1

Introduction

Dental ceramics with high crystalline content were developed with the objective to provide materials with superior mechanical properties to produce all-ceramic restorations . Although the literature reports for alumina and zirconia-based systems fracture stress values well above the stresses estimated for the posterior areas of the mouth , there are reports of clinical failures . This behavior may be attributed to the fact that the prognosis of ceramic restorations is not only related to their high initial mechanical strength but also to a phenomenon called “subcritical crack growth” (SCG) . Ceramic components are susceptible to a stress-corrosion process that involves the stable growth of pre-existing flaws. The stress field at the crack tip can be described by the stress intensity factor in the opening mode ( K _I ) and the flaw will propagate when it reaches the critical condition, K _Ic (fracture toughness or critical stress intensity factor) .

When a ceramic material is subjected to a long period of stresses below the critical stress intensity factor ( K _Ic ) but above the threshold level ( K _I0 ), pre-existing flaws may grow slowly until reaching critical size, that triggers catastrophic failure . The SCG behavior results from a combination of stress concentration at the crack tip and the presence of water or body fluids molecules that chemically react with the strained atomic bonds . Many external factors that contribute to the SCG of ceramic materials are present in the oral environment such as humidity, pH and temperature fluctuations and stresses induced by loading (i.e. chewing) .

There is plethora of ceramic studies reporting only fast fracture data and neglecting the effect of the SCG phenomenon and cyclic fatigue in the reliability of these materials . This is explained by the fact that cyclic fatigue testing has a high cost due to the large number of specimens and long time required . To overcome these drawbacks, one possibility is to use accelerated lifetime tests in which specimens are subjected to stress levels lower than those used in fast fracture test but higher than those found during mastication so as to decrease the test duration to an acceptable period of time. However, the stress level used in these in vitro tests should ideally accelerate failure without adding new unrealistic failure modes that would not occur in clinical conditions . Among these methods are the staircase or up-and-down method , the boundary technique and the step-stress method . These tests were designed to analyze long lasting materials such as dental ceramics since it is impractical to obtain use level condition lifetime data because of the long time to failure .

The staircase method allows the researcher to precisely estimate the fatigue strength at 50% failure probability and to reduce the sample size. Yet, this method is not adequate to estimate low or high points of probability of failure (1% or 99%) , which is a disadvantage since the lifetime prediction in these extreme points is more important for engineering and biomedical materials. In the boundary technique, it is possible to estimate low or high points of failure probability with greater precision compared with the staircase method . In this technique, the critical points are the lack of criteria to choose some parameters used in the method and to assume a normal distribution of the data since fatigue lifetimes fit more properly to the two-parameter Weibull distribution.

In contrast to the constant stress amplitude used for the staircase method and for the boundary technique, in the step-stress method each specimen is subjected to time-varying stresses, which means that the magnitude of load changes after a period of time, for the same specimen, until failure occurs or the test is suspended. This technique assures that failure occurs quickly because it customizes the stress amplitude to the strength of the individual specimens, and different stress profiles can be used for each specimen .

Data obtained with accelerated life testing are fitted to a life-stress model and extrapolated to normal use conditions. When time-varying stress is used, like in step-stress method, the cumulative damage model should be used. This model takes into consideration the cumulative effect of the stresses applied at each level of time-varying stress. Data on surviving specimens can be included in the analysis (censored data). It is possible to find the probability of failure over time and to predict the reliability for a specific period of time . Studies have used step-stress accelerated life testing in dental research to assess the reliability and failure modes of layered ceramic specimens, metal-ceramic and all-ceramic restorations and implants .

Different methodologies can be used to evaluate the SCG and cyclic fatigue behavior of dental ceramics. A popular methodology is to perform cyclic loading for a pre-determined period of time using a chewing simulator and to apply, subsequently, a static load until failure occurs. The objective of this methodology is to assess the strength degradation produced by aging in an environment that is similar to the human mouth. However, there is not a standard protocol for the stress amplitude, frequency and number of cycles used in these simulations . Therefore, the objective of this study was to use the step-stress method to estimate the reliability of an alumina-based ceramic as to further design an aging mechanical test. To evaluate the accuracy of the reliability prediction, a group of specimens was aged using the optimum aging profile determined by the step-stress data and ALTA Pro 7 software. The hypothesis to be tested is that step-stress analysis is effective to predict alumina ceramic reliability. The results of this research can be used for efficient design of future accelerated lifetime ceramic studies.

2

Materials and methods

Bar-shaped alumina specimens were obtained by cutting pre-sintered blocks (VITA In-Ceram AL, Vita-Zahnfabrik, Germany) using a diamond disk in a precision cutting machine (Isomet 1000, Buehler, Lake Buff, USA) at 275 rpm. Specimens were sintered in the Zyrcomat furnace (Vita Zahnfabrik, Germany). Sintering was carried out at 1530 °C for 2 h with a heating rate of 25 °C/min. After sintering, the specimens were ground and polished to 1 μm finish to their final dimensions (2 mm × 4 mm × 16 mm). All edges were chamfered at a 0.1-mm wide chamfer, following ISO 6872:2008 . Specimens were divided into 3 groups ( n = 10): (1) step-stress accelerating test; (2) flexural strength/fast fracture – control; (3) flexural strength/fast fracture after mechanical aging.

Group 1 was tested in an electromagnetic actuator (MTS Evolution, MTS Systems Corporation) using a three-point flexure fixture (span = 12 mm) at a frequency of 2 Hz ( R = 0.1) and in a 37 °C deionized water bath. Each specimen was subjected to a different stress profile, and the number of cycles to failure was recorded. Each stress profile was designed considering data from all of the previous specimens and their individual lifetimes.

The three-point flexural strength equation used to calculate the stress value at failure is as follows:

where P is the fracture load (N), l is the span size (12 mm), w is the specimen width (4 mm) and b is the thickness of the specimen (2 mm).

A cumulative damage model with an inverse power law (IPL) lifetime-stress relation and a Weibull lifetime distribution were used to fit the fatigue data (ALTA Pro 7, Reliasoft).

The combined IPL-Weibull model is:

where P _f is the probability of failure at time t , σ is the stress level, β is the Weibull modulus, K and n are constants used to fit the model to the data set. The data was used to predict a safe stress level and number of cycles to perform a subsequent aging test (group 3) that could develop damage to the specimens without causing fracture.

Groups 2 (control) and 3 were tested for fast fracture in a three-point flexural strength ( σ ) design in a universal testing machine (Sintech 5G, MTS) at a constant stress rate of 1.0 MPa/s, in 37 °C deionized water bath. Before testing for fast fracture, group 3 was subjected to a mechanical aging in a chewing simulator. Aging was performed in deionized water and the load was applied using a three-point flexure fixture, at 2 Hz frequency. The stress (80 MPa) and number of cycles (10 ⁵ ) were determined by the step-stress analysis previously performed. The flexural strength results were statistically analyzed using Mann–Whitney Rank Sum test ( α = 0.05).

Fracture surfaces were examined using a stereomicroscope to determine the mode of failure based on the fracture origin and fractographic principles . Five specimens of each experimental group were randomly chosen and sputter-coated with gold-palladium and examined using a scanning electron microscope (SEM) to confirm and measure the critical flaw (c). The equivalent semi-circular flaw was determined using the following equation:

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