In the previous chapter, procedures were described that allow prediction of the elastic response of a single lamina when loaded at an arbitrary angle to the fibre axis. It was shown that such uniaxial sheets tend to be highly anisotropic, with much greater stiffness when loaded parallel to the fibres than at significant angles to them. Moreover, other aspects of the elastic response are very different in different directions. For these reasons, it is common to stack laminae into bonded sets (laminates), making the elastic properties (and also the strength) more isotropic, and also opening up the possibility of tailoring the properties of a component to the loads that it will experience in service – potentially a major advantage of composites when compared with more conventional materials. In this chapter, the treatment of individual laminae is extended to the case of a laminate with an arbitrary stacking sequence, supplying an analytical tool of considerable value in the design of composite materials.

The previous chapter covered factors affecting strength, in terms of the stresses at which damage and failure occur in composites. In many situations, however, it is the energy that is absorbed within the material while fracture takes place that is of prime importance. A tough material is one for which large amounts of energy are required to cause fracture. Some loading configurations, such as a component being struck by a projectile, provide only a finite amount of energy that could cause failure. In fact, there are many situations in which toughness, rather than strength, is the key property determining whether the material is suitable. In this chapter, a brief outline is given of the basics of fracture mechanics, with particular reference to the energetics of interfacial damage. This is followed by an appraisal of the sources of energy absorption in composites. Finally, progressive crack growth in composites is examined under conditions for which fast fracture is not energetically favoured (sub-critical crack growth).

African states were successors in a double sense. First, they were built on a set of institutions – bureaucracies, militaries, customs facilities, post offices, and (for a time at least) legislatures – set up by colonial regimes, as well as on a principle of state sovereignty sanctified by a community of already existing states. In this sense, African states have proven durable: borders have remained largely unchanged (with the notable exceptions of the secession of Eritrea from Ethiopia and South Sudan from Sudan). Almost every piece of Africa is recognized from outside as a territorial entity, regardless of the effective power of the actual government within that space. Even so-called failed states – those unable to provide order and minimal services for their citizens – are still states, and derive resources from outside for that reason.

In the late 1930s and 1940s colonial rule choked on the narrowness of the pathways it had created. Trying to confine Africans to tribal cages, seeking to extract from them what export products and labor it could without treating them as “workers,” “farmers,” “townsmen,” or “citizens,” colonial regimes discovered that Africans would not stay in the limited roles assigned to them. Instead, the constrictions created exactly the sort of danger administrators feared. Urban unrest within a very rural continent challenged colonial governments; a small number of wage workers threatened colonial economies; a tiny educated elite undercut the ideological pretenses of colonialism; supposed “pagans” worshiping local gods and ancestors produced Christian and Muslim religious movements of wide scope and uncertain political significance; and commercial farmers in a continent of “subsistence” producers made demands for a political voice for themselves and opportunities for their children that colonial systems could not meet.