Etienne Patoor

Fatigue life characterization of shape memory alloys undergoing thermomechanical cyclic loading

This paper presents a study on the fatigue life of shape memory alloy actuators undergoing thermally induced martensitic phase transformation under various stress levels. A microstructural study characterizing specific damage patterns is conducted in the current work. A highly stressed state with formation of different types of microcracks has been observed, showing a superficial micro cracking, responsible for the growth of circular cracks localizing the failure of the specimens. The influence of the interactions between the micro cracking pattern and the corrosion occurrence is also studied. Finally, a spallation oxidation occurring at the surface of the actuator, which damages its properties, is also investigated. The failure pattern observed provides information necessary to introduce a correction to the classical Wohler curve for fatigue life of a material undergoing cyclic loading.

Inter- and Intragranular Stress Determination with Kossel Microdiffraction in a Scanning Electron Microscope

A Kossel microdiffraction experimental set up is under development inside a Scanning Electron Microscope (SEM) in order to determine the crystallographic orientation as well as the inter- and intragranular strains and stresses on the micron scale, using a one cubic micrometer spot. The experimental Kossel line patterns are obtained by way of a CCD camera and are then fully indexed using a home-made simulation program. The so-determined orientation is compared with Electron Back-Scattered Diffraction (EBSD) results, and in-situ tests are performed inside the SEM using a tensile/compressive machine. The aim is to verify a 50MPa stress sensitivity for this technique and to take advantage from this microscope environment to associate microstructure observations (slip lines, particle decohesion, crack initiation) with determined stress analyses.

Strain resolution of scanning electron microscopy based Kossel microdiffraction

Kossel microdiffraction in a scanning electron microscope enables determination of local elastic strains. With Kossel patterns recorded by a CCD camera and some automation of the strain determination process, this technique may become a convenient tool for analysis of strains. As for all strain determination methods, critical for the applicability of the Kossel technique is its strain resolution. The resolution was estimated in a number of ways: from the simplest tests based on simulated patterns (of an Ni alloy), through analysis of sharp experimental patterns of Ge, to estimates obtained by in situ tensile straining of single crystals of the Ni-based superalloy. In the latter case, the results were compared with those of conventional X-ray diffraction and synchrotron-based Kossel diffraction. In the case of high-quality Ge patterns, a resolution of 1 × 10−4 was reached for all strain tensor components; this corresponds to a stress of about 10u2005MPa. With relatively diffuse patterns from the strained Ni-based superalloy, under the assumption of plane stress, the strain and stress resolutions were 3 × 10−4 and 60u2005MPa, respectively. Experimental and computational conditions for achieving these resolutions are described. The study shows potential perspectives and limits of the applicability of semiautomatic Kossel microdiffraction as a method of local strain determination.

Estimation of the electron beam-induced specimen heating and the emitted X-rays spatial resolution by Kossel microdiffraction in a scanning electron microscope

A Kossel microdiffraction experimental setup has been developed inside a Scanning Electron Microscope for crystallographic orientation, strain and stress determination at a micrometer scale. This paper reports an estimation of copper and germanium specimens heating due to the electron beam bombardment. The temperature rise is calculated from precise lattice parameters measurement considering different currents induced in the specimens. The spatial resolution of the technique is then deduced.

Residual Stress State at Different Scales in Deep Drawn Cup of Unstable Austenitic Steel

In this study, residual stresses state at different scales in the 301LN unstable austenitic steel after deep drawing was determined. The first part of the work deals with the characterization of the martensitic transformation during uniaxial loading. The austenite/martensite content which was determined by X-Ray Diffraction increases until a maximum of 0.6 for 30% strain. Internal stress distribution was determined by coupling in-situ tensile tests with sin²ψ method. As soon as martensite appears, the magnitudes of the internal stresses in this phase were found to be 400 MPa higher than in the austenite. To establish a relation between the complex loading path effect and the phase stress state, deep drawing tests were carried out for different drawing ratios. Both macroscopic tangential residual stresses and residual stresses in the martensite were determined. It appears that the macroscopic tangential residual stresses are positive and increase with increasing drawing ratios and the maximum value is located at middle height of the cup. It is about 850MPa for the Drawing Ratio (DR)=2.00. The tangential residual stresses in the martensite were found to be positive in the external face and have a same evolution as the macroscopic ones.

Inter and Intra Granular Strain Analysis by Microdiffraction Kossel

We have developed a new convenient tool for local stress and strain analysis in the scanning electron microscope. It is based on the Kossel diffraction, physical phenomenon that is known for a long time because of its high accuracy for lattice constant determination in micron regions. The pattern is recorded on a CCD camera allowing a fast and reliable analysis. This technique has been applied to several materials. In-situ tensile tests were performed on a shape memory alloy. During loading, we observe clearly a shift of Kossel lines on the diagram, whose magnitude depends on the (hkl) crystallographic planes. The stress can be deduced from the diffracting plane strain measurement using a single crystal stress analysis.

Stress determination during the mechanically-induced martensite phase transformation in the superelastic alloy CuAlBe by neutron diffraction

This paper focuses on the study of the superelastic behavior associated to the stress induced martensite transformation in a Cu-12.5%Al-0.5%Be [wt. %] shape memory alloy. Neutron diffraction was used to track the evolution of stress in the (β1) austenitic phase during the onset of the stress-induced martensite phase change. A thin flat and a cylindrical specimen was analyzed, allowing us firstly to evaluate the stress evolution in the austenite phase during martensitic transformation with laboratory X-ray and neutron diffraction and secondly to compare differences between methods (sin2ψ, principal stress) for in-situ neutron diffraction experiments.

Determination of Residual Stresses after Tensile Tests and Deep Drawing of Unstable Austenitic Steel

The main objective of this work is to contribute to the study of the 301LN unstable austenitic stainless steel by determining the distribution of residual stresses after deep drawing, taking into account the phase transformation. In the first part, kinetics of martensitic transformation are determined for uniaxial loading. Tensile tests are performed at different pre-strains at room temperature for two different strain rates. The austenite/martensite content is measured by X-ray diffraction and is coupled with the determination of residual stresses distribution. In addition, to establish a relation between the complex loading path effect and the residual stresses state, deep drawing are done for different drawing ratios for two different temperatures. Macroscopic tangential residual stresses are determined by the separation technique. It appears that the residual stresses increase with increasing drawing ratios and the maximum value is located at middle height of the cup.

Stress Analysis by Kossel Microdiffraction on a Nickel-Based Single Crystal Superalloy during an In Situ Tensile Test – Comparison with Classical X-Ray Diffraction

A Kossel microdiffraction experimental set up is under development inside a Scanning Electron Microscope (SEM) in order to determine the crystallographic orientation as well as the inter- and intragranular strains and stresses. An area of about one cubic micrometer can be analysed using the microscope probe, which enables to study different kinds of elements such as a grain boundary, a crack, a microelectronic component, etc. The diffraction pattern is recorded by a high resolution Charge-Coupled Device (CCD) camera. The crystallographic orientation, the lattice parameters and the elastic strain tensor of the probed area are deduced from the pattern indexation using a homemade software. The purpose of this paper is to report some results achieved up to now to estimate the reliability of the Kossel microdiffraction technique.

Finite element analysis of a multilayer piezoelectric actuator taking into account the ferroelectric and ferroelastic behaviors

Ferroelasticity and ferroelectricity are the non linear behaviours exhibited by piezoceramics, especially in the case of high electric field or stress. Many studies have focused on the role of ferroelastic and ferroelectric switching in fracture of actuators. However, engineering reliability analyses are carried out with tools like finite element software that do not take into account these non linear phenomena. To overcome such a problem, a simplified phenomenological constitutive law has been developed and describe the hysteresis effect of piezoceramics. It is time-independent and relies on the introduction of remnant polarization and remnant strain as internal variables. Two loading surfaces, similar to the ones used in plasticity, provide the evolution laws for the internal variables. Besides, polarization-induced anisotropy in the piezoelectric tensor is taken into account. That constitutive law has been implemented in the commercial software ABAQUS. It has been necessary to develop a finite element with electrical and mechanical degrees of freedom: it is an eight node hexahedron. The stiffness matrix integrates the constitutive law from the four tangent operators given by the constitutive law. The non linear problem is solved by the Newtons method. This finite element tool is used to study the effects of applied voltage on the electroelastic field concentrations ahead of electrodes in a multilayer piezoelectric actuator. The study lies on the experimental observations made by Shindo et al. [1]. Electroelastic analysis on piezoceramics with surface electrode showed that high values of stress and electric displacement arose in the neighbourhood of the electrode tip. Thus, the strain, stress and electric displacement concentrations were calculated and the numerical results showed that ferroelectric switching arose in the area of the electrode tip, causing a change in remnant polarization and remnant strain.