Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech Statistical interference of crack healing on the strength of thermally-treated glass. Experiments and modelling Gabriele Pisano a , Gianni Royer Carfagni b,a, ⁎ , Jens Schneider c a Construction Technologies Institute – Italian National Research Council (ITC-CNR), Viale Lombardia 49, I 20098 San Giuliano Milanese, Italy b Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, I 43100 Parma, Italy c Institute of Structural Mechanics and Design, Technische Universitat Darmstadt, Franziska-Braun-Strabe 3, 64287 Darmstadt, Germany ARTICLEINFO Keywords: Glass Thermally-treated glass Crack healing Micromechanics Statistical model ABSTRACT The macroscopic strength of thermally-treated glass is determined by the critical propagation of surface microscopic cracks, occurring only after that the surface compression, induced by the heating and successive cooling, has been overcome. A large experimental campaign has been conducted for the statistical characterization of the bending strength of annealed (untreated) and thermally-toughened glass, after having preliminarily measured the surface compressions with non-destructive methods. A deviation is found between the measured strengths for thermally- toughened glass and the corresponding theoretical values, derived from the statistical inter- ference between the populations of untreated-glass strengths and heat-induced surface com- pressions. This discrepancy is attributed to the healing of surface microcracks. A micro-me- chanically motivated model of fracture mechanics is proposed, which allows to statistically interpret the experimental data by correlating the effects of healing with the size of the cracks. This study confirms, in general, that crack healing can alter the macroscopic strength of tempered glass, but it also evidences, in particular, that this phenomenon is of importance only for the highest quantiles of the population of strengths, which are not relevant in structural design. Therefore, neglecting this effect is certainly on the safe side, but not excessively conservative. 1. Introduction In order to enhance its bending strength, a common treatment consists in heating and successively cooling glass (tempering 1 process) so to induce a permanent eigenstress, characterized by high compressions of the glass surfaces. Failure is associated with the state in which a dominant surface crack reaches the critical opening stress, but this can only occur after that the surface pre- compression has been overcome. Therefore, in the design practice, the characteristic strength is generally calculated by summing up the characteristic values (usually the 5% lower quantile) of pristine-glass strength and thermally induced surface prestress. However, there is a noteworthy difference between the theoretically derived values and the experimental results. This discrepancy may be attributed to the statistical interference of the primary variables [34], but other phenomena, such as crack healing due to the thermal https://doi.org/10.1016/j.engfracmech.2018.11.025 Received 3 August 2018; Received in revised form 6 November 2018; Accepted 10 November 2018 ⁎ Corresponding author at: Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, I 43100 Parma, Italy. E-mail addresses: pisano@cnr.itc.it (G. Pisano), gianni.royer@unipr.it (G. Royer Carfagni), schneider@ismd.tu-darmstadt.de (J. Schneider). 1 The term quenching is usually used to denote the process of rapid cooling which in metals preserves crystalline phases stable only at high temperatures, thereby reducing the mobility of dislocations. The term tempering is here used to denote the technique designed to produce a pre- stressed state in inorganic float glass through rapid cooling, without modifying its amorphous structure. Engineering Fracture Mechanics xxx (xxxx) xxx–xxx 0013-7944/ © 2018 Elsevier Ltd. All rights reserved. Please cite this article as: Pisano, G., Engineering Fracture Mechanics, https://doi.org/10.1016/j.engfracmech.2018.11.025