Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 116

Mechanical testing in shear is more difficult to perform when compared to tension or compression and, thus, it is of interest only when shear is a significant deformation mode in the intended application. For a specimen in the shape of a cube of length l, for example, a force F is applied transversely over two opposite faces of the specimen of area A (Figure 4.1c). The horizontal faces of the specimen tend to slide relative to each other, with their edge lengths remaining the same, and the vertical faces tilt to accommodate this motion. The shear stress τ is defined as

(4.3)

where, A is the area over which the shear force acts, equal to l ² for this example. The shear strain is defined as

(4.4)

where, δ is the displacement of one horizontal face of the cube relative to the other. The shear strain is also given by

(4.5)

where, θ is the angle (in degrees) by which the one vertical face has tilted relative to the other. For small displacements ( δ /l less than ~5%), the strain is also given to a good approximation as γ = θ, where θ is now expressed in radians.