Deformation and fracture

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Deformation and fracture

When looking at different materials for mechanical purposes we use 'stress-strain' curves. We saw that for materials obeying Hooke's law the stress strain graph is a straight line. However, this straight line forms just a part of the stress strain curve. The whole of the stress-strain curve of a material is an invaluable aid to describing its mechanical behaviour.

For instance, engineers and scientists can easily compare the mechanical properties of different materials by comparing their stress strain curves and decide which material would be better suited for a particular use. Typically, the whole (tensile) stress strain curve of a material is made up of different regions.

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  1. Linear elastic region (region I): At relatively low strains (region I) the material obeys Hookes' Law and stress is proportional to strain. This part of the curve is a straight line. The constant of proportionality is the Young modulus and its value is given by the gradient of the straight line.
  2. Non-linear elastic region (region II): If we stretch the material beyond its elastic region, we soon reach the elastic limit of the material. This part of the curve is not a straight line i.e. Hooke's law is not obeyed. However, if the force (load) is removed the material can go back to its original shape
  3. Yield region (region III): the material suddenly experiences increased deformation. This point of the graph is known as the upper yield point (Y1). Interestingly, the stress begins to decrease with the increasing strain until another point the lower yield point (Y2) is reached.
  4. Beyond the lower yield point (region IV): Stress increases again with the increasing strain. However, this increase is not elastic. The material begins to change its cross sectional area uniformly. At some point, the value of the stress reaches its maximum value. This value of the stress is known as the ultimate tensile strength (UTS) of the material
  5. If the material is stretched further beyond the UTS (region V): the material shows 'necking' i.e. one part of it narrows considerably. Although the stress dramatically increases locally in the necking region; the overall stress decreases again with the increasing strain until the breaking point is reached and the material fractures in the necked region The stress at this point is called the breaking stress. We know that in the necked region the material can develop microscopic holes, reducing further, the effective cross sectional area which causes increased local stresses.

Different materials show different stress strain curves, and the size of each of the above regions may differ considerably from material to material. Here are some examples:

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Some materials, called brittle materials, are very stiff (e.g. glass, cast iron) and exhibit elastic behaviour up to relatively very small values of strains. They hardly change their shape in the elastic region. Under greater stresses they do not show any yielding but develop cracks at the surface, which open up as the stress increases and snap to fracture at the breaking point. This kind of fracture is called brittle fracture.

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Many metallic materials (e.g. tin copper, silver) on the other hand are ductile . They tend to plastically elongate under increasing tensile stress. Any cracks on the surface in ductile materials do not become large under stress because the constituent atoms slide over each other. Before breaking point, a ductile material tends to 'neck' decreasing in cross sectional area and eventually breaking.. This kind of fracture is called ductile yielding.

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Materials like rubber show hysteresis but are resilient. These materials can be stressed repeatedly through hysteresis cycles without losing their strength and plastic deformation.

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