Meinhard Kuna

Three-dimensional cell model analyses of void growth in ductile materials

Three-dimensional micromechanical models were developed to study the damage by void growth in ductile materials. Special emphasis is given to the influence of the spatial arrangement of the voids. Therefore, periodical void arrays of cubic primitive, body centered cubic and hexagonal structure are investigated by analyzing representative unit cells. The isotropic behaviour of the matrix material is modelled using either v. Mises plasticity or the modified Gurson-Tvergaard constitutive law. The cell models are analyzed by the large strain finite element method under monotonic loading while keeping the stress triaxiality constant. The obtained mesoscopic deformation response and the void growth of the unit cells show a high dependence on the value of triaxiality. The spatial arrangement has only a weak influence on the deformation behaviour, whereas the type and onset of the plastic collapse behaviour are strongly affected. The parameters of the Gurson-Tvergaard model can be calibrated to the cell model results even for large porosity, emphasizing its usefulness and justifying its broad applicability.

Finite element analyses of crack problems in piezoelectric structures

Abstract The widespread application of smart ceramic materials integrated in microelectronic, mechatronic and adaptive structures requires high reliability and durability of the ceramics under external and internal stresses. Therefore, fracture mechanics concepts have to be applied to crack-like defects in piezoelectric structures subjected to electrical and mechanical loads. Suitable numerical methods are suggested for computing the singular coupled electrostatic and anisotropic elastic fields at the crack tips and for determining the fracture controlling parameters like stress intensity factors and energy release rates. Three finite element techniques are presented: (i) special crack tip elements (CTE) with embedded singularity, (ii) numerical realisation of the crack closure integral, (iii) calculation of electromechanical energy balance integral. The efficiency and the performance of these techniques are verified with sample problems and compared to each other.

Identification of material parameters of the Gurson-Tvergaard-Needleman model by combined experimental and numerical techniques

Abstract To identify material parameters from suitable experiments it is prevalent to use global informations like force–displacement or force–necking curves. The quality of accordance between measured and calculated forces at given displacements can be expressed by a least-squares functional. In this contribution a non-linear optimization method will be presented, which minimizes the least-squares functional by use of a gradient based method. The gradient of this functional is calculated in a semi-analytical sensitivity analysis. To determine the derivatives of the force with respect to the material parameters, the local sensitivities on an intersection will be added together. On this intersection, the total nodal force and the external force have to be equal and the normal displacements have to be independent on the material parameters. The parameter identification is embedded in the finite element code SPC-PMHP for solving non-linear boundary and initial value problems on parallel computers. The Gurson–Tvergaard–Needleman model is used to describe the plastic deformation and damage behaviour of the ductile structural steel StE 690. The developed algorithm is applied to tensile tests with notched cylindrical bars.

Influence of electric fields on the fracture of ferroelectric ceramics

Abstract This paper deals with the fracture mechanics of piezoelectric solids. All investigations consider a single crack, which is exposed to combined electrical and mechanical loading. The main subject of interest is the influence of electric fields on the fracture toughness of ferroelectric ceramics and the derivation of an appropriate fracture criterion. Numerical techniques are presented, allowing for the calculation of fracture quantities, i.e. stress intensity factors and energy release rates, once the piezoelectric field problem has been solved for arbitrary crack configurations using the finite element method. In order to describe a possible shielding of the crack tip due to ferroelectric/elastic domain switching events, a micromechanical model has been developed, based on a closed form solution of the piezoelectric field problem. In order to verify the theory, fracture experiments on barium titanate DCB specimens have been evaluated and compared to predictions of the model.

Finite element analyses of three-dimensional crack problems in piezoelectric structures

In this paper, electromechanical fracture mechanics and finite element techniques for crack analyses are extended to three-dimensional crack configurations. Penny-shaped cracks and elliptical cracks are analyzed, subjected to combined mechanical tension and electric fields. For the penny-shaped crack, exact solutions originating from different resources are compared with numerical results. Some errors in the literature concerning the analytical solution for the elliptical crack are corrected. Numerical results of the stress-intensity factors and energy release rates for these crack configurations are presented.

Finite element computation of the electromechanical J-Integral for 2-D and 3-D crack analysis

Piezoelectric ceramics find an application in many fields of technology. They may serve as sensors or actuators, mostly beeing exposed to high electric and mechanical loads. Therefore, fracture mechanics of piezoelectrics is an important field preserving strength and reliability under different conditions of application. This paper deals with the calculation of electromechanical energy release rates for arbitrary cracks in spatial piezoelectric structures applying a generalized J-integral. The crack problem is solved using a commercial FEM-code obtaining electric and mechanical field variables in nodes and integration points. These results serve as input data for the numerical computation of the electromechanical J-integral. The results are compared to findings from analytical and alternative numerical methods.

Fracture analysis of a single edge cracked strip under thermal shock

Abstract For a single edge crack in a long strip quenched on the cracked side, the time-dependent stress intensity factors have been calculated by means of the methods of weight functions, finite elements and boundary elements. These quantitative results support a recently developed heuristic fracture-mechanical approach to thermal shock damage due to single and multiple crack growth.

Identification of material parameters of the Rousselier model by non-linear optimization

This work is concerned with identification of material parameters for inelastic deformation laws. In this context, non-linear boundary and initial value problems are solved using the developmental finite element code SPC-PMHP for parallel computers. The ductile damage model of Rousselier for large elasto-plastic strains is implemented as a system of non-linear differential and algebraic equations. For solving the inverse problem, the solution of the direct problem is embedded in a gradient based method. This way, material parameters could be identified analysing inhomogeneous two-dimensional displacement fields. Deterministic optimization procedures are used to identify parameters by means of a least-squares functional. A semi-analytical sensitivity analysis was adopted to calculate the gradient of the objective function. Numerical experiments with synthetically generated displacement fields were carried out to check the algorithm. The identification procedure was successful when one material parameter is allowed to vary. Experiments with two or more unknown parameters were less successful, because in some cases only a local minimum was found.

Theoretical and experimental study of superimposed fracture modes I, II and III

Abstract The authors wish to present an all-fracture mode specimen with which it is possible to conduct fracture mechanics tests for pure mode I, pure mode II, pure mode III, as well as for all possible combinations of the above-mentioned. By means of a finite element analysis of this specimen, the stress intensity factors K I , K II , and K III were computed. It was discovered that K II and K III are coupled for in-plane shear and anti-plane shear loading, i.e. a mixed state occurs locally. The integral mean along the crack front yields however only to a K II factor for in-plane shear and to a K III factor for anti-plane shear loading. Fracture experiments under mixed-mode loading, using this new specimen, demonstrate the influence of the loading type on the orientation and on the structure of the fracture surface.

A micromechanical model for the fracture process zone in ferroelectrics

Abstract Piezoelectric and ferroelectric ceramics find an application as actuators, sensors or ultrasonic transducers in many fields of technology. Because of their brittleness, problems of strength and reliability have to be major subjects of investigation. In general, the ceramic material is exposed to combined electromechanical loading conditions. An influence of the electric field upon the fracture toughness has been observed by many researchers. An established fracture criterion for ferroelectrics is not known, though. Our investigations deal with the calculation of ferroelectric/ferroelastic domain switching events near the tip of an electromechanically loaded crack. The calculations are based on a semi-analytical solution of the piezoelectric field problem yielding electric and mechanical fields around a crack tip. By means of a switching criterion, the specific work is related to a threshold value, deciding upon location and species of switching events. The thus determined extension of the fracture process zone is the basis for calculating changes in the fracture toughness due to domain processes. Thereby a fracture criterion is suggested, which requires a pure mechanical stress analysis. The influence of electric fields is taken into account permitting the critical value to be a function of the electric field. Results for one special configuration of poling and electric field directions are compared to experimental findings.