Finite element analysis to assess the effect of initial plasticity on transient creep for defects under mechanical loading

Finite element (FE) transient creep analyses have been performed for geometries of differing constraint levels, namely compact and centre-cracked tension specimens and circumferentially-cracked cylinders. Elastic-creep and elastic–plastic-creep behaviour with the same stress exponents in power-law creep and plasticity were considered. The complete time history between initial transient creep response and steady state conditions has been analysed for a range of load levels. Estimates of J(t) and C(t) have been compared with computed values.The known asymptotic behaviour in the limits as time, t→0 and t→∞ has been confirmed. At intermediate times, estimation formulae are suggested which compare well with the FE results. The suggested expressions modify existing formulae in the literature and provide improved agreement with the FE results.     

Effect of intermittent unloading or reversed loading on high temperature crack growth behaviour of Grade 91 steel under constant tensile load

Abstract

As a part of the efforts for developing a reliable assessment procedure for crack growth in high temperature components, crack growth tests at various loading conditions were performed on Grade 91 steel. 1T compact tension specimens of 20 mm thickness were kept under constant tensile load at 600°C, but periodically unloaded or reversely loaded to compressive side to observe these effects on deformation behaviour as well as crack growth behaviour. It was found that periodical reversed loading accelerates crack growth due to re-acceleration of inelastic deformation during load holding, but its extent was not as large as predicted by creep J-integral in a conventional way. The predictions were improved by introducing an additional parameter to take account of creep damage recovery which was caused by the excursion to compressive load.     

Creep crack growth data and prediction for a P91 weld at 650 °C

Creep crack growth tests have been carried out on compact tension (CT) specimens machined from a P91 weldment. Four of these specimens were cut from the parent material side of the weld and another seven specimens were cut across the weld. For the cross-weld specimens, starter cracks were positioned into (or close to) the Type IV region. The creep tests were carried out under constant loads, at 650 °C. The results obtained showed that, the creep crack growth rates for parent material specimens are about ten times lower than those for the cross-weld specimens and that the scatter in the data is relatively high. In this respect, the accuracy of the crack tip location, in the cross-weld CT specimens, plays an important role. Finite Element (FE) analyses were carried out, on notched bar and CT models, using damage mechanics material behaviour models. These analyses were used to estimate the triaxial stress factor, α, for the parent material (PM), the weld metal (WM) and the heat affected zone (HAZ). FE analyses were then used to predict the creep crack growth in the CT specimens. Results from the FE analyses for both the PM and the cross-weld CT specimens were in good agreement with the corresponding experimental results. The effect of the potential drop versus crack length calibration on the calculated C* values was also investigated.     

Difficulties in interpreting data from creep crack growth tests on type 316H weldments

Abstract

Experimental creep crack growth data are generally obtained by following standard methods such as ASTM E1457-07 and subsequently characterised using the C* parameter. These data are then used in assessment procedures, such as R5, together with reference stress estimates of C* in the component, to predict creep crack growth behaviour. Some modifications to the ASTM E1457 creep crack growth testing and analysis methods have already been proposed following a previous analysis of data from long term creep crack growth tests on type 316H parent material. This paper reports the results of creep crack growth tests on type 316H heat affected zone material at 550°C using compact tension (CT) specimens manufactured from non-stress relieved thick section butt welds. It is shown that interpretation of the data from these weldment tests is complicated by both the discontinuous nature of the cracking process and the presence of significant residual stresses in the CT specimens. Further modifications to creep crack growth testing and analysis methods are proposed to address difficulties arising from the discontinuous nature of the cracking process, and further work is identified to investigate the influence of the residual stresses present in the specimens on the observed crack growth behaviour.     

The influence of the stress state on fracture toughness

Conventional fracture mechanics treatments usually disregard biaxial loading modes, even though several authors have discussed the biaxiality effect of an additional load in the crack extension direction. Another biaxial effect, that related to an additional load parallel to the crack front, has not been investigated until now. This paper describes experiments and three-dimensional (3D) FE stress analyses which have been performed with plate-shaped cracked specimens under biaxial bending. In relation to stresses around the blunted crack tip, a fracture criterion based on achieving a critical stress is discussed.     

Evaluation of fracture mechanics parameters for bimaterial compact tension specimens

Abstract

The elastic–plastic fracture mechanics parameter J and its analogous creep fracture parameter C* are widely used to measure the fracture resistance of a material. The non-linear component of the J and C* parameters can be evaluated experimentally using the η factor. For weldments, the η factor is dependent on the relative properties of the base (parent) and weld materials, particularly the mismatch in their yield strengths. In this work, the η factor has been evaluated using non-linear finite element analyses in a standard compact tension C(T) specimen for a power law material. A range of mismatches in base/weld material properties have been considered. A through thickness strip of weld material, of height 2h, has been modelled, which was positioned at the mid height of the specimen. The η factor has been evaluated for a range of crack lengths and power law hardening exponents under both plane stress and plane strain conditions and the results compared with literature where available. For a given crack length and weld width, the η solutions of the undermatched and overmatched conditions examined show a maximum variation of 12% from the mean value. A relationship has been proposed with respect to crack length for the C(T) specimen to describe the decrease in the η factor with an increase in mismatch ratio.     

Finite element simulation of welding residual stresses in martensitic steel pipes

Abstract

Finite element (FE) simulations of the welding of two high grade steel pipes are described. The first is a P91 steel pipe welded with a similar P91 weld consumable, and the second is a P92 steel pipe welded with dissimilar nickel–chromium based weld consumables. Both welds are multipass circumferential butt welds, having 73 weld beads in the P91 pipe and 36 beads in the P92 pipe. Since the pipes and welds are symmetric around their axes, the FE simulations are axisymmetric, allowing high FE mesh refinement and residual stress prediction accuracy. The FE simulations of the welding of the P91 and P92 pipes comprise thermal and sequentially coupled structural analyses. The thermal analyses model the heat evolution produced by the welding arc, determining the temperature history throughout the FE models. Structural analyses use the computed temperature history as input data to predict the residual stress fields throughout the models. Post-weld heat treatment (PWHT) of both pipes has also been numerically simulated by assuming that the FE models obey the Norton creep law during the hold time period at 760°C. The residual stresses presented here have all been validated by corresponding experimental measurements. Before PWHT, it has been found that, at certain locations in the weld region and heat affected zone (HAZ) in the pipes, tensile hoop and axial residual stresses approach the tensile strength of the material, presenting a high risk of failure. It has also been found that PWHT substantially reduces the magnitude of residual stresses by varying degrees depending on the material.     

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.     

Creep fatigue crack behavior of two power plant steels

Crack initiation and crack growth under creep fatigue conditions were experimentally determined on a bainitic turbine rotor steel (30CrMoNiV4-11) and a martensitic pipe steel (X10CrMoVNb9-1). Side grooved compact tension (CT) specimens with 25 and 50 mm thickness as well as double edge notch tensile (DENT) specimens with 15 and 60 mm thickness have been tested in order to observe possible influences of geometry and thus to check the transferability of the specimen test results to the behavior of components.The creep fatigue crack test results can be described with the usual fracture mechanics parameters. A modified two-criteria-method can be used to estimate the crack initiation under creep fatigue conditions. The creep fatigue crack growth can be calculated from the accumulation of fatigue crack growth which is described by the Forman-law and creep crack growth which is described by the C^*-parameter.     

Creep crack growth behaviour of Type 316H steels and proposed modifications to standard testing and analysis methods

Tests have been performed on Type 316H stainless-steel compact tension specimens from four ex-service components and creep crack growth rates from these tests have been characterised using C^*$C^{*}$. Several modifications to standard creep crack growth testing and analysis methods have been proposed, including an improved approach for determining whether widespread creep conditions have been developed in the specimens. The observed behaviour has then been compared with existing creep crack growth rate data for this material. A change in cracking mode from ductile to brittle intergranular fracture was observed with increasing test duration. In addition, creep crack growth rates for several of the longest-term tests lie above an extrapolation of existing data from shorter-term tests. Models based on ductility exhaustion have been used to derive new equations for predicting creep crack growth rates in Type 316H steel at temperatures of 525 and 550 °C.     

Creep fatigue crack development in dissimilar metal welded joints between steels and nickel based alloy

Abstract

Creep and strain controlled cyclic/hold creep fatigue tests have been performed at temperatures in the range of 550–575°C on specimens extracted from dissimilar metal welded (DMW) joints between two classes of steel and a nickel based alloy. The details and results of the tests are described. While crack development in the cyclic/hold creep fatigue test specimens tends to be creep dominated, the microstructural paths followed in the steels in the vicinity of their heat affected zones are not identical to those observed in creep rupture testpieces taken from the same DMW joint. In pure creep tests, cracking may occur adjacent to the fusion line and/or in the fine grain heat affected zone (FGHAZ), with rupture location being dependent on temperature stress and microstructural condition. In contrast, creep dominated creep fatigue cracking typically occurs in the intercritical heat affected zone/FGHAZ or the overtempered parent material on the steel side of such weldments, depending on the composition of the joint.     

Creep crack growth of seam-welded P22 and P91 pipes with artificial defects. Part II. Data analysis

This paper examines several methods for assessing experimental creep and fatigue crack growth data obtained on P22 (2.25Cr1Mo) and P91 (9Cr1MoVNb) axially notched, seam-welded pipes tested at 565 and 625 °C, respectively [Creep crack growth of seam-welded P22 and P91 pipes with artificial defects—part I: experimental study and post-test metallography. Second International HIDA Conference, Advances in Defects Assessment in High Temperature Plant, MPA, Stuttgart, Germany, 4–6 October, 2000]. The overall objective of this work is to identify the nature of any correlation between component and conventional testpiece creep crack growth rates and thereby provide a supplementary tool for structural integrity analysis. Creep crack growth rate of the notch located in the heat-affect-zone of the weld was assessed in terms of both stress intensity factors, K_I, and the C^*-integral. To estimate the C^*-integral, reference stresses were developed by deriving limit load solutions which reconcile the different collapse loads of the axially notched pipes. Both minimum and average creep rate laws were utilised in the analysis to accommodate the strain rate in the C^* relation. Each test was examined independently, but the general conclusion from each analysis was the same, in that C^*-integral, rather than the stress intensity factor, gave better correlation with respect to conventional data generated using compact tension (CT) specimens. The assessment of creep crack growth demonstrates one particular aspect of interest. In terms of the C^* based correlation of creep crack growth rates, the analysis was found to be relatively independent of the stress state and correlates well with CT specimen data when appropriate reference stresses are used. In addition, cracking in the tested pipes was observed to occur between plane stress and plane strain conditions, inferring that both creep ductility and ligament straining contribute towards the failure mechanism.     

TRANSIENT THERMOELASTIC FRACTURE OF INTERFACE CRACKS

Abstract

The transient behavior of an interface crack at the center and edge of two finite dissimilar materials free to bend and subjected to a transient thermal load was studied. It was first assumed that the crack was insulated. The effect of allowing heat to conduct through the crack upon closing was also investigated. The effects of the mechanical and thermal material property ratios as well as the thickness ratio on the crack deformations and the transient strain energy release rate were calculated.     

Creep fracture mechanics parameters for internal axial surface cracks in pressurized cylinders and creep crack growth analysis

In the present study, a low alloy Cr–Mo steel cylinder subjected to internal pressure at high temperature with a semi-elliptical crack located at the inner surface is considered. The creep crack driving force parameter C1-integrals calculated by finite element (FE) method, are compared with results from previous studies, which indicates that empirical equations may be inaccurate under some conditions. A total of 96 cases for wide practical ranges of geometry and material parameters are performed to obtain systematic FE results of C1-integral, which are tabulated and formulated in this paper. It is observed that the maximum C1-integral may occur neither at the deepest point nor at the surface point when the aspect ratio is large enough and the value of C1-integral is significantly sensitive to the crack depth ratio. Furthermore, based on the proposed equations for estimating C1-integrals and a step-by-step analysis procedure, crack profile development, crack depth, crack length and remaining life prediction are obtained for surface cracks with various initial aspect ratios. It is found that when the crack depth ratio is increased, there is no obvious convergence of crack aspect ratio observed. The magnitude of half crack length increment is always minor compared with the crack depth increment. In addition, the remaining life is much more dependent on the surface crack depth than on the surface crack length.     

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.     

Creep behaviour of Waspaloy under non-constant stress and temperature

Abstract

Current creep models are derived using data from constant stress (or load) creep tests and are capable of accurately predicting creep behaviour when applied conditions are constant or near constant. However, analyses of creep curve shapes for the nickel based superalloy Waspaloy, when applied stress and/or temperature vary greatly during testing, have shown that predictive methods based purely on strain, time or life fraction are insufficient and cannot predict the observed creep rates. This is important when considering stress concentration features where stress relaxation due to creep can significantly alter the distribution of stress and thus affect fatigue life. When both stress and temperature are changed during a creep test, dislocation movement must proceed through a dislocation network formed under different conditions, resulting in greater than expected creep rates. It is proposed that this is due to a reduction in effective internal stress due to changes in dislocation structure.     

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.     

Yield load solutions of heterogeneous welded joints

The aim of this paper is to establish yield load solutions when the materials inhomogeneity within the weld is present, which is usually the case in repair welding. The effect of yield strength mismatch of welded joints performed with different geometry on the yield load value has been investigated in the context of single edge notched fracture toughness specimen subjected to bending SE(B) using the finite element method. The crack was located in the center of the weld and the two most important geometrical parameters were identified as: crack length ratio a/W as well as slenderness of the welded joint, which were systematically varied. One practical and four additional combinations of filler materials, with the same portion of overmatched part and undermatched part of the weld, were analyzed, and plane strain FE solutions for the case when the crack is located in the overmatched half of the heterogeneous weld were obtained.     

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.     

Code of practice for high-temperature testing of weldments

The present paper reports on a code of practice (CoP) for high-temperature testing of weldments for industrially relevant specimens. Novel aspects of the CoP include advice for testing weldment zones using different specimen geometries. Those specimens differ from the standard compact tension C(T) specimen recommended in the only available creep crack growth (CCG) testing standard ASTM E1457. Recommendations for the required number of tests, techniques for testing, treatment of test records, reduction of test data and data analysis are presented. Associated specimen selection guidelines for industrial creep crack initiation (CCI) and growth testing are also described. Validation tests carried out on P22 and P91 weldments, and base metals of 316H steel and C-Mn steel using relevant specimen geometries are briefly described. The CoP contains recommended K and C* solutions, Y functions and η factors, which are used to determine values of the fracture parameters K and C* for the specimen geometries considered. Information from these new tests, together with a review of previous CCG tests on non-standard geometries, have been used in recommending the best method of analysis for CCI and CCG data for a range of creep brittle to creep ductile welded materials.