## 3 Methodology for Measuring Damage in a Metal Matrix Composite and Discussion of Results
### Damage Measurement Technique  
The main non-damage-induced influences on the elastic modulus in metallic materials are texture change, residual stress formation, and phase composition evolution. In order to determine whether an oriented texture was formed in the composite during deformation, EBSD analysis was performed on the V95\(\backslash\)10% SiC MMC specimens after deformation at temperatures ranging from 300 to 500 \({}^{\circ}\)C. Figure 8 shows images of {100} pole shapes, as well as EBSD images of the specimens before and after deformation in the presence of macrocracks on the side surface. This figure shows that the shape of the grains inside the matrix particles remains close to equiaxed although the matrix particles as wholes stretch along the material flow direction. This behavior of the material matrix is attributable to the active process of dynamic recrystallization, which causes the formation of new grains. In its turn, the dynamic recrystallization process in the matrix is responsible for the absence of a predominant lattice orientation. Thus, we can say that the formed microstructure of the matrix will have no effect on the measured elastic modulus. Figure 6: Schematic damage accumulation in the sintered metal matrix composite during plastic deformation. Figure 7: The fracture surface of the V95 alloy after specimen tension at room temperature. Figure 9 shows microcracks formed at the interparticle boundary in the V95\(\backslash\)10% SiC MMC before the appearance of macroracks on the side surface of the specimen due to compressive plastic deformation. The elastic modulus of the material must decrease due to microcracking, and this can be detected via instrumented indentation by pressing a diamond indenter into the material. When the indenter is pressed into the metal matrix composite, the indentation diagram is affected by both the composite matrix and the reinforcing particles. Under low loads, the indenter penetrates either only into the matrix or only into the reinforcing material, and this causes a large scatter in the indentation diagrams [41; 42]. As the load gradually increases, this scatter decreases and reaches a certain threshold value, which is determined by the variation of the macroscopic properties of the specimen and by the measurement error of the device. The correctness of using the technique for determining damage by the indentation technique requires that the volume of the deformed material under the indenter exceed the minimum material volume (representative volume) containing the number of the _carriers_ of the structural phase state sufficient for a statistical description of the material state. Reinforcing particles, matrix phases and interphase boundaries, matrix grains and subgrains, etc. act as such _carriers_ in metal matrix composites. The representative volume during indentation, as well as the determined value of the elastic modulus, depends on the indenter depth. The variation coefficient \(\delta\) was chosen as a measure of the relative variation of the reduced elasticity modulus, and the penetration depth dependence of the variation coefficient \(\delta\) was plotted thereafter. Such dependences for the V95\(\backslash\)10% SiC MMC are shown in Figure 10a. This figure demonstrates that the detected reduced elastic modulus for the composite remains unchanged at indenter penetration depth exceeding 12 \(\upmu\)m. Thus, for the correct determination of the local value of the reduced elastic modulus for the whole composite, not its structural components, the indenter penetration depth must exceed 12 \(\upmu\)m. In order to meet this requirement, all further micromechanical tests aimed at the determination of the reduced elastic modulus were performed at an indenter penetration depth of 15 \(\upmu\)m. Typical images of indents on the specimens at this penetration depth are shown in Figure 10b.