Documents published in Scipedia

• Probabilistic modeling of LCF failure times using a epidemiological crack percolation model

  M. Harder, P. Lion, L. Mäde, T. Beck, H. Gottschalk

  eccomas2022.

  
  

  Abstract

  The analysis of standardized low cycle fatigue (LCF) experiments shows that the failure times widely scatter. Furthermore, mechanical components often fail before the deterministic failure time is reached. A possibility to overcome these problems is to consider probabilistic failure times. Our approach for probabilistic life prediction is based on the microstructure of the metal. Since we focus on nickel-base alloys we consider a coarse grained microstructure, with random oriented FCC grains. This leads to random distributed Schmid factors and different anisotropic stress in each grain. To gain crack initiation times, we use Coffin-MansonBasquin and Ramberg-Osgood equation on stresses corrected with probabilistic Schmid factors. Using these single grain crack initiation times, we have developed an epidemiological crack growth model over multiple grains. In this mesoscopic crack percolation model, cracked grains induce a stress increase in neighboring grains. This stress increase is realized using a machine learning model trained on data generated from finite element simulations. The resulting crack clusters are evaluated with a failure criterion based on a multimodal stress intensity factor. From the generated failure times, we calculate surface dependent hazard rates using a Monte Carlo framework. We compare the obtained failure time distributions to data from LCF experiments and find good coincidence of predicted and measured scatter bands.

  Abstract
  The analysis of standardized low cycle fatigue (LCF) experiments shows that the failure times widely scatter. Furthermore, mechanical components often fail before the deterministic [...]

  • 24
  •  read

• Modeling imperfect interfaces in layered beams through multi- and single-variable zigzag kinematics

  R. Massabò, I. Monetto

  eccomas2022.

  
  

  Abstract

  Multiscale structural models based on the coupling of a zigzag kinematics and a cohesive crack approach have been recently formulated to analyze the response of shear deformable layered structures with imperfect interfaces and describe progressive delamination fracture (Massabò, in Handbook of Damage Mechanics, Springer, 2022, pp.665-698). The zigzag kinematics accounts for zigzag effects associated to the elastic mismatch of the layers and displacement jumps due to interfacial imperfections, using a limited number of variables, which is independent of the number of layers. The effects of imperfect interfaces on the response of structures subjected to thermo-mechanical loading and on wave propagation and dispersion have been studied analytically and the advantages of this approach over discrete layer models and layerwise theories have been highlighted and discussed. In the presentation we review and discuss these models and present preliminary results on novel single-variable formulations, which have been inspired by a technique developed for homogeneous Timoshenko beams in (Kiendl et al.

  Abstract
  Multiscale structural models based on the coupling of a zigzag kinematics and a cohesive crack approach have been recently formulated to analyze the response of shear deformable [...]

  • 12
  •  read

• Application of an adaptive stable GFEM for fracture propagation in plain concrete

  A. El-Tohfa, F. Mukhtar

  eccomas2022.

  
  

  Abstract

  Generalized finite element method (GFEM) has proven itself as a tool of choice over the conventional FEM in fracture analysis due to enhanced computational efficiency as well as allowing cracks to propagate independently of the domain mesh ­ Thanks to the use of enrichments chosen based on the a priori knowledge of the solution behavior. With the many versions of the method's formulations in the literature, their stability issues, compared to the standard FEM, are often unresolved. This paper presents the use of an adaptive stable GFEM to plain concrete fracture propagation. Having verified the formulation's accuracy and stability based on the Linear Elastic Fracture Mechanics in previous studies and its two-scale (global-local) version on concrete fracture, the present work seeks to verify its capabilities in capturing the size effect behavior in concrete. A set of fracture simulations in geometrically similar experimental concrete beams, under a 3-point bending regime, is presented based on a bilinear cohesive model. In addition to the GFEM's agreement with the experimental load-displacement response and the effect of the initial notch-to-depth ratio, the simulation successfully captures the size effect behavior when presented on the popular Type II Size Effect plot ­ the so-called Bazant's law.

  Abstract
  Generalized finite element method (GFEM) has proven itself as a tool of choice over the conventional FEM in fracture analysis due to enhanced computational efficiency as well [...]

  • 59
  •  read

• Inverse Dynamics of Geometrically Exact Beams

  T. Ströhle, P. Betsch

  eccomas2022.

  
  

  Abstract

  This paper is concerned with the inverse dynamics of flexible mechanical systems whose motion is governed by quasi-linear hyperbolic partial differential equations. Problems that appear by applying classical solution strategies to the problem at hand, e.g. integrating the problem at hand sequentially in space and time will be adressed in this work. Motivated by the hyperbolic structure of the underlying initial boundary value problem, two methods that are based on a simultaneous space-time integration will be presented. Special emphasize will be given to the phenomena of wave propagation within geometrically exact beams and its relevance regarding the inverse dynamics problem.

  Abstract
  This paper is concerned with the inverse dynamics of flexible mechanical systems whose motion is governed by quasi-linear hyperbolic partial differential equations. Problems [...]

  • 44
  •  read

• Influence of Cooling Lubricants on the Interaction Between Indenter and Material Surface During Scratch Tests

  F. Kästner, K. de Payrebrune

  eccomas2022.

  
  

  Abstract

  Striving for the optimization and the increase of efficiency of various systems demands further developments of the classic manufacturing methods. Especially grinding processes, which are characterized by undefined cutting-edge geometries, reveal many fields where there still is a lack of understanding. In particular, the processes at and their effects on the individual abrasive grit are insufficiently researched and, therefore, do not allow sufficiently accurate behavior predictions. In order to optimize grinding processes and, ultimately, the resulting quality of the workpiece surface, it is necessary to look at the entire process in a holistic way. Due to the large number of influences to which the grinding process is subject, it is initially advisable to break down the process as far as possible into individual scratch tests and then gradually return to the overall process. One approach is the development and expansion of an FEM-based physical force model, which allows for the simulation and prediction of a scratch tests and, subsequently, also the entire grinding process with all relevant influencing factors. One of these influencing factors, which are essential but mostly unconsidered, are cooling lubricants, especially their tribologically favorable influence on the interaction between workpiece and indenter. Therefore, it is important to identify and investigate the different aspects, such as the friction phenomena of scratch tests that are influenced by the use of cooling lubricants. In addition to temperature and force characteristics, which have been found to differ with and without cooling lubricant, differences in the scratch geometry on the material surface have also been observed in recent tests. Based on these findings, this work examines the relationship between scratch geometry and cooling lubricant. It turned out that scratch tests conducted with cooling lubricants have an influence on the topography of the scratch on the workpiece surface in addition to the influence on the tangential and normal forces. The ratio of scratch width to scratch depth is used for evaluation. A reduction of this ratio is observerd in the scratches with cooling lubricants and is, therefore, interpreted as a reduction of the scratch width as a result of the use of cooling lubricants.

  Abstract
  Striving for the optimization and the increase of efficiency of various systems demands further developments of the classic manufacturing methods. Especially grinding processes, [...]

  • 9
  •  read

• Simulation of phase transformations in polycrystalline shape memory alloys using fast Fourier transforms

  J. Waimann, C. Gierden, S. Reese

  eccomas2022.

  
  

  Abstract

  The properties of shape memory alloys (SMA) are mainly influenced by phase transformations between austenite and martensite. The complex material behavior is described by a variational method which describes the evolution of the phase fractions. We combined the method with a microstructural analysis based on fast Fourier transformations. Such a highly resolved microstructural analysis comes along with a high computational effort.To reduce the later one, we propose a model order reduction technique that uses just a reduced set of Fourier modes, which is adapted to the underlying microstructure. The presentation of the theoretical background as well as of the implemented algorithm is followed by numerical results that underline the performance of our method.

  Abstract
  The properties of shape memory alloys (SMA) are mainly influenced by phase transformations between austenite and martensite. The complex material behavior is described by [...]

  • 12
  •  read

• Using a reduced set of Fourier modes in terms of a FFT-based microstructure simulation

  C. Gierden, J. Waimann, B. Svendsen, S. Reese

  eccomas2022.

  
  

  Abstract

  Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger equation. Incorporating a model order reduction technique based on calculations with a reduced set of Fourier modes, the computational cost of this algorithm can be decreased. It was shown that the accuracy of this model order reduction technique strongly depends on the choice of Fourier modes by considering a geometrically adapted rather than a fixed sampling pattern to define the reduced set of Fourier modes. Since it is difficult to define a geometrically adapted sampling pattern for complex microstructures, additionally a strain-based sampling pattern was introduced. The accuracy and adaptability of this strain-based reduced set of Fourier modes is shown by incorporating a polycrystalline microstructure.

  Abstract
  Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger [...]

  • 33
  •  read

• Fast and simple creation of powder beds for selective laser melting

  L. Luberto, K. de Payrebrune

  eccomas2022.

  
  

  Abstract

  In selective laser melting, components are produced by layer-by-layer melting of a powder bed. To investigate the interaction between the powder bed and the laser energy in the process, it is necessary to generate different powder bed configurations with a defined particle size distribution. For this purpose, based on different particle contact approaches, a simple algorithm for planar particle bed configurations was developed in the Julia programming language. Based on the so called 0and 1-particle-contact approaches, a monodisperse sphere packing with a filling ratio of up to 64%, and with a normally distributed particle size with a filling ratio of up to 67% were generated. With the 0-particle-contact approach, the individual powder beds could be generated more quickly, but showed an insufficient degree of filling. In contrast, the 1-particle-contact approach can produce powder beds realistically. An extension for spatial problems, as well as variations in the contact approaches, is given by the simple algorithm design and shall be implemented and further investigated in simulations of selective laser melting.

  Abstract
  In selective laser melting, components are produced by layer-by-layer melting of a powder bed. To investigate the interaction between the powder bed and the laser energy in [...]

  • 20
  •  read

• Efficient assessment of noise transmission through highly flexible slender structures

  F. Schneider-Jung, L. Burger, J. Linn

  eccomas2022.

  
  

  Abstract

  In this work, we propose an efficient methodology for the assessment of noise transmission through cables and hoses. An interactive simulation with a geometrically exact Cosserat rod enables simple and fast modelling of various configurations. Subsequently, we linearise the equations of motion at the static equilibrium for given boundary conditions and, using the resulting system matrices, compute the mechanical impedance matrix. The computation result, i.e. the impedance matrix, is available within seconds. The impedance matrix either can be used to compute reaction forces for given excitation or, if the excitation is unknown, allows to analyse the transmission of noise by looking at single matrix elements. The latter is especially useful in early, purely virtual development phases.

  Abstract
  In this work, we propose an efficient methodology for the assessment of noise transmission through cables and hoses. An interactive simulation with a geometrically exact Cosserat [...]

  • 31
  •  read

• Homogenization of the constitutive properties of composite beam cross-sections

  M. Stavole, R. Sato, M. Lohk, S. Leyendecker

  eccomas2022.

  
  

  Abstract

  When modelling slender bodies made of composite materials as beams, homogenized stiffness coefficients must be obtained. In [2, 3], analytic expressions for these are obtained by comparing the solutions of some Saint-Venant extension, bending and torsion 3D linear elasticity problems with their corresponding beam theory counterparts. In [2], the authors provide general expressions for the determination of these coefficients for multilayered beams. The present work consists in the study of a homogenization procedure of the stiffness coefficients for circular cross-sections with two layers. This will help in the study of the constitutive behavior of unloaded shafts of endoscopes since their cross-section could be studied as a simplified model of a three-layers hollow circular cross-section. In preparation of this geometry, results of an experimental campaign carried out at KARL STORZ GmbH & Co. KG (Tallinn, Estonia) are presented in a second part of this paper. The purpose of the testing was the experimental characterization of the torsional stiffness of such devices.

  Abstract
  When modelling slender bodies made of composite materials as beams, homogenized stiffness coefficients must be obtained. In [2, 3], analytic expressions for these are obtained [...]

  • 61
  •  read