JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS, Vol. 10, No. 9, September 2008, p. 2433 – 2437 Spring-block type models for crack propagation in glass plates ♣ E.-Á. HORVÁTH a , F. JÁRAI-SZABÓ a,b* , Z. NÉDA a a Faculty of Physics, Babeş-Bolyai University, RO-400084 Cluj-Napoca, str. Kogălniceanu nr. 1 b Interdisciplinary Computer Simulation Group, KMEI, str. Tipografiei 12, RO-400101, Cluj-Napoca, Romania Crack propagation in thin glass plates under high shock loading is investigated by computer simulations. The widely used spring-block type model is adapted in order to reproduce the main features of the glass breaking phenomenon. Blocks represent mesoscopic elements of the glass while the coupling between them is modeled by elastic springs with well defined breaking threshold values. The amorphous structure of glass is captured by randomly distributed blocks and spatially randomly distributed friction forces. The localized external stress is applied by increasing the spring constants in a central region of the studied system. Therefore, radial crack lines will nucleate and propagate through the system. The simulations reproduce qualitatively well the experimentally obtained radial crack lines and the dynamics induced by the shock is also revealed. (Received March 31, 2008; accepted August 14, 2008) Keywords: Glass breaking, Monte-Carlo simulations, Burridge-Knopoff type models 1. Introduction Cracking and fragmentation of materials is a common phenomena being present from astrological length-scales down to nano and atomic scales. This is the reason why the phenomenon is still subject of large scientific and industrial interest. The glass breaking phenomena we are going to investigate is in the middle of this scale. Crack propagation in glasses, inelastic deformation and failure mechanisms produced by external shock loading has attracted extensive research in the last decades [1-4]. In the early sixties a scaling law was obtained for the size- distribution of the resultant pieces [5]. From that point on the experimental research focused on many other interesting aspects. In the last years the cracking process was investigated also by high-speed camera snapshot series [6]. At the same time, many theoretical models have been created in order to understand the breaking mechanisms of glass rods and plates, focusing mainly on the case of parallel shock loading [7]. Glass breaking produced by perpendicular projectile impact was experimentally investigated in the framework of a student research project by the group of Y. Bréchet [8]. As a results of these experiments the group qualitatively revealed and classified the breaking patterns. As presented in Figure 1. the most common structure has two concentric circles and many radial cracklines initiating from the impact point. In the present work crack propagation in thin glass plates under localized perpendicular shock loading is investigated using computer simulations. Based on the classical Burridge-Knopoff type spring-block model a very simple model is constructed, which reproduces qualitatively well the experimentally obtained radial crack lines. The objective of the present work is to investigate the applicability of the model, to find the relevant parameter values and to reveal the crack line formation and propagation dynamics. Fig. 1. Typical glass breaking pattern after a localized perpendicular shock loading [8]. 2. Theoretical model The model incorporates the main features of glasses: the amorphous structure, the elastic response to small stresses (local reorganization) and the plasticity in case of low stresses. In order to match these requirements within the framework of the spring-block some changes relative to the original Burridge-Knopoff type model is incorporated [9]. ♣ paper presented at the Conference “Advanced Materials”, Baile Felix, Romania, November 9-10, 2007.