Notes on Deformation of Metals

Metallic and Ceramic Biomaterials: Deformation of Metals

Lecture Overview

• Instructor: Lukasz Witek MSci, PhD

• Course: Biomaterials Division at NYU Dentistry

• Focus: Understanding the deformation of metals, specifically through mechanisms such as slip and dislocations.

Deformation Fundamentals

• Definitions:

  • Brittle Material: A material that exhibits little to no plastic deformation before fracture.

  • Ductile Material: A material that can undergo significant plastic deformation prior to fracture.

Types of Deformation

• Plastic Deformation:

  • Method of fabrication that allows the permanent change of shape.

  • Techniques include rolling, forging, drawing, and extrusion.

• Mechanical Behavior:

  • Deformation can be beneficial for shaping and strengthening metals.

  • Involves processes like cold working where components are shaped while simultaneously being strengthened.

Slip Mechanism

• Definition: Slip is the mechanism by which plastic deformation occurs in metals.

• Dislocations: Defects in the crystal structure that facilitate slip at lower stresses than required for perfect crystalline materials.

  • They are linear defects in metals, which allow for easier deformation.

Characteristics of Slip

• Atomic Planes:

  • Slip occurs when planes of atoms in a metal structure move over each other, typically along close-packed planes.

• Grain Boundaries: Act as obstacles to dislocation movement, affecting the material's overall ductility.

Dislocation Properties

• An edge dislocation is represented as an extra half-plane of atoms within the material.

• The motion of dislocations allows for slip to occur at lower applied stresses.

Factors Affecting Slip

• Metals with face-centered cubic (FCC) structures possess more slip systems (12 slip systems) compared to hexagonal close-packed structures (3 slip systems), explaining their higher ductility.

Relationships & Implications

• Slip and Plastic Deformation: They are directly related, with slip providing the mechanism for deformation to occur.

• Dislocations Provide Ductility: A material can be strengthened by making dislocation motion more difficult through methods such as decreasing grain size and solid solution strengthening.

  • Examples of materials: Cu, Al, Au (ductile) vs. Zn, Ti, Mg (less ductile).

Strengthening Mechanisms for Metals

1. Grain Size Reduction:

   • Formula: $\sigma<em>{yield} = \sigma</em>0 + k y d^{-1/2}$

     • Where $d$ is the grain diameter.

2. Solid Solution Strengthening:

   • Impurity atoms distort the lattice and induce stress, creating barriers to dislocation movement.

   • Impurities affect local shear, which opposes the dislocation motion.

3. Precipitation Strengthening:

   • Involves adding hard precipitate particles in the metal matrix that impede dislocation movement.

   • Allows for increased yield strength represented as: $\sigma_y \sim \frac{1}{S}$

     • Where $S$ is the size of precipitates present.

   • Example application: Aluminum is strengthened in Boeing 767 by alloy precipitates (size: 1.5 µm).

4. Cold Work (CW):

   • Room temperature deformation that modifies the cross-sectional area of materials, significantly affecting their mechanical properties.

   • Calculated using the formula: $\%CW = \frac{A<em>0 - A</em>d}{A_0} \times 100$

     • Where $A<em>0$ is the original area and $A</em>d$ is the deformed area.

Impact of Cold Work

• Effects:

  • Increases yield strength and tensile strength of metals but decreases ductility.

  • Dislocation density increases, leading to entanglement and restricted motion further increasing hardness.

Recovery & Recrystallization

• Recovery: Annihilation of dislocations through diffusion reduces dislocation density, allowing for some recovery in ductility.

• Recrystallization Process:

  • Formation of new, dislocation-free grains at elevated temperatures promotes softening of previously cold-worked metals.

  • Leads to significant changes in grain structure over time.

  • Research shows that cold-worked brass can nucleate new crystals in seconds at given temperatures (580 °C).

Grain Growth

• Over longer periods, larger grains consume smaller ones to minimize grain boundary area thus reducing energy.

• Empirical relation represented as: $d^n - d_0^n = Kt$

  • Where $d$ is grain diameter at time $t$, $K$ is a coefficient dependent on material and temperature.

Summary

• Metal deformation is influenced by dislocations, slip mechanisms, and various strengthening strategies like grain boundary manipulation and alloying techniques.

• Understanding these principles is essential for advanced materials engineering and the design of durable metallic structures in applications such as aerospace and construction.

Weekly Notes

• Homework: Upcoming homework due via NYU Brightspace.

• Next Lecture: February 25, 2026 - Preparation for advanced applications and implications of dislocation theory in modern engineering.