Strength Of Damaged Structures Research Articles

A geometric study for determining the optimum volume fraction of pre-embedded capsules for self-healing of cracks in a cementitious matrix

Autonomous healing of cracks using capsule-based systems is emerging as a promising solution to restore durability and strength of damaged structures. For satisfactory self-healing efficiency, both capsule geometry and dosage are to be determined for the concrete mix proportion. With previous research being performed on self-healing efficiency using different capsule shapes and crack patterns, this paper introduces quantitative numerical solutions on the optimal dosage of the capsules required to completely repair cracks in a three-dimensional model of a cementitious matrix. Four different sizes of spherical capsules ranging between 0.6 mm to 4.75 mm embedded within a mortar matrix were tested in the model and the model results were validated using previous experimental findings. As the cargo of capsules could be powder or liquid self-healing agents, three different scenarios were considered in this work to calculate the volume of the healing agent in the crack. It was found that the smaller the capsules the more homogenous and uniform the distribution of capsules is. However, the bigger sizes of the capsules are much preferable in terms of the amount of self-healing materials supplied to the cracked vicinity. For instance, capsules of 2–4 mm size could fill 80% of the crack volume but were localised and unevenly distributed on the planes of the crack. Overall, the developed model in this study provides a robust and efficient tool to quantitively design the proportions of cement-based self-healing systems. Based on the results of the geometric model, an ANN model was also developed to calculate healing volume in terms of the volume fraction of the healing agents and the size of capsules. Results showed very close values to those obtained by the numerical model.

Analytical Model for the Probability Characteristics of a Crack Penetrating Capsules in Capsule-Based Self-Healing Cementitious Materials

Autonomous crack healing using pre-embedded capsules containing healing agent is becoming a promising approach to restore the strength of damaged structures. In addition to the material properties, the size and volume fraction of capsules influence crack healing in the matrix. Understanding the crack and capsule interaction is critical in the development and design of structures made of capsule-based self-healing materials. Continuing our previous study, in this contribution a more practical rupturing mode of capsules characterizing the rupturing manner of capsules fractured by cracks in cementitious materials is presented, i.e., penetrating mode. With the underlying assumption that a crack penetrating capsules undoubtedly leads to crack healing, geometrical probability theory is employed to develop the quantitative relationship between crack size and capsule size, capsule concentration in capsule-based self-healing virtual cementitious material. Moreover, an analytical expression of probability of a crack penetrating with randomly dispersed capsules is developed in two-dimensional material matrix setup. The influences of the induced rupturing modes of capsules embedded on the self-healing efficiency are analyzed. Much attention is paid to compare the penetrating probability and the hitting probability, in order to assist the designer to make a choice of the optimal rupturing modes of capsules embedded. The accuracy of results of the theoretical model is also compared with Monte-Carlo numerical analysis of crack interacting with capsules. It shows that the developed probability characteristics of a crack interaction with capsules for different rupturing modes is helpful to provide guidelines for designer working with capsule-based self-healing cementitious materials. DOI: http://dx.doi.org/10.5755/j01.ms.23.3.16888