Descriptions of the inhomogeneity including dislocations and defects based on the differential geometry forms the basic core of FTMP. This chapter first provides the basic notions of differential geometry necessary for understanding “non-Riemannian plasticity.” The fundamental concepts and quantities are presented second, which is followed by some new features peculiar to the present field theory of multiscale plasticity.

In this chapter, roughly three perspectives are presented and discussed based on the author’s own views, which are at least conceptually informative and expected to greatly help enrich the understanding of “corporation” aspects of multiscale plasticity, either directly or indirectly. The topics chosen are “small world network,” “global analysis,” and “bio-inspired mechanics.” The first subject is related to an issue how the microscopic and macroscopic degrees of freedoms are organically interrelated in hierarchically constituted complex material systems. The last topic is about much more complex systems than the materials, that is, bio-systems, from which we expect to gain numerous insights for tackling our problems in more advanced fashion. Roughly two implications are picked up here, that is, “irreducible structure of life” and “tight coupling versus loose coupling” controversy in terms of the mechanism of bio-motors. The latter is evidently associated with the previously mentioned “weak ties.”

Like the previous question about “FCC versus BCC” posed in Chapter 1, here is another interesting question of a very fundamental kind that few might be able to answer clearly and appropriately: What is (are) the substantial distinction(s) between single crystals and polycrystals in terms of plasticity? Of course the secondary and tertiary factors such as the effect of “textures” should be excluded. This question is extensively discussed in this section.

This chapter intends to overview the field theory of multiscale plasticity (FTMP) in terms of the key concepts (keywords), the basic theories, and the fundamental hierarchical recognition (i.e., the identification of important scales). This will be followed by the introductions of several new features that the author himself has found and introduced afresh. Practically, the theory is applied via the crystal plasticity formalism-based framework as a tentative and convenient vehicle. So, the constitutive framework together with some detailed sets of modeling for the evolution equations therein is are also presented in the present chapter, i.e., strain gradient terms for the dislocation-density and the incompatibility tensors.

As we have seen in Chapter 3, much of the microscopic “specificities” are renormalized into a limited number of degrees of freedom at dislocation substructure scale (Scale A), especially into those with “cellular” morphology, essentially extending over 3D crystalline space. Therefore, as a critical step toward the successful multiscale plasticity, we are required to be ready to answer the following questions about the 3D cell structure; “why do they need the 3D ‘cellular’ morphology?,” “what is the substantial role, especially against the mechanical properties?,” why does the well-documented ‘universality’ manifested as a similitude law, hold?, and “how the microscopic degrees of freedom (information) are stored and when will they be released?” The first goal of this chapter is to derive an effective theory governing the dislocation substructure evolutions, particularly, cellular patterning, from a dislocation theory-based microscopic description of Hamiltonian through a rational “coarse-graining” procedure provided by the method of quantum field theory (QFT) (see Chapter 8). Secondly, after presenting some representative simulation results, an extensive series of discussions on the cell formation mechanisms and the mechanical roles are discussed and identified.

The completion of the theory for MMMs (multiscale modeling of materials) is manifested itself partially as an identification of the right “flow-evolutionary” law explicitly, which describes generally the evolution of the inhomogeneous fields and the attendant local plastic flow accompanied by energy dissipation. The notion “duality” ought to be embodied by this law, although it still is a “working hypothesis,” deserving further investigations. Specifically, it represents the interrelationship between the locally stored strain energy and the local plastic flow as has been discussed in the context of polycrystalline plasticity in Chapter 12 for Scale C. In this final chapter, we will derive explicitly a candidate form of the flow-evolutionary law as a possible embodiment of the duality, which is followed by application examples.

The surrounding air flow around a hypersonic vehicle behaves quite differently from supersonic flows. The kinetic energy is converted into internal energy which can increase the flow temperature and induce endothermic reactions near the vehicle surface. It is a challenge to develop flow diagnostic and aerodynamic measurement technologies with high precision for high-enthalpy wind tunnel tests. There are, generally, three types of measurement technologies widely used in exploring high-enthalpy flows, including heat-transfer measurement, aerodynamic balance, and optical diagnostic techniques. In this chapter, hypersonic tests with the aforementioned measurement technologies are summarized to demonstrate the progress on high-enthalpy flow experiments. Four kinds of experiments are included here, and the topics are aerodynamic force and moment tests, aerothermal heating measurements, hypersonic boundary-layer flow diagnostics, and supersonic combustion and scramjet engine tests. Actually, there are a lot of interesting topics, but these four are important not only to understand aerothermodynamic physics but also to support the development of hypersonic vehicles.

The achievable total enthalpy and the pressure level in a shock tunnel depend on its capability to generate strong shock waves. To produce a strong shock wave, high pressure and high sound speed are two key parameters for driver gases. There are various techniques to increase the driver gas sound speed, which are essentially different approaches in the way to raise the driver gas temperature. The first technique to increase the driver gas sound speed is by the use of a light gas, and the second one is by heating the light gas to a high temperature with gas heaters. The light-gas-heated shock tunnel is introduced in this chapter, and the electrical heaters are discussed in detail, including the relatively simple electrical resistance heaters and electric-arc heaters. Strictly speaking, the electric-arc heating is not a gasdynamic technique and it is not capable of completing flight-condition duplication for hypervelocity testing. However, it is selected because it can generate extremely high total enthalpies and is useful in certain applications.

In this chapter, the aerodynamic fundamentals for the working principles of shock tunnels are summarized. The moving waves, including expansion waves, shock waves, and contact surfaces, are introduced as the key issues and their theories are based on the unsteady one-dimensional flows in textbooks of aerodynamics. As unsteady one-dimensional moving waves are also critical for the design and operation of shock tunnels, their theories are also selected and summarized in this chapter for book completeness and readers’ convenience.

The free-piston driver is a powerful technique to increase both the driver gas sound speed and pressure. Therefore, it is capable of generating high-enthalpy flows and offering high performance among various gasdynamic shock drivers. So far, it has been implemented in a number of major reflected-shock as well as shock-expansion wind tunnels around the world. The free-piston driver has the advantage that a high driver gas pressure is automatically generated in the same process. On the other hand, the driver is far more complex mechanically and requires operation-tuning in order to operate effectively. Moreover, its test time is short and the test flow is not steady because the piston motion is difficult to control. In this chapter, the basic concepts of the free-piston driver are discussed. The analytical theory that describes the piston dynamics and the method for tuned piston operation are presented. Examples of major free-piston-driven test facilities as well as their applications in hypersonic testing are also summarized.

Hypersonic and high-enthalpy wind tunnels have been a challenge in ground testing facilities in aerospace research for decades. In regard to performance requirements, theories and methods for designing hypersonic flow nozzles at high enthalpy conditions are quite difficult, but very interesting topics, especially when dissociation of air molecules take place in test-gas reservoirs. In this chapter, fundamental theories and important methods for nozzle design are reviewed with the emphasis on two-dimensional axisymmetric nozzles for hypersonic high-enthalpy wind tunnels, including the method of characteristics, the graphic design method, the Sivells method, the theory for boundary layer correction, and computational fluid dynamics (CFD)-based design optimization methods. They were proposed based on several physical issues covering the expansion wave generation and reflection, boundary layer development, and real-gas effects of hypersonic flows. Difficulties arising from applications of these methods in high-enthalpy nozzle design are discussed in detail and state-of-the-art of nozzle design technologies that have been reached over decades are summarized with some brief comments.