Maksym Gladskyi, PhD, Kostyantin Yanko

National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Low-Cycle Fatigue of Titanium alloys under Multiaxial Loading

Keywords: low-cycle fatigue, multiaxial loading, titanium alloys.

Abstract. The results of low-cycle fatigue tests of titanium alloy under non-proportional biaxial loading are given. The VT1-0 tests were carried out at three levels Mises’ strain with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. Fatigue life assessment method was proposed turned to be effective and allowed to take into consideration such factors as strain state type, strain path type and loading irregularity.

Introduction

There were many attempts to develop model based on non-linear accumulation of fatigue damages, but most of them did not consider complex influence of such factors as type of stress state, loading path, previous stress history on the process of fatigue damages accumulation. Fatemi and Yang [1] give a wide survey of the existing models and offer their classification.

In the paper it is studied influence of sequential loading effects on the titanium alloys fatigue damage and under 90° out-of-phase non-proportional loading. Damage model is proposed, which considers non-proportion effects, which appear at loading regime change.

Experimental procedure

With the purpose of getting stress-strain state close to homogeneous were used tubular specimens with outer diameters of 11,5 mm and 11 mm, wall thickness of 0,75 mm and 0,5 mm, test portion length of 20 mm and 21 mm for VT1-0 and VT9 respectively.

Specimens of VT1-0 were tested at constant deformation amplitude, and under non-proportional regular loading. The VT1-0 alloy showed behaviour which is typical for cyclic-stabilized materials under the tested loading conditions. Tests results are showed in the Table 1, where – non-proportional parameter of strain cycle [2].

Table 1

Path, strain peak values, non-proportional parameter and number of cycle to failure for VT1-0 titanium alloy

path				, cycle
i	0,55	0,75	0	1580
i	0,72	0,94	0	822
i	0,78	1,34	0	318
o_45	0,59	1,02	0,5	931
o_45	0,76	1,32	0,5	372
o_45	0,93	1,61	0,5	211
o	0,7	1,21	1,0	733
o	0,9	1,56	1,0	301
o	1,1	1,91	1,0	199

For the VT9 titanium alloy the programme of tests, given in Table 2, was carried out. The basic modes were: tension-compression, alternating torsion and 90° out-of-phase loading. The first stage of the programme was the block axial loading and/or torsion moment test with given strain ranges. During this test the strain path remained constant. The second stage of the programme was testing the specimens with changing of the strain path. Transfer from one strain path to another was conducted during making the value reach the 0.5 point and then the specimen was brought to failure. At the third stage the test with a multiple strain path change was carried out.

Table 2

Strain peak values and number of cycle to failure for VT9 titanium alloy

Test type
		%		cycle
a_01	а	0,8	-	157	293
	а	1,0	-	136
a_02	а	1,0	-	98	245
	а	0,8	-	147
a_03	а	0,6-0,8- 1,0-0,8	-	50	519
a_04	а	1,0-0,8- 0,6-0,8	-	50	491
oatota	-	0,8	1,0	50	475
oa	o	1,0	1,0	77	218
	a	1,0	-	141
atat_1/5	a	1,0	-	40	423
	t	-	1,0	130
atat_1/3	a	1,0	-	65	510
	t	-	1,0	219
t_01	t	-	0,8-1,0- 1,2-1,0	50	601
t_02	t	-	1,2-1,0- 0,8-1,0	50	528
at	a	1,0	-	97	398
	t	-	1,0	301
ta	t	-	1,0	398	603
	a	1,0	-	205
ao	a	1,0	-	98	184
	o	1,0	1,0	86
to	t	-	1,0	282	390
	o	1,0	1,0	108
ot	o	1,0	1,0	80	384
	t	-	1,0	304

Assessment Approach

The assessment of VT1-0 titanium alloy fatigue life under non-proportional loading showed that the application of Pysarenko-Lebedev modified criterion resulted in good correlation of predicted and test data due to the complex consideration of the strain state type and non-proportionality of the loading [3]. That is why it is advised to apply the Pysarenko-Lebedev modified criterion as well as the chosen damage accumulation hypothesis for assessing the VT9 titanium alloy fatigue life. In the paper the two damage accumulation hypotheses were analyzed: the linear hypothesis and the Manson’s approach, according to which the damage curve is the relative fatigue life nonlinear function and looks like this:

,

where ; – the number of one-level loading cycles; – number of cycles before failure under the given loading level; – material constant that is calculated from the test data under sequential double-level loading.

The combined application of the Pysarenko-Lebedev modified criterion and of the Manson’s approach showed the high level of predicted and test data correlation for all the loading programmes except the alternating torsion. So the following modification of the Manson’s approach is proposed:

, (1)

where ; – strain path orientation angle, which determines the dominating type of the strain state; and are fatigue strength coefficients at finite life for uniaxial and torsional loadings.

During the alternating torsion the damage accumulation is linear, during the tension-compression – with the application of the Manson’s approach, and during the biaxial proportional and non-proportional loading their linear interpolation.

The application of formula (1) resulted in the best correlation of the best correlation of the predicted and test data that is shown on the Fig.1.

Figure 1. Comparison of predicted fatigue lives by the proposed approach with experimental fatigue lives

References

[1] Fatemi A., Yang L. Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials // Int. J. Fatigue. – 1998, vol.20, No.1, pp. 9-34.

[2] Itoh T., Sakane M., Ohnami M., Kida S., Sosie D. F. Dislocation Structure and Non-Proportional Hardening of Type 304 Stainless Steel // In: Proceeding of the 5^th International Conference Biaxial-Multiaxial Fatigue and Fracture, Cracow. – 1997, vol. 1, pp. 189-206.

[3] Shukayev S., Zakhovayko O., Gladskyi M., Panasovsky K. Estimation of low-cycle fatigue criteria under multiaxial loading // Int. J. Reliability and life of machines and structures. – 2004, vol.2, pp. 127-135.