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A computational multi-scale approach for brittle materials
  • Language: en
  • Pages: 264

A computational multi-scale approach for brittle materials

Materials of industrial interest often show a complex microstructure which directly influences their macroscopic material behavior. For simulations on the component scale, multi-scale methods may exploit this microstructural information. This work is devoted to a multi-scale approach for brittle materials. Based on a homogenization result for free discontinuity problems, we present FFT-based methods to compute the effective crack energy of heterogeneous materials with complex microstructures.

Thermomechanical Modeling and Experimental Characterization of Sheet Molding Compound Composites
  • Language: en
  • Pages: 250

Thermomechanical Modeling and Experimental Characterization of Sheet Molding Compound Composites

The aim of this work is to model and experimentally characterize the anisotropic material behavior of SMC composites on the macroscale with consideration of the microstructure. Temperature-dependent thermoelastic behavior and failure behavior are modeled and the corresponding material properties are determined experimentally. Additionally, experimental biaxial damage investigations are performed. A parameter identification merges modeling and experiments and validates the models.

Homogenization and materials design of mechanical properties of textured materials based on zeroth-, first- and second-order bounds of linear behavior
  • Language: en
  • Pages: 224

Homogenization and materials design of mechanical properties of textured materials based on zeroth-, first- and second-order bounds of linear behavior

This work approaches the fields of homogenization and of materials design for the linear and nonlinear mechanical properties with prescribed properties-profile. The set of achievable properties is bounded by the zeroth-order bounds (which are material specific), the first-order bounds (containing volume fractions of the phases) and the second-order Hashin-Shtrikman bounds with eigenfields in terms of tensorial texture coefficients for arbitrarily anisotropic textured materials.

Numerically Efficient Gradient Crystal Plasticity with a Grain Boundary Yield Criterion and Dislocation-based Work-Hardening
  • Language: en
  • Pages: 288

Numerically Efficient Gradient Crystal Plasticity with a Grain Boundary Yield Criterion and Dislocation-based Work-Hardening

This book is a contribution to the further development of gradient plasticity. Several open questions are addressed, where the efficient numerical implementation is particularly focused on. Thebook inspects an equivalent plastic strain gradient plasticity theory and a grain boundary yield model. Experiments can successfully be reproduced. The hardening model is based on dislocation densities evolving according to partial differential equations taking into account dislocation transport.

Modeling martensitic phase transformation in dual phase steels based on a sharp interface theory
  • Language: en
  • Pages: 220

Modeling martensitic phase transformation in dual phase steels based on a sharp interface theory

artensite forms under rapid cooling of austenitic grains accompanied by a change of the crystal lattice. Large deformations are induced which lead to plastic dislocations. In this work a transformation model based on the sharp interface theory, set in a finite strain context is developed. Crystal plasticity effects, the kinetic of the singular surface as well as a simple model of the inheritance from austenite dislocations into martensite are accounted for.

Work-hardening of dual-phase steel
  • Language: en
  • Pages: 202

Work-hardening of dual-phase steel

Dual-phase steels exhibit good mechanical properties due to a microstructure of strong martensitic inclusions embedded in a ductile ferritic matrix. This work presents a two-scale model for the underlying work-hardening effects; such as the distinctly different hardening rates observed for high-strength dual-phase steels. The model is based on geometrically necessary dislocations and comprises the average microstructural morphology as well as a direct interaction between the constituents.

Homogenization of the Linear and Non-linear Mechanical Behavior of Polycrystals
  • Language: en
  • Pages: 216

Homogenization of the Linear and Non-linear Mechanical Behavior of Polycrystals

This work is dedicated to the numerically efficient simulation of the material response of polycrystalline aggregates. Therefore, crystal plasticity is combined with a new non-linear homogenization scheme, which is based on piecewise constant stress polarizations with respect to a homogeneous reference medium and corresponds to a generalization of the Hashin-Shtrikman scheme. This mean field approach accounts for the one- and two-point statistics of the microstructure.

Biaxial Characterization and Mean-field Based Damage Modeling of Sheet Molding Compound Composites
  • Language: en
  • Pages: 194

Biaxial Characterization and Mean-field Based Damage Modeling of Sheet Molding Compound Composites

The focus of this work lies on the microstructure-based modeling and characterization of a discontinuous fiber-reinforced thermoset in the form of sheet molding compound (SMC). A microstructure-based parameter identification scheme for SMC with an inhomogeneous fiber orientation distribution is introduced. Different cruciform specimen designs, including two concepts to reinforce the specimens' arms are evaluated. Additionally, a micromechanical mean-field damage model for the SMC is introduced.

Micromechanical Modeling and Simulation of Forming Processes
  • Language: en
  • Pages: 158

Micromechanical Modeling and Simulation of Forming Processes

The deep drawing of an aluminum alloy used in the packaging industry for the beverage can manufacturing process is investigated. In this work, the effective constitutive behavior is based on a crystal plasticity model in combination with a non-linear Hashin-Shtrikman type homogenization scheme in which a reference stiffness controls the stress and strain fluctuations. The simulation results are compared to experiments in terms of deep drawing earing profiles, texture evolution, and localization.

Deep material networks for efficient scale-bridging in thermomechanical simulations of solids
  • Language: en
  • Pages: 326

Deep material networks for efficient scale-bridging in thermomechanical simulations of solids

We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations.