Magnetoelectric (ME) coupling is an inherent property of only a few crystals exhibiting very low coupling coefficients at low temperatures. On the other hand, these materials are desirable due to many promising applications, e.g. as efficient data storage devices or medical or geophysical sensors.
Efficient coupling of magnetic and electric fields in materials can only be achieved in composite structures. Here, ferromagnetic (FM) and ferroelectric (FE) phases are combined e.g. including FM particles in a FE matrix or embedding fibers of the one phase into a matrix of the other. The ME coupling is then accomplished indirectly via strain fields exploiting magnetostrictive and piezoelectric effects. This requires a poling of the composite, where the structure is exposed to both large magnetic and electric fields. The efficiency of ME coupling will strongly depend on the poling process. Besides the alignment of local polarization and magnetization, it is going along with cracking, also being decisive for the coupling properties.
Nonlinear ferroelectric and ferromagnetic constitutive equations have been developed and implemented within the framework of a multifield, two-scale FE approach. The models are microphysically motivated, accounting for domain and Bloch wall motions. A second, so called condensed approach is presented which doesn’t require the implementation of a spatial discretisation scheme, however still considering grain interactions and residual stresses. A micromechanically motivated continuum damage model is established to simulate degradation processes. The goal of the simulation tools is to predict the different constitutive behaviors, ME coupling properties and lifetime of smart magnetoelectric devices.
The coupling of magnetic and electric fields due to the constitutive behavior of a material is commonly denoted as ME-effect. The latter is only observed in a few crystal classes exhibiting a very weak coupling which can hardly be exploited for technical applications. Much larger coupling coefficients are obtained in so called multiferroic composite materials, where ferroelectric and ferromagnetic constituents are embedded in a matrix. The MEeffect is then induced by the strain of the matrix converting electrical and magnetic energies based on the ferroelectric and magnetostrictive effects. In this paper, the theoretical background of nonlinear constitutive multifield behavior as well as the Finite Element implementation are presented. Nonlinear material models describing the magneto-ferroelectric behavior are presented. On this basis, the poling process in the ferroelectric phase is simulated and resulting effects are analyzed. Numerical simulations in general focus on the prediction of ME coupling coefficients and residual stresses going along with the poling process. Numerical homogenization, here, is a useful means to supply effective properties.
Recently, the theoretical framework of fracture mechanics of piezoelectrics has been extended to include electrostatically
induced mechanical tractions in crack models yielding a significant crack closure effect.1-3 However,
these models are still simple, neglecting e.g. the piezoelectric field coupling. In this work, an extended model for
crack surface tractions is presented yielding some interesting effects. In particular, it is predicted that the Mode-I
stress intensity factor is influenced by both a collinear normal stress parallel to the crack faces and a Mode-II
shear loading. Also, the direction of electric field vs. poling direction is clearly manifested in the calculated crack
loading quantities.
A new sensor concept for fatigue crack growth monitoring in technical structures is presented. It allows the in-situ
determination of the position of the crack tip as well as the fracture mechanical quantities. The required data are obtained
from a piezoelectric polymer film, which is attached to the surface of the monitored structure. The stress intensity factors
and the crack tip position are calculated from electrical potentials obtained from a sensor array by solving the non-linear
inverse problem.
Fatigue crack growth experiments with DCB specimens made of PZT subjected to cyclic electrical and constant mechanical loading are evaluated from the fracture mechanical point of view. Therefore, correlations have been developed from numerical simulations with the Finite Element Method providing the electric displacement intensity factor KIV which depends on crack length and electromechanical loading conditions. The simulations account for limited permeable crack faces and explain the observation of a dielectric crack closure effect. Fatigue crack growth is then described by a power law. To simulate ferroelectric domain switching, a numerical micromechanical model has been developed. Finite Element calculations shed light on the physical mechanisms of crack growth due to electric cycling.
A model is presented to calculate the influence of ferroelectric/ferroelastic domain switching near a crack tip on the effective fracture toughness of piezoelectric ceramics. The switch-toughening effect is quantified in terms of intrinsic field intensity factors accounting for residual fields within the fracture process zone which are due to constraints at the boundary of the switching zone. The intrinsic field intensity factors themselves depend on the external electromechanical loading of the cracked body and thus can clearly be expressed in terms of the intensity factors of the applied loading. These can also account for the effects of an electrical permeability of the crack. The extension of the process zone is calculated using closed-form solutions for the asymptotic crack tip fields in connection with a domain switching criterion. Subsequently, the amount of switch-toughening is calculated applying a weight function technique. Therefore, crack weight functions have been derived for the real anisotropy in piezoelectrics.
One of the most essential problems with ferroelectric ceramics is the low strength and durability of the brittle material, which prevents many most promising technical applications in mechatronics and adaptronics. In order to supply knowledge about design features and strength criteria and to improve the safety of components with smart ceramics, a more fundamental understanding about the process of fracture under combined mechanical and electrical loading is required. Therefore, numerical tools are developed permitting the stress analysis of arbitrarily shaped smart ceramics with a given crack under combined electromechanical loading boundary conditions. To solve the coupled electromechanical field problem, the FEM is used taking account of linear constitutive equations for an anisotropic piezoelectric continuum. Stress intensity factors and energy release rates are subsequently calculated inserting near tip nose values for mechanical displacements and forces as well as electrical potentials and charges. In connection with experiments on the cracking of Double Cantilever Beam specimens, the influence of electrical and mechanical loading conditions on the crack propagation is investigated. On the basis of calculated energy release rates and intensity factors as functions of the crack length, possible fracture criteria are discussed.
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