# Determination of the Filler Concentration of the Composite Tape
## 2 Materials and Methods
Thus, the content of the wear-resistant phase in the composite tape should correspond to the distance between particles, approximately equal to the average particle diameter. The performance of a composite tape is associated with the thermomechanical compatibility of the phases included in the material, and the thermomechanical compatibility of such phases depends on the thermal expansion coefficients of the matrix materials and the dimensions of the fillers. Since the process of creating a composite coating takes place in two stages (creating a composite tape and its direct welding on the cylindrical surface of the CBRTB), the mutual thermal interaction of the phases can be considered jointly in the process of thermomechanical interaction similar to the process of composite strip production (rolling the powder mixture on rolls and then sintering in an inert atmosphere furnace), and in the contact welding process. As noted earlier, the wear process of the CBRTB is varied (uneven). That is, welding a more wear-resistant composite tape to the cylindrical surface of the CBRTB will allow the wear rate to equalize at all its points, reduce the amount of wear, and thereby increase the service life of the CBRTB. The selection of the required properties for each point of wear of the cylindrical surface of the CBRTB should be based on changes in the filler concentration of the composite tape. Based on the wear of the CBRTB and the proposed hardness distribution (Figures 1 and 2), we determine the concentration of the composite tape filler for each point on the cylindrical surface of the CBRTB. The regularity of the required distribution of the filler concentration in the composite tape along the diameter of the bolster of the CBRTB is determined. Proceeding from the fact that the filler concentration per unit length by diameter is proportional to the concentration that is necessary to obtain such a wear-resistant and hardened layer, each point of the cylindrical surface of the CBRTB would have the same wear rate, i.e.,  
\[\frac{dC}{dl}=kC, \tag{1}\]  
where C is the filler concentration in the composite tape; \(k\) is the coefficient that depends on the properties of the interacting materials of the center plate of the body and the bolster of the CBRTB. This coefficient is proposed to be determined by the physical, mechanical and tribological properties of the center plate of the body and the CBRTB:  
\[k=f\frac{K_{1}\cdot H_{1}}{K_{2}\cdot H_{2}}, \tag{2}\]  
where \(f\) is the coefficient of friction; \(H_{1},\ H_{2}\) are the hardness (or microhardness) of the center plate of the body and the CBRTB, respectively; \(K_{1},\ K_{2}\) are elastic constant coefficients for the material of the center plate of the body and the CBRTB, respectively, which are determined by the expressions:  
\[K_{1}=\frac{1-\mu_{1}^{2}}{E_{1}};\ \ \ \ \ K_{2}=\frac{1-\mu_{2}^{2}}{E_{2}}, \tag{3}\]  
where \(\mu_{1},\ \mu_{2}\) are [PERSON]'s ratios for the material of the center plate of the body and the CBRTB, respectively; \(E_{1},\ E_{2}\) are the modulus of elasticity of the material center plate of the body and the CBRTB, respectively. Then, expression (2) will have the form  
\[k=f\frac{E_{2}\big{(}1-\mu_{1}^{2}\big{)}H_{1}}{E_{1}\big{(}1-\mu_{2}^{2} \big{)}H_{2}}. \tag{4}\]  
The value of the elastic modulus of the composite tape can be determined by the following formula:  
\[E_{2}=E_{M}(1-C_{F})+E_{F}C_{F}, \tag{5}\]  
where\(C_{F}\) is the filler concentration of the composite tape;  
\(E_{M}\) is modulus of elasticity of the composite tape matrix;  
\(E_{F}\) is the modulus of elasticity of the filler of the composite tape. We also write an expression for finding the hardness of a composite tape:  
Figure 1:0  
where  
\(H_{M}\) is a matrix hardness;  
\(H_{F}\) is the hardness of the filler.