Modeling of Crack Self-Healing Kinetics
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ling of Crack Self-Healing Kinetics M. N. Perelmuter1* 1
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia * e-mail: [email protected] Received July 02, 2019, revised July 02, 2019, accepted July 16, 2019
Abstract—A model based on the concept of interface crack bridging and thermofluctuation theory is proposed for analyzing the efficiency of crack self-healing in composite materials in view of three main stages: (1) crack initiation and growth under external load, (2) self-healing activation, and (3) self-healing with partial or complete bond recovery between crack faces. A system of singular integro-differential equations is derived for numerical estimations of bond tractions in bridging zones during their formation and stress intensity factors (major characteristics of crack self-healing efficiency) with account of external loads and bond tractions. Kinetic estimates are presented for the time of bond recovery during the formation of a crack bridging zone. The model is applied to an interface crack between two dissimilar materials with a self-healing adhesive. Keywords: self-healing, interface crack, bridging zone, bond rupture and recovery, stress intensity factors DOI: 10.1134/S1029959920040037
1. INTRODUCTION In the last decade, self-healing materials technologies have come to the attention of researchers [1–3]. Being borrowed from natural biological systems, the property of self-healing allows a material to recover from defects and cracks without human intervention, which is particularly needed where such intervention is hard or impossible due to remote or extreme service conditions of materials or where construction parts are inaccessible for fracture prevention. The mechanism of self-healing, showing its best on micro- and nanoscale crack scales, depends on the type of materials. In natural materials, e.g., ice [4], such healing can be conditioned by a decrease in temperature and attendant changes in their aggregate states, and in polymer materials, by heating or other processes which provide their chemical or physical activation [5]. Among the self-healing materials designed to date are composites with a microencapsulated healing agent (cyclopentadiene) released upon crack intrusion and polymerized by contact with an embedded catalyst [6], composites containing a system of reagent-filled hollow fibers or a so-called microvascular network [7], and fiber-reinforced composites with embedded shape memory alloy wires [8]. Electrically conductive carbon nanotube additives infiltrated into a host composite are highly efficient for
fast defect repair by electric current [9], and carbon tube integration with a healing agent into a polymer matrix serves not only for repair but for reinforcement as well [10]. Much attention is focused on ceramic materials whose self-healing results from hightemperature oxidation, diffusion, and phase transformations [11, 12]. In metals with their strong atomic bonds, low diffusivity, and high melting points, such self-healing can be at
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