Creep and Fracture of a Protein Gel under Stress

Abstract

Biomaterials such as protein or polysaccharide gels are known to behave qualitatively as soft solids and to rupture under an external load. Combining optical and ultrasonic imaging to shear rheology we show that the failure scenario of a protein gel is reminiscent of brittle solids: after a primary creep regime characterized by a power-law behavior which exponent is fully accounted for by linear viscoelasticity, fractures nucleate and grow logarithmically perpendicularly to shear, up to the sudden rupture of the gel. A single equation accounting for those two successive processes nicely captures the full rheological response. The failure time follows a decreasing power law with the applied shear stress, similar to the Basquin law of fatigue for solids. These results are in excellent agreement with recent fiber-bundle models that include damage accumulation on elastic fibers and exemplify protein gels as model, brittle-like soft solids.PACS numbers: 82.35. Pq, 47.57.Qk, 83.80.Kn Biogels formed through the self-association of polysaccharide coils, collagen, actin filaments or attractive globular proteins play a major role in biochemistry and microbiology [1], biological networks and cell mechanics [2] as well as in food science [3]. These biomaterials all behave as elastic solids under small deformations but display remarkable nonlinear behavior generally featuring stress-or strain-stiffening [4] and fractures prior to irreversible rupture [5,6]. Irreversibility stems from the existence of an external control parameter, e.g. temperature or pH in the case of thermoreversible or acid-induced gels respectively. This makes such biogels fundamentally different from other soft glassy materials such as emulsions, colloidal gels and glasses that can be rejuvenated by shear [7][8][9][10] or transient networks where fractures spontaneously heal [11,12]. So far, huge effort has been devoted to the design of protein gels with specific properties and textures at rest [13,14]. However, their mechanical behavior deep into the nonlinear regime has only been partially addressed [15,16] and several fundamental issues remain unexplored such as the spatially resolved rupture scenario or the physical relevance of the analogy with brittle failure in hard solids.In this Letter we report on stress-induced fracture in protein gels by means of creep experiments coupled to optical and ultrasonic imaging. Gels formed by slow acidification of a sodium caseinate solution display fractures under large strain at fixed low pH values [15,17], which makes them perfect candidates to quantify the rupture of soft solids and tackle the above-mentioned issues. We demonstrate that under an external load, these casein gels display brittle-like failure that results from two successive physical processes: (i) a primary creep regime where dissipation is dominated by viscous flow through the gel matrix without any detectable macroscopic strain localization and (ii) the irreversible nucle-

Predicting sample lifetimes in creep fracture of heterogeneous materials

“…Figure 2(a), upper inset, shows that the parts of the different creep curves corresponding to the two last regimes-logarithmic (where t ∼ t −1 ) and tertiary-can indeed be collapsed onto a single master curve using such an ansatz. Doing so also reveals a divergence of t as t c is approached, t ∝ (t c − t) −b , with b ≈ 1.0 [9,33] (see also SM, Fig. S6).…”

“…Lower inset: Time dependence of strain rate t for three example experiments, all exhibiting a minimum strain rate at time t = t m (shown with a red arrow in one case) before acceleration towards final failure at time t = t c . Upper inset: A data collapse of six creep curves after rescaling the time axis by the lifetime t c and the vertical axis by the minimum strain rate t (t m ) [9]. t m from the data-a posteriori or during an experiment-is somewhat complicated for two reasons: experimental noise and intrinsic fluctuations [24,26] in the instantaneous sample creep rate [see Fig.…”

“…In contrast to brittle materials, most real materials are often ductile to some degree and exhibit a complicated rheological creep response under constant applied loads [8][9][10][11]. To simplify the typical time-dependent creep response to constant applied loads that lead to failure, we can divide it into primary, secondary, and tertiary creep [12,13]: initial strain-hardening (described by the Andrade law) [14,15], steady-state or logarithmic creep [16], and a final phase in which the strain rate t increases, implying strain softening [17], finally leading to sample failure.…”

Spatiotemporal correlations between plastic events in the shear flow of athermal amorphous solids

“…On the other hand, if shear is applied to an amorphous solid, the response of the material is highly heterogeneous, in that small regions rearrange rapidly while the rest of the material responds elastically, in a more or less affine way [1,2]. In extreme cases, the material may fracture [3,4,5,6]; the shear strain is then entirely borne by a thin layer of matter which has lost its internal cohesion. Material fracture is the most acute case of shear localisation, whereby the deformation is localised in one region of the system.…”

Mean-Field Scenario for the Athermal Creep Dynamics of Yield-Stress Fluids

“…However, the flow curve is far from accounting for the full complexity of these systems, that involves an interplay between external driving and internal aging, potentially leading to complex thixotropic behavior. In recent years, many experiments and molecular simulations have tried to reveal this complexity using creep experiments, in which the flow rate is measured in response to a fixed stress σ applied at a given waiting time t w after sample preparation [3][4][5][6][7][8][9][10]. These experiments, that lead, for σ larger than a yield stress σ Y , to flow or failure, reveal an intriguing behavior, with two salient features: (i) the strain-rateγ(t) in response to a stress larger than the yield stress is strongly non-linear and nonmonotonous, with a so called "s-shaped" dependence ofγ(t) [4,11,12], including a nontrivial "primary creep regime" often described by a power law t −µ .…”