Interfacial cavitation

Abstract

Cavitation has long been recognized as a crucial predictor, or precursor, to the ultimate failure of various materials, ranging from ductile metals to soft and biological materials. Traditionally, cavitation in solids is defined as an unstable expansion of a void or a defect within a material. The critical applied load needed to trigger this instability -- the critical pressure -- is a lengthscale independent material property and has been predicted by numerous theoretical studies for a breadth of constitutive models. While these studies usually assume that cavitation initiates from defects in the bulk of an otherwise homogeneous medium, an alternative and potentially more ubiquitous scenario can occur if the defects are found at interfaces between two distinct media within the body. Such interfaces are becoming increasingly common in modern materials with the use of multimaterial composites and layer-by-layer additive manufacturing methods. However, a criterion to determine the threshold for interfacial failure, in analogy to the bulk cavitation limit, has yet to be reported. In this work, we fill this gap. Our theoretical model captures a lengthscale independent limit for interfacial cavitation, and is shown to agree with our observations at two distinct lengthscales, via two different experimental systems. To further understand the competition between the two cavitation modes (bulk versus interface), we expand our investigation beyond the elastic response to understand the ensuing unstable propagation of delamination at the interface. A phase diagram summarizes these results, showing regimes in which interfacial failure becomes the dominant mechanism.

Fig. 1.

The applied cavity pressure approaches an asymptotic limit of p_ic/μ → 7/2 with increasing volumes. The shape of the cavity cross-section at different dimensionless expansion volumes is shown in inset (i), where curve shades correspond to the diamond markers along the pressure–volume curve. The aspect ratio of these shapes approaches an asymptotic value of h/w ∼ 1.6, as shown in inset (ii). The power law decay of the slope of the pressure–volume curve, shown via the log–log plot in inset (iii), confirms the asymptotic behavior. The data set for the pressure–volume curve and a video of the simulated expansion process can be found in the Supplementary Material.

Fig. 2.

The dimensionless material property φ = μl₀/Γ determines the stability threshold. On the left, departure of the pressure a from the purely elastic response is shown for various values of φ, and indicted by the square markers. The corresponding critical pressure (p_c/μ) is shown as a function of φ on the right, to form a phase diagram, with the square markers corresponding to the curves on the left. In the blue region the response is stable; in the red region perturbations can lead to unstable expansion. The dashed line corresponds to the bulk cavitation pressure. The circular markers represent critical pressures measured in different materials using the PIF method, where the interface toughness is determined via conventional probe-tack test (blue) or linear theory (39) (green). Experimental details can be found in the Supplementary Material.

Fig. 3.

Evolution of interstitial biofilm exhibits a cavitation to delamination transition. (a) Theoretically predicted evolution of apparent angle, for increasing volume, shown for varying values of φ. (b) Experimentally measured apparent angle of biofilm of different volumes shown for two stiffnesses, μ = 0.16 and 4.7 [kPa], as marked by blue and red markers, respectively. (c, d) Shape evolution of a single biofilm, for each of the two stiffnesses. The colored lines represent the experimentally estimated apparent angles.

Fig. 4.

Influence of the interface toughness. (a) Theoretical prediction of apparent contact angle is shown for a range of mature volumes (as indicated by the shaded regions) for biofilm grown in confinements of different stiffness. Dashed lines correspond to two different volume expansions, V = (10⁴, 10⁶) μm³, with red and green corresponding to different interface toughness, Γ = (1.2, 2) × 10⁻²N/m, respectively, and using l₀ = 10 μm as the initial defect size. For comparison, the green markers represent the experimentally measured value for the system with the higher Γ, and error bars show the SDs. (b) Experimentally measured mature apparent angles for two systems of different interface toughness are shown in the form of a violin plot, whereby the width of the cords are reflective of the probability density.