Limit loads and fracture mechanics parameters for thick-walled pipes

In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part II: J-integral estimation

Evaluation of the J-integral plays a central part in evaluation of the critical crack length for unstable fracture for piping systems. Simplified evaluation methods for the J-integral for a circumferential through-wall crack in pipes subjected to axial and bending loading or their combination is reviewed in this paper. Use of the LBB.ENG2 method and a similar approach based on the η-factor concept were found to result in significant underestimation of the J-integral for small and medium crack angles. On the other hand, the reference stress method based on the solutions for stress intensity factor and limit load recommended in the companion paper (Part I) provides solutions which agree well with the available non-linear finite-element solutions and can be utilized as a powerful tool for J-integral evaluation for arbitrary materials, not restricted to simple power-law hardening.     

Analysis of interacting semi-elliptical surface cracks in finite thickness plates under remote bending load

Interaction effects of two coplanar self-same shallow and deep semi-elliptical surface cracks in finite thickness plates subjected to remote tension have been previously investigated by Sethuraman et al. Using the finite element based force method. In the present study, the effect of remote bending load on interacting semi-elliptical surface cracks in a finite thickness plate is analyzed. Stress intensity factors are evaluated along the entire crack front using a modified force method based on the three-dimensional finite element solution. The line spring model has also been used to evaluate stress intensity factors at the deepest point of a crack using shell finite element analysis. Parametric studies involving a wide ranges of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.2≤a/c≤1.0), crack depth ratio (0.2≤a/t≤0.9), relative crack location (0.2≤2c/d≤0.9) and normalized location on the crack front (0≤2ϕ/π≤2) are carried out for numerical estimation of crack interaction factors. Due to the crack interaction, the stress intensity factor distribution is observed to be asymmetric along the crack front. The interaction is also observed to cease when the distance between two cracks is more than five times the crack width (i.e. 2c/d less than 0.2) irrespective of crack shape aspect ratio. Finally, an empirical relation is proposed for the evaluation of crack interaction crack interaction factors for the range of parameters considered. For the ranges considered, the proposed empirical relation predicts the crack interaction factors at the inner and outer surface points of the crack within ±4% of the three-dimensional finite element solutions.     

Relevance of plastic limit loads to reference stress approach for surface cracked cylinder problems

To investigate the relevance of the definition of the reference stress to estimate J and C* for surface crack problems, this paper compares finite element (FE) J and C* results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface cracks and finite internal axial cracks are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) a local limit load, (ii) a global limit load, (iii) a global limit load determined from the FE limit analysis, and (iv) the optimised reference load. It is found that the reference stress based on a local limit load gives overall excessively conservative estimates of J and C*. Use of a global limit load clearly reduces the conservatism, compared to that of a local limit load, although it can sometimes provide non-conservative estimates of J and C*. The use of the FE global limit load gives overall non-conservative estimates of J and C*. The reference stress based on the optimised reference load gives overall accurate estimates of J and C*, compared to other definitions of the reference stress. Based on the present findings, general guidance on the choice of the reference stress for surface crack problems is given.     

Limit load and J estimates of a centre cracked plate with an asymmetric crack in a mismatched weld

The limit load and J estimates of a centre cracked plate with an asymmetric crack in the tensile properties mismatched weld were investigated. A limit load expression was derived on the basis of a simplified slip-line field. A good agreement between the predictions of the expression and finite element (FE) results was found for ratios of half-weld width to the crack ligament, H/l, of less than 0.5. The equivalent stress–strain relationship method (ESSRM) was used to predict elastic–plastic J values. Results from FE analyses show that the ESSRM is accurate for the crack with asymmetry in the mismatched weld provided an accurate theoretical or numerical value of the limit load of the same specimen is available. Defect assessment methods are discussed, and it is found that the failure assessment diagram (FAD) of an asymmetrically cracked mismatched weld can be constructed from the equivalent stress–strain relationship for the same mismatched geometry with a symmetric crack. The effect of an asymmetric crack on the FAD may then be covered by the limit load solution for the asymmetrically cracked mismatched weld.     

Fracture initiation at the root of a blunt flaw: description in terms of Kr–Lr failure assessment curves

In assessing the effect of a defect on the integrity of an engineering structure, considerable use is now being made of failure assessment diagrams. Recent work, focused on the effects of a sharp crack, has highlighted the geometry dependence of the failure assessment curve when it is expressed in terms of normalised stress intensity (K_r) and normalised limit load (L_r) parameters. This article extends the earlier work, in that it quantifies the geometry dependence of the failure assessment curve for the case of a blunt flaw, with K_r now being defined in terms of an effective K parameter, as if the flaw were a sharp crack.     

The effect of mechanical heterogeneity and limit load of a weld joint with longitudinal weld crack on the J-integral and failure assessment curve

According to the CEGB R6 (Rev.3) approach, the influence of strength mis-matching and the limit load of a weld joint with a longitudinal weld crack on the J-integral and failure assessment curve can be studied by using an elastic–plastic finite element method for Center-Cracked Panel (CCP) specimens. The results indicate that the values of the J-integral and the shapes and positions of the failure assessment curves are greatly affected by the strength mis-matching factor M, a ratio of weld metal yield strength to that of base metal. If the limit load of the base metal is adopted to normalize the applied load, then the greater the value of M, the larger the safe area is in the failure assessment curve (FAC). However, if the limit load of the weld metal is adopted to normalize the applied load, then the greater the value of M, the smaller the safe area is. Therefore, for the undermatched and evenmatched joints, it is safer to choose the limit load of the base metal as the normalized load, and for the overmatched joints, it is safer to choose the limit load of the weld metal as the normalized load. Moreover, when M is less than 0.8 for the former situation, the option 1 curve of the R6 is not a conservative assessment curve. Considering that there is no simple theoretical formula which is suitable for calculating the limit load of a mechanical heterogeneous weld joint under plane stress and a variety of crack geometries, it is recommended that no matter what the strength of the overmatched or undermatched weld joint is, it is safer to use the limit load of that metal which has the higher strength grade of base metal and weld metal as the normalized load.     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure

Published limit load formulae for circumferential defects overestimate the burst pressure for penetrating defects in pipes by the factor two in the short crack limit, because they only consider axial stress. Therefore, a class of limit load solution is discussed which takes the triaxial state of stress into account. The solutions for pressure loaded crack faces are improved analytically. Primal–dual limit analysis with the finite element method is used to adjust all solutions to numerical results. Limit loads are obtained for circumferential cracks of all sizes in thick-walled cylinders.     

A simple procedure to evaluate the stress intensity factor in internally pressurized cylinders

The evaluation of stress intensity factors in internally pressurized cylinders, with both surface and sub-surface flaws, is examined. The method of analysis is based on the equivalent linear representation of the circumferential stress distribution in accordance with ASME rules, the non-linear hoop stress distribution then being conservatively approximated by the membrane and bending stresses. The stress intensity factor for an elliptical crack embedded in an elastic solid and subjected to internal pressure is considered for two conditions of load (tension and bending) and the effects are added.The results are presented in non-dimensional form to evaluate the effect on stress intensity factor of the various parameters (outside and inside radius, crack position, cylinder thickness, form of ellipse).     

Consideration of non-steady-state crack growth in materials evaluation and design

Fracture mechanics is being used increasingly in the design and reliability assurance of reactor pressure vessels. This technology enables a quantitative assessment of the potential influence of environment-enhanced crack growth on vessel integrity to be made. The basis of such an assessment is a one-to-one relationship between the rate of crack growth and K, the applied value of the crack-tip stress intensity factor. The purpose of the work described in this paper is to examine the uniqueness of this relationship and also to elucidate and assess the significance of any deviations from such a relationship.Data on a variety of low alloy steels, exposed to aqueous environments, are presented which demonstrate that, under certain conditions, the K versus growth rate relationship appears not to be unique—that is, for a given value ofK, several distinctly different rates can occur. Tests conducted under both static and cyclic loading are shown to exhibit this behaviour following test start-up, test interruptions, or changes in loading variables such as cyclic frequency. In order to understand this phenomenon, experiments were conducted on a quenched and tempered low alloy steel exposed to distilled water. Using specimens in which K remains constant, as the crack grows under constant load, data have been obtained which demonstrate that this behaviour is due, at least in part, to non-steady state crack growth. Initially, rates are significantly less than the steady-state rate and, although crack growth eventually accelerates to the steady-state rate, significant transient periods occur. A unique, geometry independent relationship only exists between crack growth rates and the crack-tip stress intensity factor provided these non steady-state effects are eliminated.For a given material, the duration of this transient period appears to be dependent on environment chemistry, thereby suggesting that the phenomenon is controlled by the kinetics of underlying chemical processes which lead to the material's degradation. A kinetic model based on the concept of a hydrogen embrittled volume of material at the crack tip provides a unified understanding of the various transient behaviours in the steels considered in this paper.The practical significance of this time-dependent behaviour is that it can cause laboratory data to misrepresent the growth rates which occur under operating conditions in reactor pressure vessels. Recommendations are provided for identifying these non-steady-state effects when acquiring laboratory data. Approaches to dealing with transient crack growth rates in design and reliability assessments are also outlined.     

The analytical fracture behaviour of a bar in tension containing a circumferential edge crack

This paper evaluates the analytical fracture behaviour of a bar in tension containing a circumferential edge crack. The stress intensity factor and limit load solutions available in the literature are reviewed and then used to derive the compliance and J-integral functions for a test specimen. The load at which plastic necking occurs in the specimen is also evaluated for idealized material behaviour to establish the maximum fracture toughness that can be measured as a function of specimen size. The analyses enable the optimum geometry and size of a specimen for fracture toughness measurements to be deduced.     

The influence of side-grooving on pre-cracked Charpy specimens in bending

Fatigue pre-cracked Charpy specimens are sometimes used to measure the fracture toughness of steels. For most steels the dimensions of the Charpy specimens are insufficient to prevent significant plastic yielding ahead of the crack during a test. A feature of the tests is that stable crack growth results in significant crack front curvature. Side-grooving compact tension specimens has been found to inhibit crack front curvature and promote straight fronted crack growth. This paper investigates the effect of side-groove depth on the fracture behaviour of pre-cracked Charpy specimens.Elastic three-dimensional finite element analyses have been performed to assess the effect of side-groove depth on the compliance, stress state and stress intensity factor.The load displacement behaviour of Charpy specimens has been measured to determine the effect of side-groove depth on the limit load and fracture resistance.Using the finite element and experimental results an expression is derived for calculating the fracture resistance of side-grooved Charpy specimens. The expression is used to determine the critical fracture resistance of 1CrMoV steel at two temperatures using Charpy specimens with and without side-grooves.     

French experimental studies of circumferentially through-wall cracked austenitic pipes under static bending

This paper describes experimental studies performed on cracked pipes made of austenitic steel and subjected to a bending load. The studies concern the characterization of conditions for which an initial crack (fatigue precracked) initiates and then propagates along the circumference of the tube. The influences of different parameters were obtained: crack length, crack tip radius, tube geometry (radius, thickness), temperature and weldment. The predictive criteria checked in these studies are limit analysis (or net-section stress criterion) and J estimation.     

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.     

CRITICAL STRESS INTENSITY FACTORS FOR CRACKED HOLLOW PIPES UNDER TRANSIENT THERMAL LOADS

Finite element analyses of a long hollow cylinder having an axisymmetric circumferential internal edge crack, subjected to convective cooling on the inner surface are performed. The transient thermal stress intensity factor is estimated using a domain version of the J-integral method. The effect of the thickness of the cylinder, crack length, and heat transfer coefficient on the stress intensity factor history are studied. The variations of critical normalized stress intensity factor with crack length-to-thickness ratio for different parameters are presented. The results show that if a small inner surface crack begins to grow, its stress intensity factor will increase with increase in crack length, reach a maximum, and then begin to drop. Based on the results, a fracture-based design methodology for cracked hollow pipes under transient thermal loads is discussed.     

Derivation of ‘γ’ parameter from limit load expression of cracked component to evaluate J–R curve

Experimental evaluation of the J-integral requires the ‘η_pl’ function, proposed by Rice et al. [Progress in flaw growth and fracture toughness testing (1973) 231], to multiply the area under the load vs. plastic load-line-displacement curve. However, the J-integral, thus evaluated, requires modification if crack growth occurs. A ‘γ’ term was proposed by Hutchinson and Paris [Elastic–plastic fracture (1979) 37] and later generalised by Ernst et al. [Fracture mechanics (1979) 581] and Ernst and Paris [Techniques of analysis of load–displacement records by J-integral methods (1980)] to correct the J-integral to account for crack growth. The η_pl and γ functions are available for very few geometries under specific loading conditions. A limit load-based general expression of η_pl was given by Roos et al. [Int J Pres Ves Piping 23 (1986) 81], but no such expression is available for γ functions. The advantage of having limit load-based general expressions for η_pl and γ functions is that the limit load for a particular geometry subjected to a specific loading condition is easily available in the open literature. In the present paper, a limit load-based general expression for the γ function is derived. The general expression is then validated by deriving the known γ functions of various geometries subjected to various loading conditions, which are available in the open literature. The general expressions are then used to derive new η_pl and γ functions for same pipe and elbow geometries with various crack configurations under different loading conditions, for which no solutions are available in the open literature. Finally, experiments have been carried out on 200 mm nominal bore (NB) elbows with throughwall circumferential cracks under in-plane bending moment. The proposed new expressions of η_pl and γ functions for this geometry are used to obtain the J–R curve from the experimental load vs. load-line-displacement and load vs. crack growth data.     

Fracture analysis of hydrogen storage composite cylinders with liner crack accounting for autofrettage effect

An understanding of fracture behavior is crucial to the safe installation and operation of high-pressure composite cylinders for hydrogen storage. This work has developed a comprehensive finite element model to investigate axial surface flaws in cylinder liners using the fracture mechanics and a global–local finite element technique. Since the autofrettage process has a strong influence on cylinder fracture behavior, it is also considered in this analysis. The simulation process is broken down into three steps in order to precisely extract fracture parameters and incorporate the autofrettage effect. In the first step, the global model performs the autofrettage simulation to study the residual stress with consideration of both material hardening and the Bauschinger effect. In the second step, the global model uses residual stress to compute displacement for the local model. Finally, in the third step, the local model extracts the values of stress intensity factor and J-integral. Comparison is conducted on the fracture parameters with various autofrettage levels and crack shapes. The vicinity of the crack front is also studied by the size and shape of the plastic zone, and the validity of stress intensity factor and J-integral dominances is examined.     

A global limit load solution for plates with surface cracks under combined end force and cross-thickness bending

A global limit load solution for rectangular surface cracks in plates under combined end force and cross-thickness bending is derived, which allows any combination of positive/negative end force and positive/negative cross-thickness moment. The solution is based on the net-section plastic collapse concept and, therefore, gives limit load values based on the Tresca yielding criterion. Solutions for both cases with and without crack face contact are derived when whole or part of the crack is located in the compressive stress zone. From the solution, particular global limit load solutions for plates with extended surface cracks and through-thickness cracks under the same loading conditions are obtained. The solution is consistent with the limit load solution for surface cracks in plates under combined tension and positive bending due to Goodall & Webster and Lei when both the applied end force and bending moment are positive. The solution reduces to the limit load solution for plain plates under combined end force and cross-thickness bending when the crack vanishes.     

Threshold stress intensity factor for hydrogen-assisted cracking of CR-MO steel used as stationary storage buffer of a hydrogen refueling station

In order to determine appropriate value for threshold stress intensity factor for hydrogen-assisted cracking (K_IH), constant-displacement and rising-load tests were conducted in high-pressure hydrogen gas for JIS-SCM435 low alloy steel (Cr-Mo steel) used as stationary storage buffer of a hydrogen refuelling station with 0.2% proof strength and ultimate tensile strength equal to 772 MPa and 948 MPa respectively. Thresholds for crack arrest under constant displacement and for crack initiation under rising load were identified. The crack arrest threshold under constant displacement was 44.3 MPa m^1/2 to 44.5 MPa m^1/2 when small-scale yielding and plane-strain criteria were satisfied and the crack initiation threshold under rising load was 33.1 MPa m^1/2 to 41.1 MPa m^1/2 in 115 MPa hydrogen gas. The crack arrest threshold was roughly equivalent to the crack initiation threshold although the crack initiation threshold showed slightly more conservative values. It was considered that both test methods could be suitable to determine appropriate value for K_IH for this material.