Scholarly article on topic 'Measurement of local strain heterogeneities in superelastic shape memory alloys by digital image correlation'

Measurement of local strain heterogeneities in superelastic shape memory alloys by digital image correlation Academic research paper on "Materials engineering"

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{"Shape memory alloy" / "Digital image correlation" / Superelasticity / "Martensitic transformation" / "Strain heterogeneities"}

Abstract of research paper on Materials engineering, author of scientific article — Nadine Bourgeois, Fodil Meraghni, Tarak Ben Zineb

Abstract This work is focused on the displacement and strain fields measurement using the Digital Image Correlation (DIC) technique on a superelastic Shape Memory Alloy (SMA) sample submitted to uniaxial tension. The local strain heterogeneities are estimated in a CuAlBe multicrystal with one grain in the thickness and millimetric grain size. Crystallographic orientation of each grain is measured by EBSD technique. Several tests are carried out on the same specimen, in front of a long distance microscope with or without speckle pattern, and at two different magnifications. Evolutions of the martensitic transformation are investigated and analysed in terms of the strain heterogeneities. In copper SMA, the important anisotropy of the elastic moduli tensor involves high intergranular elastic strain heterogeneities. Martensite variants induce steps on the specimen surface. However, the strain fields were measured for greater load levels, when the material runs through the phase transformation. These steps interfere with the speckle patterns and may perturb the correlation process. The challenge was also to apply very fine speckle to analyze the deformation in grains. The study shows that the transformation and strain localizations mainly occur in bands involving the well crystallographic oriented grains with respect to the load direction.

Academic research paper on topic "Measurement of local strain heterogeneities in superelastic shape memory alloys by digital image correlation"

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Physics Procedía 10 (2010) 4-10

www.elsevier.com/locate/procedia

3rd International Symposium on Shape Memory Materials for Smart Systems

Measurement of local strain heterogeneities in superelastic shape memory alloys by digital image correlation

Nadine Bourgeoisa*, Fodil Meraghnib, Tarak Ben Zinebc

aLPMM-CNRS Université de Metz, Ile du Saulcy, 57045 Metz, France bLPMM-CNRS Arts et Métiers - Paris Tech, 4 Rue Augustin Fresnel, 57078 Metz, France cLEMTA-CNRS ESSTIN, 2 Rue Jean Lamour, 54500 Vandoeuvre lès Nancy, France

Abstract

This work is focused on the displacement and strain fields measurement using the Digital Image Correlation (DIC) technique on a superelastic Shape Memory Alloy (SMA) sample submitted to uniaxial tension. The local strain heterogeneities are estimated in a CuAlBe multicrystal with one grain in the thickness and millimetric grain size. Crystallographic orientation of each grain is measured by EBSD technique. Several tests are carried out on the same specimen, in front of a long distance microscope with or without speckle pattern, and at two different magnifications.

Evolutions of the martensitic transformation are investigated and analysed in terms of the strain heterogeneities. In copper SMA, the important anisotropy of the elastic moduli tensor involves high intergranular elastic strain heterogeneities. Martensite variants induce steps on the specimen surface. However, the strain fields were measured for greater load levels, when the material runs through the phase transformation. These steps interfere with the speckle patterns and may perturb the correlation process. The challenge was also to apply very fine speckle to analyze the deformation in grains. The study shows that the transformation and strain localizations mainly occur in bands involving the well crystallographic oriented grains with respect to the load direction.

©2010 Published by Elsevier Ltd

Keywords: Shape Memory Alloy ; Digital Image Correlation ; superelasticity ; martensitic transformation ; strain heterogeneities

1. Introduction

Full-field techniques for displacement or strain measurements are extensively used in experimental mechanics (Pan B. et al. [1]). Digital Image Correlation (DIC) is one of these techniques that can be applied at several levels to characterize physical phenomena governing mechanical material behaviour (Raabe D. et al. [2], Heripre E. et al. [3], Wattrisse B. and Chrysochoos A. [4], Berfield T.A. [5], etc.).

For Shape Memory Alloys (SMA), the DIC has been used to characterize the mechanical behaviour of a copper based SMA by measuring the displacement fields at the microscopic scale (Sanchez-Arevalo F.M. and Pulos G. [6], Sanchez-Arevalo F.M. et al. [7]). Although many works have been conducted to characterize the local behaviour of SMA (Fang D.N. et al. [8], Qing X. et al. [9]) there are no works investigating quantitatively the effects of heterogeneities inside and between grains on the activation of the martensite variants. Indeed, these heterogeneities

* Corresponding author. Tel.: +33-38-731-5406; fax: +33-38-737-4284. E-mail address: nadine.bourgeois@univ-metz.fr 1875-3892 © 2010 Published by Elsevier Ltd doi:10.1016/j.phpro.2010.11.066

are induced by the multicrystal elastic anisotropy and by the non homogeneous martensitic transformation.

The primary objective of this work is to develop an experimental approach aiming at quantifying and analyzing accurately microscopic strain heterogeneities of a copper based SMA multicrystal with coarse grains under macroscopic tension. The studied material exhibits a superelastic behaviour: austenite-martensite transformation is reversible. Experimental analysis is performed at both material scales by coupling complementary techniques: microstructure characterization using optical microscopy and EBSD, multiscale kinematic full-field measurements by Digital Image Correlation. The strain field measurements at microscopic and macroscopic scales have improved the comprehension and the quantification of the intragranular heterogeneities. As experimental results, one can claim that the occurrence of martensite variants generates a surface change of the sample but may not bring about a large change of the speckle pattern enabling hence the DIC computation for local strain estimation. In fact, by choosing an appropriate correlation pattern in relation with the expected width of the variant traces on the free surface, the correlation algorithm may yield to consistent microscopic strain measurements.

2. Material description

The studied material consists of a copper based Shape Memory Alloy (SMA). It is a CuAlBe alloy, with 11.5 wt. % Al and 0.5 wt. % Be. The temperature corresponding to the beginning of the martensitic transformation, noted hereafter: Ms, was measured using the Differential Scanning Calorimetry (DSC) and equals that determined by Kaouache et al. [10, 11] for the same SMA material. The authors indicated a temperature up to -85°C.

This material is provided by TREFIMETAUX S.A. Company (France). Specimens are obtained by machining rolled parts of the material. One specimen is betatized at 750 °C during one hour, to insure having no residual martensite and in order to obtain coarse grains with an average diameter from 500 microns to 1mm. The sample thickness is then reduced to 0.3mm by mechanical polishing and electro-polishing both sides. It must be noticed that there is only one grain in its thickness since the average grain size is widely larger than the specimen thickness. Crystallographic orientation of each grain is measured by the Electron Back Scattered Diffraction (EBSD) technique. Consequently, the Schmidt factor of each grain in the tensile direction is estimated from Euler angles and is given as a function of the grain location in the multicrystal (Fig. 1). Finally, the specimen is etched to reveal the microstructure. As shown in a previous work published by Merzouki et al. [12], there is a small fluctuation of the grain geometry between the upper and lower sides of the sample.

Figure 1: Etched specimen with coarse grains (thickness 0.3 mm). Numerical values confer to Schmid factor of each individual grain.

3. Experimental procedure

Since the studied Shape Memory Alloy material exhibits a superelastic behavior, several tensile tests have been performed, on the same specimen, using a micro tensile machine operating in axial displacement control. Tensile tests are carried out in front of a long distance microscope (QM100-Questar), associated with a CCD camera. The microscope and the camera are adjusted perpendicular to the top surface of the specimen. Several recorded images are necessary to study the zone of interest. The latter is larger than the central calibrated area of the specimen which is 10mm long and 3mm width. Several image series are taken at different stages during each test.

A first tensile test was carried out on the etched specimen, without any speckle, in order to observe the martensite transformation and to identify the martensite variants appearing in the grains (Merzouki [12]). Furthermore, the tensile device is coupled with a technique of surface displacement mapping via 2D Digital Image Correlation DIC (Pan et al. [1]). This means that images must have different grey levels. However, it must be noticed here that successful application of DIC at the grain scale may rely on the ability to generate and apply an appropriate speckle at this scale. Accurate adjustment of the speckle to the correlation pattern size is a crucial factor since each pattern must contain enough pixels to reach an adequate greyscale distribution (Lecompte et al. [13]). The accuracy of image correlation depends on the optical resolution of the experimental setup and on the quality of the applied speckle. Therefore, prior to the tests with DIC, a fine white colour spray is applied on the specimen etched surface. The optimum amount and size of spray droplets, the illumination of the sample surface are adjusted in order to have a large and rather uniform distribution of grey level (more experimental details in Merzouki [12]).

Images are recorded before the loading and after each loading step (displacement controlled test). Several deformed states are analyzed, one at the onset of the transformation and others when it spreads over the grains. Different tensile tests with experimental conditions leading to different magnifications are used, allowing hence presenting the measurements of local strain fields at two different scales. In what follows, on one hand, the "macroscopic" scale corresponds to a resolution of 1.9 microns per pixel, producing a field of view of 2.6 x 2 mm2 per image. It will be noted hereafter "macroscopic" scale. Ten images are required to cover the specimen calibrated zone at this scale. On the other hand, the "microscopic" scale corresponds to a resolution of 0.9 microns per pixel, producing a field of view of 1.2 x 0.9 mm2 per image. Image size is of the same order of grain size. At this scale, variants may result in variations of the local contrast, which could be detrimental to the correlation convergence. Therefore, loading steps between successive images have to be small in order to bring about only few new variants at each step. At the "micro" scale, only a part of the specimen is analyzed, to keep moderate the test duration.

Reference and deformed images are correlated using the correlation algorithm called "Correli-Q4". The specific algorithm of Correli-Q4 software is described in detail in Hild and Roux [14]. The in-plane strain fields are calculated by a numerical derivation of the measured displacement fields. For the DIC computation, the pattern size is chosen of 32 x 32 pixels. The step size is defined hence as the spatial resolution and equals 32 pixels. It must be noticed that the larger the pattern size, the smaller the displacement and strain uncertainty. In this study, 32 pixels correspond respectively to 61 microns (macro scale) and 29 microns (micro scale). The analysis of the speckle pattern using Correli_Q4 (Hild and Roux [14] or Besnard et al. [15]) enables to estimate the theoretical accuracy of the DIC method applied with the particular applied speckle. At the macroscopic scale, the displacement error is estimated as 10-3, whereas the displacement resolution is 3.10-3 pixels (theoretical smallest displacement that can be detected). One obtains also 10-4 for the theoretical strain resolution. As a consequence, the strain error is then 2.10-5. It should be mentioned that the occurrence of martensite may induce local out-of-plane displacement and contrast variations. These may probably decrease the performance of the DIC method as claimed by Sutton et al. [16].

4. Experimental results and discussion

4.1 Observation of martensitic transformation

Fig. 2 presents the martensitic transformation for a applied displacement inducing a average longitudinal strain equals to 0.8%. The transformation onset occurs with one martensite variant in some specific grains and then spreads over other grains (Fig. 4a, 4b). In some grains a second and sometimes a third martensitic variant is activated in order to better accommodate strains. Very "slim" and short variants can appear near the grain boundaries. In Fig. 2 a white circles which diameters are proportional to the martensite volume fraction are added on each grain. As expected (Kaouache et al. [11] ...), the highly transformed grains are mainly grains with a large Schmid factor in the loading direction (see Fig. 1). The main grains reached by the transformation are clustered in "bands". The most important band is located on the specimen "right" part (see Fig. 2.b). By measuring the angles between the traces of variants on the surface and the tensile direction, one can identify the variants knowing the intersection of the free surface and their habit plan (see Merzouki [12]). Some grains still have an elastic behavior at the maximum applied loading; they remain austenitic since they are misoriented compared to loading direction.

Figure 2: Martensite transformation for an applied macroscopic displacement inducing 0.8% of global longitudinal strain

a) Entire calibrated zone of the tensile specimen. Grain boundaries are underline with black lines. Martensitic transformation is highly heterogeneous: white circles which diameters are proportional to the martensite volume fraction are added on each grain.

b) "Right" part of specimen. One can observe several (one to three) variants in several grains.

4.2 "Macroscopic" strain heterogeneity

The strain maps shown in Fig. 3 illustrate the strain heterogeneities and its evolution when the tensile loading increases. In Fig. 3a, the strain heterogeneity is mainly due to elastic strain heterogeneities. At this load level, the transformation occurs only in few grains. Heterogeneity is due to the large anisotropy of the austenitic phase: Young's modulus in the [001] crystallographic direction is 23.5 GPa whereas in the [111] direction Young's modulus is about 230 GPa (see Horikawa H. et al. [7]). As the strain and stress increase, one can observe that a sort of strain localization occurs in bands, in agreement with the transformation spatial distribution. The highest strain values are located where the transformation is mainly developed (Fig. 2). At the "macroscopic" scale, the variants seem do not really disturb the correlation process. The speckle hides the transformation traces on the specimen surface. The largest variant traces are thin compared to the pattern size. Fig. 3 c shows that whereas the average tensile strain is 0.8%, the local strain widely go beyond 2%. In figure 3, one can observe that several grain boundaries correspond roughly to the limits of areas exhibiting negative strain values. Note that grains inside this area have small Schmid factors. Area concerns with the development of strain is larger than the calibrated zone (see the right part of the specimen in Fig. 2 and 3).

4.3 "Microscopic" strain heterogeneity

The same experimental procedure is applied at the « microscopic » scale. The coarse paint speckle is removed and a new one, with smaller droplets is applied. A new zone of interest is then defined; the recorded images correspond to the edge vicinity at the bottom left in Fig. 2 b. The strain heterogeneity is observed more precisely in some grains. In Fig. 4 c and 4 d the observed zone and its speckle are represented. The superimposed lines emphasize the grain boundaries. Although, it is not obvious in Fig. 4 c the transformation is already activated, very thin variants already exist in the grains where transformation occurrence is clearly visible in Fig. 4 d.

Figure 3: Strain heterogeneities and its evolution at increasing tensile load; longitudinal strain maps measured by Digital Image Correlation a) onset of transformation b) intermediate loading stages c) "final" stage : applied macroscopic displacement inducing 0.8% of global longitudinal strain. The white lines indicate the specimen sections where the boundary conditions (displacements) are measured by DIC.

At the "microscopic" scale, the correlation is more affected by the variants. Indeed, the pattern size is of the same order as the distance between variants and the lines associated with the largest variants highly change the local contrast involving bad conditions for correlation process. This explains why correlation does not converge when the transformation is highly developed locally. The correlation process stops before the average strain reaches 0.8 %.

4.4 Discussion

At the "macroscopic scale", the strain heterogeneities between grains are successfully and precisely measured. In the studied superelastic SMA, strain heterogeneities already exist while the grains have an elastic behavior. They are basically due to the high elastic anisotropy of the austenitic phase. When the martensitic transformation occurs, it is not homogeneously distributed. As expected, the transformation begins in the well oriented grains compared to the tensile direction. The variants occurrence grows up where the transformation started, but it also spreads over new grains, well oriented grain or in the neighborhood of the variants that still exist. In the tested multicrystal, some grains have still an elastic behavior at the final loading (0.8% longitudinal strain). The transformed grains are clustered in several "bands" spread over the specimen length. In most of the transformed grains, only one or two variants (with different orientations) develop. In some grains, very slim and short variants are visible in the vicinity of the grain boundaries. As the specimen has only one grain in thickness, the observed phenomena are representative of the interactions between grains, between variants and grain boundaries and between variants. Influence of the free surface also exists, but there is no effect on the transformation due to underneath grains, as there is no.

Figure 4: Images of the speckle, traces of martensite variants and longitudinal strain heterogeneities measured by DIC. Longitudinal strain fields are given at increasing tensile load. a) and c) at the onset of transformation b) and d) intermediate loading stage.

At the "macroscopic" scale, variants weakly perturb the correlation process. Strain heterogeneities are consistent with not uniform transformation. The strains are quite small, so the correlation is slightly affected by out of plane movement. At the "microscopic" scale, the strain heterogeneities evaluation is harder due the greater size of the variants compared to the pattern. But correlation is still possible as long as the variants are not too large or not too close one from another. The highest magnifications are interesting to study the local interaction and to observe the transformation from the outset. Let us notice that it is not so easy to reproduce exactly the same loading conditions on different tensile tests and so to compare precisely the measured strain fields at different magnifications.

A part of the "macroscopic" DIC results are published in Merzouki et al. [13] and compared with Finite Element Simulation results. Observations are consistent with literature and particularly with previous results on this Cu-based SMA (Kaouache et al. [11]).Further studies start to better understand interactions between variants and between variants and grain boundaries and to improve modeling.

The strain heterogeneities in a copper based SMA multicrystal with coarse grains are analyzed. The analysis is carried out on tensile specimen with one grain in thickness. It relies upon the conjunction of microstructure characterization using optical microscopy and EBSD, multiscale kinematic full-field measurements by means of Digital Image Correlation.

The observations on the martensite transformation lead to the identification of the martensite variants appearing in the grains (Merzouki et al. [12]) and to the qualitative analysis of their multiplication. As well known, in this superelactic SMA, the martensitic transformation starts in well oriented grains. At least at the beginning the transformation respects Schmid law. Then the transformation evolution is probably influence by local interactions between grains and between variants. Very slim and short variants can appear near grain boundaries.

Strain heterogeneities generated by elastic anisotropy and by non homogeneous martensitic transformation are quantified. The strain fields are measured on the total calibrated area to investigate the intergranular heterogeneities, and on a "micro" scale to underline the intragranular heterogeneities. The activation of the martensitic variants is not an obstacle to DIC as long as the correlation pattern is rather large compared to the width of the variant traces on the free surface.

5. Conclusion

As several successive tensile tests had to be done on the same specimen, it was absolutely necessary to stay in the superelastic behavior of the SMA. So, only rather small average deformations were applied. Further works will be done to study if the strain localization remains at greater transformation levels. Strain measurements at more local scale could be helpful to understand local interactions, to measure the strain field near a variant tip and so on... Coupling stress (by X-ray technique) and strain measurement (DIC) is also one of the future objectives of our laboratory, but some experimental obstacles still remain.

Experimental measurements of the displacement on the edges of the specimen show that the applied loading was not really of pure tension. Merzouki et al. [12] proved that actual boundary conditions must be introduced in Finite Element simulation to have good results: to reproduce the transformation localization and to have strain gradients in agreement with experimental measurements.

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