F. García-Sánchez

Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials

From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular displacement boundary integral equations (BIEs) are applied on the external boundary of the cracked solid, while the hypersingular traction BIEs are used on the crack faces. Three numerical examples are presented to show the path independence and the high accuracy of the J-integral in piezoelectric materials and to analyze the pros and cons of these approaches in evaluating the field intensity factors.

Fracture Analysis of Magnetoelectroelastic Composite Materials

This paper presents a crack analysis of linear magnetoelectroelastic materials subjected to static loading conditions. To this end, an efficient boundary element method (BEM) is developed. Unlike many previous investigations published in literature, two-dimensional (2-D) linear magnetoelectroelastic materials possessing fully coupled piezoelectric, piezomagnetic and magnetoelectric effects are considered in this paper. A combination of the displacement BEM and the traction BEM is used in the present formulation. The displacement BEM is applied for the external boundary of the cracked solid, while the traction BEM is used for the crack-faces. A regularization technique is implemented to compute the strongly singular and hypersingular boundary integrals in the BEM. The electric displacement intensity factor (EDIF), the magnetic induction intensity factor (MIIF), the stress intensity factors (SIF), the mechanical strain energy release rate (MSERR) and the total energy release rate (TERR) are evaluated directly from the computed nodal values at discontinuous quarter point elements placed next to the crack tip. The accuracy of the BEM is verified by analytical solutions known in literature. Results are presented for a branched crack in a bending specimen subjected to combined magnetic-electric-mechanical loading conditions.

The influences of Coulomb tractions on static and dynamic fracture parameters for semi-permeable piezoelectric cracks

In this paper, the influences of the induced Coulomb tractions on the static and dynamic crack-tip fracture parameters of semi-permeable piezoelectric cracks are studied and discussed. The static crack problems are solved by a static dual boundary element method (BEM), while the corresponding crack problems under dynamic impact loading are numerically analyzed by a time-domain BEM considering the inertial effects. In the numerical implementation, a collocation method is applied for the spatial discretization together with a quadrature formula for the temporal discretization. An iterative scheme based on the quasi-Newton method is adopted to solve the corresponding non-linear boundary-value problem resulted from the semi-permeable electric boundary conditions and the induced Coulomb tractions on the crack-faces. The crack-tip facture parameters involving the field intensity factors, the energy release rate and the mechanical strain energy release rate are evaluated by a displacement extrapolation method. Some examples are presented to compare the effects of the Coulomb tractions on the static and dynamic fracture parameters.

A 2D Time-Domain BEM for Dynamic Crack Problems in Anisotropic Solids

This chapter presents a time-domain boundary element method (BEM) for transient dynamic crack analysis in two-dimensional, homogeneous, anisotropic and linear elastic solids. Strongly singular displacement boundary integral equations (DBIEs) are applied on the external boundary of the cracked body, while hypersingular traction boundary integral equations (TBIEs) are used on the crack-faces. The quadrature formula of Lubich is used for approximating the convolution integrals and a collocation method is adopted for the spatial discretization of the time-domain boundary integral equations (BIEs). By means of a suitable change of variable an efficient regularization technique is applied to compute the strongly singular and hypersingular integrals arising in the time-domain BEM. Discontinuous quadratic quarter-point elements are implemented at the crack-tips to capture the local square-root behavior of the crack-opening-displacements (CODs) properly. Numerical examples for computing the dynamic stress intensity factors (SIFs) are shown and discussed to demonstrate the robustness, the accuracy and the efficiency of the present time-domain BEM.

Time-Domain BEM Analysis of Cracked Piezoelectric Solids under Impact Loading

In this paper, transient dynamic crack analysis of two-dimensional (2-D), homogeneous and linear piezoelectric solids is presented. A time-domain boundary element method (BEM) is applied. The method uses a combination of the strongly singular displacement boundary integral equations (BIEs) and the hypersingular traction BIEs. Strongly singular displacement BIEs are used on the external boundary of the cracked solid, while hypersingular traction BIEs are applied on the crack-faces. Collocation method is implemented for the spatial discretization, while a convolution quadrature formula is adopted for the temporal discretization. Numerical examples are presented and discussed to verify the efficiency and the accuracy of the present method, and to show the effects of the mechanical and the electrical impact loading on the dynamic intensity factors.

Semi-Permeable Cracks in Magnetoelectroelastic Solids under Impact Loading

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids by considering different electrical and magnetical crack-face boundary conditions is presented. For this purpose, a time-domain boundary element method (TDBEM) using dynamic fundamental solutions is developed. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is applied to compute the discrete boundary data and the generalized crack-opening-displacements. Iterative algorithms are implemented to deal with the non-linear electrical and magnetical semi-permeable crack-face boundary conditions.

Damage Detection in Piezoceramics via BEM

Piezoelectric ceramics have recently become one of the most used materials in all kinds of electromechanical systems. However, the presence of defects in such materials prevents them from fulfilling their function. A number of numerical, analytical and experimental works are recently being developed to understand the behaviour of piezoelectrics with presence of damage, but very few aimed at locating defects. One of the current challenges in monitoring piezoelectrics is the correct interpretation of the readings from sensors, in order to reliably recover the defect characteristics minimizing uncertainties due to noise and model. An inverse problem strategy is proposed for this reconstruction, starting from the electromechanical response measurement as input data, and incorporating a numerical model that simulates that response. This model is solved using a Boundary Element Method (BEM), whose formulation is developed for the 2D static case. The damage identification inverse problem is solved using genetic algorithms for the minimization of the discrepancy or cost functional. The effect of noise on measurements and uncertainties in the model is studied in detail through a sensitivity analysis for some simple cases of defect.

Cracks in Magnetoelectroelastic Solids under Impact Loading

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed and the elastodynamic fundamental solutions for linear magnetoelectroelastic and anisotropic materials are derived. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the generalized crack-opening-displacements. To show the effects of the coupled fields and the different dynamic loading conditions on the dynamic intensity factors, numerical examples will be presented and discussed.

Crack Surface Frictional Contact Modelling in Piezoelectric Materials

Piezoelectric materials exhibit an electromechanical coupling which allows for their use assensors or energy harvesting devices (direct piezoelectric effect) or actuators and shape control de-vices (inverse piezoelectric effect). They are applied in many technological sectors of current interestsuch as the aerospace and automotive industries, and they are generally constructed in block form orin a thin laminated composite. The study of the integrity of such materials in their various forms andsmall sizes is still a challenge nowadays. To gain a better understanding of these systems, this workpresents a crack surface contact formulation which makes it possible to study the integrity of theseadvanced materials under more realistic crack surface multifield operational conditions. The formu-lation uses the BEM for computing the elastic influence coefficients and contact operators over theaugmented Lagrangian to enforce contact constraints on the crack surface, in the presence of electricfields. The capabilities of this methodology are illustrated solving a benchmark problem.

Influence of the Deformation Rate on the Delamination of Laminated Composite Materials

It is well known that delamination is one of the most critical mechanism of failure of laminated composite materials. It supposes an important load capacity reduction, it is difficult to see and his evolution modify the failure of the component. Composite delamination depends on their fracture toughness. On the other hand, impacts are the most dangerous loads for those materials due to the important deformation rate induced in the material. This work analyses the influence of load velocity in the fracture toughness, for modes I and II, in textile carbon/epoxy, up to an impact velocity of 0,190 m/s. For that range, results show that the mode I fracture toughness decrease with velocity, while for mode II it remains nearly constant. However, the load velocities analyzed are yet far from those induced in a low speed impact. We propose to continue this research by increasing deformation rates using drop tower impact techniques, to observe if the trend observed so far is maintained on increasing speed.