## Fatigue resistance of BMGs and instability of stationary liquid sheets

### April 1, 2009

A couple of papers from the latest PNAS:

The recent development of metallic glass-matrix composites represents a particular milestone in engineering materials for structural applications owing to their remarkable combination of strength and toughness. However, metallic glasses are highly susceptible to cyclic fatigue damage, and previous attempts to solve this problem have been largely disappointing. Here, we propose and demonstrate a microstructural design strategy to overcome this limitation by matching the microstructural length scales (of the second phase) to mechanical crack-length scales. Specifically, semisolid processing is used to optimize the volume fraction, morphology, and size of second-phase dendrites to confine any initial deformation (shear banding) to the glassy regions separating dendrite arms having length scales of ≈2 μm, i.e., to less than the critical crack size for failure. Confinement of the damage to such interdendritic regions results in enhancement of fatigue lifetimes and increases the fatigue limit by an order of magnitude, making these “designed” composites as resistant to fatigue damage as high-strength steels and aluminum alloys. These design strategies can be universally applied to any other metallic glass systems.

A M Ardekani and D D Joseph

The rupture of a 3D stationary free liquid film under the competing effects of surface tension and van der Waals forces is studied as a linearized stability problem in a purely irrotational analysis utilizing the dissipation method. The results of the foregoing analysis are compared with a 2D long-wave approximation that has given rise to an extensive literature on the rupture problem. The irrotational and long-wave approximations are here compared with the exact 2D solution. The exact solution and the two approximate theories give the same results for infinitely long waves. The problem considered depends on two dimensionless parameters, the Hamaker number and the Ohnesorge number. The Hamaker number is a dimensionless number defined as a measure of the ratio of van der Waals forces to surface tension. The exact solution and the two approximate solutions differ by < 1% when the Hamaker number is small for all values of the Ohnesorge number. When the Ohhnesorge number is close to one, as in the case of water films separated by distance 100 Å, the long-wave approximation overestimates and the potential flow approximation underestimates the exact solution by similar small amounts. The high accuracy of the dissipation method shows that the effects of vorticity are small for small to moderate Hamaker numbers.

## Phase transformation kinetics under stress, solid state dendrites, Potts model for 3D grain growth, and, microstructure and magnetic properties

### March 29, 2009

Y C Liu et al

The effect of an applied constant uniaxial compressive stress on the kinetics of the austenite (γ) → ferrite (α) massive transformation in the substitutional Fe–2.96 at.% Ni alloy upon isochronal cooling has been studied by differential dilatometry. All imposed stress levels are below the yield stress of austenite and ferrite in the temperature range of the transformation. An increase in compressive stress results in a small but significant increase of the onset temperature of the γ → α transformation and a decrease of the overall transformation time. A phase transformation model, involving site saturation, interface-controlled growth and incorporation of an appropriate impingement correction, has been employed to extract the interface-migration velocity of the γ/α interface. The interface-migration velocity for the γ → α transformation is approximately constant at fixed uniaxial compressive stress and increases with increasing applied uniaxial compressive stress. Furthermore, the value obtained for the energy corresponding with the elastic and plastic deformation associated with the accommodation of the γ/α volume misfit depends on the transformed fraction and decreases significantly as the applied uniaxial compressive stress increases. An understanding of the observed effects is obtained, recognizing the constraints imposed on the phase transformation due to the applied stress.

M Greenwood et al

A new phase-field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model’s thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al. [Echebarria B, Folch R, Karma A, Plapp M. Phys Rev E 2004;70:061604]. Exploiting this thin interface analysis, the growth of solid-state dendrites are simulated with diffuse interfaces and the phase-field and mechanical equilibrium equations are solved in real space on an adaptive mesh. A morphological competition between surface energy anisotropy and elastic anisotropy is examined. Two dimensional simulations are reported that show that solid-state dendritic structures undergo a transition from a surface-dominated [Meiron DI. Phys Rev A 1986;33:2704] growth direction to an elastically driven [Steinbach I, Apel M. Phys D – Nonlinear Phenomena 2006;217:153] growth direction due to changes in the elastic anisotropy, the surface anisotropy and the supersaturation. Using the curvature and strain corrections to the equilibrium interfacial composition and linear stability theory for isotropic precipitates as calculated by Mullins and Sekerka, the dominant growth morphology is predicted.

O M Ivasishin et al

A three-dimensional Monte-Carlo (Potts) model was modified to incorporate the effect of grain-boundary inclination on boundary mobility. For this purpose, a straightforward geometric construction was developed to determine the local orientation of the grain-boundary plane. The combined effects of grain-boundary plane and misorientation on the effective grain-boundary mobility were incorporated into the Monte-Carlo code using the definition of the tilt–twist component. The modified code was validated by simulating grain growth in microstructures comprising equiaxed or elongated grains as well as the static recrystallization of a microstructure of deformed (elongated) grains.

By adding carbon nanotubes (CNTs) to SmCo6.9Hf0.1, novel SmCo6.9Hf0.1(CNTs)0.05 as-cast alloy has been prepared, which consists of Sm(Co,Hf)7 as the main phase, a small amount of SmCo5 and a particle-like grain boundary phase Hf(CNTs). SmCo6.9Hf0.1(CNTs)0.05 ribbons melt-spun at speeds of 10–50 m s−1 have a single TbCu7-type structure. Increasing the quenching speed can result in a decrease in ribbon thickness and grain boundary width. Meanwhile, the grain size tends to be smaller and the grain boundary phase tends to be more dispersed. A new Sm(Co,Hf)7(CNTs)x boundary phase may be formed in SmCo6.9Hf0.1(CNTs)0.05 ribbons. Increasing the quenching speed can also enhance coercivity, remanence and remanence ratio. The ribbons melt-spun at a speed of 50 m s−1 display the best magnetic properties: Hci = 18.781 kOe, Ms2T = 76.87 emu g−1, Mr = 66.79 emu g−1 and Mr/Ms2T = 0.87.

## Stability of solidification and melting fronts

### January 4, 2009

Stress-induced destabilization of solidification and melting fronts

J Colin

The morphological evolution of the initially planar solidification and melting fronts of a thin liquid film in a stressed binary alloy has been investigated when diffusion only proceeds in the liquid phase. A linear stability analysis has been performed and the diffusion-controlled evolution of the shape of both fronts has been characterized. The destabilizing effect of stress on the profiles of the interfaces has been identified for a liquid film at rest when the solid is submitted to constant stress and when it is migrating, due to stress gradient, in the hypothesis where concentration field of solute satisfy Laplace’s equation. The possibility of roughness formation in the early beginning of the development of the solid–liquid interfaces has been finally discussed for alloys in the context of a liquid film migration mechanism.

## Unconditonally stable time steps for diffuse interface equations

### March 17, 2007

Authors: Benjamin P. Vollmayr-Lee and Andrew D. Rutenberg

Abstract:

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre’s theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. For the Cahn-Hilliard case, we show that accuracy can be controlled with an unbounded time step $\Delta t$ that grows with time $t$ as $\Delta t \sim t^{\alpha}$. We develop a classification scheme for the step exponent $\alpha$ and demonstrate that a class of simple linear algorithms gives $\alpha = 1/3$. For this class the speedup relative to a fixed time step grows with $N$, the linear size of the system, as $N/\ln N$. With conservative choices for the parameters controlling accuracy and finite-size effects we find that an $8192^{2}$ lattice can be integrated 300 times faster than with the Euler method.