Here, the first subscript indicate the plane on which the stress act (i.e. plane is perpendicular to x -axis) and the second subscript denotes the direction of the stress. Although, there may be infinite number of planes passing through the point ‘P ', but we shall consider only on orthogonal planes mutually perpendicular to each other. Hence, the stress at any point is specified by nine components in the form of matrix as given below, where σ denotes the normal stress and τ is referred as shear stress.

Referring to an infinitesimal element of size as shown in Fig. 2.5.3-d, there are six planes on which stresses act. The planes are named and denoted as positive or negative according to the direction of outward normal to the plane. A stress component is ‘positive, when the direction of stress component and plane on which it acts are both positive or both negative. All the stresses shown in Fig. 2.5.3-d, are all positive.

Fig. 2.5.3: Description of stress in a flow field: (a) Concept of stress; (b) Normal and shear stress; (c) Force and stress components in orthogonal coordinates; (d) Notation of stress.