## FORECASTING OF TROUBLE-FREE OPERATION OF

## THE PROTECTIVE AND DECORATIVE COATINGS

## FOR BUILDING PRODUCTS AND STRUCTURES

Valentina Loganina

Penza State University of Architecture and Construction, Titovst, Penza, Russia E-Mail: loganin@mail.ru

**ABSTRACT **

Informationonthelawofdistributionoftheoperatingtimetofailureofprotectiveanddecorativecoatingsisgiven. The example of polyvinyl acetate cement and polymer coatings shows that the Weibull distribution more accurately describes the behavior of the failure probability of coatings.

**Keywords:** coating, life time, distribution law, probability of failure-free operation.

**1. INTRODUCTION **

The development of mathematical models that characterize the aging processes of coatings makes it possible, on the basis of a comparative analysis, to carry out scientifically-based selection of the paint composition and coating technology in accordance with operating conditions and customer requirements.

Existing approaches to the creation of models are based on changes in the Shine of the coatings depending on the effect of climatic factors, the application of expert qualimetry methods [1,2,3]. The results of the studies given in [4,5,6,7,8] and other scientific and technical literature sufficiently accurately characterize the change in the various properties of paint coatings during operation and are characteristic, in the authors' opinion, specifically for each coating. In this regard, the actual task is to determine the law of distribution of the probability of failure of coatings, the application of which will allow judging on the basis of accumulated statistical data about the possibility of meeting the requirements of consumers. Obviously, like any other, the law of distribution of a random variable must be determined by parameters that have a certain physical meaning. In the problem under consideration such parameters should be:

- mean time between failures; - time interval of aging;

- the shape of the curve describing the probability of failure in the aging time interval.

The well-known and widely used in the theory of reliability laws of the distribution of the operating time to failure (normal, exponential, Weibull) explicitly do not provide these requirements.

The normal distribution law determines

2 2 2 ) (

### 2

### 1

### )

### (

###

###

*x*

*x*

*e*

*x*

*f*

###

###

the position### (

*x*

### )

and scatteringThe exponential distribution *t*

*e*

*t*

*P*

### (

### )

###

### 1

###

(λ is the failure rate characterizing the aging rate), taking into account the variability of λ during operation and the approximation error, does not always make it possible to recognize the model as adequate.The Weibull distribution

###

###

0### 1

### )

### (

*t*

*t*

*e*

*t*

*P*

(t0, β, α - parameters of shear, scale, shape) more

accurately describes the behavior of the probability of failure of coatings, but its application presents certain difficulties in conducting comparative analysis, because The parameters α and β do not lend themselves to physical interpretation (they characterize the distribution curve, but not the average operating time, the aging interval or other properties of the coating).

**2. THE RESEARCH METHODS **

To study the coatings properties change factors, we used the following paints - polyvinyl-acetate-cement (PVAC), PVAC with addition of silicone fluid-94, the polimerlime. The samples were subjected wetting-drying moisture.

After curing, the samples were subjected wetting-drying according to the following conditions: 20 hours of moistening at room temperature and 4 hours of drying at a temperature of 60 ° C.

For the "failure" was accepted the condition of the coating, estimated III.4 points in accordance with GOST 6992-68 "Coatings paint and varnish. Method for determining the stability of the coating in atmospheric conditions". This condition is characterized loss of shine to 5%, a barely noticeable color change and the absence of peeling, cracking of the surface.

**3. THE RESULTS OF RESEARCH **

*s*

*t*
*t*

*e*

*t*

*P*

###

###

### 1

### )

### (

(1)where

*t*

- the mean time of failure, calculated from the
experimental data;
s is a coefficient characterizing the change in the rate of aging in the time interval, in which failures are observed.

Proceeding from the above assumptions, the coefficient s is determined by equating the first derivative

of the function (1) at a point

*t*

to the value
*t*

###

### 1

, where

*t*

###

is the time interval between the first and the last failures of the considered types of coating.We get:

*t*

*e*

*t*

*s*

*t*

*P*

###

###

###

###

###

### (

### )

### 1

, (2)whence

*t*

*e*

*t*

*s*

###

###

###

, (3)Consequently, the distribution law (1) takes the form:

*t*
*e*
*t*

*t*
*t*

*e*

*t*

*P*

###

###

### 1

### )

### (

(4)Let us consider the behavior of the function (4) for fixed values of

*t*

and ###

*t*

.
In Figure-1 shows the graphs of the dependence of the probability of the onset of failure of the operating time (the time of operation will be characterized as the number of cycles "humidification-drying" for forced coating tests) for a fixed value of

*t*

(###

*t*

###

### 200

) and different*t*

(*t*

= 100, 300, 500, 700, 900). Analysis of the
curves in Figure-1 allows us to conclude, that the value *t*

uniquely determines the position of the curve and its
change does not affect the form of the dependence.
**Figure-1. **The probability of failure of the coating at;

###

*t*

###

### 200

1 -*t*

= 100 cycles;2 -*t*

= 300 cycles;
3 -

*t*

= 500 cycles;4 -*t*

= 700 cycles; 5 -*t*

= 900 cycles.
In Figure-2 shows the graphs of the dependence of the probability of the onset of failure of the operating time for a fixed value of

*t*

(*t*

###

### 200

) and various(###

*t*

=
100, 300, 500, 700, 900). Analysis of the curves allows us
to conclude that the value uniquely determines the aging time of the coating (the time interval from the probability of failure P (t) ≈0 to P (t) ≈1).

1 _{2}

3 _{4}

5

0 0.2 0.4 0.6 0.8 1

0 100 200 300 400 500 600 700 800 900 1000

**P(t)**

**Figure-2. **The probability of coating failure at = 200 cycles; 1 -

###

*t*

= 100 cycles;2 -###

*t*

= 300 cycles
3 - ###

*t*

= 500 cycles;4 -###

*t*

= 700 cycles; 5 -###

*t*

= 900 cycles.
Data on Figures 1, 2 allow us to conclude that the shape of the distribution curve in the aging time interval of

the coating will be determined by the ratio

*t*

*t*

###

**.**

Summarizing the above conclusions, we can conclude that function (4), in general, meets all the above requirements for the distribution law and each of its parameters has a specific physical interpretation.

Experimental studies carried out on three types of coatings (polyvinyl acetate-cement (PVAC), PVAC with

addition of Silicone fluid-94 and polymer lime) have
shown that the application of the distribution law (4)
allows with rather high accuracy (the probability of
agreement between the experimental distribution and the
theoretical criterion χ2_{ with the number of degrees }

Freedom k = 3 more than 0.7) describe the probability of the time of failure of coatings.

The experimental and theoretical distributions are shown in Figures 3-5.

1

5

4

2 3

0 0.2 0.4 0.6 0.8 1

0 100 200 300 400 500 600 700 800 900

**P(t)**

2

1

0 0.2 0.4 0.6 0.8 1

0 130 150 200 250 300 350

**Figure-4. **The probability of failure of the coating of PVAC with addition of Siliconefluid-94

1 - experimental distribution;2 - theoretical distribution

200 8 , 267

8 , 267

### 1

### )

### (

*e*

*t*

*e*

*t*

*P*

###

###

**Figure-5.** The probability of failure of polymer lime coating; 1 - experimental distribution;

2 - theoretical distribution

200 1 , 192

1 , 192

### 1

### )

### (

*e*

*t*

*e*

*t*

*P*

###

###

.**4. CONCLUSIONS **

Thus, the results obtained make it possible to recommend the application of the probability distribution function of the operating time to failure (4) as a model for the service life of paint and varnish coatings.

**REFERENCES **

[1] Karjakina M.I. Physical and chemical bases of processes of formation and aging of the coatings. Moskau: Chemistry, 1970 - 215 p.

[2] Loganina V.I. 2015.Model of Aging Coatings Based on Hereditary Factors. Contemporary Engineering

Sciences. 8(4): 165 -170HIKARI Ltd, www.m-hikari.comhttp://dx.doi.org/10.12988/ces.2015.518.

[3] Loganina V.I., Makarova L.V.,Tarasov R.V. 2016. Method of assessment quality protective and decorative coating concrete cement. Case Studies in

Construction Materials.4: 81-84

DOI information: 10.1016/j.cscm.2016.01.003.

[4] Andryushchenko E.A. 1986. Lightfastness paint pokrytiy. Moskau: Chemistry. p. 182.

[5] Loganina V.I. 2015. Model of Aging Coatings Based on Hereditary Factors. Contemporary Engineering

2 _{1}

0 0.2 0.4 0.6 0.8 1

0 150 200 250 300 350

P(t)

2

1

0 0.2 0.4 0.6 0.8 1

0 100 120 130 150 200 250 300

Sciences. 8(4): 165 -170 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ces.2015.518.

[6] Loganina V.I. 2015. The Kinetics Model of Coverings’ Properties with Consideration of the Heredity Factor. Contemporary Engineering Sciences. 8(2): 85-89 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ces.2015.412257.

[7] Schllkelman R. 1964. Nonderstuctlve testing of adhesive Adhesivos. Age.