PSI - Issue 23

A. Karolczuk et al. / Procedia Structural Integrity 23 (2019) 69–76 A.Karolczuk, J. Papuga/ Structural Integrity Procedia 00 (2019) 000 – 000

70

2

Legend b

axial fatigue strength exponent shear fatigue strength exponent axial fatigue ductility exponent shear fatigue ductility exponent

b 0

c

c 0 E

Young’s modulus

’

axial fatigue ductility coefficient

 f

G

shear elastic modulus

amplitude of the applied shear strain under fully-reversed torsion loading

 f  f

’

shear fatigue ductility coefficient

components of unit normal vector n describing the plane orientation ( i = x,y,z ) number of cycles to failure estimated from the fatigue characteristic

n i N f

N cal N exp

calculated number of cycles to failure experimental number of cycles to failure

Poisson’s ratio

  f

fatigue limit under fully-reversed axial loading  f ( N f ) fatigue strength under fully-reversed axial loading at N f cycles  f ’ axial fatigue strength coefficient  u ultimate tensile strength  y yield tensile strength T (0.95) fatigue scatter band for a 95% level of confidence  f fatigue limit under fully-reversed torsion  f ( N f ) fatigue strength under fully-reversed torsion at N f cycles  f ’ shear fatigue strength coefficient

Although the physical mechanism of fatigue damage has been extensively studied, Schijve (2003), Polák & Man (2016), fatigue life calculation procedures are still burdened by large uncertainties due to the numerous factors influencing fatigue damage. One factor is the multiaxiality of the stress state. Various fatigue criteria are applied to overcome the multiaxiality problem, most of which are based on the hypothesis that there is a scalar function of stress/strain states that will enable the fatigue damage state to be estimated. Many multiaxial fatigue criteria have been based on various foundations, Ellyin (1997), Papadopoulos et al. (1997). One group of criteria, first mentioned by Stanfield (1935), is based on the critical plane concept. It assumes that the damage is directly associated with the particular plane orientation within the material. The critical plane concept was later developed by Stulen & Cummings (1954) and by Findley (1959). The concept is based on the experimental observation that fatigue damage in the form of a micro-crack is a result of material decohesion along a specific plane. The critical plane concept assumes that components of stress and strain vectors related to a given plane orientation are crucial for a correct damage state calculation. This concept gained popularity, Karolczuk & Macha (2005), Karolczuk et al. (2008), and it was applied in the strain-based criteria for the low cycle fatigue regime Brown & Miller (1973), Fatemi & Socie (1988) and in the energy-based criteria Smith et al. (1970), Liu (1993), Glinka et al. (1995), Łagoda et al. (1999) for low- and high cycle fatigue regimes. Despite the physical background of the critical plane concept, the functions applied for reducing the multiaxial stress/strain states to a scalar value are relatively simple. They are empirical functions proposed to obtain a good correlation with experimental results. Researchers have formulated rival new scalar functions for reducing the stress/strain tensors. The number of proposals is large, Karolczuk & Macha (2005), Papuga (2011), and new proposals are still being developed, Gołoś et al. (2014), Matsubara & Nishio (2014), Lu et al. (2017), (2018)a, (2018)b, Cruces et al. (2018). Researchers are still searching for a universal fatigue criterion that can be applied to the low- and high-cycle fatigue domains, and for various types of material under various loading conditions. However, the number of factors influencing fatigue behaviour is large, and the idea of formulating a universal and simple criterion may be an illusion. The general assumption underlying the various fatigue life estimation criteria mentioned here is that the weight