A new law provides the energy needed to fracture outstanding networks

Interconnected materials containing networks are ubiquitous in the world around us …rubber, Car tireshuman tissues and designed, woven sheets and Armor by post in chain. Engineers often want these networks to be as strong as possible and to withstand fracture and mechanical failure.

The key property that determines the resistance of a network is its intrinsic fracture energy, the smallest energy needed to propagate a crack through a surface of the surface, most of the network breaks down. As examples, the intrinsic fracture energy of polymer networks is about 10 to 100 Joule per square meter, 50–500 J/m² For elastomeres used in car tires, while spider silk has an intrinsic fracture energy of 150-200 j/m².

So far, there has been no way to calculate the intrinsic fracture energy (IFE) for a network material, given the mechanical behavior and the connectivity of its components.

Publication in the journal Physical review xThe US scientists have developed a scaling law that predicts IFE of a wide type of extensible networks. IFE depends only on the properties of the individual streams on the network – how much strength it is necessary to break a stream, the length of a thread when it reaches the breaking point – and the geometry of the network – how many wires exist on the unit unit.

IFE is then proportional to the product of these three quantities. Their result is supported by experiments and simulations for “a width of constituent behaviors, topologies, dimensions and stairs,” write “, including, but without limiting to polymer -like networks”.

The result is applied on multiple length scales from a nanometer to a meter and works for a range of two -dimensional and three -dimensional network architectures, such as triangular networks, square networks, hexagonal networks, networks that are centered on cubic bodies and locks.

In order to develop the new law for intrinsic fracture energy, the group from Massachusetts and Georgia universities in the United States with an Inkbit Corporation co-author, directly assembled the networks of many materials and tested them carefully.

The various network geometries began to analyze, taking into account individual strings of initial length, a final length at the breaking point and the force of the chain. These behaviors could be linear or non -linear. The materials on the network were manufactured by stratifying the streams; There could be up to several thousand layers for each network.

Started with an equation that has been developed in Book 1962 Physical properties of polymers by Frederick J. Bueche, who was modified in 1996 for a study on the elastic properties of the DNA. Both were based on a model of a polymer chain called free -joined chain model, which is a chain of statistically independent Kuhn segments whose segment orientations are unrelated to the absence of external forces.

Kuhn segments are an idealized segment of a polymer chain whose joints (at its neighboring segments) are free to align independently (again, the absence of an external force, such as a magnetic or electric field).

By modifying the model for testing and experimental validation, they used several materials with a range of two -dimensional and three -dimensional networks created with a laser cutter. Tetra-polyen (Ethylene glycol) the hydrogels (tetra-peg hydrogels) received especially attention in their paper. This hydrogel has relatively homogeneous networks, with a cubic network architecture with diamond cubes.

A Instrument The universal test machine was used to restrict the polymer network at one end, then pull at the other end, until the network has been torn.

In addition to the laboratory experiments, “I developed a simulation tool based on coarse cereals,” said Deng Dot from the Georgia Institute of Technology. The coarse granulation method, which leaves the streams with a harsh, coarse texture, has rebuilt large networks, with fewer degrees of freedom, drastically of freedom-the number of ways in which the interconnected polymer chains can move.

In a triangular network with coarse granulation created for simulations, the network had 4,000 vertical layers and 8,000 horizontal layers, with a total of 44,847 knots and 89,694 degrees of freedom. The simulations “allow us to simulate the extremely fracture energy Large networks With thousands of layers with minimum calculation costs and view the energy flow during the fracture process, ”said Deng.

The potential applications for architect materials, in which the structures and networks in the material give them unique properties, include soft robotic actuators, improving the hardness and durability of the projected tissues and creating resistant grids for aerospatal technologies.

“This scaling law offers a roadmap for the development of hard and stretched networks from the ground,” said the main author Chase Hartquist, a doctorate. Candidate in mechanical engineering at the Institute of Technology in Massachusetts.

“Instead of relying on intuition, scientists and engineers can use these discoveries to design and directly build network materials.”

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