PSI - Issue 13

Mirko Maksimović et al. / Procedia Structural Integrity 13 (2018) 1888 – 1894 Author name / Structural Integrity Procedia 00 (2018) 000–000

1889

3

C,n ΔK I  K th

Paris constants

the range of the mode-I stress intensity factor the range of threshold stress intensity factor

θ 0 the crack propagation angle K I, K II the stress intensity factors K eq

equivalent stress intensity factor cyclic yield strength fatigue ductility coefficient Finite Element Method

/

 f  f /

FEM MTS

the maximum tangential stress SED the strain energy density method 1. Introduction

Design considerations of aircraft structures based on damage tolerance approach often require prediction of mixed mode fatigue crack growth. In this approach crack propagation path is an essential aspect for the fatigue life simulation using fracture mechanics methodology. However, most of existing approaches are limited to the mode-I fatigue crack growth cases by Journet B et al. (1993), Pantelakis S et al. (1995), Pavlou DG. (2000). These approaches are generally based on correlations between the fatigue crack growth rate da/dN and the range of the mode-I stress intensity factor ΔK I . The commonly used fatigue crack growth rate equations of the type by Paris P., Erdogan F. (1963).   n da C K dN         (1) involving the experimentally determined constants C and n may not be adequate, because they are restricted to cracks running straight ahead. In damage tolerance approach the propagation path of a crack in a part is an essential aspect for the fatigue life simulation using fracture mechanics methodology. For these cases the cracks do not propagate in the direction normal to the applied load, these models need the stress intensity factor history along the crack path. The fatigue crack growth rate can be obtained by using Strain Energy Density method (SED) by Maksimović S. et al. (2011):     2 / / / / 4 1 th I f f n K K E I n dN da         (2) where:  f / is cyclic yield strength and  f / - fatigue ductility coefficient,  K I is the range of stress intensity factor,  - constant depending on the strain hardening exponent n / , I n / - the non-dimensional parameter depending on n / .  K th is the range of threshold stress intensity factor and is function of stress ratio i.e.   0 1 th th K K R      (3) ΔK th0 is the range of the threshold stress intensity factor for the stress ratio R = 0 and γ is the coefficient (usually γ = 0.71). In SED crack growth method the low cyclic material properties are used. Interesting attempts to predict the angle of crack propagation, as well as the fatigue crack growth rate for mixed-mode cracks, are divided into two categories. The first one incorporates the methodologies which consider the stress or the strain as the fatigue crack growth driving force, e.g. the maximum tangential stress criterion (MTS criterion) by Erdogan F, Sih GC. (1963), Gdoutos EE. (1984), the tangential stress factor and tangential strain factor by Stamenkovic, D. et al. (2010), the maximum tangential strain criterion by Maksimovic S. et al. (2012) etc. The second category contains the methodologies which recognize the material strain energy density as the fatigue crack growth driving force, e.g. the minimum strain energy density criterion (S-criterion) by Sih GC, Barthelemy BM. (1980), Khan SMA, Khraisheh MK. (2000) and Marija Blažić (2011), the dilatational strain energy density criterion (T-criterion) by Theoharis PS, Andrianopoulos NP. (1982) and Qian J, Fatemy A. (1996) etc. In these works the distribution of the total or the dilatational elastic strain energy density around the crack tip is evaluated along a circular