A new model for characterizing primary creep damage

Primary creep damage may occur at a crack tip in steel at room temperature and below. The effect of this time-dependent damage is generally neglected. Recently developed experimental data clearly show that, for some materials, neglecting time-dependent deformation and damage may be quite nonconservative and dangerous in certain practical applications.In this paper, a new theory is developed which incorporates the effects of time-dependent damage into the crack growth and failure process. The predictive ability of the model is verified first by finite element analyses and then by comparison to experimental data. It is clearly shown that, for the material considered here, time-dependent damage effects must be considered or the crack growth process is not adequately accounted for.     

A parameter for power law creep

Experimental investigations on the creep rupture behaviour of type 304, 304£ and 316 stainless steels, a nickel-base superalloy SuperNi 600 and a turbine disc alloy (equivalent to MAR M 200) have been carried out. Stainless steels 304£ and 316 have been tested with and without weldment, and materials 304 SS and SuperNi 600 have been tested with and without corrosive coatings. MAR M 200 was tested in air. A parametric method is suggested for obtaining the master curves for these alloys under test conditions. The applicability of the parameter to 25-20 stainless steel and a modified nuclear grade 316 type stainless steel has been verified.     

Effects of creep properties of materials on creep crack-tip constraint parameter R*

Extensive finite element analyses have been conducted to investigate the effect of creep properties of materials on the creep crack-tip constraint parameter R*. The results show that the parameter R* increases with increasing power law creep stress exponent n of materials, and it is sensitive to lower n values and lower in-plane and out-of-plane constraints. In the engineering estimations of the creep constraint parameter R*, only the creep exponent effect needs to be considered for cracked components with lower exponent n and lower constraint, and the Norton’s coefficient A of power law creep materials can be ignored due to its insensitivity to the R*. The R*-n relation formulae have been established for single-edge-notched tension specimen (it has similar constraint level to pressurised pipes) with different in-plane and out-of-plane constraints, and they may be used to estimate the creep crack-tip constraint levels for cracked pipes with lower exponent n and lower constraint.     

Inverse method for parameter optimisation in superalloy tertiary creep equations

Abstract

A new methodology has been devised for the optimisation of material parameters in equations that govern the tertiary creep deformation of single crystal superalloys. Such information is ordinarily extracted by conducting a series of mechanical experiments over a range of appropriate environmental conditions, e.g. at various fixed stresses and temperatures. However, the current technique allows material behaviour to be characterised from a limited number of tests of short duration performed under non-uniform stress. A strategy is presented in which the time dependent strain response under a distributed stress gradient is measured using a novel testpiece geometry incorporating a concave gauge length profile. Spatial strain distribution is determined by accurate post-deformation measurement of specimen shape. Both spatial and temporal deformation are then simulated using a well founded mechanistic damage model, and the agreement between model results and experimental data is optimised by systematic perturbation of model parameters using the Nelder - Mead direct search method, i.e. an inverse modelling approach is applied. The overall strategy has been successfully validated for SRR99 by direct comparison with a database of more conventional tensile creep data, but it has the potential for broad application in cost effective and efficient prototyping of new materials generally.     

A new parameter for prediction of creep crack growth rate at high temperature

By analysis based on a series of experimental data obtained by continuous observations using high temperature microscope during the creep test without interruption in vacuum of 10^?5 mm Hg for the purpose of the crack length measurements, a new mathematical equation for prediction of high temperature creep crack growth rate has been proposed in terms of disposable parameters, that is $\text{α}\text{a}{}_{\mathrm{<mtext>eff</mtext>}}\text{σ}{}_{\mathrm{g}}\text{,σ}{}_{\mathrm{g}}$ and temperature for 304 stainless steel within the range of $\text{α}{}_{\mathrm{g}}$ and temperature concerned. It can be seen that it is the best one to fit the experimental data among any other formula proposed hitherto.The new parameter proposed herein

$\text{8.48 × 10}{}^3\text{t}\text{log}{}_{10}\text{α}\text{α}{}_{\mathrm{<mtext>eff</mtext>}}\text{α}{}_{\mathrm{<mtext>g</mtext>}}\text{4.66 × 10}{}^2\text{+ 5.46}\text{log}{}_{10}\text{α}{}_{\mathrm{<mtext>g</mtext>}}$

where

$\text{α = 1.98 +0.36}\text{a}\text{w}\text{? 2.12}\text{a}\text{w}{}^2\text{+ 3.42}\text{a}\text{w}{}^3\text{, a≦0.7w}$

may be used for characterizing the creep crack growth rate just similar as Larson-Miller parameter for the creep life.     

Effects of creep properties of materials on unified creep constraint parameter Ac for cracked pipes

Extensive finite element analyses of cracked pipes with different crack sizes and orientations have been conducted to investigate effects of creep properties of materials on the unified creep constraint parameter A_c. The results show that the constraint parameter A_c is independent on Norton’s coefficient A, and it is only affected by the creep exponent n of materials. For a given crack size, with increasing n, A_c decreases and constraint level increases. The A_c of lower constraint cracks is more sensitive to n. The unified correlation equations between A_c and n have been obtained for cracked pipes with a wide range of crack sizes and constraint levels. They may be used to estimate the constraint parameter A_c at different positions along the crack fronts in cracked pipes made of materials with different n values. The two-parameter C*-A_c approach for assessing creep life of cracked pipes has also been discussed.     

Nonlinear material parameter estimation for characterizing hyper elastic large strain models

An automated, systematic, and computationally efficient methodology to estimate the material parameters for characterizing general nonlinear material models for large strain analysis (e.g., hyperelastic and hyper foam materials) is presented. Such constitutive material models often require a large number of material constants to describe a host of physical phenomena and complicated deformation mechanisms. Extracting such material constants for a model from the volumes of data generated in the test laboratory is usually a very difficult, and frustrating. The integrated code COMPARE (that is an acronym of Constitutive Material PARameter Estimator) is being developed to enable the determination of an “optimum” set material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are listed as follows: (i) primal analysis tools (response functionals) for differential form of constitutive models; (ii) sensitivity analysis; (iii) optimization technique of an error/cost function; and (iv) graphical user interface. The code COMPARE casts the estimation of the material parameters as a minimum-error, weighted-multiobjective, optimization problem. Detailed derivations and results generated by applying the proposed technique to a comprehensive set of test data are given. These results have clearly demonstrated the great practical utility of the automated scheme developed. Received 17 September 1999     

A phenomenological parameter characterizing the relaxation of stresses caused by the lattice mismatch at a heteroboundary

An analytical formula is derived describing an increase in the bandgap width for a quantum cluster considered as an inclusion of the simplest shape (spherical or flat) featuring an arbitrary lattice mismatch with the surrounding matrix. A phenomenological relationship is introduced between this quantity and the stressed boundary relaxation parameter considered as the fitting parameter. The relaxation is small (or even absent) in a system with quantum wells and is completely manifested in a system with quantum dots.     

Influence of precipitation on dislocation substructure and creep properties of P91 steel weld joints

Abstract

Two trial weld joints were prepared using the GTAW and SMAW methods and they underwent creep testing at temperatures between 525 and 625°C. The longest time to rupture was 45,811 h. Two main processes occurred during creep exposures: recovery and precipitation of secondary phases. Slight coarsenings of the M₂₃C₆ carbide, precipitation of Laves phase and Z-phase were observed after long tests at high temperatures. Some differences in microstructure and creep failure were found in the individual zones of weldments. After long exposure at temperatures up to 600°C, fractures occurred in the fine-grain heat-affected zone as a result of a low density of fine vanadium nitride and a high density of coarse particles at grain and subgrain boundaries. At 625°C, growth of Laves phase caused a softening of the ferritic matrix and crack propagation in the weld metal.     

Comparisons of fracture parameter evaluations for power law hardening creep

Convergence properties of various finite element based methods for the evaluation of the crack-tip field amplitude in creep C are examined on some representative examples. In particular, the case of non-steady-state creep, when C is contour-dependent with significant interior convergence properties, is studied. It is demonstrated that the virtual crack extension (VCE) implementation exhibits significantly better convergence properties than the conventional domain and contour integral methods. The VCE method also exhibits very good convergence for J evaluation, which does not have any direct physical interpretation for dominating creep but can be useful for C estimates. The background for these estimates is summarised.     

Inclusion of primary creep in the estimation of the C t parameter

The problem of time-dependent fracture under transient creep conditions is investigated via finite element analyses of fracture specimens with stationary cracks. The constitutive models consist of linear elasticity with combinations of power-law secondary creep and two primary creep laws. Two proposed parameters are studied. One is a contour integral, C(t), which characterizes the crack tip singularity strength. The other one, C _t, is evaluated based on the load line deflection rate and has been used successfully in correlating experimental creep crack growth data.It is evident that accurate constitutive modeling is essential to good agreement with experimental data. The inclusion of primary creep resolves earlier discrepancies between the experimental and analytical load line deflection rates which are used to calculate the respective values of C _t. The loading boundary condition is also an important factor that has been addressed. A more general formulation of C _twhich includes primary creep is presented. In small scale and transition creep, the C _tparameter does not characterize the crack tip stress singularity but rather is related to the crack tip creep zone growth rate. At times past transition time, C _tand C(t) both approach a path-independent integral, C ^*(t), which characterizes the stationary crack tip stress field. The relationship between C _tand C(t) is discussed. The interpretation and estimation of the C _tparameter are given based on the numerical results and analytical manipulations.     

Predicting creep crack initiation in austenitic and ferritic steels using the creep toughness parameter and time-dependent failure assessment diagram

Methods for evaluating the creep toughness parameter,   K ^mat _c   , are reviewed and   K ^mat _c   data are determined for a ferritic P22 steel from creep crack growth tests on compact tension, C(T), specimens of homogenous parent material (PM) and heterogeneous specimen weldments at 565 °C and compared to similar tests on austenitic type 316H stainless steel at 550 °C. Appropriate relations describing the time dependency of   K ^mat _c   are determined accounting for data scatter. Considerable differences are observed in the form of the   K ^mat _c   data and the time-dependent failure assessment diagrams (TDFADs) for both the 316H and P22 steel. The TDFAD for P22 shows a strong time dependency, but is insensitive to time for 316H. Creep crack initiation (CCI) time predictions are obtained using the TDFAD approach and compared to experimental results from C(T) specimens and feature components. The TDFAD based on parent material properties can be used to obtain conservative predictions of CCI on weldments. Conservative predictions are almost always obtained when lower bound   K ^mat _c   values are employed. Long-term test are generally more relevant to industrial component lifetimes. The different trends between long- and short-term CCI time and growth data indicate that additional long-term test are required to further validate the procedure to predict the lifetimes of high temperature components.     

A coupled creep damage evolution model and creep life evaluation

Due to the damage accumulation during creep deformation, creep failure after a certain service time is the most important failure mode for metal structures working at high temperatures. Considering the coupled damage evolution of geometric and material’s damage, a creep life evaluation method based on continuum damage mechanics has been proposed and examined. It is found that the geometric damage evolution model can be deduced theoretically from the creep constitutive equation, while the material’s damage evolution can be assumed in the same way as that for static fatigue problems. Through solving the coupled damage evolution models, creep lives under various stress levels and temperatures can be evaluated in a unified way, just by several material constants which can be determined by some creep tests only.     

Estimation of creep crack growth rate in IN-100 based on the Q* parameter concept

Since the high-strength Ni-based superalloy, cast IN-100, is considered to be brittle at high temperatures, the stable creep crack growth region is limited. Therefore, technically, it is very difficult to perform creep tests and there are few experimental results on the creep crack growth behaviour of this material. We performed creep crack growth tests using Ni-based superalloy, cast IN-100, and derived the Q* parameter for this material, which characterizes the creep crack growth rate. Using this Q* parameter, we derived a law for the creep rupture life of this material.     

Estimation of Ct parameter in transversely isotropic materials under transient creep conditions

The crack growth life assessment procedures at high temperature developed for isotropic materials need to be extended for anisotropic creeping materials. In this study, estimation of C_t in transversely isotropic creeping materials is proposed. Equivalent creep coefficient (A_eq) is defined for the transversely isotropic materials and its calculation equation is derived in terms of the ratio between the longitudinal and the transverse creep coefficients. A series of finite element analysis was conducted and values of correction factors required in calculating C_t were determined in tabular form. The newly proposed equation gave the same C_t values as the finite element results under the full range of the creep conditions including the small scale creep.