Hannes Kessler

Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack

Abstract This paper presents an exact treatment on the problem of an elliptic hole or a crack in a magnetoelectroelastic solid subject to the farfield loadings. First, based on the extended version of Eshelby-Stroh’s formulation, the general solution of an elliptical hole is obtained according to exact boundary conditions at the rim of the hole. Then, when the hole degenerates into a crack, explicit solutions are given for the field intensity factors and electric–magnetic fields inside the crack. It is shown that all the singularities of fields are dependent on the applied mechanical loads, not on the applied electric–magnetic loads. Due to its explicitness, the present solution for a crack can also serve as a benchmark to test the validity of various analysis approaches or assumptions to more complicated crack problems in magnetoelectroelastic media.

Crack problems in magnetoelectroelastic solids. Part II: general solution of collinear cracks

In this paper, we study mechanically traction-free and electromagnetically permeable crack problems in infinite magnetoelectroelastic solids with linear coupling between the elastic and electromagnetic fields. Using the Stroh-formalism, we first obtain the general solution for collinear cracks in a magnetoelectroelastic medium subjected to arbitrary loads. Then, we give specific solutions for several examples: finite or infinite number of collinear crack subjected to arbitrary remote loads, and a single crack subjected to a line load at an arbitrary point. It is found that in the most general cases, the singularity of electric-magnetic field is always dependent on that of stress. Especially when the medium is only loaded by the remote uniform field, the intensity factor of stress is the same as that of isotropic materials, and the electric-magnetic field inside any crack is uniform.

On the local and average energy release in polarization switching phenomena

Abstract We derive an expression for the energy release during polarization switching in ferroelectric/ferroelastic materials with piezoelectric coupling. The energy release density is proportional to the local changes of the remanent and material properties due to crystal reorientation, and depends on the local electromechanical fields before and after switching. Its equivalent in a representative volume element is applied to constitutive modeling of repolarization and analysis of switching stability in a ferroelectric material.

Fracture analysis of electromagnetic thermoelastic solids

Abstract This paper analyzes the problem of collinear permeable cracks in a magnetoelectroelastic solid subjected to uniform heat flow at infinity. The analysis is conducted according to the extended Stroh formalism. Concise expressions are given for the field intensity factors and the electric–magnetic field inside cracks. It is shown that all the field singularities are independent of the applied electric–magnetic loads, and the electric–magnetic field inside cracks is linearly variable with position along the crack line.

A fracture-mechanics model of the microbond test with interface friction

The microbond test is commonly used to measure the toughness of fiber/matrix interfaces. However, interfacial friction tends to stabilize the crack and increase the peak load as compared to a friction-free crack with the same interface toughness. Nevertheless, for a constant friction shear stress both the interface toughness and friction stress can be approximately determined from load vs. crack length or load vs. displacement hysteresis curves (including energy dissipation, residual displacement or compliance measurements). A friction-free crack is used as a reference solution, and friction is taken into account in the reduced crack-tip fiber load and debonded fiber elongation. When expressed in terms of these two quantities, the energy release rate and fiber end displacement are almost independent of the amount of friction. The approximation involved is verified by a finite-element analysis.

Constitutive modeling of repolarization for the ferroelectric process zone of a crack

Loading of piezoelectric materials leads to high electric fields and mechanical stresses in the near-tip-region of cracks or electrodes. The resulting polarization switching processes can contribute to ferroelectric/ferroelastic crack tip shielding or amplification, equivalent to a change of the fracture toughness. In this paper, we present an approximate constitutive law for repolarization of fully poled materials in load situations where the local poling direction is changed but not the degree of poling. Incremental piezoelectric relations are obtained from a micromechanical switching model. The derivation of the evolution laws for the remanent and material properties and of the tangent moduli resembles plasticity theory: A yield surface is postulated, based on an energy criterion for 90 degree(s) switching of randomly oriented crystallites. The switching barrier corresponds to the yield stress in plasticity. The model is tested on literature data for repolarization of homogeneously poled PZT-samples and in a simulation of the ferroelectric process zone at the tip of a conducting crack or electrode.

Finite element modeling of polarization rotation around an elongated elliptic cavity

Electromechanical loading of piezoelectric devices with high electric field and mechanical stress concentrations near electrode and crack tips may lead to a localized inhomogeneous polarization switching response which is responsible for device degradation. We present an approximate constitutive law for polarization rotation of fully poled materials in load cases which do not initiate depolarization of the material. In other words, the local poling direction is changed but the material remains poled to saturation. The structure of the constitutive law resembles incremental plasticity theory: The “yield surface” is postulated, based on an energy criterion for 90°-switching of the randomly oriented crystallites in a material point, and the energy barrier of polarization switching corresponds to the yield stress. The constitutive model is implemented into the finite element code PSU and validated for the plane sample problem of an elongated elliptic cavity in a ferroelectric material. Some implications for crack shielding models are discussed.