Shape optimization of two‐phase inelastic material with microstructure

AbstractForming of tires during production is a challenging process for Lagrangian solid mechanics due to large changes in the geometry and material properties of the rubber layers. This paper extends the Arbitrary Lagrangian–Eulerian (ALE) formulation to thermomechanical inelastic material models with special consideration of rubber. The ALE approach based on tracking the material and spatial meshes is used, and an operator-split is employed which splits up the solution within a time step into a mesh smoothing step, a history remapping step and a Lagrangian step. Mesh distortion is reduced in the smoothing step by solving a boundary value problem. History variables are subsequently remapped to the new mesh with a particle tracking scheme. Within the Lagrangian steps, a fully coupled thermomechanical problem is solved. An advanced two-phase rubber model is incorporated into the ALE approach, which can describe green rubber, cured rubber and the transition process. Several numerical examples demonstrate the superior behavior of the developed formulation in comparison to purely Lagrangian finite elements.

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A Discrete Adjoint Method for Two-Phase Condensing Flows Applied to the Shape Optimization of Turbine Cascades

Journal of Turbomachinery ◽

10.1115/1.4047781 ◽

2020 ◽

Vol 142 (11) ◽

Author(s):

M. Pini ◽

L. Azzini ◽

S. Vitale ◽

P. Colonna

Keyword(s):

Shape Optimization ◽

Adjoint Method ◽

Volume Fraction ◽

Liquid Volume ◽

Two Phase ◽

Discrete Adjoint ◽

First Case ◽

Discrete Adjoint Method ◽

Condensing Flows ◽

Turbine Cascades

Abstract This paper presents a fully turbulent two-phase discrete adjoint method for metastable condensing flows targeted to turbomachinery applications. The method is based on a duality preserving algorithm and implemented in the open-source CFD tool SU2. The optimization framework is applied to the shape optimization of two canonical steam turbine cascades, commonly referred to as White cascade and Dykas cascade. The optimization were carried out by minimizing either the liquid volume fraction downstream of the cascade or the total entropy generation due viscous effects and heat transfer. In the first case, the amount of condensate turned out to be reduced by as much as 24%, but without reduction of the generated entropy, while the opposite resulted in the second case. The outcomes demonstrate the capability and computational efficiency of adjoint-based automated design for the shape optimization of turbomachinery operating with phase change flow.

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Effect of Shock Loading on the Microstructure of Uniloy 326

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100052535 ◽

1974 ◽

Vol 32 ◽

pp. 504-505

Author(s):

K. P. Staudhammer ◽

L. E. Murr

Keyword(s):

Grain Size ◽

Shock Loading ◽

Current Investigation ◽

Two Phase ◽

05 C ◽

Shock Deformation ◽

Heat Treated

The effect of shock loading on a variety of steels has been reviewed recently by Leslie. It is generally observed that significant changes in microstructure and microhardness are produced by explosive shock deformation. While the effect of shock loading on austenitic, ferritic, martensitic, and pearlitic structures has been investigated, there have been no systematic studies of the shock-loading of microduplex structures.In the current investigation, the shock-loading response of millrolled and heat-treated Uniloy 326 (thickness 60 mil) having a residual grain size of 1 to 2μ before shock loading was studied. Uniloy 326 is a two phase (microduplex) alloy consisting of 30% austenite (γ) in a ferrite (α) matrix; with the composition.3% Ti, 1% Mn, .6% Si,.05% C, 6% Ni, 26% Cr, balance Fe.

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Exsolution and inversion in pigeonite from the Whin Sill, Northern England

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100109513 ◽

1978 ◽

Vol 36 (1) ◽

pp. 474-475

Author(s):

P.P.K. Smith

Keyword(s):

High Temperature ◽

Low Temperature ◽

Homogeneous Nucleation ◽

Silicate Mineral ◽

Antiphase Boundaries ◽

Two Phase ◽

Primitive Form ◽

The Core ◽

Nucleation Mechanisms ◽

And Inversion

Grains of pigeonite, a calcium-poor silicate mineral of the pyroxene group, from the Whin Sill dolerite have been ion-thinned and examined by TEM. The pigeonite is strongly zoned chemically from the composition Wo8En64FS28 in the core to Wo13En34FS53 at the rim. Two phase transformations have occurred during the cooling of this pigeonite:- exsolution of augite, a more calcic pyroxene, and inversion of the pigeonite from the high- temperature C face-centred form to the low-temperature primitive form, with the formation of antiphase boundaries (APB's). Different sequences of these exsolution and inversion reactions, together with different nucleation mechanisms of the augite, have created three distinct microstructures depending on the position in the grain.In the core of the grains small platelets of augite about 0.02μm thick have farmed parallel to the (001) plane (Fig. 1). These are thought to have exsolved by homogeneous nucleation. Subsequently the inversion of the pigeonite has led to the creation of APB's.

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Shock consolidation of Ni-Ti alloy powder

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143730 ◽

1986 ◽

Vol 44 ◽

pp. 430-431

Author(s):

Naresh N. Thadhani ◽

Thad Vreeland ◽

Thomas J. Ahrens

Keyword(s):

Alloy Powder ◽

Amorphous Material ◽

Ti Alloy ◽

Two Phase ◽

Near Surface ◽

Optical Micrograph ◽

Shock Compaction ◽

Powder Particles ◽

Ti Powder ◽

Rapidly Solidified

A spherically-shaped, microcrystalline Ni-Ti alloy powder having fairly nonhomogeneous particle size distribution and chemical composition was consolidated with shock input energy of 316 kJ/kg. In the process of consolidation, shock energy is preferentially input at particle surfaces, resulting in melting of near-surface material and interparticle welding. The Ni-Ti powder particles were 2-60 μm in diameter (Fig. 1). About 30-40% of the powder particles were Ni-65wt% and balance were Ni-45wt%Ti (estimated by EMPA).Upon shock compaction, the two phase Ni-Ti powder particles were bonded together by the interparticle melt which rapidly solidified, usually to amorphous material. Fig. 2 is an optical micrograph (in plane of shock) of the consolidated Ni-Ti alloy powder, showing the particles with different etching contrast.

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A Comparison of Tem and Apfim to the Interpretation of Modulated Microstructures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010011742x ◽

1985 ◽

Vol 43 ◽

pp. 70-71

Author(s):

M.G. Burke ◽

M.K. Miller

Keyword(s):

Low Temperature ◽

Microstructural Characterization ◽

Superlattice Reflection ◽

High Volume ◽

Atom Probe ◽

Dark Field ◽

Miscibility Gap ◽

Second Phase ◽

Two Phase ◽

Probe Field

Interpretation of fine-scale microstructures containing high volume fractions of second phase is complex. In particular, microstructures developed through decomposition within low temperature miscibility gaps may be extremely fine. This paper compares the morphological interpretations of such complex microstructures by the high-resolution techniques of TEM and atom probe field-ion microscopy (APFIM).The Fe-25 at% Be alloy selected for this study was aged within the low temperature miscibility gap to form a <100> aligned two-phase microstructure. This triaxially modulated microstructure is composed of an Fe-rich ferrite phase and a B2-ordered Be-enriched phase. The microstructural characterization through conventional bright-field TEM is inadequate because of the many contributions to image contrast. The ordering reaction which accompanies spinodal decomposition in this alloy permits simplification of the image by the use of the centered dark field technique to image just one phase. A CDF image formed with a B2 superlattice reflection is shown in fig. 1. In this CDF micrograph, the the B2-ordered Be-enriched phase appears as bright regions in the darkly-imaging ferrite. By examining the specimen in a [001] orientation, the <100> nature of the modulations is evident.

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