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Theory 1: Tensile testing

In a tensile test, a sample is extended at constant rate, and the load needed to maintain this is measured. The stress (σ) (calculated from the load) and strain (ε) (calculated from the extension) can either be plotted as nominal stress against nominal strain, or as true stress against true strain (definitions). The graphs in each case will be different:

Graph of nominal stress against nominal strain Graph of true stress against true strain

Graphs illustrating the difference between nominal stress and strain and true stress and strain.

There are two main types of strain - elastic strain and plastic strain. Elastic strain is the stretching of atomic bonds, and is reversible. Elastic strain can be related to the stress by Hooke's law :

σ = Eε

where E is the Young's modulus .

Plastic strain, or plastic flow, is irreversible deformation of a material. There is no equation to relate the stress to plastic strain.

Several points on the graph can be defined:

A - limit of proportionality - the point beyond which Hooke's Law is no longer obeyed. This is the point at which slip (or glide ) due to dislocation movement occurs in favourably oriented grains. The graph is linear up to this point, and begins the transition from elastic to plastic deformation above this.

B - yield stress - the stress at which yielding occurs across the whole specimen. The stress required for slip in a particular grain will vary depending on how the grain is oriented, so points A and B will not generally be coincident in a polycrystalline sample. At this point, the deformation is purely plastic.

C - proof stress - a third point is sometimes used to describe the yield stress of the material. This is the point at which the specimen has undergone a certain (arbitrary) value of permanent strain, usually 0.2%. The stress at this point is then known as the 0.2% proof stress. This is used because the precise positions of A and B are often difficult to define, and depend to some extent on the accuracy of the testing machine.

D - ultimate tensile strength (UTS) - the point at which plastic deformation becomes unstable and a narrow region (a neck) forms in the specimen. The UTS is the peak value of nominal stress during the test. Deformation will continue in the necked region until fracture occurs.

E - final instability point - the point at which fracture occurs, ie the failure point

F - fracture stress - The stress at which fracture occurs - only obtainable from the true stress-strain curve. See fracture toughness .

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