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

Small ring testing of high temperature materials

In service components such as steam pipes, pipe branches, gas and steam turbine blades, etc. which operate in engineering applications such as power plant, aero-engines, chemical plant etc., can operate at temperatures which are high enough for creep to occur. Often, only nominal operating conditions (i.e. pressure, temperatures, system load, etc.) are known and hence precise life predictions for these components, which may be complex in terms of geometry or weld characteristics, are not possible. Within complex components it can also be the case that the proportion of the material creep life consumed may vary from position to position within the component. It is therefore important that non-destructive techniques are available for assisting in the making of decisions on whether to repair, continue operating or replace certain components. Small specimen creep testing is a technique which can allow such analyses to be performed. Small samples of material are removed from the component to make small creep test specimens. These specimens can then be tested to give information on the remaining creep life of the component. This paper presents the results of small ring specimens tested under creep conditions and shows the comparison to standard (full size) creep testing for materials used under high temperature in industry

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

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

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

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

Cyclic thermo-mechanical material modelling and testing of 316 stainless steel

A programme of cyclic mechanical testing of a 316 stainless steel, at temperatures of up to 600 °C under isothermal conditions, for the identification of material constitutive constants, has been carried out using a thermo-mechanical fatigue test machine (with induction coil heating). The constitutive model adopted is a modified Chaboche unified viscoplasticity model, which can deal with both cyclic effects, such as combined isotropic and kinematic hardening, and rate-dependent effects, associated with viscoplasticity. The characterisation of 316 stainless steel is presented and compared with results from tests consisting of cyclic isothermal, as well as in-phase and out-of-phase thermo-mechanical fatigue conditions, using interpolation between the isothermal material constants to predict the material behaviour under anisothermal conditions

A basis for selecting the most appropriate small specimen creep test type

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 plain pipes, pipe bends, branched pipes etc., the manufacture of such components may also require welds to be inserted in them. In most cases, only nominal operating conditions (i.e., pressure, temperatures, system load, etc.) are known and hence precise life predictions are not possible. Also, the proportion of life consumed will vary from position to position within a component and the plant. Hence, nondestructive techniques are adopted to assist in making decisions on whether to repair, continue operating or scrap certain components. One such approach is to use scoop samples removed from the components to make small creep test specimens, i.e., sub-size uniaxial creep test specimens, impression creep test specimens, small punch creep test specimens, and small ring (circular or elliptical) creep test specimens. Each specimen type has its own unique advantages and disadvantages and it may not be obvious which one is the most appropriate test method to use. This paper gives a brief description of each specimen and associated test type and describes their practical limitations. The suitability of each of the methods for determining “bulk” material properties is described and it is shown that an appropriate test type can be chosen

Theoretical basis and practical aspects of small specimen creep testing

Interest in and the application of small specimen creep test techniques are increasing. This is because it is only possible to obtain small samples of material in some situations, for example, the scoop samples that are removed from in-service components, the heat-affected zones that are created when welds are used to join components and the desire to produce only small amounts of material in alloy development programmes. It is therefore important to review and compare the theoretical basis and practical aspects of each of the small specimen creep testing methods, in order to clearly understand which of the methods is the best for any specific application. This article provides the theoretical basis for each commonly used test method