Analysis of components at elevated temperature service

As indicated in Figure 25, the analysis of a component at elevated temperature in the creep regime, require limits for both the load-controlled stresses and strain- and deformation-controlled quantities to be satisfied. The limits have been set to avoid the following failure modes: (1) ductile rupture from short term loadings; (2) creep rupture from long-term loadings; (3) creep-fatigue failure; (4) gross distortion due to incremental collapse and ratcheting; (5) loss of function due to excessive deformation; (6) buckling due to short-term loading and (7) creep-buckling due to long-term loadings.

For failure modes (5) to (7) there are only brief guidelines provided in the code [11].

First a design should meet the requirements given in an ASME code of construction such as ASME I, VIII-1 or VIII-2, and then comply with requirements in ASME III-Subsection NH. It should however be mentioned that the temperature dependent allowable stress values vary with the different sections [14].

36

Figure 25. Procedures for structural integrity evaluations for nuclear class 1 components by the ASME Rules [58]

In subsection NH, the following maximum accumulated inelastic strain limits has been established to ensure functional requirements and structural integrity [11] :

• Strains averaged through thickness, 1% (membrane strain)

• Strains at the surface, due to an equivalent linear distribution of strain through the thickness, 2% (bending strain)

• Maximum local strains, at any point, 5%

Figure 26. Illustration of strain-limited quantities [9].

The limits above are the accumulated limits over the expected operating lifetime of a component and are to be computed for a steady state period at the end of the specified life to avoid significant effect of transients [11]. These limits require an inelastic analysis to be carried out. Due to the difficulties associated with performing inelastic analysis (which will be further discussed below) subsection NH has provided alternative methods that are based on elastic analysis [9].

The strain- and deformation-controlled limit evaluation in Subsection NH [11] can be performed using one of the three following analysis methods:

1. Elastic analysis

2. Simplified inelastic analysis 3. Inelastic analysis

These are arranged in the order from simplest to most difficult and least accurate to most accurate.

Also, the amount of material data required for the analysis and the cost to perform them increase for

1%

2%

5%

𝜎

𝜎

𝜎

37 method two and three. Of all the three criteria, the elastic limits are set to be most conservative, due to difficulties of accurately predicting inelastic strain with elastic analysis. As illustrated in the flowchart in Figure 27, when stresses from the elastic analysis cannot satisfy the elastic limits, either the component need to be redesigned or a simplified inelastic analysis can be performed. Similarly, if the simplified analysis does not meet the requirements for the simplified inelastic stress limits, the component must either be modified or an inelastic analysis be carried out [11, 14].

Figure 27. Flowchart of analysis procedure for evaluation of inelastic strain limits

2.8.1.3.1 Elastic analysis

The elastic analysis is typically preferred among engineers since it is the easiest, most convenient and least expensive analysis method. The method involves linearization to separate and categorize stresses to approximate the more accurate plastic and creep analysis. Further, there are tests provided in the code to ensure that strain- and deformation requirements are met. The method is appropriate to use when the combined primary and secondary stresses are below the yield strength of the material [14].

However, a downside with stress categorization is that it requires substantial knowledge and engineering judgement, especially for complex structures and three-dimensional stress fields [59]. In addition, strain- and deformation-controlled limits in Subsection NH require primary and secondary stress categories to be dealt with separately as opposed to the elastic method in ASME VIII-2. However, there are alternative tests for the elastic analysis which offer an alternative to avoid separation of primary and secondary stresses. The elastic analysis is not as accurate as a plastic or creep analysis, which more accurately predicts the materials stress-strain relationship. It is, however the most conservative criteria and considered adequate for most design applications [14].

2.8.1.3.2 Simplified inelastic analysis

The simplified inelastic analysis also uses the results from the stress categorization made with the elastic analysis. However, these are used to calculate a strain which is compared to the allowable strain limit, thus the name simplified inelastic analysis. The method is based on the concept that the core stress remains elastic when subjected to primary and secondary stresses (obtained from stress linearization). By normalizing the primary and secondary stresses, the magnitude of the elastic core of the component can be establish with a so-called Bree-diagram. The value of the elastic core can subsequently be used to calculate the resulting strain [9, 14].

Elastic analysis

Redesign Strain and deformation requirements are satisfied

Yes Yes Yes

38 2.8.1.3.3 Inelastic analysis

The inelastic analysis method does neither include comprehensive nor specific guidance in Subsection NH. This was an intentional decision, since material models for inelastic analysis are still under development, and it was considered that over-specific guidance would halt further progress in the field [9].

With an inelastic analysis, the inelastic strains and deformation due to service loads can be obtained directly from the analysis. The analysis does however require constitutive equations that describe both time-independent and time-dependent material response. There exist many formulations of such equations, however the prediction obtained from the various equations can vary significantly, as previously mentioned in Chapter 2.7.1. For predictions with an inelastic analysis to be meaningful, the equation selected to model the material’s response must be evaluated according to the materials load and temperature history. This typically require a large quantity of material test data which are typically not available and material testing would be required. All the above-mentioned requirements make the method both expensive and time consuming. In addition, since it is not practical to test a material for all stages of the load and temperature history, the choice of material model and the evaluation of the results therefore requires a substantial portion of engineering judgement [9, 14].