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

Modélisation des effets mécaniques des transformations de phases pour le calcul de structures

A set of constitutive equations are proposed to take into account the predominant mechanical effects due to solid state phase transformations in steels under multi-axial loading. The aim of this work is to formalize, for structural computations (heat treatment and welding), the main experimental and theoretical results available in the literature. The interna1 stresses generated by the transformation induced flow are represented by internal variables in the framework of the thermodynamics of the irreversible processes. We propose a mathematical formulation of the strain-hardening effects on the transformation induced plastic flow and of the transformation induced hardening on the "classical" plasticity. The constitutive equations have been implemented into the F.E. code ZeBuLoN and we briefly present a thermo-metallurgical and mechanical simulation with hardening couplings

Experimental Study of the Transformation-Induced Plasticity in a Cr-Ni-Mo-Al-Ti Steel

This paper shows experimental results concerning the martensitic transformation and the transformation-induced plasticity under multiaxial loading. The material investigated is a Cr-Ni-Mo-Al-Ti steel, which is submitted to a γ → α' martensitic phase transformation under an applied stress. The specimens are thin tubes loaded in tension-torsion. The tests were specially designed to provide information on classical questions related with transformation plasticity and the interaction between applied stresses and phase transformations in the case of tension-shear loadings : effect of the applied stresses on Ms temperature, definition of the transformation-induced plasticity (flow intensity, direction in stress space, evolution vs phase change), eventual presence of internal stresses. Some of the answers given by the present study confirm the usual assumptions, but the analysis of the tests also reveals new effects not predicted by the classical theories proposed to quantify the transformation induced plasticity phenomenon

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

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

Development of Understanding of The Interaction between Localized deformation and SCC of Austenitic Stainless Steels Exposed to Primary Environment

International audienceUnderstanding and quantification of interactions between localized deformation in materials and environmental-assisted cracking (EAC) could play an important role in maintaining the integrity of LWR components. Thus, a detailed understanding of strain localization during plastic deformation and of the underlying mechanisms is of great importance for the manufacturing and design of materials exposed to the environment of the primary circuit of PWRs. Thus, the crystal plasticity law of a 304L austenitic stainless steel has been identified, in order to quantify the effect of a change of strain path on the strain localization and increase the understanding of the contribution of the strain hardening and the strain incompatibilities on the mechanisms of initiation of SCC. Pre-deformation of the specimens used for SCC tests was evaluated using image correlation. Constant elongation rate tests and constant elongation tests were conducted for different levels of pre-deformations (0.07 < < 0.18). Examinations indicated the severe and deleterious effect of the strain localization due to a change of strain path on intergranular SCC susceptibility. Intergranular cracks initiated systematically in the low-deformed areas, where limited deformation (less than 1%) occurred during the exposure to the environment, and where high stress levels due to strain incompatibilities are expected

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

Development of a SERS strategy to overcome the nanoparticle stabilisation effect in serum-containing samples: Application to the quantification of dopamine in the culture medium of PC-12 cells

The analysis of serum samples by surface-enhanced Raman spectroscopy (SERS) has gained ground over the last years. However, the stabilisation of colloids by the proteins contained in these samples has restricted their use in common practice, unless antibodies or aptamers are used. Therefore, this work was dedicated to the development of a SERS methodology allowing the analysis of serum samples in a simple and easy-to-implement way. This approach was based on the pre-aggregation of the colloid with a salt solution. Gold nanoparticles (AuNPs) were used as the SERS substrate and, owing to its physiopathological importance, dopamine was chosen as a model to implement the SERS approach. The presence of this neurotransmitter could be determined in the concentration range 0.5 to 50 ppm (2.64 – 264 μM) in the culture medium of PC-12 cells, with a R2 of 0.9874, and even at lower concentrations (0.25 ppm, 1.32 μM) in another matrix containing fewer proteins. Moreover, the effect of calcium and potassium on the dopamine exocytosis from PC-12 cells was studied. Calcium was shown to have a predominant and dose-dependent effect. Finally, PC-12 cells were exposed to dexamethasone in order to increase their biosynthesis and release of dopamine. This increase was monitored with the developed SERS approach