- Brittle materials rupture, practically without plastic deformation.
- To predict the stress conditions under which rupture occurs in three-dimensional stress states, the most widely-accepted theory is the Mohr criterion. This theory is based on the intrinsic strength curve of the material.
- This curve is defined as the envelope of the Mohr circles defined by the maximum and minimum principal stress (σ1 and σ3) of the stress states which cause rupture. These circles may be obtained by two- or three-dimensional experimental tests, by gradually increasing one or more of the principal stresses, until rupture takes place.
- The Mohr circle defined by the principal stresses σ1 and σ3 at the moment of rupture is tangent to the intrinsic strength curve. By repeating this procedure for several values of the relations between σ1, σ2 and σ3, a sufficient number of rupture circles to define the intrinsic strength curve may be obtained. Figure shows this curve.
Fig: Intrinsic strength curve of a brittle material
- It is obvious that this curve does not fully define the conditions under which rupture takes place, unless the value of the middle principal stress does not play a significant role, since it is not considered in the definition of the intrinsic reference curve.
- Experimental investigations have shown that this hypothesis may be accepted without introducing a significant error. Once the material’s intrinsic strength curve is obtained, it may easily be verified if a given stress state would cause rupture or not, by drawing the Mohr circle corresponding to the maximum and minimum principal stress and confirming if it intersects that curve or not.