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Is the Bouligand architecture tougher than regular cross-ply laminates? Adiscrete element method study, Pro and Barthelat, Extreme Mechanics Letters, 2020

Novelty/impact/significance:

With capturing the main mechanisms, it is revealed that the Bouligand structure outperforms the cross-ply (0°/90°) for any crack orientation, while the former is more isotropic in-plane in stiffness and toughness.

Scientific question:

Is the Bouligand architecture tougher than regular cross-plies, given the same fibers and interfaces?

Key of how:

Using discrete element method (DEM) based models can capture the major fracture mechanisms including inelastic and post-initiation behaviors, such as crack initiation and propagation mechanisms, failure modes, and also how fiber and interface properties affect the mechanisms, thus allowing for quantitative & effective comparisons between architectures at an economical computational cost.

Major points:

1. The mechanics of crossply and Bouligand structures, widely seen in biological system, have been extensively investigated experimentally, while the much inadequate numerical and analytical studies have many limitations, e.g., linear elastic fracture mechanics based theoretical studies capture the driving force but not the fracture toughness, cohesive zone models cannot capture the fracture of fibers nor post-initiation R-curve, the phase field models did not include the pitch angle effect in Bouligand structure.

2. Capturing crack propagation in the Bouligand architecture is challenging and computationally expensive due to the very complex features: the architecture, crack propagation and mechanisms being 3D, multiple possible failure modes, multiple simultaneous toughening mechanisms, and large inelastic process zones.

3. The DEM has been applied in tooth enamel with a crossply structure; thus it is used here to explore the different fracture behaviors of the Bouligand architecture and (0°/90°) cross plies for crack initiation & propagation, failure mode, toughening mechanisms, and architecture effect.

4. The fibrous architectures (fibers with square sections arrange in layers which stack to form lamellae) are: (1) crossply C(0°/90°) where fiber orientation alternates between 0° and 90°, (2) Bouligand B(γ) where the fiber angle increases per each ply incrementally and by a pitch angle γ≤ 90°, (3) crossply C(-½γ/½γ) where the ply angle alternates between −½ γ and +½ γ.

5. DEM models are: seed fibers with nodes of uniform spacing le, use nodes to mesh each fiber with 3D Bernoulli-Euler beam elements. Fibers will fracture when tensile strength is exceeded; interface cohesive elements between fibers and between plies possess a cohesive law which considers the permanent energy dissipation and unloading due to large displacements.

6. For thick models in transverse and in-plane directions under stable/quasi-static crack propagation, all three types show initial linear elastic region until a peak force. The C(0o/90o) shows highest stiffness, peak force, and work of fracture (WOF, energy absorption).

The C(0o/90o) shows crack deflection, interface failure, and fiber fracture with periodic pinning, the B(30o) displays a periodic corkscrew (crack twisting) fracture mechanism (fiber fracture becomes prominent with large ply angle), and the C(-15o/+15o) exhibits crack deflection forming a kink-branch mechanism.

As the strength contrast (fiber over interface) increases, architecture type and the ply angle show a more pronounced effect on crack propagation and toughness, while the initiation toughness of C(0o/90o) crossply was unaffected because the crack initiation is governed by the interface fracture.

7. For thin models with semi-infinity and periodicity in the out-of-plane (z) direction, the mechanisms of crack deflection, interface delamination, fiber fracture and process zone depend on the architecture type and ply angle. All show a rising R-curve behavior, with the C(0o/90o) always highest in crack resistance. The C(0o/90o) displays largest degree of crack deflection and process zone size.

The Bouligand architecture develops delamination patterns along a periodic twisted-corkscrew creating a flower-like process zone, while the two crossply architectures show similar mechanisms as in 6.

Increasing the strength contrast/relative fiber strength, (1) increase the difference between architecture types (low fiber strength leads to comparable crack resistance among Bouligand and crossply structures with varying ply angles), (2) increases the overall toughness and toughening, showing fiber fracture, more crack deflection and larger process zone.

8. Considering mechanical isotropy, the follow plot (from Fig. 5c,d) compares the in-plane elastic modulus and fracture toughness of Bouligand and crossply in different loading directions. It’s clear (within expectation) that (1) the C(0°/90°) crossply is more anisotropic w.r.t. the B(30o); the C(0°/90°) is stiffer only along the fiber directions and has lower stiffness when loaded in 45o, while the Bouligand is isotropic; (2) the C(0°/90°) is tougher in any in-plane directions, even along weakest cracking direction, as fracture toughness is more complex process.

PS: in this work comparing the architecture effects, the mechanical properties of the constituent fiber and interface are kept same.        Considering in biology, the crossply (0o/90o) usually observed in plants, woods, bone or fish scales most probably utilize constituents that have lower strength contrast than those making the arthropod cuticles which show the Bouligand structure, thus boosting there toughness through the crossply architecture.

Thus, besides the differing needs for mechanical isotropy, it is possible that the architecture type evolves to complement the available constituents’ properties for desired/high toughness.

Here is the link of the fulltext: https://www.sciencedirect.com/science/article/pii/S2352431620302479