Lecture 9 Strengthening mechanisms-I

Jayant Jain Assistant Professor,

Department of Applied Mechanics, IIT Delhi, Hauz Khas, 110016

Lattice defect is caused by introduction of an extra half plane of atoms Insertion of extra half plane has perturbed the lattice Dislocation line is defined as the edge of the half plane

Stress field around dislocation

Compressive stress field at top half of lattice Tensile stress field at bottom half of lattice

How to increase the strength??

There are mainly two strategies to strengthen the crystal/material: Completely remove dislocations difficult, but dislocation free Whiskers (crystals with high degree of perfection) have been produced Increase resistance to the motion of dislocations or put impediments to the motion of dislocations this can be done in many ways as listed in the next slide.

Strength

Dislocation density

0

G/2

Strength vs. Dislocation density

Alloying or Solid solution strengthening Grain size strengthening Work hardening Precipitation hardening

Key ways of improving the strength of material

Alloying

Alloys are stronger than pure metals

Have you thought about why they are stronger!!

Solid solution hardening

Foreign atom distort the host lattice and generate the stress

Compressive stress Tensile stress

Substitutional element of larger and smaller size than the host atom size

Interstitial or substitutional impurities cause lattice strain and interact with dislocation strain fields thereby hinder dislocation motion

Impurities diffuse and segregate around dislocation to find atomic sites more suited to their radii: Reduces strain energy + anchors dislocation 8

Smaller and larger substitutional impurities diffuse into strained regions around dislocations leading to partial cancellation of impurity-dislocation lattice strains.

Dislocation-Solute interaction

Brass: Strength increase with wt% Zn

Empirical relation: 21 /y C~

Example: Solid solution strengthening

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Grain size hardening

Grain boundaries are narrow zones where

the atoms are not properly spaced

Grain boundary acts as a barrier to slip: discontinuity in slip plane across the boundary By decreasing crystal size, we put more barrier in the path of moving dislocations thereby the strength should increase

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Grain size hardening

Grain size hardening

Reducing grain size means more barrier to slip

Decreasing grain size

not only increases strength but it also increases toughness of the material

where o and ky are constants for a particular material, d is the average grain diameter.

Hall-Petch equation - The relationship between yield strength and grain size can be

given as-

Hall-Petch relation

70 Cu - 30 Zn brass alloy

Decreasing grain size

Experimental Validation: Hall-Petch relation