Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

A pre-crack might propagate or stick under mechanical and electrical loading

13.08.2012
Fracture under combined mechanical and electric loading is currently a hot research area in the global fracture community, while electric sticking is a major concern in the design and fabrication of micro/nanoelectromechanical systems.

Professor ZHANG Tong-Yi and his student, Mr. Tao Xie, from the Department of Mechanical Engineering, Hong Kong University of Science and Technology, found that the two problems are switchable, depending on the loading conditions, sample geometries and material properties. Based on his 20-year research experience on the fracture of dielectric and piezoelectric ceramics, Prof. ZHANG developed a novel pre-cracked parallel-plate capacitor model to analytically investigate the role of electrostatic tractions in fracture and electric sticking behaviors.


This is a schematic illustration of the hysteresis loops of a crack width versus (a) the applied displacement under a constant applied electric voltage, and (b) the applied electric voltage under a constant applied displacement.

Credit: ©Science China Press

"Prof. ZHANG and Mr. Tao Xie provided a new fracture criterion based on the energy release rate and crack opening. Their work, entitled "Effect of electrostatic tractions on the fracture behavior of a dielectric material under mechanical and/or electric loading", was published in SCIENCE CHINA Technological Sciences, 2012.

Dielectric and piezoelectric ceramics are important materials for a wide variety of applications in electronic, microelectronic, and mechatronic devices and micro/nanoelectromechanical systems because of their pronounced dielectric, piezoelectric, and pyroelectric properties. However, these materials are brittle and susceptible to cracking. They may include various defects, such as dislocations, electric domain walls, grain boundaries, flaws, pores, impurities and inclusions. The defects induce local stress and/or electric field concentrations, which may consequently cause crack initiation, crack growth, and partial discharge, leading to dielectric breakdown, fracture, and failure. Because of the importance of the reliability of these devices, there has been tremendous interest in studying the fracture and failure behaviors of such materials. The traction-free (i.e., zero mechanical surface force) boundary condition has been commonly adopted in analyzing the fracture of dielectric and piezoelectric ceramics, which ignores completely electrostatic tractions.

However, induced charges appear along crack faces of an electrically insulating crack when the dielectric constant of the crack interior differs from that of the material, thereby producing electrostatic tractions along the crack faces. The electrostatic tractions will cause the two crack faces to stick together if they are strong enough.

This is a typical coupling problem between mechanical and electrical fields, for which it is a great challenge to obtain an analytic solution. Therefore, developing a simple and ideal model, which allows one to carry out an analytic study of the fracture and electric sticking problems, is fundamentally important in capturing the essential features of the fracture and/or electric sticking behaviors and to provide fracture criteria. A pre-cracked parallel capacitor model was thus developed with rigid electrodes adhered to the two surfaces of the capacitor. The capacitor was an infinitely large plate with a semi-infinite long preexisting crack of finite thickness, loaded by mechanical displacement and electric voltage. With this model, the energy release rate for crack propagation can be easily derived analytically without calculating the complex stress and electric fields near the crack tip. Electric sticking of the two crack faces occurs when the crack-closing displacement driven by the electrostatic tractions is equal to or larger than the original crack width.

Although linear constitutive equations are employed to describe material behaviors in the mechanical and electric fields, electrostatic tractions make the capacitor behave nonlinearly, as shown in the above figure for the bifurcation phenomenon of crack opening. Under an applied electric voltage, there is bifurcation behavior between bifurcation and threshold applied displacements (Figure (a)). When the applied displacement is lower than the bifurcation displacement, there are two solutions for the crack opening displacement and the bifurcation behavior occurs until the applied displacement is decreased to the threshold. When the applied displacement is lower than the threshold, there is no physically meaningful solution for the crack opening displacement. The bifurcation behavior yields a hysteresis loop of crack displacement versus applied displacement (Figure (a)).

When the applied displacement is decreased from high values, the crack opening displacement will smoothly pass the bifurcation point and decrease to the threshold point, at which the crack opening displacement will drop from a finite value to zero. When the applied displacement is lower than the threshold, the crack is closed so the upper and lower crack faces stick together. In an experiment, if an electric voltage is applied first and then the mechanical displacement, the crack will not open until the applied displacement reaches the bifurcation value. At the bifurcation displacement, the crack suddenly opens and the crack opening displacement jumps from zero to another finite value. The bifurcation and threshold displacements both depend on the applied electric voltage and the ratio of the dielectric constants, implying that the electrostatic tractions play a critical role. Under a given mechanical displacement, the crack opening displacement will decrease with increasing applied electric voltage until crack closure (Figure (b)), at which the electric voltage is called the maximum tolerated voltage , the conjugate of the threshold displacement. There is bifurcation behavior between the maximum tolerated voltage and the bifurcation voltage, conjugate of the bifurcation displacement. If the applied electric voltage exceeds the maximum tolerated voltage, the crack will close and the fracture problem is then converted to an electric field-induced sticking problem. The crack width versus applied electric voltage under a given mechanical displacement also shows a hysteresis loop (Figure (b)). In an experiment, if a sustained mechanical displacement is applied first, and then the applied electric voltage is increased from zero, the crack width will decrease smoothly with increasing electric voltage, passing the bifurcation point, until reaching the maximum tolerated voltage, at which the crack width drops from a finite value to zero. Afterward, increasing the electric voltage will result in the two crack faces sticking together more tightly. When the electric voltage is decreased from a value higher than the maximum tolerated voltage, the crack will not open until the electric voltage is decreased to the bifurcation point, at which the crack opens suddenly and the crack width jumps from zero to another finite value.

An analytic formula of the failure criterion was derived according to the energy release rate. The results show that an applied electric field impedes crack propagation while an applied mechanical load tends to propagate the crack. The applied electric field will play a more significant role in the fracture behavior, if the material dielectric constant is higher and/or the mechanical fracture toughness of the material in terms of the critical energy release rate is lower. In an experiment on the fracture of a dielectric material under combined mechanical and electric loading, an electric field is usually applied first; a mechanical load is then applied and increased until fracture occurs. This is because increasing an applied electric field while maintaining a sustained mechanical load cannot fracture the tested samples. The pre-applied electric field may cause the crack faces to stick together. In this case, the applied displacement must be higher than the bifurcation displacement to open the crack; thus, the condition that the critical applied displacement for crack propagation must be larger than the bifurcation displacement should be an additional criterion for crack propagation.

See the article: Zhang Tong-Yi and Tao Xie. Effect of electrostatic tractions on the fracture behavior of a dielectric material under mechanical and/or electric loading. SCIENCE CHINA Technological Sciences. 2012

ZHANG, Tong-Yi | EurekAlert!
Further information:
http://zh.scichina.com/

More articles from Materials Sciences:

nachricht Plant inspiration could lead to flexible electronics
22.06.2017 | American Chemical Society

nachricht A rhodium-based catalyst for making organosilicon using less precious metal
22.06.2017 | Tokyo Institute of Technology

All articles from Materials Sciences >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Can we see monkeys from space? Emerging technologies to map biodiversity

An international team of scientists has proposed a new multi-disciplinary approach in which an array of new technologies will allow us to map biodiversity and the risks that wildlife is facing at the scale of whole landscapes. The findings are published in Nature Ecology and Evolution. This international research is led by the Kunming Institute of Zoology from China, University of East Anglia, University of Leicester and the Leibniz Institute for Zoo and Wildlife Research.

Using a combination of satellite and ground data, the team proposes that it is now possible to map biodiversity with an accuracy that has not been previously...

Im Focus: Climate satellite: Tracking methane with robust laser technology

Heatwaves in the Arctic, longer periods of vegetation in Europe, severe floods in West Africa – starting in 2021, scientists want to explore the emissions of the greenhouse gas methane with the German-French satellite MERLIN. This is made possible by a new robust laser system of the Fraunhofer Institute for Laser Technology ILT in Aachen, which achieves unprecedented measurement accuracy.

Methane is primarily the result of the decomposition of organic matter. The gas has a 25 times greater warming potential than carbon dioxide, but is not as...

Im Focus: How protons move through a fuel cell

Hydrogen is regarded as the energy source of the future: It is produced with solar power and can be used to generate heat and electricity in fuel cells. Empa researchers have now succeeded in decoding the movement of hydrogen ions in crystals – a key step towards more efficient energy conversion in the hydrogen industry of tomorrow.

As charge carriers, electrons and ions play the leading role in electrochemical energy storage devices and converters such as batteries and fuel cells. Proton...

Im Focus: A unique data centre for cosmological simulations

Scientists from the Excellence Cluster Universe at the Ludwig-Maximilians-Universität Munich have establised "Cosmowebportal", a unique data centre for cosmological simulations located at the Leibniz Supercomputing Centre (LRZ) of the Bavarian Academy of Sciences. The complete results of a series of large hydrodynamical cosmological simulations are available, with data volumes typically exceeding several hundred terabytes. Scientists worldwide can interactively explore these complex simulations via a web interface and directly access the results.

With current telescopes, scientists can observe our Universe’s galaxies and galaxy clusters and their distribution along an invisible cosmic web. From the...

Im Focus: Scientists develop molecular thermometer for contactless measurement using infrared light

Temperature measurements possible even on the smallest scale / Molecular ruby for use in material sciences, biology, and medicine

Chemists at Johannes Gutenberg University Mainz (JGU) in cooperation with researchers of the German Federal Institute for Materials Research and Testing (BAM)...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Plants are networkers

19.06.2017 | Event News

Digital Survival Training for Executives

13.06.2017 | Event News

Global Learning Council Summit 2017

13.06.2017 | Event News

 
Latest News

Individualized fiber components for the world market

23.06.2017 | Physics and Astronomy

How brains surrender to sleep

23.06.2017 | Life Sciences

Can we see monkeys from space? Emerging technologies to map biodiversity

23.06.2017 | Information Technology

VideoLinks
B2B-VideoLinks
More VideoLinks >>>