Reliability based design methodology incorporating residual strength prediction of structural fiber reinforced polymer composites under stochastic variable amplitude fatigue loading

The research presented in this dissertation furthers the state of the art for reliability-based design of composite structures subjected to high cycle variable amplitude (spectrum) fatigue loads. The focus is on fatigue analyses for axially loaded fiber reinforced polymer (FRP) composites that contain a significant proportion of fibers in the loading direction and thus have fiber-direction dominated failure. The four papers presented in this dissertation describe the logical progression used to develop an improved reliability-based methodology for fatiguecritical design. Throughout the analysis extensive experimental fatigue data on several material systems was used to verify the assumptions and suggest the path forward. A comparison of 12 fatigue model approaches from the literature showed that a simple linear residual strength approach (Broutman and Sahu) provides an improvement in fatigue life prediction compared to the Palmgren-Miner rule, while more complex residual strength models did not consistently improve on Broutman and Sahu. Evaluation of the effect of load history randomness on fatigue life was made using experimental results for spectra in terms of the first order autocorrelation of the stress events. For approximately reversed Rayleigh distributed fatigue loading, load sequence was not critical in the material behavior. Based on observations of empirical data and evaluation of the micro-mechanics deterioration and failure phenomena of FRP composites under fatigue loading, a new residual strength model for the tension and compression under any load history was proposed. Then this model was implemented in a stochastic framework and a method was proposed to enable calculation of the load and resistance factor design (LRFD) parameters for realistic reliabilities with relatively few computations. The proposed approach has significant advantages over traditional lifetime-damage-sum-based reliability analysis and provides a significant step toward enabling more accurate reliability-based design with composite materials. This research was conducted with support from the National Science Foundation Interdisciplinary Graduate Education Research and Traineeship (Award # DGE-0114346) and the Office of Naval Research (Award # N00014-06-1-0812). Note: The opinions expressed herein are the views of the author and should not be interpreted as the views of the Naval Surface Warfare Center or the Department of the Navy, nor of the National Science Foundation.

[1]  Paul Miller,et al.  Fatigue Prediction Verification of Fiberglass Hulls , 2001 .

[2]  Herbert J. Sutherland.  Fatigue case study and loading spectra for wind turbines , 1994 .

[3]  R. K. Miller,et al.  Effect of High Load on Statistical Fatigue of Unnotched Graphite/Epoxy Laminates* , 1980 .

[4]  Thomas Svensson.  Prediction uncertainties at variable amplitude fatigue , 1997 .

[5]  Shiv P. Joshi,et al.  Long-Term Strength and Damage Analysis of Laminated Composites , 1997 .

[6]  Steven R. Winterstein,et al.  Load models for fatigue reliability from limited data , 1996 .

[7]  Lj Broutman,et al.  A New Theory to Predict Cumulative Fatigue Damage in Fiberglass Reinforced Plastics , 1972 .

[8]  Z. Hashin,et al.  A CUMULATIVE DAMAGE THEORY OF FATIGUE FAILURE , 1978 .

[9]  A. A. Ten Have.  WISPER and WISPERX Final definition of two standardised fatigue loading sequences for wind turbine blades , 1992 .

[10]  Theodore V. Galambos,et al.  Probability-based criteria for structural design , 1982 .

[11]  Larry Lessard,et al.  Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling , 2000 .

[12]  R Sunder,et al.  Spectrum load fatigue—underlying mechanisms and their significance in testing and analysis , 2003 .

[13]  Shahram Sarkani,et al.  Closure of "Fatigue Experiments for Welded Joints Under Pseudo-Narrowband Loads" , 1988 .

[14]  Herbert J. Sutherland,et al.  EFFECTS OF CYCLIC STRESS DISTRIBUTION MODELS ON FATIGUE LIFE PREDICTIONS , 1994 .

[15]  M. Owen,et al.  The accumulation of damage in a glass-reinforced plastic under tensile and fatigue loading , 1972 .

[16]  W. Van Paepegem,et al.  Coupled Residual Stiffness and Strength Model for Fatigue of Fibre-reinforced Composite Materials , 2002 .

[17]  John F. Mandell,et al.  Spectrum Fatigue Lifetime and Residual Strength for Fiberglass Laminates , 2002 .

[18]  Shahram Sarkani,et al.  Stochastic fatigue damage accumulation under broadband loadings , 1995 .

[19]  John F. Mandell,et al.  Fatigue of fiberglass wind turbine blade materials , 1992 .

[20]  Zvi Hashin,et al.  Cumulative damage theory for composite materials: Residual life and residual strength methods , 1985 .

[21]  R. Brook,et al.  Cumulative Damage in Fatigue: A Step towards Its Understanding , 1969 .

[22]  W. Van Paepegem,et al.  A new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites , 2002 .

[23]  Larry Lessard,et al.  Progressive Fatigue Damage Modeling of Composite Materials, Part II: Material Characterization and Model Verification , 2000 .

[24]  Ho Sung Kim,et al.  Fatigue Damage and Life Prediction of Glass/Vinyl Ester Composites , 2001 .

[25]  W. Hwang,et al.  Statistical study of strength and fatigue life of composite materials , 1987 .

[26]  John J. Lesko,et al.  Modeling the remaining strength of structural composite materials subjected to fatigue , 2006 .

[27]  Pc Chou,et al.  Degradation and Sudden-Death Models of Fatigue of Graphite/Epoxy Composites , 1979 .

[28]  Yuris A. Dzenis,et al.  Cycle-based analysis of damage and failure in advanced composites under fatigue: 1. Experimental observation of damage development within loading cycles , 2003 .

[29]  W. Hwang,et al.  Cumulative Damage Models and Multi-Stress Fatigue Life Prediction , 1986 .

[30]  Barry D. Davidson,et al.  Life Prediction Methodology for Composite Structures. Part I—Constant Amplitude and Two-Stress Level Fatigue , 1997 .

[31]  J. Whitney,et al.  Fatigue Characterization of Composite Materials , 1979 .

[32]  Yiu-Wing Mai,et al.  Statistical prediction of fatigue failure of fibre reinforced composite materials , 1995 .

[33]  Ali Fatemi,et al.  Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials , 1998 .

[34]  Richard M. Christensen,et al.  Stress Intensity Controlled Kinetic Crack Growth and Stress History Dependent Life Prediction with Statistical Variability , 2006 .

[35]  Shiv P. Joshi,et al.  Behavior of laminated composites under monotonically increasing random load , 1993 .

[36]  C. Allin Cornell,et al.  Probability Based Load Criteria: Assessment of Current Design Practice , 1982 .

[37]  Shanyi Du,et al.  An Exploratory Study Into the Fatigue of Composites Under Spectrum Loading , 1983 .

[38]  Anastasios P. Vassilopoulos,et al.  Life prediction methodology for GFRP laminates under spectrum loading , 2004 .

[39]  Ming-Hwa R. Jen,et al.  Fatigue damage in a centrally notched composite laminate due to two-step spectrum loading , 1994 .

[40]  Konstantinos Tserpes,et al.  Modelling of fatigue damage progression and life of CFRP laminates , 2003 .

[41]  L Wenge.  Fatigue Life Prediction Under Complex Loading , 1996 .

[42]  Daoli Chen.  New approaches to the estimation of cumulative fatigue reliability , 1991 .

[43]  W. Weibull.  A statistical theory of the strength of materials , 1939 .

[44]  Joakim Schön,et al.  Fatigue life prediction and load cycle elimination during spectrum loading of composites , 2002 .

[45]  Ian P Bond,et al.  Fatigue life prediction for GRP subjected to variable amplitude loading , 1999 .

[46]  Efstratios F. Georgopoulos,et al.  Artificial neural networks in spectrum fatigue life prediction of composite materials , 2007 .

[47]  J. N. Yang,et al.  Prediction of fatigue life for matrix-dominated composite laminates , 1993 .

[48]  B. Lee,et al.  Cumulative Damage of Fiber-Reinforced Elastomer Composites under Fatigue Loading , 1994 .

[49]  Ming-Hwa R. Jen,et al.  Fatigue Response and Modelling of Variable Stress Amplitude and Frequency in AS-4/PEEK Composite Laminates, Part 2: Analysis and Formulation , 2000 .

[50]  A. Rotem,et al.  Residual strength after fatigue loading , 1988 .

[51]  T. Adam,et al.  Life prediction for fatigue of T800/5245 carbon-fibre composites: I. Constant-amplitude loading , 1994 .

[52]  Shahram Sarkani,et al.  A New Method for Predicting the Fatigue Life of Fiber-reinforced Plastic Laminates , 2006 .

[53]  J. N. Yang,et al.  Fatigue and Residual Strength Degradation for Graphite/Epoxy Composites Under Tension-Compression Cyclic Loadings , 1978 .

[54]  Jayantha Ananda Epaarachchi,et al.  A new cumulative fatigue damage model for glass fibre reinforced plastic composites under step/discrete loading , 2005 .

[55]  Steven R. Winterstein,et al.  Moment-based load and response models with wind engineering applications , 2000 .

[56]  Wei-Xing Yao,et al.  Statistical analysis of data from truncated fatigue life and corresponding residual strength experiments for polymer matrix composites , 1999 .

[57]  C. H. Lange,et al.  Fatigue design of wind turbine blades: Load and resistance factors from limited data , 1996 .

[58]  Bruce R. Ellingwood,et al.  LRFD: implementing structural reliability in professional practice , 2000 .

[59]  Darrell F. Socie,et al.  Simple rainflow counting algorithms , 1982 .

[60]  Kenneth Reifsnider,et al.  The critical element model: A modeling philosophy , 1986 .

[61]  R B Abernethy,et al.  Weibull Analysis Handbook , 1983 .

[62]  D. Schütz,et al.  Fatigue strength of a fibre-reinforced material , 1977 .

[63]  Jacob Aboudi,et al.  Micromechanics Prediction of Fatigue Failure of Composite Materials , 1989 .

[64]  Ian P Bond,et al.  Fatigue life prediction under complex loading for XAS/914 CFRP incorporating a mechanical fastener , 2000 .

[65]  H. Whitworth,et al.  Cumulative Damage in Composites , 1990 .

[66]  John J. Lesko,et al.  Residual strength prediction of composite materials: Random spectrum loading , 2008 .

[67]  Steven R. Winterstein,et al.  Application of Measured Loads to Wind Turbine Fatigue and Reliability Analysis , 1998 .

[68]  Philip Clausen,et al.  An empirical model for fatigue behavior prediction of glass fibre-reinforced plastic composites for various stress ratios and test frequencies , 2003 .

[69]  Douglas L. Jones,et al.  A Stiffness-Based Statistical Model for Predicting the Fatigue Life of Graphite/Epoxy Laminates , 1989 .

[70]  N. Otani,et al.  Fatigue life prediction of composites under two-stage loading , 1997 .

[71]  Siu-Tong Choi,et al.  A Study of Fatigue Damage and Fatigue Life of Composite Laminates , 1996 .

[72]  N. E. Dowling.  A Review of Fatigue Life Prediction Methods , 1987 .

[73]  C. H. Lange,et al.  Probabilistic fatigue methodology and wind turbine reliability , 1996 .

[74]  P. Qiao,et al.  Fatigue Life Prediction of Pultruded E-glass/Polyurethane Composites , 2006 .

[75]  H. Hahn,et al.  Proof Testing of Composite Materials , 1975 .

[76]  H. T. Hahn,et al.  Fatigue Behavior and Life Prediction of Composite Laminates , 1979 .

[77]  John F. Mandell,et al.  DOE/MSU composite material fatigue database: Test methods, materials, and analysis , 1997 .

[78]  A. Rotem,et al.  Residual Strength of Composite Laminates Subjected to Tensile-Compressive Fatigue Loading , 1990 .

[79]  Theodore P. Philippidis,et al.  Residual strength after fatigue in composites: Theory vs. experiment , 2007 .

[80]  Ming-Hwa R. Jen,et al.  Fatigue Response and Modelling of Variable Stress Amplitude and Frequency in AS-4/PEEK Composite Laminates, Part 1: Experiments , 2000 .

[81]  Herbert J. Sutherland,et al.  FREQUENCY-DOMAIN SYNTHESIS OF THE FATIGUE LOAD SPECTRUM FOR THE NPS 100-KW WIND TURBINE* , 1992 .

[82]  Richard M. Christensen,et al.  A Physically Based Cumulative Damage Formalism , 2008 .

[83]  Zheng-Ming Huang,et al.  Micromechanical modeling of fatigue strength of unidirectional fibrous composites , 2002 .

[84]  Shahram Sarkani,et al.  Stochastic Fatigue Damage Accumulation of FRP Laminates and Joints , 1999 .

[85]  Christopher M. Pastore,et al.  Stochastic damage evolution in textile laminates , 1993 .

[86]  J. N. Yang,et al.  Effect of Load Sequence on the Statistical Fatigue of Composites , 1980 .

[87]  Yuris A. Dzenis,et al.  Cycle-based analysis of damage and failure in advanced composites under fatigue: 2. Stochastic mesomechanics modeling , 2003 .

[88]  Rui Tang,et al.  An appropriate stiffness degradation parameter to monitor fatigue damage evolution in composites , 2004 .

[89]  Tonny Nyman,et al.  Effects of truncation and elimination on composite fatigue life , 2000 .

[90]  N Himmel,et al.  Fatigue life prediction of laminated polymer matrix composites , 2002 .

[91]  Kenneth Reifsnider,et al.  Fatigue of composite materials , 1991 .

[92]  Masayuki Nakada,et al.  Accelerated Testing for Long-term Durability of FRP Laminates for Marine Use , 2004 .

[93]  Travis A. Bogetti,et al.  Low Cycle Fatigue of Composite Laminates: A Damage-mode-sensitive Model , 2003 .

[94]  Jonathan D. Bartley-Cho,et al.  Damage accumulation in quasi-isotropic graphite/epoxy laminates under constant-amplitude fatigue and block loading , 1998 .

[95]  Douglas S. Cairns,et al.  EFFECTS OF MODELING ASSUMPTIONS ON THE ACCURACY OF SPECTRUM FATIGUE LIFETIME PREDICTIONS FOR A FIBERGLASS LAMINATE , 2002 .

[96]  Ne Dowling,et al.  Fatigue Failure Predictions for Complicated Stress-Strain Histories , 1971 .

[97]  Jie Zhao,et al.  A practical approach for predicting fatigue reliability under random cyclic loading , 1995 .

[98]  Cetin Morris Sonsino,et al.  Fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments , 2008 .

[99]  A. M. van Wingerde,et al.  Alternative fatigue lifetime prediction formulations for variable amplitude loading , 2002 .

[100]  T. Adam,et al.  A Power Law Fatigue Damage Model for Fibre-Reinforced Plastic Laminates , 1986 .

[101]  John F. Mandell,et al.  Strength Degradation and Simple Load Spectrum Tests in Rotor Blade Composites , 2005 .

[102]  H. Whitworth,et al.  Modeling Stiffness Reduction of Graphite/Epoxy Composite Laminates , 1987 .

[103]  John F. Mandell,et al.  New Fatigue Data for Wind Turbine Blade Materials , 2003 .

[104]  Shahram Sarkani.  FEASIBILITY OF AUTO-REGRESSIVE SIMULATION MODEL FOR FATIGUE STUDIES , 1990 .

[105]  T. Adam,et al.  Fatigue of carbon-fibre-reinforced plastics under block-loading conditions , 1997 .

[106]  Steven R. Winterstein,et al.  Effect of Load Models and Limited Data on Load and Resistance Factors for Fatigue Design , 1996 .

[107]  Hiroshi Noguchi,et al.  On the cumulative fatigue damage in short carbon fiber reinforced poly-ether-ether-ketone , 1995 .

[108]  I.A. Assakkaf,et al.  Reliability-based design of doubler plates for ship structures , 2003, Fourth International Symposium on Uncertainty Modeling and Analysis, 2003. ISUMA 2003..

[109]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[110]  Kenneth Reifsnider,et al.  A micromechanics model for composites under fatigue loading , 1991 .

[111]  M. Ichikawa.  An extension of the reliability-based design method for variable amplitude fatigue , 1987 .

[112]  J.N. Yang,et al.  Residual Strength Degradation Model and Theory of Periodic Proof Tests for Graphite/Epoxy Laminates* , 1977 .

[113]  A Murty,et al.  A new approach to fatigue strength distribution for fatigue reliability evaluation , 1995 .

[114]  Marcin Kamiński,et al.  On probabilistic fatigue models for composite materials , 2002 .

[115]  Isaac M Daniel,et al.  Modeling of fatigue damage in a polymer matrix composite , 2003 .

[116]  N. Himmel,et al.  A new cumulative fatigue damage model for fibre-reinforced plastics , 2000 .

[117]  Paraskevas Papanikos,et al.  Non‐destructive fatigue damage characterization of laminated thermosetting fibrous composites , 2001 .

[118]  Fernand Ellyin,et al.  A new methodology for the prediction of fatigue failure in multidirectional fiber-reinforced laminates , 1995 .

[119]  Zheng-Ming Huang,et al.  Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model , 2001 .

[120]  Kenneth Reifsnider,et al.  Fracture of fatigue-loaded composite laminates , 1982 .

[121]  Shahram Sarkani,et al.  Development and Application of a Model Using Center of Gravity of Hysteresis Loops to Predict Fatigue Damage Accumulation in Fiber-reinforced Plastic Laminates , 2005 .

[122]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[123]  Walter Musial,et al.  Trends in the Design, Manufacture and Evaluation of Wind Turbine Blades , 2003 .

[124]  Bruce R. Ellingwood,et al.  Toward Load and Resistance Factor Design for Fiber-Reinforced Polymer Composite Structures , 2003 .

[125]  Shahram Sarkani,et al.  Comparative Study of Nonlinear Damage Accumulation Models in Stochastic Fatigue of FRP Laminates , 2001 .

[126]  A. A. Ten Have,et al.  WISPER and WISPERX: A summary paper describing their backgrounds, derivation and statistics , 1992 .

[127]  Thomas Svensson,et al.  Fatigue life prediction based on variable amplitude tests—methodology , 2005 .

[128]  D. G. Robinson.  A survey of probabilistic methods used in reliability, risk and uncertainty analysis: Analytical techniques 1 , 1998 .

[129]  W. Hwang,et al.  Fatigue of Composites—Fatigue Modulus Concept and Life Prediction , 1986 .

[130]  Zheng-Ming Huang.  Fatigue life prediction of a woven fabric composite subjected to biaxial cyclic loads , 2002 .

[131]  Herbert J. Sutherland,et al.  On the Fatigue Analysis of Wind Turbines , 1999 .

[132]  Yasser Gowayed,et al.  Fatigue behavior of textile composite materials subjected to tension‐tension loads , 2001 .

[133]  Jayantha Ananda Epaarachchi.  A study on estimation of damage accumulation of glass fibre reinforce plastic (GFRP) composites under a block loading situation , 2006 .

[134]  R. Hertzberg,et al.  Fatigue of engineering plastics , 1980 .

[135]  Ian P Bond,et al.  Classical fatigue analysis and load cycle mix-event damage accumulation in fibre reinforced laminates , 2004 .

[136]  John J. Lesko,et al.  Modeling the variable amplitude fatigue of composite materials: A review and evaluation of the state of the art for spectrum loading , 2008 .

[137]  R. Boukhili,et al.  Life prediction for composite laminates submitted to service loading spectra , 1998 .

[138]  Steven R. Winterstein,et al.  Application of measured loads to wind turbine fatigue and reliability analysis , 1998 .

[139]  Douglas S. Cairns,et al.  Fatigue of Composite Materials and Substructures for Wind Turbine Blades , 2002 .

[140]  Douglas S. Cairns,et al.  SPECTRUM FATIGUE LIFETIME AND RESIDUAL STRENGTH FOR FIBERGLASS LAMINATES IN TENSION , 2001 .

[141]  Ramesh Talreja,et al.  A micromechanics based model for predicting fatigue life of composite laminates , 2000 .

[142]  M. Shinozuka.  Basic Analysis of Structural Safety , 1983 .

[143]  Marino Quaresimin,et al.  Two‐stage fatigue loading of woven carbon fibre reinforced laminates , 2003 .

[144]  Robert Croman,et al.  Residual Strength in Fatigue Based on the Strength-Life Equal Rank Assumption , 1978 .

[145]  Kenneth Reifsnider,et al.  A Critical-Element Model of the Residual Strength and Life of Fatigue-Loaded Composite Coupons , 1986 .

[146]  W. Van Paepegem,et al.  Effects of Load Sequence and Block Loading on the Fatigue Response of Fiber-Reinforced Composites , 2002 .

[147]  Joakim Schön.  Spectrum fatigue loading of composite bolted joints—small cycle elimination , 2006 .

[148]  E. K. Gamstedt,et al.  An experimental investigation of the sequence effect in block amplitude loading of cross-ply composite laminates , 2002 .

[149]  James C. Seferis,et al.  Modeling of tensile fatigue damage in resin transfer molded woven carbon fabric composites , 2002 .