crack front and SIFs are directly solved for at the same time as nodal displacements without any post-processing effort. The evolving crack surfaces are generated by successively adding the incremental growth surfaces and re-meshing and re-solving the finite element model using the FCPAS.

Nomenclature K I , K II , K III

mode I, mode II and mode III stress intensity factors

equivalent stress intensity factor plane-strain fracture toughness

K eq K IC SIF

stress intensity factor crack deflection angle crack growth rate

θ

d a /d N

crack growth-related material properties fracture and crack propagation analysis system

C,n

FCPAS