Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

Govorukha, Volodymyr; Kamlah, Marc; Sheveleva, A.

doi:10.1007/s00707-015-1329-z

Cited by 9 publications

(3 citation statements)

References 35 publications

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“…In a recent study [22], the possibility of forming a large contact zone for the example of one crack under the action of compressive or compressive-shear loading was considered. A similar problem, with the addition of concentrated loading, was investigated by Govorukha et al [23].…”

Section: Introductionmentioning

confidence: 93%

Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

Kozinov

Sheveleva²,

Лобода

2019

Mathematics and Mechanics of Solids

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A closed-form solution is constructed for a bi-material consisting of two piezoelectric (or piezoelectric and dielectric) half-planes, which are periodically bonded along the interface and can partially contact along the initially unbonded parts. Under compressive loading, the size of the frictionless contact zone is usually quite large; in some cases the interface is completely closed. Such a situation is frequently observed in industrial applications. Since the periodic bonding of two different materials is extremely widespread, it is very important to study the influence of the mutual material properties of the composite and the applied loading on the size and shape of the opened regions, as well as the stress intensity factor at the bonding points. To formulate the problem, the electromechanical factors are presented through piecewise analytic functions, so that the problem in question is reduced to the combined periodic Dirichlet–Riemann problem, which is solved exactly. The obtained solution provides explicit formulas for the mechanical stresses and displacements along the interface and allows one to find the dependence of the contact zones and the stress intensity factor on the ratio of the bonded parts of the interface to the period for the different values of applied loading and materials.

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Section: Introductionmentioning

confidence: 93%

Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

Kozinov

Sheveleva²,

Лобода

2019

Mathematics and Mechanics of Solids

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“…A modified capacitance model has been developed to observe the C-V characteristics of PZT thin films [25]. The interface crack between the piezoelectric materials in a compressive field is studied, to understand the reliability of these materials [26]. The effects of scaling, surface energy, and electrical boundary conditions on the formation of polarization patterns in tetragonal ferroelectrics has been studied [27].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear modeling on rate dependent ferroelectric and ferroelastic response of 1-3 piezocomposites

Jayendiran

Arockiarajan

2016

Smart Mater. Struct.

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The effect of loading rate on ferroelectric and ferroelastic behavior of 1-3 piezocomposites is presented in this work. Experiments are conducted for various loading rates under different loading conditions such as electrical and electromechanical to measure the rate dependent response of 1-3 piezocomposite compared with bulk piezoceramics. A thermodynamic based rate dependent domain switching criteria has been proposed to predict the ferroelectric and ferroelastic behavior of homogenized 1-3 piezocomposites. In this model, volume fraction of six distinct uni-axial variants are used as internal variables to describe the microscopic state of the material. Plasticity based kinematic hardening parameter is introduced as a function of internal variables to describe the grain boundary effects. Homogenization of 1-3 piezocomposite material properties are obtained by finite element (FE) resonator models using commercially available FE tool Abaqus. To evaluate the possible modes of vibration of 1-3 piezocomposite four different configuration of FE resonators are modeled. The FE resonator model is validated with the impedance spectra obtained experimentally for length extensional and thickness extensional resonator models. The predicted effective properties using the resonance based technique are incorporated in the proposed rate dependent macromechanical model to study the behavior of 1-3 piezocomposites. The simulated results are compared with the experimental observations.

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“…A mathematical body of the theory of functions of a com plex variable is widely used for constructing solutions of boundary value problems of theory of plastic deformation [12], fracture mechanics for piezoelectric solids [13,14], pi ezoceramic solids [15], and bimaterials [16] with interfacial cracks under the action of mechanical loads, electromagnetic and thermal fields [17,18].…”

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confidence: 99%

Two-dimensional elastic theory methods for describing the stress state and the modes of elastic boring

Pabyrivskyi¹,

Kuzio²,

Pabyrivska³

et al. 2020

Nauk. visn. nat. hirn. univ.

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Purpose. To find the stressed state and describe the operating regimes of an important element of mining industrial equip ment -an elastic drilling bit -based on the method of finding the solutions of problems of solid mechanics using holomorphic functions of two complex variables.Methodology. Methods for constructing the basic solutions of threedimensional boundary value problems of the theory of elasticity are based on the representation of the fundamental solution of the Lame equations in the PapkovichNeuber form using a scalar spatial harmonic function and a vectoral spatial harmonic function. This made it possible to formulate the boundary value problem in terms of holomorphic functions of complex variables. Based on the representation of the above holomorphic functions in the form polynomial of the n th order in accordance with degrees of the complex variables, corresponding boundary conditions are formulated for basic solutions and integral conditions for the principle moment of the stress vector on the lateral surface being equal to zero are additionally specified.findings. The paper formulates complexconjugate boundary value problems of spatial theory of elasticity in terms of holomor phic functions of two complex variables. We have considered the case when there is one of the spatial coordinates on which the stress tensor does not depend on, for a body whose surface is described by standard curves. For the given finite elastic cylindrical solid (a drilling bit) of canonical crosssection, a set of the basic complex solutions of the n th order and of corresponding vectors of external loads has been constructed. originality. For the first time, a scheme and a method for constructing the basic solutions of static boundary value problems of spatial theory of elasticity have been suggested and the corresponding boundary conditions have been imposed; the real and imaginary parts of the solutions of the basic boundary value problems for a cylindrical drilling bit have been constructed and an analysis of these solutions has been carried out.Practical value. An example of using the developed methods for constructing solutions of boundary value problems of spatial theory of elasticity has been considered for finding an exact analytical solution of a twodimensional boundary value problem that describes the distribution of stresses and corresponding external loads on the lateral surface of a cylindrical drilling bit of a ca nonical crosssection. Such mathematical models and analysis of the external load structure can be effectively used to describe the safe operating modes of mining boring equipment.

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Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

Cited by 9 publications

References 35 publications

Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

Nonlinear modeling on rate dependent ferroelectric and ferroelastic response of 1-3 piezocomposites

Two-dimensional elastic theory methods for describing the stress state and the modes of elastic boring

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