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MATS1101 Materials Strand/MATS9520

Ashby & Jones, Volume 1, Chapter 9 Ideal Strength of Materials Last week we saw that the slope of the interatomic force-distance curve at equilibrium spacing is proportional to Young's Modulus, E. Interatomic forces become negligible for r > 2r0.

~2Fmax Fmax


r0 2r0






Figure 8 Interatomic force-distance curve

The maximum in the force-distance curve occurs at ~1.25r0, (where F = Fmax). If applied stress is greater than Fmax per bond, bonds between atoms are broken and fracture occurs. Ideal strength, , corresponds to bond rupture at Fmax. Calculation of ideal strength:

 

Slope E
 


r0 2r0


Figure 9 Ideal Strength  ~ From the force-distance curve, where r = 1.25r0,  = 0.25 and   2  is ideal strength).

 Copyright School of Materials Science and Engineering, UNSW, 2012.


~ 2 0.25

~ 

E 8 ~  E 15 E 15

A better estimate using interatomic potential gives

Glasses and some ceramics have a yield strength of For other ceramics and polymers, For metals,

y 

 y  10 1 
E 15

E 15

 y  10 1  10 5  

Actual vs Ideal Strength
10-1 10-2 10-3
Cement (nonreinforced

Silica glass Diamond Soda glass SiC Al2O3, Si3N4 MgO, ice Alkali halides


Low density PE Epoxies PP, PMMA High density PE Nylons Polyimides Foamed polymers


Ti alloys Low-alloy steels Stainless steels Carbon steels Al alloys Cu alloys Mild steel Pb alloys Commercially pure metals

BFRP Reinforced concrete GFRP’s Woods CFRP Cermets

10-4 10-5

Ultra-pure metals



Bar chart of data for normalised yield strength, y/E

Figure 10 Normalised yield strength

From the bar chart in Figure 10, glasses and some ceramics show strengths close to their ideal strength. Polymers are also close to their ideal strength - although their strength is low, their modulus is also low. Why is y

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