Euclidean Distance Mapping for computing microstructural gradients at interfaces in composite materials
Introduction
Interfaces influence the bulk properties and overall performance of composite materials. In hardened concrete, interfaces exist between cement paste and steel reinforcement, fibres and also between the various phases within the cement paste itself. An important interface is the paste region adjacent to aggregate particles, known as the interfacial transition zone (ITZ); this is often regarded as the ‘weakest link’ that controls mechanical strength and is suspected to be detrimental to most aspects of the durability of concrete.
Researchers have used image analysis on backscattered electron (BSE) images to investigate and quantify microstructural gradients across the ITZ. This procedure, pioneered by Scrivener and co-workers [1], [2], [3], measures the distribution of phases, typically pores, anhydrous cement and calcium hydroxide, from the aggregate boundary. This is done by computing the area fractions of each phase in a series of narrow and equidistant strips or bands, starting from the interface and extending outward to the bulk paste. The relative fraction of each phase is averaged over a large number of images taken from different aggregate particles and the results plotted against distance from the aggregate surface.
The typical image analysis routine for quantitative phase analysis via a series of equidistant strips from the interface is briefly described here. The phase of interest, for example pores, is segmented from the BSE image by greyscale thresholding. A binary aggregate mask is also generated, usually by manually tracing the aggregate boundary. The binary aggregate mask is then dilated for a number of iterations depending on the pixel spacing and width of the strip to be created. The original aggregate mask is subtracted from the dilated image to give the first strip and a logical operation AND between the strip and pore mask is performed to give the fraction of pores located in the strip. To generate the subsequent strip and phase fraction, the aggregate mask is dilated again and the whole process is repeated.
The dilation–subtraction method requires significant processing time and computer memory due to the iterative nature and large number of images involved. For each strip, three images have to be created: the dilated boundary mask, the strip and the phase fraction contained within the strip. Additional steps are the area measurements of the strip and pores contained within it. A typical ITZ analysis of 50 frames at a 2.5 μm strip width up to a distance of 50 μm from the aggregate will require 20 strips per interface, hence involving 60 images per frame and 3000 images for the complete analysis. If a different strip width is needed, then the whole process would have to be repeated. Investigation using a greater number of frames in smaller bands enables phase distribution to be analysed in greater detail, but narrower strips are impractical. Another disadvantage of the strip method is that special care has to be taken so that the strips are not generated beyond mid-distance to the next aggregate. To implement this into an automated image analysis algorithm is difficult because a randomly selected area in a typical concrete may contain aggregates separated at a distance of several microns to hundreds of microns. The strips may be generated manually, but this is extremely laborious and impractical. Thus, the operator is resigned to only selectively analyse paste areas where the distances between aggregate particles are large, but these results are not representative because of biased sampling.
In this paper, an alternative approach to interfacial analysis using Euclidean Distance Mapping (EDM) is proposed. The new method is more efficient as it does not involve a repetitive strip producing stage. The method only involves two additional images per location in order to obtain a gradient plot at a single pixel resolution, i.e., at one pixel wide strips. It is also more flexible than the conventional strip method because the information obtained from the EDM is sufficient to generate distribution plots at any strip width without requiring additional images. The new method is also applicable to any paste geometries and boundary conditions. This paper presents applications of the new method to investigate microstructural gradients at the ITZ, emphasising that the same technique can be used for any type of interphase boundary.
Section snippets
Euclidean Distance Mapping for phase analysis
Euclidean Distance Mapping (EDM) is a basic operation used in computer vision, pattern recognition and robotics [4], where high speed computation is essential. It uses distance transformation to convert a binary image consisting of foreground and background pixels into a greyscale image where each pixel has a brightness value equal to its Euclidean (linear) distance to the nearest background pixel [5], [6]. This can be expressed mathematically as follows. Consider a digital image M = {mij}
Example of application
In this section, the new method will be used to investigate spatial distribution of detectable porosity and anhydrous cement at the ITZ. For this purpose, an OPC concrete at water–cement ratio 0.4 was prepared. A cylindrical sample (100 Φ × 250 mm) was cast, demoulded after 24 h and wrapped in cling film for 3 days. After curing, an 8 mm thick disc was cut from approximately 100 mm from the bottom cast face, from which a block sample (40 × 20 mm) was sectioned. The block was freeze-dried,
Conclusion
A new image analysis method for investigating microstructural gradients at interfaces in composite materials is presented. The method uses Euclidean Distance Mapping to generate microstructural gradient plots at single pixel strip width. The new method is faster and more flexible than conventional dilation–subtraction strip analysis, and is not constrained by feature geometry and boundary conditions. Therefore a truly random and unbiased sampling procedure can be achieved. The new method was
Acknowledgements
HSW would like to acknowledge the financial assistance provided by the Universities of UK, via the Overseas Research Students Awards Scheme. We thank Mr. R. A. Baxter for his help with the laboratory work.
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