Creep: Fatigue Models of Composites and Nanocomposites

Description

In recent years, the application of composites and nanocomposites has been increasing steadily in industries such as aerospace, automotive, marine, and civil engineering. It is among the most complex and crucial aspects of the mechanics of a deformable solid, due to several specific phenomena and analytic factors arising from cyclic loading. The problems are primarily associated with the development of fatigue damage, and the need to assess the cyclic and structural instability of composite and nanocomposite materials. The study of structural strength under cyclic loading has gained much attention, especially in aircraft manufacturing, power engineering, aviation, and rocket technology. Cyclic loading significantly reduces creep-fatigue lifespan during the entire frequency range. It is clear that characteristics such as endurance limit, static creep limits and long-term static strength will not suffice in the design criteria for fatigue life. New aspects have emerged in high-temperature strength - cyclical creep and long-term cyclic strength, leading to the creation of new methods and means of determining the resistance of composites and nanocomposites materials and continuum damage development under cyclic loading to the creation of appropriate physical models. Particularly relevant is the intensification of creep by high-frequency cyclic loading in composite materials, which usually occurs at high temperatures. Most studies in the field of cyclic creep are experimental, and the direct use of number of cycles to define damage model cannot escape the empirical relation that predicts multi-stress level fatigue life well. The book presents new phenomenological cyclic creep - fatigue models for describing the fatigue life and behavior of time-dependent composites and nanocomposites. Since the main difference between the creep process from the fatigue process is that from a physical point of view, the first is quasi-static, and the second is dynamic. Therefore, the functions of creep should reflect the oscillatory nature of the fatigue process. The results are supported by step-by-step practical design examples and will be useful for practicing structural engineers, code developers as well as research and university faculty. Cover Title Page Copyright Page Preface Table of Contents Nomenclature 1. Introduction and Assumptions 1.1 Introduction 1.2 Fatigue curve and endurance limit 1.3 Creep-fatigue process under cyclically changing strain 1.4 The concept of effective stresses 1.5 Use of scalar internal variable to quantify damage 1.6 The scalar measure of damage 1.7 Strength as endurance limit of composites and nanocomposites 1.8 Continuous damage accumulation model 1.9 Damage accumulation function for composites 1.10 Paris’ Law and Miner’s Rule 1.11 The Bergman-Milton theory 1.12 Failure criteria 1.13 The Bergman-Milton theory 1.14 Failure criteria 1.15 Principle of stress equivalence 1.16 Standard linear model 1.16a Standard Linear Model with different viscosity – temperature relationships 1.17 Temperature effect on viscosity 1.18 Viscosity of dispersed systems 2. Cumulative Damage Model (CDM) of Cyclic Creep-Fatigue Process 2.1 Introduction 2.2 The concept of effective stress 2.3 Classification of composite materials 2.4 Objectives of this research 2.5 Cyclic loading types 2.6 Creep-fatigue constitutive model with cumulative damage law 2.7 Proposed constitutive model of the creep-fatigue process 2.8 Analytical formulas for S – N fatigue curves 3. Phenomenological Creep-Fatigue Models 3.1 Introduction 3.2 Effect of temperature – time relationships on creep-fatigue behavior of composites 3.3 Effect of chemical energy on cyclic creep-fatigue process 3.3.1 Chemical kinetic effect on nanocomposites creep-fatigue process 3.4 Nanocomposite material under cyclic creep-fatigue conditions 3.5 Viscosity change effect at high temperature 3.6 Analytical expression of crystallization function f3 3.7 Effect of increase in frequency ‘p’ 4. Peculiarities of Phenomenological Models of Nanocomposites 4.1 Introduction 4.2 The concept of effective stresses 4.3 Creep-fatigue behavior of nanocomposites 4.4 Defining the damaged medium mechanics 5. Probabilistic Approach to Creep-Fatigue Models 5.1 Introduction 5.2 Creep-fatigue process under periodic loads 5.3 Continuum damage mechanics and durability of composites 5.4 Damage function ω and decrease of cross section area 5.5 “Forward” and “Reversed” probabilistic problem 5.6 Phenomenological models of creep-fatigue of composites 5.7 Failure criteria 5.7.1 Maximum stress theory 5.7.2 Haskin’s failure theory 5.8 Specifics of constitutive equation of creep-fatigue of composites 5.9 Effect of high temperature on fatigue curves (S – Nf) 5.10 Examples 5.11 Probabilistic approach for creep-fatigue model of composites 5.11.1 Main assumptions 5.11.2 Continuum damage and temperature effects on the probabilisticapproach Conclusions Index