**Abstract**

Information is given on the strength of the coatings of cement concrete for the exterior walls of buildings. It was found that the strength of the coating depends on the quality of its appearance. A strength model is proposed depending on the surface roughness of the coating. The influence of the scale factor on the change in the strength of coatings is established. To assess the long-term strength of the coatings, we studied the temperature-time dependence of strength. The values of the activation energy of the destruction process of some coatings are experimentally determined. The dependence of the long-term strength of the coatings on tensions is given. The kinetics of changes in the short-term strength of coatings during aging is considered from the perspective of the kinetic concept of the strength of solids. The condition for coating cracking is obtained. Taking into account the influence of the scale factor and the conditions of brittle fracture of coatings, a method for choosing the optimal coating thickness is proposed.

**Keywords:** coatings, structure, properties, coating strength, coating appearance quality, mathematical model of strength

#### **1. Introduction**

Construction and maintenance of buildings and structures require a large number of paints. The share of building paints and varnishes, including repair materials, accounts for up to 5–55% of the total volume of manufactured paints and varnishes, of which 46–48% are paints and 5–8% are varnishes. The main market share of coatings is architectural and decorative coatings.

Currently, for the decoration of building facades, compositions based on polymer binders are widely used: water-dispersion, perchlorovinyl, organosilicon, polymer-cement, silicate paint, sol silicate, and polymer silicate paint [1–3]. The proportion of organosoluble products in the total consumer market of paints and varnishes has now stabilized at about 15%, and the share of water-dispersion varnishes and paints is more than 60%.

The problem of reliability and durability of protective and decorative coatings of the exterior walls of buildings is one of the urgent scientific and technical problems in the field of materials science [4, 5]. It is known that the durability of coatings depends on the type of binder, the technology of applying the paint composition, operating conditions, etc. [6–8].

Crack resistance is the main characteristic that characterizes the durability of finishing coatings. The main reasons for the occurrence of cracks are significant

shrinkage deformations that occur during the hardening of finishing coatings as well as during operation. The property values of the coats on a cement backing are known to be variable and depend on a number of factors (the roughness and porosity of the backing, technological factors, etc.) [9, 10]. However, at present, many issues of strength and durability of coatings of cement concrete are not considered.

### **2. Strength of protective and decorative coatings**

One of the most common types of destruction of coatings is cracking and peeling [11]. Coating cracking occurs when internal tensile stresses reach the cohesive strength of the coating material, i.e.,

$$
\sigma = \mathbb{R} \text{ kog} \tag{1}
$$

*<sup>Е</sup>upr* <sup>¼</sup> *<sup>R</sup>*<sup>0</sup>

the physicomechanical properties of paint coatings. It is revealed that the

from the chart "tension deformation," MPa, and *ε*<sup>0</sup>

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

where *R*<sup>0</sup>

69.4 kgf/cm<sup>2</sup>

**Figure 1.**

**Figure 2.**

**257**

*based of paint PF-115.*

*on paint PS-160.*

time of rupture, %.

*kogi ε*0 *i*

The presence of defects on the surface of the coatings will undoubtedly affect

elastoplastic character of the destruction is characteristic for the coatings studied. Regardless of the type of paint composition, the strength and relative deformations are reduced, the plastic deformation is increased, and the elastic surfaces are reduced with increasing roughness (**Figures 1**–**4**) [13]. Thus, when the surface of coating roughness based on paint PS-160 is Ra = 0.74 μm, the tensile strength *Rp* is

*Dependence of the tensile strength (1) and the relative elongation (2) on the roughness of the film surface based*

*Dependence of the tensile strength (1) and the relative elongation (2) on the roughness of the film surface on*

*kogi* is the ultimate tensile strength at the time of the tangent separation

, the relative strain *ε* = 3.1%, and with a roughness Ra = 0.86 μm - *Rp* =

� 100 (4)

*<sup>i</sup>* is the relative lengthening at the

Thus, to assess the resistance of coatings to cracking, it is necessary to identify patterns of change in the strength of coatings.

The presence of defects on the surface of coatings will undoubtedly affect the physicomechanical properties of coatings.

The probability of destruction of protective and decorative coatings depending on the presence of defects on their surface can be defined by the formula:

$$P = \mathbf{1} - e^{-\rho \mathbf{S}} \tag{2}$$

where *p* is the defect concentration and *S* is the surface area.

As can be seen from formula (2), for the same surface area S, the probability of coating failure increases with increasing defect concentration [8].

In the study the following paint is used: alkyd enamel PF-115 grade, polystyrene paint brands PS-160, silicone enamel КО-168, polyvinyl acetate cement (PVAC) paint, silicate paint, polymer-lime paint, lime paint, and perchlorovinyl XB-161.

The surface roughness of the paintwork was evaluated which is determined by profilograph TR-100 [12].

Assessment deformation of coating was carried out with the help of a tensile machine IR 5057–50 with the samples after 28 days of curing. The method is based on the sample stretching until it ruptures (deformation speed of 1 mm/minute).

The 1 � 1 � 5 cm samples were fixed in the clips of the tensile machine so that their longitudinal axis was in the direction of stretching and the force was applied equally all over the sample section. The tests were carried out at the temperature of 20°C and relative air humidity of 60%. The ultimate tensile strength estimation was carried out for not less than four samples of each compound. The ultimate tensile strength Rkog for each sample is derived from the formula:

$$R\_{\rm kog} = \frac{F\_{\rm Pi}}{\mathcal{S}\_{Oi}} \tag{3}$$

where *FPi* is the stretching loading at the time of a rupture, N, and *S<sup>О</sup><sup>i</sup>* is the initial cross-sectional area of a sample, mm<sup>2</sup> .

The modulus of elasticity was calculated according to the chart "tension deformation" on an inclination tangent of angle to abscissa axis of the tangent, which was drawn to an initial straight section of the chart.

The modulus of elasticity for each sample (Eupr) in MPa is derived from the formula:

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

$$E\_{upr} = \frac{R\_{kogi}'}{\varepsilon\_i'} \cdot \mathbf{100} \tag{4}$$

where *R*<sup>0</sup> *kogi* is the ultimate tensile strength at the time of the tangent separation from the chart "tension deformation," MPa, and *ε*<sup>0</sup> *<sup>i</sup>* is the relative lengthening at the time of rupture, %.

The presence of defects on the surface of the coatings will undoubtedly affect the physicomechanical properties of paint coatings. It is revealed that the elastoplastic character of the destruction is characteristic for the coatings studied.

Regardless of the type of paint composition, the strength and relative deformations are reduced, the plastic deformation is increased, and the elastic surfaces are reduced with increasing roughness (**Figures 1**–**4**) [13]. Thus, when the surface of coating roughness based on paint PS-160 is Ra = 0.74 μm, the tensile strength *Rp* is 69.4 kgf/cm<sup>2</sup> , the relative strain *ε* = 3.1%, and with a roughness Ra = 0.86 μm - *Rp* =

#### **Figure 1.**

shrinkage deformations that occur during the hardening of finishing coatings as well as during operation. The property values of the coats on a cement backing are known to be variable and depend on a number of factors (the roughness and porosity of the backing, technological factors, etc.) [9, 10]. However, at present, many issues of strength and durability of coatings of cement concrete are not

One of the most common types of destruction of coatings is cracking and peeling

Thus, to assess the resistance of coatings to cracking, it is necessary to identify

The presence of defects on the surface of coatings will undoubtedly affect the

The probability of destruction of protective and decorative coatings depending

As can be seen from formula (2), for the same surface area S, the probability of

In the study the following paint is used: alkyd enamel PF-115 grade, polystyrene paint brands PS-160, silicone enamel КО-168, polyvinyl acetate cement (PVAC) paint, silicate paint, polymer-lime paint, lime paint, and perchlorovinyl XB-161. The surface roughness of the paintwork was evaluated which is determined by

Assessment deformation of coating was carried out with the help of a tensile machine IR 5057–50 with the samples after 28 days of curing. The method is based on the sample stretching until it ruptures (deformation speed of 1 mm/minute). The 1 � 1 � 5 cm samples were fixed in the clips of the tensile machine so that their longitudinal axis was in the direction of stretching and the force was applied equally all over the sample section. The tests were carried out at the temperature of 20°C and relative air humidity of 60%. The ultimate tensile strength estimation was carried out for not less than four samples of each compound. The ultimate tensile

> *<sup>R</sup>*kog <sup>¼</sup> *FPi SOi*

where *FPi* is the stretching loading at the time of a rupture, N, and *S<sup>О</sup><sup>i</sup>* is the

The modulus of elasticity for each sample (Eupr) in MPa is derived from the

. The modulus of elasticity was calculated according to the chart "tension deformation" on an inclination tangent of angle to abscissa axis of the tangent, which was

*P* ¼ 1 � *e*

on the presence of defects on their surface can be defined by the formula:

where *p* is the defect concentration and *S* is the surface area.

coating failure increases with increasing defect concentration [8].

strength Rkog for each sample is derived from the formula:

initial cross-sectional area of a sample, mm<sup>2</sup>

drawn to an initial straight section of the chart.

σ ¼ R kоg (1)

�*ρ<sup>S</sup>* (2)

(3)

[11]. Coating cracking occurs when internal tensile stresses reach the cohesive

**2. Strength of protective and decorative coatings**

strength of the coating material, i.e.,

*Engineering Steels and High Entropy-Alloys*

patterns of change in the strength of coatings.

physicomechanical properties of coatings.

profilograph TR-100 [12].

formula:

**256**

considered.

*Dependence of the tensile strength (1) and the relative elongation (2) on the roughness of the film surface based on paint PS-160.*

#### **Figure 2.**

*Dependence of the tensile strength (1) and the relative elongation (2) on the roughness of the film surface on based of paint PF-115.*

For films based on PS-160 paint, model (5) has the form

For films based on PF-115 paint,

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

**Figure 5.**

**Figure 6.**

*paint.*

**259**

depending on the surface roughness of the coatings.

*Dependence of cohesive strength of PVAC coatings on their thickness.*

change in tensile strength of PVAC and silicate of the coating.

based on a mixture of water glass and styrene acrylic dispersion.

*Rp* ¼ 110*:*5 � *e*

*Rp* ¼ 114*:*5 � *e*

The presented models make it possible to evaluate the expected tensile strength

The influence of the scale factor on the tensile stress of the films is revealed. **Figures 5** and **6** show the results of a study of the effect of film thickness on a

An analysis of the data shows in **Figure 5** that an increase in the thickness of liquid glass-based films from 0.16 to 0.52 mm leads to a decrease in tensile strength from 9.44 to 5.56 MPa, respectively. Similar patterns are also characteristic of films

An analysis of the data obtained (**Figures 5** and **6**) shows that the dependence of the tensile strength on the film thickness can be approximated by the expression

*Dependence of cohesive strength on film thickness: (1) based on silicate paint; (2) based on polymer silicate*

�0*:*761�*Ra* (6)

�0*:*548�*Ra* (7)

#### **Figure 3.**

*Tensile diagrams of films based on PS paint, 160: (1) roughness of 0.74 μm; (2) roughness of 0.77 microns; (3) roughness of 0.8 microns; (4) roughness of 0.86 microns; (5) roughness 1.2 μm.*

#### **Figure 4.**

*Tension diagrams of films based on PF paint, 115: (1) roughness 1.2 μm; (2) roughness of 1.37 μm; (3) roughness of 1.45 μm; (4) roughness of 1.54 microns; (5) roughness of 1.74 μm.*

50.5 kgf/cm<sup>2</sup> and 1.75%, respectively. At a roughness of the film based on the paint PF-115 Ra = 0.74 μm, the tensile strength *Rp* is 57.7 kgf/cm<sup>2</sup> , and the relative strain *ε* = 44.3%, at a roughness Ra = 1.74 μm - *Rp* = 44.1 kgf/cm<sup>2</sup> and 23%, respectively.

For films on the basis of the investigated paint, the flowing character of the curve "tensile strength-roughness" with a sharp decline in strength to a certain value is observed, constituting 45–55 kg/cm<sup>2</sup> at the roughness of the film, respectively, on the basis of the paint PF-115 (1.4–1.6 micrometers) and on the basis of the paint PS-160 (0.8–1 microns). With further increase in the roughness of the film surface, at least a significant reduction in tensile strength is observed.

Analysis of the data shown in **Figures 1** and **2** shows that the dependence of the tensile strength on the roughness of the surface of the films can be approximated by an expression of the form

$$R\_p = \mathfrak{a} \cdot e^{b \cdot R\_s} \tag{5}$$

where *Ra* is the surface roughness, μm; b is the coefficient that takes into account the degree of reduction in strength from roughness, μm�<sup>1</sup> ; and a is the coefficient that characterizes the value of tensile strength, at *Ra* = 0 (ideal model).

For films based on PS-160 paint, model (5) has the form

$$R\_p = \mathbf{110.5} \cdot e^{-0.\Im \mathbf{1} \cdot \mathbf{R}\_s} \tag{6}$$

For films based on PF-115 paint,

$$R\_p = \mathbf{114.5} \cdot e^{-0.548 \cdot R\_s} \tag{7}$$

The presented models make it possible to evaluate the expected tensile strength depending on the surface roughness of the coatings.

The influence of the scale factor on the tensile stress of the films is revealed. **Figures 5** and **6** show the results of a study of the effect of film thickness on a change in tensile strength of PVAC and silicate of the coating.

An analysis of the data shows in **Figure 5** that an increase in the thickness of liquid glass-based films from 0.16 to 0.52 mm leads to a decrease in tensile strength from 9.44 to 5.56 MPa, respectively. Similar patterns are also characteristic of films based on a mixture of water glass and styrene acrylic dispersion.

An analysis of the data obtained (**Figures 5** and **6**) shows that the dependence of the tensile strength on the film thickness can be approximated by the expression

**Figure 5.** *Dependence of cohesive strength of PVAC coatings on their thickness.*

#### **Figure 6.**

50.5 kgf/cm<sup>2</sup> and 1.75%, respectively. At a roughness of the film based on the paint

*Tension diagrams of films based on PF paint, 115: (1) roughness 1.2 μm; (2) roughness of 1.37 μm;*

*Tensile diagrams of films based on PS paint, 160: (1) roughness of 0.74 μm; (2) roughness of 0.77 microns;*

*(3) roughness of 0.8 microns; (4) roughness of 0.86 microns; (5) roughness 1.2 μm.*

*Engineering Steels and High Entropy-Alloys*

*ε* = 44.3%, at a roughness Ra = 1.74 μm - *Rp* = 44.1 kgf/cm<sup>2</sup> and 23%, respectively. For films on the basis of the investigated paint, the flowing character of the curve "tensile strength-roughness" with a sharp decline in strength to a certain value is observed, constituting 45–55 kg/cm<sup>2</sup> at the roughness of the film, respectively, on the basis of the paint PF-115 (1.4–1.6 micrometers) and on the basis of the paint PS-160 (0.8–1 microns). With further increase in the roughness of the film

Analysis of the data shown in **Figures 1** and **2** shows that the dependence of the tensile strength on the roughness of the surface of the films can be approximated by

where *Ra* is the surface roughness, μm; b is the coefficient that takes into account

*Rp* ¼ *a* � *e*

, and the relative strain

*<sup>b</sup>*�*Ra* (5)

; and a is the coefficient

PF-115 Ra = 0.74 μm, the tensile strength *Rp* is 57.7 kgf/cm<sup>2</sup>

*(3) roughness of 1.45 μm; (4) roughness of 1.54 microns; (5) roughness of 1.74 μm.*

the degree of reduction in strength from roughness, μm�<sup>1</sup>

an expression of the form

**Figure 3.**

**Figure 4.**

**258**

surface, at least a significant reduction in tensile strength is observed.

that characterizes the value of tensile strength, at *Ra* = 0 (ideal model).

*Dependence of cohesive strength on film thickness: (1) based on silicate paint; (2) based on polymer silicate paint.*

$$R\_p = Ah^b \tag{8}$$

where *h* is the film thickness.

Mathematical data processing (curves 1 and 2, **Figure 6**) showed that they are well described by the expression:

For silicate-based films

$$R\_p = \text{5.030h}^{-0.37} \tag{9}$$

For films based on polymer silicate paint

$$R\_p = 0.88 \text{\textdegree} h^{-1.3} \tag{10}$$

The point of intersection projected on the x-axis will be the critical volume concen-

*The dependence of viscosity on the volume fraction of pigment in the coordinates* lgη*-* C*: (1) red iron oxide; (2)*

As the results in **Figure 7** show, the viscosity of the paint increases during filling, while its change at low degrees of filling can be described by the Einstein equation:

where η<sup>0</sup> is the viscosity of the unfilled system and φ is the volume fraction of

where η<sup>0</sup> is the viscosity of the unfilled system and φ is the volume fraction of

*<sup>η</sup>* <sup>¼</sup> *<sup>η</sup><sup>o</sup>* <sup>0</sup>*:*<sup>334</sup> <sup>þ</sup> <sup>119</sup>*<sup>φ</sup>* � <sup>2110</sup>*:*47*φ*<sup>2</sup> <sup>þ</sup> <sup>12217</sup>*:*83*φ*<sup>3</sup> –for sol silicate paint (13)

We was calculated the work of adhesion of liquid glass and polysilicate solution to the pigment (filler). The contact angle of wetting was determined on the KRUSS

Testing the adequacy of the model showed that Eq. (2) is valid in the filling

In view of the foregoing, the cohesive properties and the ability of the polysilicate binder to wet the surface of the pigment (filler) were also investigated. In the work, polysilicate solutions were obtained by the interaction of stabilized solutions of colloidal silica (sols) with aqueous solutions of alkaline silicates (liquid glasses). A sodium liquid glass with a modulus M = 2.78 was used, and a potassium

With increasing concentration of the dispersed phase (more than 0.08), the interaction between particles increases, and deviations from the Einstein equation have been detected. These deviations are apparently due to the interaction of the particles and the formation of a structure in which the particles of the dispersed phase are oriented relative to each other in a certain way (structuring systems). The results of the calculations show that the model changes the viscosity of the paint from the volume concentration of the pigment (filler) which can be described by a

*φ* ¼ *φO*ð Þ 1 þ 2*:*5*φ* (11)

*<sup>η</sup>* <sup>¼</sup> *<sup>η</sup>*<sup>о</sup> *<sup>a</sup>* <sup>þ</sup> *<sup>b</sup><sup>φ</sup>* <sup>þ</sup> *<sup>c</sup>φ*<sup>2</sup> <sup>þ</sup> *<sup>d</sup>φ*<sup>3</sup> (12)

tration of the pigment (CVCP) [4, 15].

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

*ocher; (3) ultramarine; (4) chromium oxide.*

the pigment (filler).

**Figure 8.**

polynomial

the pigment (filler).

region up to φ = 0.16.

DSA-30 [13].

**261**

The following equations were obtained:

liquid glass with a modulus M = 3.29.

The correctness of the equations was checked by Fisher's criterion.
