Mines ParisTech

About: Mines ParisTech is a education organization based out in Paris, France. It is known for research contribution in the topics: Finite element method & Microstructure. The organization has 6564 authors who have published 11676 publications receiving 359898 citations. The organization is also known as: École nationale supérieure des mines de Paris & École des mines de Paris.

General models for the distributions of electric field gradients in disordered solids

Abstract: Hyperfine studies of disordered materials often yield the distribution of the electric field gradient (EFG) or related quadrupole splitting (QS). The question of the structural information that may be extracted from such distributions has been considered for more than fifteen years. Experimentally most studies have been performed using Mossbauer spectroscopy, especially on . However, NMR, NQR, EPR and PAC methods have also received some attention. The EFG distribution for a random distribution of electric charges was for instance first investigated by Czjzek et al [1] and a general functional form was derived for the joint (bivariate) distribution of the principal EFG tensor component and the asymmetry parameter . The importance of the Gauss distribution for such rotationally invariant structural models was thus evidenced. Extensions of that model which are based on degenerate multivariate Gauss distributions for the elements of the EFG tensor were proposed by Czjzek. The latter extensions have been used since that time, more particularly in Mossbauer spectroscopy, under the name `shell models'. The mathematical foundations of all the previous models are presented and critically discussed as they are evidenced by simple calculations in the case of the EFG tensor. The present article only focuses on those aspects of the EFG distribution in disordered solids which can be discussed without explicitly looking at particular physical mechanisms. We present studies of three different model systems. A reference model directly related to the first model of Czjzek, called the Gaussian isotropic model (GIM), is shown to be the limiting case for many different models with a large number of independent contributions to the EFG tensor and not restricted to a point-charge model. The extended validity of the marginal distribution of in the GIM model is discussed. It is also shown that the second model based on degenerate multivariate normal distributions for the EFG components yields questionable results and has been exaggeratedly used in experimental studies. The latter models are further discussed in the light of new results. The problems raised by these extensions are due to the fact that the consequences of the statistical invariance by rotation of the EFG tensor have not been sufficiently taken into account. Further difficulties arise because the structural degrees of freedom of the disordered solid under consideration have been confused with the degrees of freedom of QS distributions. The relations which are derived and discussed are further illustrated by the case of the EFG tensor distribution created at the centre of a sphere by m charges randomly distributed on its surface. The third model, a simple extension of the GIM, considers the case of an EFG tensor which is the sum of a fixed part and of a random part with variable weights. The bivariate distribution is calculated exactly in the most symmetric case and the effect of the random part is investigated as a function of its weight. The various models are more particularly discussed in connection with short-range order in disordered solids. An ambiguity problem which arises in the evaluation of bivariate distributions of centre lineshift (isomer shift) and quadrupole splitting from Mossbauer spectra is finally quantitatively considered.

Fatigue oxidation interaction in a superalloy—application to life prediction in high temperature low cycle fatigue

Abstract: A study of the interaction between fatigue and oxidation has been carried out in the case of a cast cobalt base superalloy MARM 509 tested in laboratory air at 900 °C. The influence of fatigue cycling on oxidation of this alloy has been studied by quantitative metallography on polished specimens exposed to air in a furnace and on strain-cycled low-cycle fatigue specimens. The oxidation kinetics were determined by thickness measurements for matrix oxidation and by oxidized depth measurements for the preferential oxidation of MC carbides. In both cases the oxidation kinetics were found to be dramatically enhanced by cycling for the matrix oxidation according to a linear relationship with plastic strain amplitude and less dramatically for carbides according to an exponential relationship with the maximum cyclic stress. From these observations a damage equation which describes fatigue damage as a crack growth process has been proposed: the elementary crack advance is a summation of a mechanical contribution due to the fatigue process itself which is described by Tomkins’ equation and of an oxidation contribution which has been evaluated from metallographic measurements. Integration of this crack growth equation gives predicted fatigue lives which are in good agreement with experimental results within a factor of two.

Frequency and wave-form effects on the fatigue crack growth behavior of alloy 718 at 298 K and 823 K

Abstract: The fatigue crack growth rate (FCGR) of Alloy 718 was measured on CT type specimens at 298 and 823 K. At 823 K, the influence of frequency was studied in the range between 5 – 10-3 Hz and 20 Hz, using a sinusoidal wave form signal. A substantial increase in FCGR occurred, particularly at low stress intensity levels, as the temperature was increased from 298 to 823 K and as the frequency was decreased at 823 K. At elevated temperature, the effect of cyclic stress wave form was equally investigated, using triangular and square wave form signals producing the same frequency of 5.10-2 Hz. The triangular load led to higher FCGR than the square wave form. In addition the hold time of 10 s both at the maximum and the minimum load associated with the square load had no significant effect on the FCGR. Electron microscopy was used to observe the substructures that developed ahead of fatigue cracks. These observations showed that in certain circumstances plastic deformation proceeded by the propagation of planar bands which were identified as twins. At room temperature, twinning was found to be abundant only in the threshold regime. At 823 K, twinning was observed in the domain of higher FCGR, particularly at low frequencies. Fractography was carried out to study the micromechanisms of crack propagation. At 823 K. intergranular cracking occurred as the frequency was decreased. The comparison between the substructures formed in low cycle fatigue and those associated with the plastic zones of propagating cracks is made. The importance of planar deformation and twinning on intergranular cracking and on the acceleration of FCGR when the loading rate is decreased at 823 K, is discussed.