Fatigue analysis of a simply supported composite plate with laminate configuration of [0n/90n]s under central patch impulse loading is presented using an analytical method. The method mainly consists of two steps, one, evaluation of vibration induced stresses for the given central patch impulse loading using modal analysis, and two, fatigue analysis using S–N curve approach, residual strength approach as well as failure function approach. The stress state in the plate was evaluated using viscous damping model as a function of time. The stress-time history was converted into block loading consisting of many sub-blocks. In the present study, the block loading consisted of four sub-blocks and a total of 175 numbers of cycles. The block loading was repeated after every 5 s. Next, fatigue analysis was carried out based on the block loading condition evaluated. Number of loading blocks for fatigue failure initiation and the location of failure were obtained. Studies were also carried out using two-dimensional (2D) finite element analysis (FEA). Number of loading blocks required to cause fatigue failure initiation under central patch impulse loading was found to be 3120 and 3170 using the analytical method and 2D FEA, respectively.
Issue Section:
Technical Brief
Keywords:
Fatigue
References
1.
Jayaprakash
, K.
, Desai
, Y. M.
, and Naik
, N. K.
, 2013
, “Fatigue Behavior of [0n/90n]s Composite Cantilever Beam Under Tip Impulse Loading
,” Compos. Struct.
, 99
, pp. 255
–263
.10.1016/j.compstruct.2012.12.0092.
Singh
, M. P.
, and Abdelnaser
, A. S.
, 1992
, “Random Response of Symmetric Cross-Ply Composite Beams With Arbitrary Boundary Conditions
,” AIAA J.
, 30
(4
), pp. 1081
–1088
.10.2514/3.110303.
Kwon
, Y. W.
, and Aygunes
, H.
, 1996
, “Dynamic Finite Element Analysis of Laminated Beam With Delamination Cracks Using Contact Impact Conditions
,” Compos. Struct.
, 58
(6
), pp. 1161
–1169
.10.1016/0045-7949(95)00202-24.
Kadivar
, M. H.
, and Mohebpour
, S. R.
, 1998
, “Finite Element Dynamic Analysis of Unsymmetric Composite Laminated Beams With Shear Effect and Rotary Inertia Under the Action of Moving Loads
,” Finite Elem. Anal. Design
, 29
(3–4
), pp. 259
–273
.10.1016/S0168-874X(98)00024-95.
Zibdeh
, H. S.
, and Abu-Hilal
, M.
, 2003
, “Stochastic Vibration of Laminated Composite Coated Beam Traversed by a Random Moving Load
,” Eng. Struct.
, 25
(3
), pp. 397
–404
.10.1016/S0141-0296(02)00181-56.
Ganesan
, R.
, and Kowda
, V. K.
, 2005
, “Free-Vibration of Composite Beam-Columns With Stochastic Material and Geometric Properties Subjected to Random Axial Loads
,” J. Reinf. Plast. Comp.
, 24
(1
), pp. 69
–91
.10.1177/07316844050429517.
Pandit
, M. K.
, Haldar
, S.
, and Mukopadhyay
, M.
, 2007
, “Free Vibration Analysis of Laminated Composite Rectangular Plate Using Finite Element Method
,” J. Reinf. Plast. Compos.
, 26
(1
), pp. 69
–80
.10.1177/07316844070699558.
Dai
, X. J.
, Lin
, J. H.
, Chen
, H. R.
, and Williams
, F. W.
, 2008
, “Random Vibration of Composite Structures With an Attached Frequency-Dependent Damping Layer
,” Compos., Part B
, 39
(2
), pp. 403
–413
.10.1016/j.compositesb.2007.01.0069.
Liu
, G. R.
, Zhao
, X.
, Dai
, K. Y.
, Zhong
, Z. H.
, Li
, G. Y.
, and Han
, X.
, 2008
, “Static and Free Vibration Analysis of Laminated Composite Plates Using the Conforming Radial Point Interpolation Method
,” Compos. Sci. Technol.
, 68
(2
), pp. 354
–366
.10.1016/j.compscitech.2007.07.01410.
Shaker
, A.
, Abdelrahman
, W. G.
, Tawfik
, M.
, and Sadek
, E.
, 2008
, “Stochastic Finite Element Analysis of the Free Vibration of Laminated Composite Plates
,” Comput. Mech.
, 41
(4
), pp. 493
–501
.10.1007/s00466-007-0205-711.
Kiral
, Z.
, 2009
, “Dynamic Response of Symmetric Laminated Composite Beams to Moving Load With Different Boundary Conditions
,” J. Reinf. Plast. Comp.
, 28
(20
), pp. 2511
–2526
.10.1177/073168440809240112.
Rezwani
, M. J.
, Kargarnovin
, M. H.
, and Younesian
, D.
, 2011
, “Dynamic Analysis of Composite Beam Subjected to Harmonic Moving Load Based on the Third Order Shear Deformation Theory
,” Front. Mech. Eng.
, 6
(4
), pp. 409
–418
.10.1007/s11465-011-0245-813.
Kahya
, V.
, 2012
, “Dynamic Analysis of Laminated Composite Beams Under Moving Loads Using Finite Element Method
,” Nucl. Eng. Des.
, 243
, pp. 41
–48
.10.1016/j.nucengdes.2011.12.01514.
Shen
, X.
, Lan
, J.
, Yang
, X.
, and Ji
, F.
, 2012
, “Modal Analysis of Laminated Composite Beam Based on Elastic Wave Theory
,” Appl. Mech. Mater.
, 151
, pp. 275
–280
.10.4028/www.scientific.net/AMM.151.27515.
Zhu
, P.
, Lei
, Z. X.
, and Liew
, K. M.
, “Static and Free Vibration Analyses of Carbon Nanotube-Reinforced Composite Plates Using Finite Element Method With First Order Shear Deformation Plate Theory
,” Compos. Struct.
, 94
(4
), pp. 1450
–1460
.10.1016/j.compstruct.2011.11.01016.
Li
, D.
, Liu
, Y.
, and Zhang
, X.
, 2013
, “A Layerwise/Solid-Element Method of the Linear Static and Free Vibration Analysis for the Composite Sandwich Plates
,” Compos. Part B
, 52
, pp. 187
–198
.10.1016/j.compositesb.2013.04.03117.
Boscolo
, M.
, 2013
, “Analytical Solution for Free Vibration Analysis of Composite Plates With Layer-Wise Displacement Assumptions
,” Compos. Struct.
, 100
, pp. 493
–510
.10.1016/j.compstruct.2013.01.01518.
Roy
, P. K.
, and Ganesan
, N.
, 1995
, “Transient Response of a Cantilever Beam Subjected to an Impulse Load
,” J. Sound Vib.
, 183
(5
), pp. 873
–880
.10.1006/jsvi.1995.029119.
Didyk
, R. P.
, and Masakovskii
, E. A.
, 1999
, “Investigation of Field of Dynamic Stress With Impulse Loading
,” Int. Appl. Mech.
, 35
(2
), pp. 170
–174
.10.1007/BF0268215120.
de la Fuente
, E.
, 2009
, “Von Mises Stresses in Random Vibration of Linear Structures
,” Comput. Struct.
, 87
(21–22
), pp. 1253
–1262
.10.1016/j.compstruc.2009.06.00821.
Broutman
, L. J.
, and Sahu
, S.
, 1972
, “A New Theory to Predict Cumulative Fatigue Damage in Fiberglass Reinforced Plastics
,” 2nd Conference on Composite Materials: Testing and Design, Anaheim, CA, Apr. 20–22, American Society for Testing and Materials, West Conshohocken, PA, ASTM
STP 497, Vol. 2
, pp. 170
–188
.10.1520/STP27746S22.
Hashin
, Z.
, and Rotem
, A.
, 1978
, “A Cumulative Damage Theory of Fatigue Failure
,” J. Mater. Sci. Eng.
, 34
(2
), pp. 147
–160
.10.1016/0025-5416(78)90045-923.
Wang
, A. S. D.
, Chou
, P. C.
, and Alper
, J.
, 1981
, “Effect of Proof Test on the Strength and Fatigue Life of a Unidirectional Composite
,” Fatigue of Fibrous Composite Materials, San Francisco, May 22-23, American Society for Testing and Materials, West Conshohocken, PA, ASTM
STP 723, pp.116
–132
.10.1520/STP27617S24.
Rotem
, A.
, and Nelson
, H. G.
, 1989
, “Failure of a Laminated Composite Under Tension-Compression Fatigue Loading
,” Compos. Sci. Tech.
, 36
(1
), pp. 45
–62
.10.1016/0266-3538(89)90015-825.
Sendeckyj
, G. P.
, 1991
, “Life Prediction for Resin Matrix Composite Materials
,” Fatigue of Composite Materials
, K. L.
Reifsnider
, ed., Elsevier
, Amsterdam
, pp. 431
–483
.26.
Otani
, N.
, and Song
, D. Y.
, 1997
, “Fatigue Life Prediction of Composites Under Two Stage Loading
,” J. Mater. Sci.
, 32
(3
), pp. 755
–760
.10.1023/A:101856042388927.
Schaff
, J. R.
, and Davidson
, B. D.
, 1997
, “Life Prediction Methodology for Composite Structures. Part 1—Constant Amplitude and Two-Stress Level Fatigue
,” J. Compos. Mater.
, 31
(2
), pp. 128
–157
.10.1177/00219983970310020228.
Schaff
, J. R.
, and Davidson
, B. D.
, 1997
, “Life Prediction Methodology for Composite Structures. Part II—Spectrum Fatigue
,” J. Compos. Mater.
, 31
(2
), pp. 158
–181
.10.1177/00219983970310020329.
Jen
, M. H. R.
, and Lee
, C. H.
, 1998
, “Strength and Life in Thermoplastic Composite Laminates Under Static and Fatigue Loads, Part II: Formulation
,” Int. J. Fatigue
, 20
(9
), pp. 617
–629
.10.1016/S0142-1123(98)00030-930.
Abousalleh
, M.
, and Boukhili
, R.
, 1998
, “Life Prediction for Composite Laminates Submitted to Service Loading Spectra
,” Polym. Compos.
, 19
(3
), pp. 241
–245
.10.1002/pc.1009631.
Barron
, V.
, Buggy
, M.
, and McKenna
, N. H.
, 2001
, “Frequency Effects on the Fatigue Behaviour on Carbon Fibre Reinforced Polymer Laminates
,” J. Mater. Sci.
, 36
(7), pp. 1755
–1761
.10.1023/A:101757672588532.
Philippidis
, T. P.
, and Vassilopoulos
, A. P.
, 2002
, “Complex Stress State Effect on Fatigue Life of GRP Laminates. Part II, Theoretical Formulation
,” Int. J. Fatigue
, 24
(8
), pp. 825
–830
.10.1016/S0142-1123(02)00004-X33.
Found
, M. S.
, and Quaresimin
, M.
, 2003
, “Two-Stage Loading of Woven Carbon Fibre Reinforced Laminates
,” Fatigue Fract. Eng. Mater. Struct.
, 26
(1
), pp. 17
–26
.10.1046/j.1460-2695.2003.00583.x34.
Epaarachchi
, J. A.
, and Clausen
, P. D.
, 2003
, “An Empirical Model for Fatigue Behaviour Prediction of Glass Fibre Reinforced Plastic Composites for Various Stress Ratios and Test Frequencies
,” Compos. Part A
, 34
(4
), pp. 313
–326
.10.1016/S1359-835X(03)00052-635.
Epaarachchi
, J. A.
, and Clausen
, P. D.
, 2005
, “A New Cumulative Fatigue Damage Model for Glass Fibre Reinforced Plastic Composites Under Step/Discrete Loading
,” Compos. Part A
, 36
(9
), pp. 1236
–1245
.10.1016/j.compositesa.2005.01.02136.
Mohandesi
, A. J.
, and Majidi
, B.
, 2009
, “Fatigue Damage Accumulation in Carbon/Epoxy Laminated Composites
,” Mater. Des.
, 30
(6
), pp. 1950
–1956
.10.1016/j.matdes.2008.09.01237.
Quaresimin
, M.
, Susmel
, L.
, and Talreja
, R.
, 2010
, “Fatigue Behaviour and Life Assessment of Composite Laminates Under Multiaxial Loadings
,” Int. J. Fatigue
, 32
(1
), pp. 2
–16
.10.1016/j.ijfatigue.2009.02.01238.
Passipoularidis
, V. A.
, Philippidis
, T. P.
, and Brondsted
, P.
, 2011
, “Fatigue Life Prediction in Composites Using Progressive Damage Modeling Under Block and Spectrum Loading
,” Int. J. Fatigue
, 33
(2
), pp. 132
–144
.10.1016/j.ijfatigue.2010.07.01139.
Mikitarenko
, M. A.
, and Perelmuter
, A. V.
, 1998
, “Safe Fatigue Life of Wind Towers Under the Action of Wind Vibrations
,” J. Wind Eng. Ind. Aerodyn.
, 74–76
, pp. 1091
–1100
.10.1016/S0167-6105(98)00100-740.
Liu
, X.
, Sooklal
, V. K.
, Verges
, M. A.
, and Larson
, M. C.
, 2006
, “Experimental Study and Life Prediction on High Cycle Vibration Fatigue in BGA Packages
,” Microelectron. Reliab.
, 46
(7
), pp. 1128
–1138
.10.1016/j.microrel.2005.09.01141.
Gupta
, S.
, Shabakhty
, N.
, and Gelder
, P. V.
, 2006
, “Fatigue Damage in Randomly Vibrating Jack-Up Platforms Under Non-Gaussian Loads
,” Appl. Ocean Res.
, 28
(6
), pp. 407
–419
.10.1016/j.apor.2007.02.00142.
Lau
, Y. L.
, Leung
, R. K. C.
, and So
, R. M. C.
, 2007
, “Vortex-Induced Vibration Effect on Fatigue Life Estimate of Turbine Blades
,” J Sound Vib
, 307
(3–5
), pp. 698
–719
.10.1016/j.jsv.2007.06.02943.
Celik
, M.
, and Genc
, C.
, 2007
, “Mechanical Fatigue of an Electronic Component Under Random Vibration
,” Fatigue Fract. Eng. Mater. Struct.
, 31
(7
), pp. 505
–516
.10.1111/j.1460-2695.2008.01227.x44.
Chen
, Y. S.
, Wang
, C. S.
, and Yang
, Y. J.
, 2008
, “Combining Vibration Test With Finite Element Analysis for the Fatigue Life Estimation of PBGA Components
,” Microelectron. Reliab.
, 48
(4
), pp. 638
–644
.10.1016/j.microrel.2007.11.00645.
Aykan
, M.
, and Celik
, M.
, 2009
, “Vibration Fatigue Analysis and Multi-Axial Effect in Testing of Aerospace Structures
,” Mech. Syst. Signal Process
, 23
(3
), pp. 897
–907
.10.1016/j.ymssp.2008.08.00646.
Mittal
, R.
, Singh
, P. K.
, Pukazhendi
, D. M.
, Bhasin
, V.
, Vaze
, K. K.
, and Ghosh
, A. K.
, 2011
, “Effect of Vibration Loading on the Fatigue Life of Part-Through Notched Pipe
,” Int. J. Press. Vessels Pip.
, 88
(10
), pp. 415
–422
.10.1016/j.ijpvp.2011.07.00447.
Jung
, D. H.
, and Gafurov
, A.
, 2011
, “Reliability Achievement of the Driving System Parts Through Development of Vibration-Fatigue Evaluation Method
,” Procedia Eng
, 10
, pp. 1906
–1916
.10.1016/j.proeng.2011.04.31748.
Yu
, D.
, Al-Yafawi
, A.
, Nguyen
, T. T.
, Park
, S.
, and Chung
, S.
, 2011
, “High-Cycle Fatigue Life Prediction for Pb-Free BGA Under Random Vibration Loading
,” Microelectron. Reliab.
, 51
(3
), pp. 649
–656
.10.1016/j.microrel.2010.10.00349.
Reddy
, J. N.
, 1999
, Theory and Analysis of Elastic Plates and Shells
, 2nd ed., CRC Press
, New York
.50.
ANSYS, 2010, Release 13.0 Documentation for ansys
, ANSYS Inc., Canonsburg, PA.51.
Tan
, S. C.
, 1988
, “Effective Stress Fracture Models for Unnotched and Notched Multidirectional Laminate
,” J. Compos. Mater.
, 22
(4
), pp. 322
–340
.10.1177/00219983880220040252.
Tan
, S. C.
, 1994
, Stress Concentration in Laminated Composites
, Technomic Publishing
, Lancaster, PA
.53.
Vinayak
, B. G.
, Jayaprakash
, K.
, and Naik
, N. K.
, 2012
, “Fatigue Behavior of Laminated Composites With a Circular Hole Under In-Plane Uniaxial Random Loading
,” Mater. Des.
, 40
, pp. 245
–256
.10.1016/j.matdes.2012.03.04454.
Satapathy
, M. R.
, Vinayak
, B. G.
, Jayaprakash
, K.
, and Naik
, N. K.
, 2013
, “Fatigue Behavior of Laminated Composites With a Circular Hole Under In-Plane Multiaxial Loading
,” Mater. Des.
, 51
, pp. 347
–356
.10.1016/j.matdes.2013.04.04055.
Moreira
, A.
, 2007
, “Characterization and Dynamic Analysis of Damping Effects in Composite Materials for High-Speed Flywheel Applications
,” Ph.D. thesis, Auburn University, Auburn, AL.56.
Petyt
, M.
, 1990
, Introduction to Finite Element Vibration Analysis
, Cambridge University Press
, Cambridge, UK, pp. 357
–361
.Copyright © 2015 by ASME
You do not currently have access to this content.
