Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 117

In torsional deformation, a torque is applied to one end of a specimen to twist it relative to the other end and the angle of twist is measured. Although the geometry is different from that described in the previous section, torsional deformation results in shearing one part of the specimen over another and, thus, we can also define a shear stress and shear strain for this mode of deformation. A force F applied to one end of a specimen in the shape of a cylinder of length l and radius r to twist it in the circumferential direction relative to the other end (Figure 4.1d) creates a torque T given by

(4.6)

The angle of twist θ is the angle of rotation in the circumferential plane of one face relative to the other and the displacement δ of one face relative to the other is given by

(4.7)

where, θ is the angle in radians. The maximum shear stress at the outer surface of the cylinder τ is given by

(4.8)

where, J is called the polar moment of inertia. For a cylinder of radius r, it is given by

(4.9)

The shear strain is given by

(4.10)

where, θ is the angle of twist (in radians).