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Section 4 Behaviour of Materials The section will cover the behaviour of materials by introducing the stress-strain curve. The concepts of elastic and plastic deformation will be covered. This will then lead to a discussion of the micro-structure of materials and a physical explanation of what is happening to a polycrystalline material as it is loaded to failure. ©  Loughborough University 2010. This work is licensed under a  Creative Commons Attribution 2.0 Licence .
Contents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Introduction ,[object Object],[object Object],[object Object]
Elasticity ,[object Object],[object Object],[object Object],Elastic limit   Loading Unloading E
Plasticity ,[object Object],[object Object],[object Object],[object Object],[object Object],Elastic limit   Loading Unloading E Point of yielding  y
Elastic-Plastic Stress-Strain Relationship ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Elastic-Plastic Stress-Strain Curves Low / Medium Carbon Steels Aluminium Alloys and Alloy Steels  ult  = Ultimate Strength  YU  = Upper yield point  YL  = Lower yield point  pr  = Proof stress   0.1% 0.2% 0.1%   pr 0.2%   pr  ult Limit of Proportionality    YU  YL  ult E Strain Hardening Necking
Secant and Tangent Modulii ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],   1  2
Unloading Modulus and Plastic Strain ,[object Object],[object Object],[object Object], p  e   0.1%   pr E sec
Example 4.1 ,[object Object],Answer: (i)   y =89 MPa (ii)   ult =127 MPa (iii)   p =9.94%
True Stress and Strain ,[object Object],[object Object],[object Object]
True Stress-Strain Curve   Onset of necking True Stress-Strain Curve Corrected for complex stress state in the neck region Engineering Stress-Strain Curve A true P x P x P x P x A
Constant Volume Concept ,[object Object],[object Object],[object Object],[object Object]
True Stress and Strain Relationships ,[object Object],[object Object],[object Object]
Ductility Index ,[object Object],[object Object]
Example 4.2 ,[object Object],Answer: (i)   true =519 MPa,   true =0.0198 (ii) d´=4.95 mm (iii) q=1.93%
Imperfections in Solids ,[object Object],[object Object],[object Object],[object Object],BCC FCC HCP
Line Defects or Dislocations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Edge Dislocations Stress Stress Stress Stress Stress Stress Slip plane Burgess vector, b
Screw Dislocations ,[object Object],[object Object],Burgess Vector Dislocation Line
Point Defects ,[object Object],[object Object],[object Object],Vacancy Interstitial Substitutional
Dislocation Movement and Strain Hardening ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Strain Hardening (cont.) (a) Edge dislocations arranged side-by-side (b) Opposing Edge dislocations Tension region Slip plane Compression region Slip plane
Microscopic Interpretation of Elastic-Plastic Stress-Strain Relationship ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],   YU  YL  ult E Strain Hardening Necking O C B A
Hardness ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Brinell Hardness Test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],D d P
Vickers Hardness Test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],d P L L
Rockwell Hardness Test ,[object Object],[object Object],[object Object],[object Object],[object Object]
Comparison of Hardness Scales ,[object Object],BHN  (10mm dia. and 300 kg force) VHN R c   (150 kg Force)  ult   (MPa) 496 465 433 397 360 322 284 247 209 540 500 460 420 380 340 300 260 220 51.7 49.1 46.1 42.7 38.8 34.4 29.8 24.0 - 1792 1655 1517 1379 1241 1110 972 834 696
This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme. © 2010 Loughborough University. Except where otherwise noted this work is licensed under a  Creative Commons Attribution 2.0 Licence .  The name of Loughborough University, and the Loughborough University logo are the name and registered marks of Loughborough University. To the fullest extent permitted by law Loughborough University reserves all its rights in its name and marks, which may not be used except with its written permission. The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence.  All reproductions must comply with the terms of that licence. The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher. Credits

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Structures and Materials- Section 4 Behaviour of Materials

  • 1. Section 4 Behaviour of Materials The section will cover the behaviour of materials by introducing the stress-strain curve. The concepts of elastic and plastic deformation will be covered. This will then lead to a discussion of the micro-structure of materials and a physical explanation of what is happening to a polycrystalline material as it is loaded to failure. © Loughborough University 2010. This work is licensed under a Creative Commons Attribution 2.0 Licence .
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  • 7. Elastic-Plastic Stress-Strain Curves Low / Medium Carbon Steels Aluminium Alloys and Alloy Steels  ult = Ultimate Strength  YU = Upper yield point  YL = Lower yield point  pr = Proof stress   0.1% 0.2% 0.1%  pr 0.2%  pr  ult Limit of Proportionality    YU  YL  ult E Strain Hardening Necking
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  • 12. True Stress-Strain Curve   Onset of necking True Stress-Strain Curve Corrected for complex stress state in the neck region Engineering Stress-Strain Curve A true P x P x P x P x A
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  • 19. Edge Dislocations Stress Stress Stress Stress Stress Stress Slip plane Burgess vector, b
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  • 23. Strain Hardening (cont.) (a) Edge dislocations arranged side-by-side (b) Opposing Edge dislocations Tension region Slip plane Compression region Slip plane
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  • 30. This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme. © 2010 Loughborough University. Except where otherwise noted this work is licensed under a Creative Commons Attribution 2.0 Licence . The name of Loughborough University, and the Loughborough University logo are the name and registered marks of Loughborough University. To the fullest extent permitted by law Loughborough University reserves all its rights in its name and marks, which may not be used except with its written permission. The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence.  All reproductions must comply with the terms of that licence. The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher. Credits