Strain hardening is possible both in single crystals and polycrystalline materials. When metallic materials are cold worked, their strength increases. Generally, an annealed crystal contains a dislocation density of about 108 m~2. However, moder­ately cold worked materials may contain 1010-1012 m~2 and heavily cold worked materials 1014-1016 m~2. Plastic deformation carried out in a temperature regime and over a time interval such that the strain hardening is not relieved is called cold working. At the first sight, one might think that with increase in the dislocation density, the material would be more ductile. But that is not the case. As the disloca­tion density increases, the movement of dislocation becomes increasingly difficult due to the interfering effect of the stress fields of other dislocations. In polycrystalline metals/alloys, multiple slips occur more readily due to the mutual interference of adjacent grains, leading to significant strain hardening. In the early stages of plastic deformation, slip is generally limited on primary glide planes and the dislocations tend to form coplanar arrays. However, as the deformation proceeds, cross-slip takes place and dislocation multiplication processes start to operate. The cold worked structure then forms high dislocation density regions or tangles that soon develop into tangled networks. Thus, the characteristic structure of the cold worked state is a cellular substructure. The cell structure is schematically shown in Figure 4.31.

With increasing strain, the cell size decreases at initial deformation regime. However, the cell size tends to reach a fixed size implying that as the plastic defor­mation proceeds, the dislocations sweep across the cells and join the tangles into the cell walls. The exact nature of the cold worked structure depends on the mate­rial, strain, strain rate, and deformation temperature. The development of cell structure, however, is less pronounced for low temperature and high strain rate deformation and in materials with low stacking fault energy.

Strain hardening is an important process that is used in metals/alloys that do not respond to heat treatment easily. Generally, the rate of strain hardening is lower in HCP metals compared to FCC metals and decreases with increasing temperature.

Furthermore, the final strength of the cold worked solid solution alloy is always greater than that of the pure metal cold worked to the same extent. Cold working may slightly decrease density and electrical conductivity, whereas thermal expan­sion coefficient and chemical reactivity increase (i. e., corrosion resistance decreases). Figure 4.32 shows the variation of tensile parameters (strength parame­ters of tensile strength, yield strength, and ductility parameters of reduction in area and elongation to be discussed in the Chapter 5) as a function of percentage cold

reduction. Torsteels are used as reinforcing bars for concrete is cold twisted to increase the strength. However, it acts upon the effective ductility of material.

A high rate of strain hardening implies mutual obstruction of dislocations glid­ing on intersecting slip systems. This can arise from three sources: (a) through interaction of the stress fields of dislocations, (b) through interactions that produce sessile locks, and (c) through the interpenetration of one slip system by another (like cutting trees in a forest) that results in the formation of jogs. The basic equa­tion relating flow stress to structure is

Gb

t — a —-,

where ‘ is the obstacle-obstacle spacing with a having a value between 0.5 and 1. If dislocations are acting as obstacles like trees in dislocation forest, ‘ = 1Д/р, so strengthening due to dislocations is given by

t — t0 + aGbp1/2, (4.33)

where t is the stress needed to move a dislocation in a matrix of dislocation density q, t0 is the stress to move the dislocation in the same matrix with no dislocation density, G is the shear modulus, and b is the magnitude of Burgers vector. The constant a may change value, but may be considered as 0.5.

4.4.2