PSI - Issue 46

Jakub Šedek et al. / Procedia Structural Integrity 46 (2023) 69–74 Jakub Šedek / Structural Integrity Procedia 00 (2021) 000–000

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the crack growth retardation or acceleration appears and affects the fatigue life of a cracked part. The retardation/acceleration is driven mainly by the crack tip plasticity and the plastically deformed wake on crack lips formed during crack growth. To simulate a crack growth under VAL, several crack growth models were introduced; surveys are given in Khan (2017) or Sander (2004). Common feature of most cycle-by-cycle based models, that consider interaction effects, is that the plasticity at a crack tip and a wake shall be sufficiently appreciated. The full finite element (FE) solution of crack growth is still very difficult and computationally cost demanding with no general technique available. To cover degradation processes at the crack tip, a very fine mesh and local approach should be used as carried out by Materna (2011). Therefore, the FE models are mainly utilized to analyse individual crack states and the crack growth is driven by crack growth law, originally introduced by Paris (1961, 1963), in connection to forced crack advance in FE model. Branco (2015) demonstrated the dependency between accuracy and computational effort. It shows the fact, that the lower the maximum crack growth increment, the more accurate results. The crack tip blunting caused by material plasticity at the crack tip is commonly evaluated by measuring crack opening displacement (COD) in experimental practice. Toyosada (2005) presented physical meaning of the fictitious crack opening displacement in crack model according to Dugdale (1960). Similar measuring can be applied on a numerical model as well. Moreover, the model can introduce boundary conditions, that are very difficult to experimentally apply, like plane strain or plane stress. A strip yield model (SYM) based on Dugdale (1960) is widely utilized in damage tolerance analyses. The model is implemented in software packages for prediction of crack growth; i.e. NASGRO (2014), Fatigue & Fracture (2013) or Grooteman (2006). The SYM model is unique in that way, that the load history is taken into account and the model is able to react on individual overloads/underloads. The semi-analytical body of the model yields the opening stress that depends on the previous loading. The COD can be also determined and therefore the results of COD of FEM and SYM are evaluated in present work. 2. FE solution The one-eighth symmetric finite-element model (FEM) of the middle-crack tension M(T) specimen was used to study plastic zone and to evaluate constraint at a crack tip utilizing ABAQUS finite-element program (see Fig.1). The model contained six layers of elements through the half-thickness. The elastic–perfectly plastic material model with yield stress σ yield = 500 MPa, E = 71 500 MPa and ν = 0.3 represented a high strength aluminum alloy. The specimen configurations with crack length to specimen width ratio 2 a/W of 0.25, 0.5 and 0.75 and thicknesses of 1.25, 2.5, 5, 10 and 20 mm were analysed. The mesh with reduced 8-noded hexahedral elements of C3D8R type was utilized. The mesh size was variable with decreasing value toward down to crack tip to 0.03 mm. The plastic zone development during load application was analysed in FE solution and the plastic constraint factor as well. The constraint factor should characterize the plastic constraint at the crack tip and be usable for two dimensional models of a crack by Newman (1981), Wang (1991) or Machniewitcz (2012). Some of these models require constant stress in the tensile plastic zone and so an average value of local constraint over the plastic zone should be an appropriate parameter. More sophisticated stress description at a crack tip was also implemented by Wang (1991) and Machniewitcz (2012), but constant average constraint factor in a plastic zone is used mostly in engineering practice so far. The average concept is therefore also used in this work. The constraints factor α introduced by Newman (1993) was determined in local form from relation (1), where the ratio of stress component in loading direction σ yy over flow stress σ 0 as the average of strength σ Rm and yield stress σ yield is used.

yy 

2 Rm yield   

(1)





0 



0 

;