[Image above] Just as microscale calculations can predict macroscale friction, so too can grain shrinkage lead to an understanding of macroscale cracks. Credit: Pixabay
The first time I created a piece of ceramic art was in middle school art class. Everyone was given clay and directed to design a mask, which was then bisque fired in the school’s kiln. When we returned to class two days later to apply glazes, some students faced significant disappointment—their masks had cracked during the initial firing, so they needed to design a new mask from scratch.
What caused some of the masks to crack? The culprit lies in the fact that clay, on a molecular level, consists of hydrated packings of grains. During firing, water evaporates from between the grains and the grains shrink, which can initiate cracking.
While cracking caused disappointment for some students in my class, cracking can be dangerous in other contexts, such as damaging structures built on clay-rich soil and allowing waste to leak from clay barriers. Additionally, clay is not the only material in which individual hydrated grains shrink when dried—paint and human skin also experience this phenomenon, which can lead to disruption in biological tissues and limit the performance of gel particle coatings.
Researchers have investigated several material properties that influence cracking, including grain size and stiffness, packing size, drying rate, capillarity, and surface adhesion. Yet these properties have been investigated in terms of bulk gels and packings of nonshrinkable grains—how shrinkable grains affect cracking remains largely unexplored, according to Princeton University researchers.
“[D]espite its ubiquity, the influence of grain shrinkage on cracking has thus far been overlooked,” they write in a paper published this May. So they investigated the phenomenon themselves, and the results of their research are described in two papers published this year.
How grain shrinkage affects cracking
In their first paper published in May, the Princeton researchers used non-Brownian, cross-linked hydrogel beads as a model system to show how differential shrinkage can alter crack evolution during drying. They found packings respond in one of three different ways depending on the radius of the overall packing following pendular configuration initialization (Rwet).
“Packings with small Rwet shrink with no cracking. For sufficiently large Rwet, cracks form at the periphery … for even larger Rwet, we observed irreversible cracking (IC) wherein packings break up into clusters that cannot self-close,” they write.
However, for a range of Rwet, they found something “remarkable.”
“[W]e found that the cracks spontaneously self-close in a process we term reversible cracking (RC) to reflect the morphological similarity to the initial uncracked state,” they report.
Upon close inspection, the researchers found larger differential shrinkage occurred between the periphery and interior beads in clusters with larger Rwet, “suggesting that the rate of intra-packing water transport cannot match the rate of periphery drying.” When the differential shrinkage became large enough, capillary bridges between the periphery beads overstretched and broke, initiating cracks. “Interestingly, cracks close upon themselves when this differential shrinkage subsides, highlighting the central importance of differential shrinkage in crack evolution,” they note.
Based on these observations, the researchers developed a discrete-element model (DEM) that incorporates bead shrinkage, inter-bead water transport, and inter-bead forces during drying to determine cracking behavior; they also developed a continuum model that can describe the ultimate state of cracking.
In the second paper published this month, two authors from the first study—H. Jeremy Cho (postdoctoral research associate) and Sujit S. Datta (assistant professor)—looked to clarify further the role of individual grain shrinkage in determining crack patterning by extending classical Griffith crack theory. As in the first study, the researchers used hydrogel beads to experimentally test the role of individual grain shrinkage.
“By explicitly incorporating grain shrinkage into the classical cracking theory, we show that the cluster sizes can be predicted by balancing the mechanical energy required to break capillary bridges at the boundary of a cluster and the strain energy resulting from grain shrinkage and substrate friction,” they write in the paper. “[O]ur scaling prediction provides a way to predict crack patterning in diverse shrinkable granular packings—including clays, soils, coatings, biological tissues, and foods.”
In a press release on the two studies, Datta expresses how he feels about the findings. “The application of materials that spontaneously heal themselves, by leveraging shrinkability, is something I’m very excited about,” Datta says.
The first paper, published in Soft Matter, is “Crack formation and self-closing in shrinkable, granular packings” (DOI: 10.1039/C9SM00731H).
The second paper, published in Physical Review Letters, is “Scaling law for cracking in shrinkable granular packings” (DOI: 10.1103/PhysRevLett.123.158004).