Технические науки/2. Механика

Gladskyi Maksym, PhD

National Technical University of Ukraine “KPI”

Fatigue behavior of notched tubular specimens under axial and torsion loading

The most common cause for fatigue crack initiation in structural components is at stress concentrators such as notches. Grooves and keyholes on shaft, holes, fillets, thread, and welded joints are all notches. Even nominal elastic behavior may effects in exciding of yield limit around the notch.

Atzori at al. [1] conducted a multiaxial fatigue experimental study on V-notched specimens. They found that multi-axial fatigue strength is significantly affected by the nominal load ratio, whereas the influence of the load phase angle seems to be negligible. Yi-Ming and Wei-Wei [2] investigated crack initiation life for solid cylinders with transverse circular holes made from AISI 316 stainless steel under in-phase and out-of-phase multiaxial loading. The crack initiation life of notched specimens under out-of-phase multiaxial loading is shorter that that under in-phase multiaxial loading due to additional cyclic hardening effect. Gao at al. [3] studied fatigue behavior of V-notched shafts made of 16MnR steel with sharp and blunt notch radii. They showed that significant notch size effect on the fatigue life under different loading paths and notch effect is more significant for higher loading cycle fatigue. Sun at al. [4] conducted strain-controlled fatigue tests for GH4169 superalloy thin tubular and V-notched specimens under in-phase and two different out-of-phase loading paths at 650^oC. As can be found from experimental results for notched specimens, all of 90^o out-of-phase fatigue lives are longer in comparison with in-phase data. This effect may be also explained by sufficient additional hardening for this material at the root of the notch due to high plastic deformation. As a result, a fatigue damage parameter was proposed to predict the fatigue crack initiation life for notched specimen. Many engineering notched structures are also subjected to different combination of cyclic and static loadings. These results show that the addition of static compression to torsion cycling gives longer lifetime and static tension – shorter fatigue life in comparison with pure torsion cycling due to notch-weakening.

In this paper correlation of predicted and observed fatigue life of axial and torsion loadings of structural steel 20 are presented.

Low-carbon steel 20 was used at this study. The chemical composition of the material is as follows (mass%): C 0.24, Si 0.25, Mn 0.45, Cr 0.2. The basic geometry for two different types of specimens has 1.1 mm wall thickness, 22 mm inside diameter, and 40 mm gauge length. One type was a tubular smooth thin-walled specimens, the other type was the same thin-walled specimen with 3.4 mm circular through-thickness hole at the middle of gauge length.

Fully-reversed sinusoidal axial and torsion waveforms were applied for load/strain controlled constant amplitude tests. The 5% load drop for uniaxial strain control tests and 5% strain and rotation angle increment for uniaxial and torsion load control tests respectively, as compared to midlife stable cycle for smooth specimens were considered as a small crack initiation life.

Axial and shear applied strain and stress amplitudes as well as cycles to failure, for each constant amplitude fatigue test of low-carbon steel 20 are listed in Tables 1.

From Peterson’s plot, the tensile and shear stress concentrator factors are 3.29 and 3.98, respectively. Fatigue behavior of notched components depends on not only elastic stress concentrator factor. Materials strength is considered by fatigue notch factor, . The fatigue notch factor takes 2.73 and 3.21 for axial and torsion loading, respectively.

The following shear form of the Fatemi-Socie critical plane parameter was also used to correlate constant amplitude fatigue data

where and , are elastic and plastic Poisson’s ratios. = 1.0 was assumed for studied steel. The shear strain-life curve was generated based on von Mises criterion. The FS parameter was associated with local stress-strain condition based on FE analysis results. Correlation of constant amplitude data by the FS parameter is presented in Figure 1. As can be seen from these Figures, FS parameter fits the experimental data both for smooth and notched specimens very well. Based on FE analysis, the critical shear planes locate at the notch root on 0°, ±180° under axial loading and ±45°, ±135° for torsion loading. The same locations were found from experimental results. In addition, the fracture surfaces for both cases of loading associated with maximum shear plane. It explains FS parameter ability to predict fatigue life very well.

Table 1. Constant amplitude axial and torsion fatigue tests of smooth and notched specimens

Control mode		MPa	MPa	MPa	MPa	MPa	Cycles
Smooth specimens
Axial	0.0100	411	-	411	411	206	50
Axial	0.0070	350	-	350	350	175	135
Axial	0.0030	277	-	277	277	139	3,400
Axial	0.0020	261	-	261	261	131	13,120
Axial	0.0015	232	-	232	232	116	51,500
Axial	0.0010	192	-	192	192	96	>972,000
Axial	0.0031	300	-	300	300	150	2,050
Axial	0.0016	230	-	230	230	115	151,000
Torsion		-	190	190	329	0	8,573
Torsion		-	175	175	303	0	45,810
Torsion		-	149	149	258	0	242,000
Notched specimens
Axial		269	-	269	269	135	315
Axial		250	-	250	250	125	495
Axial		200	-	200	200	100	2,115
Axial		144	-	144	144	72	20,900
Axial		106	-	106	106	53	140,500
Torsion		-	149	149	258	0	5,407
Torsion			149	149	258	0	5,910
Torsion		-	121	121	209	0	34,700
Torsion		-	87	87	151	0	120,000
Torsion		-	87	87	151	0	276,000
Torsion		-	65	65	113	0	>1,150,000

Figure 1. Correlation of axial and torsion data by usingF-S parameter

References:

1. Atzori B, Berto F, Lazzarin P, Quaresimin M. Multi-axial fatigue behavior of a severely notched carbon steel. Int J Fatigue 2006;28:485-93.

2. Jen YM, Wang WW. Crack initiation life prediction for solid cylinders with transverse circular hole under in-phase and out-of-phase multiaxial loading. Int J Fatigue 2005;27:527-39.

3. Gao Z, Qui B, Wang X, Jiang Y. An investigation of fatigue of a notched member. Int J Fatigue 2010;32:1960-9.

4. Sun GQ, Shang DG. Prediction of fatigue lifetime under multiaxial cyclic loading using finite element analysis. Materials and Design 2010;31:126–33.