What do you need to measure?

The platforms described in the previous chapter access a range of states via a number of thermodynamic loading paths taken by a material as it deforms. Some load to the elastic limit, some up to the finis extremis where electronic bonding changes its nature, and some beyond that. What follows will concern loading from the elastic limit to the point at which ambient descriptions of strength cease to apply. A few of the loading paths necessary to define an equation of state for a material are shown in the schematic of Figure 4.1. There are a range of outputs which may be sensed to give insight into the response of materials under load. Experiments should aim to map their states beyond the yield point statically and dynamically. In the first case they induce an ideal stress state to define operating mechanisms represented in suitable models, which are later tested against other loading down more complex paths. Thus shock experiments map out Hugoniot curves but can also yield information that allows one to deduce compression isotherms and isentropes. Isotherms are generally measured using static compression experiments at some fixed temperature in the diamond anvil cell (DAC). To briefly recap, the isentrope generally lies between the isotherm and Hugoniot curves and is in fact tangent to the Hugoniot at the common starting state. Although shock experiments generally yield only a final P–V state on the Hugoniot, an ideal isentropic compression experiment (ICE) yields a continuous locus of points along a different loading path. Although not precisely following the isentrope, it is certainly possible to load more slowly and avoid the adiabatic conditions of shock, and so this is better dubbed shockless loading. To record this data demands sensors capable of acquiring pressure, density and temperature as a function of time, which requires sub-nanosecond data collection under the fastest loadings. To measure deviatoric quantities entails measures of the stress state in the target which is itself directional. Thus a series of accurate, time-resolved sensors has been developed to make such measurements in these experiments. Another means of recording the data is to use a quantitative imaging technique (such as X-rays) to deduce state parameters from the flow. Imaging itself allows the visualisation of geometries changing under load whist offering non-invasive measurements of flow parameters.

In the text a range of problems encountered by materials under extreme conditions has been described. To understand them, knowledge of the response of structure at the microscale is necessary and this has been assembled in the ambient state by materials science. Chemical reaction is possible in some substances in the condensed phase, and these are described as energetic, but in general physical deformation precedes chemistry in loaded materials. A fundamental focus for this field will be to try and understand the nature of the strength of solids. It will become clear that this is a difficult objective since complex behaviour results from the two classes of process that define strain: that in which length or volume changes with constant shape and one in which the shape changes at constant volume.

In what follows the response of these will be followed through from the microstructure at the atomic level to their form at the continuum. The various materials classes – metals, brittle materials, polymers and composites of all three – will be looked at to highlight particular features of their behaviour which go towards defining how the macroscopic boundary conditions of the loading excite response from the individual atomic architectures. The framework to describe observations is materials physics and this will be summarised below to aid the reader. It is by no means complete and much more rigorous texts exist for the student of materials science; however, it serves to allow a reader from an alternative background access to the necessary concepts to make the comments elsewhere in the text more tractable.

Introduction

To obtain high strength often suggests inorganic and non-metallic materials where hardness provides resistance against high thermal or mechanical loads. In a book concerned with dynamic extremes, these stimuli include materials propelled to impact at high velocity. The design paradigm requires a material to deliver an easily formed structural component capable of resisting impulsive loads of high amplitude and arbitrary duration. At the present time the reality is that these aspirations are only partially met. The response of these materials to idealised one-dimensional loading under shock is not yet understood in full detail and fully three-dimensional loading is only described empirically. Nevertheless the response of glasses and ceramics to dynamic loading has been investigated by the impact community over the past 30 years so that at least a library of data exists. In that time much has been learnt but vital questions remain unresolved, particularly understanding contact, penetration, fragmentation, inelastic behaviour and failure that are encountered in the response of a brittle material to impulsive loading.

Even the qualitative understanding of the response of brittle materials to dynamic loading has not been reflected in advances in constitutive models for them. This results from an incomplete knowledge of operating mechanisms that are consequently not reflected in global models. Further, there is a wide range of microstructures represented in this grouping, ranging from amorphous silicate glasses to polycrystalline ceramics containing both crystalline and amorphous phases. Clearly to construct adequate models for such heterogeneous materials to work on numerical platforms requires a macroscale description of behaviour, yet at present even subscale approaches have not described the processes operating in these heterogeneous media where the phases interact at the mesoscale. It is scale that remains the key frontier that bridges the continuum to microscale behaviour, and it is the mesoscale where the defects that control failure in the bulk are found.

Introduction

The man-made and the natural environment surrounds man with a wide array of plastics and polymers both natural and man-made. A polymer is a molecule which contains repeated units of a particular chemical base segment, and there are many types found across organic chemistry. A plastic is a term that covers a wide range of mostly synthetic but also some natural organic products that can be moulded or extruded. Thus while all plastics are organic polymers, not all polymers are plastics and in general may need to be modified with other additives to form useful materials. In everyday parlance plastic and polymer are terms often used interchangeably but in fact there are many other types of molecules, both biological and inorganic, that are also polymeric.

The word polymer has ancient Greek roots, compounded from poly (meaning many) and meros (meaning parts or units), whilst plastic has a root that indicates a solid that is malleable being easily shaped or moulded. Natural plastics may originate in biological systems such as tar and shellac, tortoise shell and horns, as well as tree saps that produce amber and latex. These plastics may be processed with heat and pressure into a host of different products. If natural polymers are chemically modified then other plastics result and during the 1800s these processes produced such materials as vulcanised rubber and celluloid. In 1909 a semi-synthetic polymer was produced called Bakelite, soon followed by fibres such as rayon (1911). The ability to work and particularly to cast or mould them to component shapes made plastics increasingly dominant for manufacturing. However, restrictions on supply of natural materials during the Second World War led to the modern predominance of synthetic plastics. This time period saw development of nylon, acrylic, neoprene, polyethylene and many more to replace the natural products that could no longer be imported. Post-war the plastics business has developed into one of the fastest growing industries in the world.

Introduction

In the next chapters, four groups of materials will be introduced and discussed. These will embrace metals, brittle solids, polymers and energetic materials. Some of these will be pure elements in various microstructures, others will be composites of several in different conformations. A lot of what follows has been described and studied by materials science and much terminology and commonplace understanding will be borrowed from there. Appendix A at the end of the book summarises some key concepts for those trained in other disciplines. At the most basic level, materials can be classified as metals or non-metals according to their ability to conduct electricity. The metals consist of cations in a delocalised electron cloud with structure determined by electrostatic bonds formed between the ions and the electron cloud. As pressure increases this bonding changes nature and above the finis extremis localisation of the electron density away from the nucleus occurs leading to new states.

Metals are the most common class of elements in the periodic table (Figure 5.1). Atomic stacking rules define a lattice of ions surrounded by a delocalised cloud of electrons, but from the point of view of the electronic states, one may equally consider them as materials where conduction and valence bands overlap. This definition opens the descriptor to metallic polymers and other organic metals and, considering the context within this book, one must consider the behaviour of materials that change their characteristics under high pressures and cause them to achieve metallic states (to conduct) at pressures below the finis extremis. A diagonal line drawn from aluminium (Al) to polonium (Po) separates the metals from the non-metals, and within that region the elements order themselves into subgroups defined by their electronic structures.

Introduction

This chapter will detail the response of a class of materials dubbed energetic to signify that they can break bonds and react under load. These substances contain a large amount of stored chemical energy that can be released if appropriate thermal thresholds are exceeded. Such materials combine a fuel and an oxidiser; fuels are typically carbon or hydrogen, oxidisers are oxygen or a halogen like chlorine, for example. Combining hydrogen and oxygen to form water liberates 13 260 J kg–1 and burning petrol with oxygen (air) 30000 J kg–1. Yet the high explosive TNT liberates only 4080 J kg–1, less than 15% of the amount liberated by petrol. The difference is that fuel alone burns only where oxygen is present; a spillage will burn for minutes with oxygen from air, for example. Yet a TNT molecule contains oxygen within it and can liberate energy in the microseconds the reaction front takes to transit the molecule and break bonds. Therefore the difference between these fuels lies in the power that the molecule supplies in the form in which the material exists on ignition. Energetic materials may be solids, liquids or gases, but condensed-phase materials will be followed here as earlier in the book. Further, they need not necessarily be organic. There is increasing need for higher performance, lighter weight and safer composites which use reacting metals as well as more conventional materials and using new material morphologies which have increased surface areas, such as mixtures of nano-materials or designed nano-composites. However, the principal energetics used at the present time include a range of elements that react with oxygen and these will be discussed in what follows.

Introduction

Matter in the universe exists in a series of states; three that are well known from standard experience, solid, liquid and gas, and the plasma state in which gas is ionised. Other more esoteric states are possible but the four above occupy the main thrust of this book. This volume has confined itself to pressures in the range up to a megabar and temperatures below 10000 K in which solids exhibit strength that is based upon the interaction of valence electrons. Beyond a critical energy density bonding is determined by further interactions of inner orbital electrons and concepts from the ambient cannot be extended.

Equally the forces acting on matter applicable to this work are electrostatic or gravitational. Electrostatic forces may act over great distance but as length scale increases there is sufficient matter that substances behave as neutral. The long-range attractions at the microscale are due to Van de Waals’ forces that might operate over distances of the order of 10 nm between polymer chains and are important in binding matter at the mesoscale. Components on a scale of centimetres are naturally held under gravity in stacks or compressed under lateral forces by some restraint. The strength of such an interface in tension is determined by that of the pin or joint that constrains the interface between the two components. At this scale, flow occurs by hinging around pivots under load or by slip along the fracture line with frictional heating at the interface. At the planetary scale forces are gravitational and slip occurs down faults that allow flow under shear.

I cannot explain my curiosity about extreme phenomena in nature; nevertheless I have been drawn to the science that surrounds them – from those occurring on the scale of solar systems to those at work at the smallest regimes within matter. Extreme forces surround us; they govern our weather, the cores of planets, components of engineering structures and the ordering of particles within atoms. At the scales of interest in this book they are either gravitational or electrostatic in origin. Forces drive mechanical routes to impose change and materials are forced to respond to these pressures in non-linear, counter-intuitive and utterly fascinating manners; frequently more quickly than not only the senses, but the recording media that exist today can track. Nothing that changes does so instantaneously; every mechanism takes some time, however small. This mean that the integrated response follows a delicate framework of competing pathways that reorder as the driver for the forces changes. As with many processes, one can only see patterns apparent in retrospect. Furthermore, the difficulties encountered achieving these states mean that there are many untracked routes that matter can take to respond about which we know little. Thus despite the years this book has taken to come to this point, it can only provide a snapshot of behaviour as I see it.

Nevertheless, matter allows the nature of its bonding to be probed by subjecting it to load and the reader will learn to appreciate the variety of materials behaviours and their causes that allow the design of structures or even new materials to withstand the environments considered. The behaviours observed are complex and seemingly counter-intuitive, and quantifying them has frequently filled books in the past with extended solid mechanics. This has made texts rich in analysis and specialised in application and required the reader to be expert in the mathematics of non-linear behaviour. However, it seemed that a reader with an appreciation of the physical sciences and elementary algebra required an open text to emphasise behaviours not analytical subtleties. Thus this book unites principles covering a broad canvas at a level accessible to graduate students. Further, it addresses the regime in which the strength of matter may be described with extensions of solid mechanics at the continuum rather than extrapolation of atomic theory and quantum mechanics at the atomic scale.