UDK 539.374:620.186 ISSN 1580-2949 Original scientific article/Izvirni znanstveni članek MTAEC9, 46(4)355(2012) DIGITAL IMAGING ANALYSIS OF MICROSTRUCTURES AS A TOOL TO IDENTIFY LOCAL PLASTIC DEFORMATION DIGITALNA ANALIZA POSNETKOV MIKROSTRUKTUR KOT ORODJE ZA UGOTAVLJANJE LOKALNE PLASTIČNE DEFORMACIJE Marjan Suban, Robert Cvelbar, Borut Bundara Institute of metal constructions, Mencingerjeva 7, 1001 Ljubljana, Slovenia marjan.suban@imk.si Prejem rokopisa - received: 2011-10-25; sprejem za objavo - accepted for publication: 2012-03-22 This paper presents a methodology to detect plastic deformation at the micro level. The analysis is based on the statistical data describing the morphological and crystallographic textures of a sample microstructure. This data was obtained from optical microscopy using a digital imaging analysis. The important parameters necessary to describe the microstructure were identified as the grain-size and grain-orientation distributions. A change in the weighted product of these two parameters, the grain size as the area of grains and the grain orientation as the moment of inertia of grains, can represent a measure to identify plastic deformation on a small area. A demonstration of its applicability was performed on a real object as part of a ruptured-pipe-failure analysis in a thermal-power-plant boiler. The presented analysis leads to a fast identification of the local plastic deformation and, in the case of periodical analysis of the same sample, it can even be used as a measure to identify creeping. Keywords: digital imaging analysis, plastic deformation, grain orientation, local-deformation analysis V prispevku je predstavljena metodologija za odkrivanje plastične deformacije na mikroravni. Metoda temelji na podlagi statističnih podatkov, ki opisujejo morfološke in kristalografske teksture mikrostrukture. Vir podatkov je digitalna analiza posnetkov, pridobljenih iz optične mikroskopije. Kot pomembna parametra, potrebna za opis mikrostrukture, sta opredeljena distribucija velikosti zrn in usmerjenosti zrn. Sprememba tehtanega zmnožka teh dveh parametrov: velikosti zrna kot površine zrna in usmerjenosti zrna kot vztrajnostni moment zrna, je lahko merilo za identifikacijo plastičnih deformacij na majhnem področju. Za prikaz uporabnosti metode je bila izvedena analiza na realnem objektu kot del analize poškodb počene cevi v kotlu termoelektrarne. Predstavljena analiza omogoča hitro identifikacijo lokalne plastične deformacije, pri časovno zaporedni analizi istega vzorca pa se lahko celo uporablja za identifikacijo lezenja. Ključne besede: digitalna analiza posnetkov, plastična deformacija, orientacija kristalnega zrna, analiza lokalne deformacije 1 INTRODUCTION the shape (elongation) and the orientation. The new proposed methodology for evaluating these three parameters The quantification of a material microstructure is is presented in the following sections. important for an evaluation of a material and some of its properties. Many properties of the material are strongly j j ^^ ^tal ima in influenced by the size and shape of the grains. Obser- ' a '■maag''nlg vations of the changes in the geometric features of the There are many imaging techniques available for grains may be quantified by an image analysis. Micro- viewing a microstructure in 2D and thus useful for scopy is a powerful non-invasive tool for studying a collecting images of each cross section. These imaging material microstructure, especially if complemented with methods include the techniques like secondary electron an image analysis. (SE), back-scattered electron (BSE), ion-induced secon- The paper presents the possibilities of evaluating dary electron (ISE) and electron back-scatter diffraction2 plastic deformation based on microstructural grain (EBSD) (Figure 2). While each method generates an layouts. Contrary to the other researchers' work, our image in 2D, important issues are to be discussed with methodology of identifying the grain shape and regard to some of the techniques3. evaluating their orientation is based on the moments of Many laboratories are unfortunately limited to the inertia of individual grains. When a load is applied to a use of the optical microscopy as an essential and the only material, it will cause the material to change its shape. available method for evaluating microstructures. If grain The observed effects of the deformation process on the boundaries are very clearly defined, the computer material's microstructure using optical microscopy1 can programs can be written in such a way that they allow be evidently seen on Figure 1. The changes in the higher-dimensional measurements (the area and shape microstructure can be easily described for the grain level measurements) recorded on digital images, but often by using three parameters: the change in the grain area, many grain boundaries are hard to distinguish. The Figure 1: Microstructures of the C-Mn steel: a) the initial state; b) the microstructure after a deformation1 Slika 1: Mikrostruktura C-Mn-jekla: a) za~etno stanje; b) mikrostruk-tura po deformaciji1 current state of the optical recognition software offers many tools to improve image resolutions, so that grain boundaries can be easily recognized. 1.2 Quantitative chi^^^cte^^zation The quantitative characterization is an obvious tool for the researchers to use when attempting to establish a relationship between a microstructure and its properties. As a result of many studies numerous different methods and rules have been developed. In reality the application of the characterization greatly dictates the nature of the measurement technique chosen. Often the measurements are performed only in 2D using optical microscopy and digital imaging. In order to maximize the value of the data, microstructural quantification should be designed effectively. Almost an infinite number of parameters and correlations can be used to describe a microstructure, but just some of these parameters are actually important. The measurement of the grain size is the most used method of all the techniques for quantifying the micro-structural features. It is known that the grain size of a polycrystalline material is extremely important for determining its properties. Various properties exhibit a correlation with the grain size, such as: yield stress, ductility, and hardness4. Generally, the grain size is measured as an average scalar value, such as the intercept length, the grain area or the grain volume5. 1.3 Gi^^^n sh^^e an^ the pi^^nc^^ial-i^i^^s o^^ent^t^on The shape of grains is likely to be of major significance in a number of applications, but irregular geometries of the grains in a polycrystalline microstructure make the grain shape a difficult parameter to quantify. The difficulty lies in the need for the data to express the true grain shape. Usually a number of simplifying assumptions are made. Like the calculation of the grain size, the determination of the grain shape has been greatly aided by the EBSD maps. The boundaries of each grain can be clearly found and measured by identifying the local changes in the orientation. A problem may occur when two neighboring grains have the same orientation. The image analyzer can consider these two grains as one grain and that can lead to an error in determining the grain size and its shape. The difference between quantifying a grain shape and a grain size is related to the inability to clearly describe the shape. Determining a grain area is a relatively straightforward measurement yielding a scalar value, while a shape really needs to be described by the local curvatures, which is more complicated and requires higher-order mathematical descriptors. It is most common in everyday work to use simple objects to describe a shape, such as an ellipse. In this case, a Figure 2: Analysis of the microstructure with: a) optical microscopy, b) secondary electron microscopy image, c) EBSD3 Slika 2: Analiza mikrostrukture: a) opti~na mikroskopija, b) SEM, c) EBSD3 Figure 3: Schematic representation of the grains approximation with the equivalent ellipse Slika 3: Shematski prikaz aproksimacije kristalnega zrna z njemu enakovredno elipso quantification of the grain shape is done with the calculation of the length of an equivalent ellipse major Emax and minor axis Emin, where the area of a grain is equivalent to the area of the approximated ellipse. The ratio of the minor axis of the equivalent ellipse to its major axis represents the measure for grain roundness. The roundness is a measurement of the length - width relationship, with a value in the range from 0 to 1. A perfect round grain has a roundness of 1, while a very narrow, elongated grain has a roundness of about 0. In addition, many shape descriptors involve combining groups of size parameters to generate dimension-less values like length/width (aspect ratio), area/convex area (solidity) and length/fiber length (curl)6, which can sometimes be ambiguous. Some scalar parameters, such as the moments of inertia, can do an adequate, or a better, job of expressing the grain shape and orientation. The principal-axes orientation quantifies the orientation of the grains' principal axes relative to the global coordinate system of the cross section. It is important to distinguish between the principal-axes orientation, which is the orientation referring to the principal axes and the crystal-lattice (crystallographic) orientation, which is usually determined with EBSD. In the case of an ellipse, the orientation is presented as angle ^ measured counterclockwise from the horizontal axis x to the axis of lowest moment of inertia Xi, as shown on Figure 3. 2 METHODOLOGY Generally, the microstructure images suffer from the defects of improper illumination, artifacts and noise that are developed at the time of the sample preparation. The first stage is important for attaining higher grain-segmentation accuracy. An RGB microstructure image was processed using the tools of digital imaging with the final goal to achieve an image without any noise, showing a set of individual grains and excluding the border grains. This is also the most important step for analyzing the differentiation between individual grains in the microstructure. If the grains are not clearly distinguished then the next steps of the methodology are purposeless. An application called the Particle Analysis, or the Blob Analysis, in the National Instruments IMAQ Vision software was used for digital imaging and calculating. The blob analysis is the process of detecting and analyzing distinct two-dimensional shapes within a region of the image. It can provide information about the number of grains, location, shape, area, perimeter, and the orientation of grains. One of main results provided by the analyzing software is the moment of inertia, or the second moment of area, which is a property of a cross section and can be used to predict the resistance of the cross-section areas to the bending and deflection around an axis lying in the cross-sectional plane. The moments of inertia for any cross section defined as a simple polygon on the x - y plane can be computed in a generic way by summing the contributions from each segment of the polygon. The equations marked as 1, 2 and 3 can be used to calculate the moments of inertia, where the parameters Xi and yi represent the distance from the origin to the elementary triangle center point and ai represents the area of this triangle. 1 n-1 ix = ^ y2 + yiyi+1 + yL )ai 1 n-1 Iy = ^ ]L(X2 + XiXi + 1 + x2+1 )ai (1) (2) 1 n-1 = Xiyi+1 + 2Xiyi + 2Xi+1 yi+1 + Xi+1 y^ )ai (3) From these values that represent the moment of inertia for the X - y axis, the moments of inertia for the principal axis X1 - y1 can be calculated (for the axis presentation see Figure 3). L +1. -+„ L -1. +12 (4) In this case Ix1 represents the minimum eigenvalue of the moment of inertia, while Iy1 is the maximum value. The roundness of a grain can then be calculated using the ratio of these two values and it ranges from 0 (an extremely elongated grain) to 1 (a round grain). R = I 1. (5) The angle of the rotation of the coordinate system around the grain center of mass ^ can be calculated using Eq. 6. It is used as a parameter to quantify the orientation of an individual grain. A correction of angle (p is needed to transform the angle range from 0-180° to I Figure 4: Schematic representation of the steps of digital imaging and the calculated result for one grain Slika 4: Shematski prikaz faz digitalne obdelave posnetkov in rezultat izra~una za eno kristalno zrno 0-90° (e.g., the grain orientation for the angle of 1° almost equal to the one for the angle of 179°). 1 is > = 2atan -^-y (6) 3 EXPERIMENTAL RESULTS AND DISCUSSION For the experimentation we have used many micro-structure images of low-carbon and austenitic stainless steel at various resolutions (i.e., magnifications) and with different grain shapes. These images were obtained with optical microscopy. An example of a microstructure Figure 5: a) Correlation between the roundness and the orientation angle