Wieland Beckert

Modelling piezoelectric modules with interdigitated electrode structures

The Interdigitaded Electrode Design, which allows to utilise the primary piezoelectric effect in longitudinal direction for piezoelectric sheet actuators, is investigated with the help of a detailed finite element analysis. Two different set-ups have been studied, based on (a) a piezoelectric bulk film and (b) a composite with piezoelectric fibres as the piezoelectric active component. The models allow to investigate the influence of various geometrical and material parameters on the deformation performance and on failure hazards due to field concentrations. For the bulk film actuator case, the development of an inhomogeneous poling state from the poling process of the piezoceramic material may be included into the model in an approximate way. For the composite actuator case, special emphasis has been laid on the problem of indirect contact between electrodes and embedded piezoelectric fibres. Specific proposals for the parameter design could be derived, which have been used as a starting point for the practical optimisation process.

Compression Shear Test (CST) – A Convenient Apparatus for the Estimation of Apparent Shear Strength of Composite Materials

A convenient apparatus for the determination of apparent shear strength of flat as well as curved composite materials and adhesive joints, the compression shear device (CSD), is described in detail. Compared with other commonly used tests the sample preparation is very easy, inexpensive, and consumes less material. The obtained values of apparent shear strength for different classes of materials are comparable with values determined by established tests. Using an additional extensometer, the estimation of shear strain and shear modulus is also possible with the proposed equipment.

Calculation of adhesion strength at the interface of a coated particle embedded within matrix under multiaxial load

Analytical and finite element solutions of the stress fields around a particle under multiaxial thermomechanical load are derived as functions of the properties of the particle, the matrix and an interphase. The motivation for these calculations is to answer the question of how to load a sample containing a particle to measure the adhesion strength at the interfaces. The calculations provide the stress field and show that an interphase with a Youngs modulus lower than that of the matrix reduces stress concentration in the neighbourhood of the particle. The superposition of loads in different directions results in the creation of a more or less uniform distribution of tensile stresses (hydrostatic tension) around the particle, a stress situation that allows the determination of adhesion strength. The ratio of the applied stresses in different directions determines the extension of the area which is under high tensile loads. This provides the basis to develop a test technique for the examination of statistical effects which in addition to the bonding quality may influence adhesion strength at interfaces.

Fracture mechanics analysis of the microbond test

The microbond test is simulated using a fracture mechanics concept and finite element (FE) analysis. The FE model takes into account the elliptical geometry of the droplet and frictional contact caused by surface roughness and local compression from the microvise. The effects of interface parameters, some geometrical parameters and coulomb friction on load versus displacement curves and load versus crack length curves are investigated. A simple data reduction scheme for friction influenced curves is suggested. From the results it appears that the debonding process is strongly influenced by interfacial friction. Therefore a simple estimation of interfacial adhesion from the microbond test seems difficult.

Single fibre transverse debonding: stress analysis of the Broutman test

The paper presents an extended analytical approach for the interfacial transverse stress that is generated by the Broutman test specimen under compression. The analysis is based on the division of the specimen into a bulk region and a near fibre region. Treating separately each region a compound equation for the interfacial stress can be derived. The equation also includes residual thermal stress and fibre anisotropy. A 3D finite element model was used to validate the approach. The calculations are performed for two commonly used material systems (carbon/glass fibre, epoxy resin). A comparison between the finite element results and the analytical solutions indicates that the accuracy of the analytical approach is very good.

Fracture mechanical characterisation of mixed-mode toughness of thermoplast/glass interfaces

Abstract According to studies conducted by, e.g. Liechti and Chai [J. Appl. Mech. 58 (1991) 680], Yuuki et al. [Eng. Fract. Mech. 47 (3) (1994) 367] and Ikeda and Miyazaki [Eng. Fract. Mech. 59 (6) (1998) 725], a significant increase of interfacial toughness is observed, whenever the magnitude of the bond tangential shear load of the asymptotic elastic mixed-mode state is increased in either direction. Between these extremes the interfacial toughness curve exhibits a pronounced minimum, which, according to Hutchinson and Suo [Mater. Sci. Eng. A 107 (1989) 135] is believed to represent the so-called intrinsic adhesion, i.e. the failure toughness under pure local mode I loading. Within linear elasticity, the biaxial, singular near-tip solution for an open interface crack may be employed for characterising the local stress state as long as non-linearities such as, e.g. crack-wall contact and plastic flow are contained within a zone small enough compared to the extension of the singular opening-dominated fields. Then, the critical stress state is given in terms of bimaterial stress intensity factors K 1, c , K 2, c and the fracture toughness under mixed-mode loading may be expressed in terms of the critical energy release rate as a function of the mode-mixity ψ=tan−1K2,c/K1,c. The stress intensities have to be extracted from a stress analysis of the specimen under the critical load, which in the present work is performed by means of an FE-model of the loaded sample.

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.

Analysis of the deformational behaviour of a bimorph configuration with piezoelectric actuation

The stimulation of controlled deformation in lightweight constructions by means of actuator units as an integrated part of the structure currently represents an attractive subject in engineering. A common design uses a piezoelectric film that is bonded to a shell component by an adhesive layer and induces a bending deformation in the structure. A simplified beam design has been used as a test set-up to characterize the actuator performance of a given system under practical conditions. The bimorph configuration consists of an actuator unit, the bonding adhesive and the substrate material from which the lateral bending deflection of the free end, induced by actuation of the piezoelectric film, is measured. An improved theoretical approach is presented that combines a comprehensive composite theory analysis of the bending with a detailed analytical approach for the gradual stress transfer from the edges of the piezoceramic induced by a deformational misfit between the layers. The results are validated by a finite element analysis of the system. They reveal a substantial influence of the assumptions for the transverse (width direction) state of deformation for which free bending appears to be the most realistic for the test geometry. The study is completed by an experimental analysis that investigates the influence of adhesive stiffness and layer thickness on the actuator performance of a system consisting of a steel substrate and a carbon fibre reinforced substrate and a prototypic PZT actuator module. The results are correlated to the model providing a confirmation of the essential trends.

Numerical simulation of micro-scratch tests for coating/substrate composites

In this paper the micro-scratch test is simulated by ANSYS finite element code for thin hard coating on substrate composite material system. Coulomb friction between indenter and material surface is considered. The material elastic-plastic properties are taken into account. Contact elements are used to simulate the frictional contact between indenter and material surfaces, as well as the frictional contact after the detachment of coating/substrate interfaces has taken place. In the case of coating/substrate interfaces being perfectly bonded, the distributions of interfacial normal stress and shear stress are obtained for the material system subjected to normal and tangential loading. In the case of considering the detachment of interfaces, the length of interfacial detachment and the redistribution of stresses because of interfacial detachments are obtained. The influences of different frictional coefficients and different indenter moving distances on the distributions of stresses and displacements are studied. In the simulation, the interfacial adhesion shear strength is considered as a main adhesion parameter of coating/substrate interfaces. The critical normal loading from scratch tests are directly related to interfacial adhesion shear strengths. Using the critical normal loading known from experiments, the interfacial adhesion shear strength is obtained from the calculation. When the interfacial adhesion shear strength is known, the critical normal loading is obtained for different coating thicknesses. The numerical results are compared with the experimental values for composite materials of thin TiN coating on stainless steel substrate.

Single-fibre transverse debonding: tensile test of a necked specimen

Abstract The aim of the paper is the development of a test to measure the adhesion strength between a fibre and a matrix material. The basis is the necked sample with a single fibre under compressive load proposed by Broutman (Broutman LJ. Measurement of the fiber-polymer matrix interfacial strength. Interfaces in composites 1969; ASTM STP 452:27–41. American Society for Testing and Materials). The essential innovation is to load the specimen in tension and to generate the interfacial load by an optimized specimen geometry. Starting from a stress analysis of a specimen without a fibre a stress ratio is introduced to describe the level of optimization. Optimized geometric dimensions and the corresponding interfacial transverse stress are derived. The paper provides tools for developing new micromechanical tests and the appropriate data reduction schemes. The tensile loading removes several problems of the original Broutman test, especially fibre buckling and breaking. The attainable interfacial stress is higher. If an axisymmetrically necked specimen is used, the stress state will be really axisymmetrical.