Post on 19-Dec-2015
description
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