Micromechanics of Composite Materials

ISBN-13: 9789400797819 / Angielski / Miękka / 2015 / 442 str.

George Dvorak

Opis

This book presents a broad exposition of analytical and numerical methods for modeling composite materials, laminates, polycrystals and other heterogeneous solids, with emphasis on connections between material properties and responses on several length scales, ranging from the nano and microscales to the macroscale. Many new results and methods developed by the author are incorporated into the rich fabric of the subject, which has developed from the work of many researchers over the last 50 years. Among the new results, the book offers an extensive analysis of internal and interface stresses caused by eigenstrains, such as thermal, transformation and inelastic strains in the constituents, which often exceed those caused by mechanical loads, and of inelastic behavior of metal matrix composites. Fiber prestress in laminates, and modeling of functionally graded materials are also analyzed. Furthermore, this book outlines several key subjects on modeling the properties of composites reinforced by particles of various shapes, aligned fibers, symmetric laminated plates and metal matrix composites. This volume is intended for advanced undergraduate and graduate students, researchers and engineers interested and involved in analysis and design of composite structures.

Recenzje

From the book reviews:

"The book is a fundamental contribution to micromechanics of composite materials. ... it is a book for specialists who want to have a complete reference on the subject. It is a book for professors, researchers, and postgraduate students professionally working on or teaching composite materials. I recommend this book for research universities and research institute libraries." (Alexander G. Kolpakov, Mathematical Reviews, November, 2014)

Spis treści

1  Tensor component and matrix notation.-  2   Anisotropic elastic solids.-  2.1  Elastic strain energy density.-  2.2  Material symmetries.-  2.3  Transversely isotropic composite materials.-  2.4  Cylindrically orthotropic materials.-  2.5  Young’s modulus, shear modulus and Poisson’s ratio.-  3   Elementary concepts and tools.-  3.1  Aggregates and constituent phases.-  3.2  Herogeneous microstructures.-  3.3  Representative volume.-  3.4  Local and overall stress and strain fields.-  3.5  Overall properties and local fields.-  3.6  Transformation fields.-  3.7  Work, energy and reciprocal theorems.-  3.8  The Levin formula and the Hill lemma.-  3.9  Universal connections for elastic moduli of fibrous composites.-  3.10  Constitutive relations and local fields in heterogeneous aggregates.-  4  Inclusions, inhomogeneities and cavities.-  4.1  Homogeneous ellipsoidal inclusions:  The Eshelby solution.-  4.2  Ellipsoidal inhomogeneities:  The equivalent inclusion method.-  4.3 Transformed inhomogeneities.-  4.4  Dilute approximation of overall properties.-  4.5  Green's function and Eshelby's tensor in elastic solids.-  4.6  Coefficients of the P tensors for selected ellipsoidal shapes.-  4.7   Summary of principal results.-  5  Energies of inhomogeneities, dilute reinforcements and cracks.-  5.1  Energy changes caused by mechanical loads.-  5.2  Energy changes caused by uniform phase eigenstrains.-  5.3  Energy changes caused by mechanical loads and phase eigenstrains.-  5.4  Energy and stiffness changes caused by cracks.-  6  Evaluations and bounds on elastic moduli of heterogeneous materials.-  6.1  Elementary energy bounds.-  6.2  Hashin-Shtrikman and Walpole bounds on overall elastic moduli.-  6.3  Evaluation of H-S bounds for ellipsoidal inhomogeneities.-  6.4. Composite element assemblage bounds.-  6.5  The generalized self-consistent method.-  7  Estimates of mechanical properties of composite materials.-  7.1  The self-consistent method (SCM).-  7.2 The Mori-Tanaka method (M-T).-  7.3  The differential scheme.-  7.4  The double inclusion and double inhomogeneity models.-  7.5  Applications of SCM and M-T to functionally graded materials.-  8  Transformation fields.-  8.1  Uniform change of temperature in two-phase composites and polycrystals.-  8.2  Transformation influence functions and concentration factors.-  8.3 Uniform change in temperature in multiphase systems.-  8.4  Capabilities of bounds and estimates of overall and local fields.-  9  Interfaces and interphases.-  9.1  Perfectly bonded interfaces.-  9.2   Imperfectly bonded inhomogeneities and cavities.-  10  Symmetric laminates.-  10.1  Constitutive relations of fibrous plies.-  10.2  Coordinate systems and transformations.-  10.3  Overall response and ply stresses in symmetric laminates.-  10.4  Ply and constituent stress and strain averages .-  10.5  Design of laminates for cylindrical pressure vessels.-  10.6  Dimensionally stable laminates.-  10.7  Auxetic laminates.-  10.8  Laminates with reduced free edge stresses.-  11  Elastic-plastic solids.-  11.1  Yield and loading surfaces, normality and convex.-  11.2   Hardening and flow rules.-  11.3  Matrix form and consistency of the instantaneous tangent stiffness.-  12  Inelastic composite materials.-  12.1  Transformation field analysis (TFA) of inelastic deformation.-  12.2   Experimental support of theoretical predictions.-  12.3    Thermal hardening.-  References.                                                                                                     

Blurb

This book presents a broad exposition of analytical and numerical methods for modeling composite materials, laminates, polycrystals and other heterogeneous solids, with emphasis on connections between material properties and responses on several length scales, ranging from the nano and microscales to the macroscale.

Many new results and methods developed by the author are incorporated into a rich fabric of the subject, which has been explored by several researchers over the last 40 years.   The first  part of the book reviews anisotropic elasticity theory, and then it describes the frequently used procedures and theorems for bounding and estimating overall properties, local fields and energy changes in elastic inhomogeneities, heterogeneous media, fiber composites and functionally graded materials.  Those are caused by mechanical loads and by phase eigenstrains, such as thermal, transformation and inelastic strains, and also by cavities and cracks.    Worked examples show that the eigendeformations may contribute a major part of the overall response and of interior stress and strain fields in the constituents.   Separate attention is given to perfect and imperfect interfaces, and to evaluation of interface stresses induced by mechanical and transformation loads.  Micromechanical methods are extended to analysis of symmetric laminates.  Applications include design of laminate configurations for pressure vessels, for dimensionally stable and auxetic laminates, for laminates with reduced free edge stresses and with fiber prestress, and for those sustaining damage by transverse cracking and fiber breaks.   A review of the incremental theory of plasticity, of the transformation field analysis method, and of modeling and experimental results for metal matrix composites, are extensively described in the closing chapters.

This volume is intended for advanced undergraduate and graduate students, researchers and engineers interested and involved in analysis and design of composite structures.