A closed-form solution for a crack approaching an interface

Nuller, B.M.; Ryvkin, Michael; Chudnovsky, A.

doi:10.2140/jomms.2006.1.1405

Cited by 7 publications

(3 citation statements)

References 14 publications

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“…As the FGM3 approaches maximum elongation, the T10 core begins to undergo mode I fracture due to tensile stress. Stress intensifies as the crack tip approaches the multilayer interface (Figure B), but the crack is arrested and stress is confined by the surrounding T7 copolymer layer due to modulus mismatch once the tip reaches the interface (Figure C) . The crack exhibits competing modes of stress‐relaxing fracture propagation once in contact with the copolymer interface, including deflection across the interface, penetration into the layer above, or both .…”

Section: Resultsmentioning

confidence: 99%

Bioinspired Functional Gradients for Toughness Augmentation in Synthetic Polymer Systems

Chorazewicz

Sundrani

Ahn

2018

Macro Chemistry & Physics

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In nature, load‐bearing polymeric materials that do not present significant trade‐off between elongation and elastic modulus are often found, but are rare in synthetic systems. One mechanism for emulating these natural systems is with functionally graded materials (FGMs). The development of synthetic FGM systems with varying moduli gradient using tuned poly(meth)acrylate multilayers is shown. Such localized tuning of crosslink density is shown as a mechanism to increase rigidity without significant compromise to maximum strain. The toughest FGM shows 43% higher tensile strength and 9% higher stiffness than copolymer elastomers with similar maximum strain (εmax ≈ 110%), increasing toughness by 25%. These improved tensile mechanical properties can be due to beneficial interlayer crack deflection and delamination. This gradient approach provides potential to improve toughness of various load‐bearing polymeric materials.

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Section: Resultsmentioning

confidence: 99%

Bioinspired Functional Gradients for Toughness Augmentation in Synthetic Polymer Systems

Chorazewicz

Sundrani

Ahn

2018

Macro Chemistry & Physics

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“…Solutions of a simplified problem of crack propagation across an interface demonstrated shielding and anti-shielding effects for compliant/stiff and stiff/compliant transitions, respectively. [40][41][42][43][44] Recently, Fratzl et al [39] presented an analytical solution for crack propagation in materials with periodically varying elastic modulus. Their results indicate that if elastic modulus ratio of stiff to compliant layer is larger than five then the crack driving force becomes negative when the crack tip approaches the compliant/stiff interface.…”

Section: Finite Element Analysis Of Local Crack Shieldingmentioning

confidence: 99%

Nanoindentation, Modeling, and Toughening Effects of Zirconia/Organic Nanolaminates

Zlotnikov¹,

Dorogoy²,

Shilo³

et al. 2010

Adv Eng Mater

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The biological composite nacre, with its unique combination of stiffness, strength, and toughness has long inspired researchers to reproduce nature's achievements and synthesize structural materials using the similar design. A number of theoretical models have been developed to explain nacre's extraordinary mechanical performance, [1,2] however the exact deformation mechanisms of this material are far from being fully understood. The toughness of nacre is believed to originate from its unique micro-nanoscale ''brickand-mortar'' architecture composed of alternating layers of soft organic biopolymer and hard inorganic material (aragonite). [3][4][5][6][7] The reproduction of this highly complex structure is still beyond the current capabilities of materials processing techniques, however some morphological aspects of nacre can be imitated by a simplified nanolaminate model comprised of alternating ceramic and organic nanolayers. Several attempts to produce synthetically laminated organo-ceramic nanocomposites with nacre-like structure under ambient or biomineralization-like mild conditions have been reported. [8][9][10] These attempts mainly fall into two categories. In one, calcium carbonate or clay is used as the ceramic constituent in order to reproduce, as closely as possible, the composition and structure of nacre. [11][12][13][14][15][16] In the second category, the general design concept is to replace the relatively weak inorganic constituent found in nacre (aragonite) with structural ceramics (e.g., oxides) such as: silica, [17] alumina, [18] zinc oxide, [19] titania [20] and zirconia, [21] with the goal of producing structural composite materials with high performance. In both cases, a polyelectrolyte based layer-by-layer (LbL) technique [22] demonstrated an advantage in the preparation of simplicity, uniformity, and precise width control while preparing the organic layer. [23] Nanoindentation has been extensively used to evaluate the elastic modulus and hardness of nanolaminates. Very few reports on nanoindentation testing of man-made inorganic-organic laminates can be found in literature. Characterization by nanoindentation of other hard-soft structures such as ceramic-metal nanolaminates is more widely reported, however the results are often contradictory. For example, Wang et al. [24] found that the hardness of TiC/metal (Cr, Mo, and Fe) multilayer nanostructures synthesized by ion beam sputtering was higher than that of pure TiC. Conversely, for SiC/Al sputtered nanolaminates, reported by Chawla et al. [25] , both hardness and elastic modulus measured employing nanoindentation fell in-between the corresponding values forThe present research is motivated by the remarkable toughness of natural nanostructured composites, specifically nacre, whose highly regular ''brick-and-mortar'' structure is composed of alternating layers of aragonite sheets separated by thin layers of organic material. Robust multilayer zirconium oxide (ZrO 2 )-organic nanolaminates are deposited on Si wafers. Organic layers are synt...

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“…Consequently, a crack approaching the interface with a weak/stiff material will be unstable/stable. The exact condition for the crack stability/instability was established by Nuller et al (2006). Based on this discussion, the actual crack tip has to be located somewhere within the matrix region.…”

Section: Crack In a Fiber Reinforced Compositementioning

confidence: 99%

A continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack

Ryvkin

Aboudi

2007

International Journal of Solids and Structures

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The stress field in a periodically layered composite with an embedded crack oriented in the normal direction to the layering and subjected to a tensile far-field loading is obtained based on the continuum equations of elasticity. This geometry models the 2D problem of fiber reinforced materials with a transverse crack. The analysis is based on the combination of the representative cell method and the higher-order theory. The representative cell method is employed for the construction of Green's functions for the displacements jumps along the crack line. The problem of the infinite domain is reduced, in conjunction with the discrete Fourier transform, to a finite domain (representative cell) on which the Born-von Karman type boundary conditions are applied. In the framework of the higher-order theory, the transformed elastic field is determined by a second-order expansion of the displacement vector in terms of local coordinates, in conjunction with the equilibrium equations and these boundary conditions. The accuracy of the proposed approach is verified by a comparison with the analytical solution for a crack embedded in a homogeneous plane.Results show the effects of crack lengths, fiber volume fractions, ratios of fiber to matrix Young's moduli and matrix Poisson's ratio on the resulting elastic field at various locations of interest. Comparisons with the predictions obtained from the shear lag theory are presented.

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A closed-form solution for a crack approaching an interface

Cited by 7 publications

References 14 publications

Bioinspired Functional Gradients for Toughness Augmentation in Synthetic Polymer Systems

Bioinspired Functional Gradients for Toughness Augmentation in Synthetic Polymer Systems

Nanoindentation, Modeling, and Toughening Effects of Zirconia/Organic Nanolaminates

A continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack

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