Weizmann Institute of Science scientists have uncovered laws of physics that explain why cracks in a material propagate asymmetrically, laying the foundation for developing more durable materials.
The materials that make up all the structures and systems around us, as well as our bodies, are not perfect – they contain defects in the form of tiny cracks. When one of the cracks suddenly spreads rapidly, it can be life-threatening, but it can also arouse astonishment and wonder at the rich, unique, and branched paths that cracks leave in a material. Until now, physicists have had difficulty theoretically explaining what causes cracks to split, bend, and as a result, move at a slower speed than expected. In two new studies, the findings of which were recently published, scientists at the Weizmann Institute of Science are bringing order to the disorderly phenomenon of crack propagation in a material and showing that although each crack seems unique, there are quantitative physical properties that shape the process of crack propagation and can explain why they split and form asymmetrical patterns.
Decades of controlled experiments in the field of materials failure have shown that even when a perfectly symmetrical crack is created under tensile forces, as it progresses through the material, the symmetry is spontaneously broken and it deviates from its trajectory and moves at a lower speed than expected. "These observations are in stark contrast to the theoretical predictions we know," explains Prof. Eran Buchbinder"All theoretical calculations show that even if we put a small obstacle in front of a symmetrical crack under tension, it should return to its symmetrical and smooth path. In light of the experimental observations, we hypothesized that there must be missing links – physical properties that were not taken into account and that underlie the observations."
In the study thatHis findings were published in the journal Nature Communications.Led by Dr. Yuri Lubomirsky, at the time a doctoral student in Prof. Buchbinder's group from the Department of Chemical and Biological Physics, the researchers used a computer model that simulates the progression of a crack in a three-dimensional material. "To understand the propagation of the crack, we focused on its edge, the place where a material changes from being whole to broken," explains Dr. Lubomirsky. "While in most materials and for most of the time, the conditions are moderate and the behavior of the material can be understood by looking at its average properties, at the edge of the crack there are extreme conditions. The physical quantities that are familiar to us - force, temperature and velocity - are so large that they can be treated mathematically as infinity, and they do not play by the usual rules. We assumed that at the edge of the crack we could locate the mysterious properties that explain the asymmetric propagation of cracks."
The path of hardships that the scientists went through in search of these new physical properties lasted seven years and was frustrating at times. "The basis for the breakthrough that was ultimately achieved was the introduction of significant disorder into the simulations, an element that had not been taken into account in dynamic theories of material failure. We ran many computer simulations relying on advanced computational capabilities and saw that the crack moves straight up to a certain point where local splitting occurs, and from there the crack can change its direction," describes Prof. Buchbinder. "The challenge was to formulate, from the vast amount of information we had, the basic principle that explains why the crack splits and deviates from its smooth, symmetrical path. One day I asked Yuri to cross two graphs and we got the answer - the disorder that characterizes materials in the real world, combined with the extreme conditions at the edge of the crack, are the missing link all along the way."
Crack rules
The laws of physics explain the properties of uniform materials well, but most materials in our world are not. Glass, for example, may appear smooth and uniform to the naked eye, but if you look closely at the particles that make it up and the bonds between them, it is actually a material without permanent order. As such, the internal forces that compress or stretch each area in it vary. To date, most engineers and scientists who have tried to study the dynamics of refraction of materials have used their average properties, and therefore have not been able to understand why refraction is asymmetric. What Prof. Buchbinder and Dr. Lubomirsky realized is that the explanation for this lies in the degree of disorder in the material itself, that is, in the degree to which the strength of different areas of the material changes.
The scientists applied variable-intensity fracture forces to the computer model of the material and characterized the relationship between crack propagation and disorder. They saw that when the fracture forces are weak, the crack does indeed propagate symmetrically without secondary bifurcations and is not affected by the disorder of the material. In contrast, when the fracture forces are moderate, the crack propagation in the material is affected by disorder: when the crack tip reaches a weak area in the material, instability develops, and instead of continuing to propagate directly, it splits locally. The splits compete with each other, one is stopped and the other continues as the main crack that does not necessarily move in the direction of the previous progression, and thus the crack curves; when you look at those points afterwards, you see microfractures in the material where the various secondary bifurcations were stopped. In other words, in this scenario, the degree of bifurcation depends on the degree of disorder. Finally, when the fracture forces exceed a certain threshold, instead of the crack being stopped at the points of instability, it splits into completely separate branches that expand and penetrate the entire depth of the material. In this regime, disorder no longer plays a major role. The deviation of the crack from its axis of symmetry and the appearance of bifurcations is accompanied by an energetic cost of breaking a larger amount of material and a slowdown of the crack relative to the speed it would have gained if it had remained symmetrical and smooth.
Another phenomenon that is often seen in cracks, and also related to symmetry breaking, is the formation of steps consisting of two interacting fracture surfaces. The scientists investigated the formation of this pattern in a follow-up study, whichHis findings were published in the scientific journal Physical Review LettersThey discovered that the formation of the steps also depends on the degree of internal disorder in the material, but also on the deviation of the external tensile forces from a perfectly symmetrical state. It turned out that in addition to the tensile forces that open the crack, it is almost never possible to avoid the forces perpendicular to the crack that cause its banks to slide over each other in a rotational motion. When the scientists gave a mathematical expression to the disorder and these forces, they were able to predict and explain how the step pattern is formed.
"These discoveries provide a physical and mathematical framework that allows us to understand the phenomenon of material failure mediated by the cracking dynamics that we encounter in everyday life," says Prof. Buchbinder. "They also lay the potential foundation for designing materials that are more resistant to catastrophic cracking. The findings suggest that increasing the degree of disorder can slow the propagation of a crack and this could be of great importance in the design of structures and physical systems," adds Dr. Lubomirsky. "Natural materials, such as those that make up our bones and teeth, have evolved to be resistant to failure, and one of the key ways in which this is done may be related to their degree of disorder. Thus, a new layer in our understanding of nature is also revealed."
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