MATERIALS MECHANICS INSIDE THE SCANNING ELECTRON MICROSCOPE

Thierry BRETHEAU, Jérôme CREPIN,Michel BORNERT

Laboratoire de Mécanique des Solides.UMR-CNRS 7649,Ecole Polytechnique, 91128 Palaiseau Cedex, France
bretheau@lms.polytechnique.fr

Abstract

   In order to observe the phenomena occurring during deformation, mechanical test stages working inside a scanning electron microscope (SEM) chamber have been developed; they allow performing tests step by step, without unloading, with a fixed tensile axis, and making observations in a large range of magnification. Two stages are available:
o a tensile stage with a load cell in the range 0-500 daN and a micro furnace to heat the specimen up to 800 °C,
o a biaxial tension/torsion out-of-phase fatigue stage with a tension compression load up to ±1000 daN and a torque up to ±50 Nm.
  This system is completed by an image analyzer used to quantify microstructure morphologies and by an electron backscattering diffraction device (EBSD) that allows determining the local crystalline orientation and following its evolution under deformation.
  A fiducial grid technique have been developed to measure some components of the local strain tensor. The microgrids are deposited on the surface sample by an electrolithographic technique; their pitch ranges from 1 to 15 µm or more; they provide a good contrast for SEM and the underlying microstructure remains visible. From a qualitative point of view, a grid gives informations on the mechanisms occuring at the local scale during deformation. Their quantitative use gives average strain values per phase and strain distribution functions. Strain maps can also be obtained throuh the use of image analysis techniques.

ESTUDO EXPERIMENTAL EM ESCALA MESOSCOPICA DA PLASTICIDADE E DA DEFORMAÇÃO

Resumo:

   Afin de observar os fenômenos que ocorrem durante a deformação, teste mecanicos foram desenvolvidos em platinas situadas no interior de uma camâra do "scanning electron microscope" (SEM). Elas permitiram a realização dos testes, passo à passo, sem descarga, com um eixo fixo de tracção e para realizar as observações com uma larga gama de aumento.
Duas platinas foram obtidas :
- uma platina de tracção fixa com uma célula carregada na gama de força 0 -500daN e com um micro-forno para aquecer a proveta até 800°C,

- uma platina biaxial, tracção/torsão, defasada com uma carga de tracção /compressão que atinge até ± 1000daN e trela de ± 50Nm.
Este sistema foi completado pelo uso de um analisador de imagem para quantificar a morfologia da micro estrutura e de "um electron backscattering diffraction devise" (EBSD) que permite determinar a orientação cristalina local e seguir a evolução sob deformação.
A montagem de um a grelha sinótica foi desenvolvida para medir alguns componentes do tenser da deformação local. Elas foram depositadas na superfície do espécimene através de uma técnica de electrolitografia, a distancia entre cada celula é de 1 à 15 mm ou mais. Foi obtido um bom contraste pelo SEM para que a micro-estrutura sub-jacente permaneça visível. De um ponto de vista qualitativo, a deformação da grelha fornece indicações sobre os mecanismos (na escala local) que ocorrem durante a deformação do especimene ; o uso da quantificação fornece os valores médios da deformação para cada fase e funções de distribuição da deformação; mapas de deformação também podem ser calculadas pelo uso de técnicas de análise de imagem.

Keywords Scanning electron microscope; In situ mechanical tests; Electron backscattering diffraction; Fiducial microgrids; Local strain measurements; Deformation maps; Image analysis.

1. Introduction

Materials Mechanics has a two-fold scope [1]:

·       The prediction of the overall mechanical behavior of multiphase materials that can be integrated in structural calculations to predict the behavior of structures under service conditions,

·       The formulation of rules for optimizing the mechanical properties of materials through the optimization of their microstructure.

Both of these scopes pass by the production of microstructurally and physically based models.
The estimation of the overall elastoplastic behavior of inhomogeneous materials from the behavior of their constituents, is a classical but still unsolved problem. All the existing models make very different assumptions on the local interactions, which induce very different levels of stress and strain heterogeneities. The main microstructural characteristics of a considered material allow choosing the pertinent type of model. As a matter of fact, the overall behavior can be strongly influenced by very local events such as damage nucleation, initiation and propagation of micro-cracks or shear bands, recrystallization processes, that depend mainly on the local scale mechanical state. Thus, the pertinence of a model has of course to be tested on its ability to give a good estimation of the global (macroscopic) behavior; but it is also of great interest to check the model hypotheses and estimations at the local (microscopic) scale.

2. The micro-macro experimental approach

In general, the physical mechanisms responsible for plastic deformation of crystalline materials are known with many details, but they are often difficult to introduce directly in scale transition models based on continuum mechanics; it must be proceeded to their transcription in terms of stress and strain fields. Nevertheless, in most cases that transcription is not enough because the knowledge of these mechanisms has been acquired thanks homogeneous and monotonous tests performed on model materials; this is not relevant to represent the mechanical state inside the real heterogeneous material even under macroscopic uniform conditions. Of course the list of all the potential physical mechanisms is valid but the effectively active mechanisms, their conditions of activation and their interactions under complex loading (multi-axial, non-radial, cyclic...) have to be studied on the real material; the chronology and location of their occurrence have to be specified with respect to the microstructure. All this leads to the development of specific experimental techniques, often at the grain scale, devoted to the determination of the "missing links" concerning the active mechanisms and the morphological description of the initial and induced microstructure.
The experiments have two main objects:
o the implementation of the basic necessary elements into a scale transition model,
o the validation of the estimations of the model at the different pertinent scales. Then it is needed to be able:
o to observe and characterize the initial state and the evolution of the microstructure by the identification of the phases, of their morphology, their space distribution, and their crystalline orientation,
o to identify and characterize the effectively active deformation and damage mechanisms (crystallographic glide, twinning, cavity nucleation and growth, decohesion, phase rupture, grain boundary sliding,...), precise their role and influence for the overall behavior and measure their kinetics and space distribution,
o to measure, at the pertinent local scale(s) and at the global scale, the parameters defining the mechanical state (stress and strain fields).

Thus, in situ mechanical test devices are neededto be able to observe, at the different pertinent scales, the activated deformation mechanisms; it is crucial to complement them with appropriate techniques to measure the mechanical parameters at the proper scales and to follow the evolution of morphological and crystallographic parameters.

3. Description of the system

The block diagram on figure 1 gives a sketch of the equipment used for the local scale approach of material mechanics. On the basis of a Scanning Electron Microscope (SEM) several complimentary accessories give an access to the essential parameters of the material and allow following their evolution with deformation. 

Figure 1 : Micromechanical tests system

3.1 Scanning Electron Microscope 

It allows the observation of surfaces under magnifications from 5 to 100 000. The different contrast modes allow enhancing either the topography induced by plastic deformation and damage, or the heterogeneities in chemical composition or in crystallographic orientation. A SEM with a large chamber is essential to the installation of in situ mechanical test stages suitable for specimen much larger than the material microstructural heterogeneities.

3.2 Tensile Stage 

The use of an in situ tensile stage allows performing mechanical tests and recording the events induced by deformation with or without unloading; it can also be proceeded step by step. The flat specimen, with a 5 to 10 mm² cross section and a 10 to 40 mm gauge length, is set on the tensile stage inside the SEM chamber. Under load, it can be rotated 360° around the Y tensile axis and translated in X and Y directions to give access to the observation of more than 2 cm². The tensile tests are performed under cross-head displacement control in the range 0.1 - 60 µm/s giving a strain-rate from 10^-5 to 10^-2 s^-1, for usual sample gauge length; this is a classical range for quasi-static macro-tests. The tensile force is given by a load cell in the range 0 - 500 daN. A micro furnace can be fixed under the specimen to heat it up to 800°C. Different accessories allow to test in tension, compression or bending, metallic, polymeric, ceramic or composite materials.

3.3 Tension-Torsion Fatigue Stage

A biaxial fatigue-stage (eventually out-of-phase) gives access to fatigue and/or non-radial loadings. More realistic tests, closer to service conditions, can be performed. Various specimens can be used depending on the type of test: crack propagation in mode I, II or in mixed mode can be performed on CT type specimens.

Tension/compression fatigue tests can be performed on cylinders or parallelepipeds and torsion or tension/torsion tests need tubular specimens. The specimen can be rotated 360° around the tension/torsion axis and translated in X and Y directions. The axial force is given by a load-cell (range ±1000 daN); the torque can be applied in the range ±50 mN. In fatigue mode, the frequency cannot exceed 0.1 Hz. The tests are monitored by a micro-computer.

3.4 Electron Back-Scatterring Diffraction (EBSD)

An EBSD camera, fitted to the SEM chamber, allows determining very quickly the crystallographic orientation of volumes as small as a few µm3, giving access to the non-ambiguous characterization of deformation mechanisms (slip systems, twins,...) (Fig2) and to the measurement of local crystallographic rotations. An automated system gives orientation maps that can be correlated to the observed mechanisms and to the measured mechanical parameters (Fig3).

Figure 2: Cross-slip from a prismatic plane to a pyramidal plane in a zirconium alloy. (horizontal tensile axis, T=200°C)

3.5 Image acquisition, stocking and treatment 

An electronic device linked to the SEM controls the electron-beam scanning-rate and operates the video signal digitization; the image quality is improved by filtering and summation. The system can record very large-size images (> 4000 ↔ 4000 pixels) in order to work at high resolution (small area) or at low magnification (large area). These images can be treated to extract, statistical parameters characterizing the microstructure by means of the operations of mathematical morphology (Fig4) [2].

Figure 3: Zirconium polycrystal. The grey level of each grain refers to the Schmid factor value of the best oriented prismatic plane with respect to an horizontal tensile axis.

Figure 4: Covariograms representing the distribution heterogeneity of the Schmid factors shown on figure 3

4. Local scale mechanical measurements

In order to check the ability of a model to take a pertinent account of the incompatibilities at the local scale (the microstructure scale), measurements of mechanical parameters (stress and strain) at that very scale, must be performed.

4.1 The Local Scale Mechanical Parameters

In an heterogeneous material subjected to plastic deformation, elastic strain (e^e), plastic strain (ep), elastic rotation (w^e) and plastic rotation (w^p) coexist at the local scale:

·       e^e is the deformation of the crystal lattice

·       e^p = e - e^e is the deformation of a basis attached to the material (e is the total strain)

·       w^e is the relative rotation of the crystal lattice vs. an external basis; it can be given by EBSD

·       w^p is the relative rotation of the crystal lattice vs. a basis attached to the material

·       w = w^e + w^p is the total rotation and is the relative rotation of a basis attached to the material vs. an external basis.

Several consequences can be drawn from these definitions:

·       e^e is the origin of the local stresses; it can be obtained only by diffraction techniques (X-rays, electrons, neutrons); but these techniques give only mean global scale values, the local values being up to now out of reach. Then neither e^e nor e^p can be measured at the local scale.

·       a basis attached to the material is essential to the determination of the local total strain e; it will be provided by the deposition on the samples of fiducial microgrids.

·       a fixed external basis is needed; the loading axis of the in situ deformation stages gives such a fixed basis.

·       the 3 components of the local rotation can be obtained.

Figure 5 : Microgrid on a deformed Cu polycrystal (e=15%)

4.2 The Microextensometry Technique 

Prior to any mechanical test, the specimen is covered by a square fiducial microgrid made of gold lines or dots by means of a microelectrolithographic technique that have been described elsewhere in details [3]. The pitch of the grid has to be chosen so that it remains small in comparison to the smallest wavelength of the expected strain field; it may easily be varied in the range 1 - 15 µm (Fig5). Each grid covers an area close to 2↔2 mm².

                                                            A                                                                     B

Figure 6 : In situ loading of an aluminum base metal matrix composite reinforced by silicon carbide particles.
a) Interfacial decohesion in the overall elastic regime;
b) Closing of the decohesion when unloading (vertical tensile axis)  

Figure 7: Alumina inclusion in a nickel base superalloy matrix (vertical tensile axis, e=11%). Linear moiré pattern is formed by the interference of the horizontal scanning with the grid. The fringe spacing allows visualizing the strain gradients (large spacing = small gradient; narrow spacing = strong gradient). Moreover, a rotation of the inclusion vs the matrix can be noted.

Figure 8: Grain boundary sliding in zinc at room temperature. The sliding amplitude is exactly one pitch of the grid.

 

Figure 9: Average strain per phase in a two-phase Fe/Ag material (C_Fe=60%). Comparison between experimental measures (dots) and simulated values via micro-macro models and finite elements calculations.

The grids have several different uses:

·       they facilitate the identification during the in situ tests of the areas of interest;

·       they allow the unambiguous detection of the inception of micro-events induced by deformation (Fig6);

·       observed with an appropriate scanning pattern in the SEM, they form moiré patterns that give an enhanced view of very weak strain heterogeneities allowing the precocious detection of some events (Fig7);

·       they allow the qualitative and quantitative study of grain boundary sliding (Fig8);

·       associated with efficient image processing techniques, they give the in-plane components of the local total strain field; different averages per phase (Fig9) or distribution functions can be calculated; it is also possible to get contour plots of these components over the considered domain; the obtained maps give a powerful qualitative information on the strain localization modes during deformation [4].

5. Conclusion

We have presented here a complete and coherent system associating in situ (under the SEM) mechanical tests, local crystallographic orientation capability by EBSD and a microextensometry technique. Qualitative studies are quite easy to perform and give very useful informations on heterogeneous materials behavior. An effectively quantitative approach needs much heavier investments mainly for the processing of microgrid images. Such efforts must be justified by a parallel development of heterogeneous material models needing experimental validations.

References

[1] M.Bornert, T.Bretheau et P.Gilormini, Homogénéisation en mécanique des matériaux, Milieux aléatoires élastiques et milieux périodiques, série Alliages Métalliques, éditeur : Hermès Science (2001)        [ Links ]

[2] M.Bornert, Morphologie microstructurale et comportement mécanique; caractérisation expérimentales, approches par bornes et estimations autocohérentes généralisées. Thèse de doctorat, Ecole Nationale des Ponts et Chaussées, (1996)        [ Links ]

[3] L.Allais, M.Bornert, T.Bretheau and D.Caldemaison, Experimental characterization of local strain field in a heterogeneous elastoplastic material, Acta Metall. Mater., 42 (1994), pp 3865-3880        [ Links ]

[4] P.Doumalin and M.Bornert, Micromechanical applications of digital image correlation techniques, in Interferometry in speckle light theory and applications, Proc. Int. Conf., 25-28 sept 2000, Lausanne, pp. 67-74, Jacquet, Fournier Ed., (2000) Springer        [ Links ]