Stretching of a steel wire

One of the simplest loading conditions of a material is that of tension, in which the fibres of the material are stretched. Consider, for example, a long steel wire held rigidly at its upper end, Figure 1.1, and loaded by a mass hung from the lower end. If vertical movements of the lower end are observed during loading it will be found that the wire is stretched by a small, but measurable, amount from its original unloaded length. The material of the wire is composed of a large number of small crystals which are only visible under a microscopic study; these crystals have irregularly shaped boundaries, and largely random orientations with respect to each other; as loads are applied to the wire, the crystal structure of the metal is distorted.
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For small loads it is found that the extension of the wire is roughly proportional to the applied load, Figure 1.2. This linear relationship between load and extension was discovered by Robert Hooke in 1678; a material showing this characteristic is said to obey Hooke’s law. As the tensile load in the wire is increased, a stage is reached where the material ceases to show this linear characteristic; the corresponding point on the load-extension curve of Figure 1.2 is known as the limit of proportionality. If the wire is made from a hgh-strength steel then the load-extension curve up to the breakingpoint has the form shown in Figure 1.2. Beyond the limit of proportionality the extension of the wire increases non-linearly up to the elastic limit and, eventually, the breaking point. The elastic h u t is important because it divides the load-extension curve into two regions. For loads up to the elastic limit, the wire returns to its original unstretched length on removal of the loads; tlus properly of a material to recover its original form on removal of the loads is known as elasticity; the steel wire behaves, in fact, as a still elastic spring. When loads are applied above the elastic limit, and are then removed, it is found that the wire recovers only part of its extension and is stretched permanently; in tlus condition the wire is said to have undergone an inelastic, or plastic, extension. For most materials, the limit of proportionality and the elastic limit are assumed to have the same value. In the case of elastic extensions, work performed in stretching the wire is stored as strain energy in the material; this energy is recovered when the loads are removed. During inelastic extensions, work is performed in makmg permanent changes in the internal structure of the material; not all the work performed during an inelastic extension is recoverable on removal of the loads; this energy reappears in other forms, mainly as heat. The load-extension curve of Figure 1.2 is not typical of all materials; it is reasonably typical, however, of the behaviour of brittle materials, which are discussed more fully in Section 1.5. An important feature of most engineering materials is that they behave elastically up to the limit of proportionality, that is, all extensions are recoverable for  loads up to this limit. The concepts of linearity and elasticity’ form the basis of the theory of small deformations in stressed materials.
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