**1. Introduction**

Fiber–cement is a natural material that is widely used in construction. Its creator was Czech engineer Ludwig Hatschek. At the beginning of the last century, to produce such elements, asbestos was used. In the 1970s and 1980s, asbestos cement sheets were popularly called eternit [1–5].

Since then, the method of fiber–cement production has undergone many transformations. First of all, asbestos has been eliminated and replaced with completely harmless materials. The appearance of fiber–cement products has also changed significantly [6–8].

The relatively high strength parameters of fiber–cement boards are the result of their production process. The components are made of Portland cement (90%) and rayon staple (10%). Cement binds

**<sup>\*</sup>** Correspondence: aadamczak@tu.kielce.pl; Tel.: +48-723-790-363

the material and determines its final strength. Cellulose provides the right amount of water in the cement setting process, fills the gaps and increases the density of the product. It also serves as the reinforcement. In the production process, mineral materials are also used as fillers to improve the flexibility and appearance of the boards [9–13].

The fiber–cement production technology consists of applying successive thin layers of a mixture of materials, which are pressed well together before the slow hardening process. The applied technological process allows fiber–cement to achieve high strength parameters [14–16].

As mentioned above, boards can be used both inside and outside buildings. Installation of the components in an outdoor environment involves exposure of the boards to weather conditions. Therefore, it is considered appropriate to perform tests on fiber–cement components taking into account the conditions to which they will be exposed during use. Among the typical interactions, the authors indicate atmospheric precipitation and the recurring process of freezing and defrosting the boards. Certain factors, specified in the standard guidelines, should be taken into account when testing the physical and mechanical parameters. Attempts to evaluate the condition of fiber–cement components must also take into account the likelihood of special factors, which include high temperatures and direct fire [17–20].

The paper presents the application of the acoustic emission (AE) method, based on unsupervised pattern recognition (k-means algorithm), to evaluate the change of the mechanical parameters of fiber–cement components. Three-point bending tests were performed on material samples in an air-dry state, which were then subjected to environmental (soaking in water, and recurring freezing and defrosting) and special (flaming with a gas burner and exposing to a high temperature—230 ◦C for 180 min) operating factors. According to the authors, the environmental factors listed above correspond to the typical operating conditions of external cladding boards, which must always be taken into account in the test procedures. The flame action reflected the fire conditions that impact directly on the partition covered with cement–fiber boards. The high temperature was also intended to reflect fire conditions (range of the high temperature zone) and heat accumulation in the material. The recorded AE signals (generated by active developing destructive processes) were divided into four classes. Each of them reflects certain processes taking place in the structure of components under an external load. The frequencies occurring over time in each of the tested samples were also analysed.

After the three-point bending strength test, fragments of fractures were extracted from the tested components for microstructure tests, performed with a scanning electron microscope. Parallel to the observations of the fracture surfaces, an analysis of the elemental composition of the material was performed using the EDS (Energy Dispersive X-Ray Spectroscopy) microprobe.

The authors undertook the indicated research topics because they believe that the use of the AE method may enable the assessment of the condition of the cement–fiber boards in operation. So far, most of the research on cement–fiber boards has been devoted to the influence of operational factors [21,22] and the action of high temperatures, examined by testing some of the physicochemical parameters of the boards, especially their bending strength (Modulus of Rupture MOR)). The nondestructive testing of fiber–cement boards was mainly limited to detecting imperfections arising at the production stage. Articles by Drelich et al. [23] and Schabowicz and Gorzela ´nczyk [24] present the possibility of using Lamb waves in a non-contact ultrasonic scanner to detect such defects. In the literature on the subject, there is little information on the use of other nondestructive testing methods for fiber–cement boards. The research described in the works of Chady et al. [25] and Chady and Schabowicz [26] showed that the terahertz (T-Ray) method is suitable for testing fiber–cement boards. Terahertz signals are very similar to ultrasonic signals, but their interpretation is more complicated. In [27], the microtomography method was used to identify delaminations and low-density areas in fiber–cement boards. Test results indicate that this method clearly reveals di fferences in the microstructures of the elements. Therefore, the microtomography method can be a useful tool for testing the structure of fiber–cement boards, in which defects may arise due to manufacturing errors. However, this method can only be used for small size boards. It should be noted that, so far, few cases of testing fiber–cement boards using acoustic emissions have been reported. Ranachowski and Schabowicz et al. [27] conducted pilot studies on fiber–cement boards manufactured by extrusion, including exposing boards to 230 ◦C for 2 h. In this research, an acoustic emission method was used to determine the impact of cellulose fibers on boards' strength, and they attempted to distinguish between the AE events emitted by the fibers and the cement matrix. The results of these tests confirmed the usefulness of this method for testing fiber–cement boards. In [28], by Gorzela ´nczyk et al., the use of the acoustic emission method was proposed to examine the e ffect of high temperatures on fiber–cement boards. It should be noted that the e ffect of high temperatures on concrete, as well as the interrelationships associated with this process, have been extensively described using the acoustic emission method; an example is Ranachowski's work [5]. AE was used to assess the state of concrete-like material and consider the e ffects of extreme conditions on it, such as fire or frost (papers [29–32]). It should also be mentioned that the acoustic emission method is often used to test thin materials, e.g., steel and polymer composites, and even fragile food products [15,33]. Nondestructive tests have also been used to show decay, and the correlation between static and energy performances [34].

Analysing the results of the conducted works [35–39], it can be stated that for cement matrix panels reinforced with fibers, the biggest threat is the damage or degradation of the reinforcing fibers, as well as any decrease in the degree of binding between the matrix and reinforcement, as these decrease the mechanical parameters of the composites. In turn, taking into account the fact that these panels are mounted on facades of public buildings classified as high, a decrease in the strength of cladding elements may be associated with a real threat to human health and life. On the other hand, the wide applicability of the acoustic emission method suggests that it will also give positive results when assessing the condition of fiber–cement boards.

To sum up, it has been found that there is no methodology in the existing literature for assessing the condition of fiber–cement boards. For this reason, the authors conducted research using the acoustic emission method, the results of which clearly show that the signals recorded for samples with high mechanical parameters di ffer significantly from those for elements with a degraded structure and reduced strength. The di fferences consist in the number of recorded signals, belonging to classes corresponding to the destructive processes occurring in the material, as well as the frequencies emitted.

### **2. Materials and Methods**

The tests were performed on rectangular samples cut out from a 3100 × 1250-mm fiber–cement board. Information about the components intended for the three-point bending strength test is presented in Table 1.


**Table 1.** The conditioning and testing plan.

The tests were performed using a Zwick Roell universal testing machine. The bending speed for each sample was 0.1 mm/min (each test was carried out with a constant increase in deflection). The scheme of the test stand is shown in Figure 1. The axial distance between the support points *ls* was 200 cm, and the radius of the support points and the loading beam *r* was 10 mm. Based on the measurement data, the *MOR* bending strength of the elements was calculated in accordance with EN 12467 Fibre-cement flat sheets - Product specification and test methods.

**Figure 1.** The fiber–cement element in three-point bending with installed AE sensors: (**a**) photograph of the specimen; (**b**) scheme of loading and AE sensors.

During each test, acoustic emission signals were recorded. The eight-channel Vallen AE processor board was used for this purpose. The acquisition was carried out using two sensors with built-in preamplifiers—VS30-SIC (25–80 kHz range) and VS150-RIC (100–450 kHz range). During the tests, 13 typical AE parameters (AE signal duration, AE rise time, mean effective voltage, number of counts, number of counts to maximum signal amplitude, amplitude of AE signal, signal energy, average frequency, reverberation frequency, initiation frequency, absolute energy of the AE signal, signal strength and average signal level), and the values of strength increase and deformation of the samples, were recorded. The sensors were attached with a clamp near the supports on the inside.

Analysing the literature, it can be assumed that the course of the destruction of ordinary concrete (mortar, cement matrices) under short-term loading is three-stationary. These stages are stable microcracks initiation, stable microcracks development and propagation, and unstable microcracks propagation.

The stage of stable crack initiation is characterised by microcracks, that were initiated already at the stage of this material's formation, appearing at isolated points of the concrete material, in the form of micro-gaps, pores and local concentrations of tensile stresses. The formation of these microcracks alleviates existing stress concentrations, leading to the restoration of the balance of internal forces. It is characteristic that at this stage of destruction, the existing microcracks do not develop, while the phenomenon of their increase occurs.

The increase in load causes the destruction of concrete to enter the second stage, in which two simultaneous processes occur: the phenomenon of crack propagation created in the first stage, and the further formation of stable microcracks. The cracks multiply and spread in a stable manner, in the sense that if the external load increase is stopped, the development of the cracks will also cease.

The third, final stage occurs when, as a result of a further increase in load, the crack system develops to such an extent that it becomes unstable. Under the influence of the released energy of deformation, the cracks spread automatically until the structure is completely destroyed. Destruction at this stage can occur even without further increase in external load.

The works of Kanji Ono, Othsu and Fowler [40–43] state that the sources of the AE signals in elements made of a concrete (cement) composite can be:


The recorded signals were divided into classes using the k-means algorithm, using Vallen software. In the course of the procedure, a standard sample was selected, in which, during the bending process, all the processes characteristic of the fiber–cement material were generated. The standard file was used to divide the signals recorded for the remaining samples.

The test components came from the type of fiber–cement board that is available on the construction market, which has a broad application range (installed inside and outside buildings). As declared by the manufacturer, the samples contained Portland cement, mineral binders, natural organic reinforcing fibers and synthetic organic reinforcing fibers. Elemental composition was confirmed by performing analyses using an EDS micro probe during microscopic observations (Figure 2). The comparison of the data provided by the manufacturer with the EDS analysis performed is presented in Table 2. The analysis of the elemental composition of the matrix and fiber allowed us to assess the type of binder used. In the previous research on fibrous cement materials carried out by the authors, it was found that cement matrices are made using only Portland cement, or Portland cement with the addition of other mineral binders. Performing such an analysis in this case gave the information that Portland cement and a silicate mineral binder were used in the production of the matrix. Technical data from the tested boards are presented in Table 3.

Microscopic observations were performed after the strength tests, and were combined with the AE signal generation. A 10 × 10-mm piece was cut out from the fracture surface of each sample. The components placed in the microscope chamber had not been sprayed before. The observations were performed at 5 kV with an LFD (Low vacuum Secondary Electron) detector designed for operation in low vacuum.



**Figure 2.** EDS analysis results for a mock sample: (**a**) distribution of measuring points; (**b**) analysis results from point 1—fiber; (**c**) Analysis results from point 2—matrix.


**Table 3.** Technical data of the tested board.

### *2.1. K-Means Algorithm in the AE Method*

To build the base of reference signals, used to assess the change of mechanical parameters in cement–fiber composites, the pattern recognition method was used, specifically, the version with arbitrary division into classes (unsupervised)—USPR. Arbitrary pattern analysis is mainly used when creating a database of reference signals if the number of classes is unknown. The k-means grouping method was used to divide the signals into classes corresponding to the destructive processes in cement composites.

K-means is a standard cluster analysis algorithm, in which the value of parameters determining the number of groups to be extracted from a data set is initially determined. Representatives are randomly selected, so it is important that they are as far apart as possible [44–47]. The selected components are the seedbed of the groups (prototypes). In the next step, each component of the set is assigned to the nearest group. Initial groups are designated at this stage. In the next step, a centre is calculated for each group, based on the arithmetic mean of the coordinates of the objects assigned to a group. Then, all the objects are considered and reallocated to the nearest (with respect to their distance from individual centroids) group. New group centres are designated until the migration of objects between clusters ceases. According to the same principle, the assignment correctness of particular objects to particular groups is checked. If in the next two runs of the algorithm there is no change in the division made (at which point it is said that the stabilisation is achieved), the processing is finished [48–50]. In this method, the number of groups is constant and consistent with the *k* parameter; only the group object assignment can be changed. In the k-means method, the search for the optimal division corresponds to the designation of the prototypes of groups that minimises the following criteria function [51,52]:

$$J\_{(v,B)} = \sum\_{i=1}^{k} \sum\_{k=1}^{N} b\_{ik} d^2 (v\_{i\prime} v\_k)\_{\prime} \tag{1}$$

In this function, *d(v,x)* is the distance of the element represented by the vector *x* from the group designated by the prototype (centroid, centre of the group) *v, N* is the number of the set *O, B* is the division matrix, and the other parameters have the same meaning as stated above. The principle of the method can be described as follows:


Creating a base of reference signals involves several stages. These are:


• final verification on the elements during their normal operation (this stage will be carried out in subsequent tests).

The characteristics of the signals contained in the database include the geometric, energy and frequency parameters of the signals. In addition, the database contains typical noise signals.

It should be emphasised that the main purpose of the research was to register the AE signals generated by destructive processes. Therefore, no additional tests, e.g., deformation of concrete under compression, or measurement of Young's modulus, were carried out, and no statistical calculations were carried out regarding the spread of parameters. This approach was derived from the fact that the actual element lacks information about the state of the concrete at the test site, and the purpose of the research was to collect the most real AE signals generated during the destruction of the tested samples.

A total of 13 AE parameters was used to create the base of reference signals for the destructive processes that take place in cement–fiber boards:


The second step was the adoption of the basic parameters necessary to create a base of reference signals, namely:


The standard file, with four classes obtained in this way, was then checked with real samples in laboratory tests of individually destructive processes.

The result of the research was the obtaining of a base of reference signals intended for the assessment of the technical condition of the boards. Using the base of reference signals, individual AE parameters (individual graphs) are only an illustrations of the processes taking place, not a source of analysis. That is why it is so important to use BIG DATA analysis to create "BLACK BOX", which can be used by persons without any academic knowledge of AE to analyse the technical condition of the structure.

In the presented research, the issue of signal localisation was not addressed. This issue will be addressed in further studies on full-size elements. So far, the focus has been on identifying active destructive processes.

### *2.2. Scanning Electron Microscopy with Elemental Composition Analysis*

Scanning electron microscopy (SEM) allows the recording of a surface image of samples at high magnification, by means of secondary or backscattered electron recording. Unlike optical microscopy, it allows for much higher magnifications, with incomparably higher resolution. The electron beam surface scanning of samples is a simple and quick way to obtain images that reflect differences in the elemental composition of the sample [53–55]. Accessories, such as the EDS microprobe analyser, allow for quick elementary composition determination at points and areas of different sizes. The element identification is based on the recording of the X-ray energy spectrum emitted by the sample atoms induced by the electron beam. The software automatically determines the elementary composition of the sample based on the characteristic radiation. The combination of electron microscopy with elementary analysis allows us to record high-resolution images at very high magnifications, determining the elementary composition of very small objects (even less than 1 mm), and creating change profiles for the composition of components and two-dimensional colour maps of element distribution on samples' surfaces. The method is considered to be non-invasive as the destructive effect of the electron beam on samples is very rare, and, in addition, such effect occurs (if it occurs) on a microscopic scale. The scanning electron microscope does not require the spraying of conductive layers on the surface of the materials to be tested, thanks to a special measurement mode at low pressure (called low vacuum measurement) [56].
