Three-dimensional Phase Field Research Articles

The Isothermal Dendritic Growth Experiment: Evolution of Teleoperational Control of Materials Research in Microgravity

AbstractExactly one year ago, the Isothermal Dendritic Growth Experiment (IDGE) completed its third and final orbital space flight aboard the United States Microgravity Payload (USMP) on STS-87. The IDGE conducted 180 experiments on dendritic growth in 5-9's succinonitrile (SCN), a BCC material used on USMP-2 and USMP-3, and over 100 experiments on 4-9's pivalic acid (PVA), an FCC material used on USMP-4. IDGE film and telemetry data provide benchmark tip velocity and radii versus supercooling for critically testing transport theory and the interfacial physics of diffusion-limited dendritic growth. Post-flight application of optical tomography is providing the first tip shape data allowing quantitative tests of three-dimensional phase field calculations. Several new discoveries were made during each flight concerning the behavior of dendrites at low driving forces, and the influences of time-dependent pattern features and noise. A summary of these scientific highlights will be provided.The IDGE instrument was upgraded on each successive flight, improving its optics and electronics, especially the capability for teleoperational control. Near real-time, full gray-scale video was accommodated on USMP-4, allowing investigation of non-steady-state features and time-dependent growth dynamics. A short example of video from space will be shown. USMP-4 science was teleoperated by a student cadre for 16 days from a remote site established by NASA at RPI. This operational experience provides valuable insights, which will be drawn upon for future microgravity experiments to be conducted on the International Space Station.

Theory of martensitic phase transformations in inelastic materials in local description

Thermodynamically consistent, three-dimensional (3D) phase field approach (PFA) for coupled multivariant martensitic transformations (PTs), including cyclic PTs, variant–variant transformations (i.e., twinning), and dislocation evolution is developed at large strains. One of our key points is in the justification of the multiplicative decomposition of the deformation gradient into elastic, transformational, and plastic parts. The plastic part includes four mechanisms: dislocation motion in martensite along slip systems of martensite and slip systems of austenite inherited during PT and dislocation motion in austenite along slip systems of austenite and slip systems of martensite inherited during reverse PT. The plastic part of the velocity gradient for all these mechanisms is defined in the crystal lattice of the austenite utilizing just slip systems of austenite and inherited slip systems of martensite, and just two corresponding types of order parameters. The explicit expressions for the Helmholtz free energy and the transformation and plastic deformation gradients are presented to satisfy the formulated conditions related to homogeneous thermodynamic equilibrium states of crystal lattice and their instabilities. In particular, they result in a constant (i.e., stress- and temperature-independent) transformation deformation gradient and Burgers vectors. Thermodynamic treatment resulted in the determination of the driving forces for change of the order parameters for PTs and dislocations. It also determined the boundary conditions for the order parameters that include a variation of the surface energy during PT and exit of dislocations. Ginzburg–Landau equations for dislocations include variation of properties during PTs, which in turn produces additional contributions from dislocations to the Ginzburg–Landau equations for PTs. A complete system of coupled PFA and mechanics equations is presented. A similar theory can be developed for PFA to dislocations and other PTs, like reconstructive PTs and diffusive PTs described by the Cahn–Hilliard equation, as well as twinning and grain boundaries evolution.