Theories of Failure
Failure is generally perceived to be fracture or complete separation of a member. However, failure may
also occur due to excessive deformation (elastic or inelastic) or a variety of other reasons.
During the latter part of the 19th centur y and continuing up to the present, a number of basic failure
theories were proposed and tested on a few materials. Most of the theories were based on the
assumption that failure occurs when some physical variable such as stress, strain, or energy reaches a
limiting value.
Stress Theories
Maximum Principal Stress Theory (Rankine, Lamé) (Fig. 1)
Applied satisfactorily to many
brittle materials, the theory is based on a limiting normal stress. Failure occurs when the normal stress
reaches a specified upper limit.
1
Fig. (1) Fig. (2)
Maximum Shear Stress Theory (Tresca, Guest, Coulomb) Fig. (2)
Applied satisfactorily to ductile materials, the theory is based on the concept of limiting shearing stress at
which failure occurs.
1
Failure by yielding in a more complicated loading situation is assumed to occur when the maximum
shearing stress in the material reaches a value equal to the maximum shearing stress in a tension test at
yield.
This yield criterion gives good agreement with experimental results for ductile materials; because of its
simplicity, it is the most often used yield theory.
2
The main objection to this theory is that it ignores the
possible effect of the intermediate principal stress, σ
2
. However, only one other theory, the maximum
distortional strain energy theory, predicts yielding better than does the Tresca theory, and the differences
between the two theories are rarely more than 15%.
