PSI - Issue 23

Tomáš Oplt et al. / Procedia Structural Integrity 23 (2019) 101–106 Tomáš Oplt / Structural Integrity Procedia 00 ( 2019) 000 – 000

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ΔK , which is usually obtained from either analytical solution or two-dimensional (2D) finite element analysis assuming plane stress or plane strain conditions. However, 2D solution does not assume curved crack front but straight. That does not correspond to real fatigue crack shape, which is always curved as a consequence of two effects in particular. First reason for curvature is the effect of the free surface, which influences the stress field singularity around the crack front and causes slower crack propagation close to the free surface. This effect may be observed separately on specimens cyclically loaded at high asymmetry as was published by (Oplt et al. 2018). In case of loading at lower asymmetries, plasticity induced crack closure (PICC) effect described by (Elber 1970) appears. Its presence causes retardation of the fatigue crack growth, as the crack is closed while the external loading force is still tensile. Since the crack can propagate only when it is opened, real driving force of the crack is lower than one would expect based on external loading conditions. Therefore, real fatigue lifetime is higher and engineers who are aware of this fact are able to design structures with longer service life or save significant economical expenses. Furthermore, crack closure effect in combination with always-present free surface effect causes even bigger crack curvature. Some authors, e.g. (Branco et al. 2008; Camas et al. 2012; Gardin et al. 2016), published their studies on crack front shape influenced by crack closure effect, but scientific community is still lacking clear three-dimensional (3D) description of crack closure behavior. This paper presents proposed methodology for 3D numerical modelling of plasticity induced crack closure. Methodology and input parameters setting were adopted from previously published 2D solution (Oplt et al. 2019). Studied geometry was M(T) specimen with straight crack, which was cyclically loaded and crack propagated through the specimen in order to create plastic wake of residual strains. Monitoring of first nodes behind the crack front after two loading schemes load-debond-unload (LDU) and load-debond-unload-load-unload (LDULU) was the methodology applied for the determination of closure levels. Impact of various load ratios from R = -1 to R = 0.1 were compared together with Pokorny’s experimental results (Pokorný et al. 2017) . Distribution of elastic stress intensity factor K max through thickness was shown and closure levels K cl together with effective SIF K eff were determined locally at each node along the straight crack front. Discussion on processes leading to fatigue crack front curvature due to the effects of free surface and crack closure was provided.

Nomenclature 2D

K max

two-dimensional

maximum stress intensity factor

½ of specimen’s length element length ( L e = ∆a )

L

3D three-dimensional FCPR fatigue crack propagation rate FEA Finite Element Analysis LDU Load-Debond-Unload scheme LDULU Load-Debond-Unload-Load-Unload scheme M(T) Middle tension specimen PICC Plasticity Induced Crack Closure SIF stress intensity factor ∆ a crack increment (∆a = L e ) a 0 initial crack length ( a 0 = a f - N c ⋅ L e ) a f final crack length B specimen’s thickness E Young’s modulus He element height K cl closure stress intensity factor

Le n*

substep at u y = 0 n, n +1 substeps around u y = 0 N c no. of cycles R load ratio r p forward plastic zone size U closure level ratio u y

displacement of the first node behind the crack tip

½ of specimen width

W

ΔK

stress intensity factor range

ΔK eff

effective stress intensity factor range

Poisson’s ratio

ν

σ y,c

cyclic yield strength

2. FEA modelling methodology

In following section, description of input parameters and the numerical modelling methodology affecting behaviour of crack closure is outlined. 3D model of M(T) specimen was created in ANSYS Mechanical APDL 19.2. Fig. 1a shows a scheme with geometry dimensions W=30 mm, L=100 mm and B = 5 in order to satisfy experimentally tested specimens by (Pokorný et al. 2017) . Advantage of triple symmetry was used and only one eighth of the specimen was