Characterization of Microvascular-Based Self-healing Coatings

Abstract

A protocol is described to assess self-healing of crack damage in a polymer coating deposited on a substrate containing a microvascular network. The bio-inspired coating/substrate design delivers healing agent to cracks in the coating via a three-dimensional microvascular network embedded in the substrate. Through capillary action, monomer flows from the network channels into the crack plane where it is polymerized by a catalyst embedded in the coating. The healing efficiency of this materials system is assessed by the recovery of coating fracture toughness in a four-point beam bending experiment. Healing results for the microvascular networks are compared to data for a coating containing microencapsulated healing agents. A single crack in a brittle epoxy coating is healed as many as seven times in the microvascular systems, whereas microcapsule-based healing occurs for only one cycle. The ability to heal continuously with the microvascular networks is limited by the availability of catalyst in the coating.

Appendix

The two types of specimen were tested in four-point bending to create cracks in the brittle coating. The outer and inner support spans for the bend tests were A = 40 mm and B = 20 mm, respectively. Assuming the load is distributed equally among the four supports, the bending moment between the inner supports is therefore constant and depends on the load P and span distances according to the relation,

$$M = \frac{1}{4}P\left( {A - B} \right)$$

(5)

The axial stress in the coating is then calculated by

$$\sigma = \frac{{My}}{{I_{{\text{composite}}} }},$$

(6)

where I _composite is the composite moment of inertia and y is the distance from the neutral axis.

The microcapsule beams are comprised of two materials with different elastic properties. The elastic modulus of the coating is approximately 1.4 times that of the substrate (3.5 GPa and 2.5 GPa, respectively). The difference in stiffness of the two materials leads to a more complicated stress calculation. A factor of 1.4 is introduced in the calculation for the coating moment of inertia, I _c, to account for the difference in the elastic moduli of the two materials:

$$I_{\text{s}} = \frac{1}{{12}}bh^3 ,\;I_{\text{c}} = \frac{{1.4}}{{12}}bt^3 .$$

(7)

The subscripts s and c refer to properties of the substrate and coating, respectively. The composite centroid of the microcapsule beam, y _capsule, and the moment of inertia of the composite are calculated,

$$y_{{\text{capsule}}} = \frac{{A_{\text{s}} y_{\text{s}} + A_{\text{c}} y_{\text{c}} }}{{A_{\text{s}} + A_{\text{c}} }},$$

(8)

$$I_{{\text{capsule}}} = I_{\text{s}} + A_{\text{s}} d_{\text{s}}^{\text{2}} + I_{\text{c}} + A_{\text{c}} d_{\text{c}}^{\text{2}} ,$$

(9)

where A is the area of the individual sections, y is the distance to the centroid of each area from the base. The distance, d, between each individual centroid and the composite centroid is given by

$$A_{\text{s}} = bh,\;A_{\text{s}} = 1.4bt,$$

(10)

$$y_{\text{s}} = {h \mathord{\left/{\vphantom {h 2}} \right.\kern-\nulldelimiterspace} 2},\;y_{\text{s}} = h + {t \mathord{\left/{\vphantom {t 2}} \right.\kern-\nulldelimiterspace} 2},$$

(11)

$$d_{\text{i}} = y_{{\text{capsule}}} - y_{\text{i}} .$$

(12)

Adding a microvascular network to the substrate changes the effective cross-sectional area and therefore changes the moment of inertia of the beam. Because the cross sections of the network beam vary depending on the location along the beam, a rule-of-mixtures approach is used to calculate the corresponding moment of inertia. Two cross sections are shown in Fig. 12(a) one with no vertical channels and Fig. 12(b) the other with maximum-diameter vertical channels. The centroid of cross section (b) is assumed equal to that of (a). The difference between the centroidal positions of the two sections is negligible for thin coatings in which the height of the vertical channels is approximately equal to the height of the total cross section. The composite centroid of (a) is found and then used to calculate the composite moment of inertia for both cross sections:

$$y_{{\text{net}}} = \frac{{A_{\text{s}} y_{\text{s}} + A_{\text{c}} y_{\text{c}} - \sum {A_{h1_{\text{i}} } y_{h1_{\text{i}} } } }}{{A_{\text{s}} + A_{\text{c}} - \sum {A_{h1_{\text{i}} } } }},$$

(13)

$$I_{{\text{net1}}} = I_{\text{s}} + A_{\text{s}} d_{\text{s}}^{\text{2}} + I_{\text{c}} + A_{\text{c}} d_{\text{c}}^{\text{2}} - \sum {\left( {I_{h1} + Ad_{h1}^2 } \right)} ,$$

(14)

$$I_{{\text{net2}}} = I_{\text{s}} + A_{\text{s}} d_{\text{s}}^{\text{2}} + I_{\text{c}} + A_{\text{c}} d_{\text{c}}^{\text{2}} - \sum {\left( {I_{h1} + Ad_{h1}^2 } \right)} - \sum {I_{h2} + 2rhd_{h2}^2 } .$$

(15)

Fig. 12

Two cross sections of network beams with (a) out-of-plane channels, and (b) in-plane and out-of-plane channels

The new subscripts, h1 and h2, refer to out-of-plane and in-plane channels, respectively, and r is the radius of the channels. The area of the out-of-plane channels in the cross section is A = πr ². The locations of the out-of-plane channels (y _{h 1}) are determined by the spacing between channels, and the location of the in-plane channels is y = h/2. The areas, moments of inertia, and distances y and d for the coating and substrate are previously defined. Because the spacing between the centerline of the channels is five times the diameter of the channels, the approximate ratio of cross sections with and without the in-plane channels is 1:4. By the rule of mixtures, 80% of the beam has I _net1 for the moment of inertia and 20% has I _net2, or

$$I_{{\text{network}}} = 0.8I_{{\text{net1}}} + 0.2I_{{\text{net2}}} .$$

(16)