Increasing the rigidity of an elastic working tool for processing thin sheet metal by creating composite material based on polyurethane elastomers and synthetic aramid fabrics

The paper presents the results of both experimental and theoretical studies on the creation of a new composite working tool for pressure treatment of thin sheet metals. The composite working tool is made on the basis of SKU-7L polyurethane with reinforcement with one layer of kevlar-type aramid fabric.


Introduction
In the aerospace and energy fields, various sheet metal products are widely used, such as elements of aircraft parts and various types of flat heat exchangers and the like. The analytical review showed that the production of parts from sheet blanks by stamping with a working tool made of polyurethane elastomers has been mastered [1,3,4,5]. The method is particularly cost-effective for single and small-scale production, but in some cases it is also used for batch production, for example, in the production of plates for flat heat exchangers up to 50 thousand pieces. At the same time, the production does not always have powerful pressing equipment for the introduction of polyurethane stamping of parts. In these cases, the most profitable are rotary shaping methods, characterized by lower energy consumption and high productivity. The disadvantage of this method is the limited technological capabilities of the elastic working tool, associated primarily with the low values of the conditional modulus of elasticity of modern polyurethane elastomers. Maximum thickness of processed materials: for steel -0.5 mm, for sufficiently soft non-ferrous metals and alloys -0.8-1 mm. [6][7][8][9][10]. Currently, one of the promising ways to obtain the required properties of materials is the development and creation of composite structures. One of the existing methods of increasing the rigidity of elastomers is its reinforcement with high-strength fabrics. One of the important tasks was the choice of a mathematical model of hyperelastic materials. Hyperelastic material is a model type of ideally elastic material for which the dependence of stresses on deformations is calculated based on a function of the strain energy. A hyperelastic material is a special case of an elastic Cauchy material. The behavior of a hyperelastic material can be described using one of the common mathematical models -Neoguk, Mooney-Rivlin, Ogden, Blatz-Ko, Arruda-Boyes. We have chosen the two-parameter Mooney -Rivlin model, which is widely used for deformations up to 50%. [1,2].

Determination of Mooney-Rivlin constants
The Mooney-Rivlin constants for the hyperelastic state were determined by minimizing the standard deviation between the stress-strain diagram obtained experimentally and determined by the equation [1][2][3]: Where 11 -deformation stress (specific force on the surface), MPa; 1 -degree of deformation;

Method and results of studying samples according to the biaxial compression scheme
At the stage of experimental studies to determine the Mooney-Rivlin coefficients, upsetting of prismatic samples was carried out according to the biaxial compression scheme. The objects of the study were the following samples ( Figure 2): 1) Prismatic specimens 20mm x 10mm x100mm, which are glued polyurethane blanks 10mm x 10mm x100mm, used polyurethane brand SKU-7L.

2)
Prismatic specimens 20 mm x 10 mm x 100 mm, representing a composite structure: the matrix is SKU-7L polyurethane, the reinforcing elements are aramid fabric, the binder is cyanoacrylate.
The true stress value is determined from the incompressibility conditions: Expressions (4), (5) allow us to determine the desired values of the parameters 1 and 2 , however, with a large number of measurement points, it is advisable to create a computer program that will perform all mathematical transformations according to a given algorithm [8][9][10][11].
Calculations were made to determine the Mooney-Rivlin coefficients in the MathCad software package. According to the results of the experiment, the Mooney-Rivlin constants were determined. From the graphs obtained as a result of experimental studies, the numerical values of the degrees of deformation at the corresponding points (λi) and stresses were determined as the ratio of the upsetting forces to the actual area of the contact surface of the working tool with the sample.
To determine the dependences of stresses on deformations, the samples were studied under loading according to the scheme of biaxial nonuniform compression.

Method and results of the study of samples according to the scheme of biaxial uneven compression
At the stage of experimental research according to the scheme of biaxial uneven compression ( Figure 5). Samples 100x100 mm, 20 mm high. Used polyurethane brand SKU-7L.

2)
Samples 100x100 mm, 10 mm high, representing a composite structure: the matrix is SKU-7L polyurethane, the reinforcing elements are aramid fabric, the binder is cyanoacrylate. Figure 6 shows the prepared elements for the manufacture of a composite sample and a control one-piece sample.

Mathematical modeling of the deformation process of a sheet blank
At the first stage, the deformation of the sheet in the cavity of the matrix was simulated with a working tool made of SKU-7L polyurethane, at the second -from a composite tool reinforced with 8601-90 fabric. The calculation was carried out in the Ansys software package. The process of deformation of the sheet in the cavity of the matrix (the degree of deformation of the shell is 30%) was carried out according to the scheme shown in Figure 8. The working tool is a cylindrical shaft with a diameter of 100 mm: density 3000 kg/ 3 , Poisson's ratio 0.49, elastic shell -outer diameter 140 mm, Mooney-Rivlin ratios for polyurethane SKU-7L: С10 = 2,42, С01 = 0,81, for composite material reinforced with 8601-90 fabric: С10 = 12,88, С01 = 4,86. Rigid shaft -a cylinder, outer diameter 100 mm, adopted by an absolutely rigid body. To speed up the calculation, we used symmetry conditions in three planes. The matrix and the shaft were defined by absolutely rigid bodies (Rigid). The behavior of a deformable material (AD0) was described by a bilinear model (yield stress 40 MPa, ultimate strength 80 MPa with a relative elongation of 0.35), and the behavior of a polyurethane shell using a two-parameter Mooney-Rivlin model. To describe the contact between the matrix and the sheet, a frictional contact with a friction coefficient of 0.2 was used, a rigid shaft and polyurethane -a bonded contact, between polyurethane and a sheet, a frictional contact with the same friction coefficient of 0.2.  Figure 8. Diagram of the process of sheet deformation in the depression The sheet is divided into parallelepipeds using the edgesizing command with dimensions of 0.05×4.5×5 mm. The polyurethane shell is broken up into parallelepipeds using the edgesizing command with dimensions of 1×1.25×3.8. For a better picture of the SSS in the near-contact area, the contactizing command was used, which reduced the size of the elements in the near-contact area. Thus, the task has 40413 nodes and 8500 elements. As a result, the following results were obtained, presented in Figures 9-12: Figure 9. (a,b) -Fields of equivalent stresses a-polyurethane, b-reinforced polyurethane. Equivalent stresses of polyurethane tools: maximum equivalent stress eq.max = 7 MPa, minimum equivalent stress eq.min = 0,007 MPa. Equivalent stresses of the composite tool: maximum equivalent stress eq.max = 33 MPa, minimum equivalent stress eq.min = 0.004 MPa.

Conclusions
Mathematical modeling of the process of deformation of a metal sheet by a tool made of a composite material showed a significant increase in the forces required to deform a composite tool, as well as a significant increase in stresses on the contact surface at the same degree of deformation. The maximum equivalent stress in the composite tool was 33MPa, which is about 4.7 times that of a conventional polyurethane tool. The maximum normal stress in the X-axis in the composite tool was 33.5 MPa, about 2.5 times that of a conventional polyurethane tool. Thus, the reinforcement leads to a significant increase in the rigidity of the working elastic working tool, contact stresses will make it possible to process not only sheet parts up to 1 mm from aluminum alloys, but also steel billets, which is not possible with the use of conventional polyurethane. The use of a new composite material will significantly expand the range of products obtained by processing with this composite tool.