Stress Analysis of Spherical Defects in Unequal-Thickness P92 Steel Elbows

Literature Overview

This paper by Ye Shengchun et al. (2022), published in Physicochemical Testing (Physical Section), presents a finite element analysis (FEA) study on the stress state of spherical defects in unequal-thickness P92 steel elbows. The research is conducted by Fujian Huadian Shaowu Energy Co., Ltd. in collaboration with China Huadian Corporation's Electric Power Research Institute. P92 steel (9Cr-0.2V-1Mo-W-NbVN) is a martensitic ferritic steel widely used in supercritical and ultra-supercritical power plant boilers and piping systems due to its excellent high-temperature creep strength and oxidation resistance. The study focuses on establishing stress prediction equations for spherical defects at various positions within the elbow wall thickness.

Core Technical Content

P92 Steel Characteristics and Elbow Fabrication

P92 steel presents unique challenges for elbow fabrication:

Property	Typical Value	Significance for Elbow Fabrication
Yield strength (room temperature)	490–540 MPa	High strength requires careful forming
Yield strength (600°C)	220–260 MPa	Reduced strength at service temperature
Hardness (as-received)	250–300 HB	Hard material, difficult to cold form
Weldability	Requires preheat and PWHT	Risk of brittle martensite in HAZ
Creep rupture strength (600°C, 10⁵ h)	~100 MPa	Design stress basis for long-term service

Unequal-thickness elbows are produced when elbows are fabricated from pipes with non-uniform wall thickness, or when the bending process results in wall thickness variation. In P92 elbows, this is particularly concerning because stress concentrations at thickness transitions can initiate creep damage or cracking.

Spherical Defect Stress Analysis

The study investigates spherical defects (representing internal voids, inclusions, or porosity) within the elbow wall thickness. The key findings are:

Axial section angle effect: Different axial cross-sections (15°–85°) have minimal influence on the maximum equivalent stress at the defect location.
Inner arc stress concentration: Defects located on the inner arc side of the elbow experience higher stress concentration than those on the outer arc side.
Wall thickness distance effect: As the distance from the defect to the inner wall increases, the stress at the defect decreases progressively.

Stress Prediction Equation

The authors established a prediction equation relating the maximum equivalent stress at the spherical defect to wall thickness and circumferential angle. This equation takes the general form:

σ_max = f(t, θ)

where σ_max is the maximum equivalent stress, t is the wall thickness (or distance from defect to inner surface), and θ is the circumferential angle position within the elbow. The equation is valid for axial sections from 15° to 85° of the elbow.

Finite Element Analysis Methodology

Model Configuration

Parameter	Specification
Element type	3D solid elements (tetrahedral or hexahedral)
Boundary conditions	Pressure loading on inner surface, constrained at pipe ends
Material model	Elastic-plastic with P92 stress-strain curve
Defect representation	Spherical void with various diameters and positions
Analysis type	Static structural analysis
Mesh refinement	Concentrated mesh around defect region

Key Stress Distribution Patterns

The FEA results reveal several important stress distribution characteristics:

Stress concentration factor (SCF): The SCF at the spherical defect depends on the defect size relative to wall thickness. Larger defects relative to wall thickness produce higher SCF values.
Triaxiality effect: The stress state at the defect location is highly triaxial, with significant hydrostatic stress components. This is critical for P92 because high triaxiality promotes void growth and creep damage.
Inner arc dominance: The inner arc of the elbow experiences compressive stresses due to bending, but the presence of a defect creates a local stress concentration that can be tensile in nature.

Engineering Practice Implications

Defect Acceptance Criteria

For P92 elbows in power plant service, the following considerations are important for defect acceptance:

Defect Type	Location	Acceptance Criterion (Typical)
Spherical void	Inner 1/3 wall thickness	Diameter < 20% of wall thickness
Spherical void	Middle 1/3 wall thickness	Diameter < 30% of wall thickness
Spherical void	Outer 1/3 wall thickness	Diameter < 40% of wall thickness
Linear inclusion	Any location	Length < 50% of wall thickness
Weld porosity	Weld zone	Per NB/T 47013 or equivalent

Impact on Remaining Life Assessment

The stress concentration caused by defects in P92 elbows has direct implications for remaining life assessment:

Creep damage acceleration: Higher local stress at the defect location accelerates creep damage accumulation according to the Larson-Miller parameter approach.
Crack initiation probability: The probability of crack initiation from a defect increases with stress concentration factor and triaxiality.
Inspection requirements: Defects detected by NDE (particularly UT or RT) in P92 elbows require careful evaluation against applicable fitness-for-service criteria.

Key Questions and Reflections

The study raises several important questions for engineering practice:

First, the use of spherical defects as the model geometry is a simplification. In reality, defects in P92 elbows may be irregularly shaped, elongated, or clustered. The stress concentration at an irregular defect can be significantly higher than at a spherical defect of equivalent volume. Future studies should investigate the effect of defect shape on stress concentration.

Second, the study appears to focus on elastic-plastic stress analysis at room temperature or elevated temperature without considering creep. For P92 elbows in service at 550–620°C, creep is the dominant damage mechanism over long periods. The interaction between stress concentration from defects and creep damage accumulation is critical for life prediction.

Third, the finding that axial section angle has minimal effect on defect stress is practically valuable — it means that a defect detected at one axial position can be evaluated using the same stress prediction equation regardless of its axial location within the elbow. This simplifies the fitness-for-service evaluation process.

Fourth, the emphasis on inner arc stress concentration is counterintuitive at first glance, since the inner arc is in compression during bending. However, the presence of a spherical void creates a local stress concentration that can be tensile regardless of the global stress state. This is consistent with the well-known principle that voids and inclusions create local tensile stresses due to the stress redistribution around the discontinuity.

Study Insights and Outlook

This paper makes a valuable contribution to the fitness-for-service evaluation of P92 elbows in power plant service. The establishment of stress prediction equations for spherical defects at various positions within the wall thickness provides a quantitative basis for evaluating defect significance. For engineers responsible for asset integrity management in supercritical and ultra-supercritical power plants, where P92 elbows are increasingly used, this type of analysis is essential for making informed decisions about defect acceptance, repair, or replacement.

The practical value of this work extends beyond P92 to other high-strength martensitic steels (such as P91, P95, and P96) used in similar applications. The methodology of combining FEA with defect position parameterization can be applied to other materials and geometries. However, engineers should be aware that the prediction equations are valid only within the range of parameters studied and should not be extrapolated beyond those limits without additional verification.