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2022 | Book

Material Modeling and Structural Mechanics

Editors: Univ.-Prof. Holm Altenbach, Univ.-Prof. Michael Beitelschmidt, Univ.-Prof. Markus Kästner, Prof. Konstantin Naumenko, Univ.-Prof. Thomas Wallmersperger

Publisher: Springer International Publishing

Book Series : Advanced Structured Materials

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About this book

This book presents various questions of continuum mechanical modeling in the context of experimental and numerical methods, in particular, multi-field problems that go beyond the standard models of continuum mechanics. In addition, it discusses dynamic problems and practical solutions in the field of numerical methods. It focuses on continuum mechanics, which is often overlooked in the traditional division of mechanics into statics, strength of materials and kinetics. The book is dedicated to Prof. Volker Ulbricht, who passed away on April 9, 2021.

Table of Contents

Frontmatter
1. The Use of the Homogenization Method in the Analysis of Anisotropic Creep in Metal-Matrix Composites
Abstract
The primary purpose of this study is tumerical homogenization of the nonlinear creep properties of unidirectionally reinforced fiber composites. The constitutive relations for a homogeneous material, equivalent to composite, are based on the hypothesis of the existence of a potential for the strain rates of steady-state creep. The generalization of the power-law dependence of the strain rate on stresses for the case of a complex stress state is achieved by introduction of an equivalent stress using a 4th rank tensor. The structure of this tensor allows to take into account the required symmetry class for a particular form of fiber packing. The homogenization procedure is based on micromechanical analysis of a representative composite volume. A technique for the numerical simulation of physical experiments necessary for the identification of the material parameters of the theoretical model is proposed. A series of numerical calculations by the finite element method in the ANSYS software for a boron-aluminum composite has been carried out.
Holm Altenbach, Gennady Lvov, Ivan Lvov, Oleg Morachkovsky
2. General Forms of Limit Surface: Application for Isotropic Materials
Abstract
Limit surfaces are a tool used in theory of plasticity and failure analysis for dividing the safe from the unsafe regions. Their mathematical formulations are given by yield and strength criteria. The number of suggested criteria is unmanageable. By lack of the sufficient conditions only plausibility assumptions can limit this variety. Typically, the Tresca, von Mises, and Schmidt-Ishlinsky criteria are employed for the modeling of yielding. The effect of pressure-sensitivity is accounted for with the criteria of Rankine and Burzyński-Yagn. Generalizations are obtained with linear combinations of these and further criteria. However, methods for the selection of efficient criteria for a particular application are still missing. In this work, a nomenclature for isotropic yield criteria is introduced. Proposed systematization restricts the number of appropriate yield criteria. Global convexity limits for the yield criteria of trigonal and hexagonal symmetry are defined. The basic idea is to find a general form of isotropic yield surface that satisfies the plausibility assumptions. This surface should contain possible yield surfaces lying between the lower and the upper bounds of the convexity restrictions. Any known or new criteria can then be considered as a special cases of the general criterion. The discussed yield criteria are extended for pressure-sensitive materials. The selection of the effective criterion for a particular application is simplified.
Holm Altenbach, Vladimir A. Kolupaev
3. Model Order Reduction: The Bridge Between Structural Mechanics and System Simulation
Abstract
System simulation using the multibody systems method is a standard procedure for the design of machines, plants and vehicles. It can be used to investigate large movements including the behavior of drives and control. Often, individual bodies have to be modeled elastically because relevant elastic deformations already occurs in the frequency range under investigation. The state of the art is the “Floating Frame of Reference” method, in which the motion of a body is divided into a rigid-body motion and small, superimposed, linear-elastic deformations. Elastic bodies are usually discretized using the finite element method, sometimes producing very large models. For the integration of such models into the MBS, a model order reduction must be performed beforehand. This typically consists of a sequence of steps: After a model preparation the actual reduction follows. Several different methods therefore have been developed in the last years. Subsequently, the quality of the reduced model can be estimated by correlation methods. Finally, the data is converted for import into the MBS tool. For this purpose, the software tool MORPACK was developed at the Chair of Dynamics and Mechanism Design at the TU Dresden. MORPACK can perform all steps of the model order reduction and outputs models that can be directly imported into MBS tools. In addition to numerous MOR algorithms, various correlation methods are also stored in the software, ensuring the greatest possible automation and standardization for the EMBS user.
Michael Beitelschmidt, Claudius Lein
4. Identification of Temperature Dependent Material Properties in Composite Plates Utilizing Experimental Vibration Data
Abstract
In recent three decades, composite materials have received an increasing interest among engineers and scientists. These materials are characterized by a higher stiffness with reduced weight, compared to commonly used materials such as aluminum or steel. It is not surprising that a wide range of applications emerged within the aerospace and transportation sector for example for aircraft and high-speed train hulls. However, these composite materials are generally made out of fiber and matrix material. This material behavior strongly depends on the environmental conditions such as temperature. This results in a complex macroscopic material behaviour and the precise knowledge of the corresponding properties is a key factor for computer aided engineering and virtual prototyping. Especially when composite structures are subjected to dynamic loading and changing temperatures, resonances can occur and ultimately lead to fatal dynamic behavior in the absence of sufficient damping. Therefore, the experimental investigation of the material behavior under dynamic loading for different temperatures together with a proceeding parameter identification scheme is necessary to precisely capture the material properties of the underlying model, which is the essence of the work at hand. Utilizing the presented approach, the parameter identification is easy to implement and reliable.
Marcus Maeder, Sourav Chandra, Steffen Marburg
5. Unilateral Constraints and Multibody Dynamics
Abstract
Constraints are the most important design elements of all moving mechanical systems. They decide about the structure of the system allowing its components only certain directions of free motion. Most applications deal with smooth constraints and thus with no interruption of the smooth flow of motion. Mechanical systems with contacts, being able to be open or closed, do not possess this property. Motion might be interrupted, be it as a wanted design element, be it as suddenly appearing constraints, or be it as a consequence of unavoidable tolerance effects in all machine interconnections. Chapter will give some review about the dynamics of such systems, theoretically and practically.
Friedrich Pfeiffer
6. Influence of Thermal Stabilisation on the Thermal Regime in the Strapdown Inertial Navigation System
Abstract
This paper proposes an approach to modeling the temperature field of a strapdown inertial unit that is part of an inertial navigation system based on fiberoptic gyroscopes. Mathematical and finite element models for heat transfer analysis of the strapdown inertial unit has been developed. Results of numerical simulations including the effect of changes in external temperature on the temperature field in the device and temperature rates at specified points of the device are presented. It is found that the application of thermal stabilisation in the considered makes it possible to form a temperature field with a temperature difference of 2 K on the fibre optic gyroscopes platform, which provides a minimum level of thermal strains and reduces the fluctuations of external temperature to 0.2 K/min.
Sergiy Yu. Pogorilov, Valeriy L. Khavin, Konstantin Naumenko, Holm Altenbach
7. Experimental-Numerical Analysis of Microstructure-Property Linkages for Additively Manufactured Materials
Abstract
The innovation of new or improved products fabricated from additive manufacturing processes with desired properties depends on a multitude of trials as stated by the Materials Genome Initiative for Global Competitiveness of the US National Science and Technology Council. Therefore, a systematic approach is essential to accelerate materials development. This can be realised by developing systematic materials knowledge in the form of process-structure-property linkages. In this envisioned framework, the present work aims to derive the structure-property linkages of additively manufactured Ti-6Al-4V alloy. One main focus is to investigate the influence of potential defects, in the form of pores, inherited from the fabrication process on the fatigue properties. For this purpose, the pore microstructure is obtained by x-ray computed tomography and a low-dimensional representation of the structure is derived by a statistical analysis. In a following numerical analysis, statistical volume elements (SVEs) with varying pore microstructures are reconstructed and microscale crystal plasticity simulations are performed in DAMASK to obtain the material properties such as yield strength and fatigue indicator parameters (FIPs). The influence of pore statistics on FIPs is obtained numerically and a comparison with Murakami’s empirical square root area concept is made. In a second part, the influence of the grain microstructure on mechanical properties is analysed. To this end, the grain microstructure is obtained by scanning electron microscopy (SEM) for specimens manufactured with different process configurations. Those structures are characterised through spatial three-point auto-correlation functions. The main properties of this high-dimensional descriptor are transformed to a low-dimensional representation by employing principal component analysis (PCA). Using LASSO regression, a meta model is derived, which allows for linking the microstructure to experimentally obtained micro hardness. This makes predictions of the hardness for new, unknown microstructures possible.
Benjamin Schmidt, Alexander Raßloff, Robert Kühne, Martina Zimmermann, Markus Kästner
8. Multisurface Theory of Plasticity with One Active Surface: Basic Relations, Experimental Validation and Microstructural Motivation
Abstract
Constitutive equations, experimental foundation, and comparison with other inelastic models are considered for the multisurface theory of plasticity with one active surface. The proposed variant of multisurface theory is aimed to describe the inelastic deformation processes under the complex passive loading. The conditions of thermodynamic consistency of the theory are obtained. Generalization of the theory for the case of arbitrary shape of surfaces with equal compliances and the anisotropy of elastic properties was carried out. Surfaces of equal compliances for the multilink loading paths and for the complex cyclic loading with total and partial unloading are experimentally studied. Comparison of experimental data and the theory predictions was carried out on the polycrystalline nickel, steel and aluminium alloy specimens under complex non-proportional loading.
Artem S. Semenov, Boris E. Melnikov
9. A Damage Model for Corrosion Fatigue Due to Hydrogen Embrittlement
Abstract
Predicting the durability of components subjected to mechanical load under environmental conditions leading to corrosion is one of the most challenging tasks in mechanical engineering. The demand for precise predictions increases with the desire of lightweight design in transportation due to environmental protection. Corrosion with its manifold of mechanisms often occurs together with the production of hydrogen by electrochemical reactions. Hydrogen embrittlement is one of the most feared damage mechanisms for metal constructions often leading to early and unexpected failure. Until now, predictions are mostly based on costly experiments. Hence, a rational predictive model based on the fundamentals of electrochemistry and damage mechanics has to be developed in order to reduce the costs. In this work, a first model approach based on classical continuum damage mechanics is presented to couple both, the damage induced by the mechanical stress and the hydrogen embrittlement. An elaborated two-scale model based on the selfconsistent theory is applied to describe the mechanical damage due to fatigue. The electrochemical kinetics are elucidated through the Langmuir adsorption isotherm and the diffusion equation to consider the impact of hydrogen embrittlement on the fatigue. The modeling of the mechanism of hydrogen embrittlement defines the progress of damage accumulation due to the electrochemistry. The durability results like the S-N diagram show the influence of hydrogen embrittlement by varying, e.g. the fatigue frequency or the stress ratio.
Yuhao Shi, Sven Harzheim, Martin Hofmann, Thomas Wallmersperger
10. A Thermodynamics-Based Wear Model and Its Application with the Finite Element Analysis
Abstract
In the paper a generalized wear equation for sliding solid bodies at contact is derived from the fundamental law of thermodynamics. The wear model consists of a physical correlation between the wear, the binding potential of the materials in the contact area and the work done by friction in the tribological system. The wear model is based on the knowledge of material parameters of the bodies in sliding contact which can only be derived from measurements. The application of the wear model for analyzing industrial problems requires a powerful numerical solution approach. The finite element analysis (FEA) is a customary and widespread applied simulation approach in industry. Consequently, it is obvious to include the developed wear model into the frame of a commercial FEA software tool, where the FEA software Abaqus is used in the paper. Finally, as a complex industrial application problem the wear of automotive timing chains is presented. The simulated numerical wear results are compared with measurements at engines after mileage of about 50000 km.
Robert Tandler, Ulrich Gabbert
11. Discrete Description of Crack Kinematics in Regularized Free Discontinuities of Crack Faces
Abstract
The fracture mechanical free discontinuity problem can be associated with a generalized, variational approach of GRIFFITH’s fracture theory. By introducing a regularization for the sharp displacement discontinuity at cracks and crack surfaces, stable computational fracture models are developed, e.g., the phase-field fracture formulation and the eigenfracture approach. The presented work summarizes recent findings regarding unrealistic deformation kinematics at cracks predicted by conventional formulations of both models and introduces the variational framework of Representative Crack Element to overcome these discrepancies. Illustrative examples for crack propagation and post-fracture behavior at small and finite deformations, brittle and cohesive failure as well as for rate-dependent materials frictional crack contact demonstrate the flexibility and the generality of the introduced Representative Crack Element.
Bo Yin, Johannes Storm, Michael Kaliske
12. Applications of Viscoplasticity and Damage Models, the Thermomechanical Consistency and the Prospect of a Microstructural Representation
Abstract
Material models in the framework of continuum mechanics cover the experimentally observed phenomena with a mathematical representation and a correspondingsetofmaterialparameters,whichneedtobeestablishedandvalidated. The theory of viscoplasticity plays an important role to describe the material behaviour of polymers and metals for a conventional as well as an additive manufacturing process. Naturally, the manufacturing process influences the microstructure and is to be reflected in the analysis and the characterisation of the material. The geometry reconstruction of microscopic images supports the extension of well-known material models and motivates the investigation of the interaction in bicontinuous composites. A universal measurement method as the contactfree thermography can be applied to validate the analytical assumption by an extended set of characteristics.
Matthias Ziegenhorn, Rainer Adelung, Rainer Franke, Robert Roszak, Ilja Sagrado, Daniela Schob, Holger Sparr, Tomasz Kurzynowski
Metadata
Title
Material Modeling and Structural Mechanics
Editors
Univ.-Prof. Holm Altenbach
Univ.-Prof. Michael Beitelschmidt
Univ.-Prof. Markus Kästner
Prof. Konstantin Naumenko
Univ.-Prof. Thomas Wallmersperger
Copyright Year
2022
Electronic ISBN
978-3-030-97675-0
Print ISBN
978-3-030-97674-3
DOI
https://doi.org/10.1007/978-3-030-97675-0

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