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Theories of failure in explain in stress theories and strain theories.
Typology: Lecture notes
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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 century 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
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)
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%.
Strain Theories
The theory is based on the assumption that inelastic behavior or failure is governed by a specified maximum normal strain.^1 Failure will occur at a particular part in a body subjected to an arbitrary state of strain when the normal strain reaches a limiting level.
Fig. (3) Fig. (4)
Applicable to many types of materials, the theory predicts failure or inelastic action at a point when the strain energy per unit volume exceeds a specified limit.
The theory is based on a limiting energy of distortion, i.e. energy associated with shear strains.^1
Strain energy can be separated into energy associated with volume change and energy associated with distortion of the body. The maximum distortion energy failure theory assumes failure by yielding in a more complicated loading situation to occur when the distortion energy in the material reaches the same value as in a tension test at yield.
This theory provides the best agreement between experiment and theory and, along the Tresca theory, is very widely used today.^2
Note: This theory gives the same results as the octahedral shear stress theory.
Fig. (5)