Finite Element Modelling of Cracks as Acoustic Emi

Authors: Markus G R Sause Stefan Richler

Publish Date: 2015/02/03

Volume: 34, Issue: 1, Pages: 4-

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Abstract

This paper presents results for a new acoustic emission crack source model based on a finite element modelling approach which calculates the dynamic displacement field during crack formation The specimen modelled is statically loaded until conditions for crack growth as defined by a failure criterion are fulfilled Subsequently crack growth is modelled by local degradation of the material stiffness utilizing a cohesive zone element approach The displacements due to crack growth generate the acoustic emission signal and allow detailed examination of the principles of acoustic emission sources operation Subsequent to crack growth signal propagation is modeled The signal propagation is modeled superimposed on the static displacement field The presented model comprises a multiscale and multiphysics approach to consider the signal propagation from source to sensor the piezoelectric conversion of the elastic wave to an electric signal and the interaction to the acquisition electronics Validation of the modeling approach is done by investigating the acoustic emission signals of micromechanical experiments Using a specifically developed load stage carbon fiber filament failure and matrix cracking can be prepared as model sources A comparison of the experimental signals to the modeled signals shows good quantitative agreement in signal amplitude and frequency content A comparison between the present modeling work and analytical theories demonstrates the substantial differences not considered in previous modeling work of acoustic emission sourcesThe formation and propagation of cracks in solid media is a field of research that has been active for decades Still the theoretical description of the physics at the crack tip and the crack dynamics are active fields of research 1 2 3 4 A phenomenon that is closely related to the crack dynamics is the generation of acoustic waves due to the crack motion due to the release of stored elastic energy These acoustic waves propagate within the solid and can be detected at the surface by suitable sensor systems This method is known as acoustic emission analysis and has already proven its significance for structural health monitoring as well as its ability to improve material testing procedures 5 Despite of the broad range of technical applications only a small amount of work has been performed recently to advance the understanding of the physical processes involved in the generation of acoustic emissionIn order to interpret the detected acoustic emission signals in terms of their relevance to material failure it is required to have concise knowledge of the underlying physics The whole process of the acoustic emission technique can be categorized into three subsequent parts The first part comprises the acoustic emission source the second part considers the acoustic emission signal propagation from source to sensor and the third part consists of the acoustic emission signal detectionIn the past various valuable attempts have been made to provide a theoretical description of acoustic emission sources The source model concept used in most of the analytical approaches was derived from seismology and is most of the time based on the work of Aki and Richards 6 Here source models are geometrically approximated as point sources while the dynamic of the source is either approximated from iterative refinement of model parameters to fit experimental data or is based on assumptions on the source dynamics derived from structural mechanics Various stepfunction descriptions exist which are used to describe the 3dimensional spatial displacement of the crack surface during crack formation 7 8 9 10 11 In particular the risetime of the initial crack surface displacement is an essential parameter to model the crack surface motion 12 However there are no reports in literature of successful measurements of risetimes of real acoustic emission sources eg due to crack formation in materials Instead the risetime is typically estimated based on the elastic properties of the bulk material This type of source modeling has been successfully applied to many cases and the basic concept has been used within the generalized theory of acoustic emission by Ono and Ohtsu 8 13 the work of Scruby 14 and numerous other analytical descriptions 7 9 15 16In recent years it has become convenient to use numerical methods to model acoustic emission sources In this field Prosser Hamstad and Gary applied finite element modeling to simulate acoustic emission sources based on body forces acting as a point source in a solid 10 17 Hora and Cervena investigated the difference between nodal sources line sources and cylindrical sources to build geometrically more representative acoustic emission sources 18 At the same time we proposed a finite element approach using an acoustic emission source model taking into account the geometry of a crack and the inhomogeneous elastic properties in the vicinity of the acoustic emission source 11Different types of acoustic emission source model descriptions used in literature employing point sources a or extended sources b in conjunction with analytic source functions New source model description presented herein using dynamic changes of the source geometry based on fracture mechanics cCurrently all source models proposed in literature are of type one or type two since they all require the definition of an explicit source function Therefore no details of the dynamics arising from the crack formation process and the subsequent crack surface motion are predicted or considered by those modelsFrom a mathematical modeling and simulation point of view there are two main challenges in providing a numerically based acoustic emission source model of the third type The first challenge consists of the different scales involved in the problem crack length of the order of microns versus signal wavelength of the order of millimeters to centimeters and the proper scale bridging Owing to the vastly different observations scales a full multiscale approach is thus necessary The second challenge stems from the calculation of temporal and spatial evolution of the surfaces of the crack This is a level of detail that is typically not studied in modeling approaches used to describe crack formation by means of cohesive zone elements extended finite element methods or similar implementations

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