The fatigue damage to polymers generally depends on the material properties as well as on the mechanical, thermal, chemical, and other environmental influences. In this article, a methodology for modeling the dependence of the PA66 S-N curves on the material parameters, the material state, and the operating conditions is presented. The core of the presented methodology is a multilayer perceptron neural network combined with an analytical model of the PA66 S-N curve. Such a hybrid approach simultaneously utilizes the good approximation capabilities of the multilayer perceptron and knowledge of the phenomenon under consideration, because the analytical model for the S-N curves was estimated on the basis of the existing experimental data from the literature. The article presents the theoretical background of the applied methodology. The applicability and uncertainty of the presented methodology were assessed for the available data from the literature. The results show that it was possible to approximate the PA66 S-N curves for different input parameters if the space of the input parameters was adequately covered by the corresponding S-N curves.

References

1.
Orbanic
,
P.
, and
Fajdiga
,
M.
, 1999, “
R&D Process Located at Automotive Industry Suppliers
,”
M.
Fajdiga
,
T.
Jurejevcic
, and
F.
Trenc
, eds.,
Proceedings of 4th Conference and Exhibition Innovative Automotive Technology – IAT’99
,
Nova Gorica, Slovenia
, April 8–9, pp.
233
240
.
2.
Nagode
,
M.
, and
Fajdiga
,
M.
, 1998, “
On a New Method for Prediction of the Scatter of Loading Spectra
,”
Int. J. Fatigue
,
20
(
4
), pp.
271
277
.
3.
Nagode
,
M.
,
Klemenc
,
J.
, and
Fajdiga
,
M.
, 2001, “
Parametric Modelling and Scatter Prediction of Rainflow Matrices
,”
Int. J. Fatigue
,
23
(
6
), pp.
525
532
.
4.
Shen
,
H.
,
Lin
,
J.
, and
Mu
,
E.
, 2000, “
Probabilistic Model on Stochastic Fatigue Damage
,”
Int. J. Fatigue
,
22
(
7
), pp.
569
572
.
5.
Tovo
,
R.
, 2001, “
On the Fatigue Reliability Evaluation of Structural Components Under Service Loading
,”
Int. J. Fatigue
,
23
(
7
), pp.
587
598
.
6.
Zhao
,
Y. X.
,
Yang
,
B.
, and
Zhai
,
Z. Y.
, 2008, “
The Framework for a Strain-Based Fatigue Reliability Analysis
,”
Int. J. Fatigue
,
30
(
3
), pp.
493
501
.
7.
Spoormaker
,
J. L.
, 1996, “
The Role of Polymer Engineering in Designing for Reliability of Plastic Products
,”
Mater. Sci.
,
32
(
4
), pp.
396
402
.
8.
Bernasconi
,
A.
,
Davoli
,
P.
,
Basile
,
A.
, and
Filippi
,
A.
, 2007, “
Effect of Fibre Orientation on the Fatigue Behaviour of a Short Glass Fibre Reinforced Polyamide-6
,”
Int. J. Fatigue
,
29
, pp.
199
208
.
9.
McCrum
,
N. G.
,
Buckley
,
C. P.
, and
Bucknall
,
C. B.
, 1988,
Principles of Polymer Engineering
, 2nd ed.,
Oxford Science Publications
,
New York
.
10.
Tsang
,
K. Y.
,
DuQuesnay
,
D. L.
, and
Bates
,
P. J.
, 2008, “
Fatigue Properties of Vibration-Welded Nylon 6 and Nylon 66 Reinforced With Glass Fibres
,”
Composites, Part B
,
39
, pp.
396
404
.
11.
Zupancic
,
B.
,
Nikonov
,
A. V.
,
Florjancic
,
U.
, and
Emri
,
I.
, 2007, “
Time-Dependent Behaviour of Drive Belts Under Periodic Mechanical Loading: Analysis of the Location of a Single Line Spectrum
,”
J. Mech. Eng.
,
53
(
10
), pp.
696
705
.
12.
Zupancic
,
B.
, and
Emri
,
I.
, 2009, “
Time-Dependent Constitutive Modelling of Drive Belts – II. The Effect of the Shape of Material Retardation Spectrum on the Strain Accumulation Process
,”
Mech. Time-Depend. Mater.
,
13
, pp.
375
400
.
13.
Wyzgoski
,
M. G.
,
Krohn
,
J. A.
, and
Novak
,
G. E.
, 2004, “
Fatigue of Fiber-Reinforced Injection Molded Plastics I: Stress-Lifetime Data
,”
Polym. Compos.
,
25
(
5
), pp.
489
498
.
14.
Crawford
,
R. J.
, 1998,
Plastic Engineering
, 3rd ed.,
Butterworth-Heinemann
,
Oxford
.
15.
Moet
,
A.
, and
Aglan
,
H.
1988,
Fatigue Failure, Engineered Materials Handbook
, Vol.
2
, Engineering Plastics,
ASM International
.
16.
Ward
,
I. M.
, and
Hadley
,
D. W.
, 1997,
An Introduction to the Mechanical Properties of Solid
,
John Willey & Sons
,
New York
.
17.
DuPont Engineering Polymers: DuPont Minlon and Zytel naylon resins
:
Design information—Module II
.
DuPont Company
, 2002.
18.
Wyzgoski
,
M. G.
,
Krohn
,
J. A.
, and
Novak
,
G. E.
, 2004, “
Fatigue of Fibre-Reinforced Injection Molded Plastics II: Tensile Versus Flexural Loading
,”
Polym. Compos.
,
25
(
6
), pp.
569
576
.
19.
Crawford
,
R. J.
, and
Benhem
,
P. P.
, 1975, “
Some Fatigue Characteristics of Thermoplastics
,”
Polymer
,
16
, pp.
908
914
.
20.
Lee
,
J. A.
,
Almond
,
D. P.
, and
Harris
,
B.
, 1999, “
The Use of Neural Networks for the Prediction of Fatigue Lives of Composite Materials
,”
Composites, Part A
,
30
, pp.
1159
1169
.
21.
Vassilopoulos
,
A.
,
Georgopoulos
,
E.
, and
Keller
,
T.
, 2008, “
Comparison of Genetic Programming With Conventional Methods for Fatigue Life Modelling of FRP Composite Materials
,”
Int. J. Fatigue
,
30
(
9
), pp.
1634
1645
.
22.
Freire
,
S. J.
,
Carlos
,
R.
,
Neto
,
D.
,
De Aquino
,
A. D.
, and
Freire
,
E. M.
, 2009,
Comparative Study Between ANN Models and Equations in the Conventional Analysis of Fatigue Failure of GFRP
,”
Int. J. Fatigue
,
31
(
5
), pp.
831
839
.
23.
Al-Assadi
,
M.
,
El Kadi
,
H.
, and
Deiab
,
I. M.
, 2010, “
Predicting the Fatigue Life of Different Composite Materials Using Artificial Neural Networks
,”
Appl. Compos. Mater.
,
17
, pp.
1
14
.
24.
Agarwal
,
M.
, 1997, “
Combining Neural and Conventional Paradigms for Modelling, Prediction and Control
,”
Int. J. Syst. Sci.
,
28
(
1
), pp.
65
81
.
25.
Klemenc
,
J.
, and
Fajdiga
,
M.
, 2002, “
A Neural Network Approach to the Simulation of Load Histories by Considering the Influence of a Sequence of Rainflow Load Cycles
,”
Int. J. Fatigue
,
24
(
11
), pp.
1109
1125
.
26.
Klemenc
,
J.
, and
Fajdiga
,
M.
, 2004, “
An Improvement to the Methods for Estimating the Statistical Dependencies of the Parameters of Random Load States
,”
Int. J. Fatigue
,
26
(
2
), pp.
141
154
.
27.
Bucar
,
T.
,
Nagode
,
M.
, and
Fajdiga
,
M.
, 2006, “
A Neural Network Approach to Describing the Scatter of S-N Curves
,”
Int. J. Fatigue
,
28
(
4
), pp.
311
323
.
28.
Bucar
,
T.
,
Nagode
,
M.
, and
Fajdiga
,
M.
, 2007, “
An Improved Neural Computing Method for Describing the Scatter of S-N Curves
,”
Int. J. Fatigue
,
29
(
12
), pp.
2125
2137
.
29.
Janezic
,
M.
,
Klemenc
,
J.
, and
Fajdiga
,
M.
, 2010, “
A Neural-Network Approach to Describe the Scatter of Cyclic Stress-Strain Curves
,”
Mater. Des.
,
31
(
1
), pp.
438
448
.
30.
Fatigue and Tribological Properties of Plastics and Elastomers
,
Plastics Design Library
;
Norwich
, 1995.
31.
Buxbaum
,
O.
, 1992,
Betriebsfestigkeit: sichere und wirtschafliche Bemessung schwingbruchgefaehredeter Bauteile
,
Strahleisen
,
Duesseldorf
.
32.
Haibach
,
E.
, 1989,
Betriebsfestigkeit: Verfahren und Daten zur Bauteilerechnung
,
VDI Verlag
,
Duesseldorf
.
33.
Dowling
,
N. E.
, 1999,
Mechanical Behaviour of Materials: Engineering Methods for Deformation, Fracture, and Fatigue
,
Prentice-Hall
,
Upper Saddle River, NY
.
34.
Adkis
,
D. W.
, and
Kander
,
R. G.
, 1988, “
Fatigue Performance of Glass Reinforced Thermoplastics
,”
Proceedings of the 4th Annual Conference on Advanced Composites
, Vol.
4
, pp.
437
445
.
35.
Coffin
,
L. F.
, 1954, “
A Study of the Effects of Cyclic Thermal Stresses on a Ductile Material
,”
Trans. ASME
,
76
(
6
), pp.
931
950
.
36.
Manson
,
S. S.
, 1965, “
Fatigue: A Complex Subject—Some Simple Approximations
,”
Exp. Mech.
,
5
(
7
), pp.
193
226
.
37.
Haykin
,
S.
, 1994,
Neural Networks, a Comprehensive Foundation
,
Macmillan College
,
New York
.
38.
Press
,
W. H.
, 1988,
Numerical Recipes in C
,
Cambridge University, Cambridge
.
39.
Bishop
,
C. M.
, 1995
Neural Networks for Pattern Recognition
,
Clarendon, Oxford
.
40.
Akaike
,
H.
, 1974, “
A New Look at the Statistical Model Identification
,”
IEEE Trans. Autom. Control
,
19
(
6
), pp.
716
723
.
41.
Burnham
,
K. P.
, and
Anderson
,
D. R.
,
Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach
, 2nd ed.,
Springer-Verlag
,
Berlin
, 2002.
42.
McQuarrie
,
A. D. R.
, and
Tsai
,
C. L.
, 1998,
Regression and Time Series Model Selection World Scientific
.
43.
Hastie
,
T.
,
Tibshirani
,
R.
,
Friedman
,
J.
, 2001,
The Elements of Statistical Learning: Data Mining, Inference and Prediction
,
Springer-Verlag
,
New York
.
44.
Cochran
,
W. G.
, 1977,
Sampling Techniques
, 3rd ed.,
John Wiley & Sons
,
New York
.
45.
Cohen
,
A. C.
, 1965, “
Maximum Likelihood Estimation in the Weibull Distribution Based on Complete and on Censored Samples
,”
Technometrics
,
7
(
4
), pp.
579
588
.
46.
Todorovski
,
L.
,
Ljubic
,
P.
, and
Dzeroski
,
S.
, 2004, “
Inducing Polynomial Equations for Regression
,”
Proceedings of the 15th European Conference on Machine Learning ECML 2004
(Lecture Notes in Computer Science, Lecture Notes in Artificial Intelligence, Vol.
3201
).
Berlin
, pp.
441
452
.
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