J Predictions for Defective Pipe Elbows via the Reference Stress Method

In R6, the J-based failure assessment diagram (FAD) method is used in the fracture assessment, and is underpinned by the reference stress J scheme. Therefore, an assessment using the R6 FAD method is equivalent to a J prediction using the reference stress method. In this paper, the effect of global and local limit load solutions for defective elbows on the reference stress and hence the J predictions is investigated using published three dimensional elastic-plastic finite element (FE) J results, in order to create guidance for users to follow when performing structural integrity assessments of defective elbows using the R6 procedure. The results show that using the global limit load solutions recommended in this paper can lead to good and reasonably conservative J predictions. However, the availability of global limit load solutions is very limited. The results also show that using the local limit load evaluated from the local limit load model recommended in this paper can lead to conservative J predictions for most of the cases considered.

Thick-Wall Cylinder Reference Stress Crack Solutions for API 579-1/ASME FFS-1 Annex 9C

A new set of reference stress solutions for cracks in thick-wall cylinders were computed for addition in the next edition of the API 579-1/ASME FFS-1 standard, and are described in this paper. The geometry cases used ratios for the cylinder radius, wall thickness, crack depth, and crack length. The crack locations included axial, circumferential, internal, and external cracks. 3-D crack meshes were generated for each case to compute J-integral versus pressure result trends, which were used to determine the reference stress. The Failure Assessment Diagram (FAD) method uses reference stress solutions to compute the Lr ratio on the FAD x–axis to evaluate cracks for plastic collapse; the FAD y-axis Kr ratio evaluates fracture failure. The elastic-plastic J-integral reference stress method will be briefly reviewed using results from this project. A stress-strain curve was selected to represent typical material used for high-pressure components. The computed reference stress was shown to depend on the yield strength to tensile strength ratio, and a ratio of 90% was selected for use in this project. Some shallow internal cracks in the thicker cylinder cases showed unexpected behavior in the J-integral versus pressure results, which prevented the reference stress from being computed. An alternative method was developed to use the maximum converged pressure as the nominal load to obtain reference stress solutions for those cases.

A COUPLED PETROPHYSICAL AND GEOMECHANICAL WORKFLOW TO INTERPRET DIPOLE SONIC VELOCITIES FOR IN-SITU STRESS

Petrophysicists often find sonic velocities difficult to interpret, especially when choosing values for the mineral and fluid endpoints. This difficulty is always caused by stress sensitive formations where dipole sonic velocities vary with stress, even when the petrophysical properties are constant. The goal of this coupled workflow is to quantify the compositional influences of porosity, mineralogy, and fluids, while isolating and quantifying the geomechanical influence of stress. I first estimate the petrophysical properties using a standard multi-mineral petrophysical solver void of sonic inputs. This allows one to independently observe and quantify variations in both compressional and shear velocities with variations in petrophysical properties. I then normalize the sonic velocities to an idealized formation having compositional properties constant with depth by applying both matrix and fluid substitution algorithms. If these normalized velocities are constant with depth, then the formations are insensitive to stress, and I apply the standard petrophysical workflow using the measured sonic inputs. In addition, the standard geomechanical workflow that assumes linear elasticity is appropriate to estimate the in-situ stresses. However, if the normalized velocities vary with depth, the formations are sensitive to stress, which requires modifications to both the standard petrophysical and geomechanical workflows. Specifically, one must quantify and remove the velocity variations due to stress or else misinterpret velocity changes due to stress for changes in petrophysical properties. For formations sensitive to stress, I quantify the stress sensitivity by using the observed change in normalized velocity with depth with an estimate of the change in stress with depth. I then compute a second velocity normalization that quantifies and removes the acoustical sensitivity to stress in favor of a constant reference stress. I can now more accurately quantify the petrophysical properties by including the stress normalized velocities in the multi-mineral petrophysical solver. At this point in the workflow, there are two methods for quantifying the in-situ horizontal stress. The first method uses the velocities normalized to the constant reference stress to compute the dynamic elastic moduli. These dynamic elastic moduli are now appropriate to input into the standard geomechanical workflow. The second method uses the velocities normalized for the changing petrophysical properties, together with the stress sensitivity coefficients, to directly invert the velocities for the in-situ horizontal stresses. A comparison between the two methods supplies a consistency check. I emphasize both methods require in-situ horizontal stress calibration data for correct results. To clearly illustrate the workflow, this paper specifies the mathematical formulations with example calculations. This coupled workflow is novel because it highlights and clarifies improper assumptions while acknowledging the rock physics of stress sensitive formations. In the process, it improves the accuracy of both the derived petrophysical properties and geomechanical stresses.

Reference Stress Estimation for Anisotropic Materials Using Linear Elastic Finite Element Results

Components in the hot section of a gas turbine engine experience extended high temperature dwells and cycles composed of multiple starts, changes in load, and variable duration. These loading profiles can lead to damage from cyclic viscoplasticity which is heavily path dependent as dwell stress, yield strength, and stress range change constantly during operation. Since an accurate prediction of accumulated damage is critical to managing an engine, reduced order methods for tracking material behavior over complex operation cycles are necessary tools to help avoid unplanned down time and optimize cost over the operational period. One method for tracking the material behavior during path dependent cyclic viscoplasticity requires the use of reference stress. Reference stress is a bulk representative stress that can be used in conjunction with various lifing methodologies to determine component durability. Previous papers provided a method for calculating reference stress for isotropic materials using limit load estimation. The goal of this paper is to extend these methodologies to a reference stress estimation method for anisotropic materials to estimate life for single crystal turbine blades. Derived equations will be shown and results from simple Finite Element (FE) test cases will be discussed to demonstrate the accuracy of the anisotropic reference stress estimation. Once reference stress is obtained, the long term forward creep stress of a component can be estimated for any given initial stress state. This approach can be used to calculate damage during shakedown resulting from redistribution and relaxation due to plasticity and creep, which can be critical for accurately predicting remaining useful life and optimizing engine management.