A novel method for obtaining the multiaxiality constant for damage mechanics which is appropriate to crack tip conditions

Many engineering components, such as power plant steam pipes, aero-engine turbine discs, etc, operate under severe loading/temperature conditions for the majority of their service life. As a result, cracks can initiate and subsequently propagate over time due to creep. Damage mechanics is a robust method for the prediction of behaviour of components subjected to high temperature creep conditions and in particular, the Liu and Murakami model has proven to be a useful tool for the prediction of creep crack growth under such conditions. Previous methods for obtaining the constant of multiaxiality required for the use of such models, i.e. α, have relied upon the steady load testing of specimens designed to give a specific multiaxial stress-state, such as notched bars, and the failure time obtained. A series of results from finite element (FE) analyses based on the same geometry and loading/temperature conditions as the experiment, each performed with a different α-value, are then interpolated in order to identify the α-value which results in the same failure time, tf , as that of the experimental test. However, the stress-state present within such a specimen geometry (and therefore the α-value obtained) does not reflect the multiaxial severity of the stress state ahead of a crack tip. Therefore, for the application of the Liu and Murakami model to crack tip (i.e., creep crack growth) conditions, it follows that the α-value should be obtained from a multiaxial stress-state of equal severity to that to which it is to be applied, i.e. a crack tip. Therefore compact tension (CT) specimen creep crack growth data has been used in order to obtain the α-value. The process for the α-value determination is similar to that discussed for the notched bar, except that the interpolation of the time to failure is replaced with an interpolation of the time to a given crack length, ta . The resulting FE predictions based on CT and thumbnail crack specimen geometries, for a 316 stainless steel, are shown to be accurate in comparison to experimental results

Thermo-mechanical fatigue testing and simulation using a viscoplasticity model for a P91 steel

An experimental programme of cyclic thermo-mechanical testing for a P91 power plant steel, under isothermal, and in-phase and out-of-phase thermo-mechanical, temperature-strain cycle conditions, has been implemented. Using the experimental data, an optimisation procedure has been developed for the accurate determination of the material constants under isothermal conditions, in which the Chaboche model is employed to describe material responses. The material was found to exhibit cyclic softening throughout the full life cycles, which is believed to be related to the evolution of microstructure and the propagation of micro-cracks. The model developed shows good predictive capability of cyclic stress–strain behaviour and cyclic softening

Numerical study of the effects of crack location on creep crack growth in weldment

A numerical study on the effects of crack location on creep crack growth, in a P91 weldment, was carried out using a finite element package (ABAQUS). Models of compact tension specimens were used. The obtained results showed that, the creep crack growth in the weld metal are much higher than that in the parent metal. However, the creep crack growth in cross-weld specimens is controlled by the properties of the weakest component of the weld. This highlights the importance of the heat affected zone (HAZ) as the weakest region of the weldment. Effects of the width of HAZ are presented, too

Pragmatic optimisation methods for determining material constants of viscoplasticity model from isothermal experimental data

A procedure to estimate material constants for the unified Chaboche viscoplasticity model from experimental data has been published elsewhere; however several critical assumptions are made to enable this and potential numerical problems can limit the effectiveness of the optimisation. Pragmatic optimisation procedures are therefore required to determine the material properties accurately and efficiently. This is made more complex by the presence of several deformation mechanisms and their interactions. Automation is critical due to the large amounts of data generated in testing. Complications that inhibit this process can arise due to factors such as experimental scatter. In this paper, a general optimisation framework is discussed and investigated using data from isothermal tests on a P91 steel at 600°C. Potential obstacles in the procedure are addressed and solutions (such as pre-optimisation experimental data ‘cleaning’) are suggested. Methods to maximise the amount of confidence a user has in a particular optimised constant set are also discussed

Effective determination of cyclic-visco-plasticity material properties using an optimisation procedure and experimental data exhibiting scatter

It may be inevitable in the design and analysis of most high temperature components (such as power industry pipe work) that variations in load and/or temperature will occur in normal operation. This presents complications in the prediction of the response of such components due to potential hardening or softening effects caused by the accumulation of plastic strain. Furthermore, interactions between hardening (or softening) behaviour and creep may be observed, particularly in high temperature applications. In this paper, the Chaboche model is described as it has the potential to represent this type of behaviour. An optimisation procedure for fine tuning material constants is developed and presented. This is a key step as the determination of initial estimates requires several assumptions to be made. Several potential pitfalls in optimisation procedures are described and addressed, mainly through the application of experimental data cleaning as a pre-processing procedure. This removes unavoidable experimental scatter that inhibits optimisation. Investigations into the effects of variations in the initial conditions on optimised material constant values and the number of data points selected on computational times are made to aid in the application of similar optimisation procedures. The superior fitting given by the implementation of an optimisation procedure is verified by applying it to the results of strain controlled cyclic tests of a P91 steel at 600°C

Comparison of several optimisation strategies for the determination of material constants in the Chaboche visco-plasticity model

Determining representative material constant sets for models that can accurately predict the complex plasticity and creep behaviour of components undergoing cyclic loading is of great interest to many industries. The Chaboche unified visco-plasticity model is an example of a model that, with the correct modifications, shows much promise for this particular application. Methods to approximate material constant values in the Chaboche model have been well established; however, the need for optimisation of these parameters is vital due to assumptions made in the initial estimation process. Optimisation of a material constant set is conducted by fitting the predicted response to the experimental results of cyclic tests. It is expected that any experimental data set (found using the same values of test parameters such as temperature; the dependency of which is not accounted for in the original Chaboche model) should yield a single set of optimised material parameters for a given material. In practice, this may not be the case. Experimental test programs usually include multiple loading waveforms; therefore, it is often possible to optimise for separate, different sets of material constants for the same material operating under comparable conditions. Several optimisation strategies that utilise multiple sets of experimental data to form the objective functions in optimisation programs have been applied and critiqued. A procedure that evaluates objective functions derived from the multiple experimental data types simultaneously (i.e. in the same optimisation iteration) was found to give the most consistently high-quality fitting. In the present work, this is demonstrated using cyclic experimental data for a P91 steel at 600 °C. Similar strategies may be applied to many constitutive laws that require some form of optimisation to determine material constant values

Small ring testing of a creep resistant material

Many components in conventional and nuclear power plant, aero-engines, chemical plant etc., operate at temperatures which are high enough for creep to occur. These include steam pipes, pipe branches, gas and steam turbine blades, etc. The manufacture of such components may also require welds to be part of them. In most cases, only nominal operating conditions (i.e. pressure, temperatures, system load, etc.) are known and hence precise life predictions for these components are not possible. Also, the proportion of life consumed will vary from position to position within a component. Hence, non-destructive techniques are adopted to assist in making decisions on whether to repair, continue operating or replace certain components. One such approach is to test a small sample removed from the component to make small creep test specimens which can be tested to give information on the remaining creep life of the component. When such a small sample cannot be removed from the operating component, e.g. in the case of small components, the component can be taken out of operation in order to make small creep test specimens, the results from which can then be used to assist with making decisions regarding similar or future components. This paper presents a small creep test specimen which can be used for the testing of particularly strong and creep resistant materials, such as nickel-based superalloys

Elastic–plastic analysis of offset indentations on unpressurised pipes

AbstractThe results of investigations to determine the elastic–plastic behaviour of unpressurised pipes with long offset indentations and unsymmetric support conditions are presented in this paper. They include the results of experimental tests, FE analyses and analytical methods. Three different materials and five different geometries are used to investigate their effects on the behaviour. A comparison of the experimental results, FE and analytical solutions indicates that the general analytical formulation developed in this paper for predicting the peak indenter loads in offset indented pipes, is reasonably accurate. Also, the analyses presented in this paper indicate that using a representative nominal flow stress, which is the average of yield and ultimate tensile stresses, in the analytical method, is appropriate for predicting the peak indenter loads

Experimental reference stress techniques for the prediction of creep deformation using lead alloy models

It is necessary at the design stage to predict the creep behaviour of components and structures operating at high temperature. The direct calculation of the creep behaviour requires extensive material data for the long service lives of the components and engineering methods are needed to minimise the amount of data needed. This can be achieved in some cases by use of the so called Reference stress method and the objective of this work was the experimental prediction of the creep deformation of some components using developments of this idea. It has been achieved by the determination of Reference stresses from accelerated room temperature creep tests of lead alloy models. Reference stresses, which characterise the creep response of components in relation to uniaxial tests, have previously been determined by calculation. Reference stresses determined by the new experimental methods have been compared with analytical predictions for beams in pure bending, cantilevers, thin cylinders and thin spheres under internal pressure. Acceptable agreement was found for the Reference stresses and consequent predictions of creep deformations. The method has also been used successfully to predict creep strains in a cylindrical pressure vessel with a hemispherical end. The methods of chill-casting models from a lead-antimony-arsenic alloy have been improved and the material has been calibrated by constant and stepped load, uniaxial and biaxial (combined pressure and torsion of thin cylinders) tests. The creep strains cannot be characterised by separate. stress and time functions; a strain hardening law best describes its stepped load response; the von-Mises criterion gives accurate predictions of creep strains in the tension-compression quadrant but underestimates the creep strains in the tension-tension quadrant