A Fractal Model of Cracking of Cement Matrix Composites

The modern methods of materials (including cement matrix materials) design and testing impose the application of an approach appropriate to materials engineering. A quantitative description of the association between the properties of these materials and their structure is a necessity. What remains...

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Main Author: Janusz Konkol
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Buildings
Subjects:
Online Access:https://www.mdpi.com/2075-5309/10/3/52
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spelling doaj-219dbdfa183246cb9d0fb0e15eec9a632020-11-25T01:37:45ZengMDPI AGBuildings2075-53092020-03-011035210.3390/buildings10030052buildings10030052A Fractal Model of Cracking of Cement Matrix CompositesJanusz Konkol0Department of Materials Engineering and Technology of Building, Rzeszow University of Technology, 35-959 Rzeszow, PolandThe modern methods of materials (including cement matrix materials) design and testing impose the application of an approach appropriate to materials engineering. A quantitative description of the association between the properties of these materials and their structure is a necessity. What remains the scientific aim, however, is the clarification and description of the occurring phenomena by means of models mapping their actual behavior in the closest way possible. The article presents a cracking fractal model based on tests on the morphology of concrete fracture surfaces. The recorded fractal nature of the cracking of cement matrix materials enabled fractal geometry in the model development to be applied. Owing to the application of statistical analysis, together with an extensive base of data on the profile lines separated out of the real fracture surfaces of concrete, it was possible to develop a cracking fractal model. Not only does this model satisfy the condition of the equality of the fractal dimension of the real and model profile lines, it also offers the possibility of introducing an order to the apparently chaotic phenomena, such as the cracking process. An advantage and novelty of the model is that unlike the other authors&#8217; proposals, there is a possibility of reaching an infinitely large number of solutions for model profile lines, which approximates the model to the real-life scenario. The results of fractal tests were supplemented with strength measurements, identifying concrete&#8217;s compressive and fracture toughness (determining the critical stress intensity factor <i>K<sub>Ic</sub><sup>S</sup></i>). A connection between the fractal dimension and the investigated properties of concrete was demonstrated. A higher fractal dimension was observed in the profile lines separated out of the fracture surfaces of concretes of higher water&#8722;cement ratio. The advantages of the model include the simplicity and applicability in model studies on other materials of the cement matrix.https://www.mdpi.com/2075-5309/10/3/52fractal modelfractal dimensionfracture toughnessconcretemetakaolinite
collection DOAJ
language English
format Article
sources DOAJ
author Janusz Konkol
spellingShingle Janusz Konkol
A Fractal Model of Cracking of Cement Matrix Composites
Buildings
fractal model
fractal dimension
fracture toughness
concrete
metakaolinite
author_facet Janusz Konkol
author_sort Janusz Konkol
title A Fractal Model of Cracking of Cement Matrix Composites
title_short A Fractal Model of Cracking of Cement Matrix Composites
title_full A Fractal Model of Cracking of Cement Matrix Composites
title_fullStr A Fractal Model of Cracking of Cement Matrix Composites
title_full_unstemmed A Fractal Model of Cracking of Cement Matrix Composites
title_sort fractal model of cracking of cement matrix composites
publisher MDPI AG
series Buildings
issn 2075-5309
publishDate 2020-03-01
description The modern methods of materials (including cement matrix materials) design and testing impose the application of an approach appropriate to materials engineering. A quantitative description of the association between the properties of these materials and their structure is a necessity. What remains the scientific aim, however, is the clarification and description of the occurring phenomena by means of models mapping their actual behavior in the closest way possible. The article presents a cracking fractal model based on tests on the morphology of concrete fracture surfaces. The recorded fractal nature of the cracking of cement matrix materials enabled fractal geometry in the model development to be applied. Owing to the application of statistical analysis, together with an extensive base of data on the profile lines separated out of the real fracture surfaces of concrete, it was possible to develop a cracking fractal model. Not only does this model satisfy the condition of the equality of the fractal dimension of the real and model profile lines, it also offers the possibility of introducing an order to the apparently chaotic phenomena, such as the cracking process. An advantage and novelty of the model is that unlike the other authors&#8217; proposals, there is a possibility of reaching an infinitely large number of solutions for model profile lines, which approximates the model to the real-life scenario. The results of fractal tests were supplemented with strength measurements, identifying concrete&#8217;s compressive and fracture toughness (determining the critical stress intensity factor <i>K<sub>Ic</sub><sup>S</sup></i>). A connection between the fractal dimension and the investigated properties of concrete was demonstrated. A higher fractal dimension was observed in the profile lines separated out of the fracture surfaces of concretes of higher water&#8722;cement ratio. The advantages of the model include the simplicity and applicability in model studies on other materials of the cement matrix.
topic fractal model
fractal dimension
fracture toughness
concrete
metakaolinite
url https://www.mdpi.com/2075-5309/10/3/52
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