Creep Continuum Damage Mechanics Research Articles

Analysis of unified continuum damage mechanics model of gas turbine rotor steel: Life assessment

In this research, the unified creep continuum damage mechanics model of Lemaitre is used to model the stress–strain behavior of a gas turbine rotor. The unified damage law can model the creep and low cycle fatigue damage. It is based on the increment of the accumulated inelastic strain, which may be due to either creep damage or low cycle fatigue damage. The parameters of the unified continuum damage mechanics model, including Q, Norton constants, and constants of the nonlinear kinematic hardening model are determined and optimized by cyclic tension and relaxation tests. A careful three-dimensional thermal analysis is carried out and the temperature gradient is obtained. This analysis is used to determine stresses of the gas turbine rotor. Creep and low cycle damage are also modeled and stress–strain evolution in the gas turbine rotor is obtained. The replica tests are performed on four points of the rotor surface and formation of the creep voids is verified under a scanning electron microscope. Based on the continuum damage mechanics analysis, the creep–fatigue interaction is considered in modeling and the remaining life of the rotor is estimated.

Reduced numerical solution times for combined boundary‐initial value problems using parallel computing

Purpose — The purpose of this paper is to seek improved solution techniques for combined boundary‐initial value problems (IVPs) associated with the time‐dependent creep deformation and rupture of engineering structures at high temperatures and hence to reconfigure a parallel iterative preconditioned conjugate gradient (PCG) solver and the DAMAGE XXX software, for 3‐D finite element creep continuum damage mechanics (CDM) analysis.Design/methodology/approach — The potential to speed up the computer numerical solution of the combined BV‐IVPs is addressed using parallel computers. Since the computational bottleneck is associated with the matrix solver, the parallelisation of a direct and an iterative solver has been studied. The creep deformation and rupture of a tension bar has been computed for a range of the number of degrees of freedom (ndf), and the performance of the two solvers is compared and assessed.Findings — The results show the superior scalability of the iterative solver compared to the direct solver, with larger speed‐ups gained by the PCG solver for higher degrees of freedom. Also, a new algorithm for the first trial solution of the PCG solver provides additional speed‐ups.Research limitations/implications — The results show that the ideal parallel speed‐up of the iterative solver of 16, relative to two processors, is achieved when using 32 processors for a mesh of ndf = 153,238. Originality/value — Techniques have been established in this paper for the parallelisation of CDM creep analysis software using an iterative equation solver. The significant computational speed‐ups achieved will enable the analysis of failures in weldments of industrial significance.

Microstructure-based creep modelling of a 9%Cr martensitic steel

Martensitic 9 –12%Cr steels can undergo significant changes in their microstructure during thermal/mechanical exposure. Four elements of their microstructure seem to be of particular importance: (i) strain-dependent coarsening of subgrains within the initial tempered martensitic lath microstructure; (ii) an accompanying proportionate decrease in the density of subgrain network dislocations; (iii) Ostwald ripening of MX carbo-nitrides within the subgrains; and (iv) depletion of subgrain matrix-strengthening solid solution elements (Mo/W) due to low density precipitation of large, strength-benign particles of Laves phase. A body of data now exists within the literature on the evolution kinetics of each of these processes but this can only be utilised for life prediction by one or two of the many creep models developed over the decades. In the present work, a microstructure-based Continuum Creep Damage Mechanics (CDM) model has been used to generate strain trajectories by incorporating previously published evolution kinetics for (iii) and (iv) into the kinetic creep equation as well as introducing strain-dependent coarsening of subgrains and network dislocations in a novel way. Using data specific to 9Cr –1Mo–V,Nb steel, the CDM calculations demonstrate that although subgrain-coarsening dominates tertiary creep trajectories (as Blum has long suggested), lifetimes may be significantly reduced further both by solid-solution depletion of Mo and coarsening of MX carbo-nitrides, depending upon stress/temperature.

Microstructure-based creep modelling of a 9%Cr martensitic steel

Martensitic 9 –12%Cr steels can undergo significant changes in their microstructure during thermal/mechanical exposure. Four elements of their microstructure seem to be of particular importance: (i) strain-dependent coarsening of subgrains within the initial tempered martensitic lath microstructure; (ii) an accompanying proportionate decrease in the density of subgrain network dislocations; (iii) Ostwald ripening of MX carbo-nitrides within the subgrains; and (iv) depletion of subgrain matrix-strengthening solid solution elements (Mo/W) due to low density precipitation of large, strength-benign particles of Laves phase. A body of data now exists within the literature on the evolution kinetics of each of these processes but this can only be utilised for life prediction by one or two of the many creep models developed over the decades. In the present work, a microstructure-based Continuum Creep Damage Mechanics (CDM) model has been used to generate strain trajectories by incorporating previously published evolution kinetics for (iii) and (iv) into the kinetic creep equation as well as introducing strain-dependent coarsening of subgrains and network dislocations in a novel way. Using data specific to 9Cr –1Mo–V,Nb steel, the CDM calculations demonstrate that although subgrain-coarsening dominates tertiary creep trajectories (as Blum has long suggested), lifetimes may be significantly reduced further both by solid-solution depletion of Mo and coarsening of MX carbo-nitrides, depending upon stress/temperature.

Continuum damage mechanics modelling based on simulations of microstructural evolution kinetics

Continuum creep damage mechanics modelling of creep has been combined with the recently developed Monte Carlo simulations of precipitation kinetics in power plant ferritic steels. The precipitation simulation has been validated by applying it to a 9 wt-%Cr ferritic steel, P92 and using the microstructural data published in the literature. The microstructural evolution results of precipitation kinetics simulation are used in the continuum creep damage mechanics model to calculate the damage evolution instead of the model equations developed for specific creep damage. This approach has been applied to P92 to study the effects of different creep damage mechanisms on the creep behaviour. Reasonable agreement with experimental creep rupture data and creep curves has been obtained. The new approach shows promise to provide a useful tool for both new alloy development and component life prediction.

CDM predictions of creep damage initiation and growth in ferritic steel weldments in a medium-bore branched pipe under constant pressure at 590° C using a four-material weld model

The paper reports the use of three-dimensional creep continuum damage mechanics techniques to study the creep failure of a medium-bore low-alloy ferritic-steel cylinder–cylinder branched pressure vessel welded connection, tested at a constant pressure of 4 MPa, at a uniform temperature of 590°C. The development of computational techniques is reported to analyse this problem with a four-material model of the welded connection which includes: parent, type IV, heat-affected zone (HAZ) and weld materials. The results of analyses are presented for two sets of creep damage constitutive equations. For both equation sets, lifetimes are conservatively, yet accurately predicted; however, the results of metallographic examinations of a tested vessel are not accurately predicted. To overcome this deficiency further analyses of the vessel are recommended which include: a coarse-grained HAZ (CGHAZ), adjacent to the weld material; and, more-refined finite element modelling.

Creep damage and grain boundary precipitation in power plant metals

There is clear evidence that creep damage in power plant steels is associated with grain boundary precipitates. These particles provide favourable nucleation sites for creep damage such as grain boundary cavities and microcracks. Monte Carlo based grain boundary precipitation kinetics is combined with continuum creep damage mechanics (CDM) to model both the microstructural evolution and creep behaviour in power plant metals. It is found that grain boundary precipitates, such as M23C6 in most Cr containing ferritic steels, are harmful to the creep properties of the material, in line with experimental observations. It is also found that to improve the creep behaviour of the material, means should be found either to increase the proportion of MX type particles, such as VN, or to decrease or remove the larger grain boundary precipitates, such as M23C6. Hafnium has been ion implanted into thin foils of a 9 wt-%Cr ferritic steel to study the effect of hafnium on the grain boundary precipitation kinetics. It is found that the implantation of hafnium to the steel completely prohibits the formation of the common grain boundary M23C6 particles. Instead, two new types of precipitates are formed. One is hafnium carbide, which is an MX type precipitate, and is very small in size and has a much higher volume fraction as compared with the volume fraction of VN in conventional power plant ferritic steels. The other is Cr- and V-rich nitride of formula M2N. CDM modelling shows that implantation of hafnium can markedly improve the creep property of the material. In addition, the replacement of M23C6 with hafnium carbide increases the concentration of Cr in the matrix and is expected to improve the intergranular corrosion resistance of the material.

Lifetime Predictions For High-Temperature Low-Alloy Ferritic Steel Weldments

The paper reports the finite element creep continuum damage mechanics (CDM) analysis of the creep rupture behaviour of thin-section butt-welded, internally pressurized pipes, and of uniaxial cross-welded tension testpieces made of Cr-Mo-V steels. The CDM analyses are shown to predict accurately lifetimes and failure mechanisms observed from metallographic analyses of sectioned components. The paper then addresses the lifetime prediction of components by comparing predictions made using British Standards BSi PD 5500 with the results of the experiments. Predictions have been based on uniaxial plain bar data for both parent and Type IV materials; both of these have been obtained by integration of constitutive equations. Comparison of predicted and experimental weldment lifetimes has been made using a weld strength reduction factor. It is found that the required factors are very dependent on temperature and the ratio of axial to hoop pipe stresses. Finally, the paper examines the British Energy Generation Limited R5 assessment procedure and compares lifetime predictions with those made using the British Standards BSi PD 5500 approach. It is noted that the stresses in both approaches are in good agreement for the external/internal radius ratio of 1.25 considered in the butt-welded pipe experiments.

3D boundary element analysis of creep continuum damage mechanics problems

In this paper, a boundary element formulation of creep damage problems for three-dimensional problems using isoparametric quadratic elements is presented. The Euler method with automatic time-step control scheme is implemented for time integrations. Creep rupture life is predicted using a continuum damage mechanics approach. The proposed formulation is applied to the FE Benchmark problems, uniaxial, perforated plate and Multi-material cross-weld problems.

Continuum damage mechanics predictions of creep damage initiation and growth in ferritic steel weldments in a medium bore branched pipe under constant pressure at 590 °C using a five-material weld model

The paper reports three-dimensional creep continuum damage mechanics (CDM) analyses of creep failure in a medium bore Cr–Mo–V low alloy ferritic steel welded branched-pressure vessel that has been tested under a constant pressure of 4 MPa, at a uniform temperature of 590 °C. The use of the CDM computer software Damage XXX to analyse the initiation and growth of creep damage and subsequent failure in the branch weld is reported for a five-material model that includes: parent, Type IV, refined heat affected zone (R-HAZ), coarse grained heat affected zone (CG-HAZ) and weld materials. The results of the analyses are presented for two cases: the first without the CG-HAZ; and, the second with the CG-HAZ included. For both cases, lifetimes are conservatively, yet accurately predicted. It is shown that it is necessary to use a Type IV thickness of 0.7 mm to accurately predict the failure location and mode. The results of metallographic examinations of a tested vessel and the predicted damage fields are in close accord. Failure is predicted to take place, by steam leakage, from the interior of the vessel, through the Type IV zone adjacent to the main pipe, connecting through the R-HAZ to the CG-HAZ, where leakage takes place at the weld toe in the crotch plane.

A critical damage criterion for creeping solids

A critical damage criterion for creeping solids

Relationship between time to reach Monkman–Grant ductility and rupture life

Based on continuum creep damage mechanics approach, we propose a new relationship between time to reach Monkman–Grant ductility and rupture life in terms of damage tolerance factor, and show the validity of this relationship for creep data on 9Cr–1Mo steel and AISI 304 stainless steel. Its implications to tertiary creep damage and engineering creep design are also discussed in this paper.

Benchmarks for finite element analysis of creep continuum damage mechanics

Creep rupture life can be predicted using a continuum damage mechanics approach incorporated within a finite element (FE) formulation. The rate of change of a damage parameter, ω, ranging from ω=0 (no damage) to ω=1 (100% damage), is computed within each element, until failure occurs in the material cross-section. The main difficulty in the numerical formulation arises due to the very small time steps needed as the damage parameter increases to 1. This paper presents the results of a number of benchmark tests involving the FE analysis of creep continuum damage mechanics that can be used to verify the FE solutions. Two independent FE codes are used; an in-house code (FE-DAMAGE) and a commercial code (ABAQUS) in which a user-subroutine (UMAT) is incorporated. The results of a series of tests used to represent uniaxial, biaxial, triaxial and multi-material creep and damage behaviour are presented.

Creep and Fatigue at Elevated Temperatures. Finite Element Creep Continuum Damage Mechanics Analysis of Pressurised Pipe Bends with Ovality.

This paper is concerned with the creep analysis of pressurised pipe bends in which ovality of the circular cross-section is considered. A creep continuum damage mechanics analysis is performed using the Finite Element method. The failure times and failure positions are predicted and compared to steady-state creep solutions. A comparison of the two solutions shows that the steady-state creep solutions for failure times are conservative compared to the damage solutions.

Use of CDM in Materials Modeling and Component Creep Life Prediction

Physically based continuum creep damage mechanics (CDM) has been reviewed and shown to provide a unifying framework for some seemingly diverse methods of predicting design and remanent creep lifetimes. These methods—theta projection, omega parameter, Larson-Miller parameter, and Robinson’s life fraction rule—exhibit certain strengths in common with CDM, but also weaknesses which CDM identifies and avoids. CDM consists of sets of coupled rate equations for inelastic strain, internal stress, and microstructural evolution (damage) which can then be integrated under boundary conditions appropriate to the test or service operating conditions: constant load/temperature for creep; constant total strain for stress-relaxation, variable stress/temperature, etc. Other state-variable approaches to creep and cyclic plasticity (for example, those due to Bodner, Miller, Chaboche, and Robinson), differ from CDM mainly in concentrating on the primary/secondary stages of creep (or cyclic work-hardening) and/or by their introduction of damage in an empirical Kachanov manner. The application of physically based CDM to LCF/thermal fatigue and its potential for predicting lifetimes of welded joints are also discussed. [S0094-9930(00)00903-3]

Continuum damage mechanics analyses of type IV creep failure in ferritic steel crossweld specimens

A major high temperature failure mechanism for weldments in ferritic steel steam pipework is circumferential creep cracking within the region of the heat affected zone, adjacent to the parent material, that experiences the lowest temperatures during the welding process. This is commonly known as type IV cracking. In recent years a number of experimental studies have investigated the occurrence of type IV failure in laboratory test pieces, however, there have been few attempts at theoretical modelling of type IV failure to assist in the formulation of design and assessment procedures. This report discusses the use of the creep continuum damage mechanics method for the analysis of the deformation and failure of weldments that are known to fail within the type IV region. The creep behaviour of each of the material regions of a weldment is described with a set of physically based constitutive equations, which incorporate a number of state variables. The finite element creep continuum damage mechanics method is used, with the physically based constitutive equations, to analyse the deformation and failure of the welded testpieces. The computations are shown to be in good agreement with the experimental results. The implications of the analyses are discussed with reference to the assessment of weldments that are susceptible to type IV failure.

Creep of welded pipes

Creep continuum damage mechanics analyses and peak stationary state stresses in the base, heat-affected zone and weld materials of a welded joint in a pipe were used to obtain failure times. The properties related to a1/2Cr1/2Mo1/4V:21/4Cr1Mo welded joint were used in the analyses. Similar analyses were performed on cross-weld specimens. The predictions indicate that, for moderate systems loading, using the mean diameter hoop stress in conjunction with cross-weld creep test data would result in safe failure predictions for the welded pipes. The results also indicate that reasonably accurate predictions of safety factors would be obtained using peak stationary state stresses, thus eliminating the need for the more complex and time-consuming creep continuum damage mechanics analyses.

Use of the reference stress method in estimating the life of pipe bends under creep conditions

The effect that the change of ovality of pipe bends, due to creep under internal pressure, has on the stationary-state stress state has been investigated using a reference stress approach. Attention has been focused on practical pipe bend geometries and loading conditions in power plant applications. Prediction of failure times based on stationary-state stresses, for cases in which ovality changes are neglected and in which ovality is included, indicate that the change of ovality can be very significant in some practical situations. Failure times obtained using a creep continuum damage mechanics approach have also been compared with those obtained using the stationary-state predictions with ovality changes included. These results indicate that even sophisticated damage mechanics analyses are inadequate unless the effects of the changing ovality which occurs are taken into account.

FATIGUE, CREEP AND CREEP/FATIGUE BEHAVIOUR OF A NICKEL BASE SUPERALLOY AT 700°C

Abstract— This paper presents the results of an experimental testing programme to examine the uniaxial creep, low cycle fatigue and creep/fatigue interaction behaviour of a Ni‐base superalloy at 700°C. The material is used in the manufacture of aeroengine turbine discs. A creep continuum damage mechanics model is shown to be capable of accurately predicting the creep and creep rupture behaviour of the material. A healing term has been incorporated into the damage mechanics model to allow the behaviour under creep/fatigue conditions to be described.

The ridged uniaxial testpiece: creep and fracture predictions using large-displacement finite-element analyses

A creep continuum damage mechanics (CDM) finite-element solver, DAMAGE XX, has been used to study deformation and fracture behaviour in ridged uniaxial testpieces under constant load with the objective of improving testpiece design and performance. Materials' behaviour has been modelled by a physically based multiaxial constitutive equation with damage state variables; and the CDM solver has had an updated Lagrangian formulation incorporated to take account of the large displacements and rotations specifically addressed in this work. Previous computations on this testpiece geometry using small-displacement methods predicted that fracture would only take place at the extensometer ridges, whereas these large-displacement analyses can also predict fracture within the parallel gauge section, as determined experimentally. The transition locus between the two fracture fields was computed to be a function of stress level, the material's uniaxial creep ductility and, most importantly, the damage criterion chosen for material fracture under the statically indeterminate stress field of the ridge region. As a consequence of constraints imposed by the ridges, strain inhomogeneities and associated multiaxial stress fields are formed within the guage section and can cause two problems for materials metrologists: (i) a monotonically increasing error in the average gauge length strain \`measured' by an axial extensometer as strain accumulates; (ii) an even larger discrepancy between \`measured' strain at fracture and the material's uniaxial ductility input into the model, due to effects of stress state on ductility. Computations on testpieces having an additional circumferential vee groove to simulate a machining defect led to the conclusion that a state-of-the-art surface finish should have no influence on creep and fracture behaviour.