Crack Face Pressure Research Articles

Modified Williams’ crack tip solution including crack face pressure

Williams’ series expansion crack tip solution in linear elasticity is modified to include a uniform crack face pressure. It is shown that the crack face pressure p only enters the constant or the T-stress term. Practical ways to calculate the T-stress from near crack tip stresses are outlined. The analytical results are consistent with numerical results such as from ABAQUS.

On formulations for modeling pressurized cracks within phase-field methods for fracture

Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the effects of pressure loads on the crack faces have been developed. This work investigates the performance of these models and compares them to a relatively new formulation for incorporating crack-face pressure loads. It is shown how the new formulation can be obtained either by modifying the trial space in the traditional variational principle or by postulating a new functional that is dependent on the rates of the primary variables. The key differences between the new formulation and existing models for pressurized cracks in a phase-field setting are highlighted. Model-based simulations developed with discretized versions of the new formulation and existing models are then used to illustrate the advantages and differences. In order to analyze the results, a domain form of the J-integral is developed for diffuse cracks subjected to pressure loads. Results are presented for a one-dimensional cohesive crack, steady crack growth, and crack nucleation from a pressurized enclosure.

Evaluation of crack opening displacement of through-wall circumferential-cracked pipe using direct weight function method

This paper presents a direct weight function-based method to evaluate the crack opening displacement (COD) which is a key parameter in leak-before-break (LBB) assessment and in probabilistic fracture mechanics (PFM) assessment of nuclear piping systems. The focus of this study is a circumferential-cracked pipe with non-linearly through-wall distributed stress loaded on the crack face. Parametric finite element analyses (FEA) were performed to calculate COD associated with different crack face pressure (CFP) loadings. The analyses matrix covers a wide range of pipe size and crack lengths. The crack mouth COD values at three locations: at outside surface, inner surface and mid-thickness were considered. The numerical results were then used to determine the coefficients that construct the direct weight functions. The proposed solution can be used to predict the COD resulted from given weld residual stress (WRS) field with the general prediction error being less than 8%. The research outcome can provide more computational efficiency in both deterministic LBB assessment as well as PFM analyses of pressurized pipes.

Cracking simulation of a tubesheet under different loadings

For shell-and-tube heat exchangers, tubesheet cracking is a major failure form. Owing to complicated structures, loadings and environments, mechanisms for the crack nucleation and propagation often puzzle engineers and as a result, it is hard to take effective measures to prevent this kind of failure from happening again. In this paper, three dimensional finite element models were established to investigate a real tubesheet cracking with the emphasis on the driving forces for the crack propagation from a fracture mechanics point of view. Three different loadings, namely residual expansion stress, crack face pressure and transverse pressure, and three crack growth patterns were considered. In order to obtain the residual stresses, the hydraulic expanding process of tube-to-tubesheet joint was simulated. Residual contact pressures between the tube and tubesheet and the induced residual stress distributions in the tubesheet were computed. The possibility for crack propagation in the tubesheet under the action of the different loadings was investigated in terms of the strain energy density factor. Results show that surface crack propagation may be driven by all the three loadings especially the transverse pressure. But when surface cracks come into the interior of the tubesheet along the thickness, as acted along the whole tubesheet thickness, the residual expansion stress would play key roles in crack propagation.

The T-stress solutions for through-wall circumferential cracks in cylinders subjected to general loading conditions

The elastic T-stress is a parameter used to define the level of constraint at a crack tip. It is important to provide T-stress solutions for practical geometries to apply the constraint-based fracture mechanics methodology. In the present work, T-stress solutions are provided for circumferential through-wall cracks in thin-walled cylinders. First, cylinders with a circumferential through-wall crack were analyzed using the finite element method. Three cylinder geometries were considered; defined by the mean radius of the cylinder ( R) to wall thickness ( t) ratios: R/ t = 5, 10, and 20. The T-stress was obtained at eight crack lengths ( θ/π = 0.0625, 0.1250, 0.1875, 0.2500, 0.3125, 0.3750, 0.4375, and 0.5000, θ is the crack half angle). Both crack face loading and remote loading conditions were considered including constant, linear, parabolic and cubic crack face pressures and remote tension and bending. The results for constant and linear crack face pressure were used to derive weight functions for T-stress for the corresponding cracked geometries. The weight functions were validated against several linear and non-linear stress distributions. The derived weight functions are suitable for T-stress calculations for circumferential cracks in cylinders under complex stress fields.

Weight Functions for T-Stress for Edge Cracks in Thick-Walled Cylinders

This paper presents T-stress solutions for an internal edge crack in thick-walled cylinders. Elastic fracture mechanics analysis using the boundary element method (BEM) is performed to determine the T-stress solutions for a wide range of radius ratios and relative crack lengths. The loading cases considered in the BEM analysis for the cracked cylinder are crack-face pressures with polynomial stress distributions acting on the crack face. T-stress results for the uniform and linearly varying crack-face pressure cases are subsequently used as the reference solutions to derive weight functions for T-stress. Boundary element results of T-stress for other stress distributions, namely, other nonlinear crack face loading, internal pressure, and steady-state thermal loading, are used to validate the derived T-stress weight functions. Excellent agreement between the results from the weight function predictions and those directly computed is shown to be obtained. The weight functions derived are suitable for obtaining T-stress solutions for thick-walled cylinders with an internal edge crack under any complex stress fields.

Surface Crack Growth Path and Fatigue Life Prediction Due to Repeated Rolling/Sliding Contact

This paper deals with the surface crack growth path description and the fatigue life prediction due to repeated rolling/sliding contact on the elastic half-space, accompanied by frictional heat generation and crack-face pressure. The stress intensity factors are analyzed for the surface crack which is kinked in multiple times from the inclined initial main crack. The rolling/sliding contact is simulated as a Hertzian contact pressure and a frictional load with heat generation, moving with constant velocity over the surface of the half-space. Applying the maximum energy release rate criterion to each kinked angle, the crack growth path can be described, and employing a mixed mode fatigue crack growth law, the associated fatigue life also can be predicted. The effects of frictional coefficient, slide/roll ratio and crack-face pressure on the crack growth path and associated life are considered for a high carbon-chromium bearing steel (AISI52100).

Surface Crack Growth Path and Fatigue Life Prediction due to Repeated Rolling/Sliding Contact.

This paper deals with the surface crack growth path description and the fatigue life prediction due to repeated rolling/sliding contact on the elastic half-space, accompanied by frictional heat generation and crack-face pressure. The stress intensity factors are analyzed for the surface crack which is kinked in multiple times from the inclined initial main crack. The rolling/sliding contact is simulated as a Hertzian contact pressure and a frictional load with heat generation, moving with constant velocity over the surface of the half-space. Applying the maximum energy release rate criterion to each kinked angle, the crack growth path can be described, and employing a mixed mode fatigue crack growth law, the associated fatigue life also can be predicted. The effects of frictional coefficient, slide/roll ratio and crack-face pressure on the crack growth path and associated life are considered for a high carbon-chromium bearing steel (SUJ 2).

918 ガスタービン動翼の熱疲労下における複数き裂進展挙動評価

Frequent start-stop operation of a gas turbine sometimes causes coating cracks on the surface of the first stage blades. Since the coating cracks tend to propagate into the substrate, accurate prediction of crack propagation behavior is important to make a reasonable judgment for the repair or replacement of blades. This paper describes the development of a crack propagation prediction methodology for first stage blades, which includes evaluation of the stress intensity factor K, and estimation of temperature distribution and stress distribution between the outer surface and the inner cooling hole of blades. Since the coating cracks of blades reveal themselves as multiple parallel cracks with narrow intervals, a primary concern was directed to establish evaluation method of K values of multiple parallel cracks. For this purpose, a series of finite element analyses were performed for multiple edge cracked plate with finite width subjected to a crack face pressure expressed as σ=σn (x/W)n , where x is a distance from the mouth of the crack and σn is the stress at plate surface (x=W). The result was used to make approximate equations for the influence coefficient Gn , defined as K=Gn σn (a/W)n (πa)1/2 , where a is a crack length. Temperature distribution was evaluated by observation of microstructure (gamma prime phase) change of a first stage blade used in a power plant for more than 20,000 hrs. Thermal stress distribution was calculated by finite element analysis using the evaluated temperature distribution. These results and the approximate equation of Gn were used to evaluate the crack propagation behavior of the blade surface, together with the fatigue crack propagation data of blade material that had been obtained in other studies.Copyright © 2004 by ASME

Free surface effect on moving crack under impact loading by BEM

This paper deals with the implementation of a 3D time-domain boundary integral formulation for a moving center-crack in a finite solid under suddenly applied crack face pressure. The BEM displacement time-domain formulations have, hitherto, been limited to analyzing two-dimensional crack problems, though hypersingular formulations have been used to analyze finite cracks in infinite domains. In this paper, variation of dynamic stress intensity factor (DSIF) along the crack front for a moving, through-thickness straight crack is studied for a finite solid under step loading. The state of stress is evaluated at the crack vertex, where crack front meets the free surface. The effect of free surface on DSIF is investigated. It is possible to estimate accurately the critical intersection angle of the crack front with the free surface at which square-root singularity is restored at the crack vertex under step loading for various speeds of crack propagation. It is also predicted in this work that for high speeds of crack propagation, crack front maintains its straight profile.

Numerical investigations of crack-tip constraint parameters in two-dimensional geometries

In this study, detailed finite element analyses have been carried out on conventional laboratory specimens such as Centred Cracked Panel (CCP), Three Point Bend Bar (TPBB) and Compact Tension (CT) specimens to study the characteristics of crack-tip constraint parameters, Q and h. It is observed that the loss of constraint is gradual with increasing deformation for CCP, irrespective of crack depth and shallow cracked TPBB and CT geometries. Conversely, deeply cracked TPBB and CT geometries maintain high constraint to fairly high deformation levels. This paper also addresses the nature of crack-tip constraint conditions in axi-symmetric circumferentially flawed pipe (CFP). Two loading configurations are analysed: (a) CFP under axial pull only; and (b) CFP under internal pressure with associated crack-face pressure and axial pull. It is found that the axi-symmetric CFP under internal pressure exhibits lower constraint than those under pure axial pull. The radial compressive stresses resulting from internal pressure leads to stress biaxiality, which reduces the constraint.

Loading Rates and the Dynamic Initiation Toughness in Brittle Solids

The experimentally determined marked rise of the stress intensity factor required to initiate crack propagation in brittle solids under variably high loading rates, is analyzed. This problem of fracture initiation at the tip of a crack is considered in terms of activating a flaw at some distance away from the tip. By using a semi-infinite crack in an unbounded two-dimensional solid subjected to spatially uniform but temporally varying crack-face pressure, we consider the evolution of stress at the failure initiation site. Fracture initiation is assumed synonymous with attaining a critical stress at the fracture site. The results conform to typical experimental data of dynamic crack initiation in brittle solids.

Analytical expressions for crack opening displacements of edge cracked specimens under a segment of uniform crack face pressure

In this paper, Muskhelishvili's complex variable method was used to derive the primary equations of crack opening displacements (CODs) for edge cracked specimens when only the boundary conditions of the crack surface are satisfied. By means of fitting the COD weight function solutions based on the obtained primary COD equations, approximate equations of COD were obtained for edge cracked specimens under a segment uniform pressure acting on the crack surfaces. The equations are more accurate outside the near crack tip region. Because the crack closure level is sensitive to the variation of CODs in the near crack tip region, approximate COD-expressions with high accuracy in the near crack tip region were also developed for the edge cracked specimens under the corresponding loading condition based on the COD-expression for a central crack in an infinite width plate subjected to segment uniform pressure acting on crack surface. The equations with better accuracy outside and in the near crack tip region can be combined to rapidly calculate the COD on the whole crack surface, thus greatly facilitating fatigue crack growth analysis for edge cracked specimens.

The calculation of crack opening area and crack opening volume from stress intensity factors

This report describes a method which permits the calculation, directly from the elastic stress-intensity factors of the crack opening area of a two-dimensional crack or the crack opening volume of a penny-shaped crack when subjected to uniform or non-uniform stress distributions. Although stress intensity factors are well documented, especially for two-dimensional cracks (see e.g. [1-3]), it is sometimes necessary to obtain additional information pertaining to particular crack configurations or non-uniform loading systems. A quantity which can be calculated directly from the stress intensity factor is the crack opening area, as shown recently by M't)ller and Harris [4] for uniformly loaded two-dimensional crack configurations. The crack opening area may be of interest, e.g. in estimating leakage rates from cracks in fluid-containing components, such as thin-walled tubes in cooling circuits or chemical plant. Miiller and Harris [4] used the interrelation between the energy release rate and the stress intensity factor to derive an equation for the crack opening area of a two dimensional crack subjected to a uniform applied stress in terms of the corresponding stress intensity factor. In the present paper, starting from the weight function fomaulation, we derive a more general equation for computing the crack opening area of arbitrarily non-uniform loaded two-dimensional crack configurations from stress intensity factors. An analogous relationship for the crack opening volume of a penny-shaped crack subjected to radially symmetric stress distributions is also derived. Application of the results is demonstrated by selected examples. Two-dimensional cracks: Consider first a centre-synametric crack of length 2a in a finite sheet subjected to a non-uniform crack face pressure p(x)=-cy(x) corresponding to the centre-symmetric applied normal stress distribution ~(x) = cy(-x) at the prospective crack site. The coordinate x coincides with the crack line with its origin at the crack centre. Then the stress intensity factors Kin(a) and Kc2~(a) of the same cracked body subjected to two different load cases oo~(x) and ~2~(x), respectively, are interrelated according to Betti's reciprocal theorem and the superposition principle by (cf. e.g. [3])

Exact elastodynamic analysis of some fracture specimen models involving strip geometries

A procedure for analysing a class of transient elastodynamic crack problems is presented. These problems model certain experimental situations which can be used to infer fracture toughness values for materials under stress-wave loadings. In particular, the present analysis provides exact expressions for the elastodynamic stress intensity factor at the tip of a long external crack in a striplike body whose lateral (upper and lower) boundaries are parallel to the crack line. Plane stress/strain conditions are assumed to prevail. In this class of problems, the crack may be situated asymmetrically with respect to the mid-strip line, and various dynamic loadings are considered, including crack face tractions and lateral face displacements. The loadings considered will have an arbitrary time dependence, but will be spatially uniform. The problem analysis is based on integral transforms and an asymptotic usage of the Wiener-Hopf technique. Two useful cases are considered in detail as examples; the symmetrically cracked strip with traction-free lateral boundaries under sudden crack face pressure, and the symmetrically cracked strip with suddenly displaced shear-free lateral boundaries.

Effect of inclined planar fractures on borehole performance

Excessive borehole pressurization may cause damage to the borehole with a large possibility of the initiation of new cracks and/or the propagation of minute flaws appearing as surface cracks or embedded cracks in the vicinity of the borehole. When these flaws propagate under the control of the borehole pressure-induced symmetrical radially, rapidly decaying stress field and internal crack face pressure they extend along spacially curved surfaces trying to realign themselves again in a plane, the direction of which is governed by the relative magnitude of the pressures in the borehole and the crack. A 3D-crack propagation algorithm serves for the evaluation of the nucleation possibility of borehole cracks and embedded cracks as a function of the state of stress. Numerical modelling concentrates on a centrally bored cube with an inclined semi-elliptical surface starter crack and an embedded elliptical planar starter crack subjected to various boundary conditions. The distributions of the stress intensity factors K1, K2 and K3 along the crack periphery as a function of the pressures and the state of primary stress have been established. Examples for the behaviour of crack initiation and extension due to pressurization are given. An application to high pressure injection in steep boreholes extending from inspection galleries in high arch dams is presented.

The stress intensity factors for pressed cracks in arbitrary shapes

A boundary element method (BEM) was specially developed for a crack under crack face pressure in arbitrary two-dimensional problems. It is based on the basic stress solutions for an infinite plane with a crack loaded by body forces and moment at arbitrary point, which were derived by Erdogan from the Kolosov-Muskhelishvili fundamental functions, and the basic solution for a crack in an infinite plate under crack surface pressure, so that the crack surface need not be modelled. Therefore, minimal modelling efforts are needed to obtain stress intensity factors with the method and its accuracy was established by comparing the obtained results with the exact SIF results and acceptable results for various problems of arbitrary shapes and loadings.

Ontario hydro's leak before break approach: Application to the darlington (candu) nuclear generating station a

Ontario Hydro has developed a leak before break (LBB) approach for application to the large diameter heat transport piping for Darlington NGS A as an alternative to the provision of pipewhip restraints. This approach has been applied to pipe sizes which are equal to or greater than 530 mm (21 in. NPS). The proposed LBB approach incorporates assessments at several levels to provide assurance against catastrophic rupture. A comprehensive and systematic review of pipe failure mechanisms is considered the first important step in establishing role and applicability of the LBB concept. The elements integral to the approach are those related to demonstration of crack stability utilizing fracture mechanics methods and those related to leak rate predictions and leakage detection capability. For evaluation of crack stability the J-integral/tearing modulus (J/T) method has been selected. Results from an extensive material test program from actual heat transport piping, forgings, associated welds and heat affected zones as inpur to EPFM analyses provide the J-resistance and J— T curves. The details of EPFM analyses for a straight pipe with a circumferential crack and a piping elbow with a central longitudinal throughwall crack are presented here. Additionally, results of crack opening detail, the effects of crack face pressure, the predictions of LEAK RATE code and an assessment of the leakage detection capability are presented.

Tabulated stress intensity factor solutions for flawed fastener holes

Several sets of stress intensity factor solutions are provided for through-the-thickness, corner and surface flawed holes. Results are given for both remote tensile and crack face pressure loading. It is suggested that the crack face pressure solutions can be used with the linear superposition method to analyze many other practical crack problems. The superposition technique is demonstrated with several sets of example calculations.

Stress Intensity Factors for Corner Cracked Holes Under General Loading Conditions

A linear elastic analysis is conducted with the finite element-alternating method for quarter-elliptical corner cracks located at fastener holes. Mode-one stress intensity factors are presented along the crack periphery for a crack face pressure loading which can be represented by a third order polynomial. Results are also given for remote tensile loading applied perpendicular to the crack plane. Two example problems describe application of the polynomial crack face pressure solutions to other loading configurations through a simple linear superposition.