skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Why does an elastomer layer confined between two rigid blocks grow numerous cavities?
For a thin layer of elastomer sandwiched between two rigid blocks, when the blocks are pulled, numerous cavities grow in the elastomer like cracks. Why does the elastomer grow numerous small cracks instead of a single large crack? Here we answer this question by analyzing an idealized model, in which the elastomer is an incompressible neoHookean material and contains a penny-shaped crack. To simulate one representative crack among many, the model is axisymmetric with zero radial displacement at the edge. When the rigid blocks are pulled by a pair of forces, a hydrostatic tension develops in the elastomer. At a critical hydrostatic tension, a small crack deforms substantially, as predicted by an elastic instability, resulting in an unbounded energy release rate. Consequently, the small crack initiates its growth, regardless of the toughness of the elastomer. As the crack grows, the energy release rate decreases, so that the crack arrests. Meanwhile, the rigid blocks constrain deformation of the elastomer far away from the crack, where hydrostatic tension remains high, allowing other cracks to grow. For an elastomer of thickness H, shear modulus , and toughness , the crack radius and spacing decrease as the normalized toughness increases. Therefore, a tough elastomer of small modulus and thickness will grow numerous small cracks when confined by two rigid blocks and pulled beyond a critical force.  more » « less
Award ID(s):
2011754
PAR ID:
10500456
Author(s) / Creator(s):
; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal of the Mechanics and Physics of Solids
Volume:
173
Issue:
C
ISSN:
0022-5096
Page Range / eLocation ID:
105223
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, International Journal of Fracture)
    The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate (J) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of J for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate (J) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for J that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks. 
    more » « less
  2. ; ; ; (, Journal of the Mechanics and Physics of Solids)
    Living tissues and some engineering materials contain water. When a wet material loses water, high triaxial tensile stress may build up and cause instability. The mechanism of instability under triaxial tension has attracted great attention, but quantitative study remains an ongoing chal- lenge. Here we develop an experimental method to apply well-controlled triaxial tensile stress and observe osmotic instability in situ. We synthesize a hydrogel in an elastomer tube with strong adhesion between them. The elastomer dissolves minute amount of water, but allows water to diffuse out and places the hydrogel under homogeneous, equal-triaxial, tensile stress. We develop a method to determine the stress as a function of time. The transparent setup enables observation of various types of osmotic instabilities, including cavity nucleation, crack propagation, and surface undulation. Notably, our method enables the measurement of crack speed from ~10−5 m/ s to a limit comparable to the Rayleigh wave speed ~1 m/s. We observe a large jump in crack speed at a critical energy release rate. This work opens opportunities to study the physics of soft materials under high triaxial tension. 
    more » « less
  3. ; (, Physical Review E)
    Polyurethane (PU) elastomers are among the most used rubberlike materials due to their combined merits, including high abrasion resistance, excellent mechanical properties, biocompatibility, and good processing performance. A PU elastomer exhibits pronounced hysteresis, leading to a high toughness on the order of 104 J/m2. However, toughness gained from hysteresis is ineffective to resist crack growth under cyclic load, causing a fatigue threshold below 100 J/m2. Here we report a fatigue-resistant PU fiber–matrix composite, using commercially available Spandex as the fibers and PU elastomer as the matrix. The Spandex fibers are stiff, strong, and stretchable. The matrix is soft, tough, and stretchable. We describe a pullout test to measure the adhesion toughness between the fiber and matrix. The test is highly reproducible, showing an adhesion toughness of 3170 J/m2. The composite shows a maximum stretchability of 6.0, a toughness of 16.7 kJ/m2, and a fatigue threshold of 3900 J/m2. When a composite with a precut crack is stretched, the soft matrix causes the crack tip to blunt greatly, which distributes high stress over a long segment of the Spandex fiber ahead the crack tip. This deconcentration of stress makes the composite resist the growth of cracks under monotonic and cyclic loads. The PU elastomer composites open doors for realistic applications of fatigue-resistant elastomers 
    more » « less
  4. ; ; ; (, Journal of the Mechanics and Physics of Solids)
    An experimental and theoretical study of delayed fracture of polydimethlsiloxane (PDMS) is presented. Previous works have demonstrated that delayed fracture in single edge notch specimens is caused by time dependent damage due to chain scission. Here we study the interactions between damage and the elastic field using different specimens and crack geometries with blunt and sharp cracks. Our experiments show that initial toughness is not well defined, as stable slow crack growth can occur over a range of applied loads. Our experiments demonstrate that there is a universal relation between crack growth rate and applied energy release rate. A model coupling the nonlinear elastic deformation and rate dependent bond scission is proposed and is in good agreement with experimental data. 
    more » « less
  5. ; (, Materials)
    In this study, the fracture mechanics of eastern spruce were characterized in relation to end-grain orientation. Compact tension-type specimens with small pre-formed cracks were prepared such that grain angle varied relative to the load axis. Specimens were loaded under crack mouth opening displacement (CMOD) control as to maintain stable crack growth. Specimen fracture was characterized using both R-curve and bulk fracture energy approaches. The results showed that under a RT grain orientation, as well as grain deviations up to about 40∘, cracks will follow a path of least resistance in an earlywood region. As the grain angle exceeds 40∘, the crack will initially move macroscopically in the direction of maximum strain energy release rate, which extends in the direction of the pre-crack, but locally meanders through earlywood and latewood regions before settling once again in an earlywood region. At 45∘, however, the macroscopic crack takes a turn and follows a straight radial path. The results further show that RT fracture is macroscopically stable, while TR fracture is unstable. None of the end-grain fracture orientations showed rising R-curve behavior, suggesting that there is not a traditional fracture process zone in this orientation. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email