Технические науки/2. Механика

M. Gladskyi, PhD, V. Frolov, PhD, N. Zylov, A. Rubanenko

National Technical University of Ukraine “Kyiv Polytechnic Institute”,
Institute of Mechanical Engineering

A Method for Low-Cycle Fatigue Life Assessment of Metallic Materials under Program Multiaxial Loading

Keywords: multiaxial low-cycle fatigue, irregular loading, titanium alloys, damage accumulation, limit state criteria.

Abstract. The method of fatigue life assessment under multiaxial low-cycle block loading, which is based on the Pysarenko-Lebedev modified criterion, the linear damage rule as well as non-linear Manson’s approach was proposed.

The results of low-cycle fatigue tests of titanium alloy BT9 under block are given. The proposed approach was found to be effective and confident to take into consideration such factors as strain state type, strain path type and loading irregularity.

Introduction.

Construction elements often undergo irregular multiaxial cycle loading. Though multiaxial materials fatigue has been studied for a long time and enough of experimental data has been accumulated, problem of including of loading irregularity in low-cycle fatigue area is still actual. Many attempts to describe fatigue damage process were made, which resulted in many developed models of damage accumulation. The well known one is the conception of linear damage rule. This approach is easy to use but it does not give adequate estimation of life in many cases. 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, describe advantages and disadvantages of each one.

In the paper it is studied influence of sequential loading effects on the titanium alloys BТ9 fatigue damage and under tension-compression, torsion and 90° out-of-phase non-proportional loading. It is proposed life estimation method both under regular and irregular multiaxial 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 mm, wall thickness of 0,5 mm, test portion length of 21 mm.

Strain controlled tests under both proportional and non-proportional irregular loading were carried out.

Testing program and results are given in Table 1. 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.

Proposed method.

The Pysarenko-Lebedev modified criterion as well as the two damage rules for assessing the BT9 titanium alloy fatigue life was chosen. In the paper the damage accumulation hypotheses were analysed [2]: 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.

Table 1

Strain peak values and number of cycle to failure for BT9 titanium alloy

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

Analyzing Fig.1 and Fig.2 one can see that during the application of the Pysarenko-Lebedev modified criterion and the linear damage accumulation hypothesis the best correlation of the predicted and test data is obtained for alternating torsion (path t).

Figure 1 ‒ Comparison of predicted fatigue lives by the linear damage rule with experimental fatigue lives	Figure 2 ‒ Comparison of predicted fatigue lives by the damage curve approach with experimental fatigue lives

As a result, one can come to a conclusion about the linearity of damage accumulation process for a given loading type. 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.

So, 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.3.

Figure 3 ‒ Comparison of predicted fatigue lives by the proposed approach with experimental fatigue lives

Conclusions.

The proposed method of fatigue life assessment under multiaxial low-cycle regular and irregular loading, which is based on the Pysarenko-Lebedev modified criterion, the linear damage accumulation hypothesis and the non-linear Manson’s approach turned to be effective and allowed to take into consideration such factors as strain state type, strain path type and loading irregularity.

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. 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.