Features of deformation resistance of polypropylene polymer films

The article studies the physical and mechanical properties of experimental polymer materials, which are determined by parameters such as Tensile strength s, tensile model E, relative elongation at break ε, which affect the quality of printing under other equal conditions. Experimental studies on the elongation of biaxially oriented polypropylene and polyethylene polymer films were carried out in accordance with the requirements of GOST 14236-81. The tensile modulus E was determined according to Hooke’s law when observing a rectilinear area in the limit of small deformations on the stretching diagram of polymer films.


Introduction
The modern level of development of the technique and technology of the printing industry allows processing and printing on polymer films of different chemical nature.But the lack of paint absorbing properties of such materials causes a number of problems in terms of wetting and paint adhesion.Since almost all polymer films are printed by gravure printing, all the problems associated with printing have to be considered [1,2].
During printing process, the printing material is under certain pressure in the process of interacting with the polymer surface solid printing mold.The accuracy of the printed images will depend on whether the printed material interacts with the mold under a certain pressure.For this reason, it is very important to study the deformation properties of the printed material.When the printed material is significantly deformed during the printing process, this can lead to negative consequences that lead to the ambiguity of the printed images.Mechanical properties determined by indicators such as strength σ at the junction, tension modulus E, relative stretch ε at the junction occupy an important place among the physicochemical properties affecting print quality under other equal conditions [3][4][5].
The rapid development of the packaging industry is associated with the development of printing in the packaging printing industry.Packaging should be bright, colorful and presentable.The beautiful appearance of the packaging depends on the methods of printing on it.The quality of the packaging depends on the strength of its layers [2][3][4].

Materials and methods
The most commonly used polymer films in the packaging industry are polyethylene and polypropylene films.Table 1 lists the polymer materials selected for this research and their abbreviations.In the printing process, it is important to know the roughness value of the surface of the printed material in order to ensure the high quality of the quality indicators of the printed product, which is of practical importance.Multi-layer polymer materials occupy an important place in modern packaging.As a result of combining different layers, it is possible to improve the mechanical and protective properties of the packaging.The mechanical properties determined by parameters such as strength at break s, stress model E, relative elongation at break е are among the physical and mechanical properties that affect the quality of printing, other things being equal.These indicators generally adequately describe the ability of a material to resist deformation in tension and elastic deformation.[5][6][7].

Results and discussion
Tension-elastic deformations of printed materials occur when exposed to pressure in the printing device of the printing equipment.The results of these experiments will help to select printing materials for printing and develop recommendations for mass introduction into production.
Experimental studies on tensile strength were carried out on the "SHIMADZU" AG-X PLUS breaking equipment (Fig. 1).This equipment is equipped with a charting device, which allows convenient recording of stress-strain curves both when the test is carried to failure and when the specimen is stressed at the limit of tensile deformations.2 provides additional descriptions of the printed materials.Experimental studies on the elongation of polymer films were carried out in accordance with the requirements of GOST 14236-81.The normal tensile stress was calculated according to the following formula Here Fupload, H;  The information obtained from the elongation diagram (Figure 2) is considered to be applicable to half-cycle failure characteristics, where samples are carried to failure [3].
In this case, the maximum relative deformation corresponding to the failure of the sample is equal to =61% and the maximum stress (breaking stress) is equal to  =250.4MPa.
It was found in the experiment that the dependence of the BOPP film deformation in the longitudinal direction on  is similar to the deformation  in the transverse direction, which indicates that the material has isotropic properties.The stress modulus E can be determined according to Hooke's law when observing a straight line field in the limit of small deformations according to the elongation diagram: But, it is because of The ratio   is accepted as the hardness of the material in the theory of tension, but this quantity is also divided by the area  0 that is, the hardness is relative.
Therefore, the concept of tensile modulus is replaced by relative stiffness in most cases.If small deformations are considered and assumed to be fully reversible, it is possible to calculate the tensile modulus for polymeric materials.Therefore, such moduli are called initial [4], where it is assumed that they are obtained for the initial conditions of stretching.For the BOPP film sample, the tensile modulus at e=4% is E=2544 MPa (average value).
The pattern of the initial stage of deformation of BOPP film samples can be seen in Figure 5, where there is almost a linear relationship between stress and strain up to ε= 0.3%.Figure 4 and Figure 5 show the elongation diagrams of the PE film samples in the transverse and longitudinal directions, respectively.The semi-cycle characteristics are significantly different compared to the BOPP film samples: it was found that the polyethylene film has a higher elasticity. = 761% (Transverse direction) and  = 1000% longitudinal direction.The breaking stress is  = 34,21 and 21.03 MPa, respectively.Such a high value of elongation at low values of tension can have a negative effect on the quality of the printed product.Analyzing the strain diagrams (Fig. 4 and Fig. 5) shows that the area of "yield" in the polyethylene film, that is, the deformation of the sample at constant stress, and the sudden increase in stress in the strain diagram are observed.At the same time, the continuity of deformation in the longitudinal direction is clearly broken (Fig. 5), which can confirm the anisotropy of polyethylene.The modulus of elasticity (ε=0.3%) was E=91.9 MPa and E=35.9 MPa in the longitudinal and transverse directions [5][6].Elongation diagrams of PE film samples at small deformations ( =15…20%) are shown in Fig. 6 and Fig. 7.As seen in the experiments, in the initial part of the deformation, a nonlinear connection between σ and ε can be observed, which significantly complicates the determination of the strength modulus.Table 3 summarizes the tensile test results of selected polymer film samples.Based on these obtained results, it can be concluded that since the dependence of the deformation  of the BOPP polymer film on ε in the longitudinal direction has the same index as the deformation in the transverse direction, this index has been generalized, this index indicates that the BOPP polymer material has isotropic properties.We can see that the relative elongation at break is very elastic in the PE material.It can be seen from the research that the tensile stress modulus is relevant in BOPP polymer films.These obtained results are conditional in terms of stress, since in its determination the breaking load is divided by the initial cross-sectional area of the sample, but it actually decreases due to the decrease in film thickness.
Analysis of the deformation curve during stretching of the BOPP film sample (Fig. 2) made it possible to approximate the relationship between stress and deformation with a parabola of the following form: () ̅̅̅̅̅̅ = a +  =  2 (5) у, it is usually used in the formulation of the variable speed decay equation [7][8][9][10][11][12][13][14][15][16].Here n is the number of observations; ∑ changed from i=1 to n.
(6) is explained by the fact that the description of the relationship between the stress  and the relative strain  is similar to the variation of the decay z as a function of time x.
A stress-strain equation of state for the stretching of BOPP film was established.For this, the data of the deformation curve was used: For this case, in the parabolic approximation, we use the first two equations of the system (6) at b=0, that is, we approximate the parabola in the form x=a+cz^2. Here ; The system of equations in numerical form was equal to the following 2 + (110 2 + 210 3 ) = 0,12 + 0,36 (110 + 210) + (110 3 + 210 3 ) =0,12 * 110 +0,36 * 210 The solution of this system of equations gives the value of parameters a=0.02925 and c=0.0000075.Thus, the equation of the parabola was obtained  = 0,0000075  2 + 0,02925 ;

Conclusion
In conclusion, it should be said that from the physic-mechanical properties that have an integral effect on the quality of the printed product, such as strength σ, at break ε, tensile modulus E, relative elongation at break e, the stress-strain state equation for the stretching of the BOPP film was created.The equation of the parabola was derived using the obtained results and equations  = √ −0,02925 0,0000075

, МPа
This equation made it possible to calculate the standard value of the normal stress s depending on the relative deformation ε during stretching of the BOPP film and to formulate the strength conditions for the allowable breaking load (tension).

Figure 1 .
Figure 1."SHIMADZU" AG-X PLUS cutting equipment.Table 2 provides additional descriptions of the printed materials.
mm 2 b, d -respective thickness and width of the specimen, mm; The relative strain in elongation corresponding to rupture was calculated according to the following relationship here ∆l-absolute deformation in elongation, mm;  0 − initial length of the sample, mm;  − final length of the sample, мм;The results of tensile testing of printed material samples are shown in Figures2 and 3(BOPP films) and Figures 4 and 5 (PE film).

Figure 2 .
Figure 2. In the longitudinal direction v=1 mm/min.deformation diagram of polypropylene (BOPP) film under speed stretching.

Figure 3 .
Figure 3. v=2mm/min.diagram of the deformation of polypropylene (BOPP) film at the limit of tension-elastic deformations (before failure) during rapid stretching

Figure 4 .
Figure 4.In the transverse direction v=100 mm/min.diagram of the deformation of polyethylene (PE) film during speed stretching

Figure 5 .
Figure 5.In the longitudinal direction v=1 mm/min.diagram of the deformation of polyethylene (PE) film during speed stretching.

Figure 6 .
Figure 6.In the longitudinal direction v=5mm/min.diagram of the deformation of polyethylene (PE) film at the limit of tension-elastic deformations (up to failure) during rapid stretching.

Figure 7 .
Figure 7.In the transverse direction v=5mm/min.diagram of the deformation of polyethylene (PE) film at the limit of tension-elastic deformations (up to failure) during rapid stretching.

( 7 )
The system of equations has the following form in relation to the conditions of tensile tests: equation made it possible to calculate the standard value of the normal stress  depending on the relative deformation ε during stretching of the BOPP film and to formulate the strength conditions for the allowable breaking load (tension).

Table 1 .
Polymer materials selected for the research and their abbreviations.

Table 2 .
Physico-mechanical properties of experimental materials.

Table 3 .
Mechanical properties of experimental polymer films in stretching.