Continuum and Molecular-Level Modeling of Fatigue Crack Retardation in Self-Healing Polymers

[+] Author and Article Information
Spandan Maiti

Department of Mechanical Engineering—Engineering Mechanics,  Michigan Technological University, Houghton, MI 49931

Chandrashekar Shankar

Department of Materials Science and Engineering,  University of Michigan, Ann Arbor, MI 48109

Philippe H. Geubelle1

Department of Aerospace Engineering,  University of Illinois at Urbana-Champaign, Urbana, IL 61801geubelle@uiuc.edu

John Kieffer

Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109


Corresponding author. 306 Talbot Lab., 104 S. Wright St., Urbana, IL 61801.

J. Eng. Mater. Technol 128(4), 595-602 (May 19, 2006) (8 pages) doi:10.1115/1.2345452 History: Received September 20, 2005; Revised May 19, 2006

A numerical model to study the fatigue crack retardation in a self-healing material (White, 2001, Nature, 409, pp. 794–797) is presented. The approach relies on a combination of cohesive modeling for fatigue crack propagation and a contact algorithm to enforce crack closure due to an artificial wedge in the wake of the crack. The healing kinetics of the self-healing material is captured by introducing along the fracture plane a state variable representing the evolving degree of cure of the healing agent. The atomic-scale processes during the cure of the healing agent are modeled using a coarse-grain molecular dynamics model specifically developed for this purpose. This approach yields the cure kinetics and the mechanical properties as a function of the degree of cure, information that is transmitted to the continuum-scale models. The incorporation of healing kinetics in the model enables us to study the competition between fatigue crack growth and crack retardation mechanisms in this new class of materials. A systematic study of the effect of different loading and healing parameters shows a good qualitative agreement between experimental observations and simulation results.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic representation of the progressive degradation of the cohesive properties due to fatigue loading along with the effect of insertion of a wedge of final thickness Δn*. The dotted lines represent the time evolution of the wedging effect associated with the polymerization of the healing agent. The shaded area corresponds to the monotonic fracture toughness GIc.

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Figure 2

Comparison between experimental (symbols) and computed (solid curve) fatigue response of epoxy. The experimental results are taken from (7).

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Figure 3

Ball and stick model of the dicyclopentadiene monomer. Panel (a) shows the two rings, each of which has a reactive site delimited by sp2CH groups. The six-membered ring, which has the buckle, is more reactive. A ring-opening metathesis is invoked when a ruthenium-carrying Grubbs catalyst docks with the reactive site of a ring (b). As the ring opens, the ruthenium atom is transferred to the monomer (c). This monomer polymerizes by dock with reactive sites in other monomers (d) or partially reacted chains.

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Figure 4

Simulated DCPD structures at various stages during the polymerization reaction: (a) 14% and (b) 35% of all possible bonds have formed. Only bonds between particles that have reacted are shown. Unreacted monomers are omitted for clarity.

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Figure 5

Degree of cure as a function of time, simulated using the CGP approach for three different catalyst concentrations (given in mol.%). The lines represent the best fit of the PT model (as described in the text).

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Figure 6

Bulk modulus, Young’s modulus, and Poisson’s ratio of CGP-simulated DCPD configurations, as a function of the degree of cure. For the bulk modulus results, different symbols denote the results of various simulations carried out under different catalyst concentrations and reaction rates, indicating the existence of a master curve.

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Figure 7

Time evolution of the degree of cure obtained with the five cure kinetics models listed in Table 1. The solid circles represent the degree of cure corresponding to the characteristic time for healing τheal.

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Figure 8

Evolution with respect to the crack length a of (a) the cohesive zone length lc and (b) the rate of crack advance per cycle da∕dN in the absence of self healing. The loading frequency ω is 1Hz.

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Figure 9

Evolution of τcrack with crack length for three amplitudes of the cyclic load (ω=1Hz)

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Figure 10

Effect of τheal on the fatigue crack propagation in a self-healing DCB specimen with Δn*=0.7Δnc(ω=1Hz)

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Figure 11

Effect of the thickness Δn* of the inserted wedge on the fatigue crack propagation (τheal=100s)

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Figure 12

Effect of the rest period on the fatigue crack propagation in the self-healing DCB specimen with τheal=100s for rest periods of various durations (a) all starting at 500s and (b) all ending at 2000s

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Figure 13

Effect of the loading amplitude Pmax on the crack propagation. The solid curves correspond to the reference solution in the absence of healing. The dashed curves denote the crack advance in the presence of self-healing, with or without a 900s rest period (Δn*=0.7Δnc and τheal=100s).



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