A cement composite is a conglomerate of aggregate grains combined into an artificial stone as a result of hardening of cement paste. This group consists of concretes—containing fine and coarse aggregate, mortars—containing fine aggregate and cement pastes, which in a sense can be considered as the micro-concretes. In this definition, the internal structure of a mature cement paste is composed of: relics of cement grains—as aggregate, gel-crystalline form of hydrated cement grains—as binder, free water remaining after the hydration reaction, as well as contractionary gel and capillary air pores of various moisture content [1
]. The basic features of a fresh cement composite mix are its workability and potential strength. The latter feature manifests itself only after hardening but its value is pre-determined by the composition of the mixture and technology of its preparation. The mechanical strength first of all depends on the quality of the cement paste, i.e., the properties of the cement and the water/cement ratio (w/c
). A fresh cement composite mix should contain enough cement and water to achieve the desired consistency on the one hand, and the hardened concrete on the other hand has the designed strength with filled aggregate cavities.
At the end of the 1920s, Brandtzaeg [2
], who investigated longitudinal and transverse deformations of a concrete sample subjected to a uniaxial compression, found an increase in volume at close to destructive stress, which he attributed to an intensive increase in the number and size of the microcracks. Several years later the same phenomenon was observed by Yoshida [3
]. For the next two decades, the phenomenon observed by the two aforementioned researchers was of little interest. It was only the growing problems related to safety and durability of reinforced concrete structures that drew the researchers’ attention again to the changes occurring in the structure of concrete under a short- and long-term load. The increasingly improved measuring equipment made it possible to develop new research methods, both direct and indirect, allowing to conclude on the destruction of structural bonds at various stages of loading. The first property that has been observed is the fact that in the case of strong aggregate grains, the cracks run through the contact surface of the cement paste-aggregate, the so-called Interfacial Transition Zone (ITZ). On the other hand, in the case of grains weaker than hardened cement matrix, these grains may be broken up. Today, this feature of the cement composite is considered crucial in terms of its durability and strength.
The disadvantage of cement composites is their ability to brittle cracking. Nevertheless, they are characterized by low plasticity, because the destruction under a static load occurs with moderately low total deformation. The brittle behavior limit is assumed to be a deformation of the order of 0.001 to 0.005 (relative value) at destruction stage, with high strength concrete being more brittle than normal strength concrete [1
]. A sudden release of an elastic energy causes the local tensile strength of the cement matrix to be exceeded, resulting in a crack formation [5
]. A characteristic feature of cement matrix and cement composites is the propagation and development of cracks under increasing load or duration of impact. The cracks, by joining and intersecting, form a network of cracks in the material, which is also referred to as the cracking pattern [8
]. An example of the cracking pattern on the surface of a cement matrix is presented in Figure 1
. In the cement composite technology, one of the key research areas is the analysis of the process of crack formation and development, because the formation of the cracking pattern is accompanied by a decrease in durability of the material. This is manifested by the deterioration of virtually all properties of cement composites, ranging from a decrease in mechanical strength, through reduced frost resistance, water resistance or resistance to aggressive chemicals. In the final stage of development of the cracking pattern there is a total loss of material cohesion, which results in its destruction.
The aim of the article is to provide a current state-of-the-art in the field of the analysis of the cracking patterns in cement composites. This research issue has a very high scientific potential and a great practical significance, but due to its multidisciplinary character it is sometimes difficult to implement. The analysis of the cracking patterns combines many fields of science, including the fracture mechanics, image analysis and technical aspects of the materials engineering—in this case, the cement composites technology. The scope of the work includes mainly consideration of the surface cracks. This literature review is divided into 6 main parts. The first section is an introduction to the topic of the cracking patterns in cement composites. The second section discusses the basics related to the process of formation and propagation of cracks in brittle cement materials. The process of evolution of single cracks into a complete, branched system of cracks present in the structure of the material is discussed. The analysis of the cracking patterns requires their extraction from the material structure. Since computer image analysis is definitely the dominant method of an automatic crack detection, Section 3
discusses the most important techniques used to extract cracks for further quantitative analyses. Section 4
discusses the most important and most frequently used quantitative parameters, which are used to describe the morphology and complexity of the cracking patterns. Then, in Section 5
, the results of the most important studies on the influence of the structure of the cracking patterns on the functional properties of a wide range of cement composites are discussed in a synthetic way. The last section is a summary of the literature review, which indicates the most important problems and difficulties in quantitative analysis of the cracking patterns, and indicates possible further directions of research and development in this area.
What distinguishes this review from others of similar subject matter is the fact that the paper presents in a comprehensive way the problem of analysis of the cracking patterns in the structure of cement composites. There are reviews on image analysis itself, in which only methods of the digital cracks extraction are discussed. In such works there is a lack of information about the influence of the cracking patterns on the functional properties of cement composites. So far, no work has been recorded in which this subject has been discussed in a collective way, i.e., starting from the presentation of the mechanism that causes cracks and their transformation into a cracking pattern, through the techniques used for analysis, as well as quantitative parameters that can characterize the cracking patterns, to the most important thing from the point of view of the cement composites technology—i.e., how the cracking patterns affect the functional properties of this group of materials.
2. Causes of Cracks and Cracking Patterns in Cement Composites
Destruction of the cement composite is a consequence of its cracking, so it is important to consider this problem in detail. The actual strength of a cement composite or other brittle material is much lower than the theoretical strength, determined on the basis of molecular cohesion (strength of ionic or atomic bonds), and calculated on the basis of surface energy of a perfectly homogenous solid body (without internal damage). Theoretically, the strength should be approximately equal to tenth of the Young’s module, but practically it is much smaller. This state gave rise to the application of the Griffith’s theory [17
] to describe the physical and mechanical properties of cement composites. Griffith was a pioneer of the fracture mechanics and he assumed that crystals always have defects that cause stress concentration in a small area, which is enough to locally exceed the theoretical fracture strength of the material. Starting from the energy balance of the process, Griffith determined the so-called crack propagation criterion. It gives the stress value which causes further cracking of the brittle material:
—the Young’s modulus of elasticity [N/m2],
—the surface energy [N/m],
—half the length of the crack [m].
Thus, for brittle materials that have a certain elasticity, the strength is dependent on the Young’s modulus, surface energy and a crack length. However, the energy required to produce a new surface due to cracking is actually higher than σk
. In order to take this into account, the Griffith formula has therefore introduced the fracture work W
] = [N/m], which, in addition to the surface energy, includes the plastic deformation of the material that accompanies the crack propagation:
The literature contains numerous studies on the applicability of Griffith’s theory to hardened cement matrix [18
]. According to Mindess [19
], the W
for a cement matrix is in a fairly wide range of 7–14 J/m2
. The determination of W
itself is problematic, however, it is not necessary to determine σk
. For this purpose, it is sufficient to experimentally determine the critical stress intensity factor (KIC
), which is the product of W
and the Young’s modulus of the material. During the determination of KIC
, the stress at which the material breaks is determined, which is equivalent to the moment when the crack begins to grow rapidly. The practical significance of the KIC
lies in the fact that by knowing its value it is possible to determine the value of destructive stress depending on the shape and dimension of the crack and vice versa, i.e., by knowing the value of an operational stress in the element, it is possible to calculate the size of the critical crack at which it will break. In the light of the tests carried out so far, it appears that the KIC
value for pastes made of Portland cement is in the range from 0.4–0.5 MN/m3/2
]. The current guidelines for the KIC
testing of cement composites are contained in the RILEM Draft Recommendations [25
It is known that the physical and mechanical properties of cement composites are mainly determined by such factors as: total porosity, pore size distribution, the presence of material defects and the degree of structure variation. In the literature there are many studies [26
] which indicate a strong correlation between the porosity of a cement composite and its strength. In this aspect, however, the pore structure is also of more importance, where it has been shown that the strength increases with decreasing pore dimensions [30
]. Thus, the application of the classical fracture mechanics to the cement matrix means that the factor determining the strength will not be the total porosity, but the dimension of the largest gap—in this case the air pore [32
]. An experiment conducted by Birchall et al. [34
] proved that the bending strength of classical cement pastes lies on the curve determined from the Griffith’s equation (Figure 2
a). The width of the gap (pore) was substituted for the dimension of the largest defect, naturally occurring in the material or artificially produced. On the other hand, the compliance of strength of cement paste with the overall porosity results from the fact that factors that reduce the overall porosity also reduce the dimension of the critical gap (pore) [35
The dependence of W
on the porosity of the cement matrix is complicated. Beaudoin [24
] developed a qualitative course of this dependence, as shown in Figure 2
b. Both of the above parameters depend to a large extent on the way the material is dried, i.e., ultimately on the humidity of the environment in which the cement matrix matures, as the effect of water on the strength of the cement paste is commonly known. The results of [20
] show that a decrease in relative humidity of the environment from 100% to 0% results in an increase in W
from 7 to 14 J/m2
from 0.20 to 0.46 MN/m3/2
. Samples of cement paste soaked in water have a much lower tensile strength than dry ones. In the case of compressive strength, this feature increases slightly after drying the material [36
]. Water, absorbing on the crack walls, shows the pushing pressure, which significantly facilitates the cracking process. On the other hand, the drying process removes the pushing water pressure on the crack planes near the crack limit. This was indirectly confirmed by an experiment conducted by Robertson and Mills [37
]. They soaked the cement paste with organic solvents, which prevented significant reduction of tensile strength when moistened. Large molecules of organic solvents could not penetrate the microcracks, which prevented the pushing pressure.
The analysis of the effect of morphology of hydrated cement matrix on the cracking process was based on the hypothesis that portlandite crystals weaken its structure [38
]. It was found that the cracks largely surround the areas where Ca(OH)2
crystals occur. However, in the light of other studies [39
] it was found that the strength of portlandite is similar to that of the CSH phase. On the other hand, the reason that cracks form relatively easily and run along these crystals is the morphology of the CH crystals themselves in the transition zone and high porosity in ordinary concretes. Ultimately, this results in a reduction in concrete strength. A radical change in this situation occurs when the w/c
ratio is reduced or microsilica is applied. In his considerations, Mindess [18
] believes that empirical formulas combining porosity with strength can be used, but only for the classical cement matrix. In the case of significant modification of the structure resulting, e.g., from the presence of an additive or reactive admixture, or as a result of a hydrothermal treatment, the classical empirical formulas cannot be used.
The properties of concrete are mostly determined by the properties of the cement matrix. It is known that the hydrated cement matrix contains numerous discontinuities in the form of pores, microcracks and voids, which do not necessarily act as defects themselves. A defect can be, e.g., a crack in the grain that is associated with the presence of such a void, or it can be caused by shrinkage or insufficient adhesion. This is a natural situation in a cement composite, taking into account the heterogeneous structure of the material and the way the different phases combine. It has been confirmed [40
] that pores in the cement paste are not the only possible critical defects of the structure. The application of the Griffith’s hypothesis assumes that first of all the voids in an unsegregated cement composite must be distributed at random, which is in line with the actual state of affairs [41
]. Secondly, it is assumed that in the place where the defect exists there is a microscopic destruction, and the unit of material volume containing the weakest place determines the strength of the whole sample. Thus, each crack spreads over the entire section of the specimen subjected to a given stress or, in other words, a phenomenon occurring in an element is identified with the same phenomenon occurring in the entire volume. This occurs under the assumption of an even distribution of stresses and under the condition that the second consecutive weakest point in the material is not capable of carrying a stress n/(n−1)
times greater than the stress at which the weakest point is destroyed, where n is the number of elements in the loaded section, each containing one defect. Thus, colloquially speaking, a cement composite is as strong as its weakest link.
] indicate that in the ITZ and in the cement matrix itself there are very small cracks even before the load is applied to the cement composite. They are most probably the result of unavoidable differences in properties between the aggregate and hydrated cement matrix, combined with shrinkage and thermal stress. Microcracks are observed not only for cement composites of normal strength but also in unloaded concretes of w/c
< 0.25, which mature in moist environment [45
]. According to some studies [46
], it is believed that the microcracks existing before loading are mainly responsible for low tensile strength of the cement composite. The microcracks are defined as cracks with a maximum width of up to 0.1 mm [1
], which usually means the smallest dimension that can be followed by the naked eye.
The process of development of the microcracks under the compressive stress is already known. When a growing load is applied, the cracks remain stable to a load of about 30% of the limit load. Then the microcracks begin to propagate in terms of both length and width, and their number also increases. The stress at which the cracks develop depends on the w/c
ratio of the cement matrix. This state is called as the stable crack propagation. As a result of further increase of the load up to a value between 70–90% of the maximum load, cracks are formed in the mortar. The cracks are then connected to the cracks caused by the breaking of adhesion and thus a certain system of continuous cracks is created, the so-called cracking pattern. This state is called as the state of rapid propagation of the cracks [42
]. The stress level at the beginning of this state is higher in high strength concretes than in normal concretes. The increase in cumulative crack length is very large, while it is lower in high strength concretes [47
]. The beginning of the state of rapid crack propagation corresponds to the point of discontinuity in volumetric deformations. If the load is fixed, the material can be destroyed as a function of time. However, as long as the cracks are stable, their presence is not harmful. This state is characteristic for the whole family of cement composites.
The structural heterogeneity of concrete is sometimes beneficial. For example, when the contact between coarse aggregate and cement paste is the site of local microcracks, it means that the presence of coarse aggregate grains prevents the opening of a single wide crack. These grains act as a blocking factor for the microcracks. The adhesion surfaces in the ITZ are formed at any angle to the direction of external force. As a result, local stresses differ significantly, upwards and downwards, from the nominal applied load. In the cement composite, cracks occur at each level of structural heterogeneity of the material [48
]. Using an electron scanning microscope, the existence of a sub-microcracks was detected in the cement gel. However, there is no clear evidence that these sub-microcracks have a significant effect on concrete strength.
As shown above, the process of cracking and crack propagation is not a simple and unambiguous process. Very often, the formation of a crack may be initiated by one particular cause, and its development may be associated with a different cause [52
]. Under certain physical conditions, the total width of cracks per unit length of the cement composite is usually constant. It is advantageous for the width of cracks to be as small as possible, which results in the fact that it is better if there are more cracks, but with a smaller widths than if there were fewer of them, but with a larger widths [12
]. For example, the introduction of reinforcement controls shrinkage cracks by reducing the width of individual cracks, but does not change the total width of all cracks. The importance of the cracking process and the minimum width of the crack, which is considered significant, depend on the function of the structural element and on the exposure conditions of the cement composite. Table 1
summarizes the classification of cracks occurring in cement composites, together with the reasons for the formation and approximate time of occurrence of a given type of cracks.
The paper provides a literature review of the development process, analysis and impact of the cracking patterns on the properties of cement composites. The review focuses on four main aspects related to the analysis of the cracking patterns:
the process of cracks formation in brittle cement composites and their evolution into an extensive and complex system of cracks,
methods and techniques of digital extraction of the cracking patterns for their further evaluation,
quantitative parameters used to describe the complexity of the cracking patterns,
evaluation of the influence of morphology of the cracking patterns on selected properties of cement composites.
Each of these four aspects requires a different scientific approach, making comprehensive analysis of the cracking patterns a difficult and multidisciplinary issue. The three main scientific areas that underpin this research area are the fracture mechanics, image analysis and cement composites technology.
The factors that determine the cracking process, i.e., the number and type of structure defects and the composition of the material, are discussed. It was found that critical stress intensity factor (KIC) being the product of crack work and Young’s modulus is the most commonly studied parameter which determines the ability of the material to propagate and develop cracks in the branched cracks system. The methodology of analysis of the cracking patterns requires the use of advanced tools for the detection and extraction of cracks. Research carried out so far in this field indicates that by far the most effective and popular group of tools is the computer image analysis. The simplest of them are threshold operations, e.g., the global thresholding, locally adaptive thresholding or the Otsu thresholding. However, such operations, despite the fact that they are simple to implement, are sometimes characterized by a very large detection error. More advanced techniques, such as the genetic algorithms, artificial neural networks or machine learning algorithms, are characterized by very good detection accuracy. Their disadvantage is the need for much more computational resources, which slows down the whole process and makes it sometimes impossible to analyze a large set of data. The literature review shows that the most accurate methods of cracks detection on cement composite surfaces are characterized by an accuracy of more than 95%.
Previous research indicates that the simplest parameter to measure, in terms of the complexity and morphology of the cracking patterns, is the width of the crack opening. However, this indicator does not provide information on the layout and organization of the cracks structure in the material. The parameter that provides this information is the crack density and the resultant the crack spacing. Recent studies postulate the use of fractal geometry to quantify the cracking patterns. In these studies, the concept of fractal dimension is used, which by definition determines the degree of complexity of the analyzed structure. Analyses carried out with the use of this parameter indicate a strong relationship with the mechanical features of a degraded cement composite. In the research results published so far, the greatest attention is paid to determining the influence of the cracking patterns on the performance of cement composites at elevated temperatures. The system of cracks formed due to the shrinkage and drying of the material as well as those formed due to chemical corrosion is also analyzed. The influence of the cracking patterns on water permeability and mechanical strength of cement composites is also evaluated. The presented results indicate that with the progressive development of the cracking patterns, practically every property of the hardened cement composite deteriorates.
The authors of many research point to the key importance of the degree of development of the cracking patterns for the functional properties and durability of cement composites. However, there are still few works in which the dependence of the cracking patterns on the physical and mechanical properties of the material is determined directly, in a numerical way. Knowledge in this area seems to be crucial in the aspect of designing durable cement composites, which would be resistant to cracking and crack development process in specific environments. From the methodological point of view, further development of works aimed at developing more and more accurate, automatic crack detection systems is indicated. Such systems could be used very successfully by building managers to effectively detect areas in need of remedial action. The search for new methods and the development of the relationship between the cracking patterns and material properties is crucial in the development of non-destructive testing methods in cement composite technology.