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Structural Integrity
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Procedia Structural Integrity 2 (2016) 1853-1860
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21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Synthesis of crack initiation life in steel notched specimens under torsional fatigue based on the averaged strain energy density
Filippo Bertoab, Alberto Campagnoloc, Giovanni Meneghettic*, Keisuke Tanakad
"University ofPadova, Department of Management and Engineering, Stradella S. Nicola 3, 36100, Vicenza (Italy) bNTNU, Department opEngiaeering Design and Materials, Richard Birktlandt vei 2b, 7491, Trondheim, (Norway) cUniversity ofPadova, Department of ladustrial Enginnnring, Via Venezia 1, 35131, Padova (Italy) dMeijo University, Department of Mechanical Engineering, 468-8502, Nagoya (Japan)
Abstract
The torsional fatigue behaviour of circumferentially notched specimens made of austenitic stainless steel, SUS316L, and carbon steel, SGV410, choracterizef by (different notch ro ot radii lias been recsntly investigaten by Tanaka. In that contribution, it was observed that the total fatigue life of the austenitic stainless steel increases with incrtaTng siess concentration factor for a given applied nominal shear stress amplitude. By using the electrical potential drop method, Tanaka observed that Hie crack; nucleation life was reduced with increasing stress concrntrotion, on the other hand the crack pbopaga^m life increased. The experimental eatigue results, originally expressed in terms of nominal shear s^r(ifi^ amplitude, have been reanalysed by meana of the local strain energy density (SED) averaged over p conirol volume having radios Ro surrounding the notch tip. To exclude all extrinsic iffecis acting during ahe fatigue crack propagption jphafi^, such as eliding contact ^d/'or friction between fracture surfaceg, crack igetiatinn life has been considered in the prerent wosk (*). In the original paper, inigiotion life was defitsed in correspondenee of a f.l-;-a.4-mm-deef crack. The control radius Ro foaeatigue strength asteisment of notched componente, thoufht o fas a material Oroferty, had been estimated by imposing the aonstancy of the averaged SED for bot° smooth af-(r cracked specimens ot Na = 2 million loading; cycles.
(*) A eerston of tche present contribution has alsegdy been prerented at the; 11th International Conference on Multiaxial Fatigue and Fracture (ICMFF11).
Copy-relit © 20tf The AuChors. Published bs Eltevier B.V. This is an ojaen access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-reviewunder responsibility of the Scientific Chmmitfee ofECF21.
* Corresponding author. Tel.: 0039 049 8276751 E-mail address: giovsnni.meneglirtti@unipV.e
Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer review under responsibility of the Scientific Committee of ECF21.
10.1016/j.prostr.2016.06.233
Keywords: Torsional fatigue; notch effect; crack initiation; averaged SED; electrical potential drop.
1. Introduction
Dealing with torsional and multiaxial fatigue, an anomalous phenomenon of the notch-strengthening effect was observed in circumferentially notched specimens made of austenitic stainless steels (Ohkawa and Ohkawa, 2011; Tanaka, 2010; Tanaka et al., 2009). The fatigue life of notched specimens resulted longer than that of smooth ones, and the longer the higher was the stress concentration factor under the same amplitude of the nominal shear stress. This notch-strengthening effect was also observed in NiCrMo steel (Berto et al., 2011), pure titanium (Okano and Hisamatsu, 2012), but it was not found in carbon steels (Atzori et al., 2006; Ohkawa and Ohkawa, 2011; Tanaka et al., 2011). In circumferentially notched bars subjected to torsion fatigue loadings, factory-roof type fracture surfaces are obtained under low stress amplitudes and the sliding contact of the fracture surfaces causes the retardation of crack propagation (Ritchie et al., 1982; Tanaka et al., 1996; Tschegg, 1983, 1982; Yu et al., 1998). At high stress amplitudes, instead, flat fracture surfaces are observed and the crack retardation due to sliding contact is reduced. The presence of a superimposed static tensile stress also reduces the crack surfaces contact (Tanaka et al., 1996).
Recently, Tanaka (2014) has deeply investigated this phenomenon dealing with the fatigue behaviour of notched bars made of austenitic stainless steel, SUS316L, and carbon steel, SGV410, subjected to torsion loadings and characterized by different notch tip radii. In the present work, the experimental fatigue results have been reanalysed by means of the averaged strain energy density (SED) approach, first proposed by Lazzarin and Zambardi (2001). The crack initiation life has been considered, in order to exclude all extrinsic effects acting during the fatigue crack propagation phase, such as sliding contact and/or friction between fracture surfaces.
2. Experimental fatigue results
The materials tested in (Tanaka, 2014) were an austenitic stainless steel (SUS316L) and a carbon steel (SGV410) for structural use in nuclear power plants. The yield strength and tensile strength of SUS316L were 260 and 591 MPa, and those of SGV410 were 275 and 470 MPa.
Figure 1 reports the geometry of the cylindrical specimens weakened by circumferential notches with three different root radii. The specimens with a notch radius p equal to 4.5, 1.07, and 0.22 mm are named NA, NB, and NC, respectively. The elastic stress net-section concentration factor for the shear stress under torsion for NA, NB, and NC specimens calculated by the finite element method (FEM) was 1.17, 1.55, and 2.54, respectively, while that for the tensile stress was 1.50, 2.50, and 5.07, respectively.
The experimental fatigue test results were obtained by adopting a nominal load ratio R equal to -1. The applied shear stress amplitude was expressed in terms of nominal stress calculated elastically from the applied torque for the minimum cross section. The fatigue tests under torsion loadings were conducted with and without superimposed static tension. In the first case, the applied static tensile stress (am) equalled the applied shear stress amplitude (xa).
Tanaka (2014) employed a DC electrical potential method to monitor the fatigue crack initiation and propagation phases. The initiation life was defined in correspondence of a 0.1^0.4-mm-deep crack. It was observed that the total fatigue life of the austenitic stainless steel (SUS316L) increases with increasing stress concentration factor for a given applied nominal shear stress amplitude. In particular, Tanaka (2014) observed that the crack nucleation life was reduced with increasing stress concentration; on the other hand the crack propagation life increased. The notch-strengthening effect has been attributed to the retarded propagation promoted by the crack surfaces contact, which occurs especially for the sharper notches. Indeed, the superposition of static tension on the fatigue torsion loading resulted in a notch-weakening behaviour, being the contact between the crack surfaces reduced. The notch strengthening effect was not observed in the SGV410 carbon steel.
On the basis of fracture surfaces and crack paths analyses (Tanaka, 2014), the difference in the notch effect on the fatigue behaviour of SUS316L and SGV410 appeared to be tied to different crack path morphologies of small cracks and three-dimensional fracture surface topographies observed by using scanning electron microscopy (SEM).
More details concerning both the experimental results, expressed in terms of nominal shear stress amplitude, and
the fracture surfaces analysis can be found in the original paper (Tanaka, 2014).
Fig. 1. Geometry of the cylindrical notched specimens (Tanaka, 2014) (dimensions are in mm).
3. Averaged strain energy density approach
The strain energy density (SED) averaged over a control volume, thought of as a material property according to Lazzarin and Zambardi (2001), proved to efficiently account for notch effects both in static (Berto and Lazzarin, 2014; Lazzarin and Zambardi, 2001) and fatigue (Atzori et al., 2006; Lazzarin and Zambardi, 2001) structural strength problems. The idea is reminiscent of the stress averaging to perform inside a material dependent structural volume, according to the approach proposed by Neuber.
Such a method was formalized and applied first to sharp, zero radius, V-notches (Lazzarin and Zambardi, 2001) and later extended to blunt U and V-notches (Lazzarin and Berto, 2005a). When dealing with sharp V-notches, the control volume is a circular sector of radius R0 centered at the notch tip (Lazzarin and Zambardi, 2001). For a blunt V-notch, instead, the volume assumes the crescent shape shown in Fig. 2 (Lazzarin and Berto, 2005a), where R0 is the depth measured along the notch bisector line. The outer radius of the crescent shape is equal to R0 + r0, where r0 depends on the notch opening angle 2a and on the notch root radius p according to the following expression:
r0 =-p
with q defined as:
2% - 2a
The control radius R0 for fatigue strength assessment of notched components has been defined by equalling the averaged SED in two situations, i.e. the fatigue limit of un-notched and cracked specimens, respectively (Berto et
al., 2011; Lazzarin and Berto, 2005b). Therefore Ro combines two material properties: the plain material fatigue limit (or the high-cycle fatigue strength of smooth specimens) and the threshold value of the SIF range for long cracks. The following expressions have been derived under plain strain hypothesis (Berto et al., 2011; Lazzarin and Berto, 2005b) dealing with tension (mode I) and torsion (mode III) loadings, respectively:
Rw = 2e1
_ (1 + v)(5 - 8v)
V act0 y
It should be noted that, in principle, the control radius R0 could assume different values under mode I and mode III, so that the energy contributions related to the two different loadings should be averaged in control volumes of different size (Berto et al., 2011). The idea of a control volume size dependent on the loading mode has been proposed for the first time in (Berto et al., 2011) dealing with the multiaxial fatigue strength assessment of notched specimens made of 39NiCrMo3 steel. It is important to underline that using a Poisson's coefficient v = 0.30, Eq. (3) (being valid under plain strain hypothesis) can be re-written as follows (Lazzarin and Berto, 2005b; Livieri and Lazzarin, 2005):
R0I _ 0.85 — , n
AKU ACT0
0.85 • a0
Therefore, Ro in Fig. 2 results on the order of the El Haddad-Smith-Topper length parameter (El Haddad et al., 1979).
Fig. 2. Control volume for specimens weakened by rounded V-notches (Lazzarin and Berto, 2005a).
Once the control volume is properly defined, the averaged SED can be evaluated directly from the FE results,
AW, by summation of the strain-energies Wfem,i calculated for each i-th finite element belonging to the control area (A in Figs. 2 and 3):
AW = cw^AW^ (6)
where the coefficient cw accounts for the effect of the nominal load ratio R (Lazzarin et al., 2004), when the range value of the nominal stress is applied to the FE model. It is equal to 1 for R = 0 and to 0.5 for R = -1. Equation (6) defines the so-called direct approach to calculate the averaged SED. According to a recent contribution of Lazzarin et al. (2010), very coarse FE meshes can be adopted within the control volume A (see Fig. 3b).
4. SED-based synthesis of crack initiation experimental data
The fatigue properties of the considered materials have been taken from (Tanaka et al., 1999; Yu et al., 1998) and are reported in Table 1. All parameters are expressed in terms of range, defined as maximum minus minimum value. The control radii R0,i and R0,iii have been calculated from Eqs. (3) and (4), respectively, where parameters e1 and e3 equal 0.133 and 0.414, respectively, for a Poisson's ratio v = 0.3.
Table 1. Mechanical properties
Material ACTO (MPa) AKith (MPa m05) ro,i (mm) ATo (MPa) AKni,th (MPa m05) ro,iii (mm)
SUS 316L 442 10.30 0.144 266 9.86 0.438
SGV 410 436 10.60 0.157 270 12.80 0.716
The averaged SED values were calculated using the direct approach, AW, according to Eq. (6) (with about 500 finite elements inside the control volume). FE analyses have been carried out by means of Ansys® software and by adopting free mesh patterns consisting of two-dimensional, harmonic, 8-node linear quadrilateral elements (PLANE 83 of Ansys® element library), as shown in Fig. 3. The adopted finite element enables to analyse axis-symmetric components subjected to external loads that can be expressed according to a Fourier series expansion. Therefore, it can be employed for modelling three-dimensional axis-symmetric components under axial, bending or torsional loadings, keeping the advantage of treating two-dimensional FE analyses.
The results of the synthesis based on the local strain energy density are reported in Fig. 4. In order to exclude all extrinsic effects acting during the fatigue crack propagation phase, such as sliding contact and/or friction between fracture surfaces, crack initiation life, defined in correspondence of a crack depth in the range of 0.1+0.4-mm as proposed by Tanaka (2014), has been considered in the present reanalysis. Moreover, it is important to underline that the range of the averaged strain energy density, AW, has been taken into account, so that the constant energy contribution of static tensile stresses has been neglected. This engineering approximation is acceptable if crack initiation life, and not the total life, is considered, because the static tensile stress contributes more to the crack growth behaviour (i.e. sliding contact and friction between the mating surfaces) than to the crack initiation phase. The control radius Ro,i has been calculated and reported in Table 1 only for comparison purposes.
It can be observed that in the case of SUS 316L steel, the crack initiation experimental results are well summarized in a scatter-band (Fig. 4a), characterised by an equivalent stress-based scatter index Tn (= ^TW) equal to 1.23; this value is practically coincident with the intrinsic scatter of the original data expressed in terms of nominal stresses, which was found equal to Tn= 1.24. However, the effects of sliding contact and/or friction between fracture surfaces during the propagation phase are evident, because the experimental results in terms of total fatigue life (see the smaller symbols: the black ones are related to pure torsion fatigue loading, while the gray ones are for torsion fatigue loading with superimposed static tension) are characterized by a high scatter, due to the difference between the fatigue lives of specimens tested with and without static tensile stress.
In the case of SGV 410 steel (Fig. 4b) the crack initiation experimental data are more scattered, T being higher and equal to 1.51,while the intrinsic scatter of the original data expressed in terms of nominal stress resulted equal to Tn= 1.17. However, in this case, the influence of extrinsic effects is almost negligible and the experimental data in terms of total fatigue life fall within the scatter-band determined using crack initiation data.
Fig. 3. FE mesh adopted in the numerical analyses: (a) refined one (about 500 FE inside the control volume) to evaluate the exact SED value and (b) coarse one (about 50 FE inside the control volume) producing a reduced error of 1%. The Y-axis coincides with the axis of the specimen. Considered case: NB specimen made of SGV 410 steel, with p = 1.07 mm, R0-m = 0.716 mm, r0 = 0.428 mm.
5. Conclusions
In the present contribution, some recent experimental fatigue test results, obtained from circumferentially notched specimens made of stainless and carbon steels, with different notch root radii and subjected to torsional fatigue loadings, have been reanalysed by means of the averaged strain energy density (SED) approach. Crack initiation life has been taken into account to exclude all extrinsic effects acting during the crack propagation phase, particularly of severely notched specimens made of stainless steel. The synthesis based on the local SED allowed to correlate fairly well the notch fatigue data for each tested material.
SUS316L
R0,m = 0.438 mm AWa,50„/o = 0.280 MJ/m3 Na = 2 -106 cycles Scatter Index (10%-90%) TW= 0.346/0.227 = 1.52 _Slope k = 5.27
ANA oNB
□ NC ANA' oNB
□ NC
- Torsion fatigue loading, R = -1
Torsion fatigue loading, R = -1 with superimposed static tension cm = Ta
I I I I I I I I I
■ .....
I I I I I I I
.......
1,E+03
1,E+04 1,E+05 1,E+06
Number of cycles to crack initiation
1,E+07
2.00 1,00
SGV 410-
ANA ONB
□ NC ANA" ONB
□ NC
- Torsion fatigue loading, R = -1
Torsion fatigue loading, R = -1 with superimposed static tension cm = Ta
R0III = 0.716 mm AWa,50% = 0.145 MJ/m3 Na = 2 ^106 cycles Scatter Index (10%-90%) TW= 0.220/0.096 = 2.29
_Slope k = 5.01 ♦
—I_I_I_I_I_I I I I
—I_I_I_I_I_I I I I
—I_I_I_I_I_I I I I
0.220 0.145 0.096
.......
1,E+03
1,E+04 1,E+05 1,E+06
Number of cycles to crack initiation
1,E+07
Fig. 4. Averaged SED-based scatter-band calibrated on the crack initiation experimental fatigue results for (a) SUS 316L and (b) SGV 410 steels. The smaller symbols indicate the total fatigue life for comparison purposes: the black ones are for pure torsion loading, while the gray ones are for torsion loading with superimposed static tension.
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