臺灣博碩士論文加值系統

本研究之要旨在探討二階段疲勞負載之調整對複合積層板動態可靠度之影響。本研究主要有四部分。首先，在經過驗證之後，確認以可靠度表示的失效率函數h(R)=eo+c(1-R)^p 稱為(eocp)模型可以有效的描述複合積層板受固定振幅循環應力作用下之動態可靠度。為了研究(eocp)模型對複合積層板受到疲勞負載調整下之特性，運用蒙地卡羅模擬，產生大量在各種負載情形下的疲勞失效資料。第二，基於強度與壽命同級假設定義二個參數-過渡期和可靠度驟降，此二個參數可以分別描述從高到低及從低到高調整疲勞負載對複合積層板可靠度退化之影響。第三，將(eocp)模型在一階段疲勞負載的應用擴展到二階段疲勞負載的情形，使用分段結合過渡期或可靠度驟降的方法來描述動態可靠度的全貌。經估算後發現，在負載從高調整到低的情形，線性累積損傷會大於1；從低到高的情形則會小於1。高階和低階應力的差距越大，則線性累積損傷偏離1的幅度也越大。最後，本研究提出另一個以可靠度表示之失效率函數h(R)=eg+u(-lnR)^q 稱為廣義Gompertz模型。由於此模型之內在缺陷參數eg可以描述材料受負載後之初始失效率，此模型比韋伯失效率函數更具物理意義，而且此模型之應用範圍可以涵蓋韋伯型失效率函數。

This thesis aims to investigate the effects of two-stage fatigue loading adjustment on the dynamical reliability of composite laminates. The major achievements can be divided into four parts. First, the proposed reliability-dependent hazard rate function h(R)=eo+c(1-R)^p named the (eocp) model is verified to be useful for describing the dynamical reliability of composites under constant-amplitude cyclic stress. A large amount of simulated fatigue data are generated to study the characteristics of the (eocp) model for composites subjected to fatigue loading adjustment. Secondly, based on the strength-life equal rank assumption, two parameters, the transition period and reliability drop, are defined to depict the effects of high-low and low-high adjustment, respectively, on the reliability degradation of composites. Thirdly, the application of the (eocp) model for single-stage fatigue loading is extended to two-stage cases, using a piecewise combination with transition period or reliability drop to show the whole picture of dynamical reliability. The linear damage sum is examined and found to be larger than unity for high-low loading, and on the contrary for low-high cases. Bigger the difference between the high and low level stresses results in the larger deviation from unity. Finally, another reliability-dependent hazard rate function h(R)=eg+u(-lnR)^q named generalized Gompertz model is proposed. The proposed model, with the intrinsic weakness parameter eg denoting the initial hazard rate of material under loading, has greater physical meaning than does the Weibull-type hazard rate function. Furthermore, the proposed model could be more flexible in describing the dynamical reliability than the Weibull function.

Contents
摘要..................................................................................................... i

Abstract.............................................................................................. ii

誌謝…................................................................................................. iii

Contents ............................................................................................ iv

List of Figures……………………………………………………… vii

List of Tables………………………………………………………. xi

Nomenclatures…………………………………………………….. xii

Chapter 1 Introduction ..………………………………………... 1
1.1 Classifications of Failure of Composite Laminates…………………… 3
1.2 Literature Survey about Composite Laminate Degradation………… 4
1.3 Literature Survey about Dynamical Reliability and the Models…….. 6
1.4 Basic Assumptions………………………………………………………. 13
1.5 Development of this Study……………….……………………………... 14

Chapter 2 Characteristics of a Hazard Rate Model for
Composites under Cyclic Stresses…………………..
21
2.1 Verification of Model with Experimental Data………………
21
2.2 Correlation between the Model and the S-N Equation………
25
2.3 Yang’s Equation of Residual Strength…………………………………. 29
2.4 Preparation of a Monte Carlo Simulation and its Verification……… 31
2.5 Results of Residual Strength Degradation…………………………….. 35
2.6 Characteristics of Model……………………………………….
36

Chapter 3 Effects of Loading Adjustment on the Reliability Degradation………………………………………….
55
3.1 Residual Strength Distribution under Loading Adjustment………… 55
3.2 Derivation of Transition Period and Reliability Drop………………... 56
3.2.1. Transition Period at the High-low Adjustment………………... 57
3.2.2. Reliability Drop at the Low-high Adjustment………………… 59
3.3 Simulation of Strength and Reliability Degradation………………….. 60
3.3.1. Strength Degradation…………………………………………… 60
3.3.2. Overview of Reliability Degradation…………………………... 62
3.4 Characteristics of Transition Period and Reliability Drop…………... 64

Chapter 4 Piecewise Combination of Hazard Rate Function Based on Model……………………………...
77
4.1 Modification of Parameter after High-low Adjustment…………
77
4.2 Piecewise Combined Hazard Rate Function…………………………... 80
4.3 Mean Fatigue Cycle and Linear Damage Sum………………………... 81
4.4 Results of Simulation…………………………………………………… 83

Chapter 5 Generalized Gompertz Model of Reliability-dependent Hazard Rate Function……..
101
5.1 An extension of hazard rate function for Weibull-type reliability…… 101
5.2 Verification with Simulated Data……………………………………… 108
5.3 Fit of the Model with Some Experimental data………………………. 110
Chapter 6 Conclusion…………………………………………… 129
References.......................................................................................... 133
Appendix............................................................................................ 141

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