Cementitious composites embedded in a real building structure are subjected to constant stresses and deformations due to changes in environmental parameters, e.g., changes in air humidity, air temperature, sunlight, etc. The effect of these deformations is the development of cracks in the material that arise in its weakest place [1
]. As a result of propagation, these cracks merge and form a characteristic crack image on the surface of a cementitious element, known as the cracking pattern. Depending on the literature source and cracking factor, the cracking patterns are also referred to as the cluster cracks, thermal cracks, or mapcracking [3
]. The cracking patterns described using the quantitative parameters, such as the crack density or crack width, determine the further durability and strength of a cementitious material because the progressive development of cracks is a simple method of the material’s destruction.
In order to be able to quantitatively describe the cracking patterns, the concept of the cluster [3
] was introduced. It is defined as the area on the surface of a material which, on each side, is limited by a crack or the edge of a sample. Clusters have a fractal character and are observable in both the micro- and macrostructure of the material. In order to describe the formation process of the cluster structures, the theory of dispersion systems is used because it is assumed that the final properties and structure of the material are the result of transformation and physical interactions occurring in the binder-water dispersion system, i.e., when a cement paste is still in the liquid phase. The properties of such a system depend on many factors, such as the cement grain size, w/c ratio, and the presence of pozzolanic additives or inert fillers [7
]. The final properties of the cement matrix are largely dependent on the spatial configuration of cement grains. They, when hydrated, form a mutually tied, rigid structure composed of hydration products that are able to transfer external loads. In this structure, air voids are also present, which are defects and the places where the cracks begin to develop [10
]. These cracks propagate as a result of increasing material deformations resulting from external influences and eventually create a cracking pattern that can be observed in both micro- and macro-scale.
Nanotechnology is the future of every field of technical sciences, which is why research on the material modification at the nanoscale is also carried out in the context of cement matrix modification. Nano-modification of a cement matrix usually involves two directions, i.e., introducing nanoparticles into the cement paste, which can seal the structure or possess pozzolanic properties, which are the main, but not the only, function in the reaction with cement components to form the CSH phase [12
]. Additionally, the introduction of dispersed nano-reinforcement mechanically bonds the structure of a cement matrix, causing the phenomenon of crack bridging [16
]. In this context, in many countries of the world, research is ongoing on the use of carbon nanotubes as the dispersed nano-reinforcement of a cement matrix [18
]. The results of research to date indicate that the addition of CNTs may improve the mechanical properties of a cement matrix, increase the crack resistance, increase the local rigidity of the CSH phase [16
], or reduce the porosity [24
Carbon nanotubes (CNTs) can occur as single- (SWCNTs), double- (DWCNTs), and multi-wall (MWCNTs) structures [25
]. They have unique mechanical parameters (the Young’s modulus about 2 TPa, and tensile strength of about 50 GPa), and very good thermal and electrical conductivity. Depending on the manufacturer, CNTs with a diameter of 1–100 nm and a length of 10 nm–10−2
m can be found on the market [26
]. The process of obtaining them is energy-consuming and requires specialized equipment [26
], which means that this material is still expensive, but due to its properties, it is the future of many engineering fields.
The use of CNTs in concrete technology is very problematic due to its tendency to form strongly bonded agglomerates, which causes them to be entangled in large aggregates. This is due to the fact that CNTs have a large specific surface area and a large slenderness. Using them in such a form as an addition to the cement matrix does not cause any beneficial effects, but generates only unnecessary costs. To prevent this (i.e., “untangle”) they should be used in the presence of a surfactant, which, by absorbing on the surface of CNTs, causes them to repel each other. In the context of the use of CNTs for cement pastes, their dispersion is usually made in water with a surfactant, which is then added to the cement and mixed. Research is continuing to find a surfactant that is as neutral as possible to the cement paste. To this end, the CNTs’ dispersions have already been made in the presence of, among others, H2
], isopropanol [23
], sodium dodecyl sulfate (SDS) [31
], sodium dodecyl benzene sulfonate (NaDDBS) [37
], and di-methyl acetamide (DMAc) [31
]. By using the above surfactants, a stable dispersion of CNTs is obtained, even over a period of several months.
Quantitative analysis of cracking patterns is difficult for methodological reasons, therefore, there are few such analyzes in the literature. However, numerical analyzes were carried out regarding the process of developing the cracking patterns in a cement matrix [2
]. The most commonly used parameter for the quantitative description of cracking patterns is the crack density [40
], which was defined and used for the first time by Mobasher et al. [43
]. Kim et al. [44
], as a result of the conducted analyzes, pointed out that the phenomenon of spalling occurring in concrete exposed to fire temperatures is mainly caused by the formation of a crack network, which significantly weakens the material structure. Weng et al. [45
] observed cracking patterns resulting from shrinkage of the cement paste, which was modified by various types of fibers. The total area of cracks was smaller compared to the classical cement paste. In [46
] it was pointed out that the cracking pattern’s characteristics on the cement matrix surface depends on such parameters as drying rate, the sample thickness, and the crack depth. The author of this work in his earlier studies conducted a quantitative analysis of the cracking patterns on the surface of a cement paste modified with metakaolinite [47
], microsilica [48
], and polypropylene fibers [49
The purpose of the research presented below was to determine how the addition of the dispersed nano-reinforcement in the form of MWCNTs affects the quantitative characteristics of the cracking patterns on the surface of a cement matrix. A total of four series of a cement paste were tested, which differed in the class of cement used and the presence of MWCNTs. For quantitative analysis of the cracking patterns, the computer image analysis and four parameters were used, such as the average cluster area, the average cluster perimeter, the average crack width, and the crack density. To facilitate the image analysis process, the samples’ surfaces were prepared by applying a thin film of white color. Using the statistical analysis tools, the article assesses whether the preparation method used affects the cracking process of the surface of the cement paste. This work is a continuation of the research described in [50
], where the physico-mechanical properties of cement paste with the addition of MWCNTs were analyzed in detail.
2. Materials and Methods
2.1. Components Used and Mixtures
The binder used to make the cement matrix was ordinary Portland cement (OPC) of two different classes—CEM I 42.5R and CEM I 52.5 (Cemex, Chelm, Poland). Both cements were very similar in chemical composition; content of SiO2—20.18% and 20.19% (respectively for CEM I 42.5R and CEM I 52.5R); CaO—64.79% and 64.76%; Al2O3—4.38% and 4.33%; Fe2O3—3.39% and 3.30%; MgO—1.17% in both; SO3 —2.91% and 3.16%; Cl—0.083% and 0.078%; Na2O—0.26% in both; K2O—0.49% and 0.48%.
Using Bogue’s formulas [51
], the percentage content of the main cement phases was calculated, i.e., alite (C3
S)—63.41% and 62.97%, belite (C2
S)—8.92% and 9.28%, tricalcium aluminate (C3
A)—5.88% and 5.90%, and tetra calcium aluminate (C4
AF)—10.31% and 10.03%. Like the chemical composition, the phase composition is very similar. However, the cements used differ from each other in the degree of grain fragmentation (fineness), because the CEM I 42.5R has the Blaine’s specific surface area of 4010 cm2
/g, while the CEM I 52.5R–4596 cm2
/g. The difference in the surface area is 14.6%. With almost identical chemical and mineral composition, the difference in grain size affects, among others on the rate of hydration of cement grains, or the number of connections between them. This has a large impact on the final properties of a hardened cement matrix.
The cement matrix has been reinforced with the multi-wall carbon nanotubes (MWCNTs) of the NC 7000 type, manufactured by the NanocylTM
company (Sembreville, Belgium). According to the technical card, they are characterized by an average length of 1.5 μm, average diameter—9.5 nm, specific surface area—250–300 m2
/g, Young’s modulus—1 TPa, tensile strength—60 GPa, and carbon purity—90%. Figure 1
shows image of MWCNTs used in the study, obtained from a scanning electron microscope (SEM, Quanta Feg 250, FEI, Hillsboro, OR, USA).
Due to the very large specific surface area, MWCNTs tend to agglomerate forming centers of nanotubes coiled together. Applying them in this form to a cement matrix has no effect, so they should be evenly distributed. For this purpose, MWCNTs were applied to the cement matrix in the form of an aqueous solution in which the surfactant—sodium dodecyl sulfate (SDS—C12H25OSO2ONa) was used (Merck Milipore, Billerica, MA, USA). It is a white powder with a bulk density ranging from 0.49 to 0.56 g/cm3, specific density—1.1 g/cm3, and pH—6–9.
As part of the tests conducted, four series of cement pastes were made, which consisted of twelve different recipes. It is schematically shown in Figure 2
. Within each series, samples were made with three water/cement (w/c) ratios—0.4, 0.5, and 0.6. In the series in which MWCNTs were used, their content was assumed at the level of 0.1% in relation to the mass of cement.
2.2. Procedure of the Mixture Preparation
Cement paste was created in the same way as in [50
the cement and water mixture was mechanically mixed until it obtained a uniform consistency,
MWCNTs was used as the aqueous solution with surfactant (SDS); then this aqueous solution was mechanically mixed with cement,
the MWCNTs/SDS weight ratio was 1:5,
an aqueous MWCNTs-SDS solution was sonicated for a period of 30 min; sonication took place in a glass jar, which was placed in a bucket of cold water to remove excess heat resulting from ultrasonic mixing; the amount of the solution produced at one time was sufficient to produce six samples of the cement paste,
for the sonication, the UP400S ultrasonic homogenizer of the HIELSCHER Ultrasound Technology company (Teltow, Germany) was used, it was equipped with the H22 horn sonotrode with a tip diameter of 22 mm, maximum amplitude—100 μm, sound power density—85 W/cm2, operating frequency—24 kHz; sonication took place in the continuous mode of the device operation, with maximum power, which in connection with the H22 sonotrode giving 300 W of power,
test samples were made as 40 × 40 × 160 mm beams, which is in line with the requirements for testing cement pastes and mortars; the mix was laid in molds in two layers, successively compacted, using a standardized shaker, in accordance with the EN 196-1 [52
samples were demolded 24 h after forming; maturation took place in dry-air conditions (average air temperature—22 °C, average relative air humidity—50%; maturation period was equal to 28 days).
2.3. Cracking Patterns Formation Process
The cracking patterns being the subject of the analysis were created as a result of loading the material with an increased temperature. The thermal load process consisted of three phases:
Phase I—preheating the furnace to 250 °C,
Phase II—placing the samples in the furnace and heating them at the above temperature (250 °C) for a period of 4 h, and
Phase III—removing samples from the furnace and cooling them as a result of a natural decrease in the samples temperature under laboratory conditions (average air temperature—20 °C, average relative air humidity—50%); the samples reached ambient temperature within two hours of being removed from the furnace.
The application of the thermal load procedure causes the cement paste to be subjected to the thermal shock. In the case of a cement matrix, which contains some free water in its volume, the application of a thermal load on the principle of the thermal shock causes much more damage to the material structure than it would be in the case with gradual heating. The main destructive factor is the effect of saturated steam pressure, which is more intensified in the case of the thermal shock. Not without significance is the occurrence of a large temperature gradient between the inside of the sample and its external surface. This leads to the formation of stresses associated with the thermal deformation of the material.
The saturated steam pressure causes the local tensile strength of the material to be exceeded, which results in cracks on the surface and in a volume of the cement matrix. In addition, this phenomenon is compounded by volume changes of the paste, i.e., swelling due to the heating (the cement matrix, like most physical bodies, is subjected to the thermal expansion) and shrinkage in the cooling phase. The resultant of these interactions is the formation of a characteristic cracking pattern (an example is shown in Figure 3
) on the surface of a cementitious material. Previous studies [53
] have proved that the cement matrix is chemically stable in the temperature range up to 250 °C (up to this temperature occurs, among others breakdown of the brownmillerite, Ettryngite, or gypsum phases), and the main structural damage is caused by physical changes occurring in the matrix volume.
2.4. Basic Physico-Mechanical Properties of the Cement Matrix
] describes in detail the research methodology and results of physico-mechanical properties of the cement pastes tested. Table 1
summarizes the values of the most important parameters, i.e., compressive strength (fc
), tensile strength (fcf
), apparent density (D
), and shrinkage after the maturation period (S28
). The (R
) index represents the values obtained on the reference samples (after 28 days of maturation), the (T
) index represents the values determined for samples that have been subjected to the thermal load.
2.5. Quantitative Analysis of the Cracking Patterns—Image Analysis
Quantitative analysis of the cracking patterns was carried out using computer image analysis techniques. For this purpose, the ImageJ v. 1.51j8 software (National Institute of Health, Bethesda, Rockville, MD, USA) was used, and the flat image of the cracked surface of the cement paste sample was analyzed. The image was obtained by scanning the surface on an optical scanner. In order to obtain a very detailed image of the sample surface, the scanning was carried out in a very high 2400 DPI resolution. Cracks are identified at their width of about 2–3 pixels, which at this scanning resolution gives a width of about 0.021 mm. Thus, by scanning the sample in such a high resolution, cracks can be identified that are not visible to the naked eye which, in the case of scanning without any additional magnifying optics, should be considered as a very good result.
To quantify the cracking patterns, the following parameters were used:
—the average cluster area (mm2),
—the average cluster perimeter (mm),
—the average crack width (mm),
CD—the crack density (m−1).
In the case of
, each cluster present on the sample surface was measured. For this purpose, the “analyze particles” module was used. The “plot profile” module was used to measure
. The crack width was measured along a line parallel to the longitudinal axis of the sample, located halfway across the sample width. In the case of CD
, the measurement for each sample was made along 3 lines parallel to the longitudinal axis of the specimen. The measuring lines were arranged so that they divided the sample surface into four equal parts. The values of all parameters describing the cracking patterns are the average of the measurements taken on four samples. Detailed procedures for measuring the
, and CD
values using ImageJ v.1.51j8 software are described in Appendix A
The process of image analysis of the unmodified sample surface causes many difficulties in properly separating the cracks from the remaining surface of the sample (cracks are dark gray or black, the remaining areas on the sample are gray). Due to the unsatisfactory contrast of cracks in relation to the cluster surface, the graphical processing and the image analysis become very time and labor consuming. Additionally, there may be a risk that elements of the phase tested may be mistakenly removed in the course of image processing, which results in an incorrect result of the analysis. Thus, the author decided to prepare the sample in order to achieve greater contrast between the cracks and the clusters even before scanning. In addition, the goal was to use such means that the surface of the element operating in a real construction could be prepared in such a way, not only in the laboratory conditions. Thus, it was decided to use a thin acrylic film (Figure 4
) in white color on the tested surface of a sample. The film was made using a painting method, by a roller. After the film had dried, the white surface of the clusters was in great contrast compared to cracks formed by the temperature load. This significantly improved the process of further processing of the scans.
In the case of applying the thin film on the entire scanned surface of the sample, it is important to examine whether, as a result of the increased temperature, the film cracked independently of the sample, whether the cracks on the film reflect the crack network on the actual surface of the sample. For this purpose, additional samples of one of the series (C42) were made and subjected to the and measurement procedure, but before the thermal loading the samples were not subjected to the surface preparation. The result was an analysis of the actual sample surface. Then the results were compared with the results obtained on samples of the same series but subjected to the preparation process.