Issue 30

L. Guerra Rosa et alii, Frattura ed Integrità Strutturale, 30 (2014) 438-445; DOI: 10.3221/IGF-ESIS.30.53 439 Glass failure is the consequence of the growth of flaws, its behaviour strongly depends on the surface condition as well as on the environmental conditions and the thermal and mechanical loading history to which they are exposed to. Due to the much more scatter in the data of glass materials, very large safety factors are often used in glass element design, up to 8 or more. These large safety factors are somewhat arbitrary and not satisfactory, because it is not very clear what the true factor of safety really is. In recent years, considerable research efforts have been paid to improve the understanding of the load-carrying behaviour of structural glass elements, and many new design approaches have been proposed to improve the safety and serviceability of the structural glasses [2-6]. In 1972, Brown [7] proposed the “Load Duration Theory” (LDT), which combined the static fatigue theory of Charles & Hillings [8] with the statistical failure probability function proposed by Weibull [9]. In 1974, Evans [10] developed the “Crack Growth Model” (CGM) on the basis of the principles of Linear Elastic Fracture Mechanics. This method makes use of the empirical description of the sub-critical propagation of cracks (deduced from the experimental relationship between crack growth rate and stress intensity factor K I ) together with the Weibull failure probability under the hypotheses that a sub-critical crack growth takes place in all surface micro-cracks. Fishercripps & Collins [11] proposed a modified crack growth model, which is able to predict failure probabilities for both short and long term stresses [11]. Fernandes & Rosa [12, 13] presented a review on the “ring-on-ring” and “piston-on-3-ball” equibiaxial tests for ceramics and glasses, stress distributions in the test pieces were analysed, the importance of the effect of friction at the contact zones was discussed. Based on the Weibull statistics and experimental data obtained from testing silica glass rod specimens with diameters between 0.5 and 1 mm [14], a theoretical model was developed for estimating their fracture strength under different loading conditions [15]. By this method, the test results of strength from one testing type can be extrapolated to other test types, such as the uniaxial tension, 3-point bending, 4-point bending, etc. Besides, Rosa et al [16] studied the subcritical crack growth in three engineering ceramics under biaxial conditions, the results from the ring-on- ring tests were compared with 4-point bending tests. In 2001, Porter [6] proposed the Crack Size Design method (CSD); and in 2006 Haldimann [4] developed the Lifetime Prediction Model (LPM) where he calculated directly the failure probability of a glass element starting from the probability distribution of its defects and from the deterministic knowledge of loading time-history [4]. Recently, Santarsiero and Froli [2] formulated a new semi-probabilistic failure prediction method, called "Design Crack Method” (DCM), defining a new quantity called Design Crack, which takes into account of the probability of failure and the surface damaging level. Moreover, it is still a major concern to extrapolate the laboratory test results to applications for components under in- service conditions. A number of effects have to be considered, such as the size effect, the gradient effect or notch size effect, and multi-axial stress effect, etc. In Ref. [17], the extension of the weakest-link model to multiaxial stress states was verified by comparing fracture stress distributions obtained in four-point bending and in a concentric ring-on-ring test, and it was discussed about how the selected failure criterion influences the predicted distribution of the fracture stress of a component. Danzer et al [18] presented a new method for biaxial strength testing of brittle materials, the so-called ball on three balls (B3B) test method. A detailed analysis of the stress field in the specimens and of possible measuring errors were studied. The B3B-testing method has several advantages compared to common three or four-point bending tests and the ring-on- ring tests. From the above brief review of literature, it is shown that the mechanical behaviour of glass at breakage is very complex, more and more theoretical models as well as experimental methods have been developed. However, for engineering applications, the complexity of calculation procedures needs to be simplified reasonably. The motivation for this present work is to develop an integrated approach for analyzing the crack problem of the glass components in the CSP industry, to incorporate the probabilistic modelling, the principles of fracture mechanics and the details of the specific design in question. M ECHANICAL C HARACTERIZATION OF G LASSES FOR USE IN S TRENGTH F ORECASTING he most commonly used mathematical representation of the relationship between applied stress and probability of survival for glasses is the two parameter Weibull distribution as defined [19]: T