PSI - Issue 13

Daniele Rigon et al. / Procedia Structural Integrity 13 (2018) 1638–1643 D. Rigon et al./ Structural Integrity Procedia 00 (2018) 000 – 000

1639

2

Nomenclature Q

specific heat loss per cycle [MJ/m 3 cycle]

specific heat [J/kg∙K] material density [kg/m 3 ] load test frequency [Hz] biaxiality ratio (  a /  a )

c 

f L 

phase angle between stress components [°]



Introduction Considering a volume of metallic material subjected to cyclic stresses, the mechanical input energy is partly stored internally in the material, the remaining part being converted into heat. Regarding the multiaxial fatigue, a general energy-based approach was proposed by Ellyin, (1997) by adopting the sum of the plastic strain energy and the positive elastic strain energy as a fatigue damage parameter. Despite the fact that such parameter is a scalar quantity, the severity of the particular multiaxial loading is accounted by a multiaxial constraint function, which takes into account the mean stress effect and non-proportional cyclic loading (Ellyin, (1997)). In the case of multiaxial fatigue of notched components and structures another energy-based approach was proposed by Lazzarin and coworkers, in which the averaged linear elastic strain energy density within a material dependent and properly defined control volume is assumed as a fatigue damage parameter (Lazzarin et al. (2004)(a), Atzori et al., (2006); Lazzarin et al., (2008)(b)). The internal energy stored within a material, which is indeed correlated to the fatigue damage mechanism, can be evaluated in principle as difference between the mechanical input energy and the thermal energy (Kaleta et al., (1991)). However, due to the fact that most of the mechanical input energy is converted into heat, such difference may be affected by uncertainties especially in high cycle fatigue (HCF), where calculating the area of the hysteresis cycle cannot be straightforward (Ellyin, (1997). a) b)

Data from Meneghetti et al. (2013(a,b),2016) Plain material, axial load Plain material, torsional load Data from Meneghetti et al. (2013(a,b)) Blunt notches, r n =3 ÷ 8 mm

AISI 304L

10

Data from Meneghetti et al. (2016), Rigon et al. (2017) severe V-notches r n =0.5 ÷ 3 mm 2 a =90 °÷ 135 °

1

 140 experimental data

0,1 Q [MJ/(m 3 ·cycle)]

Scatter band: 10-90% survival probabilities, from Meneghetti et al.(2013) k=2.11, T Q =2.04, T N =4.50 Q A,50% =0.133 MJ/(m

3 cycle) (N

A =2·10

6 cycles)

R=-1

0,01

1,E+2 1,E+3 1,E+4 1,E+5 1,E+6 1,E+7 1,E+8 1,E+9

N f , number of cycles to failure

Fig. 1. Fatigue test results of plain and notched AISI 304L in terms of specific heat loss Q (a). Qualitative rappresentation of temperature evolution during a fatigue test and evaluation of the cooling gradient immediately after a test stop (b) . For this reason, Meneghetti, (2007) proposed to adopt the specific heat loss per cycle (Q) as a fatigue damage index for fatigue strength analysis, since it can be measured quite easily also in HCF, at least for certain engineering materials. By using Q, more than 140 experimental uniaxial fatigue test results (R= -1) on plain, bluntly and severely notched AISI 304L stainless steel specimen were rationalised in a single scatter band calibrated in Meneghetti et al., (2013)(a), (Fig.1(a)). The fatigue test details are reported in Meneghetti and Ricotta, (2012), Meneghetti et al., (2013)(a); Meneghetti et al., (2013)(b); Meneghetti et al., (2016); Rigon et al., (2017).