## Abstract

## Objectives

Evaluate the flexural strength ( *σ *) and subcritical crack growth (SCG) under cyclic loading of glass-infiltrated alumina-based (IA, In-Ceram Alumina) and zirconia-reinforced (IZ, In-Ceram Zirconia) ceramics, testing the hypothesis that wet environment influences the SCG of both ceramics when submitted to cyclic loading.

## Methods

Bar-shaped specimens of IA ( *n *= 45) and IZ ( *n *= 45) were fabricated and loaded in three-point bending (3P) in 37 °C artificial saliva (IA _{3P }and IZ _{3P }) and cyclic fatigued (F) in dry (D) and wet (W) conditions (IA _{FD }, IA _{FW }, IZ _{FD }, IZ _{FW }). The initial *σ *and the number of cycles to fracture were obtained from 3P and F tests, respectively. Data was examined using Weibull statistics. The SCG behavior was described in terms of crack velocity as a function of maximum stress intensity factor ( *K *_{Imax }).

## Results

The Weibull moduli ( *m *= 8) were similar for both ceramics. The characteristic strength ( *σ *_{0 }) of IA and IZ was and 466 MPa 550 MPa, respectively. The wet environment significantly increased the SCG of IZ, whereas a less evident effect was observed for IA. In general, both ceramics were prone to SCG, with crack propagation occurring at *K *_{I }as low as 43–48% of their critical *K *_{I }. The highest *σ *of IZ should lead to longer lifetimes for similar loading conditions.

## Significance

Water combined with cyclic loading causes pronounced SCG in IZ and IA materials. The lifetime of dental restorations based on these ceramics is expected to increase by reducing their direct exposure to wet conditions and/or by using high content zirconia ceramics with higher strength.

## 1

## Introduction

The use of ceramic materials in prosthetic dentistry has increased considerably over the past decade. Ceramics have been used to fabricate a wide variety of restorations including inlays, onlays, implants, crowns and fixed partial dentures on account of their biocompatibility, wear resistance and better esthetics. Due to their better esthetics, in particular, patients have become more demanding regarding the appearance of their restorations . Although all-ceramic restorations have shown enhanced esthetics compared with traditional metal-based restorations, the former are more prone to catastrophic failure .

Catastrophic failure of dental ceramics is caused by their brittle nature or, in other words, their inability to deform plastically at elevated stresses. In addition to brittleness, pre-existing defects in ceramics can gradually enlarge with time because of the reactivity of their ionic-covalent bonds towards water when submitted to external load. This phenomenon, known as subcritical crack growth (SCG) occurs at stress levels lower than the failure strength of the material and can markedly decrease the durability of ceramic restorations .

Cyclic fatigue is another phenomenon that can degrade the strength of ceramic materials over time by reducing its inherent toughness through progressive and localized structural damage. This degradation effect is particularly relevant in ceramic materials exhibiting toughening mechanisms, as for example the tetragonal-monoclinic transformation toughening observed in zirconia.

Data on clinical performance of all-ceramic restorations suggest that subcritical crack growth under cyclic loading is a major reason for premature failure of dental restorations.

Several methods have been used to evaluate the subcritical crack growth of ceramics under static or cyclic loading conditions . “Dynamic fatigue” tests, in which the flexural strength of specimens is measured as a function of the crosshead speed in a mechanical testing machine , is often used to determine SCG in the absence of cyclic load. Statistical methods based on experimental data for the initial strength and lifetime of specimens have also been successfully applied to evaluate the SCG of ceramics under static or cyclic load .

The fracture of ceramic materials originates from the largest and/or most favorably located flaw. The size and spatial distribution of flaws justify the need for a statistical approach to failure analysis . Weibull analysis is often used to statistically describe the strength of ceramics because it takes into account the typical asymmetric distribution of strength values of brittle materials . Higher values of Weibull modulus ( *m *) correspond to a higher level of structural integrity of the material (less variability), assuming comparable levels of strength between ceramics .

Despite its major importance for predicting the lifetime of ceramic prosthesis, few authors have studied the effect of SCG on dental ceramics . Fatigue studies on veneer–framework layered structures have shown that the failure of all-ceramic bridges is likely to start with the onset of SCG in the outer veneer ceramic layer that is in direct contact with saliva. Under cyclic loading and wet conditions, cracks on the veneer layer develop and eventually propagate towards the inner framework material . For zirconia-based frameworks, crack propagation from the veneer layer is usually arrested at the veneer–framework interface, exposing the inner framework material to the aqueous environment of the mouth . The influence of slow crack growth of pre-existing surface flaws as a failure mechanism in dental ceramics has also been demonstrated in dynamic flexure tests on a feldspathic porcelain typically used as veneer material in dental restorations . Since complete failure of zirconia-based all-ceramic prosthesis is likely to be determined by the mechanical behavior of the inner framework material, studies on the subcritical crack growth of dental ceramic frameworks are highly demanded.

The objective of this study was to evaluate the effect of an aqueous environment on the subcritical crack propagation (SCG) under cyclic loading of glass-infiltrated alumina-based (IA) and zirconia-reinforced (IZ) dental ceramics typically used as framework structures in all-ceramic restorations. To test the hypothesis that the wet environment influences the strength ( *σ *) and SCG of both ceramics, a statistical approach based on the Weibull distribution of strength and lifetime of identical specimens was used to determine the SCG behavior of these ceramics under wet and cyclic conditions.

## 2

## Materials and methods

Two slip-casted glass-infiltrated ceramics (Vita Zahnfabrik, Bad Säckingen, Germany) were used in this study: an alumina-based ceramic (IA, In-Ceram ^{® }Alumina; powder-batch 14450, liquid-batch EJ192, additive-batch 20660, glass powder-batch 10680) and an alumina-based zirconia-reinforced ceramic (IZ, In-Ceram ^{® }Zirconia; powder-batch 12110, liquid-batch EJ192, additive-batch 7620, glass powder-batch 12610).

Bar-shaped specimens (20 mm × 4 mm × 1.2 mm) of IA ( *n *= 45) and IZ ( *n *= 45) were fabricated according to the manufacturer’s instructions and the ISO 6872:2008 standard . This included chamfering of the specimens’ edges to minimize local stress concentration during mechanical testing.

The ceramic specimens were subjected to two types of tests: three-point bending (3P) and cyclic fatigue (F), which was performed either in dry (D) or wet (W) environment. The experimental groups ( *n *= 15) are presented in Table 1 .

Ceramics | Groups ( n = 15) |
Mechanical tests |
---|---|---|

IA | IA _{3P } |
Three-point bending in wet environment |

IA _{FD } |
Cyclic fatigue in dry environment | |

IA _{FW } |
Cyclic fatigue in wet environment | |

IZ | IZ _{3P } |
Three-point bending in wet environment |

IZ _{FD } |
Cyclic fatigue in dry environment | |

IZ _{FW } |
Cyclic fatigue in wet environment |

Before testing, the average surface roughness ( *R *_{a }) of all specimens was measured using a profilometer (Surface Roughness Tester SJ 400, Mitutoyo Corporation, São Paulo, SP, Brazil). Measurements used a cut-off value of 0.8 mm on a surface length of 4 mm. Five readings per surface were averaged and used to calculate the mean *R *_{a }value for each specimen.

## 2.1

## Flexural strength

All specimens from groups IA _{3P }and IZ _{3P }were placed in artificial saliva at 37 °C and subjected to three-point bending using a universal testing machine (Instron Model 4301, Instron Corp., Nowood, MA, USA). These measurements were carried out using a crosshead speed of 0.5 mm/min and a span of 16 mm between support rollers. A thermostat (Master, São Paulo, SP, Brazil) was used to maintain the artificial saliva at 37 °C.

Failure loads were recorded and the flexural strength values were calculated in accordance to the ISO 6872:2008 standard .

## 2.2

## Cyclic fatigue

Cyclic loading tests were performed using a MTS 810 Universal Testing Machine (Material Testing System/MTS Systems Corp., Minneapolis, MN, USA). Sinusoidal cyclic loading was applied to the ceramic specimens at a frequency of 10 Hz with a constant maximum load level of 70 N for IA and 80 N for IZ specimens. These maximum load values are equivalent to applied stress values of 264 MPa and 316 MPa ( *σ *_{max }) for the IA and IZ samples, respectively, which correspond to approximately 60% of the average flexural strength of the specimens . The fatigue tests were performed in dry (D) and wet environment until fracture of the specimens occurred. A constant relative humidity of 60% and temperature of 21 °C were used in the dry (D) tests, whereas the wet (W) condition was provided by keeping the specimens inside a chamber containing artificial saliva during testing.

## 2.3

## Weibull analysis

The strength and lifetime data obtained from the bending and cyclic fatigue tests, respectively, were described using Weibull statistics .

The initial mechanical strength data ( *σ *) were analyzed using the following equations :

ln ln 1 1 − F x = m ln σ − m ln σ 0

F x = x − 0.5 n

where *F *_{x }is the failure probability of the “ *x *” specimen after ranking the specimens in ascending order according to their strength ( *σ *), *n *is the total number of specimens tested, *σ *_{0 }is the characteristic mechanical strength or scale parameter that represents the strength at which 63.21% of the specimens fail, and *m *is the Weibull modulus or shape parameter of the distribution of strength data as a function of failure probability. The Weibull parameters, *σ *_{0 }and *m *, indicate the magnitude and scattering, respectively, of the measured strength data . The *σ *_{0 }and *m *were calculated from the *y *-scale intercept and the slope, respectively, of linear fittings to the strength data when plotted in a ln ln(1/(1 − *F *)) versus ln( *σ *) graph.

The lifetime data was described in terms of the number of cycles to failure ( *N *_{f }) using the following equation:

ln ln 1 1 − F x = m ln N f − m ln N f , 0

where *F *_{x }is the failure probability of the “ *x *” specimen (Eq. (2) ) after ranking the specimens in ascending order according to their lifetime ( *N *_{f }), *N *_{f ,0 }is the characteristic number of cycles to failure at 63.21% failure probability, and *m ** is the lifetime Weibull modulus. Similar to the strength distribution, the Weibull parameters *m ** and *N *_{f ,0 }were calculated from the *y *-scale intercept and the slope, respectively, of linear fittings to the lifetime data when plotted in a ln ln(1/(1 − *F *)) versus ln( *N *_{f }) graph.

## 2.4

## SCG parameters

The SCG under cyclic loading of the ceramic materials investigated in this study was described by the empirical law of Paris , which correlates the velocity of the propagating crack ( <SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='v’>vv

v

) with the stress intensity factor, *K *_{I }, as follows:

v = A Δ K I n = A ( 1 − R ) n K Imax n = A K Imax n

where Δ *K *_{I }is the amplitude of the stress intensity factor applied ( *K *_{Imax }− *K *_{Imin }), *K *_{Imax }and *K *_{Imin }are the maximum and minimum stress intensity factors applied, *R *is the stress ratio *K *_{Imin }/ *K *_{Imax }, *n *and *A *(or *A **) are the SCG parameters under cyclic loading.

In case of cyclic loading, the crack velocity is given by the crack size increment (d *c *) per number of cycles applied (d *N *): d *c */d *N *. *K *_{Imax }and Δ *K *_{I }are directly related to the maximum applied stress ( *σ *_{max }) and to the stress amplitude Δ *σ *, respectively, through Griffith’s law :

K Imax = σ max Y c

Δ K I = Δ σ Y c

where *Y *is a geometrical constant that depends on crack location and shape (equal to 1.3 for surface cracks) and *c *is the crack size.

For the tests performed in this study the applied cyclic stress varied between 0 and *σ *_{max }; thus *σ *_{min }= *K *_{Imin }= *R *= 0, Δ *σ *= *σ *_{max }, Δ *K *_{I }= *K *_{Imax }and *A *= *A **.

The SCG parameters in the empirical law of Paris are often derived from direct experimental data on the crack velocity as a function of applied *K *_{Imax }. Using the statistical approach described by Munz and Fett , *A *and *n *can also be calculated from the Weibull distributions of initial mechanical strength and lifetime of the test specimens. This method is applicable if (1) the group of specimens submitted to the strength tests is assumed to statistically display the same flaw size distribution as that of specimens submitted to the lifetime experiments and (2) cracks initiate from surface flaws in both tests. This is a reasonable assumption in this study, since identical, relatively rough, specimens were used for the strength and lifetime measurements.

To determine the SCG parameters *A ** and *n *from the strength and lifetime Weibull parameters, the following equations were used :

n = m m + 2

A = 2 ( K IC ) 2 − n ( σ 0 ) n − 2 N f , 0 Y 2 ( n − 2 ) ( σ max ) n

where *K *_{IC }is the critical stress intensity factor of the material.

The calculations of the SCG parameters *A *and *n *using Eqs. (7) and (8) were performed using *K *_{IC }values obtained from the literature: 4.4 MPa m ^{1/2 }for IA and 6.4 MPa m ^{1/2 }for IZ .

Taking into account the initial mechanical strength and SCG parameter results, the lifetime of dental restorations prepared with IZ and IA as framework materials was estimated, hence, Eq. (8) was slightly rearranged, and the number of cycles to failure ( *N *_{f }) was estimated as follows:

N f = 2 ( K IC ) 2 − n ( σ 0.05 ) n − 2 A Y 2 ( n − 2 ) ( σ max ) n