An Overview of ASME B&PV Design by Analysis

The Design by Rule methods of Section VIII, Division 1 and Section VIII, Division 2, Part 4, of the ASME Boiler & Pressure Vessel Code typically involve calculating a required thickness of a pressure vessel component or an allowable pressure based on a component thickness. The approach of the Design by Analysis methods of Section VIII, Division 2 is different in that required thicknesses and allowable pressures are generally not explicitly calculated. Rather, the proposed details of the pressure vessel component are analyzed to ensure it will not fail when subjected to the expected loading.

Part 5 of Section VIII, Division 2 (Design by Analysis) of the ASME Code lists four failure modes to be investigated. The pressure vessel or component must be evaluated for each of these failure modes (as applicable). These failure modes are:  plastic collapse, local failure, buckling, and fatigue.

An overview of the methods used in evaluating for these four failure modes is provided below.

This article is based on the 2021 Edition of the ASME Boiler & Pressure Vessel Code. The applicable edition of the ASME Code should be consulted when designing pressure vessels to ensure all of the necessary requirements are met.

Protection Against Plastic Collapse

Plastic collapse occurs when a material has undergone plastic (permanent) deformation to the extent that the pressure vessel component can no longer sustain the applied loads. This results in a fracture or collapse of the component.

In order to ensure that plastic collapse does not occur for the expected loads, the ASME Code requires one of three analysis methods be performed. These are:  Elastic Stress Analysis Method, Limit Load Method, and Elastic-Plastic Stress Analysis Method.

With the Elastic Stress Analysis Method, stresses are computed using elastic analysis, classified into categories (e.g., primary, secondary, general, local, etc.), and limited to allowable values. Specifically, linearized membrane and linearized membrane plus bending equivalent (von Mises) stresses are compared to allowable stress limits. The magnitudes of the allowable stress limits vary depending on the stress category.     

Alternately, a limit-load analysis can be performed. Using scaled loads (e.g., pressure is scaled by a factor of 1.5 or 1.3) and elastic-perfectly plastic material behavior, the design is considered acceptable if the analysis converges, indicating the vessel (or component) can sustain the applied loads.

Lastly, an elastic-plastic stress analysis can be performed. An elastic-plastic stress analysis performed in accordance with the ASME Code consists of using scaled loads and modeling elastic-plastic material behavior. If the analysis converges for the scaled loads, the design is considered acceptable.

Protection Against Local Failure

While performing one of the above analyses to ensure protection against plastic collapse may predict a failure in a local area of a pressure vessel or component, the ASME Code requirement to ensure protection against local failure specifically pertains to hydrostatic (triaxial) loading of pressure vessel components.

In a state of significant hydrostatic stress ductile materials behave in a brittle manner. Basically, the material doesn’t have anywhere to deform to. This results in a lower plastic strain to cause failure than material that is not loaded triaxially.

The ASME Code provides two options for ensuring protection against local failure. The first is performing an elastic stress analysis, the other is an elastic-plastic analysis. With the elastic stress analysis method, the sum of the three principal stresses is compared to an allowable stress limit. The elastic-plastic analysis method compares the sum of the equivalent triaxial strain and forming strain to an allowable triaxial strain limit.

It is noted that the ASME Code considers the elastic-plastic analysis method more accurate. This is due to questions concerning the accuracy of the elastic stress analysis method which uses pseudo-elastic stresses to evaluate a failure mode associated with local plastic strain. Nevertheless, both methods are considered acceptable by the Code.

Protection Against Collapse from Buckling

The ASME Code requires one of three methods to ensure collapse from buckling will not occur. These are:  1) bifurcation buckling analysis using an elastic stress analysis, 2) bifurcation buckling analysis using an elastic-plastic stress analysis, and 3) a nonlinear buckling analysis using an elastic-plastic stress analysis with imperfections explicitly modeled.

With elastic bifurcation buckling analysis, geometric nonlinearities are not considered in determining the pre-stress in the component. Load case combinations and load factors are the same as those used in evaluating for protection against plastic collapse using the elastic stress method.

The elastic-plastic bifurcation buckling analysis includes geometric nonlinearities in determining the pre-stress in the component. However, the load case combinations and load factors are not those used in evaluating for protection against plastic collapse using the elastic-plastic method, but rather those using the elastic stress method.

Design factors are used for the elastic bifurcation and elastic-plastic bifurcation buckling analyses to account for imperfections not being included in the numerical models. With bifurcation buckling analyses, the collapse load computed by the analysis is compared to a minimum design factor. If the collapse load is greater than the minimum design factor, the design is considered satisfactory.

The last option is an elastic-plastic stress analysis where imperfections are explicitly modeled. The load case combinations and load factors for this method are the same as those used in evaluating for protection against plastic collapse using the elastic-plastic analysis method. Since imperfections are included in the model, the design factor (factor of safety to ensure buckling doesn’t occur) is accounted for in the factored load combinations.

Protection Against Failure from Cyclic Loading (Fatigue)

Since fatigue life is a function of the magnitude of the stress and number of applied cycles, the question often arises whether or not a fatigue assessment is necessary. The ASME Code provides criteria for answering this question. The Code provides two methods for determining if a fatigue analysis is required.  Alternately, the Code also allows for a fatigue analysis to be deemed unnecessary if successful experience with comparable equipment subjected to similar loading can be shown.

Part 5 of Section VIII, Division 2, of the ASME Code provides several options in performing a fatigue assessment.

An elastic stress analysis can be performed. With this method, alternating equivalent stresses are calculated. Depending on the details of the numerical (FEA) model and magnitude of the stresses, various scaling factors are applied to the calculated stresses. Once the scaled stresses are calculated for the various cyclic loads, the number of permissible cycles and corresponding fatigue damage are determined.

Alternately, an elastic-plastic analysis can be performed. With this method, an effective strain range is used to evaluate the fatigue damage. The effective strain range is calculated for each cyclic load using either a cycle-by-cycle analysis, or calculated for a single load step based on a stabilized cyclic stress range-strain range curve and load range representing a cycle (known as the Twice Yield Method).

Either of the above two analysis methods are acceptable for weld joints with smooth profiles (e.g., welds that have been machined or ground smooth). The ASME Code recommends and provides a fatigue assessment procedure for weld joints that do not have a smooth profile. This procedure is used to capture the effects of stress concentrations on fatigue behavior of welded joints not usually predicted by finite element analysis. It involves performing an elastic analysis, calculating local nonlinear stress and strain ranges (using Neuber’s Rule), and calculating an equivalent structural stress range parameter which takes into account material thickness and mean stress. Using the equivalent structural stress range parameter, the number of permissible cycles and corresponding fatigue damage are determined.

Lastly, in evaluating for protection against failure from cyclic loading, the ASME Code requires a ratcheting assessment. The ratcheting assessment can be performed using either elastic stress analysis or elastic-plastic stress analysis.

Closing Remarks

The Design by Analysis methods of Part 5 of Section VIII, Division 2 primarily consist of evaluating pressure vessel components for failure modes seen in the pressure vessel industry. The Code has specific requirements in the analysis and evaluation for each of these failure modes. As always, the applicable edition of the ASME Boiler & Pressure Vessel Code should be consulted when performing these analyses to ensure all of the requirements are met.