Maksym Gladskyi, PhD, Kostyantin Yanko^{}
National Technical
University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
LowCycle Fatigue of Titanium alloys
under Multiaxial Loading
Keywords: lowcycle fatigue, multiaxial loading, titanium alloys.
Abstract. The
results of lowcycle fatigue tests of titanium alloy under nonproportional
biaxial loading are given. The VT10 tests were carried out at three levels
Mises’ strain with various combinations of proportional and nonproportional
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 nonlinear 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° outofphase nonproportional loading.
Damage model is proposed, which considers nonproportion effects, which appear
at loading regime change.
Experimental procedure
With
the purpose of getting stressstrain state close to homogeneous were used
tubular specimens with outer diameters of
Specimens
of VT10 were tested at constant deformation amplitude, and under
nonproportional regular loading. The VT10 alloy showed behaviour which is
typical for cyclicstabilized materials under the tested loading conditions. Tests
results are showed in the Table 1, where – nonproportional
parameter of strain cycle [2].
Table 1
Path, strain peak values, nonproportional
parameter and number of cycle to failure for VT10 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: tensioncompression, alternating torsion and 90° outofphase 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 





% 
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 
0,60,8 1,00,8 
 
50 
519 
a_04 
а 
1,00,8 0,60,8 
 
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 
 
0,81,0 1,21,0 
50 
601 
t_02 
t 
 
1,21,0 0,81,0 
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 VT10 titanium alloy fatigue life under nonproportional loading
showed that the application of PysarenkoLebedev modified criterion resulted in
good correlation of predicted and test data due to the complex consideration of
the strain state type and nonproportionality of the loading [3]. That is why
it is advised to apply the PysarenkoLebedev 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
onelevel loading cycles; – number of cycles
before failure under the given loading level; – material constant
that is calculated from the test data under sequential doublelevel loading.
The
combined application of the PysarenkoLebedev 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
tensioncompression – with the application of the Manson’s approach, and during
the biaxial proportional and nonproportional 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. 934.
[2] Itoh T., Sakane M., Ohnami
M., Kida S., Sosie D. F. Dislocation
Structure and NonProportional Hardening of Type 304 Stainless Steel // In:
Proceeding of the 5^{th} International Conference BiaxialMultiaxial
Fatigue and Fracture,
[3] Shukayev S., Zakhovayko O., Gladskyi
M., Panasovsky K. Estimation of lowcycle
fatigue criteria under multiaxial loading // Int. J. Reliability and life
of machines and structures. – 2004, vol.2, pp. 127135.