Crack Resistance of Paint Coatings, Cement Concretes

Information on the method for assessing the crack resistance of paint and varnish coatings is given. A method is proposed, based on the ratio between the length of the crack, the Vickers indenter imprint, and the fracture toughness. Numerical values and stress intensity factor in coatings are given, depending on the type and duration of aging, porosity of the cement substrate, and the quality of the appearance of the coatings. It is established that with an increase in the roughness of the coating surface, the value of the stress intensity coefficient is increased. The increase in the moisture content of the substrate at the time of application of the paint composition leads to the appearance of a more defective structure of the contact layer “coating-substrate” and a greater propensity to cracking. It is revealed that there is a value of the optimum substrate moisture, for each particular coating in terms of its fracture toughness. It is shown that during the aging of protective and decorative coatings of the exterior walls of buildings, a mechanism of their destruction from elastic ductile to brittle changes occurs.


Introduction
Building and maintaining the working condition of buildings and structures require a large number of paint and varnish compositions. Growing competition in the market of finishing materials, increasing demands of consumers require manufacturers to obtain high-quality painted surfaces. However, the practice of finishing works shows that often the quality of the finish is bad. It leads to premature unscheduled repairs and additional costs.
Coatings for finishing facades of buildings must have a high-quality appearance. The conditions for obtaining and the quality of the appearance of cured inking coatings largely depend on the rheological properties of paint and are determined by the processes of wetting and application of paint. In literature, the quality of the appearance of coatings on metal substrates is studied. When selecting paint systems for concrete, the features of this material (strength, roughness, humidity, alkalinity, etc.) should be taken into account. Features of concrete affect the quality coating.
In this regard, the development of a methodology for ensuring the quality of the painted surface of building products and structures and control methods is an important scientific, technical, and economic problem. The solution of this problem as a whole will contribute to an increase in the service life of protective and decorative coatings. One of the common types of destruction of coatings of cement concrete is the appearance of cracks. There are known works [1][2][3][4][5][6][7][8] in which the regularities of the appearance of cracks in coatings on metal substrates are described. However, the resistance of coatings of cement concrete has not been studied sufficiently.

Stress state of coatings under exposure operational factors
For analysis, the reasons for the destruction of the paint and varnish facades of buildings were used, the Pareto diagram, allowing for a variety of existing defects to distinguish those that make a significant contribution to the assessment of the quality of the appearance of coatings. When analyzing the Pareto chart, the 80/20 rule was used. For example, priority factors were identified, which fall into 80% of the cumulative curve [9][10][11][12][13][14][15][16]. The survey was carried out on residential 5-storey houses, which are located in accordance with GOST 9.039-74 "Corrosive aggressiveness of the environment" in the climatic region IY (moderately cold) and GOST 16350-80 "Climate of the USSR. Regionalizing and statistical parameters of climatic factors for technical purposes." The facades were painted with calcareous and cement per chlorinated vinyl CPCV paints. Colorful compositions were applied to the plaster thickness of 1.5-2 cm. When inspecting the painted surface, the following types of defects were detected: cracking, flaking, weathering, dirt retention of coatings, wet spots, and different tonality. The number and types of defects were determined visually (GOST 9.407-2015 Unified system of protection against corrosion and aging. PAINTWOOD COATINGS. Appraisal method). The names of the types of defects and the number of their appearances for calcareous and CPCV coatings that take after different service lives are given in Table 1.
Pareto diagrams with all types of defects for their calcareous CPCV coatings are shown in Figures 1-3. Analysis of survey results indicates that the list of defects in coatings, constituting 80% of the cumulative curve, consists mainly of cracks along the vertical joint at the end of the building, different tonality of color, and peeling. All of these factors remain constant for both coatings. This allows us to consider them a source of "failure" regardless of the type of coating. In this case, such a defect as cracks in the coating along the vertical joint of the panels goes in the Pareto diagram in the first place and is 22.6-66.6% of the total number of defects, depending on the type of coverage and exploitation term.
As the coatings age, there is a change in the specific gravity of the priority defects that affect the quality of their appearance, as well as the appearance of new types of defects. Therefore, after 3 years of operation of the calcareous coating, defects such as flaking of the coatings at the base of the metal roofs of the porch and at the ends of the fencing panels of the loggias are observed, the total specific gravity of which is 41.4%. The priority defects after 5 years of operation include cracks in the coating, along the vertical joint at the end of the building, exfoliation coating, and different tonality of color. A similar list of defects is also characteristic for CPCV coatings. Of this follows that the efforts of all specialists in developing the formulation of building paint compositions, the technology of their application should be aimed at increasing the crack resistance of protective-decorative coatings, since this type of defect is the most characteristic and widespread.   Results of the experimental researches testify that in use of protective-decorative coatings of external walls of buildings, there is a change of the mechanism of their destruction from elastic-plastic to friable, that is, "embrittlement" of coatings is observed. According to the linear mechanics of destruction, a cracking fissuring of coatings happens [17,18], if -critical value of coefficient of intensity of tensions.
Considering that a main type of destruction of protective-decorative coatings is cracking fissuring, it is of practical interest to estimate parameters of crack formation of coatings during an aging. At present, there are several methods for assessing the crack resistance of coatings [19][20][21][22]. The determination of critical coefficient of intensity of tensions К 1с was carried out by  us according to the technique [23] based on a ratio between the crack length, a print of the Vickers indenter, and viscosity of destruction. We are invited to assess the cracking of polymer coatings using the technique, based on the ratio between the crack length, the Vickers indenter print, and the fracture toughness. This technique is successfully used to assess the fracture toughness (K 1c ) of ceramics.
In this method, the value of the stress intensity factor K 1c is determined from the length of the radial cracks formed in brittle materials from the corners of the Vickers indentation. To obtain a semi-empirical dependence of the length of radial cracks on crack resistance and hardness, the approach proposed by A. Evans and E. Charles is used. Dependence "normalized crack resistance (К 1с /Нα 1/2 )⋅(Н/Е) 1/2 -normalized length of radial cracks С/α" is described by the following equation: where H is Vickers hardness; A and B are empirical coefficients.
From expression (2), we obtain: If the value of hardness does not depend on the load on the indenter, then Eq. (3) can be written in the form: where P is the load on the Vickers indenter.
The most common semi-empirical equation of this type is given as follows: where H is Vickers hardness; E: the modulus of elasticity; C: half-length of radial cracks; α: half-length of the diagonal of the print.
The critical coefficient of intensity of tensions was determined by a formula: where hardness by Vickers; Р: loading on indents; a: semi-length of print diagonal.
As colorful structures in the work, polyvinyl acetate cement PVAC and polymer-calcareous paints were applied, and as a substrate-cement and sand solution. After curing, the painted solution exemplars were subjected to alternate freezing and thawing and also to humidification and a thermal aging. During tests with the help of Vickers indenter, we measured a print diameter and length of radial cracks which are formed on both sides from a print. Hardness by Vickers was calculated on a formula: where d: diameter of a print; α : angle at indenter top.
The dependence of the size of the semi-diagonal of the imprint on the load on the indenter is described by the equation: The exponent is 0.5, as it should be when the hardness of the material does not depend on the magnitude of the load. The dependence of the length of radial cracks on the load is fairly accurately approximated by an equation of the form: In order that the critical value of the intensity factor К 1с , measured by the method of indentation, did not depend on the load, exponent must be equal to 2/3 ( ≈ 0.67 ). The results of previous research work show that most protective and decorative coatings have a fragile character of destruction, which gives grounds to apply this technique to assess the crack resistance of paint and varnish coatings. From the experimental data obtained, a correlation was established between the semi-diagonal of the imprint and the load on the indenter P, which is described by expression (8).
For the PVAC coatings tested after curing obtained dependence For polymer-calcareous coatings For coatings based on oil paint For coatings KO-168 Eqs. (10)- (13) indicate that the exponent a is a = 0.5, that is, this should be the case if the hardness is independent of the load in accordance with Eq. (8). After a certain duration of thermostating of the coatings, a decrease in coefficient A in Eq. (8) indicates an increase in their hardness. So, for example, after 100 h of thermostating, the following dependences were obtained: For the PVAC coatings For polymer-calcareous coatings For coatings based on oil paint The analysis of the obtained results testifies that the dependence of the half-length of radial cracks C on the load P in the coatings is approximated by the equations: For polymer-calcareous coatings For the PVAC coatings For coatings KO-168 In the work applied, the following types of paints are listed in Table 2.
The results of experimental studies indicate that in the process of aging protective-decorative coatings of external walls of buildings, there is a change in the mechanism of their destruction from elastic-plastic to brittle, that is, "embrittlement" of coatings is observed [24][25][26][27][28][29]. Test results are provided in Table 3. It was established that in PVAC and the polymer-calcareous coatings on a solution substrate, the "embrittlement" occurs after a particular duration of impact of alternate freezing and thawing. The presence of a crack was determined visually and also with the aid of a magnifier at a magnification of 30 times.
The critical coefficient of intensity of tensions was determined by formula (6). The size of the diagonal of the Vickers indenter print was measured using a magnifier. Cracks in coatings at cave-in of an indenter Vickers appear only after 15-20 testing cycles. The value of critical coefficient of intensity of tensions of PVAC coating is equal to K 1c = 0.088 MH/m 3/2 , and for polymer-calcareous coating, K 1c = 0.069 MH/m 3/2 .
Introduction into a compounding of PVAC paint, the fibrous asbestos increases crack resistance of coatings. Thus, even after 20 cycles of alternate freezing-thawing, the "embrittlement" of coating is not observed. The comparative analysis of data shows that at the same intensity of influences of the environment coatings with a fibrous asbestos possess the smaller value of coefficient of intensity of tensions, after eight cycles of alternate freezing-thawing K 1 (PVAC) = 0.078 MH/m 3/2 and K 1 (PVAC with 1% of asbestos) =0.073 MH/m 3/2 .
Humidification of coatings leads to a decrease of an elastic modulus and hardness of coatings that reduces a danger of crack formation at deformation of a wall construction. Humidification of coatings for 30 days does not cause crack fissuring of coatings. The coefficient of intensity of tensions of PVAC coating after curing is equal to K 1c = 0.06 MH/m 3/2 , and after humidification K 1c = 0.054 MH/m 3/2 . Similar data are obtained and for the polymer-calcareous coatings.
At studying a thermo aging, it was recorded that the increase of time of thermoaging leads to natural increase of value of coefficient of intensity of tensions. For example, after a thermoaging of polymer-calcareous coatings for a 100-h increase, the value of coefficient of intensity of tensions is observed from K 1c = 0.044 MH/m 3/2 (after curing) to KK 1c = 0.053 MH/m 3/2 , and after 200 h value makes KK 1c = 0.0546 MH/mm 3/2 . Considering that properties of a protective-decorative coatings are defined among other factors by properties of the painted construction and are heterogeneous on an extension, we followed up and carried out the calculation of tensions arising in coatings as a result of the influence of various factors according to a technique [30]. It will allow approaching the choice of materials research factors of the increase of crack resistance of coatings more reasonably. The conducted researches are justification for recommendations at developing the compounding of colorful structures, at carrying out research works with the use of technique of an assessment of crack resistance of coatings according to the offered scheme.
It will allow to more reasonably predict firmness of coatings and also to optimize finishing structures for the purpose of receiving coatings with a complex of the given properties. Nitrocellulose NC-123 60-100 3 1 3 Polymer-calcareous 40-60 24 2 5 Acrylate class "Universal" 40-60 3 Table 2. Technical characteristics of the paints.

Persistence of varnish-and-lacquer coatings to cracking in the process of environmental impact
In accordance with the statistical theory of the strength of solids, the probability of destruction of coatings is determined by the presence and concentration of defects, including on the surface of the coatings. Thus, the quality of the appearance of the coatings among other factors   Table 5. Crack resistance of coatings depending on the quality of their appearance in the process of moistening-drying.
Coatings and Thin-Film Technologies "Universal," and acrylic water dispersion paint (facade). Different quality of the appearance of the coatings was created by changing the porosity of the substrate and the rheological properties of the paint compositions. During the tests, the colored solution samples were subjected to various types of corrosion attack, namely alternating freezing-thawing according to the regime: 4 h freezing at a temperature of −18°C, 20 h of thawing, moistening-drying according to the regime: 20 h of moistening at room temperature and 4 h of drying at a temperature of 60°C.
During the experiment, the concentration of defects on the surface of the coating was also determined. The number of defects was determined on the surface area of 64 cm 2 . The coating surface roughness was determined by profilograph TR-100 state. The results of the studies are given in Tables 3 and 4. It was found that during the test, the cracks appear locally and are formed near the defects on the surface of the coating. In particular, after five test cycles on the surface of the coating based on MA-15 paint, surface roughness, R a = 0.23 μm, surface cracks visible to the naked eye appeared, and on the coating with a roughness index Ra = 0.14 μmafter 15 test cycles. Similar patterns are also characteristic for other coatings ( Table 4). It is established that with an increase in the roughness of the coating surface, the value of the stress intensity coefficient is increased. Therefore, for example, the surface roughness of a coating based on PF-115 ink is R a = 0.12 μm, the stress intensity factor K 1 = 0.01561 MN/m 3/2 , a decrease in the roughness of the coating surface Ra = 0.08 μm leads to a decrease in the stress intensity factor to K 1 = 0.01002 MN/m 3/2 . Similar patterns are also characteristic for other types of coatings.
The results ( Table 5) show that the nature of the destruction of the coatings during the corrosive action of the medium is not the same. Therefore, coatings based on oil and alkyd paint are characterized by peeling, coatings based on acrylate class Universal, nitrocellulose, and water dispersion paint-cracking. Regardless of the type of coating and the corrosive effect of the medium, there is an increase in the roughness of the coating surface and coefficient of intensity of stresses.

The influence of the porosity of the substrate on crack resistance of protective-decorative coating
The operational stability of protective-decorative coatings of the outer walls of buildings is significantly influenced by processes occurring both in the coating itself and at the interface of the "substrate-coating" contact [6]. The strength of the adhesion of protective-decorative coatings to the concrete substrate depends significantly on the quality of the substrate. The quality of the substrate, first of all, is understood as its macro-and microstructure, the degree of its homogeneity, providing the desired solidity contact layer, its density, and porosity. Features of the porous substrate, such as cement concrete, mortar, and so on, have a significant effect on the formation of the structure and properties of the coatings applied. The analysis of the results ( Table 6) indicates that the porosity of the substrate has a great influence on the nature of the destruction of the protective and decorative coating. At the same time, it should be noted that the nature of the destruction, for example, of PVAC coatings, has a significant difference from polymer-based coatings. Thus, for example, an increase in the porosity of the substrate from 20 to 28% leads to a reduction in the crack resistance of polymer-calcareous coatings.

Coatings and Thin-Film Technologies
The appearance of cracks in indentation of the Vickers indenter in a polymer-calcareous coating on substrates with a porosity of P = 20% is observed after 20 cycles of freezing-thawing. The critical coefficient of intensity of stresses is K 1c = 0.06 MN/m 3/2 . At porosity of the substrate, P = 28%, the appearance of cracks in indentation of the Vickers indenter occurs in the coatings after 14 cycles of freezing-thawing. This is explained by the appearance of a more inhomogeneous stress state in the coating. For PVAC coatings, it is characteristic that the fracture toughness increases with increasing porosity of the substrate from 20 to 28%. The critical value of coefficient of intensity of stresses for PVAC coatings in substrate porosity of 20% is K 1c = 0.088 MN/m 3/2 . In this case, the appearance of cracks in the coating during the introduction of the Vickers indenter was recorded after 11 cycles of freezing-thawing. With a substrate porosity of 28%, the appearance of cracks is observed only after 15 cycles of freezing-thawing.
However, the change in the coefficient of intensity of stresses for PVAC coatings is extreme. So, for example, when using as a substrate of brick samples with a porosity of P = 40%, the fracture toughness of PVAC coatings is significantly reduced. Thus, the presence of cracks at the indentation of Vickers indenter is observed after five cycles of freezing thawing.
Preliminary preparation of the substrate surface has a significant effect on the crack resistance of protective and decorative coatings. So, for example, priming the surface of the substrate leads to an increase in the crack resistance of the coatings. At the same time, the appearance of cracks with the indentation of the Vickers indenter in the PVAC coating on a substrate with a porosity of P = 20% was observed after 15 cycles of alternating freezing-thawing. For some types of coatings PF-115 and water dispersive acrylate paint of the "Universal" class, it is very important in advance application of putty to the surface before staining to reduce the porosity of the substrate. This leads to an increase in the crack resistance of these coatings. Thus, the coefficient of the intensity of stresses of the acrylate coating applied to the surface of the substrate after its preliminary preparation was 0.004 MN/m 3/2 , while without preparation-0.027 MN/m 3/2 .
It was found that in coatings, "embrittlement" occurs after a certain time of moistening. Thus, cracks in the coatings with the indentation of the Vickers indenter appear on the coating of PF-266 on a substrate with a surface porosity of P = 0% and on a substrate with a surface porosity of P = 6.2% and humidity at the application of paint of 9.9%. For coatings MA-115 on a substrate with P = 6.7% and humidity at the time of application of paint W = 10.2%, peeling of the coating after 2 months of moistening is characteristic. Analysis of the experimental data ( Table 7) shows that with increasing surface porosity of the substrate, a decrease in the stress intensity factor is observed up to a certain limit. Thus, with a load П = 25.39 N, the value of the stress intensity factor K c for coating PF-115 on a substrate with a surface porosity P = 0.13-1.2% after 2 months of moistening is K c = 0.0376МН/m 1.5 , and on a substrate with a surface porosity, P = 10.5%-0.0256 МН/m 1.5 , and for the MA-15 coating, the values of the stress intensity factor are, respectively, 0.0257 МН/м 1.5 and 0.02147 МН/m 1.5. .
Obviously, this is due to the fact that the pores on the surface of the substrate to some extent "extinguish" internal stresses and reduce the tendency to crack coatings. Increasing the substrate moisture at the time of application of the paint results in a more defective structure of the contact layer "coating-substrate" and a greater propensity to cracking. The stress intensity factor for PF-115 coatings at substrate moisture at the time of application of a paint composition equal to W = 10.4% after 2 months of wetting is K c = 0.404 МН/m 1.5 . Among other factors, the state of the painted surface of the facades of buildings is determined by the time of application of the paint. So, for example, if the paint is applied in April-May, when the moisture of the substrate and the coating is high due to moisture migration from the side of the wall material, this can lead to premature failure of the coating. We evaluated the effect of substrate moisture on the properties of protective and decorative coatings, in particular, on their crack resistance. The analysis of the results ( Table 8) shows that the substrate moisture at the time of application of paint has a significant effect on the crack resistance of the coatings. For example, when PVAC coating is applied to a dry surface, the appearance of cracks in the coating when Vickers indenter is introduced occurs after 20 cycles of freezing-thawing, the critical value of the stress intensity factor being K 1c = 0.09 MN/m 3/2 . An increase in the initial moisture content of the substrate to W = 1% leads to a significant increase in the fracture toughness of the PVAC coating, with the appearance of cracks in the introduction of the Vickers indenter only after 25 cycles of freezing-thawing. A further increase in the substrate moisture during painting leads to the appearance of a more defective structure of the contact layer "coating-substrate" and a greater tendency of the coating to crack formation. Thus, an increase in substrate moisture to W = 4% led to the appearance of cracks in the introduction of the Vickers indenter after 10 cycles of freezing-thawing.
The results of the analysis of fracture toughness indexes of coatings PF-115 indicate that after 15 cycles of freezing-thawing, the coefficient of intensity of stresses in coatings on absolutely dry substrate is K 1 = 0.057 MN/m 3/2 , whereas for substrate moisture W = 4%-  freeze-thaw cycles. The obtained results make it possible to assume that an increase in the moisture content of the substrate leads to a significant decrease in internal stresses in the coating, which is apparently due to a decrease in the adhesion strength due to the presence of moisture on the surface of the substrate. However, for different types of coatings, the optimum moisture content of the substrate is characteristic. Increasing the optimum moisture content of the substrate leads to a decrease in the crack resistance of coatings.
Thus, the value of the moisture content of the substrate, established in the regulatory and technical documentation, in particular, W = 8% for water paint, is not correct. There is a value for the optimum moisture content of the substrate for each particular coating in terms of its fracture toughness. It is necessary to conduct extensive research to create a databank on the influence of substrate moisture on the crack resistance of protective and decorative coatings. This will help in the future to develop measures to create crack-resistant coatings.

Conclusion
A method for evaluating the fracture toughness of coatings of cement concrete is proposed. This is a method based on the relationship between the crack length, the Vickers indenter  imprint, and the fracture toughness that is proposed. The numerical values of the coefficient of intensity of stresses in coatings are given, depending on the type and duration of aging, the porosity of the cement substrate.
It is established that with an increase in the roughness of the coating surface, the value of the stress intensity coefficient is increased. Increasing the substrate moisture at the time of application of the paint composition results in a more defective structure of the contact layer "coating-substrate" and a greater propensity to cracking. It has been revealed that there exists a value for the optimum substrate moisture for each particular coating in terms of its fracture toughness. It is shown that during the aging of protective and decorative coatings of the exterior walls of buildings, a mechanism of their destruction from elastic-ductile to brittle changes occurs.
The conducted researches are justification for recommendations at developing paints, at carrying out of research works with use of technique of an assessment of crack resistance of coatings according to the offered scheme. It will allow to more reasonably predict firmness of coatings and also to optimize finishing structures for the purpose of receiving coatings with a complex of the given properties.