Christoph Beckermann

Bio: Christoph Beckermann is an academic researcher from University of Iowa. The author has contributed to research in topics: Dendrite (crystal) & Casting. The author has an hindex of 52, co-authored 204 publications receiving 10935 citations. Previous affiliations of Christoph Beckermann include Los Alamos National Laboratory & State University of Campinas.

Phase-Field Simulation of Solidification

Abstract: ▪ Abstract An overview of the phase-field method for modeling solidification is presented, together with several example results. Using a phase-field variable and a corresponding governing equation to describe the state (solid or liquid) in a material as a function of position and time, the diffusion equations for heat and solute can be solved without tracking the liquid-solid interface. The interfacial regions between liquid and solid involve smooth but highly localized variations of the phase-field variable. The method has been applied to a wide variety of problems including dendritic growth in pure materials; dendritic, eutectic, and peritectic growth in alloys; and solute trapping during rapid solidification.

A volume-averaged two-phase model for transport phenomena during solidification

Abstract: A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.

The Superalloys: Fundamentals and Applications

Abstract: 1. Introduction 2. The physical metallurgy of nickel and its alloys 3. Single crystal superalloys for blade applications 4. Superalloys for turbine disc applications 5. Environmental degradation: the role of coatings 6. Summary and future trends.

Boundary Layer Theory

Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Phase-Field Models for Microstructure Evolution

Abstract: ■ Abstract The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.

Nickel-Based Superalloys for Advanced Turbine Engines: Chemistry, Microstructure and Properties

Abstract: The chemical, physical, and mechanical characteristics of nickel-based superalloys are reviewed with emphasis on the use of this class of materials within turbine engines. The role of major and minor alloying additions in multicomponent commercial cast and wrought superalloys is discussed. Microstructural stability and phases observed during processing and in subsequent elevated-temperature service are summarized. Processing paths and recent advances in processing are addressed. Mechanical properties and deformation mechanisms are reviewed, including tensile properties, creep, fatigue, and cyclic crack growth. I. Introduction N ICKEL-BASED superalloys are an unusual class of metallic materials with an exceptional combination of hightemperature strength, toughness, and resistance to degradation in corrosive or oxidizing environments. These materials are widely used in aircraft and power-generation turbines, rocket engines, and other challenging environments, including nuclear power and chemical processing plants. Intensive alloy and process development activities during the past few decades have resulted in alloys that can tolerate average temperatures of 1050 ◦ C with occasional excursions (or local hot spots near airfoil tips) to temperatures as high as 1200 ◦ C, 1 which is approximately 90% of the melting point of the material. The underlying aspects of microstructure and composition that result in these exceptional properties are briefly reviewed here. Major classes of superalloys that are utilized in gas-turbine engines and the corresponding processes for their production are outlined along with characteristic mechanical and physical properties.