Martin Abendroth

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.

Assessment of Material Properties by Means of the Small Punch Test

In recent years the small punch test (SPT) method has become an attractive alternative compared to traditional material testing procedures, especially in cases where only small amounts of material are available. We provide a literature review with focus on the history and application of the method. The main difficulty using the SPT is the fact that relevant material parameters cannot be as simply obtained by SPTs as by standard test methods, because of its non-uniform stress and deformation state. However, this can be achieved by comparing the experimental SPT results with those obtained by finite element computations of SPTs using advanced material models. Then the task is to determine the parameters of the material models using special optimization techniques. This paper presents SPT techniques for a broad temperature range. Work done on both ductile and brittle materials is presented. The analysis will focus on different advanced methods for determining parameters of state of the art material models for elastic-plastic, ductile damage and brittle failure behaviour. Results are provided for a weld line of a pressure gas pipe and brittle ceramic refractory materials.

Prüfung duktiler Werkstoffe mit dem Small-Punch-Test

Kurzfassung Der Small-Punch-Test (SPT) ist ein Kleinstprobenversuch, der sich zur Bestimmung des aktuellen lokalen Materialzustandes in technischen Anlagen unter Betriebsbedingungen eignet. Dieser Artikel stellt ein kombiniertes experimentell-numerisches Verfahren zur Identifikation von Verfestigungs- und Versagenseigenschaften duktiler Werkstoffe aus dem SPT vor. Das schädigungsmechanische Modell von Gurson-Tvergaard-Needleman dient zur Beschreibung des Materialverhaltens. Die Einflüsse der Parameter des schädigungsmechanischen Materialmodells auf das Versuchsergebnis werden anhand von FEM-Simulationen des SPT dargestellt. Neuronale Netze werden mit diesen Simulationen trainiert und stellen so einen generalisierten Zusammenhang zwischen Materialparametern und Versuchsergebnis dar, der in einem Optimierungsalgorithmus zur Identifikation der unbekannten schädigungsmechanischen Materialparameter benutzt wird. Die identifizierten Materialparameter lassen sich auf andere Probengeometrien übertragen und ermöglichen eine Vorhersage von bruchmechanischen Werkstoffkennwerten.

FEM Analysis of Small Punch Tests

In recent years the small punch test method has become an attractive alternative compared to traditional material testing procedures, especially in cases where only small amounts of material are available. In contrast to standard test methods, the relevant material parameters can not be as simply obtained from the experimental measurements of SPTs because of its non-uniform stress and deformation state. However this can be achieved by comparing the experimental SPT results with those obtained by finite element simulations of SPT using advanced material models. Then the task is to determine the parameters of the material models using special optimization techniques. This paper gives an overview about the common techniques used to simulate SPT experiments. It should give the reader answer to the questions: Why are FEM simulations useful How should such simulations be performed Which material laws can be used What are the limitations of finite element simulations How to determine material parameters from SPT-experiments and the corresponding simulations

Determination of Fracture Mechanical Properties of Carbon Bonded Alumina Using Miniaturized Specimens

Open cell ceramic foam filters are utilized to reduce non-metallic inclusions during casting of metals and therefore to enhance the quality of cast parts. A new generation of multifunctional filters made of carbon bonded alumina (Al2O3-C) has been developed within the scope of the collaborative research center CRC 920 [1]. The assessment of the resistance against high thermal and mechanical loads requires a mechanical characterization of the ceramic filter material. The mechanical properties show a distinctive size dependency, that’s why the specimen dimensions should be similar to the strut size of the real filter structures. The tensile fracture behavior is investigated by means of the Small Punch Test (SPT) using miniaturized disk-shaped specimens. During the mechanical tests a load-displacement curve is measured until failure occurs and a fracture stress is calculated from the experimental results. An estimation about the failure probability by means of Weibull statistics is performed because of the large scatter of the strength of the material. Furthermore, a modified version of the SPT, the so called Ball On Three Balls Test (B3B), is applied and compared to the SPT. In a final step numerical simulations of the B3B tests are performed by means of the finite element method to identify fracture mechanical material parameters like the fracture toughness.

Influence of the Microstructure on the Fracture Behavior of Carbon Bonded Alumina

Carbon bonded alumina (Al2O3-C) in various compositions are developed for the production of open cell filters, which are used for melt metal filtration processes [. The Small Punch Test (SPT) is used to determine the mechanical properties of such materials. Previous investigations showed two different types of fracture behavior [2,, which can be distinguished by typical features of the load deflection curves of the SPT. This paper clarifies this behavior by examining the fracture surfaces using scanning electron microscopy (SEM).

Fracture Toughness Characterization of Carbon Bonded Alumina Using Chevron Notched Specimens

A new generation of multifunctional filters is made of carbon bonded alumina and is investigated within the collaborative research center 920 (CRC920). These filters are used during a casting process with the aim of reducing non-metallic inclusions in the cast product. The high thermal and mechanical loading of the filter requires a fracture mechanical characterization of the investigated ceramic material. In order to determine the fracture toughness of the ceramic material, a chevron-notched beam method (CNB) is applied. A 4-point-bending test set-up was constructed and brought into service, at which the load-displacement curve of small chevron-notched specimens (5 x 6 x 25 mm3) can be measured. The set-up offers the possibility of testing specimens at temperatures up to 1000oC. Preceding numerically work using the finite element method was performed to identify a suitable notch geometry. For this purpose a cohesive zone model was used. A parameter study is presented, which shows the influence of the notch parameter on the load-displacement curve.

Fracture Mechanical Analysis of Open Cell Ceramic Foams Under Thermal Shock Loading

Ceramic foams made by replica techniques containing sharp-edged cavities, which are potential crack initiators and therefore have to be analyzed using fracture mechanical methods. The ceramic foams made of novel carbon bonded alumina are used as filters in metal melt filtration applications, where the filters are exposed to a thermal shock. During the casting process the filters experience a complex thermo-mechanical loading, which is difficult to measure. Modern numerical methods allow the simulation of such complex processes. As a simplified foam structure an open Kelvin cell is used as a representative volume element. A three-dimensional finite element model containing realistic sharp-edged cavities and three-dimensional sub-models along these sharp edges are used to compute the transient temperature, stress and strain fields at the Kelvin foam. The sharp edges are evaluated using fracture mechanical methods like the J-integral technique. The results of this study describe the influence of the pore size, relative density of the ceramic foam, the heat transfer and selected material parameters on the fracture mechanical behaviour.