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Slow crack growth can be described in a v (crack velocity) versus KI (stress intensity factor) diagram. Slow crack growth in ceramics is attributed to corrosion assisted stress at the crack tip or at any pre-existing defect in the ceramic. The combined effect of high stresses at the crack tip and the presence of water or body fluid molecules (reducing surface energy at the crack tip) induces crack propagation, which eventually may result in fatigue. The presence of a threshold in the stress intensity factor, below which no crack propagation occurs, has been the subject of important research in the last years. The higher this threshold, the higher the reliability of the ceramic, and consequently the longer its lifetime.

We utilize the Irwin K-field displacement relation to deduce crack tip stress intensity factors from the near crack tip profile. Cracks are initiated by indentation impressions. The threshold stress intensity factor is determined as the time limit of the tip stress intensity when the residual stresses have (nearly) disappeared.

The intention of the present paper is to stress the point that the threshold stress intensity factor represents a more intrinsic property for a given ceramic material than the widely used toughness (bend strength or fracture toughness), which refers only to fast crack growth. Considering two ceramics with identical threshold limits, although with different critical stress intensity limits, means that both ceramics have identical starting points for slow crack growth. Fast catastrophic crack growth leading to spontaneous fatigue, however, is different. This growth starts later in those ceramic materials that have larger critical stress intensity factors.

Slow crack growth is most suitably described in a v (crack velocity) versus K I (stress intensity factor) diagram. Slow crack growth in ceramics is attributed to corrosion assisted stress at crack tips or at any defect pre-existing in the ceramic [1]. The combined presence of body fluid molecules (mainly water), which reduce the surface energy at the crack tip, and the presence of high stresses are the reasons for subcritical crack growth (SCCG) in ceramics.

The presence of stress intensities above a critical value (KI > KIc) initiates fast catastrophic crack growth, followed by the deterioration of a dental or a body restoration machined from ceramics. The presence of stress intensities above a threshold value (KI > KI0) initiates SCCG in ceramics, followed by a slow, however continuous, erosion of the strength of a restoration which also may result in final fatigue. In an early stage of ceramic research it was believed that this lower limit for SCCG is very close to zero. In the mean time, however, one has learned that for most ceramic materials the lower limit for SCCG is significantly larger than zero. Indeed, it may even be just below K Ic .

The threshold limit K I0 corresponds to a crack equilibrium at null crack velocity. Therefore, it allows a safety range of clinical use. The higher the value of K I0 , the higher the reliability, and hence the lifetime of a restoration. Bio-components should be designed to work in a region of the v-K I - diagram where the upper border line of that region corresponds to the threshold limit.

In principle, the proper test for existence of a threshold lies in the observation of reversibility of crack growth. The threshold can be regarded as a Griffith quiescent point, where forward and backward fluctuations just balance, i.e., the mean velocity of the crack tip becomes zero. The forward and backward fluctuations take place over discrete energy barriers definable as G = W = 2γ, where G is the energy release rate, W is the Dupré work of adhesion, and γ is the surface energy. If G

Another method uses a side grooved specimen with a crack propagating along its length, and under a bending condition similar to four point bending. The crack velocity can be obtained from the rate of load relaxation at constant displacement and the initial crack length. Having established the v - K diagram, the threshold is determined as described above. For further details refer to [10].

Using a micro-hardness testing machine, a Vickers indentation is made on the carefully polished surface of a sample of the ceramic to be investigated. Radial cracks emanate from each of the four indentated corner sources.

Example of a Vickers indentation. Only one of four corners is shown (length of diagonal 115 μ m). With the crack tip as a starting point (x = 0) the crack width 2*u(x) is measured at the distance x (COD after Irwin [15]; ceramic material for this example: Empress 1). The residual tensions cause crack growth over a long time interval until, at the end of the crack, K tip is equal to K I0 . Crack tip shielding by secondary effects (micro structural elements which toughen material as the crack extends) may slightly distort results (measured K I0 then lower than true K I0 ). Insert: idealized COD.

The measured profiles can be attributed to the crack opening displacement (COD) near the crack tip [14]. The near crack tip profiles for stress-free crack surfaces are usually represented by the Irwin K-field displacement relation [15], with 2u being the total COD, x the distance from the crack tip, and the plane strain Young's modulus E' = E/(1-v2);(v = Poisson's constant) being.

We assume that there is no crack shielding. Then, in equilibrium, the currently acting crack tip stress intensity factor K tip is balanced by the toughness of the material K Ic (mode I loading [15]):

We carried out ESEM analyses of crack profiles after 1 hour and then after up to 420 days, at 5 dates distributed over the whole time interval (Fig. 3). After indentation and between two measurements the samples were stored at normal lab environmental conditions (21°C, 65 % humidity).

As examples, Fig. 1 shows a crack starting at the corner of a Vickers indentation (right hand) and Fig. 2 shows a plot representing data for "Cerec Mark II" two days after indentation, as a function of distance from crack tip x (2 μ m

K tip (t) values of nine out of the thirteen ceramics investigated. The gradual decrease of K tip (t) with time due to decaying stress intensity at the crack tip becomes apparent.

K Ic is the lower limit for (fast) catastrophic crack growth. Stress intensities exceeding this limit cause fast crack growth at supersonic velocity, and eventually result in destruction of ceramic components. This kind of destruction, however, is not the most common or important, since it can be avoided by strictly limiting the stress intensities existing throughout a component by a suitable shape of construction.

K I0 is the upper limit of stress intensities for absence of crack growth and the lower limit for (slow) subcritical crack growth (SCCG). Limiting stress intensities such that they stay always below K I0 means infinite life time for a component, since SCCG becomes irrelevant. Hence, the most favorable characteristic stress intensity values are obvious: K Ic as high as possible and K I0 as close as possible to K Ic . Such a selection minimizes the extension of the interval in which subcritical crack growth can take place, and it maximizes resistance to catastrophic crack growth due to overloading. Fig. 5 gives a ranking of all ceramics currently tested, based on threshold values related to the corresponding critical values K I0 /K Ic . Favorable ceramics within their class of toughness are situated at the right hand side of the chart. Note, however, that a perfect ceramic material dependent on the focused area of application has not only a favorable (threshold/critical) stress strength relationship but also a high K Ic value.

There is one other aspect to be considered when comparing zirconia and alumina. The exponents n of SCCG of both ceramics are high (in principle meaning slow SCCG), and the answer to the question of which of the materials has the larger exponent depends on whether static or cyclic behavior is addressed: nstatic = 39 vs 104 and ncyclic = 28 vs 16 for Al2O3 and Y-PSZ, respectively [16]. These parameters show that lifetimes are shortened and crack growth rates are significantly accelerated by cyclic loading compared to static loading.

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