Issue 38

M. Springer et alii, Frattura ed Integrità Strutturale, 38 (2016) 155-161; DOI: 10.3221/IGF-ESIS.38.21 156 I NTRODUCTION atigue failure and the mechanism leading to fatigue crack nucleation and propagation are of great concern in today’s design of engineering components. There are two groups of modeling concepts towards fatigue failure in materials and structures. First the classical fatigue laws of Basquin [1] and Coffin-Manson [2,3] to predict crack nucleation, i.e. the number of cycles till some detectable crack emerges. To account for multiaxial loading conditions more complex models like critical plane approaches are utilized, e.g. Fatigue Indicator Parameters (FIP) [4]. Second, methods treating the spatial advance of a failed region like fracture mechanics concepts as the Paris law [5,6] for crack propagation or Continuum Damage Mechanics based models for material degradation under cyclic loading. Various approaches have been proposed to merge these two considerations in one unified or generalized concept. One way to do so is the generalization of crack propagation laws. Different fatigue laws [7-12] have been proposed to find a relation between the Paris law and the fatigue laws of Basqin and Coffin-Manson. Another approach is the combination of fatigue considerations with continuum damage mechanics [13,14] or crack propagation modeling [15]. Such attempts are often suited in the field of numerical simulations especially in the framework of the Finite Element Method (FEM). Fatigue Indicators predict crack nucleation followed by the modeling of crack propagation realized, by crack modeling or material degradation. This way, a continuous simulation of the entire fatigue failure process is obtained. The present paper studies the estimation of the structural response due to the degradation of ductile materials. The focus is set on reversed cyclic plasticity, which is characterized by steady plastic strains from cycle to cycle with no net accumulation of directional plastic strains. This is the typical case for the Low Cycle Fatigue (LCF) regime. A two level approach is implemented within the framework of the Finite Element Method. Cyclic loading on the structural level induces time varying multiaxial stress and strain states at the material level which, of course, are location dependent. FEM simulations are utilized to compute the local constitutive response of the material points. A critical plane method is employed at all considered material points to identify the location most prone for material failure. There, crack emergence in the structure is modeled by material degradation in the region of the critical material points. Crack propagation is obtained by repetitive application of the approach which results in an evolving spatial zone of material failure. Consequently, a changing structural behavior is modeled by this propagating damage zone. M ETHODOLOGY computational methodology is set up in which a Fatigue Indicator Parameter (FIP) is utilized to predict crack nucleation. The same indicator is also employed to model “crack propagation” in the sense of a spatial evolving region of material failure. Depending on the fatigue damage behavior of the considered material different indicators can be appropriate [17, 18]. F ATIGUE CRACK NUCLEATION he Fatemi-Socie [19] Fatigue Indicator is employed in the present work which is typically used for ductile materials. This shear strain based critical plane method predicts fatigue crack nucleation and is given by, n FS y p k ,max 1 2              (1) The parameters governing crack nucleation are the shear strain amplitude, 2   , occurring on a particular plane and the maximum normal stress in a cycle, ,max  n , acting on that plane. y  is the yield stress and k is a factor defining the influence of n ,max  . The critical plane is identified as the plane experiencing the maximum value of the Fatigue Indicator. In case of non-proportional loading the determination of the shear strain amplitude usually requires numerical search F A T