A statistical based circumferentially cracked pipe fracture mechanics analysis for design or code implementation

This paper discusses a simple engineering approach to evaluate surface flaws in carbon steel or stainless steel piping and their weldments. It is based on statistical data from a large number of pipe fracture experiments. To ensure a reasonably conservative approach, a 95-percent confidence level was established. Toughness and pipe size effects are accounted for in one correction factor, while ovalization and flow stress effects are accounted for in two other factors. The limitations and possible improvements to such an approach are also discussed.     

Elasto-plastic behavior of pipe subjected to steady axial load and cyclic bending

The elasto-plastic behavior of a pipe subjected to a steady axial force and a cyclic bending moment is studied. By using two parameters c and d, which describe the elasto-plastic interfaces of beam cross-section, the boundary curve equations between various types of elasto-plastic behavior, such as shakedown, plastic fatigue, ratcheting, and plastic collapse, are derived. The results are applicable for beams of any cross-section with two orthogonal axes of symmetry. As a result, the load regime diagram for a pipe is obtained, which gives an intuitive picture of the elasto-plastic behavior of the pipe under a given combination of constant axial load and cyclic bending moment.     

Lower bound limit load of a circumferentially cracked pipe under combined mechanical loading

In a study on extension of the reference stress method, for J simplified assessment, to a three dimensional (3D) configuration under combined loading, lower bound limit analysis has been developed by J. Desquines. In the present paper the limit load for cracked pipe, with a 3D circumferential flaw, under pressure, tension and bending is detailed. The limit load is explicitly defined as a yield surface is the 3D space loading. A simple algorithm is proposed to solve the non linear problem associated to the reference stress calculation. Moreover, the lower bound solution is compared with Elastic Compensation Method (ECM) results computed on a 3D finite element mesh of the cracked pipe. The lower bound yield surface underestimates the numerical limit loads with a discrepancy lower than 20%.     

Effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load

The objective of this study was to investigate the effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load. This study evaluated the global deformation behavior and collapse moment of the elbows, which contained various types of local wall-thinning defects at their intrados or extrados, using three-dimensional elastic–plastic finite element analysis. The analysis results showed that the global deformation behavior of locally wall-thinned elbows was largely governed by the mode of the bending and the elbow geometry rather than the wall-thinning parameters, except for elbows with considerably large and deep wall thinning that showed plastic instabilities induced by local buckling and plastic collapsing in the thinned area. The reduction in the collapse moment with wall-thinning depth was considerable when local buckling occurred in the thinned areas, whereas the effect of the thinning depth was small when ovalization occurred. The effects of the circumferential thinning angle and thinning length on the collapse moment of elbows were not major for shallow wall-thinning cases. For deeper wall-thinning cases, however, their effects were significant and the dependence of collapse moment on the axial thinning length was governed by the stress type applied to the wall-thinned area. Typically, the reduction in the collapse moment due to local wall thinning was clearer when the thinning defect was located at the intrados rather than the extrados, and it was apparent for elbows with larger bend radius.     

Creep of a straight pipe under combined bending and internal pressure

Several analyses are presented for the isothermal creep behaviour of a thin, constant thickness, circular crosssection cylindrical shell under the action of conbined bending and internal pressure loading. Results are presented in a way that should be helpful for general pipework design. Previous analyses are summarised and discussed.     

Fracture behavior of carbon steel pipe with local wall thinning subjected to bending load

To evaluate the structural integrity of power plant piping, monotonic bending tests are conducted on 4- and 3.5-in. diameter full-scale carbon steel pipe specimens with local wall thinning. The local wall thinning is simulated as erosion/corrosion metal loss. The eroded area of the wall thinning is subjected to tensile or compressive stress by applied bending moment. The deformations or fracture behaviors at maximum moments are found to be classified into three types. When the eroded area is subjected to tensile stress, ovalization or crack initiation/growth occurs at the maximum moment. When an eroded area is subjected to compressive stress, ovalization or local buckling occurs. The occurrence of ovalization, crack initiation/growth, or local buckling depends on the initial size of local wall thinning. From the relationships among ovalization, crack growth and local buckling, allowable sizes for local wall thinning are proposed.     

Characteristics relevant to ductile failure of bimetallic welds and evaluation of transferability of fracture properties

Life management and structural integrity assessment of bimetallic welds in its state-of-the-art form relies on practical methods derived on the basis of years of experience in operation and simplistic strength of materials analyses. The complex conditions and properties of the weldment, as resulting from the elaborate interaction of different microstructures with gradients in material properties, have limited the ability of currently existing methods to construct the assessment on the basis of actual failure mechanisms of bimetallic welds. Current work addresses the assessment procedure by combining experimental and numerical fracture mechanics comprising a micro-mechanical evaluation of the relevant damage mechanisms. The studied dissimilar ferrite (SA508)–austenite (AISI 304) circumferencial weld is one with a Ni-enriched buttering layer.The experimental work comprises tensile and fracture mechanical characterization of the different microstructural zones of the bimetallic weld. Tensile properties are determined with microstructure specific flat bar specimens as well as round bar specimens enabling better inference of true stress–strain curves. Fracture resistance curves are established by applying small-specimen testing techniques. Different crack configurations are modeled by finite element analysis (FEA) to assess the relationships between fracture types, toughness and local near crack tip constraint parameters. Transferability and characterization question are considered by determining J–Q-trajectories and employing small-scale yielding corrections (SSYCs). On the basis of the experimental and numerical results and a fractographical investigation, the micromechanics of fracture are interpreted. Differences in strain hardening capacities of microstructural zones are found to most severely affect the toughness transitions of the weld and the associated failure modes. Two prime failure types are noted, one for cracks located at outer heat affected zone (HAZ) resulting in an unstable crack deflection towards the fusion line (FL) and another type associated with cracks positioned near the fusion line, wherein a low-toughness ductile fracture process results. Small fracture mechanics specimen is found applicable for fracture resistance determination of bimetallic weldments.     

Application of statically indeterminate fracture mechanics, SIFM, to a circumferentially cracked cylinder problem

The method of statically indeterminate fracture mechanics called SIFM is an application of elastic–plastic fracture mechanics to statically indeterminate problems. Application of SIFM has been developed for axially cracked cylinder problems. Its application was modified to a circumferentially cracked cylinder. The component might be loaded by combined transient thermal and mechanical loading. This was applied to simulate pressurized thermal shock, PTS, experiment, NKS-3, carried out by MPA. The predicted result from SIFM shows good agreement with the NKS-3 experimental one.     

Fully coupled strain and damage finite element analysis of ductile fracture

The local approach to fracture presented in this paper is based upon the continuum damage theory. The numerical implementation of this theory is made within the framework of the displacement approach of the finite element method. The fully coupled approach used to predict both initiation and propagation is described in detail. To demonstrate the usefulness of this type of local approach, it is applied to the prediction of initiation in an axisymmetrically notched tensile bar subjected to monotonous loading in ductile fracture conditions. The numerical problems arising when propagation of a localized completely damaged zone is modelled are outlined. To overcome these convergence problems, it is proposed to implement a new local fracture criterion together with a new method ensuring a C₀ continuity of the damage field throughout the finite element discretized structure.     

Behaviour of materials subjected to an impact force and new evaluation method for impact strength

The size dependence of the amplitude of a stress pulse produced in a rod subjected to an impact force is theoretically considered. Impact fatigue experiments were performed to see the size dependence of the strength of structural materials. According to these results, impact fatigue life of a short specimen was shorter than that of a long one. Based on these considerations, it is shown that the superposition of stress waves with reversed phase is effective to improve the impact fatigue life. In addition, a new method is proposed to evaluate the impact strength of materials with stress unit. By this method, influences of strain rate on the impact tensile strength I_m,t and impact bending strength I_m,b are investigated for carbon steel, aluminium alloy and PMMA using their dynamic stress strain relations which are measured directly on each specimen.     

The ratchetting behavior of pressurized plain pipework subjected to cyclic bending moment with the combined hardening model

A series of six tests have been conducted using carbon steel and stainless steel cylindrical specimens having mean diameter/thickness ratios in the range 8 ≤ D_m/t ≤ 28. Each cylinder is pressurized up to its calculated design pressure and is loaded with an alternative bending moment at frequencies typical of seismic events simultaneously. Ratchetting of the cylinder wall has been observed and recorded in the hoop direction. A finite element analysis with the nonlinear isotropic/kinematic (combined) hardening model has been used to evaluate ratchetting behavior of the cylinder under mentioned loading condition. Stress-strain data and material parameters have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The finite element results are compared with those obtained from experimental set-up. The results show that initial the rate of ratchetting is large and then it decreases with the increasing cycles. The FE model predicts the hoop strain ratchetting rate to be near that found experimentally in all cases that M/M_P0.2 ≤ 1. Also, M/M_y ratios for the onset of ratchetting in stainless steel specimens are less than carbon steel specimens with same D_m/t ratios.     

Crack opening displacement of a through-wall crack in a plate subjected to bending load

This study was performed in order to clarify crack opening displacement (COD) of through-wall cracks in a plate subjected to bending load. The former COD evaluation methods were mainly developed corresponding to tensile load, but there has been nothing that has been developed corresponding to bending load. Therefore, the authors evaluated CODs of the through-wall cracks in plates which were subjected to a bending load using finite element method (FEM) analyses, and proposed a simplified COD evaluation method accounting for both tensile and bending loads. The proposed method is useful for leakage evaluation at a crack opening of an elbow crown or in the vicinity of the coolant surface of a vessel in which the bending stress is relatively large.     

Residual load method for modal analysis of piping systems subjected to seismic excitation

Due to the fact that piping systems normally possess a large number of unknowns, the computation of eigenvectors and frequencies is limited. It does not seem to be reasonable to calculate all modes because of the wellknown phenomenon that the accuracy of the higher modes is deteriorating the more the higher the frequency of these eigenforms. When the modal-analysis method is used, this means, that the complete response of piping systems remains unknown.In this paper two methods which pretend to take the neglected higher modes into account are discussed. These are the residual-load-method and the modal-acceleration-method. Error investigations on both methods reveal that the residual-load-method might be given preference.Two examples are presented in which piping systems are dealt with the residual-load-method. It seems surprising, that even for branched systems it is sufficient to compute a few eigenvectors and then apply the residual load.     

Investigation of the ductile fracture properties of type 304 stainless steel plate, welds, and 4-inch pipe

J-integral fracture toughness tests were performed on welded 304 stainless steel 2-inch plate and 4-inch diameter pipe. The 2-inch plate was welded using a hot-wire automatic gas tungsten arc process. This weldment was machined into 1T and 2T compact specimens for single specimen unloading compliance J-integral tests. The specimens were cut to measure the fracure toughness of the base metal, weld metal and the heat affected zone (HAZ). The tests were performed at 550°F, 300°F and room temperature. The results of the J-integral tests indicate that the J_Ic of the base plate ranged from 4400 to 6100 in lbs/in² at 550°F. The J_Ic values for the tests performed at 300°F and room temperature were beyond the measurement capacity of the specimens and appear to indicate that J_Ic was greater than 8000 in lb/in². The J-integral tests performed on the weld metal specimens indicate that the J_Ic values ranged from 930 to 2150 in lbs/in² at 550°F. The J_Ic values of the weld metal specimens tested at 300°F and room temperature were 2300 and 3000 in lbs/in² respectively. One HAZ specimen was tested at 550°F and found to have a J_Ic value of 2980 in lbs/in² which indicates that the HAZ is an average of the base metal and weld metal thoughness. These test results indicate that there is a significant reduction in the initiation fracture toughness as a result of welding.The second phase of this task dealt with the fracture toughness testing of 4-inch diameter 304 stainless steel pipes containing a gas tungsten arc weld. The pipes were tested at 550°F in four point bending. Three tests were performed, two with a through wall flaw growing circumferentially and the third pipe had a part through radial flaw in combination with the circumferential flaw. These tests were performed using unloading compliance and d.c. potential drop crack length estimate methods. The results of these test indicate that the presence of a complex crack (radial and circumferential) reduces in the initiation toughness and the tearing modulus of the pipe material compared to a pipe with only a circumferentially growing crack.     

Prediction of semi-elliptical defect form, case of a pipe subjected to internal pressure

The fatigue propagation of a semi-elliptical surface crack in a pipe subjected to internal pressure is always an open question in spite of a number of numerical works. The crack front development is generally predicted by empirical relationships or parameters c and m of the crack propagation law. This fatigue propagation in the case of a pipe subjected to internal pressure have been obtained using a special device allowed to produce an internal pressure up to 700 bars. The crack aspect ratio development is similar to that of a crack in a plate submitted to tension.     

Structural evaluation of a piping system subjected to thermal stratification

Piping systems in nuclear power plants are often designed for pressure, mechanical loads originating from deadweight and seismic events and operating thermal transients using the equations in the ASME Boiler and Pressure Vessel Code, Section III. In the last few decades a number of failures in piping have occurred due to thermal stratification caused by the mixing of hot and cold fluids under certain low flow conditions. Such stratified temperature fluid profiles give rise to circumferential metal temperature gradients through the pipe leading to high stresses causing fatigue damage. A simplified method has been developed in this work to estimate the stresses caused by the circumferential temperature distribution from thermal stratification. It has been proposed that the equation for the peak stress in the ASME Section III piping code include an additional term for thermal stratification.     

Estimation of fracture toughness of 20MnMoNi55 steel in the ductile to brittle transition region using master curve method

Fracture toughness is an important material property to assess the critical load for structural integrity of reactor pressure vessel steel. In this paper, master curve method proposed by Kim Wallin is used to estimate the fracture toughness of 20MnMoNi55 steel in the ductile to brittle transition regime. Reference temperature (T₀) is evaluated using both single temperature and multi-temperature method for one inch thick compact tension (1T-CT) specimens. Reference temperature (T₀) is also determined from Charpy V-notch test data and compared. Effect of selection of temperature range and number of test temperatures on the value of T₀ is also studied. It is observed that Charpy test results yield lower values of unirradiated T₀ compared to 1T-CT specimen tests. It is also observed that most of the fracture toughness values fall between 5% and 95% boundary of fracture toughness curves for all the evaluations.     

Seismic analysis and fracture evaluation of stabilized core shroud

This paper deals with the seismic analysis and fracture evaluation of a stabilized core shroud in a boiling water reactor of nuclear power plant. To study the adequacy of original seismic loadings, the dynamic behaviors of core shrouds with cracks, without cracks and with stabilizers are analyzed. Seismic analysis of a lumped-mass model of reactor internals is then performed to obtain the seismic loadings around various weldments of the repaired core shroud. The interaction between the core internals and this repaired core shroud is thus taken into account in this study. Further, fracture analysis of the stabilized core shroud is performed to obtain the stress intensity factors along the crack front of horizontal welds based on these seismic loadings. The computed results show that the influence of existing cracks in the stabilized core shroud is insignificant on the overall structural integrity.     

Numerical prediction of the fracture of a thick pressurized shell subjected to a liquid nitrogen shock

The probabilistic elastoplastic stress criterion for cleavage fracture is used in the frame of the local approach to fracture to analyse a fracture experiment in which a one meter long cylinder, with a longitudinal straight crack, was submitted to a thermal shock by liquid nitrogen. The computation, which gives the variation of the probability of fracture with time during the cooling transient, leads to predict a value for the most probable fracture time which is very close to the experimental one. The LEFM approach, which would predict a later initiation time can be improved by incorporating the probabilistic criterion in the frame of the small scale yielding analysis.