Imaging in-plane and normal stresses near an interface crack using traction force microscopy

Abstract

Colloidal coatings, such as paint, are all around us. However, we know little about the mechanics of the film-forming process because the composition and properties of drying coatings vary dramatically in space and time. To surmount this challenge, we extend traction force microscopy to quantify the spatial distribution of all three components of the stress at the interface of two materials. We apply this approach to image stress near the tip of a propagating interface crack in a drying colloidal coating and extract the stress intensity factor. fracture mechanics | colloids | ceramics T he mechanical failure of coatings plagues electronic, optical, and biological systems (1-3). In many cases, fracture occurs at the interface of dissimilar materials. These interface cracks have been the subject of extensive theoretical and experimental study (4-13). Although much progress has been made in understanding the fracture of hard materials, relatively little is known about the fracture mechanics of soft matter. An extremely challenging and familiar example is the drying of a colloidal coating, such as paint, which starts off as a fluid and fails as a solid (14). We present a robust experimental approach for studying fracture mechanics in systems with complex spatially and temporally varying mechanical properties. Our approach is inspired by recent work in the mechanics of biological cells, where the spatial distribution and magnitude of forces are inferred by the deformation of a compliant substrate (15)(16)(17)(18)(19)(20)(21)(22). We extend this technique, called traction force microscopy, to image the stress near the tip of an advancing interface crack. We compare our results to the anticipated universal scaling of stress near a crack tip to measure the stress intensity factor directly. Results and DiscussionWe study interface cracks formed during the drying of a colloidal coating. Our samples start off as aqueous suspensions of 11-nm radius silica particles (Ludox AS-40) at a volume fraction ϕ ¼ 0.2. Drying transforms this fluid suspension into a brittle solid that cracks prodigiously. To simplify the geometry, we confine the suspension to a rectangular capillary tube, which allows evaporation of solvent from only one edge (23,24). During the course of drying, the composition and material properties are highly heterogeneous, with coexistence of low volume fraction fluid regions and relatively high volume fraction brittle regions. The concentration gradient is localized to a compaction front that moves steadily into the sample (25, 26). The tip of an interface crack, debonding the colloidal coating from the substrate, follows about 500 μm behind the compaction front, as shown in Fig. 1A.We visualize the flow and deformation of the colloid by imaging fluorescent tracer particles with time-lapse 3D confocal microscopy, as shown in Fig. 1 B and C and Movies S1 and S2. The leading edge of the crack is clearly visible in confocal micrographs in a plane near the substrate. Using a simple edge detection algorithm, we can re...

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