Finite element based evaluation of stress intensity factors for interactive semi-elliptic surface cracks

A finite thickness plate with two coplanar self-same shallow and deep semi-elliptical surface cracks subjected to remote tensile surface traction is considered for fracture analysis. Based on three-dimensional (3D) finite element solutions, stress intensity factors (SIFs) are evaluated along the entire crack front using a force method. The line spring model has also been used to evaluate crack depth point SIFs using shell finite element analysis. A wide range of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.3≤a/c≤1.2), crack depth ratio (1.25≤t/a≤6), relative crack location (0.33≤2c/d≤0.9) and normalized location on the crack front (0≤2φ/π≤2) are considered for numerical estimation of crack interaction factors. SIFs evaluated at the depth point using the force method from the 3D finite element results are compared with SIFs evaluated using the line spring model. Finally, using finite element results, an empirical relation is proposed for the evaluation of crack interaction factors. For the ranges considered, the proposed empirical relation predicts crack interaction factors at critical locations within ±2% of the 3D finite element solutions.     

Computation of leak areas of circumferential cracks in piping for application in demonstrating leak-before-break behaviour

This paper presents a simplified engineering method to evaluate lower bounds of leak areas for circumferential through-wall cracks in view of their application in demonstrating the Leak-Before-Break behaviour of pipes. Starting from the simple elastic solution in a flat plate, bulging and plasticity correction factors are applied to determine leak rates in pipes. An amplification factor due to bulging is based on Sanders' shell solutions while, for plasticity, the Dugdale-Barenblatt model is used, introducing the reference-stress concept. The method is thus applicable for a large range of diameter-to-thickness ratios and for non-uniform applied loading situations. The method is tested against a number of results obtained either numerically (finite-elements analysis) or experimentally. The results are also compared with other known simplified methods used in the USA and FRG. The simplified approach presented here, to evaluate the crack leak areas in circumferential through-cracks, has been validated on a large range of diameter-to-thickness ratios and for non-uniform applied loads. The method seems promising for demonstration of Leak-Before-Break behaviour of pipes.     

The effect of multiple cracks on the leak-before-break case of pipe

The growth/coalescence behavior of multiple cracks is investigated through computer simulation to present the effects of multiple cracks on the pipe leak-before-break (LBB) case. For the multiple crack behavior simulation, randomly distributed initial cracks are postulated in a typical vulnerable zone (such as weld) of pipe. The parameters such as the initial crack number, initial crack locations, initial crack lengths and the growth rates of the cracks are taken as random variables. Different crack distribution parameters, different crack growth laws, and different crack interaction rules are adopted to examine the sensitivity of the LBB case to these factors. The simulation results show that the effects of multiple cracks on the LBB case are different for different failure mechanisms, while the general trend is that multiple cracks always lead to shorter leak-free lifetimes and shorter allowable response time. Moreover, the undesired situation of sudden catastrophic break without previous leak may also be derived in the cases where the amount of initial cracks is large and the degree of crack interaction is strong.     

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

A J integral estimation method for cracks in welds with mismatched mechanical properties

A J integral estimation method is proposed for a crack located in the middle of a weld with a mismatch in mechanical properties from the surrounding base material. The method covers both yield stress over/under-matching and differences in hardening behaviour between weld and base material. The method involves the definition of an ‘equivalent stress-strain relationship’ based on the mechanical properties of both the weld and base materials. The value of J is then estimated using the equivalent stress-strain relationship in conjunction with the EPRI method. An approximate solution for the equivalent stress-strain relationship has been obtained by assuming that the average resistance along a slip-line controls the plastic stress and strain fields near the crack tip. Detailed formulae for plane strain centre-cracked panel (CCP) specimens have been derived on the basis of limit load solutions.

Nonlinear finite element analysis of 26 cases with various degrees of mismatch in yield stress and hardening behaviour have been performed for plane strain CCP specimens. The results show good agreement with those estimated using the equivalent stress-strain relationship method. Traditional defect assessment methods based on the use of ‘weaker material’ properties in a mismatched weld are compared to the results of the finite element analyses. It is proposed that the equivalent stress-strain relationship may be used to define the R6 failure assessment diagram for particular weld defects using the Option 2 procedure of R6.     

Leak rate experiments for through-wall artificial cracks

An experimental program of leak rate testing has been carried out for different geometries of artificial cracks in piping under various thermo-hydraulic conditions. The objective of these tests was to obtain a database of measured leak rates from artificial piping cracks and to compare test results with leak rate predictions obtained from the EPRI developed analytical model called PICEP. Experimental results for leak rates associated with rectangular and flare crack geometries are presented. Initial results of comparing analytical leak rate predictions with the experimental data is also presented.     

Determination of the elastic-plastic fracture mechanics Z-factor for alloy 182 weld metal flaws

One of the ways that the ASME Section XI code incorporates elastic-plastic fracture mechanics (EPFM) in the Section XI Appendix C flaw evaluation procedures for circumferential cracks is through a parameter called Z-factor. This parameter allows the simpler limit-load (or Net-Section-Collapse) solutions to be used with a multiplier from EPFM analyses. This paper shows how 3-D finite element (FE) analyses were employed to investigate the sensitivity of the crack-driving force as a function of crack location (i.e., crack in the center of weld, or closer to the stainless or low alloy steel sides) in an Alloy 182 dissimilar metal weld (DMW), and how an appropriate (or equivalent) stress-strain curve was determined for use in the J-estimation schemes. The J-estimation schemes are then used to cover a wider range of variables, i.e., pipe diameters, cracks lengths, and also incorporate crack growth by ductile tearing. The Z-factor equations as a function of pipe diameter were calculated using the LBB.ENG2 J-estimation scheme along with the most conservative equivalent stress-strain curve from the FE analyses. The proposed Z-factor approach was then validated against an Alloy 182 DMW full-scale pipe test that had a circumferential through-wall crack in the fusion line. The predicted EPFM maximum load showed excellent agreement with the experimental result. Furthermore, it was shown that the proposed Z-factor equation is not sensitive to the location of the crack.     

Predictions for fatigue crack growth life of cracked pipes and pipe welds using RMS SIF approach and experimental validation

The objective of the present study is to understand the fatigue crack growth behavior in austenitic stainless steel pipes and pipe welds by carrying out analysis/predictions and experiments. The Paris law has been used for the prediction of fatigue crack growth life. To carry out the analysis, Paris constants have been determined for pipe (base) and pipe weld materials by using Compact Tension (CT) specimens machined from the actual pipe/pipe weld. Analyses have been carried out to predict the fatigue crack growth life of the austenitic stainless steel pipes/pipes welds having part through cracks on the outer surface. In the analyses, Stress Intensity Factors (K) have been evaluated through two different schemes. The first scheme considers the ‘K’ evaluations at two points of the crack front i.e. maximum crack depth and crack tip at the outer surface. The second scheme accounts for the area averaged root mean square stress intensity factor (K_RMS) at deepest and surface points. Crack growth and the crack shape with loading cycles have been evaluated. In order to validate the analytical procedure/results, experiments have been carried out on full scale pipe and pipe welds with part through circumferential crack. Fatigue crack growth life evaluated using both schemes have been compared with experimental results. Use of stress intensity factor (K_RMS) evaluated using second scheme gives better fatigue crack growth life prediction compared to that of first scheme. Fatigue crack growth in pipe weld (Gas Tungsten Arc Welding) can be predicted well using Paris constants of base material but prediction is non-conservative for pipe weld (Shielded Metal Arc Welding). Further, predictions using fatigue crack growth rate curve of ASME produces conservative results for pipe and GTAW pipe welds and comparable results for SMAW pipe welds.     

Stress intensity factors for an axially oriented internal crack embedded in a buried pipe

In this paper, the finite element method has been used to study the effect of soil weight on the stress intensity factors of an axially oriented semi-elliptical crack located on the inner surface of a buried pipe. The Burns and Richard model has been utilized to take into account the interaction between the soil and the pipe. The finite element results revealed that the cracks in a buried pipe are subjected to mixed mode loading. The mode I and mode II stress intensity factors depend on the circumferential location of internal crack. K_I is always significantly larger than K_II and is maximum when the internal crack is along the vertical direction. A comparison between the results of two-dimensional and three-dimensional cracks also signified that the two-dimensional analysis always represents more conservative results. Depending on the crack aspect ratio (a/c), the discrepancy between the results of two and three-dimensional analyses can be significant.     

Compound cracks in pipes under combined bending and tension

Limit load and J-resistance curve solutions are developed for a compound crack in a pipe under combined tension and bending. The solution is based on a thick-walled cylinder assumption and the J solution can be applied with load-displacement data from one pipe test. Material resistance curves are developed for compound cracks in Type-304 stainless steel, Inconel 600 and A106 GrB base materials and a 304 stainless steel TIG weld. Tearing instability analyses are performed to assess the load-carrying capacity of pipes containing compound cracks and to evaluate nonconservatism associated with the use of C(T) specimen J-R data.     

A study on fatigue crack growth in the high cycle domain assuming sinusoidal thermal loading

The assessment of fatigue crack growth due to turbulent mixing of hot and cold coolants presents significant challenges, in particular to determine the thermal loading spectrum and the associated crack growth. The sinusoidal method is a simplified approach for addressing this problem, in which the entire spectrum is replaced by a sine-wave variation of the temperature at the inner pipe surface. The loading frequency is taken as that which gives the shortest crack initiation and growth life. Such estimates are intended to be conservative but not un-realistic. Several practical issues which arise with this approach have been studied using newly-developed analytical solutions for the temperature and stress fields in hollow cylinders, in particular the assumptions made concerning the crack orientation, dimensions and aspect ratio. The application of the proposed method is illustrated for the pipe geometry and loadings conditions reported for the Civaux 1 case where through wall thermal fatigue cracks developed in a short time, but the problem is relevant also for fast reactor components.     

A weight function approach to stress-intensity factors for half-elliptical surface cracks in cylindrical pressure vessels subjected to thermal shock

Root-mean-square averaged (RMS-averaged) stress-intensity factors were calculated for internal half-elliptical surface cracks in cylindrical vessels using a weight function method. The weight function was derived based on an approximate crack surface displacement representation. Stress-intensity factors for longitudinal half-elliptical inner surface cracks subjected to polynomial stress distribution have been presented and compared favorably with the existing numerical solutions. Superposition of the polynomial stress-intensity factors has provided an extremely efficient solution to the thermal shock crack problems. The crack geometries analyzed were R_i/R₀ = 10/11 and 4/5, a/c = 0·3333 and 0·8, the ratio of crack depth to wall thickness ranged from 0 to 0·8. The results, as well as the proposed method, offer a very powerful and economic way for the safety assessment of pressure vessels subjected to complex and varying load conditions.     

A study on three-dimensional crack tip fields

In this paper several kinds of crack problems are numerically analyzed by the three-dimensional finite element method. They are (1) CT specimens with different thicknesses; (2) stable crack growth in CT specimens: (3) surface cracked plate subjected to bending: (4) pipe with surface crack subjected to bending: (5) CT and surface cracked specimens made of welded plate. The crack tip singular fields are compared with HRR solutions and the Q-factor is evaluated. The effects of the J-integral and Q-factor on the crack growth behavious are discussed with the comparison of the experimental results. It is concluded that the J-integral does not uniquely control the stable crack growth behaviors in many three-dimensional crack problems. It is also found that both J-integral and Q-factor play important roles in the stable crack growth especially in the welded plate.     

Three-dimensional analyses of surface cracks in pressurised thick-walled cylinders

Stress intensity factors for semi-elliptical surface cracks in internally pressurised thick-walled cylinders of radius ratio 3 are presented for a wide range of crack sizes. These solutions were obtained using the boundary integral equation method for three-dimensional stress analysis. Only one crack shape is considered—a semi-ellipse with the length of its semi-minor axis equal to 0·6 times the length of its semi-major axis —but the ratio of crack depth to wall thickness ranged from 0·2 to 0·8. Hoop strain distributions at the outer circumference of the cylinder are also presented for the different crack sizes analysed; the results are useful for experimentally monitoring crack growth.     

Apparatus for total hemispherical emittance measurements of full-scale receiver pipes from 100 to 300°C

An apparatus is described for measuring the total hemispherical emittance of pipes of a length suitable for use in a prototype solar collector. The calorimetric method used requires measurement of the temperatures of the surface of the test pipe and of a concentric outer cylinder and measurement of the electrical power used to heat the test pipe.

Measurements were made of the total hemispherical emittance of black chrome, nickel, and bare steel pipes as a function of temperature. The emittance of the black chrome surfaces increased signicantly from an extrapolated value of about 0.1 at 25°C to values on the order of 0.3–0.4 at 300°C. The extrapolated values for black chrome agreed with measurements made using other techniques at room temperature. The results for the nickel-plated pipe agreed with total emittance calculated from spectral reflectance data.     

Assessment of the flexural capacity of corroded steel pipes

Flexural capacity of corroded pipes can be determined analytically assuming a full plastic failure mode for the pipe. A set of generalized solutions for flexural capacity of the pipe can be developed if the shape of the corrosion is known a priori. The generalized solutions derived in this paper are able to account for the simultaneous action of internal pressure and axial force. For practical purposes, the generalized solutions thus derived are simplified into approximate closed-form equations using three idealized corrosion shapes, namely, constant-depth, elliptical, and parabolic corrosions. Numerical examples indicate that the closed-form approximate solutions provide good comparison with the generalized solutions. The closed-form approximate solutions are subsequently compared to experimental results from full-size tests of pipes with different corrosion depth and width. Parameter study conducted as part of this paper indicates that the shape of a corrosion defect has significant influence on the flexural capacity of the corroded pipes.     

Assessment of resistance to fatigue crack growth of natural gas line pipe steels carrying gas mixed with hydrogen

Hydrogen embrittlement of line pipe steels in the natural gas transmission and distribution network is investigated. The objective is to assess whether the existing network can be used to safely transport a mixture of hydrogen and natural gas. The surveyed literature indicates that the hydrogen-induced acceleration of fatigue crack growth induced by natural gas pressure fluctuations can be the most probable type of failure. We analyzed the fatigue crack growth in line pipe steels containing a long axial crack in the inner diameter (ID) surface by accounting for random cyclic loading due to random and realistic pressure fluctuations, crack closure, and accurate calculation of the stress intensity factor. Using the available experimental data for the crack growth rate vs. stress intensity factor range in the presence of hydrogen, we simulated crack growth over a period of 100 years. The results show that under typical pressure fluctuations in the natural gas network, cracks with depths less than 40% of the wall thickness will never reach depths equal to 75% of the wall thickness. This is a conservative estimate that results from i) the nature of the geometry of the initial flaw in the ID surface that we used in the analysis, ii) the fact that the existing experimental data for the effect of hydrogen on the Paris law are for pressures that are orders of magnitude larger than the partial pressures intended for the hydrogen gas in the mixture, and iii) the experimental data are for fatigue crack growth in pure hydrogen gas without impurities normally present in natural gas, such as oxygen or methane, that can inhibit hydrogen uptake.     

Thermoelastic Models of Continua

Axially symmetric thermal stresses in an elastic pipe weakened by two cylindrical cracks are provided. The surfaces of the cracks are assumed to be thermally insulated. The outer surface of the pipe is heated to maintain a constant temperature T _d , and the inner surface of the pipe is cooled to maintain a constant temperature T _b . As a first step, the boundary conditions related to the temperature field are reduced to dual integral equations using the Fourier transform technique. To satisfy the boundary conditions outside the cracks, the temperature difference at the crack surfaces is expanded into a series of functions that diminish to zero outside the cracks. The unknown coefficients in the series are determined by the Schmidt method so as to satisfy the thermal insulation inside the cracks. Next, the boundary conditions related to the stress field are reduced to dual integral equations. To solve the equations, the differences in the displacements at the crack surfaces are again expanded in a series of functions that diminish to zero outside the cracks. The Schmidt method is also used to solve the unknown coefficients in the series so as to satisfy the stress-free conditions inside the cracks. The stress intensity factors are defined and calculated numerically for several configurations of the pipe.     

Elasto-plastic fracture properties of an all-aluminium gas cylinder with different cracks

All-aluminium cylinders are used for on-board storage of compressed natural gas in vehicles. Besides being subjected to the maximum fill pressure, these cylinders are subjected to fluctuating pressures, due to refuelling operations. In order to establish a relevant test method to ensure leak before break failure performance, elasto-plastic finite element stress analysis of the design containing various defects was carried out to obtain a theoretical basis for the establishment of the test method. Axial semi-elliptical cracks in the central portion of the cylinder and circumferential cracks in the bottom of the cylinder are modelled using 20-node hexahedron elements. Not only the cylindrical body but also the neck and transition areas of the cylinder are considered in the modelling. Slender cracks with lengths approximately five times the wall thickness of the cylinder, which often appear in applied all-aluminium gas cylinders, are considered. Crack depths varied from 22.5% to 100% of the wall thickness. Through discussions about the calculated J-integral and crack mouth opening displacement (CMOD) of the axial and circumferential cracks, the effects of the different cracks on all-aluminium cylinders in the elasto-plastic deformation state are made clear. The analyses show that under the elasto-plastic deformation state, axial cracks in the centre of the cylinder are more dangerous for the cylinder than circumferential cracks in the bottom of the cylinder, if these are of the same size and under the same conditions. The axial external crack is found to be most severe among these different crack types. Finally, the CMOD of cylinders with an axial external crack have been measured by the experimental method and a good agreement between the calculated CMOD and the tested CMOD was reached.