Solidification and Grain Size Strengthening

Solidification and Grain Size Strengthening

• Stages of Solidification– Nucleation: occurs when a small piece of solid forms in the liquid

and must attain a minimum critical size before it is stable

– Growth: occurs as atoms from the liquid are attached to the tiny solid until no liquid remains

– Both conditions are met when the free energy of the particular phase is lower

Solidification Terminology

• To get the solidification process started, the liquid phase must be undercooled, cooled to a temperature below the freezing point.

• Once a nucleus forms, it can proceed to grow as fast as the latent heat of solidification and specific heat can be carried away. Controlled by:– thermal conductivities

– relative masses

– shapes of the melt, the solid, and mold

Growth Interfaces

• Growth of Interfaces depends on– Concentration Gradient

– Temperature Gradient

– undercooling

– Growth Rate

• Types of Interfaces– Planar

– Cellular

– Dendritic

– Equiaxed

Schematic Illustration of Solidification Morphologies

Solidification Time

• Chvorinov’s Rule

2

A

VBts

ts: Solidification time

B: Mold Constant

V: Volume of the Casting

A: Surface Area of the casting in contact with the mold

Cooling Curves

Casting or Ingot Structure

Solidification Defects

• Shrinkage - the degree, size, and location of shrinkage defects is dependent on the type of solidification of the alloy. For castings, can be corrected with risers.

• Microshrinkage - commonly occurs in dendritic and equiaxed growth types.

• Gas Porosity - metal dissolve considerable gas, higher concentration in liquid than solid. Thus, on solidification, gas bubbles form and are trapped by surrounding solid metal.

Control of Solidification

• Inoculation or Grain Refining Practice - introduction of nuclei to encourage rapid solidification (reduce and minimize undercooling)

• Directional Solidification - control the growth rate and temperature gradient to manipulate growth interface.– Use of chills in castings produce finer grain structure

– Specialized solidification techniques to create single crystals castings

Atom Movement in Materials

• Diffusion is the movement of atoms to produce a homogenous, uniform composition

• Applications– Heat Treatment of Metals

– Manufacturing of Ceramics

– Solidification of Materials

– Curing of Cement and Refractories

– Manufacture of Electronic Components

Stability of Atoms

• Imperfections and normal atoms are not stable or at rest

• Atoms possess thermal energy that allow from atom movement

RT

QcRate o exp

Co is a material constant

Q is the activation energy

R is the gas constant

T is temperature

Diffusion Mechanism

Diffusion Mechanisms

Activation Energy

• A diffusing atom must squeeze past the surrounding to reach its new location

Rate of DiffusionFick’s First Law

• Diffusion Coefficient or Diffusivity is dependent on temperature from Arrhenius rate equation

x

CDJ

Composition ProfileFick’s Second Law

• Applications– Heat Treatment of Steels

– Plating and Metallic Coating

)2(

Dt

xerf

CCCC

os

xs

Diffusion and Material ProcessingGrain Growth

Diffusion and Material ProcessingDiffusion Bonding

Diffusion and Material ProcessingSintering

Solidification and Solid Solution Strengthening

• Mechanical properties of materials can be controlled by the addition of point defects, particularly substitutional and interstitial atoms.

• In addition, the introduction of point defects changes the composition of the material and influences the solidification behavior.

• Definition of a Phase– has the same structure or atomic arrangement throughout

– has roughly the same composition and properties throughout

– is a definite interface between the phase and any surrounding or adjoining phases

Illustration of Phases and Solubility

Unary Phase Diagram

Unlimited Solubility

• Regardless of the ratio of A and B, only one phase is produced by mixing them together.

• Example: Cu-Ni alloy system

Limited Solubility

• A is soluble in B, only one phase is found. However, if excess A is added to B and either A precipitates or A-B compound forms, then A has limited solubility in B.

• Example: Cu-Zn alloy system

Conditions for Unlimited Solid Solubility in Metals and Some Ceramics

• Atoms of the metals must be of similar size, with no more than a 15% difference in atomic radius.

• Metals must have the same crystal structure.

• Atoms of the metals must have the same valence.

• Atoms of the metals must have about the same electronegativity.

Solid Solution Strengthening

Effect of Solid Solution Strengthening

Isomorphous Phase Diagrams

Phase Compositions

Lever Law

Relationship Between Strength and the Phase Diagram

Equilibrium Solidification of a Solid Solution Alloy

Cooling Curve

Solidification Simulation

“Growth of Solutal Dendrites: A Cellular Automation Model and Its Quantitative Capabilities”, L. Beltran-Sanchez and D.M. Stefanescu, Metallurgical and Materials Transactions A, Volume 34A, Feb. 2003, p. 367-382

Nonequilibrium Solidification of Solid Solution Alloys

Effect of Nonequilibrium Solidification

• Microsegregation - centers of dendrites (typical growth condition) are rich in solute. Lower mechanical properties result. Effect reduced by homogenization heat treatment.

• Macrosegregation - similar to microsegregation but on a large scale. Effect reduced by hot working.

• Zone Refining

Effect of Freezing Range on Shrinkage