The current surface area of the preform was then determined based on the current porosity. In the third part, the micromechanical behavior of the CVI-produced porous composite materials is studied.
Introduction
Introduction
However, because the surface between the fiber and the matrix material can be a path for the crack to propagate quickly, coating is often added to the fiber as an intermediate phase. This is because the fibers are not uniformly arranged, fiber size and coating thickness are generally not uniform, and the crack propagation can be achieved according to time.
Outlines of the dissertation
The deposition rate is proportional to the surface area within the preform, and carbon deposition is directly related to increasing preform density and decreasing porosity. Through the numerical analysis model, the preform density and spatial distribution and temporal change of porosity can be determined in detail during the densification process.
Process Analysis
Introduction
Compaction is the result of carbon deposition in the pores, which are initially flow paths for the reaction gas. In the present study, a full 3D physical-chemical CVI model was applied to simulate an isothermal CVI process for an actual industrial-scale product.
Manufacturing of a C/C composite tube
- Industry-scale CVI reactor
- Preform configuration
The densities were calculated from the mass measurement of the preform at the specific time, with the volume defined by the dimensions in the previous section. Preform architecture consisting of two UD layers and one felt layer with needle-punched fibers.
CVI process model
- Overview
- Chemical reactions
- Gas-phase chemical reactions
- Surficial chemical reactions
- Surface area evolution in a preform
- Fluid flow
- Diffusion
- Deposition and densification
The stoichiometry and rates of the gas phase reactions in figure 4 are summarized in table 1. The surface area per volume is defined as the ratio of the active fiber boundary length to the RVE area.
CVI process simulation
- Model descriptions
- Reactor model and initial conditions
- Preform parameters
- Simulation results and discussion
- Model validation
- Gas flow behavior in the reactor
- Chemical reactions
- Preform densification
As shown in Figure 2(a), a single layer of the preform consisted of two UD layers and one felt layer. Given these initial porosities, the effective initial porosity of the preform was found to be 0.775. Figure 10 shows the volume-averaged porosity changes of the preform and its individual layers.
In the initial reaction stage, the porosity of the UD layer decreased very rapidly, implying that the chem. The surface area of the UD layer was much larger than that of the felt layer as shown in Figure 9. The flow velocity distribution in the half-section plane of the reactor is shown in Figure 11(b).
As shown in Figure 18 and Figure 19 , the lower part of the preform showed a significant density gradient along its thickness direction.
Summary
The left axis represents hydrogen and methane and the right axis represents ethylene, acetylene and benzene. The results also indicate that uniform densification can be achieved with the aid of a well-designed reactor in addition to optimal processing conditions. The result of this study may benefit the design of CVI reactors and processes and reduce the need for pilot runs when processing conditions change.
Appendix
Homogenization method
- Introduction
- Thick 3D woven textile composite
- Textile geometry
- Material properties
- Effective properties of tows
- Effective properties of T3DWC
- Specialized periodic boundary conditions
- Homogenization scheme of RVE
- Results and discussion
- Effective tow properties
- Effective T3DWC properties
- Summary
Poisson's ratio of the SiC fiber is assumed to be the same as that of the matrix material. The constitutive equation for the fiber drag can be expressed in terms of the average stress 𝝈 and strain 𝜺:. The thermal conductivity of the drag can also be obtained from the Mori-Tanaka method [85].
As illustrated in Figure 27, the effective property of the matrix material with a pore is obtained first. Mechanical and thermal properties of the fiber tows and matrix material calculated with the Mori-Tanaka method are implemented. In contrast to the case of stiffness, the relationship with the matrix material is related to the property change.
Similar to the case of the temperature change analysis, since the RVE model is strongly influenced by the matrix material, the reduction rate in the y direction behaves the least.
Microstructural Fracture Analysis
Introduction
Such RVEs have been used to study the effects of fiber arrangement non-uniformity on stress distribution [123,124]. 125] studied the effect of the spatial arrangement of fibers on the interfacial normal stresses between fibers for thermally and transversely loaded fiber reinforced epoxy materials. They took into account the plastic deformation of the matrix material and the debonding at the fiber/matrix interface.
They considered the fracture behavior of matrix and coating materials using the crack band method. However, no statistical correlation of the random patterns with the underlying patterns or experimental observations was reported. In addition to the previous works mentioned here, there are numerous examples of RVE-based micromechanical analyzes in the literature.
Here we present a study on the effects of fiber spatial arrangement on the microstructural fracture behavior occurring within CMC materials subjected to different loading configurations.
Characterization of a CMC microstructure
RVE construction process
- Random generation of the fiber and coating dimensions
- Random distribution of the coated fibers
The zero tolerance is strictly enforced on the fiber volume fraction because the volume fraction mainly determines the representativeness of the reduced model. When 𝑉𝑓,mea is the measured fiber volume fraction of the original microstructure, the optimization problem can be formulated as. with the objective function defined as a sum of squared errors for the mean and the standard deviation;. In addition to the volume fraction constraint, the optimization formulation in Eq. 61) limits the errors of the mean and the standard deviation, 𝜖𝜇𝑓 and 𝜖𝜎𝑓, respectively, while performing the minimization process.
When the subscript 𝑐 denotes quantities associated with the coating and 𝒕 is the vector composed of the layer thicknesses, the optimization formulation can be expressed as. 66) and the errors for the mean and the standard deviation are. After the dimensions of the coated fibers are fully determined, they are randomly placed in the RVE area. The virtual spring of the two connected 𝑖th and 𝑗th fibers in Figure 42(a) is considered to be in a compressed state, thus producing a virtual repulsive force (see Figure 42(b)) that eventually separates the two fibers.
The virtual force, 𝑓𝑥′,𝑖, of fiber 𝑖 with respect to the coordinate system 𝑥′𝑦′ can be expressed as.
Micro-fracture mechanics model of CMCs
- Finite element model
- Periodic boundary conditions
- Smeared crack approach
When a crack is initiated in an element at an angle of 𝜃 as shown in figure 48, the stress increase due to the crack in the local coordinate system associated with the normal and tangent vectors of the crack can be transformed into the global stress increase so that. It should be noted here that the present study considers mode I cracking only assuming that the crack is opening due to principal principal stress [133]. When the continuity stiffness of the element in Figure 48 is 𝐃𝐜𝐨, the constitutive relationship between the continuous strain in Eq. 85) and the increase in continuous strain 𝚫𝛔, can be expressed as. 89) can be written in terms of the crack stiffness matrix and the transformation matrix which reads,.
Note that 𝐃 contains the crack stiffness matrix determined from the current crack situation as illustrated in Figure 49 and thus the effect of the crack is incorporated into the continuum model. When the maximum principal stress of the element exceeds the cohesive strength, a crack is initiated in the element and the elemental stiffness is degraded by 𝐃. Before the crack strain increases to the final strain, 𝛿𝑓, as defined in Figure 49, the element is considered damaged due to the crack growth.
When the cracking stress reaches 𝛿𝑓, the crack axis is completely opened and the element completely loses its stiffness.
Results and discussion
- Effective elastic properties
- Transverse tensile loading case
- Pure shear tests
- Effect of the pores on the transverse tensile response
Note that the dramatic changes of the crack zone are closely related to the load drops in the stress-strain curve as shown in Figure 50. The shear response of the RVE models was also studied using the shear loading condition described in Table 8. Shear The responses of the RVE models differ significantly from each other beyond a shear stress of 0.003.
The closed area of the RVE 1 model is the largest among other RVE models. As a result, the fracture toughness of the RVE 1V model is smaller than that of RVE 1. For the matrix phase, the stress concentrations are generally found in the top and bottom of the fiber.
Similarly, for the case of the RVE 1V model, in the same way, the matrix damage propagates into the coating layer and the crack is formed.
Summary
These results are based on the fracture process with a specific fiber arrangement and difficult to be applied to the microstructures of common fiber reinforced composites. Note: This chapter is partially or fully adapted from Hye-gyu Kim et al., "Effects of Nonuniform Fiber Geometries on the.
Concluding Remarks
Conclusions
As a result, it has been found that the fiber arrangement greatly changes the fracture pattern, and the toughness of the microstructure also changes differently. The order of cracking in the microstructure and the roles of each component are also found. Furthermore, by introducing a fabrication-induced pore to one of the RVE models and comparing the results, it is found that the microstructure breaks earlier due to the existence of the pore, and the fracture toughness is consequently reduced.
Consequently, through this research, for the life of CMC, comprehensive observation and analysis is carried out from macroscopic to microscopic scales through numerical analysis. This process is a numerical analysis technique that is necessary for the global and local use of CMC and, therefore, effective applications of CMC are expected throughout this process, improving the underestimation of CMC structures and behaviors.
Future works
Effects of Microstructural Variability on Thermomechanical Properties of a Woven Ceramic Matrix Composite,” Journal of Composite Materials pp. Effect of carrier gas on bulk density and microstructure distribution of carbon/carbon composites prepared by thermal gradient chemical vapor infiltration”, Carbon pp. 1243-1252. Fabrication of laminated SiCw/SiC ceramic composites by CVI”, Journal of the European Ceramic Society pp.
50] Tang, Z., Li, A., Hatakeyama, T., Shuto, H., Hayashi, J., and Norinaga, K., “Transient three-dimensional simulation of the densification process of carbon fiber preforms via chemical vapor infiltration of carbon matrix from methane ”, Chemical Engineering Science pp.107-115. Numerical simulation of the effect of methyltrichlorosilane flux on isothermal chemical vapor infiltration processes of C/SiC composites”, Journal of the American Ceramic Society pp. Elastic Properties of Reinforced Solids: Some Theoretical Principles”, Journal of the Mechanics and Physics of Solids pp.
Numerical characterization of elastic material properties for random fiber composites, Journal of Materials and Structures pp.
