where: sh ¼hoop stress on the outer surface P ¼internal pressure ri ¼inner radius of the sample ro ¼outer radius of the sample The internal pressure (P) in Eq. (46.1) is back calculated using the hoop and axial strains measured on the aluminum adapter, based on thick-wall cylinder theory and generalized Hooke’s law. The calculated internal pressure P matches closely to that indicated on the analog pressure gage of the pressure generator. During the test the internal pressure was varied between 6.9 MPa (1,000 psi) and 96.5 MPa (14,000 psi), in loadingunloading cycles. Results for the cumulative AE energy and the average hoop strains plotted vs. the time are shown in Fig. 46.4. Surface strain data measured by the DIC method and the strain gage are both shown in Fig. 46.4. For internal pressures of less than 27.6 MPa (4,000 psi) the strain calculated using the DIC method and strain gage readings track each other fairly well, except that the DIC data have more noise than the strain gage readings. Above 27.6 MPa (4,000 psi) the obtained DIC strain values are higher than that of the strain gage readings, except at 96.5 MPa (14,000 psi). The SiCf-SiCm sample has an uneven and textured surface which contains rather large wavy fiber tows, as shown in Fig. 46.1. The active element of strain gage is about 2 ~ 3 the width of the fiber tow. Before mounting the strain gage, the SiCf-SiCmsample surface was not abraded due to concerns of abrasive affecting the strength properties of the sample; hence the adhesion quality may not be as good and as uniform as what can be achieved on abraded flat metal surfaces. Under large hoop stress, the fiber tows will tend to rotation (scissoring) and align with the principal stress direction. This might have induced some local debonding of the strain gage, which reduces the strain gage reading. However, the edge of the foil gage may still be bonded, so when the sample stretch to a certain extent, the active element gage gets pulled and bend over the protrusion of the fiber tow, the gage bending strain may have caused the strain gage readings exceeding that of the DIC value in the last loading-unloading cycle. In contrast, the DIC, as a non-contact method, can tolerate surface irregularities much better than the strain gages up to relatively high strain amplitude before the speckle paint layer starts to spall off. The cumulative AE energy is an indicator of the damage accumulation process in the SiCf-SiCmsample during the test. The hoop stress on the outer surface of the sample can be calculated by Eq. (46.1); when this hoop stress is below 41.4 MPa (6,000 psi internal pressure) the cumulative AE energy is very low. The AE energy sharply increases whenever the strain surpasses the highest peak strain of the past loading history, known as Kaiser effect [14]. The AE energy curve thus forms a distinct stair shape. The rise of AE energy is believed to be associated with internal material damage events, such as matrix cracking and fiber sliding. For this test, the SiCf-SiCm sample tube did not fail at the end of this test (pressurized up to 14,000 psi) and no apparent cracks or permanent deformation could be seen by visual examination however some internal damage has occurred as indicated by the emission of acoustic waves [15]. In another test, failure of the sample occurred at an internal pressure of 131 MPa (19,000 psi). Fig. 46.4 Cumulative AE Energy and Calculated Hoop Stress vs. Time 46 High Pressure Burst Testing of SiCf-SiCmComposite Nuclear Fuel Cladding 391
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