A solution method for finding dynamic stress intensity factors for arbitrarily oriented cracks in transversely isotropic materials

This paper describes a new stress-intensity factor (SIF) solution for an internal surface crack in a sphere that expands capabilities for this common pressure vessel geometry. The SIF solution employs the weight function (WF) methodology that enables rapid calculations of SIF values. The WF methodology determines SIF values from the nonlinear stress variations extracted in the uncracked geometry, e.g., from service stresses and/or residual stresses. The current approach supports two degrees of freedom that denote the two crack tips located at the deepest location and the surface of the sphere. The geometric formulation of this solution enforces an elliptical crack front, maintains normality of the crack front with the free surface, avoids non-physical crack shapes with protruding “ears”, and supports two degrees of freedom for fatigue crack growth from an internal crack tip and a surface crack tip. The new SIF solution enables all spherical geometries with the exterior diameter greater than or equal to four times the thickness. This WF SIF solution has been combined with stress variations common for spherical pressures vessels: internal pressure on the interior surface, uniform tension on the crack plane, and bending on the crack plane. These stress variations facilitate solution usability. This work builds on earlier efforts for an external surface crack (PVP2021-61397[1]) and provides a comprehensive solution capability for spheres. This paper provides a complete overview of this solution. We present for the first time the geometric formulation of the crack front that enables the new functionality and set the geometric limits of the solution, e.g., the maximum size and shape of the crack front. The paper discusses the bivariant WF formulation used to define the SIF solution and details the finite element (FE) analyses employed to calibrate terms in the WF formulation. A summary of verification efforts demonstrates the credibility of this solution against independent results from FE analyses. We also compare results of this new solution against independent SIFs computed by FE analyses, legacy SIF solutions, API 579, and FITNET. These comparisons indicate that the new WF solution compares favorably with results from FE analyses. Finally, we summarize the capabilities of this solution in NASGRO®.

Tribological contact analysis of a rigid ball sliding on a hard coated surface, Part III: Fracture toughness calculation and influence of residual stresses

This paper summarizes an emerging process to establish credibility for surrogate models that cover multidimensional, continuous solution spaces. Various features lead to disagreement between the surrogate model's results and results from more precise computational benchmark solutions. In our verification process, this disagreement is quantified using descriptive statistics to support uncertainty quantification, sensitivity analysis, and surrogate model assessments. Our focus is stress-intensity factor (SIF) solutions. SIFs can be evaluated from simulations (e.g., finite element analyses), but these simulations require significant preprocessing, computational resources, and expertise to produce a credible result. It is not tractable (or necessary) to simulate a SIF for every crack front. Instead, most engineering analyses of fatigue crack growth (FCG) employ surrogate SIF solutions based on some combination of mechanics, interpolation, and SIF solutions extracted from earlier analyses. SIF values from surrogate solutions vary with local stress profiles and nondimensional degrees-of-freedom that define the geometry. The verification process evaluates the selected stress profiles and the sampled geometries using the surrogate model and a benchmark code (abaqus). The benchmark code employs a Python scripting interface to automate model development, execution, and extraction of key results. The ratio of the test code SIF to the benchmark code SIF measures the credibility of the solution. Descriptive statistics of these ratios provide convenient measures of relative surrogate quality. Thousands of analyses support visualization of the surrogate model's credibility, e.g., by rank-ordering of the credibility measure.

General analytical solution for stress intensity factors of two asymmetrical radial cracks emanating from a single hole in an infinite isotropic plate

Engineering Critical Assessment (ECA) has become essential for establishing if a mooring line in service is fit for continued service when low fracture toughness in some components is suspected or inspection results may suggest possible presence of discontinuities. Existing ECA codes and standards such as BS 7910 has rather limited stress intensity factor (K) solutions suitable for this type of applications, e.g., elliptical crack stress intensity factor solutions valid for a short crack regime with a/D ratio far less than 0.1 with different aspect ratios other than a/b =1. Here, D refers round bar diameter and a crack depth (minor axis) and b crack half length (major axis). As a result of a recent joint industry project (JIP), referred to as Mooring Component Assessment (MCA), a comprehensive set of K solutions have been developed for covering crack size a/D from 0.005 to 0.15 which associated with existing K solutions allows to cover a/D from 0.05 to 0.6, along a unified treatment of local stress gradients, e.g., at knuckle positions, for supporting ECA of mooring components and chain links. These K solutions are presented in a set of simple parametric forms and can be readily used for ECA assessment of shackle and chain-link components.

In order to improve the fracture resistance of undermatched butt joint, the influence of joint shape parameters on the stress intensity factor (SIF) of undermatched butt joint with mode I centre crack was studied, and the solution of SIF was obtained by combining the analytical method with the finite element method as well. The results are useful to guide the shape design of undermatched butt joint with mode I centre crack under both static load and fatigue load conditions.

This paper presents the calculation of stress intensity factor (K) solutions for surface cracks in the thread ground of bolts subjected to axial loading directly applied by the nut. The stress-strain computations have been done by means of the finite element method with quarter-point singular isoparametric elements along the crack front. The stress intensity factor is calculated through the stiffness derivative method, by using a virtual crack extension technique to compute the energy release rate. Two modifications are made to improve the accuracy of the results: the displacement not only of the main node, but also of the quarter-point nodes located in the normal plane and the adjacent nodes in the crack line, avoiding both the change of the singularity and the crack curving. The results show that direct loading on the thread flank by a nut increases the stress intensity factor. This effect decreases with the crack length. For the deepest circular cracks, however, nut loading relaxes the K-value, mainly at the crack surface.

In order to obtain good estimates of stress intensity factors in a structural integrity assessment, the accuracy with which a residual stress distribution is represented should be commensurate with the importance of localised peaks in residual stress, in particular where such peaks lie within the region under assessment. This paper describes work undertaken to investigate the importance of accurately representing residual stress distributions in structural integrity assessments. This has been carried out by comparing regular polynomial representations of residual stress distributions, combined with available weight function stress intensity factor solutions (as provided in the R6 procedures) with alternative polynomial representations of residual stress distributions, which provide a more accurate fit in the region of the crack. Such improvements in representation of residual stress profiles provide an indication as to how stress intensity factor solutions could, in future, be modified in order to result in improved accuracy of calculated stress intensity factors. Representation by partitioning residual stress profiles into membrane, bending and self-balancing components, in terms of providing a more straight-forward route for curve-fitting of residual stress profiles is considered. The investigation considers several transverse, through-thickness residual stress distributions. Stress intensity factors are calculated for a variety of crack sizes. Representation of the residual stress profiles in the stress intensity factor solutions are compared, as are the results of the stress intensity factor calculations. The conclusions arising provide guidance as to how current methods of curve fitting a residual stress distribution may be improved in cases where current methods may not be accurate. Advice is also provided as to the relative merits of representing residual stress distributions as a set of partitioned components or as a single distribution.

Stress intensity factor solutions are often used as a dominant fracture mechanics parameter for fatigue crack growth analysis. In ASME Boiler and Pressure Vessel Code Section XI as well as JSME Rules on Fitness-for-Service for Nuclear Power Plants, fatigue crack growth is predicted on the basis of the stress intensity factor range. Stress intensity factor solutions are frequently provided by the correction factors, which are tabulated as the functions of structure and/or crack sizes. In this study, the effect of the variation of the correction factors on the crack growth analysis results was investigated for pipes with surface cracks. The evaluation accuracy required for the correction factors of the stress intensity factor solutions was then examined and recommended from the comparison with the necessary accuracy of the parameters used for the fatigue crack growth analysis.

Analytic solutions to problem of elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals

Mechanics and fracture of crack tip deformable bi-material interface

Review and synthesis of stress intensity factor (SIF) solutions for elliptical surface cracks in bolts under nut loading: A Tribute to Agustín de Betancourt

An analytical solution has been attained to establish the closed form expression of stress intensity factor at the tip of a semi‐infinite crack, dynamically propagating in an initially stressed transversely isotropic poroelastic strip due to Love‐type wave for the case of concentrated force of constant intensity as well as for the case of constant load. The study presents the sound effect of various affecting parameters viz. speed of the crack, length of the crack, horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter on the stress intensity factor. In order to delineate the effects of these aforementioned parameters on the stress intensity factor graphically, numerical simulations have been accomplished. One of the major highlight of the paper is the comparative study carried out for horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter with the case when the strip is isotropic, non‐porous and free from initial stresses. Wiener–Hopf technique and the Fourier integral transform has been effectuated for the procurement of the closed form expression (exact solution) of stress intensity factor.

Stress intensity factor and T-stress solutions for three-dimensional clamped single edge notched tension (SENT) specimens

The transient analysis of a subsurface inclined crack subjected to a buried dynamic dilatational source