Allowable stress intensity

Pressure vessels are subjected to other loads in addition to pressure (see Section 13.4.7) and must be designed to withstand the worst combination of loading without failure It is not practical to give an explicit relationship for the vessel thickness to resist combined loads. A trial thickness must be assumed (based on that calculated for pressure alone) and the resultant stress from all loads determined to ensure that the maximum allowable stress intensity is not exceeded at any point. 

The material of the vessel is SA 533 Gr. B Class 1 for which the allowable stress intensity (Sm.) from the ASME Boiler and Pressure Vessel Code, Section 111 is 184 MPa. We can take P = 17 MPa, R = 2 m = 2000 mm. From Eq. (5.15) with the joint efficiency E, taken as 100 percent or unity, and S = Sm (this equation also appears in ASME Code Section 111, Paragraph, NB 3324.1) ... 

Local membrane stress intensity. The maximum allowable stress intensity for S derived from <7l stresses is 1.5<7n, times the factor k when applicable. 

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. 

The boundary layer approach is used to investigate the mode I plane strain fields near the crack. The symmetry of the problem allows consideration of only half the geometry (see Fig. 7), which consists of an initial blunted crack of radius n with traction-free surfaces along the crack. Along the boundary of the remote region at a distance R with R % 200rt, the mode I elastic field at stress intensity factor Ki is prescribed [8,22],... 

Another aspect to be considered is the difficulty in producing curved structures with the same fibre content as flat laboratory panels. This effect is shown in Figure 16, at the comer the laminate thickness is larger than at the flat section and fibre content is rather lower. This will affect the bending stiffness of the arm and the predicted failure load. This figure also shows the fillet, which is critical to initiation in the specimens without implanted defects. It is well known that fillets can significantly alter the load path in lap shear joints and increase the failure loads (see [1] and Figure 3 for example). If a fracture mechanics approach is to be applied this effect must be considered. Some recent studies on stress intensity factors for such cases may allow this to be addressed [22]. 

The vessel wall thickness must be sufficient to ensure the maximum stress intensity does not exceed the maximum allowable stress (nominal design strength) for the material of construction, at any point. The AS ME BPV Code Sec. II Part D should be consulted for the maximum allowable stress values in tension or in compression. 

The lower hmit of integration (at or ai) is usually defined on the basis of nondestructive inspection (NDl) capabilities, or on prior inspection the upper limit is defined by fracture toughness or a predetermined allowable crack size that is consistent with inspection requirements (a/ or 2)- Equations (7.5) and (7.6) may be rewritten in terms of the stress intensity factor K ... 

Because allowable stress for design (called stress intensity in the Division 2 code) has been raised above that given in Division 1, a stress analysis may be required. The criteria for determining the necessity of a stress analysis for a particular pressure vessel are left to the judgment of the vessel engineer. 

To allow for the slow crack propagation at stress intensity factors Ki < Xic, the criterion of Eq. (9.14) is re-expressed as... 

ASME Code, Section VIII, Division 2, and Section III use the term stress intensity, which is defined as twice the maximum shear stress. Since the shear stress is compared to one-half the yield stress only, stress intensity is used for comparison to allowable stresses or ultimate stresses. To define it another way, yielding begins when the stress intensity exceeds the yield strength of tlie material. 

Figure 8.37 Complex void shapes have been modeled by a eircular eraek emanating from a spherical void. This allows the stress intensity factor to be calculated. For short cracks, the solution approaches that of a surface crack, while for long cracks that for a circular crack of radius (R+a).

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