Research Papers

Swelling Driven Crack Propagation in Large Deformation in Ionized Hydrogel

[+] Author and Article Information
Jingqian Ding

Department of Mechanical Engineering,
Eindhoven University of Technology,
P.O. BOX 513,
Eindhoven 5600 MB, The Netherlands
e-mail: j.ding@tue.nl

Joris J. C. Remmers

Department of Mechanical Engineering,
Eindhoven University of Technology,
P.O. BOX 513,
Eindhoven 5600 MB, The Netherlands
e-mail: j.j.c.remmers@tue.nl

Szymon Leszczynski

Procter & Gamble Service GmbH,
Sulzbacher Straße 40,
Schwalbach am Taunus 65824, Germany
e-mail: leszczynski.s@pg.com

Jacques M. Huyghe

Bernal Institute,
University of Limerick,
Limerick V94 T9PX, Ireland
e-mail: Jacques.huyghe@ul.ie

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 31, 2017; final manuscript received December 6, 2017; published online December 20, 2017. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(2), 021007 (Dec 20, 2017) (12 pages) Paper No: JAM-17-1609; doi: 10.1115/1.4038698 History: Received October 31, 2017; Revised December 06, 2017

Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many 1000's %. In this paper, we present a swelling driven fracture model for ionized hydrogel in large deformation. Flow of fluid within the crack, within the medium, and between the crack and the medium are accounted for. The partition of unity method is used to describe the discontinuous displacement field and chemical potential field, respectively. In order to capture the chemical potential gradient between the gel and the crack, an enhanced local pressure (ELP) model is adopted. The capacity of this numerical model to study the fracture and swelling behaviors of ionized gels with low Young's modulus (< 1 MPa) and low permeability (< 10−16 m4/Ns) is demonstrated. Two numerical examples show the performance of the implemented model (1) swelling with crack opening and (2) swelling with crack propagation. Simulations demonstrate that shrinking of a gel results in decreasing macroscopic stress and simultaneously increasing stress at crack tips. Different scales yield opposite responses, underscoring the need for multiscale modelling. While cracking as a result of external loading can be prevented by reducing the overall stress level in the structure, reducing overall stress levels will not result in reducing the crack initiation and propagation due to swelling.

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Fig. 3

Schematic representation of the enhanced local chemical potential. The dark gray area represents the crack. The chemical potential variation across the crack is composed of two parts: (1) the chemical potential degree-of-freedom which is discontinuous over both boundaries of the crack (bold continuous line); (2) the analytical solution of consolidation (dotted line) from which the flux of the fluid between crack and hydrogel is calculated.

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Fig. 2

A domain is crossed by a discontinuity Γd (dashed line) with two resulting subdomains Ω+ and Ω. nΓd is defined as the normal of the discontinuity surface Γd pointing to the subdomain Ω+.

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Fig. 1

Swollen SAP particle showing cracking cross-linked surface during swelling

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Fig. 4

Sketch of the dry, swollen reference and current state of the gel. Xd, X, and x are points of the dry, swollen reference, and current state, respectively.

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Fig. 11

The geometry and boundary conditions of the sample. A changing chemical potential is applied along the outer surface. (ROuter = 0.5 mm, RCore = 0.2 mm).

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Fig. 12

Traction versus opening of the crack

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Fig. 8

Simulated normal Second Piola–Kirchhoff stress distribution S22 (MPa) after an increase of external salt concentration from 0.15 M to 0.2 M

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Fig. 9

Macroscopic stress (above) and local stress of the crack tip (below) (MPa)

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Fig. 10

Displacement plots of the middle point of left side (above) and the top surface of the crack (below) (mm)

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Fig. 5

The geometry and boundary condition of swelling verification test

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Fig. 6

The height change at the top is caused by the change of salt concentration at the bottom. The curve denotes the transient numerical solution and the horizontal line is the equilibrium analytical solution.

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Fig. 7

The left side of the sample and crack are in contact with a salt solution of concentration cex. The right side is a symmetry plane. The crack (0.5 mm) is placed in the middle of the right side (length: 1 mm height: 0.5 mm).

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Fig. 14

Initial state of the sample

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Fig. 15

Displacement distribution of the sample at 15 s

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Fig. 16

Displacement distribution of the sample at 30 s

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Fig. 13

Crack propagation over time



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