Stress, allowable yield

The allowable yield stress Ty of the shaft material under pure tensional loading is obtained from the yield stress in simple tension a-y since from the shear strain energy theory of failure ... 

Allowable stresses Allowable unit stress shall be based on yield strength, Fy, at design temperature with AISC factors for tension, bearing, shear, etc. 

Yielding of the inner surface begins when the maximum shear stress is equal to the yield point shear stress. As the pressure, or force, is increased the plastic deformation penetrates farther into the vessel wall until it reaches the outer surface. At that point the entire shell has yielded. If the internal pressure is removed after the cyhnder is in plastic state, a residual stress will remain in the wall. This residual stress allows the cylinder to contain more pressure then would be possible to without it. 

Division 2. With the advent of higher design pressures the ASME recognized the need for alternative rules permitting thinner walls with adequate safety factors. Division 2 provides for these alternative rules it is more restrictive in both materials and methods of analysis, but it makes use of higher allowable stresses than does Division 1. The maximum allowable stresses were increased from one-fourth to one-third of the ultimate tensile stress or two-thkds of the yield stress, whichever is least for materials at any temperature. Division 2 requkes an analysis of combined stress, stress concentration factors, fatigue stresses, and thermal stress. The same type of materials are covered as in Division 1. 

If the sum of the mechanical allowances, c, is neglected, then it may be shown from equation 15 that the pressure given by equation 33 is half the coUapse pressure of a cylinder made of an elastic ideal plastic material which yields in accordance with the shear stress energy criterion at a constant value of shear yield stress = y -... 

Code-allowable stresses are conservative with respect to stmctural failure that occurs when the limit load is reached, ie, the load that results when component deflections and distortions have destroyed its serviceabiUty. The limit load is generally reached when the stresses throughout a main portion of the component cross section exceed the material yield strength (29). 

In shaded areas, allowable-stress values wliich are printed in italics exceed two- tliirds of the expected yield strength at temperature. All odier allowable-stress values in shaded areas are equal to 90 percent of expected yield strength at temperature. See ANSI B31.3. 

For use in code piping at the stated allowable stresses, the tensile and yield strengths listed in these tables must be verified by tensile tests at the mill such tests shall be specified in the purchase order. 

External-pressure failure of shells can result from overstress at one extreme or n om elastic instability at the other or at some intermediate loading. The code provides the solution for most shells by using a number of charts. One chart is used for cylinders where the shell diameter-to-thickness ratio and the length-to-diameter ratio are the variables. The rest of the charts depic t curves relating the geometry of cyhnders and spheres to allowable stress by cui ves which are determined from the modulus of elasticity, tangent modulus, and yield strength at temperatures for various materials or classes of materials. The text of this subsection explains how the allowable stress is determined from the charts for cylinders, spheres, and hemispherical, ellipsoidal, torispherical, and conical heads. 

But crystals (like everything in this world) are not perfect they have defects in them. Just as the strength of a chain is determined by the strength of the weakest link, so the strength of a crystal - and thus of our material - is usually limited by the defects that are present in it. The dislocation is a particular type of defect that has the effect of allowing materials to deform plastically (that is, they yield) at stress levels that are much less than [Pg.95]

In metals, inelastic deformation occurs at the crack tip, yielding a plastic zone. Smith [34] has argued that the elastic stress intensity factor is adequate to describe the crack tip field condition if the inelastic zone is limited in size compared with the near crack tip field, which is then assumed to dominate the crack tip inelastic response. He suggested that the inelastic zone be 1/5 of the size of the near crack tip elastic field (a/10). This restriction is in accordance with the generally accepted limitation on the maximum size of the plastic zone allowed in a valid fracture toughness test [35,36]. For the case of crack propagation, the minimum crack size for which continuum considerations hold should be at least 50 x (r ,J. 

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