Research Papers

Tunable Toughness of Model Fibers With Bio-Inspired Progressive Uncoiling Via Sacrificial Bonds and Hidden Length

[+] Author and Article Information
Yichen Deng

Laboratory of Nanotechnology
in Civil Engineering (NICE),
Department of Civil and Environmental
Northeastern University,
360 Huntington Avenue,
Boston, MA 02115

Steven W. Cranford

Laboratory of Nanotechnology in Civil
Engineering (NICE),
Department of Civil and Environmental
Northeastern University,
360 Huntington Avenue,
Boston, MA 02115
e-mail: s.cranford@neu.edu

1Corresponding author.

Manuscript received April 17, 2018; final manuscript received June 21, 2018; published online July 17, 2018. Assoc. Editor: Yashashree Kulkarni.

J. Appl. Mech 85(11), 111001 (Jul 17, 2018) (11 pages) Paper No: JAM-18-1222; doi: 10.1115/1.4040646 History: Received April 17, 2018; Revised June 21, 2018

Nature has a proven track record of advanced materials with outstanding mechanical properties, which has been the focus of recent research. A well-known trade-off between ultimate strength and toughness is one of the main challenges in materials design. Progress has been made by mimicking tough biological fibers by applying the concepts of (1) sacrificial bond and (2) hidden length, providing a so-called “safety-belt” for biological materials. Prior studies indicate a relatively common behavior across scales, from nano- to macro-, suggesting the potential of a generalized theoretical mechanistic framework. Here, we undertake molecular dynamics (MD) based simulation to investigate the mechanical properties of model nanoscale fibers. We explore representative models of serial looped or coiled fibers with different parameters—specifically number of loops, loop radii, cross-link strength, and fiber stiffness—to objectively compare strength, extensibility, and fiber toughness gain. Observing consistent saw-tooth like behavior, and adapting worm-like chain (WLC) mechanics (i.e., pseudo-entropic elasticity), a theoretical scaling relation which can describe the fiber toughness gain as a function of the structural factors is developed and validated by simulation. The theoretical model fits well with the simulation results, indicating that engineering the mechanical response based on controlled structure is possible. The work lays the foundation for the design of uniaxial metamaterials with tunable and predictable tensile behavior and superior toughness.

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Grahic Jump Location
Fig. 2

Schematic of bead-spring representation for elastic fiber model, depicting functional forms of axial stretching and bending potentials

Grahic Jump Location
Fig. 1

Representation of fiber model indicating pull-direction, sequential loops (i.e., hidden length), and the sacrificial cross-links that initiate uncoiling upon failure

Grahic Jump Location
Fig. 3

Representation of the model setup and subsequent loading geometry of the tensile test. (a) Simulation model; fiber with n serial loops; tension is loaded in the direction of the Δ in a constant rate, sacrificial bond is represented by the blue short line, and the measure of the force is achieved by the stiff spring attached at the left end (e.g., a virtual force transducer). (b) Schematic of the stepwise sequential unfolding of a loaded fiber (black lines indicate sections carrying load, lighter gray lines indicate unloaded section): (i) only linear of fiber carries load; (ii) first cross-link ruptures (sacrificial), first loop now loaded; (iii) significant extension while first loop unfolds (hidden length); (iv)-(v) process repeated for second cross-link and loop (the depicted geometric configurations of (i)-(v) are intended to represent the general behavior only, not necessarily the simulated results).

Grahic Jump Location
Fig. 4

Idealized theoretical representative force–elongation curve for elastic fiber, each triangle represents a peak in force peak in the real plot of simulation datapoints; used as basis for toughness scaling model (Eqs. (1)(3))

Grahic Jump Location
Fig. 7

(a) and (b) Force–elongation curves for the fibers with the loop radius of 30 and 40, indicating that larger radius corresponds to a larger unfolding domain. (c) Toughness versus radius plot, depicting the fiber toughness is linearly related to the loop radius, as per inset Eq.(5); R2 = 0.9635.

Grahic Jump Location
Fig. 8

(a) and (b) Force–elongation plot for sacrificial bond strength of the 4000 and 8000, respectively; higher strength means a greater force peak value corresponding to a larger unfolding domain. (c) Toughness versus sacrificial bond plot, showing a good curve fitting as per inset Eq. (6); R2 = 0.9997.

Grahic Jump Location
Fig. 5

Snapshots of simulation trajectory, illustrating the sequential cross-link rupture and unfolding of the fiber model, in agreement with Fig. 3

Grahic Jump Location
Fig. 6

(a) and (b) Characteristic force–elongation curve for the fiber with 2 and 6 loops, respectively, illustrating that each sacrificial bond rupture corresponds to a force peak in the curve. (c) Linear relation between fiber toughness with respect to the loop number, as per inset Eq. (4); R2 = 0.9992.

Grahic Jump Location
Fig. 9

Toughness versus backbone (axial) stiffness plot, serving as a proxy for size (fiber radius) dependence; the curve fitting result is in good agreement with inset Eq. (7b); R2 = 0.9969



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