Transcript An Experimental Study and Fatigue Damage Model for Fretting Fatigue Aditya A.

An Experimental Study and Fatigue
Damage Model for Fretting Fatigue
Aditya A. Walvekar
Ph.D. Research Assistant
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Outline
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Motivation
Objective
Fretting Fatigue Test Rig
Experimental results
Fatigue Damage Model
Fretting Fatigue Life Predictions
Summary
Future work
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Motivation
•
Fretting is associated with the small amplitude relative oscillatory motion
between two solid surfaces in contact
•
Fretting fatigue is a damage mechanism observed in a machine components
subjected to fretting in tandem with fluctuating bulk stresses
•
If the material is concurrently subjected to partial slip fretting and
fluctuating bulk loading, stress concentration at the contact region results in
premature nucleation and acceleration of crack growth when compared to
fatigue situations without fretting
Fretting Fatigue Test configuration*
* ASTM E2789-10 : Standard Guide for Fretting Fatigue Testing
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Objective
•
Experimental investigation of the fretting fatigue behavior of AISI
4140 vs. Ti-6-4 in a cylinder-on-flat contact configuration
– Analyze the effect of bulk stress on the fretting fatigue life at a
fixed normal load
– Analyze the crack propagation i.e. crack length vs. number of
cycles
•
Develop a model based on damage mechanics to analytically
investigate fretting fatigue
– Incorporate Voronoi tessellation to account for the randomness of
the material microstructure and conduct life variability studies
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Fretting Fatigue Test Rig
𝑭𝒃 − 𝑭𝒖 = 𝟐𝑭𝑻
Schematic of fretting fatigue test rig
•
Fretting fatigue fixture mounted on
MTS machine
A fretting test fixture was designed and developed which was
coupled with an MTS machine to impose the fretting fatigue damage
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Experimental Results
Picture of contact pads and specimen
assembled in the test rig
Fretting and bulk stress vs. life
•
Fretting fatigue tests were conducted in a cylinder-on-flat contact configuration under
completely reversed constant-amplitude axial load control conditions (R = -1) at 5 Hz
frequency
•
The amplitude of the axial bulk stress was varied from 100 MPa to 600 MPa while the
normal force was held constant at 11 kN (peak Hertzian pressure of 3 GPa)
•
Fretting stress (𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔 ) at the trailing edge of the contact is calculated using –
𝝈𝒇𝒓𝒆𝒕𝒕𝒊𝒏𝒈 = 𝝈𝟎 + 𝟐𝒑𝒉
𝛍𝑭𝑻
𝑭𝑵
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Determination of estimated crack initiation
(Bulk Stress = 348 MPa)
1
2
3
4
5
6
• Estimated crack initiation life – 34000 cycles
• First visible crack observed at 33420 cycles
with a length of 765 microns
7
8
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Figure 1: Pictures of the crack growth taken as the test is running for test #7 (red line
denotes the effective crack length).
Crack length vs. life cycles
(Bulk Stress = 348 MPa)
Pictures of the crack growth taken as the test
is running (Bulk Stress = 348 MPa)
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Coefficient of Friction Measurement
• A fretting test was performed in the gross slip
regime to determine the coefficient of friction
• The specimen was only held with the bottom
grip while the top end of specimen was free
• Completely-reversed sinusoidal displacement
at a frequency of 1 Hz was applied to the
specimen
𝐶𝑂𝐹 =
Fretting wear test at gross slip
(displacement amplitude = 150 μm)
Disp. Amp.
(micron)
150
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙 𝐹𝑜𝑟𝑐𝑒 𝑎𝑡 𝑔𝑟𝑜𝑠𝑠 𝑠𝑙𝑖𝑝
𝑁𝑜𝑟𝑚𝑎𝑙 𝐹𝑜𝑟𝑐𝑒
Normal
force
(N)
417.2
Contact
stress
(MPa)
585.45
Average tangential
load at gross slip
(N)
250
COF
0.60
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Finite Element Model
• Randomness of material microstructure topology is simulated
using Voronoi tessellation to account for the variability in
fretting fatigue life
• The sinusoidal reaction stress with amplitude “σreaction” is
applied on the left edge of the lower body in phase with the
bulk stress to model FT
𝝈𝒓𝒆𝒂𝒄𝒕𝒊𝒐𝒏 = 𝝈𝒐 −
𝑭𝑻
𝑭𝑵
𝒍𝒊𝒏𝒆 𝒇𝒊𝒕
∗ 𝑭𝑵
𝑨𝒔
FT/FN obtained from experiments and FE model
Finite element mesh using Voronoi
Tessellation
The geometry and the applied loading
conditions (a = 365 μm)
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Model Validation
• To validate the stress distribution obtained from the FE model, shear and
tangential stress distribution on the contact surface were compared with
the analytical solution
Comparison of shear stress and normalized tangential stress distribution on
the contact surface at the positive peak of the fretting cycle obtained using
FE model and analytical solution. (Bulk Stress = 400 MPa)
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Fatigue Damage Model
• In order to introduce randomness into the life predictions, the alternating
normal stress (𝜎𝑛 𝑎 ) acting along the Voronoi grain boundary during the
fretting cycle is assumed to cause damage
• Damage evolution rate equation –
• Alternating Normal Stress –
𝝈𝒏 𝒂 =
𝝈𝒏 𝒂
𝒅𝑫
=
𝒅𝑵
𝝈𝑹 (𝟏 − 𝐃)
𝒎
𝝈𝒏 𝒎𝒂𝒙 − 𝝈𝒏 𝒎𝒊𝒏
𝟐
• σn max and σn min are the maximum and the
minimum normal stresses acting on the Voronoi
grain boundary during a fretting cycle
Stresses resolved along the Voronoi
grain boundaries
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Variation of Elasticity Modulus
• Increase in the internal damage as the fatigue cycles progress, manifests as the
reduction in the modulus of elasticity. Elastic modulus of the damaged element 𝑬=𝑬 𝟏−𝑫
𝑬
Rearranging, 𝑫 = 𝟏 − 𝑬
• Accurate strain measurements are important for measuring elasticity modulus so
a strain gauge was installed on in the constant cross sectional area region of the
specimen
Iteration No.
E (1-D) (GPa)
D
1
176.0
0
2
167.1
0.051
3
160.6
0.088
4
157.3
0.106
5
155.8
0.115
6
155.2
0.119
7
154.5
0.123
8
154.5
0.122
Stress vs. strain plot at various cycles for the
variation of elasticity modulus test
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Evaluation of Damage Parameters
• The peak in the tensile stress at the trailing edge of the contact (𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔 ) drives the
crack initiation in fretting fatigue. The critical stress component causing the damage
is assumed to be the fretting stress
• The damage parameters σR and m were evaluated using the maximum fretting stress
𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔 and fretting fatigue life data from experiments. Applying a power law curve
fit to the data: 𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔 = 𝐴𝑁 𝑏
where, 𝐴 = 11440 𝑀𝑃𝑎, 𝑏 = −0.13
𝑑𝐷
𝑑𝑁
=
𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔 𝑚
•
𝜎𝐑 (1−𝐷)
Integrating,
𝑁𝑓
𝑑𝑁
0
𝑁𝑓 =
𝑏
1
− +1
𝑏
𝐷𝑐𝑟𝑖𝑡
1
1
1−
𝑚 = − , 𝜎𝑅 = 𝐴
−
1
1
𝑏
− +1
− +1
𝑏
𝑏
𝑚
𝐷𝑐𝑟𝑖𝑡 𝜎𝑅 (1−𝐷)
𝑑𝐷
0
𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔
𝑚
𝜎𝑅
1
1−𝐷𝑐𝑟𝑖𝑡 𝑚+1
−
𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔
𝑚+1
𝑚+1
=
𝒎 = 𝟕. 𝟓, 𝝈𝑹 = 𝟏𝟔𝟎𝟔𝟏 𝑴𝑷𝒂
Rearranging,
𝜎𝑓𝑟𝑒𝑡𝑡𝑖𝑛𝑔 = 𝜎𝑅
Comparing Coefficients –
1
1
𝑚+1
−
1−𝐷𝑐𝑟𝑖𝑡 𝑚+1 𝑚
𝑚+1
1
𝑁𝑓 −𝑚
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Fretting Fatigue Life Predictions
• Fatigue Damage model was used for predicting fretting fatigue life of 30 randomly generated
microstructure domains for four different loading conditions
• Degree of scatter is quantified using two-parameter Weibull probability distribution
Material properties used in the analysis
Comparison between the fretting fatigue lives from
model and experiments
Loading conditions applied and predicted Weibull
slope and strength parameters
Weibull probability plot for fretting fatigue lives
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Summary
• A fretting fixture was designed, built and used with an MTS 810
machine simulating the fretting fatigue in a cylinder-on-flat
configuration
• For a fixed contact pressure, the fretting fatigue life decreased with
increasing bulk stress
• A fatigue damage finite element model was proposed to replicate the
fretting fatigue experiments and numerically estimate the fretting
fatigue life
• The fretting fatigue lives predicted by the fatigue damage model are in
good agreement with the experimental results
• The predicted fatigue life data displayed a larger degree of scatter for
the lower bulk stress when the contact pressure is fixed
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Future Work
• Modify the fatigue damage model to include crack
propagation
• Evaluate the effects of shot-peening, residual stress on Fretting
Fatigue behavior
• Analyze the effects of inclusions and voids on the fretting
fatigue life
• Incorporate plasticity in the fatigue damage model
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013