Principal component analysis of morphological descriptors for monitoring surface defects induced by thermal shock

Abstract

Pattern recognition techniques are applied to various morphological descriptors to monitor the formation and propagation of surface defects of materials subjected to thermal shock. A low-cement high-alumina castable was synthesized, cured, sintered, and exposed to thermal stability testing using the water quench test. After a certain number of thermal shock cycles, photographs of the samples’ surfaces were taken and subjected to image analysis. The influence of the sintering temperature on the morphology of the detected defects was studied using principal component analysis (PCA) as a pattern recognition technique that is the most informative for extracting possible differences. The morphological descriptors of the defects correspond to the previous results regarding the influence of sintering temperature on the structure of a castable during thermal shocks.

Introduction

Refractory concretes belong to the group of monolithic refractory materials and can be considered as composites since they are complex mixtures of refractory aggregates, binders, fillers, additives, and water (in cases where cement is used as a binder). All these components can be classified into two groups, namely large particles of aggregates and small fractions of other components that make up the so-called matrix. The role of the matrix is to connect the aggregate particles, so that it represents the binding phase. More precisely, the matrix consists of a binder (e.g., hydraulic cement), filler (reactive alumina, micro silica), a fine fraction of aggregates (alumina, spinel, and magnesium oxide), and additives. If hydraulic cement is used as a binder in refractory concrete, hydrated phases are formed in the matrix during synthesis and throughout the curing process at room temperature, which are responsible for setting and hardening of concrete. During heating at high temperatures, initial dehydration is followed by sintering, which causes the formation of a ceramic bond [1,2].

Refractory concretes can be used found in the linings of walls of industrial furnaces and other thermal reactors, in environments exposed to cyclic and sudden changes in temperature of different intensity, often accompanied by the effect of additional loads. There is uneven cooling and heating when the material is exposed to such conditions (called thermal shock), so different parts of the walls expand and shrink, causing internal stresses that induce crack nucleation and its growth, loss of strength, and fracturing of the wall. Therefore, it is very important to have information about the behavior of refractory concretes during thermal stresses, in order to know the degree of damage caused by thermal shock. This will enable the selection and definition of their composition, as well as post-synthesis treatments. Investigations of thermal shock resistance of the material are aimed at establishing a correlation between the structure and thermal stability, in order to ensure an appropriate structure with desired thermal properties by adjusting process parameters (grain size of initial components, quantity and type of binder, care conditions, sintering temperature). Two approaches can be followed to monitor changes in refractory materials during exposure to thermal shock, namely resistance to damage and resistance to thermal stress. In general, thermal stability can be analyzed in several ways, including monitoring of mechanical properties, heat transfer, and fracture mechanics [[3], [4], [5], [6], [7]].

The sensitivity of refractory materials to thermal shock is one of the main factors that determines and limits their implementation [[4], [5], [6]]. For materials used as linings in thermal aggregates such as high-temperature furnaces, hot gas or molten metal filter systems, heat exchangers, gas turbines, solid oxide fuel cells, and catalyst supports, thermal shock resistance is a crucial factor in determining their durability [4,[8], [9], [10], [11], [12]].

Over the past few decades, numerous theories and methods have been proposed to predict as precisely as possible the resistance of refractory materials to thermal shock [4,5,[13], [14], [15], [16], [17], [18], [19], [20]]. All current approaches are based on the research and theories proposed by Kingery and Hasselman, which were developed on resistance parameters (R) widely used to present an assessment of material resistance to thermal shock [5,[13], [14], [15], [16]]. However, assessment of resistance to thermal shock is quite complex due to the numerous parameters that affect it. Although theoretical knowledge plays an important role in understanding the basic mechanisms of the behavior of ceramic and refractory materials exposed to thermal shock, an unique comprehensive standard test that quantifies the thermal resistance of these materials and presents its indicator has not been developed yet, despite attempts of the academic sector [[18], [19], [20], [21], [22], [23], [24], [25], [26]]. Available standards involve subjective assessment or they use destructive tests that need many testing samples that are destroyed and cannot be utilized for any other purpose [27,28].

Almost all the methods used to determine the resistance of materials to thermal shock consist of three steps:

• The first step involves immersing heated samples in a refrigerant/fluid such as water, oil, or air.

• The second step is based on monitoring the change in some material properties that are commonly tracked to assess resistance to thermal shock in different ranges of temperature differences. These properties are often determined after only one cycle of thermal shock. Weight loss [13] and decreases in mechanical strength and elasticity modulus are generally measured [18,19].

• The third step is the determination of a factor that describes the resistance of a ceramic or refractory material to thermal shock, based on the data collected in the first two steps. Among the numerous proposed methods for estimating resistance to thermal shock, the basic indicator is the critical temperature difference (ΔT), which represents the temperature difference at which there is a sharp drop in the flexural strength or elasticity modulus [23] or a large crack that causes the sample to break. The greater the critical temperature difference ΔT, the greater the resistance of the material to thermal shock [24]. Unfortunately, these thermal shock resistance parameters cannot be easily determined because the desired critical temperature range depends largely on a complex experimental procedure.

According to ASTM standard C1525−004, the resistance of ceramic materials to thermal shock is determined by a method where the test samples are first heated to an elevated temperature and then subjected to rapid quenching in a water bath at room temperature. Quantitative estimation of thermal shock resistance is based on the determination of a critical temperature interval during which there is a reduction of at least 30 % in the mean flexural strength after one cycle of thermal shock, compared to the average flexural strength of the initial samples [27]. Similarly, according to European standard EN 820−3, the thermal shock resistance parameter is based on the determination of the critical quenching temperature difference at which a fracture is initiated or the mean strength decreases by more than 30 % of the initial mean strength [28]. Unfortunately, standardized procedures that use a 30 % reduction in the initial mean strength as an indicator cannot estimate thermal stability precisely because proposed approaches not only require time but also have a limited ability to clearly distinguish between different levels of thermal shock resistance of a wide range of ceramic and refractory materials. A group of authors [25,26] has proposed the application of non-destructive methods to characterize the elastic properties of refractory materials in relation to thermal shocks. For example, ultrasonic measurements and forced resonance techniques. However, there are no published sources that deal with methods aimed at validating quantitative evaluation of different ceramic or refractory materials. A group of scientists [4] has proposed a normalized method based on the introduction of an index for estimating the resistance to thermal shock of various ceramic materials in the range from 1 to 100, based on a formula derived directly from monitoring changes in flexural strength before and after the thermal shock cycle. This method showed that the thermal shock resistance index decreases as the thermal expansion coefficient increases.

Although numerous attempts have been made to date, no singular and simple parameter or index has been established to assess the resistance of various ceramic and refractory materials to thermal shock, widely accepted by both the academic community and industry. The authors of the present study proposed in earlier published papers the application of a well-known non-destructive method – image analysis [[29], [30], [31], [32], [33]]. Namely, with the development of cameras and microscopes, it is possible to record the surface of the sample with appropriate magnification and then monitor and quantify the degree of damage using various image analysis tools. Image analysis provides a morphological assessment of damage through a number of parameters (shape, diameter, surface, length, fractal dimension, etc.). This paper proposes an approach based on analysis of morphological descriptors of surface defects using image analysis tools, while calculated values are subjected to a pattern recognition method [[34], [35], [36]]. Since the morphology descriptors of induced surface defects can be determined by observing and analyzing the “items” selected from the images, such that they represent measurable characteristics like texture, pore and grain shape and size, density, distance, aspect ratio, fractal dimension, and many others, pattern recognition techniques such as principal component analysis (PCA) can provide information on extracted morphological descriptors that describe the main difference among the observed defects and identify variations among them [36]. The proposed approach provides more information about the structure of the material, so it can be used to monitor and predict the resistance of the material under extreme or harsh conditions such as thermal stress. Principal component analysis is an unsupervised pattern recognition technique used to reduce n-dimensional space of morphological descriptors to a low-dimensional space (two-dimensional in this case) of maximal variance. The differences among the objects can be observed in the reduced space, while the morphological descriptors that are most informative about such differences can be extracted. Principal component scores (PC-scores) make it possible to recognize differences among the objects (i.e. internal structure of the dataset), while loading values enable the extraction of morphological descriptors that are the most informative for the dataset structure. Consequently, the most informative descriptors can be used to characterize not only the thermal resistance of the material but also the structure of the material.