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Identification of a Critical Time with Acoustic Emission Monitoring during Static Fatigue Tests on Ceramic Matrix Composites: Towards Lifetime Prediction^{ †}

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^{†}

## Abstract

**:**

_{f}/[Si-B-C] composite with a self-healing matrix at intermediate temperature under air. Static fatigue experiments were performed below 600 °C and a lifetime diagram is presented. Damage is monitored both by strain measurement and acoustic emission during the static fatigue experiments. Two methods of real-time analysis of associated energy release have been developed. They allow for the identification of a characteristic time that was found to be close to 55% of the measured rupture time. This critical time reflects a critical local energy release assessed by the applicability of the Benioff law. This critical aspect is linked to a damage phase where slow crack growth in fibers is prevailing leading to ultimate fracture of the composite.

## 1. Introduction

_{f}/[Si-B-C] composites in order to improve the lifetime under medium and high temperatures thanks to the formation of sealant glasses [8,9].

_{f}/SiC composites and the damage mechanisms occurring at high temperatures [1,2,3,4,5,6,7]. Now more information is needed at intermediate temperatures: the oxidation kinetics of the different constituents are complex, and the effect of matrix sealing on the lifetime of the composite has to be examined. Expected lifetimes in use conditions are several thousands of hours, which can hardly be reached by laboratory tests for practical reasons. Therefore, a real-time prediction of the remaining lifetime during tests is necessary. It requires the monitoring of damage evolution for which AE measurement is a suitable technique. In fact, the AE technique consists in the recording and analysis of elastic waves created during material damage. It provides real-time data on initiation and evolution of damage in terms of location and mode.

_{f}/[Si-B-C] composite with a self-healing matrix. A lifetime diagram is presented, and the evolution of several damage indicators is discussed. The objective of this approach is to propose a method based on acoustic energy in order to evaluate the remaining lifetime during long-term mechanical tests. This approach is based on the determination of energy released and identification of a critical point, in energy release during mechanical test. Therefore, two criteria have been defined which allow predicting the end of a static fatigue test knowing the AE activity emitted during the first half of the test. Therefore, beyond this characteristic point the criticality can be described by a power-law in order to evaluate time to failure. Moreover, a supervised classification method was used to differentiate the signals generated during fatigue tests performed on composites at intermediate temperature and build a specific library [16]. This library was used to identify the damage modes generated during fatigue tests performed at various temperatures, in order to establish a link between this critical time and the damage mechanisms.

## 2. Experimental Procedure

#### 2.1. Material

^{2}.

**Figure 1.**(

**a**) SEM micrograph of the cross-section of SiC

_{f}/[Si-B-C] composites; (

**b**) Typical fracture surface of SiC

_{f}/[Si-B-C] composite.

#### 2.2. Static Fatigue Tests

_{0}is the elastic modulus in the undamaged state.

**Figure 2.**Schematic hysteresis loop and measure of the hysteresis loops modulus, E

_{0}is the initial Young’s modulus, E

_{i}is the secant elastic modulus for the unloading-reloading cycle i.

#### 2.3. Acoustic Emission Monitoring

_{0}was determined before tests using a pencil lead break procedure on as received composites. This velocity was measured equal to 10,000 m/s. Since the elastic modulus decreases as damage occurs in the material, it is important to take into account the evolution of Ce during the mechanical test in order to better evaluate the location of the AE sources. As proposed by Morsher [25], the elastic secant modulus during unloading E

_{i}(ε) was measured during a cycled tensile test, where hysteresis loops were obtained at different strains. The velocity Ce(ε) was then determined by using the Equation (1):

_{0}and E

_{0}are respectively the velocity and the elastic modulus in the undamaged state and C

_{e}(ε), E

_{i}(ε) respectively the velocity and the elastic modulus under a maximum strain ε. At the end of the tensile test, the velocity on SiC/SiC composite was found to be equal to 6480 m/s, instead of 10,000 m/s on the undamaged state. This decrease of wave velocity is thus not negligible. The location of sources has been calculated using the difference in times of arrival on each sensor. Only the signals coming from the working length of the specimens are then analyzed.

## 3. Acoustic Emission Analysis

#### 3.1. Definition of the Acoustic Energy

_{s}(n) is the energy released at source n in the form of elastic waves. Due to differences in coupling between sensors and material surface or in sensors frequency responses, for a source at equal distance, the sensors may record significantly different amounts of energy. Thus, A

_{1}is the proportion of source energy that is recorded by sensor 1. It is a constant characteristic of sensor. L + x(n) is the propagation distance from source n to the sensor 1 (2L is the distance between two sensors). The attenuation coefficient B is linked to the propagation medium, which may change with damage evolution. Similarly, AE signal energy received at sensor 2 is expressed as:

#### 3.2. Attenuation Coefficient B

#### 3.3. Coefficient of Emission R_{AE}

_{loading}is the cumulative AE energy for all the signals recorded during the initial loading up to the nominal load of the test, $\Delta E$ is the cumulative AE energy for all signals recorded during the interval [t; t + $\Delta t$].

#### 3.4. Power Law

_{i}is the energy of the ith AE signal detected and N(t) is the number of AE signals recorded and located along the gauge length until time t.

_{R}, t

_{R}is the failure time. $B=-\frac{\mathsf{\varphi}}{1-\mathsf{\gamma}}$ is negative, $1-\mathsf{\gamma}$ is an exponent and φ is a constant.

_{start}when the AE energy is well simulated by the Benioff law. Two approximations are carried out on the energy release resulting from each time interval [t

_{start}; t

_{r}]: a power-law approximation using the Benioff law and a linear approximation (Ω(t) = αt + β) used as reference. The c-value is defined by the ratio of the root mean square error of the approximation by the Benioff law over that of the linear fit. When the c-value is lower than 1, there is a positive contribution of the Benioff law since the approximation error is lower than that of a linear fit. It is a relative validation of the relevance of the approximation by the Benioff law. Therefore, to ensure quality of the approximation, only c-values lower than 0.5 are considered to be relevant.

#### 3.5. Identification of Damage Mechanisms with Supervised Clustering

## 4. Results and Discussion

#### 4.1. Mechanical Analysis

**Figure 3.**(

**a**) Lifetimes obtained during static fatigue at 450 °C, 500 °C and 560 °C under air on SiC

_{f}/[Si-B-C] composites for several applied stresses; (

**b**) Lifetimes on the fibers bundles [34] and on SiC

_{f}/[Si-B-C] composites in static fatigue at 500 °C under air.

_{i}. Then the damage parameter D = 1 − E

_{i}/E

_{0}was calculated, E

_{0}being the initial Young’s modulus of the composite. The evolution of D is plotted versus time in Figure 5, for several σ/σ

_{R}ratios. The biggest increase of D occurs during the loading step and the first 24 h of static fatigue. Then D is observed to rise monotonically up to the failure of the specimen. The general trend is that the highest the σ/σ

_{R}ratio, the highest the D parameter for similar durations of test. The final D values obtained at failure are not exactly the same: they vary in the range 0.6–0.8, and it seems that this value decreases when the σ/σ

_{R}ratio decreases. However it seems difficult to define a failure criterion based on the damage parameter.

**Figure 4.**Stress versus strain during static fatigue experiments for different σ/σ

_{R}ratios: 0.44, 0.71 and 0.95 at 500 °C on SiC

_{f}/[Si-B-C] composites. The grey curve represents the monotonic tensile curve.

**Figure 5.**Evolution of the damage parameter D during static fatigue experiments for various σ/σ

_{R}ratios 0.44, 0.56, 0.62, 0.71, 0.79 and 0.95 at 500 °C on SiC

_{f}/[Si-B-C] composites.

_{R}= 0.44. Under the steady loading the strain rate is important at the beginning then decreases before reaching a constant value. At this time, strain rises monotonically up to the final failure for the majority of the specimens (Figure 6b). The AE activity recorded during the constant load hold is also plotted in Figure 6b. The acoustic emission activity evolves with the same trend. Figure 6c shows the evolution of the cumulated acoustic energy. The main activity occurred at the beginning of the test and then reached a plateau. The renewal of AE activity (Figure 6c) just before failure seems to be an interesting way to anticipate the fracture but was not always noticeable on the AE energy vs. time plot.

**Figure 6.**(

**a**) Stress-strain curve and cumulated number of acoustic emission (AE) events recorded during initial loading up to the nominal load, and during the static loading at a constant load (σ/σ

_{R}= 0.44 and T = 500 °C); (

**b**) Strain and cumulated number of AE events versus time; (

**c**) Cumulated acoustic energy versus time.

**Figure 7.**Number of AE events recorded during initial loading up to the nominal load and during the static loading at a constant load.

#### 4.2. Identification of Critical Time

_{m}, and then to increase up to the failure of the composite at time t

_{R}. This ultimate increase in AE activity was not always visible on the curves of AE energy versus time, but it was revealed by this representation. The ratio t

_{m}/t

_{R}appears to be quite reproducible: t

_{m}/t

_{R}=0.57 ± 0.06 (Figure 9). Therefore, the ${R}_{AE}$ ratio may be used as a criterion for predicting the remaining lifetime of a specimen under static loading. During static fatigue test, attenuation coefficient B growths significantly during the first part of tests up to a plateau value near 50% of the rupture time (Figure 10). For each test, the slight increase of B observed during initial loading is very low compared to the one occurring during static fatigue. Therefore, the increase of attenuation coefficient B may be related to matrix crack opening and to the recession of interfaces.

_{AE}, the value plateau of B indicates the beginning of the critical damage phase and provides an estimation of the remaining lifetime.

**Figure 8.**Evolution of the R

_{AE}coefficient during the static load hold on SiC

_{f}/[Si-B-C] composites.

**Figure 9.**Critical times obtained with the minimum value of R

_{AE}and the optimum t

_{sart}for the Benioff law obtained with the OCM method.

**Figure 10.**Evolution of the attenuation coefficient B during the static load hold (σ/σ

_{R}= 0.95, σ/σ

_{R}= 0.71 and T = 500 °C).

_{AE}is calculated for several damage mechanisms identified with clustering analysis of AE data. The Figure 11 show the activities of several damage mechanisms identified with the supervised analysis. During static fatigue, clusters B and D are more active. The evolution of the coefficients B obtained for the two classes A and B go through a minimum, contrary to those of classes C and D (Figure 12). For the B class (mainly fiber failure at the end of the tests), the minimum value of the coefficient B is observed around 65% of the lifetime. For the A class (mainly yarn fractures or collective fiber breaks at the end of the tests), the minimum is also observed at 65%. One may noticed that the minimum is observed only for clusters A and B corresponding to fibers breaks during the second part of the test. If the growth of the attenuation coefficient B is linked to matrix crack opening, coefficient B also allows considering the plateau observed on the evolution of attenuation coefficient B shows that matrix crack opening leads to an equilibrium state near 40%–50% of the rupture time. The significant increase of matrix crack opening pointed out before 50% of the rupture time is linked to carbon oxidation in the interphases provoking an increase in length of the debonded region of fibers in the vicinity of matrix cracks. Beyond 50% of the rupture time, the oxygen flux, determined by the degree of matrix crack opening, controls the rate of fibers break by slow crack growth. This critical time corresponds to the beginning of a second damage phase where slow crack growth in fibers is prevailing, leading to the ultimate fracture of the composite.

**Figure 12.**Evolution of the coefficient of emission for several clusters at 500 °C and σ/σ

_{R}= 0.79.

#### 4.3. Toward Lifetime Prediction

_{r}, γ, φ and t

_{r}).

_{AE}were in better agreement with the Benioff law than those before the minimum. This point was confirmed with the estimation of the c-value.

_{start}are reported on the Figure 9, which means that the approximation by the Benioff law was relevant for the data collected behind this time. A value of t

_{start}was taken every hour in time interval of 10% to 90% of rupture time t

_{r}. The minimum c-value appears clearly around on average 40%–50% of rupture time. The energy release prior to rupture under static fatigue exhibits a critical evolution at 50% of rupture time regardless of the applied stress level. Thus, the Benioff law, initially used to study the activation of earthquakes, may also be applied to the damage of composites. However, this procedure requires preliminary tests until rupture to determine γ and φ for the studied material.

## 5. Conclusions

_{f}/[Si-B-C] composite. The lifetime as a function of applied stress follows a power-type law, which can be used to predict lifetimes. Additional information is obtained from strain measurement and AE monitoring during the tests. Two criterion based on the AE cumulative energy has been defined, which can be used to predict the final failure of a specimen if the AE activity during the first half of the test is known. This could be a way to shorten such static fatigue experiments, and to divide their duration by 1.5. The coefficient R

_{AE}and the attenuation coefficient B confirm the existence of two distinct phases during damage of CMCs in static fatigue at intermediate temperatures. The first phase being mainly attributed to interfacial changes and the second one to the predominance of subcritical crack growth in fibers. Beyond this characteristic point, energy release may be modelled with the Benioff law in order to extrapolate AE activity and hence evaluate time to failure. The same analysis is in progress for the behavior during cyclic fatigue tests. Future works will focus on the use of the Benioff law as a predictive model.

## Acknowledgment

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Godin, N.; Reynaud, P.; R’Mili, M.; Fantozzi, G.
Identification of a Critical Time with Acoustic Emission Monitoring during Static Fatigue Tests on Ceramic Matrix Composites: Towards Lifetime Prediction. *Appl. Sci.* **2016**, *6*, 43.
https://doi.org/10.3390/app6020043

**AMA Style**

Godin N, Reynaud P, R’Mili M, Fantozzi G.
Identification of a Critical Time with Acoustic Emission Monitoring during Static Fatigue Tests on Ceramic Matrix Composites: Towards Lifetime Prediction. *Applied Sciences*. 2016; 6(2):43.
https://doi.org/10.3390/app6020043

**Chicago/Turabian Style**

Godin, Nathalie, Pascal Reynaud, Mohamed R’Mili, and Gilbert Fantozzi.
2016. "Identification of a Critical Time with Acoustic Emission Monitoring during Static Fatigue Tests on Ceramic Matrix Composites: Towards Lifetime Prediction" *Applied Sciences* 6, no. 2: 43.
https://doi.org/10.3390/app6020043