## 3 Methodology for Measuring Damage in a Metal Matrix Composite and Discussion of Results
### Damage Measurement Technique
Figure 8: The initial state (**a**), the state after deformation at 300 (**b**), 400 (**c**), and 500 \({}^{\circ}\)C (**d**) for the V95\(\backslash\)10% SiC metal matrix composite. Figure 11 shows the behavior of the reduced elastic modulus \(E*\) on the side surface of the metal matrix composite specimen depending on specimen strain \(\varepsilon\) at test temperatures of 300, 400 and 500 \({}^{\circ}\)C. The strain at each time \(t\) is calculated by the formula \(\varepsilon=\sqrt{\frac{2}{3}\varepsilon_{ij}\varepsilon_{ij}}\)  
Figure 10: The penetration depth dependence of the variation coefficient \(\delta\) for the V95\(\backslash\)10% SiC MMC (**a**) and a typical image of an indent on the specimens (**b**) at an indenter penetration depth of 15 \(\upmu\)m.  
Figure 9: The microstructure near the side surface of the sintered V95/10% SiC MMC specimen after compression at temperatures of 300 \({}^{\circ}\)C and \(D_{E}=0.28\) (**a**), 400 \({}^{\circ}\)C and \(D_{E}=0.27\) (**b**), 500 \({}^{\circ}\)C and \(D_{E}=0.28\) (**c**,**d**). The images were obtained from a longitudinal thin section with a plane passing through the symmetry axis of the specimen (see Figure 2). where \(e_{ij}\) denotes strain tensor deviator components determined from the results of the finite element simulation of cylindrical specimen compression (see Section 2). The data in Figure 11 show that the value of \(E*\) decreases with increasing strain. For temperatures of 300 and 400 \({}^{\circ}\)C, as soon as the strain reaches the value \(\varepsilon=0.65\), there is a sharp decrease in the reduced elastic modulus \(E*\). At a temperature of 500 \({}^{\circ}\)C, this occurs as early as at \(\varepsilon=0.4\). Figure 9 shows the microstructures of the composite specimens in the region close to the side surface. These microstructures were obtained after compression to the strain \(\varepsilon=0.76\) at temperatures of 300 and 400 \({}^{\circ}\)C and \(\varepsilon=0.59\) at a temperature of 500 \({}^{\circ}\)C. As seen from this figure, the microstructures of the specimens before fracture are similar to each other. For all the test temperatures, the specimens have plenty of microcracks at the interparticle boundaries and micropores inside the matrix. Further deformation of the specimens leads to the appearance of macroracks on the side surface at \(\varepsilon=0.78\) for temperatures of 300 and 400 \({}^{\circ}\)C. For a temperature of 500 \({}^{\circ}\)C, macroracks appear at \(\varepsilon=0.63\). Figure 9c shows a cavity defect on the specimen side surface, which may come out to the surface and develop into a macrocrack with further specimen compression. Material damage \(D_{E}\) is here considered to mean a measure that characterizes the degree of strain-induced material defectiveness. At the same time, the value of material damage is equal to 0 prior to deformation. At the time of macrocrack formation, damage takes the value equal to 1. In order to determine the moment of macrocracking, the specimens were deformed to different strains, and the moment of macrocrack appearance was determined iteratively. The presence of a macrocrack was detected by means of an optical microscope with \(\times\)20 magnification. The parameter \(D_{E}\) is calculated by the formula found in [7],  
\[D_{E}=1-\frac{E_{cur}}{E_{in}} \tag{1}\]  
where \(E_{in}\) is the elastic modulus of the specimen in the initial (undeformed) state; \(E_{cur}\) is the elastic modulus of the specimen before macrocracking, i.e., at a current value of strain \(\varepsilon\). The data obtained by the instrumented indentation technique do not allow us to determine the elastic modulus directly.