Failure theories maximum normal stress

By definition, a brittle material does not fail in shear failure oeeurs when the largest prineipal stress reaehes the ultimate tensile strength, Su. Where the ultimate eompressive strength, Su, and Su of brittle material are approximately the same, the Maximum Normal Stress Theory applies (Edwards and MeKee, 1991 Norton, 1996). The probabilistie failure eriterion is essentially the same as equation 4.55. 

When the material behavior is brittle rather than ductile, the mechanics of the failure process are much different. Instead of the slow coalescence of voids associated with ductile rupture, brittle fracture proceeds by the high-velocity propagation of a crack across the loaded member. If the material behavior is clearly brittle, fracture may be predicted with reasonable accuracy through use of the maximum normal stress theory of failure. Thus failure is predicted to occur in the multi-axial state of stress when the maximum principal normal stress becomes equal to or exceeds the maximum normal stress at the time of failure in a simple uniaxial stress test using a specimen of the sane material. 

Maximum normal stress theory (Lame-Navier) Failure occurs when the... 

The maximum shear-stress theory has been found to be suitable for predicting the failure of ductile materials under complex loading and is the criterion normally used in the pressure-vessel design. 

The maximum intensity of stress allowed will depend on the particular theory of failure adopted in the design method (see Section 13.3.2). The maximum shear-stress theory is normally used for pressure vessel design. 

The maximum principle stress theory (Rankine s theory) states that the largest principle stress component, 03, in the material determines failure regardless of the value of normal or shearing stresses. The stability criterion is formulated as... 

However, it is a general practice to provide detailed stress analysis for the vessel components outside the Code approved details using either the maximum-stress or the maximum-shear theory of failure and to select allowable stresses for design conditions other than normal operations or for computed stresses other than direct membrane or direct membrane plus primary bending Code stresses. CEGB R6 method based on fracture mechanics is highly recommended. This method later on has been thoroughly discussed in this chapter. 

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