Section 6: Material modelling in solid mechanics - GAMM 2012

More documents

Recommendations

Info

26 Section 6: Material modelling in solid mechanics Starting with the theoretical concept of Prandtl, who introduced the idea of a hardening substance in a material, and the investigations of Mughrabi, who established a composite model for chromium steels, the advanced steels are treated as a composition of at least two continua, in the sense of the theory of mixture. Therefore the general balance equations for a mixture will be presented. The example of a 12% chromium steel will be used to illustrate this approach and to derive a material model for a mixture of two constituents. It will be shown that the model predicts tension-, compression-, cyclic-creep, uniaxial monotonic tension und low-cycle-fatigue loading in a satisfying manner in comparison with experimental results. Zur Abtragssimulation beim Strömungsschleifen (AFM) Joachim Schmitt, Stefan Diebels (Universität des Saarlandes) Im Zuge konkurrenzfähiger Produktionsverfahren werden seit einigen Jahren schwer zugängliche Kanten im Inneren von komplex aufgebauten Fertigungsteilen (wie beispielsweise die Gehäuse von Einspritzanlagen) mittels des Strömungsschleifens (Abrasive flow machining - AFM) verrundet bzw. oberflächenvergütet. Dazu wird eine mit Schleifpartikeln versetzte Silikonpaste mehrfach durch das Bauteil gepresst. Das viskose Verhalten der Paste ist dabei für die effektive Wirkung dieses Verfahrens sehr wichtig. Beim Überströmen von Kanten steigt die Schergeschwindigkeit und damit auch die Viskosität je nach Materialmodell überproportional an. Die so geänderten Druckund Geschwindigkeitsverhältnisse an der Bauteiloberfläche verändern auch den Materialabtrag durch die Schleifpaste. Im Rahmen dieser Studie werden zunächst die viskosen Eigenschaften der Paste anhand von Experimenten untersucht und die Modellparameter bestimmt. Im zweiten Teil wird die Paste hinsichtlich ihrer abrasiven Eigenschaften vorgestellt und eine Abschätzung des Materialabriebs vorgenommen. Ein daraus gebildetes einfaches Abtragsmodell wird mittels einer FEM-Simulation an elementaren Bauteilgeometrien umgesetzt und qualitativ überprüft. Material parameter identification using model reduction to uniaxial tensile tests Stephan Krämer, Steffen Rothe, Stefan Hartmann (TU Clausthal) Uniaxial tensile tests are commonly used for material parameter identification. It is also common to use one-dimensional formulations of a constitutive model to identify the corresponding material constants, although these material parameters are not necessarily identical to the material parameters in the three-dimensional material model. We present an easy way to reduce a three-dimensional material routine to the case of uniaxial tension and to use the reduced form to derive material parameters using common trust-region algorithms. With this approach one is able to use the full three-dimensional model for parameter identification. Instead of using a full finite element software, one is able to use the material driver routine, which leads to a more straight forward calculation of material parameters. In this respect, it is shown that the classical structure of stress algorithms and consistent tangent operators are necessary within the threeto one-dimensional problem reduction. This procedure is also extendable to further homogeneous stress- and strain-states. Systematic representation of the yield criteria for isotropic materials Vladimir A. Kolupaev (DKI Darmstadt), Holm Altenbach (Universität Magdeburg) The theory of plasticity operates with different flow criteria of incompressible material behavior. These criteria have hexagonal symmetry in the π-plane and do not distinguish between tension and compression (non-SD-effect). Many tasks in the engineering practice are treated on the basis
Section 6: Material modelling in solid mechanics 27 of these criteria and the flow rule. Selection of an appropriate criterion for a specific material is challenging. The models of Tresca and Schmidt-Ishlinsky, representing two regular hexagons in the π-plane, define accordingly the lower and the upper limit of convexity. The criteria of Sokolovskij and Ishlinsky-Ivlev describe the regular dodecagons in the π-plane and have only geometrical meaning. In difference to these four criteria, the model of von Mises has no singular corners and delivers unique results by the strain rates calculation. The evaluation of the measurements shows that the material behavior differs from the idealized models. The models proposed by Drucker, Dodd-Naruse, Edelman-Drucker and Hershey aim to better adapt the flow surface. These models are the functions of one parameter. They have no claims on the generality and are used only for the approximation of the measurements. Three models with one parameter are known as generalized models: Unified Yield Criterion (UYC) of Yu, Bi-Cubic Model (BCM), and Multiplicative Ansatz (MA) [1]. These models include the models of Tresca and Schmidt-Ishlinsky. They allow approximating of existing measurements better than other models. This work compares the flow criteria. For this aim their geometries in the π-plane will be considered in polar coordinates R and ϕ. The radii of the surface at the angles of ϕ = 15 and 30 ◦ are related to the radius at ϕ = 0 ◦ : h = R(15 ◦ )/R(0 ◦ ), k = R(30 ◦ )/R(0 ◦ ). On the basis of these two relations, well-known criteria will be systematized and shown in the h − k–diagram. New criteria will be introduced. The convexity limits for them will be stated. From the h−k–diagram, it is clear that UYC and MA set left and right boundary of convexity. Thus, the extreme solutions for parts can be found. The two models UYC and MA are the functions of the parameter k. The linear combination of UYC and MA provides a universal model with two parameters k and ξ ∈ [0, 1] describing all convex surfaces of incompressible material behavior of hexagonal symmetry in the π-plane. The proposed consideration of the flow criteria simplifies the selection of the model and is suitable for didactic purposes. All known and new flow criteria can be described by universal model, and thus can be omitted. [1] Kolupaev, V. A., Altenbach, H.: Considerations on the unified strength theory due to Mao- Hong Yu, Forschung im Ingenieurwesen 74(3), (2010). S6.11: Special Methods in Material Modeling Thu, 16:00–18:00 Chair: Bernhard Eidel, Markus Scholle S1|01–A03 Modeling of Carbon Nanotubes by Molecular Mechanics Oliver Eberhardt, Thomas Wallmersperger (TU Dresden) Carbon Nanotubes (CNTs) are structures in the nanoscale consisting of carbon atoms which are arranged in a hexagonal lattice. Hence, they can be imagined as a plane sheet of graphene rolled into a seamless tube. By doing so we obtain a so called Single Wall Carbon Nanotube (SWCNT). Besides Single Wall Carbon Nanotubes also Double Wall Carbon Nanotubes (DWCNT) and, in general, Multi Wall Carbon Nanotubes (MWCNT) exist. Their high stiffness and active deformation of approx. 1 % at applied low electric voltages (approx. 1 V) make the Carbon Nanotubes a very promising material for applications e.g. in new classes of composites and actuators/sensors. In this research the approach to model Carbon Nanotubes is made by using molecular mechanics. The aim of these efforts is to determine the mechanical properties, for example the Young’s
Page 1 and 2: Section 6: Material modelling in so
Page 25: Section 6: Material modelling in so

Section 6: Material modelling in solid mechanics - GAMM 2012

Create successful ePaper yourself

Delete template?

Save as template?