Cellulose crystals plastify by localized shear

Abstract

Cellulose microfibrils are the principal structural building blocks of wood and plants. Their crystalline domains provide outstanding mechanical properties. Cellulose microfibrils have thus a remarkable potential as eco-friendly fibrous reinforcements for structural engineered materials. However, the elastoplastic properties of cellulose crystals remain poorly understood. Here, we use atomistic simulations to determine the plastic shear resistance of cellulose crystals and analyze the underpinning atomic deformation mechanisms. In particular, we demonstrate how the complex and adaptable atomic structure of crystalline cellulose controls its anisotropic elastoplastic behavior. For perfect crystals, we show that shear occurs through localized bands along with noticeable dilatancy. Depending on the shear direction, not only noncovalent interactions between cellulose chains but also local deformations, translations, and rotations of the cellulose macromolecules contribute to the response of the crystal. We also reveal the marked effect of crystalline defects like dislocations, which decrease both the yield strength and the dilatancy, in a way analogous to that of metallic crystals.

Keywords: crystalline cellulose; dislocations; molecular mechanics simulation; nanoscale plasticity; shear bands.

Fig. 1.

Atomic structure of $I_{\beta }$ cellulose. From Left to Right, molecular chains are shown in the $xy$ (A), $xz$ (B), and $yz$ (C) planes. The direction of the applied shear strain is shown in each case. D is a 3D geometrical volume fitted on the cellulose chains to highlight their corrugation. Three-dimensional interactive representations are shown in SI Appendix, Figs. S2 and S3. (The hydrogen atoms bonded to carbon atoms are not shown here.)

Fig. 2.

Shear deformation in different planes. (A–C) Shear stress–strain curves in the $xy$, $xz$, and $yz$ planes. (D–F) Corresponding axial strains. Atomic-scale deformation mechanisms are shown in Movies S1–S3. In A and B, Insets, the local coarse-grained shear strain is shown just after the first plastic event.

Fig. 3.

Evolution of chain tilt angles in the $xy$ plane as a function of shear strain (A) and corresponding forward and reverse stress/strain curves (B). Atomic-scale deformation is shown in Movie S4.

Fig. 4.

Relative position of the corrugated cellulose chains during shear in the $xz$ plane. The blue and black curves show the distance in the $z$ direction between a reference carbon atom in an upper chain, $C_3^T$, and two carbon atoms, $C_3^i$ with $i=\mathrm{1,2}$ in a lower chain. The stress–strain curve is in red. Molecular-level deformation is shown in Movie S5.

Fig. 5.

(A) Coarse-grained shear strain map in projection perpendicular to the shear direction (in the $xy$ plane) with a 3D sketch of the molecular structure and orientation of the applied shear strain. (B) O5-C5-C6-O6 dihedral angles of the chains shown in C and D in the shear band as a function of applied deformation. (C and D) Local atomic structure before (C) and after (D) the first large stress drop.

Fig. 6.

Shear in the $xz$ plane in the presence of two edge dislocations forming a dipole. A schematic representation of the dislocated crystal is shown in A, and details of the molecular structure near and far from a dislocation core are shown in B. The resulting stress–strain curve is compared with that of a perfect crystal in C.