Superplasticity, the ability of certain materials to undergo very large tensile strains, was first described in 1912. It became the subject of intense research in the early 1960s following a review of Soviet work and the illustration of the potential commercial applications of superplasticity.

There have been enormous advances in the field, of superplasticity since that time. The field has clear commercial applications, but also retains fascinating scientific challenges in understanding the underpinning physical mechanisms. Recent breakthroughs include the development of superplasticity in polycrystalline ceramics, composites and intermetallics, and also the observation of superplasticity in metallic materials at high strain rates. Superplasticity at high strain rates, in particular, is expected to have a significant technological impact on promoting the commercial applications of superplastic materials.

This book emphasizes the materials aspects of superplasticity and thus was written from the materials point of view. A brief history of the development of superplasticity is first introduced. Then, the two major types of superplasticity, i.e. fine-structure and internal-stress superplasticity, and their operative mechanisms are discussed. Other possible superplastic mechanisms, such as Class I solid solutions and superplasticity at dynamic high strain rates are also described. In addition, microstructural factors controlling the ductility and fracture in superplastic materials are presented. The observations of superplasticity in metals (including Al, Mg, Fe, Ti, Ni), ceramics (including monolithics and composites), intermetallics (including Ni-, Ti-, Fe- aluminides), metal-matrix composites (including Al-, Mg- base), and laminates are thoroughly described.

We have discussed fine-structure superplasticity in various materials, including metals and ceramics, in Chapters 5–9. In these chapters, our discussions focused primarily on experimental observations, deformation mechanisms, and microstructural characteristics. Tensile ductility, which is determined by cavitation and fracture, was not emphasized. In this chapter, we will focus on the latter issue. A fracture mechanics model will be examined with available tensile elongation data for superplastic ceramics and superplastic intermetallics. The analysis permits a broad understanding of tensile elongation behavior of superplastic materials.

Tensile ductility in superplastic metals

It is well accepted that two competing processes govern the failure of superplastic materials at high temperature. One is related to macroscopic necking, and the other is related to microscopic cavitation and cracking. Macroscopic necking is governed by the strain-rate-sensitivity exponent, m, in the simplified constitutive equation σ=km, where σ is the true flow stress, is the true strain rate, and k is a material constant. A high m value usually indicates a diffuse neck development and, thus, a delay of the onset of tensile failure, which leads to high tensile elongations. The fracture profile of many superplastic metals with m≥0.4, however, reveals that there is no sharp pinpoint necking. This is because final fracture is caused by the evolution of cavities at grain boundaries, and in this sense, cavities lead to premature failure of test samples.

Creep mechanisms

Creep is a plastic deformation process that occurs in solids at high temperatures, typically, above approximately 0.5 of the homologous temperature, i.e. T/Tm, where Tm is the absolute melting point of the solid. During creep, a solid deforms permanently, under external forces, initially with negligible formation of cracks or voids. This capacity for plastic flow is associated with three discrete mechanisms that can occur at the atomic level. These mechanisms are (a) slip by dislocation movement, (b) sliding of adjacent grains along grain boundaries, and (c) directional diffusional flow. To a first approximation, the three mechanisms can be generally considered to occur independently of one another. Although, in some cases, one mechanism may be necessary to permit accommodation of another, e.g. diffusional flow or slip may be an accommodation mechanism for grain boundary sliding. For the case of large plastic strains, these mechanisms are all thermally activated and are controlled by the diffusion of atoms. They are, therefore, both temperature- and time-dependent.

Creep is commonly characterized by a strain–time curve, i.e. a creep curve. The creep rate is measured directly from the slope of such a creep curve. There are usually two basic types of creep curves: a metal type and an alloy type. As shown in Figure 4.1, for the metal type, the curve normally starts with a primary regime during which the creep rate decreases with time; this region is usually followed by a steady-state regime during which the creep rate is essentially constant; eventually, cavitation and necking begin to develop in the specimen which results in an acceleration of creep rate and leads to a tertiary region and the final failure.

Titanium alloys

Superplastic forming of titanium alloys has been widely used by the aerospace industry. A well-known example of superplastic forming carried out at Rockwell International using a Ti–6Al–4V alloy was shown in Figure 14.2. The component shown was a nacelle center-beam frame. (A number of such parts formed a proposed structure in the B–1 aircraft.) In this example, a single superplastic forming and diffusion bonding operation was designed to replace a production route which had involved the forming of eight separate pieces of the same alloy, which then had to be joined together with 96 fasteners. Estimated cost savings of 55% and weight savings of 33% were estimated using this fabrication route compared with the conventional production technique. Superplastically formed Ti–6Al–4V was also used for service doors and panels for Airbus aircraft, missile fins, turbofan blades, and turbine disks.

For non-aerospace applications, the most significant commercial product is probably golf club heads, shown in Figure 15.1. A titanium golf club head offers a light weight, large volume, and a wide sweet spot area. It is now produced in both Japan and China. In Japan, the head is made of SP–700 Ti alloy which has the nominal composition of Ti–4.5Al–3V–2Fe–2Mo. The alloy, marketed by Nippon Kokan (NKK), features a low SPF temperature (as low as 775 °C) for the maximum formability, and can be age-hardened.

A practical method for superplastic forming of bulk material is through the use of powder metallurgy methods. The approach here is to achieve net-shaped products, with high density, by compaction of both metal and ceramic powders, using fine-structure or internal-stress superplasticity (FSS and ISS) methods. Studies have been performed by Ruano et al. on the use of ISS in enhancing the densification of white cast iron powders. Caligiuri and Isonishi and Tokizane, on the other hand, used FSS to enhance the densification of ultrahigh carbon steel (UHCS) powders. In addition, Allen used FSS to consolidate Ni-based IN-100 powders (GatorizingTM* process). For ceramics, Kellett et al. used FSS to extrude fine zirconia powders and Wakai et al. to perform the bulge forming of YTZP pipes directly from powders. Panda et al. Akmoulin et al., Uchic et al., and Kwon et al. have sinter forged nanometer zirconia, titania, and alumina powders.

ISS compaction of white cast iron powders

The advent of new technologies centered on fine powders often requires development of methods of enhancing densification wherein the fine structures present in such powders are retained. Low temperatures must be used to achieve this goal, but this usually requires the application of high pressures if a high density is to be achieved. High pressures are often a limiting factor in the manufacture of powder products.

Many metal-matrix composites (MMCs) and laminates have been developed in recent years for advanced structures. Both materials are attractive for many structural applications because they exhibit unusual combinations of structural, physical, and thermal properties including high modulus and strength, good wear resistance, good dimensional stability and low thermal expansion, and low density. Many studies have shown that discontinuously reinforced MMCs can behave superplastically. These composites are mainly aluminum-based, but some magnesium-based and zinc-based composites have also been studied.

Aluminum-based metal-matrix composites

Comparative superplasticity data from some of the representative Al-based composites are summarized in Table 8.1. All of these composites are reinforced by SiC, either in whisker or particulate form. Up to the present time, superplasticity has not only been observed in MMCs produced by powder metallurgy (PM) methods but also in MMCs produced by ingot metallurgy (IM) methods. The composites listed in Table 8.1 were made by conventional PM techniques, except for the 15 vol % SiCw–7475Al, which was manufactured using SiCw layered between specially prepared foils of superplastic 7475A1 alloy. The IM composite, 10 vol % SiCp–2024Al, was produced by stir-casting. For discussion purposes, the composites listed in Table 8.1 are hereafter abbreviated as reinforcement–matrix alloy, e.g., 20 vol % SiCw–2124Al becomes SiCw/2124. As shown in Table 8.1, the reported strain rate sensitivities (m) vary significantly.

Most superplastic metal alloys exhibit large tensile elongations of about 500% to over 1000%. For the most advanced structures, however, the forming strains are typically less than 200 to 300%. Thus, these elongation values are sufficient to make extremely complex shapes using superplastic forming technology. In so doing, large cost and weight savings (through redesign) have provided the driving force for the change from conventional forming to superplastic forming technology. The principal, fine-structured alloy systems that have been commercially exploited for superplastic forming are those based on aluminum, magnesium, iron, titanium, and nickel alloys. Other alloy systems, e.g., Zn–Al, Cu–Al, and Pb–Sn, have also been widely explored. The study of these alloys, however, is usually for achieving basic understanding rather than for structural applications. Many reviews already exist to cover these alloys, so in the following sections, we will only discuss those that are important for structural applications.

Aluminum-based alloys

It is instructive to review the evolution of superplastic aluminum alloys to gain a basic understanding of how a structural alloy group is developed. For this purpose, an overview of the development of superplastic aluminum alloys from 1966 to 1984 is presented in Figure 5.1, where each box represents an individual publication. The description within each of the boxes refers to the nominal alloy composition (in wt%) or to the commercial designation, if appropriate.

In addition to the fine-structure superplasticity (FSS) described in the previous chapters, there is another type of superplasticity known as internal-stress superplasticity (ISS). In these materials, in which internal stresses can be developed, considerable tensile plasticity can take place under the application of a low, externally applied stress. This is because internal-stress superplastic materials can have a strain-rate-sensitivity exponent as high as unity; i.e., they can exhibit ideal Newtonian viscous behavior. Such superplastic materials are believed to be deformed by a slip-creep mechanism.

There are many ways in which internal stresses can be generated. These include thermal cycling of composite materials, such as whisker- and particulate-reinforced composites, in which the constituents have different thermal expansion coefficients; thermal cycling of polycrystalline pure metals or single-phase alloys that have anisotropic thermal expansion coefficients; and thermal cycling through a phase change. In addition, pressureinduced phase changes have been cited as a possible source of superplastic flow in geological materials. For example, there is a phase transformation in the earth's upper mantle, because of pressure, from orthorhombic olivine to a spinel phase at a depth of about 400 km below the earth's surface. And it is believed that internal-stress superplasticity, arising from the transformation stresses through pressure cycling (analogous to temperature cycling), leads to a mixed-phase region of low effective viscosity.

Ordered intermetallic alloys and their composites generally have good high-temperature strength, low density, and environmental resistance and are, therefore, potential materials for high-temperature structures. However, ordered intermetallic alloys are also known to be brittle, have low toughness because of their ordered structure, and show a propensity for grain-boundary embrittlement. As a result, intermetallic alloys often either have poor fabricability and machinability or require a fabrication process that is complicated and tedious. The generic brittleness problem in intermetallics, particularly aluminides, has been studied extensively in recent years and some breakthroughs have been made. For example, polycrystalline Ni3Al that has an Ll2 structure exhibits almost no ductility, but Ni3Al containing a small amount (0.2 wt%) of boron exhibits room-temperature tensile ductility of up to 40%. Because of these technological breakthroughs, there is great interest in using these materials for engineering structures.

Superplasticity in intermetallics has only been recently demonstrated. Although large tensile elongations (∼100%) for an intermetallic (also known as Sendust, Fe–9.6 wt% Si–5.4 wt% Al) were indicated as early as 1981, true superplastic intermetallics were not observed until 1987. At present, several intermetallics of the Ll2 structure (e.g., Ni3Al and Ni3Si), iron aluminide, titanium aluminide (TiAl), and trititanium aluminides (Ti3Al) have demonstrated superplasticity. These intermetallics are being investigated for their structural applications.

Tests for the lack of a centre of symmetry

As we have seen in § 1.4 measurements of crystals with an optical goniometer can, in favourable circumstances, reveal the crystal class. Such measurements should be carried out on many crystals for there is a tendency for crystals to exist in a number of slightly different forms in each of which some facets may not be present. By-and-large, when incorrect conclusions are drawn from optical goniometry it is in the direction of assigning too high a symmetry to the crystal. However it is sometimes possible to be reasonably sure by means of such measurements that a crystal structure either has or does not have a centre of symmetry.

There are a number of physical properties of crystals, the measurements of which can be used unequivocally to detect the lack of a centre of symmetry in a crystal structure. We shall briefly consider these, the physical principles involved and the apparatus which may be used for the tests.

Piezoelectric effect

The first physical phenomenon we shall consider is that of piezoelectricity. This is the process whereby when a material is placed in an electric field it undergoes a mechanical strain and, conversely, when the material is mechanically strained it becomes electrically polarized and produces a field in its environment. Let us see what mechanism can produce this effect. In fig. 7.1(a) there is a schematic representation of a pair of atoms with their surrounding electron density. The two atoms are bonded together and the electron density is distorted from the configuration it would have for the superposition of that from two isolated atoms.

The purpose of this book is to give an introduction to some of the non-experimental techniques available for studying the interaction of energetic particles with solid surfaces. By energetic we mean particles with energies from <1 eV up to the mega-electronvolt range. The word non-experimental is chosen carefully because much of the book focuses on computer simulation in addition to basic theory. Simulation is a relative scientific newcomer, which contains elements both of theory and of experiment within its borders. A simulation is not a theory but a numerical model of a system. If it is a good model one may explore the behaviour of the real system by changing the numerical value of its input parameters and noting the changed responses. Simulations enable one to determine which are the important factors in a physical system that control its behaviour without the need necessarily to perform complex and expensive experiments. Sometimes we can probe areas that no experiment can determine, for example, the displacement and mixing of identical atoms in an atomic collision cascade. Usually, in performing the computational experiments on a model, the important parameters should be identified and need to be fixed at the start of the calculations. Usually we perform a sensitivity analysis by varying one parameter at a time.

This book is intended to describe methods that will be applicable both to hard collisions between nuclear cores of atoms and to soft interactions in which chemical effects or long-range forces dominate.

Introduction

The energetic interaction of a particle beam with a solid cannot be described fully by the path of a single projectile. The path a particle takes and the paths of the subsequent recoils are dependent upon the initial impact point on the surface. Thus, to get a clear description of the effects of particle interaction with a solid, many such paths must be followed. A typical ion beam experiment would entail the interaction of 1011–1020 particles per cm2 of the target.

Trajectory simulations obtain an ensemble – or set – of independent particle solid impact histories. Each history is followed from a different starting point on the solid to simulate the arrival of many particles at random points on the surface.

Conceptually the molecular dynamics (MD) simulation method (see Chapter 8) is the simplest and most complete simulation method to model the behaviour of a solid undergoing energetic particle bombardment; in particular, for calculating the displacement of particles in the solid during a single particle impact. In principle, the development of the ensuing collision cascade is followed chronologically in time as the energy of the ions propagates through the target system. The complexity comes from the solution of the many-body equations of motion which must be performed at successive time steps.