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In uniaxial tension, a common testing mode for metals and polymers, a specimen of uniform cross section is pulled in one direction along its length, that is, uniaxially (Figure 4.1a), whereas in uniaxial compression the specimen is compressed in one direction (Figure 4.1b). In tension, a load (force) F is applied at the larger ends of the specimen of circular or rectangular cross section, and the stress and strain are measured for the central portion, called the gage length. For a specimen of gage length l_o and uniform cross section A, the applied stress σ is defined as

(4.1)

and the strain ε is defined as

(4.2)

where, δ is the increase in the gage length from l_o to l.

Figure 4.1 Different loading modes in mechanical testing of materials: (a) tension, (b) compression, (c) shear, (d) torsion, and (e) four‐point bending (flexure).

As the specimen does not have to be gripped at its ends in compression testing, the use of a cylindrical or tetragonal specimen of uniform cross section, that is, without the larger ends, is easier and less expensive. The common convention in mechanics is that tensile stresses and strains are positive in sign whereas compressive stresses and strains are negative in sign.