Strand Plasticity Governs Fatigue in Colloidal Gels

The repeated loading of a solid leads to microstructural damage that ultimately results in catastrophic material failure. While posing a major threat to the stability of virtually all materials, the microscopic origins of fatigue, especially for soft solids, remain elusive. Here we explore fatigue in colloidal gels as prototypical inhomogeneous soft solids by combining experiments and computer simulations. Our results reveal how mechanical loading leads to irreversible strand stretching, which builds slack into the network that softens the solid at small strains and causes strain hardening at larger deformations. We thus find that microscopic plasticity governs fatigue at much larger scales. This gives rise to a new picture of fatigue in soft thermal solids and calls for new theoretical descriptions of soft gel mechanics in which local plasticity is taken into account.

Figure 1

Stress-strain curves as a result of sawtooth strain cycles shown in the inset (only the first two sets are shown) with $\dot{\gamma }={10}^{-2}{\mathrm{s}}^{-1}$. From blue to yellow: ${\gamma }_{\max }=0.005$, 0.02, 0.035, 0.05, 0.065, 0.08, 0.095 (note that only a selection of the sets is shown).

Figure 2

(a) Stress-strain curves for $\dot{\gamma }={10}^{-1}{\mathrm{s}}^{-1}$, from blue to yellow: ${\gamma }_{\max }=0.005$, 0.02, 0.035, 0.05, 0.065, 0.08, 0.095. (b) Elastic midlines for curves in Fig. 1. (c) The initial modulus as function of ${\gamma }_{\max }$ for $\dot{\gamma }={10}^{-1}{\mathrm{s}}^{-1}$ (squares) and $\dot{\gamma }={10}^{-2}{\mathrm{s}}^{-1}$ (circles). The inset shows the same data on a double-logarithmic scale. (d) Collapse of every second elastic midline for both strain rates. The inset shows the dependence of ${\gamma }^{*}$ on ${\gamma }_{\max }$ for $\dot{\gamma }={10}^{-1}{\mathrm{s}}^{-1}$ (squares) and $\dot{\gamma }={10}^{-2}{\mathrm{s}}^{-1}$ (circles).

Figure 3

(a) Visual representation of the noncumulative average plastic deformation per particle in oscillation cycles 1, 2, 4, 6, 10, and 14 of a single gel strand (${\gamma }_{\max }=0.04$, data in Supplemental Fig. 2 [27]). The color bar indicates the noncumulative plastic deformation $m_i$ per particle in each cycle from low (purple) to high (yellow). The cumulative plastic deformation of this gel strand is shown in Supplemental Fig. 10 [27]. (b) Plastic deformation in a gel strand after the first cycle ($F1$), before fracture ($F11$), and after fracture ($F12$).

Figure 4

(a) Force-strain curves for BD simulations of 24 ($8\times 3$) oscillations of a single gel strand at strain amplitudes (purple to orange) ${\gamma }_{\max }=0.02$, 0.04, and 0.06. (b) Collapse of the average force-strain curves (positive parts of the loading and unloading curve) of the fourth oscillation cycle scaled by ${\gamma }^{*}$ on the $x$ axis and $k·{\gamma }^{*}$ on the $y$ axis. Data are obtained from Supplemental Fig. 2 [27]. (c) Spring constant $k$ (in units $k_{B}T{a}^{-1}$) as a function of ${\gamma }_{\max }$. (d) ${\gamma }^{*}$ as a function of ${\gamma }_{\max }$.