Strain
When stress is present, strain will also be a factor. The two types of strain will be discussed in this article.
Definition of Strain
In the use of metal for mechanical engineering purposes, a given state of stress usually exists in a considerable volume of the material. Reaction of the atomic structure will manifest itself on a macroscopic scale. Therefore, whenever a stress (no matter how small) is applied to a metal, a proportional dimensional change or distortion must take place.
Such a proportional dimensional change (intensity or degree of the distortion) is called strain and is measured as the total elongation per unit length of material due to some applied stress. The equation below illustrates this proportion or distortion.
where:
ε = strain (in./in.)
δ = total elongation (in.)
L = original length (in.)
Note that the equivalent SI metric units to inches are the millimetre, centimetre, and metre.
Types of Strain
Strain may take two forms: elastic strain and plastic deformation.
Elastic Strain
Elastic strain is a transitory dimensional change that exists only while the initiating stress is applied and disappears immediately upon removal of the stress. Elastic strain is also called elastic deformation. The applied stresses cause the atoms in a crystal to move from their equilibrium position. All the atoms are displaced the same amount and still maintain their relative geometry. When the stresses are removed, all the atoms return to their original positions and no permanent deformation occurs.
Plastic Deformation
Plastic deformation (or plastic strain) is a dimensional change that does not disappear when the initiating stress is removed. It is usually accompanied by some elastic strain.
The phenomenon of elastic strain and plastic deformation in a material are called elasticity and plasticity, respectively.
At room temperature, most metals have some elasticity, which manifests itself as soon as the slightest stress is applied. Usually, they also possess some plasticity, but this may not become apparent until the stress has been raised appreciably. The magnitude of plastic strain, when it does appear, is likely to be much greater than that of the elastic strain for a given stress increment. Metals are likely to exhibit less elasticity and more plasticity at elevated temperatures. A few pure unalloyed metals (notably aluminium, copper and gold) show little, if any, elasticity when stressed in the annealed (heated and then cooled slowly to prevent brittleness) condition at room temperature, but do exhibit marked plasticity. Some unalloyed metals and many alloys have marked elasticity at room temperature, but no plasticity.
The state of stress just before plastic strain begins to appear is known as the proportional limit, or elastic limit, and is defined by the stress level and the corresponding value of elastic strain. The proportional limit is expressed in pounds per square inch in imperial units, or Newton per metre squared in metric units. For load intensities beyond the proportional limit, the deformation consists of both elastic and plastic strains.
As mentioned previously in this article, strain measures the proportional dimensional change with no load applied. Such values of strain are easily determined and only cease to be sufficiently accurate when plastic strain becomes dominant.
When metal experiences strain, its volume remains constant. Therefore, if volume remains constant as the dimension changes on one axis, then the dimensions of at least one other axis must change also. If one-dimension increases, another must decrease. For example, a shape may change from short and fat, to long and thin, but the volume remains the same. There are a few exceptions. For example, strain hardening involves the absorption of strain energy in the material structure, which results in an increase in one dimension without an offsetting decrease in other dimensions. This causes the density of the material to decrease and the volume to increase.
If a tensile load is applied to a material, the material will elongate on the axis of the load (perpendicular to the tensile stress plane), as illustrated in the image below (Tension). Conversely, if the load is compressive, the axial dimension will decrease, as illustrated in the image below (Compression). If volume is constant, a corresponding lateral contraction or expansion must occur. This lateral change will bear a fixed relationship to the axial strain. The relationship, or ratio, of lateral to axial strain is called Poisson's ratio after the name of its discoverer. It is usually symbolised by the letter ν.
Change of Shape of Cylinder Under Stress
Deformation of Cubic Structures
Whether or not a material can deform plastically at low applied stresses depends on its lattice structure. It is easier for planes of atoms to slide by each other if those planes are closely packed. Therefore, lattice structures with closely packed planes allow more plastic deformation than those that are not closely packed. Also, cubic lattice structures allow slippage to occur more easily than non-cubic lattices; this is because of their symmetry which provides closely packed planes in several directions. Most metals are made of the body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal close-packed (HCP) crystals. A face-centered cubic crystal structure will deform more readily under load before breaking than a body-centered cubic structure.
The BCC lattice, although cubic, is not closely packed and forms strong metals. α-iron (a form of iron called ‘alpha’ iron) and tungsten have the BCC form. The FCC lattice is both cubic and closely packed and forms more ductile materials. Silver, gold, and lead are FCC structured. Finally, HCP lattices are closely packed, but not cubic. HCP metals like cobalt and zinc are not as ductile as FCC metals.
Summary
The important information in this chapter is summarised below.
Strain Summary
- Strain is the proportional dimensional change, or the intensity or degree of distortion, in a material under stress.
- Plastic deformation is the dimensional change that does not disappear when the initiating stress is removed.
- Proportional limit is the amount of stress just before the point (threshold) at which plastic strain begins to appear, or the stress level and the corresponding value of elastic strain.
- There are two types of strain:
Elastic strain is a transitory dimensional change that exists only while the initiating stress is applied and disappears immediately upon removal of the stress.
Plastic strain (plastic deformation) is a dimensional change that does not disappear when the initiating stress is removed.