Introduction

Flexible composites, which are described in Chapter 8, behave very differently from conventional rigid polymer composites in the following ways:

1. (1) Flexible composites are highly anisotropic (i.e. longitudinal elastic modulus/transverse elastic modulus » 1). Figure 9.1 compares the normalized effective Young's modulus (Exx/E22) vs. fiber orientation for two types of unidirectional composites. The upper curve obtained from Kevlar- 49/silicone elastomer shows that the stiffness of the elastomeric composite lamina is very sensitive to the fiber orientation. At a 5δ off-axis fiber orientation, for example, a 1° change in fiber angle causes the effective stiffness to change by 53%. The lower curve obtained from Kevlar- 49/epoxy shows less than 7% change at the same off-axis angle.

2. (2) Flexible composites show low shear modulus and hence large shear distortion, which allows the fibers to change their orientations under loading.

3. (3) Flexible composites have a much larger elastic deformation range than that of conventional rigid polymer composites. Thus, the geometric changes of the configuration (i.e. area, direction, etc.) need to be taken into consideration.

4. (4) The nonlinear elastic behavior with stretching–shear coupling, due to material and geometrical effects, is pronounced in flexible composites under finite deformation.

Therefore, the conventional linear elastic theory, based on the infinitesimal strain assumption for rigid matrix composites, may no longer be applicable to elastomeric composites under finite deformation.

The theories of non-linear and finite elasticity made a major advancement during the Second World War, in response to the development of the rubber industry. M. Mooney, in 1940, advanced his well-known strain–energy function.

Introduction

The term ‘textile structural composites’ is used to identify a class of advanced composites utilizing fiber preforms produced by textile forming techniques, for structural applications. The recent interest in textile structural composites stems from the need for improvements in intra- and interlaminar strength and damage tolerance, especially in thick-section composites. Textile composites offer the potential of providing adequate structural integrity as well as shapeability for near-net-shape manufacturing (Chou and Ko 1989).

Textile structural composites provide the unique capability that the microstructure of fiber preforms can be designed to meet the needs of the performance of composite structures. Textile structural composites can be fabricated directly to their final shapes or can be assembled or readily machined to specified contours and dimensions. A total system approach is necessary to optimize the composite performance through the consideration of preform availability, cost, ease of processing, needs for secondary work such as machining, joinability of parts, and the overall performance of the composite structure. Chapters 6 and 7 discuss the fundamental characteristics of two- and three-dimensional textile preforms and the analysis of composite behavior based upon these preforms. The following discussions of yarn assembly, as well as textile preforms and characteristics, are based upon the review of Scardino (1989).

The forming of textile preforms requires knowledge of the structure of yarns and fibers. Yarns are linear assemblages of fibers formed into continuous strands having textile characteristics, i.e. substantial strength and flexibility.

In this chapter, we utilize the basic concepts and some of the earlier quantitative results to predict and understand many of the morphological feature developments that are found in crystals and films. We begin with macroledge development in both films and crystals.

Layer flow instabilities

For vicinal surface orientations, although the growth conditions are not such as to produce the massive instability characterized by Eq. (5.13a), a range of less severe growth conditions exist wherein instabilities can develop in the layer front flowing across the crystal surface at Vℓ ≫ V. Thus, instead of the layer front being straight and smooth or faceted, it is rumpled with edge waves that are growing in amplitude as the front proceeds. This is just the two-dimensional analog of the instabilities already discussed (see Fig. 5.21). Like its three-dimensional counterpart, microsegregation events and microdefects are built into the growing crystal when such layer flow instabilities develop and the quantitative assessment of the onset of these instabilities is important to the growth of high quality crystals.

There are two types of perturbation consequences that interest us here: (1) that giving rise to a ledge density instability leading to ledge bunching and the growth of h/a as indicated in Fig. 6.1(b) and (2) that giving rise to ledge front instability of the lateral kind as indicated in Fig. 6.1(c).

This book first reviews the important findings described in the companion volume The science of crystallization: microscopic interfacial phenomena. It then deals specifically with convection, heat transport and solute transport to describe both steady state and transient solute distributions in bulk crystals, small crystallites of various shapes and thin films. It integrates all these factors to describe interface instability for interfaces of different shapes and predicts the dominant morphological characteristics found in crystals during either single phase or polyphase crystallization. These concepts have been extended to embrace biological crystallization and the connecting links between the morphological features of polymer crystallization and simple organic molecule crystallization.

These concepts are put to work to treat the generation of physical and chemical defects in both bulk crystals and thin films showing both the origin of these faults as well as some procedures for eliminating them.

The present book and its companion are the culmination of over 35 years of thought and personal study concerning modern-day science and technology of the crystallization process. A special perspective and a special approach have been developed for understanding the intricacies of any phase transformation in a fundamental and scientific way so that technological utilization can be readily engineered.

This pair of books differs from others available in the “crystal growth” area in that they are sufficiently broad-ranging to provide the scientific basis for understanding and treating any application area – single crystal growth, chemical crystallizers, film formation, ingots and castings, welding, frozen food processing, cryogenic organ storage, geological sleuthing, etc.

Coupling equations

Crystallization is a many-variable, many-parameter interaction event in Nature and in technology and scientific understanding of this area feeds the very large application field illustrated in Fig. 1.1. For the territory lying within the scientific understanding box, it is necessary to treat the crystallization event as a dynamic system with many interacting parts or subsystems. These are illustrated in Fig. 1.2 for a typical case. The unique morphology and special phenomena associated with the crystallization event arise out of the conjunction of these subsystems interacting with each other in pairs, triplets, etc.

It is in the far-field domain of a growing crystal where the macroscopic or global thermodynamic state variables, (C, T, P, φ) = (C∞, T∞, P∞, φ∞) are fixed or changed dynamically according to some particular program (Ċ∞, Ṫ∞, Ṗ∞, ∞). However, it is mainly at the interface of the growing crystal that all the morphological, chemical segregation and embryonic physical defect phenomena arise in the crystallization event. Thus, scientific understanding of the overall process requires a description in terms of the thermodynamic state variables and their gradients at the growing interface; i.e., (Ci, Ti, Pi, φi) and (∇iC, ∇iT, ∇iP, ∇iφ). The connection between the interface conditions and the far-field conditions occurs via a set of partial differential equations and their boundary value constraints.