The effect of dispersion degree of calcium carbonate particles in polyvinyl chloride matrix on the mechanical properties of composites

By establishing representative volume units of polyvinyl chloride (PVC) matrix composites filled with calcium carbonate (CaCO3) particles with different agglomeration degrees, finite element simulation analysis is conducted to predict the degree of improvement of the mechanical properties of the CaCO3/PVC composites by the dispersion degree of calcium carbonate particles. When the agglomeration coefficient is 0.4, the stress concentration phenomenon of the CaCO3/PVC composites is the weakest, and the stress distribution of the entire CaCO3/PVC composites is relatively uniform. At the same time, the reinforcement effect of the CaCO3/PVC composites’s stiffness is also the best, increasing by 13.8%.


Introduction
Calcium carbonate (CaCO 3 ) is abundant in nature, easy to extract, and inexpensive.Making it into powder and filling it into a plastic matrix can effectively improve the mechanical properties of plastics and reduce the production cost of plastic parts.Many scholars have used various preparation methods to obtain CaCO 3 particles with different crystallization modes and studied their filling effects, effectively improving the utilization rate of calcium carbonate and improving the mechanical properties of calcium carbonate-filled polymer matrix composites [1][2][3] .The surface of calcium carbonate powder is hydrophilic and oil repellent, and when compounded with polymer, it is difficult to evenly disperse in the polymer matrix, forming a serious agglomeration phenomenon, leading to a decrease in the mechanical properties of the composite material, thereby affecting its use effect [4][5] .To achieve a good filling effect, surface modification of calcium carbonate is necessary to improve its dispersibility and compatibility in composite materials [6][7] .Scholars have used various experimental methods to modify the surface of calcium carbonate particles to improve their dispersion effect in polymer matrices [8] .The experimental method makes it difficult to predict the degree to which the dispersion of calcium carbonate particles improves the mechanical properties of composite materials and has certain unpredictability.It is also difficult to explore the laws and mechanisms by which the dispersion of calcium carbonate particles improves the mechanical properties of composite materials.
This article establishes representative volume units (RVE) of calcium carbonate-filled polyvinyl chloride (PVC) composites with different dispersion degrees, and further uses the finite element method to simulate and predict the improvement effect of dispersion degree on the mechanical properties of the composite materials.From a microscopic perspective, the modification mechanism of the modified calcium carbonate dispersion effect on CaCO 3 /PVC composites is studied.

Composite material components
This article uses PVC as the matrix of composite materials, filled with calcium carbonate particles to enhance the mechanical properties of PVC materials.The most common shape of calcium carbonate powder particles is a sphere.This article uses spherical calcium carbonate particles with a diameter of 1 micrometer as filling materials.The specific material characteristic parameters are shown in Table 1.
Table 1 PVC as the matrix in composites is the object for us to improve mechanical properties.Due to the high Young's modulus of calcium carbonate, the improvement in the mechanical properties of the PVC matrix is mainly manifested in stiffness.The performance of stiffness enhancement is described by the increase in Young's modulus.The calculation method for Young's modulus E of elastic materials is shown in Equation (1).
In the equation, "F" is the tensile force exerted on the material; "S" is the cross-sectional area; '∆' is the elongation, and "L" is the original length.

Establish representative volume units
The dispersion degree of CaCO 3 in the PVC matrix is described by the agglomeration coefficient K, which is the ratio of the volume of aggregated CaCO 3 to the volume of all filled CaCO 3 , as shown in Equation (2).
In the equation,  is the volume of aggregated CaCO 3 ;  is the total volume of all CaCO 3 .

Figure 1. RVEs of each agglomeration coefficient.
According to previous research [9] , spherical calcium carbonate particles are filled into PVC, and the composite material has the optimal tensile and compressive properties when the proportion of calcium carbonate in the volume of the composite material is 25%.On this basis, this article uses 25% as the filling ratio of calcium carbonate particles.In Digimat software, representative volume units (RVE) with aggregation coefficients K of 0, 0.2, 0.4, 0.6, 0.8, and 1 are established by setting different clustering coefficients.The dimensions of RVEs are all side lengths of 5 μm.The cube of m is shown in Figure 1.

Establishing a finite element simulation model
The representative volume units of the composite materials established above are imported into the Workbench simulation platform of ANSYS 2020 R2 software, the setting of various material parameters (as shown in Table 1) is completed, and automatically the mesh using tetrahedrons is divided.Fixed constraints are applied on one side of the six faces of the RVE, and a tensile load of 40 MPa is applied on the opposite side, with a loading time of 1 s.The final simulation model obtained on the workbench platform is shown in Figure 2.

Stiffness enhancement effect
Under the tensile load of 40 MPa, the RVE of Calcium carbonate PVC composite material undergoes elastic deformation in the load direction.The deformation results obtained from the simulation of CaCO 3 /PVC composites' RVEs with various aggregation coefficients in the workbench are displayed in cloud graph form, as shown in Figure 3.  1), the Young's modulus E of CaCO 3 /PVC composites' RVEs can be calculated, as shown in Table 2.The reinforcement ratio of Young's modulus of composites compared to pure PVC is shown in Figure 4.
Table 2. Deformation values and Young's modulus of CaCO   2 and Figure 4, it can be seen that under the same filling ratio of calcium carbonate particles, the stiffness enhancement effect of the composite material decreased.The cohesion coefficient shows an upward trend before 0.4, and a downward trend when it is greater than 0.4.When the aggregation coefficient is between 0.2 and 0.4, the enhancement effect is better; When the aggregation coefficient is 0.4, the reinforcement effect of the composite material's stiffness is the best, with a Young's modulus value of 6825.94MPa.Compared to pure PVC material, the Young's modulus is increased by 13.8%.The results indicate that the presence of appropriate agglomeration of filled ICAMIM-2023 Journal of Physics: Conference Series 2720 (2024) 012011 IOP Publishing doi:10.1088/1742-6596/2720/1/0120115 calcium carbonate particles in the PVC matrix helps to improve the stiffness of the CaCO 3 /PVC composites.When the agglomeration phenomenon is severe, the effect of improving the stiffness of the CaCO 3 /PVC composites rapidly decreases.

Improvement effect of stress concentration
The stress cloud diagram of the simulation results is shown in Figure 5.The maximum stress values of CaCO 3 /PVC composites' RVEs are shown in Figure 6.By observing Figure 6, it can be inferred that the stress concentration phenomenon is the most obvious at the connection between calcium carbonate particles and PVC, which is also the location where cracks are most likely to occur.When the agglomeration coefficient is 0.4, the stress concentration phenomenon is the weakest, with a maximum stress value of 187.5 MPa.The stress distribution of the entire composite material is relatively uniform.Based on the above analysis, in PVC composite materials filled with calcium carbonate particles, there is a small amount of agglomeration phenomenon inside the matrix that helps to promote the improvement of composite material stiffness and reduce stress concentration.The optimal agglomeration coefficient is 0.4.

Conclusion
When the agglomeration coefficient is between 0.2 and 0.4, the stiffness enhancement effect of the CaCO 3 /PVC composites is better; When the agglomeration coefficient is 0.4, the reinforcement effect of CaCO 3 /PVC composites stiffness is optimal.
When the agglomeration coefficient is 0.4, the stress concentration phenomenon of the CaCO 3 /PVC composites is weakest, and the stress distribution of the entire CaCO 3 /PVC composites is relatively uniform.

Figure 3 .
Figure 3. Deformation cloud chart results of CaCO 3 /PVC composites' RVEs.By using the deformation value of CaCO 3 /PVC composites' RVEs and combining it with Equation (1), the Young's modulus E of CaCO 3 /PVC composites' RVEs can be calculated, as shown in Table2.The reinforcement ratio of Young's modulus of composites compared to pure PVC is shown in Figure4.Table2.Deformation values and Young's modulus of CaCO 3 /PVC composites' RVEs.

Figure 4 .
Figure 4. Enhancement ratio of Young's modulus.According to Table2and Figure4, it can be seen that under the same filling ratio of calcium carbonate particles, the stiffness enhancement effect of the composite material decreased.The cohesion coefficient shows an upward trend before 0.4, and a downward trend when it is greater than 0.4.When the aggregation coefficient is between 0.2 and 0.4, the enhancement effect is better; When the aggregation coefficient is 0.4, the reinforcement effect of the composite material's stiffness is the best, with a Young's modulus value of 6825.94MPa.Compared to pure PVC material, the Young's modulus is increased by 13.8%.The results indicate that the presence of appropriate agglomeration of filled

Figure 6 .
Figure 6.The maximum stress values of RVEs.Based on the above analysis, in PVC composite materials filled with calcium carbonate particles, there is a small amount of agglomeration phenomenon inside the matrix that helps to promote the improvement of composite material stiffness and reduce stress concentration.The optimal agglomeration coefficient is 0.4.

.
Performance parameters of each component of CaCO 3 /PVC composites.