Strain rate induced toughening of individual collagen fibrils

Abstract

The nonlinear mechanical behavior of individual nanoscale collagen fibrils is governed by molecular stretching and sliding that result in a viscous response, which is still not fully understood. Toward this goal, the in vitro mechanical behavior of individual reconstituted mammalian collagen fibrils was quantified in a broad range of strain-rates, spanning roughly six orders of magnitude, from 10^-4 to 35 s^-1. It is shown that the nonlinear mechanical response is strain rate sensitive with the tangent modulus in the linear deformation regime increasing monotonically from 214 ± 8 to 358 ± 11 MPa. More pronounced is the effect of the strain rate on the ultimate tensile strength that is found to increase monotonically by a factor of four, from 42 ± 6 to 160 ± 14 MPa. Importantly, fibril strengthening takes place without a reduction in ductility, which results in equivalently large increase in toughness with the increasing strain rate. This experimental strain rate dependent mechanical response is captured well by a structural constitutive model that incorporates the salient features of the collagen microstructure via a process of gradual recruitment of kinked tropocollagen molecules, thus giving rise to the initial "toe-heel" mechanical behavior, followed by molecular stretching and sustained intermolecular slip that is initiated at a strain rate dependent stress threshold. The model shows that the fraction of tropocollagen molecules undergoing straightening increases continuously during loading, whereas molecular sliding is initiated after a small fibril strain (1%-2%) and progressively increases with applied strain.

FIG. 1.

(a) Stress–stretch ratio (σ–λ) curves from tests carried out at seven different strain rates between 10^–4 and 35 s⁻¹. The dashed arrow points to increasing strain rate. Insets: collagen fibril mounted on a MEMS device, and reconstituted mammalian collagen fibril with D-banding of 67 nm. (b) Stress vs stretch ratio of a fibril (wet diameter: 240 nm) tested in PBS at a nominal strain rate of 0.0026 s⁻¹. Three typical deformation regimes are distinguished: (i) an initial, nonlinear “toe-heel” regime (I), (ii) a linear regime (II), and (iii) a softening regime (III) extending to failure.

FIG. 2.

(a) Tangent modulus derived from the linear regime of σ–λ curves. (b) Ultimate tensile strength vs applied strain rate. The error bars represent one standard deviation. The circles represent the actual experimental data.

FIG. 3.

(a) Fibril σ–λ response for three strain rates spanning the experimental range. The inset table shows the calculated model parameters. Under uniaxial tension, first molecular kinks gradually straighten in the gap regions ①, followed by stretching of collagen triple helices ②. Intermolecular sliding ③ is initiated at σ₀, leading to softening (conceptual fibril schematics were adapted from Fratzl et al. but modified to reflect the present model). (b) Fraction of tropocollagen molecules that are straightened (solid lines), or began sliding (dashed lines) vs λ. Inset: Weibull PDF of the fitted model. The parameters α_s, β_s are provided in the table in (a).