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E-raamat: Phenomenological Creep Models of Composites and Nanomaterials: Deterministic and Probabilistic Approach

Leo Razdolsky

Formaat: 414 pages
Ilmumisaeg: 02-Jan-2019
Kirjastus: CRC Press
Keel: eng
ISBN-13: 9781351378697

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Formaat: 414 pages
Ilmumisaeg: 02-Jan-2019
Kirjastus: CRC Press
Keel: eng
ISBN-13: 9781351378697

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The use of new engineering materials in the aerospace and space industry is usually governed by the need for enhancing the bearing capacity of structural elements and systems, improving the performance of specific applications, reducing structural weight and improving its cost-effectiveness. Crystalline composites and nanomaterials are used to design lightweight structural elements because such materials provide stiffness, strength and low density/weight. This book reviews the effect of high temperature creep on structural system response, and provides new phenomenological creep models (deterministic and probabilistic approach) of composites and nanomaterials.

Certain criteria have been used in selecting the creep functions in order to describe a wide range of different behavior of materials. The experimental testing and evaluation of time variant creep in composite and nanomaterials is quite complex, expensive and, at times, time consuming. Therefore, the analytical analysis of creep properties and behavior of structural elements made of composite and nanocomposite materials subjected to severe thermal loadings conditions is of great practical importance.

Composite elements and heterogeneous materials, from which they are made, make essential changes to the classical scheme for constructing the phenomenological creep model of composite elements, because it reflects the specificity of the composite material and manifests itself in the choice of two basic functions of the creep constitutive equation, namely memory and instantaneous modulus of elasticity functions. As such, the concepts and analytical techniques presented here are important. But the principal objective of this book is to demonstrate how nonlinear viscoelastic engineering creep theory can be incorporated into the general theory of mechanics of materials so that composite components can be designed and analyzed. The results are supported by step-by-step practical structural design examples and will be useful for structural engineers, code developers as well as material science researchers and university faculty. The phenomenological creep models presented in this book provide a usable engineering approximation for many applications in composite engineering.

Preface

iii

Notations

1 Introduction and Overview

(27)

1.1 Definition of structured composites and nanomaterials

(3)

1.1.1 The use of nanocomposites in space technology

(2)

1.1.2 Classification of polymers

(1)

1.2 What is the main difference between the composites and ordinary solid bodies?

(1)

1.3 Composite structural systems

(8)

1.3.1 Classification according to a structured feature

(2)

1.3.2 Reinforced media theory

(1)

1.4 Model of elastic deformation of a unidirectional multilayered composite material

(7)

1.4.1 Elastic deformation model of cross-reinforced composite material

(4)

1.5 Optimization of multi-layered composite structure parameters

(2)

1.5.1 Influence of fiber length

(1)

1.5.2 Elastic behavior---longitudinal loading

(1)

1.6 Molecular mechanisms of chemical reactions

(4)

1.6.1 Chemical reaction kinetics

(2)

1.6.2 Methods for determining the order of reactions

(1)

1.6.3 Ostwald's "isolation method"

(1)

1.6.4 Graphic method

(1)

1.6.5 The differential method of Van't Hoff

(1)

1.6.6 Dependence of the reaction rate on temperature

(1)

References

(2)

2 Creep Laws for Composite Materials

(41)

2.1 Introduction

(1)

2.2 Phenomenological creep model: single integral type constitutive equation (CE)

(11)

2.2.1 Temperature and kinetic energy

(6)

2.2.2 Use of classical relations of composite elastic modulus

(1)

2.2.3 Instantaneous creep modulus

(2)

2.2.4 Effects of θg on modulus of elasticity

(3)

2.3 Engineering creep of composites

(1)

2.4 Maxwell model

(1)

2.5 Standard linear model

(3)

2.6 Effect of variable dimensionless parameters on STS diagram (Standard Linear model)

(21)

2.6.1 Allowable creep stresses vs. parameter β

(9)

2.6.2 Allowable creep stresses vs. parameter β and n

(8)

References

(3)

3 Creep Models of Fibrous and Dispersed Composites: Deterministic Approach

(72)

3.1 Micromechanics and macromechanics

(2)

3.2 Brief classification of non-newtonian fluids

(2)

3.3 Composite design process

(1)

3.3.1 Artificial composite materials

(1)

3.4 Mechanical testing of composites

(1)

3.5 Resilient properties of composites

(1)

3.6 The phenomenological approach in mechanics of heterogeneous media

(22)

3.6.1 Structured---phenomenological approach to the solution of boundary value mechanics of composites

(2)

3.6.2 Equilibrium equations of multilayered composites

(4)

3.6.3 Hooke's law for each layer

(2)

3.6.4 Elastic deformation model of cross-reinforced composite material

(12)

3.7 Phenomenological creep models of composite structures

(3)

3.8 Temperature-time dependent structured heterogeneous composites

101

(23)

3.9 General form of Equation (3.37)

124

(8)

3.10 Phenomenological creep models of composites with dispersed filler

132

(7)

References

139

(2)

4 Creep Models of Nanocomposites: Deterministic Approach

141

(89)

4.1 Introduction

141

(6)

4.1.1 Small scaled materials

145

(1)

4.1.2 Approaches to larger surface area

146

(1)

4.1.3 Size effect and the nanomaterials properties

147

(1)

4.2 Physical aspects of nanocomposite structures

147

(3)

4.3 Chemical aspects of nanocomposite structures and reaction kinetics

150

(7)

4.3.1 Rate of reaction

151

(1)

4.3.2 Integrated rate laws

151

(2)

4.3.3 Dependence of the conversion of metal ions on time

153

(1)

4.3.4 Physicochemical aspects of formation of structured nanocomposites

154

(3)

4.4 Mechanical properties of nanocrystalline metals and alloys

157

(1)

4.4.1 Yield strength

157

(1)

4.5 Creep of small coarse grained and nanocrystalline materials

158

(6)

4.5.1 Creep mechanisms in small coarse grained materials

158

(1)

4.5.2 Phenomenological creep models of nanocrystalline materials

159

(1)

4.5.3 Nucleation and growth process of nanoparticles

160

(1)

4.5.4 Modeling of nucleation and growth process of nanoparticles

161

(3)

4.6 Basic creep equations and nanomaterials parameters relations

164

(64)

4.6.1 Effect of function f3 (nucleation and growth process of nanoparticles) type on creep process

165

(44)

4.6.2 Effect of EQ/E2 ratio on creep process

209

(3)

4.6.3 Effect of volumetric fillers ratio φf on creep process

212

(16)

References

228

(2)

5 Physical Chemistry of Nanoparticles

230

(50)

5.1 Introduction

230

(2)

5.2 Disperse systems

232

(4)

5.2.1 Classification by degree of dispersion

232

(1)

5.2.2 Classification of disperse systems

232

(3)

5.2.3 Sensitivity of tension stresses to concentration surfactants

235

(1)

5.3 The rate of chemical reaction

236

(1)

5.4 Temperature effect on chemical reaction rate

237

(3)

5.5 Phenomenological kinetics

240

(3)

5.5.1 Basic definitions and postulates

240

(3)

5.6 Kinetics of simple irreversible reactions

243

(5)

5.6.1 First-order chemical reactions

244

(2)

5.6.2 Second-order reactions

246

(1)

5.6.3 Third-order reaction

247

(1)

5.6.4 Zero-order reactions

248

(1)

5.7 Determination of the chemical reactions order

248

(2)

5.7.1 Method for determining the order of chemical reaction

249

(1)

5.8 Activation energy

250

(20)

5.8.1 Kinetics of complex reactions

251

(1)

5.8.2 The principle of independence

252

(1)

5.8.3 The concept of a rate determining stage

253

(1)

5.8.4 Reversible reactions of the first order

253

(1)

5.8.5 Reversible second-order reactions

254

(1)

5.8.6 Kinetics of parallel reaction with reversibility in one stage

255

(15)

5.9 Autocatalytic chemical reactions

270

(8)

References

278

(2)

6 Phenomenological Creep Models of Fibrous Composites (Probabilistic Approach)

280

(62)

6.1 Introduction

280

(4)

6.1.1 Basic concepts and definitions of applied probability theory

280

(1)

6.1.2 The distribution function and the distribution density of a random variable

281

(1)

6.1.3 The Poisson probability distribution

282

(1)

6.1.4 Correlation and dependence

282

(2)

6.2 Continuous probability distributions

284

(7)

6.2.1 Normal probability distributions

284

(3)

6.2.2 Weibull distribution

287

(1)

6.2.3 Rayleigh distribution

288

(1)

6.2.4 Chi-squared distribution

289

(2)

6.3 Joint probability distribution

291

(1)

6.4 Characteristic function

292

(2)

6.5 Functions of random variables and their distribution

294

(5)

6.5.1 One-to-one functions of an absolutely continuous random variable

296

(1)

6.5.2 Probabilistic transformation (linearization) method

297

(2)

6.6 Confidence interval

299

(6)

6.6.1 Confidence interval (poisson distribution)

301

(1)

6.6.2 Confidence interval (binomial proportion)

302

(3)

6.7 Probability distributions and concept of random success (failure)

305

(14)

6.7.1 The binomial probability distribution

306

(13)

6.8 Probabilistic creep models of composites

319

(15)

6.8.1 Deterministic formulation of stochastic problems: numerical modeling

322

(1)

6.8.2 Statistical data: composites and stress effect

323

(11)

6.9 Structural composites failures in time

334

(6)

References

340

(2)

7 Phenomenological Creep Models of Nanocomposites (Probabilistic Approach)

342

(57)

7.1 Construction of a stochastic creep model of nanocomposites

342

(6)

7.1.1 Selection of filler material

343

(1)

7.1.2 Remarkable properties of nanomaterials

344

(1)

7.1.3 Promising nanomaterials

345

(1)

7.1.4 Creation of new construction materials

346

(2)

7.2 Creep models of nanocomposites: probabilistic approach

348

(13)

7.2.1 General computer code and effect of different types of function f3

351

(10)

7.3 Compilation of statistical data based on creep constitutive equation solutions

361

(14)

7.4 Creep deformation process of nanocomposites as an ergodic random process

375

(3)

7.5 Creep of the nanocomposite in the framework of the correlation theory of probability

378

(2)

7.5.1 Mean value of allowable creep stress and strain

378

(1)

7.5.2 Standard deviation and autocorrelation function of allowable creep stress and strain

378

(2)

7.6 The first-occurrence time problem and the probability density P (a, t)

380

(2)

7.7 Allowable creep stress vs. volumetric content of nanoparticles

382

(14)

References

396

(3)

Index

399

Leo Razdolsky has 45 years of experience in structural engineering, with focus on composite structures, power plants and cooling towers. He is also adept in computer modeling, material science and nanomaterials. Dr. Razdolsky has been teaching engineering courses at the University of Illinois and Northwestern University, and is currently conducting research work connected with high temperature creep of composite structural elements and systems. He has authored three books in this area.

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