Constitutive modelling of the creep behaviour of single crystal superalloys under non-isothermal conditions inducing phase transformations

The prediction of the viscoplastic behaviour of Ni-based single crystal superalloy is still a challenging issue due to the non-isothermal loadings which can be encountered by aeronautic engines components such as high pressure turbine blades and vanes. Under particular in-service conditions, these materials may experience temperature cycles which promote the dissolution of the strengthening g’-phase of the material on (over)heating, and subsequent precipitation on cooling, leading to a transient viscoplastic behaviour. New internal variables representing the microstructural changes under those specific thermal loadings have been introduced in the framework of crystal plasticity using a macroscopic approach (no representation of the g/g’ microstructure of the alloy) to account for the transient creep behaviour induced by microstructure changes. This modelling approach captures first order effects on the creep behaviour due to (a) g’ precipitates volume fraction evolution of each kind of particles of a bimodal distribution of precipitates (which evolves according to thermal history), (b) recovery of the dislocation density and, (c) material orientation. In addition, a damage law keeping in memory all the thermal history and recovery processes has been introduced to account for the unconventional post-overheating creep life. This model is calibrated on non-isothermal creep experiments on [001] oriented single crystals made of MC2 alloy. It is able to predict creep strain (primary, secondary, tertiary), whatever the temperature history of the material

Computational Crystal Plasticity: From Single Crystal to Homogenized Polycrystals

Crystal plasticity models for single crystals at large deformation are shown. An extension to the computation of polycrystals is also proposed. The scale transition rule is numerically identified on polycrystal computations, and is valid for any type of loading. All these models are implemented in a finite element code, which has a sequential and a parallel version. Parallel processing makes CPU time reasonable, even for 3D meshes involving a large number of internal variables (more than 1000) at each Gauss point.Together with a presentation of the numerical tools, the paper shows several applications, a study of the crack tip strain fields in single crystals, of zinc coating on a steel substrate, specimen computation involving a large number of grains in each Gauss point. Finally, polycrystalline aggregates are generated, and numerically tested. The effect of grain boundary damage, opening and sliding is investigated

Numerical modelling of the microstructure effect on fatigue behaviour of Ni-base superalloys for turbine disk

Nickel-based alloy like N18 can present various types of precipitate distributions according to the applied heat treatment. A model involving a three scale homogenization procedure is developed to characterize the influence of this microstructure on fatigue life. The microstructural parameters are the size and the volume fraction of the secondary and tertiary precipitates of γ\u27 phase. Experimental results at 450 °C, specially designed to calibrate the model, allow to understand the role of tertiary precipitation. The first identification of the three scale homogenization model is shown

Reliability of metal/glass-ceramic junctions made by solid state bonding

The solid state diffusion bonding leads to helium-tight ceramic-metal junctions. However this technique induces residual stresses due to expansion mismatches which may cause ceramic flaws to propagate hence junction delayed failure. This phenomenon is evidenced on glass-ceramic/Al/Invar junctions from which a better reliability is ensured by a reduction of surface flaws

Modelling of fatigue damage in aluminum cylinder heads

International audienceCar manufacturers are very much concerned with thermal fatigue ....

A Microstructure Sensitive Approach for the Prediction of the Creep Behaviour and Life under Complex Loading Paths

The prediction of the creep behaviour and life of components of aeronautic engines like high pressure turbine blades is still a challenging issue due to non-isothermal loadings. Indeed, certification procedures of turboshaft engines for helicopters consist of complex thermomechanical histories, sometimes including short and very high temperature excursions close to the γ’-solvus (T~1200°C) of the blade alloy. A better design of those components could be gained using a model that takes into account non-isothermal loadings inducing microstructural changes. Most of the commonly used models consider only a nearly constant (or slowly evolving) microstructure, i.e. far from the rapid microstructure evolutions encountered during close γ’-solvus overheatings where a rapid dissolution/precipitation of the γ’-phase and fast recovery mechanisms were observed by Cormier et al. (2007b). A new constitutive modelling approach was hence recently proposed in a crystal viscoplasticity framework to capture the transient effects of such rapid microstructure evolutions on the creep behaviour and life (Cormier and Cailletaud (2010a)). In this article, an updated version of this model is detailed. Special attention will be paid to (i) the effect of the accumulated plastic strain on the microstructure evolution, (ii) the introduction of an additional damage formulation, and (iii) the creep strain at failure. The performances of the model are illustrated on the basis of isothermal or complex non-isothermal creep experiments performed on nearly [001] oriented samples

FE modelling of bainitic steels using crystal plasticity

International audienceModels classically used to describe the probability of brittle fracture in nuclear power plants are written on a macroscale. Physical phenomena are not naturally captured by this type of approach, so that the application of the models far from their identification domain (temperature history, loading path) may become questionable. To improve the quality of the prediction of resistance and life time, microstructural information, describing the heterogeneous character of the material and its deformation mechanisms has to be taken into consideration. The purpose of the paper is to propose a model able to describe local stress and strain fields in 16MND5 bainitic steel. These data will then be used as critical variables for multiscale failure models. The microstructure of 16MND5 steel is made of bainitic packets coming from former austenitic grains, which are not randomly oriented. Knowing the macroscopic stress is thus not sufficient to describe the stress-strain state in ferrite. An accurate model must take into account the actual microstructure, in order to provide realistic local stress and strain fields. After providing some observations and the analysis of the bainitic microstructure, the paper shows a quantitative model of the morphology and the crystallography, then a finite element analysis involving crystal plasticity

Computational Homogenization of Architectured Materials

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials