Definition of Mohr circle

Mohr's circle, invented by Christian Otto Mohr, is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. ... , of each point on the circle are the magnitudes of the normal stress and shear stress components, respectively, acting on the rotated coordinate system. The Mohr circle is used to find the stress components and , i.e., coordinates of any point on the circle, acting on any other plane passing through making an angle with the plane. For this, two approaches can be used: the double angle, and the Pole or origin of planes.The Mohr circle is used to determine graphically the stress components acting on a rotated coordinate system, i.e., acting on a differently oriented plane passing through that point. Mohr's circle is a graphical representation of a general state of stress at a point. It is a graphical method used for evaluation of principal stresses, maximum shear stress; normal and tangential stresses on any given plane. ... The normal stresses are plotted along the abscissa. it enables you to visualize the relationships between the normal and shear stresses acting on various inclined planes at a point in a stressed body. 
Mohr's circle also tells you the principal angles (orientations) of the principal stresses without your having to plug an angle into stress transformation equations. Starting with a stress or strain element in the XY plane, construct a grid with a normal stress on the horizontal axis and a shear stress on the vertical. 
The three principal stresses are conventionally labelled σ1, σ2 and σ3. σ1 is the maximum (most tensile) principal stress, σ3 is the minimum (most compressive) principal stress, and σ2 is the intermediate principal stress
shear stress acting on a positive face is positive if it acts in the positive direction of an axis, and negative if it acts in the negative direction of an axis. A shear stressacting on a negative face is positive if it acts in the negative direction of an axis and negative if it acts in the positive direction.

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