4 - Strengthening Mechanisms for Metals

General Introduction

• AERO 481 Materials Engineering for Aerospace

• Primarily based on "Materials Science and Engineering: An Introduction" by Callister & Rethwisch.

Plastic Deformation and Dislocations

• To deform metals plastically, dislocations must move or be created.

• Engineering applications generally require alloys with:

  • High strength

  • Ductility

  • Toughness

• Strength and hardness are linked to the mobility of dislocations.

  • To reduce dislocation mobility:

  • Greater forces are necessary to cause dislocation motion leading to metal strengthening or hardening.

  • To increase dislocation mobility:

  • The metal becomes weaker or softer.

• Strengthening mechanisms for metals aim to restrict dislocation mobility.

Strengthening Mechanisms Overview

• Reduce Grain Size:

  • Grain boundaries act as barriers to dislocation motion.

Polycrystalline Materials and Grain Boundaries

• Grain boundaries are regions between grains (crystals).

• Features of grain boundaries include:

  • Crystallographic misalignment ^[1].

  • Slight atomic disorder.

  • High atomic mobility and high chemical reactivity.

  • They hinder dislocation motion.

Solidification and Grain Types

• Grains can be:

  • Equiaxed: Roughly the same dimension in all directions.

  • Columnar: Elongated in one direction, typically in regions with slower cooling.

• Rapid cooling leads to a shell of equiaxed grains due to significant temperature difference (ΔT).

• Grain refiners are added to produce smaller and more uniform equiaxed grains during solidification.

Mechanism 1: Reduce Grain Size

• Smaller grain sizes create more barriers to dislocation movement:

  • Slip planes change direction at grain boundaries.

  • Increased grain boundary area results in increased strength, yield strength, and hardness.

• Example: Dislocation pile-up against a grain boundary in 309 stainless steel.
  ![Micrograph example not included in notes]

Hall-Petch Equation

• The relationship of yield strength (𝜎𝑦) to average grain diameter (𝑑): $ext{𝜎𝑦} = 𝜎<em>{0} + k</em>{y} d^{-1/2}$

  • 𝜎_{0}: Material constant representing overall lattice resistance to dislocation movement.

  • 𝑘_{y}: Locking parameter (also a material constant).

• Implication: A fine grain structure results in a harder and stronger polycrystalline material, as dislocations must cross more grain boundaries, necessitating more stress for plastic deformation.

• Limitations: This equation is not valid for very coarse or very fine grain sizes.

Grain Size vs. Yield Strength

• Grain size vs. yield strength graph for a 70Cu-30Zn brass alloy demonstrates non-linear relationship: grain diameter increases from right to left.

• Smaller grain sizes typically correlate with higher yield strengths.

Effects of Grain Size Reduction

• Grain size reduction generally improves the strength and toughness of alloys.

• Small-angle grain boundaries are less effective in inhibiting slip processes.

• Twin boundaries can also enhance material strength.

• Phase boundaries play a significant role in restricting dislocation motion and strengthening complex alloys.

Methods for Controlling Grain Size

• Techniques include:

  • Encouraging grain formation during solidification from the molten state.

  • Rapid cooling can reduce grain size.

  • Grain refiners facilitate uniform grain sizes.

  • Controlled grain growth through recrystallization processes (to be discussed in future lectures).

Mechanism 2: Solid-Solution Strengthening

Definition of Solid Solutions

• Solid Solution: Atoms of element B dissolve homogeneously into element A, the host (solvent).

• Results in a single new phase, preserving the crystal structure of the host.

• Types of solid solutions include:

  • Substitutional (e.g., Cu in Ni)

  • Interstitial (e.g., C in Fe)

Lattice Strains due to Impurities

• Small Substitutional Impurities: Introduce tensile strains affecting adjacent dislocations.

• Large Substitutional Impurities: Imparts compressive strains that affect dislocations below the slip line.

• Concept:

  • Impurities cause partial cancellation of strains leading to a higher shear stress required for dislocation motion, contributing to solid solution strength.

Empirical Observations

• Alloying Cu with Ni enhances yield strength (𝜎𝑦) and tensile strength (𝑇𝑆).

• Empirical data indicates increases in both tensile strength (MPa) and yield strength (MPa) with varying wt% Ni.

• Ductility of the solid solution decreases as Ni concentration increases.

Mechanism 3: Strain Hardening

Definition and Process

• Strain Hardening: Plastically deforming metals at room temperature increases hardness and strength through interaction of dislocations.

• This process is also referred to as 'cold working.'

• Deformation is often reflected as a reduction in cross-sectional area.

• Amount of Deformation Equation:
  ext{%CW} = rac{A{0} - A{d}}{A_{0}} imes 100

Effects on Mechanical Properties

• As percentile cold work (%CW) increases:

  • Yield strength (𝜎𝑦) and tensile strength (𝑇𝑆) increase significantly.

  • Ductility (%EL or %AR) decreases.

• The deformation effects on yield and tensile strength are correlated and can be graphed.

Dislocation Density and Strengthening

• Dislocation density increases with cold deformation, and the distance between dislocations decreases.

  • Dislocation-dislocation interactions are primarily repulsive, hindering dislocation motion.

Practical Applications of Strain Hardening

• Commonly used to strengthen components during final manufacturing stages (e.g., cold rolling, stretching, bending).

• Relationship expressed in power law: $ext{𝜎}_{T} = K ext{𝜖}^{n}$

  • Variables:

  • K: constant

  • n: strain hardening exponent

Design Problem & Example of Cold Working

Procedure and Calculations for Diameter Reduction

1. The original diameter is 10 mm and intended to be reduced to 7.5 mm via cold drawing, maintaining a circular cross-section.

2. Desired properties after cold work:

   • Tensile strength > 380 MPa

   • Ductility > 15% EL

3. Calculate % cold work: ext{%CW} = rac{(D{o})^2 - (D{d})^2}{(D_{o})^2} imes 100

   • Using D{o} = 10 mm and D{d} = 7.5 mm results in %CW = 43.8%.

4. Values need to be evaluated for tensile strength and ductility. Adjustments may require multiple stages of cold work and annealing.

Mechanism 4: Precipitation Hardening

Concept

• Precipitation Hardening (age hardening): It refers to the process where dislocation movement is hindered by small precipitated particles.

• Important in specific alloy systems:

  • Al-Cu

  • Cu-Be

  • Mg-Al

• Achieved through applications of phase diagrams and controlled heat treatments.

Procedure for Precipitation Hardening

1. Heat to a designated temperature (T0), hold until the only α-phase is present.

2. Rapid quench to prevent diffusion and create a super-saturated solid solution (SSSS).

3. Reheat (T2) to enable diffusion, allowing fine precipitates to form which strengthen the material.

Microstructure Implications

• Coarse precipitates result from slow cooling, leading to weaker alloys. Conversely, close and small precipitates provide significant strengthening effects, as these precipitate particles serve as obstacles to dislocation motion.

Other Strengthening Mechanisms

Dispersion Strengthening

• Involves adding hard particles (often oxides) that obstruct dislocation movement.

• This mechanism is common in particle-reinforced composites, further explored in composite materials lectures.

Fiber Reinforced Composites

• Prominent and widely utilized composite materials framework, which will also be elaborated on in future lectures.

Martensitic Transformation

Definition and Eutectoid Reaction

• Martensite forms when steel undergoes rapid cooling from austenite (γ phase) where diffusion does not occur, causing atoms to be trapped.

• Eutectoid reaction leads to a transformation of austenite into pearlite under slow cooling conditions, while rapid cooling will yield martensite.

Martensite Characteristics

• Extremely hard but brittle; requires tempering to reduce brittleness while regaining some ductility.

• Tempering Process:

  • Involves heating martensitic steel to allow diffusion, reducing the residual stress and creating a rough microstructure containing small Fe3C particles within a ferrite matrix.

Summary of Transformations

• Austenite to Pearlite to Bainite to Martensite to Tempered Martensite.

• Strength and ductility can be optimized through strategic heat treatment cycles:

  • Cooling rate impacts microstructural characteristics and thus the mechanical properties of the steel.

Final Notes on Tempering Techniques

• The strength achieved by precipitation-hardened materials outweighs that of cold wrought steels, emphasizing the requisite optimization of processing techniques to balance properties such as ductility, strength, and toughness.