NUI Galway – UL Alliance First Annual ENGINEERING AND - ARAN ...

A multiaxial damage mechanics methodology for fretting fatigue prediction
T. Zhang, P.E. McHugh, S.B. Leen
Department of Mechanical and Biomedical Engineering, NUI Galway, Ireland
t.zhang2@nuigalway.ie
Abstract
A multiaxial damage mechanics methodology is
developed to predict fretting crack nucleation. Material
degradation and wear behaviour are predicted
incrementally during each fretting cycle using an
energy-based wear simulation method. A combined
wear-fatigue methodology is implemented in a finite
element (FE) adaptive mesh framework. Predictions are
validated against published data.
1. Introduction
Fretting occurs when two contacting bodies experience
small amplitude oscillatory motion. Fretting in different
layers of flexible marine risers is one application of the
present work. The aim is to develop a continuum
damage mechanics (CDM) methodology for fretting
fatigue prediction. Two specific contact arrangements -round-on-flat
(RF) and rounded punch-on-flat (RPF) are
compared in terms of the prediction of evolution of
wear, plasticity, fatigue damage and the contact
geometry across a range of fretting variables. An
incremental wear simulation method based on the
energy approach of Fouvry et al [2] and previous work
[1] is implemented within an adaptive mesh user
subroutine. A non-linear kinematic hardening plasticity
formulation is employed along with a critical-plane,
Smith-Watson-Topper approach to predict multiaxial
fretting crack nucleation. Wear evolution and crack
nucleation predictions are validated against existing
published data for Ti-6Al-4V [1]. CDM (user
subroutine) implementations of the uniaxial Basquin
equation and multiaxial Lemaitre and Chaboche [3]
cumulative fatigue damage model are developed. To
apply this fretting methodology to flexible riser
pressure armour layer material, a tribology test
programme is proposed.
(a) (b)
Figure 1. FE model in ABAQUS of (a) RF and (b) RPF
2. Method
Fig 1 shows FE models of the RF and RPF contact
geometries for fretting wear simulation. Hertzian theory
was used to validate the initial (no-wear) stress and
contact pressure distributions. Non-linear kinematic
183
hardening plasticity is employed to capture a cyclic
plasticity ratchetting phenomenon.
For both the gross slip (no stick) and partial slip (central
stick region) fretting regimes, a user subroutine
UMESHMOTION was used to incrementally simulate
wear damage, based on the energy wear approach
proposed by Fouvy et al [2]. A multiaxial
implementation of the Lemaitre and Chaboche nonlinear-continuous-damage
(NLCD) model [3] is
adopted to predict the evolution of fretting-induced
fatigue damage via a UMAT user subroutine. The
evolution of multiaxial damage is given by:
β
β α
AII
dD [ D ] dN
M b σ H mean D ⎥ ⎡
⎤
+ 1
= 1−
( 1−
) ⋅ ⎢
⎣ 0 ( 1−
3 2 , )( 1−
) ⎦
where AII is the amplitude of octahedral shear stress and
σH,mean is the mean hydrostatic stress. The material is
softened by the damage as follows:
E = E ( 1−
D)
0
3. Results and conclusion
A validated fretting wear-fatigue methodology has been
developed for Ti-6Al-4V. The key role of slip regime
for crack nucleation is highlighted. Wear is predicted to
have a significantly more profound effect on fatigue
crack nucleation life for the RF case, reducing life in
the partial slip regime and increasing it in the gross slip
regime. The predicted (with wear) life for the RPF
geometry under nominally identical load conditions, is
significantly larger than for the RF case at low
displacements but similar at high displacements. Fig 2
shows the predicted evolution of fatigue damage.
Fig. 2. Preicted evolution of fatigue damage.
4. References
1. Ding, J. et al., Trib Int, 42 (2009) 1651-1662
2. Fouvry, S. et al., Wear, 255 (2003) 287-298.
3. Lemaitre, J. and Chaboche, J.L. (1990) Mechanics of Solid
Materials.: Cambridge University Press, Cambridge.