432 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1964 



process of separation can take a variety of forms : A rubbery material 

 elongates enormously before tearing; metals often deform before 

 breaking (ductile fracture) ; glass fractures with little previous de- 

 formation (brittle behavior) ; and crystals frequently cleave along 

 definite crystallographic planes. It is important to realize that a 

 given material does not fall into a specific class regardless of the con- 

 ditions in which it is used. A rubbery solid, for example, if taken to 

 a low enough temperature, will fracture in a brittle fashion, and metals 

 show similar temperature transitions from ductile to brittle behavior. 

 A factor as important as temperature is the time taken in applying the 

 stress to the material. If the stress is applied in a short time (i.e., a 

 high rate of strain) the effect is analogous to that of decreasing the 

 temperature of the body. The variation of behavior with strain rate 

 is readily apparent with polymers such as Perspex. If a steel ball 

 is pressed slowly against the surface the material deforms to give a 

 permanent depression. If, however, the ball is allowed to fall from a 

 height of a few inches, a circular ring fracture similar to those pro- 

 duced on glass is formed. 



STRENGTH OF SOLIDS 



Theoretical calculations of strength are usually based on the way 

 that the forces between the atoms vary with separation. Usually the 

 maximum force occurs when the separation between the atoms has 

 been increased by 10 to 20 percent, or in other words, the theoretical 

 strengths of solids lie between E/^ and -fi'/lO, where E is the Young's 

 modulus of the solid. However, one of the more striking features 

 about the strength of solids is the divergence between practical meas- 

 ured strengtlis and theoretical estimates: This divergence is greatest 

 with brittle solids. Calculations on glass, for example, predict 

 strengths as high as 2 million p.s.i., but plate glass has usually a 

 strength only about one-hundredth of this and even glass in fiber form 

 rarely exceeds one-tenth of the theoretical estimate. 



A possible explanation for the low practical strengths was put for- 

 ward in 1920 by A. A. Griffith, who suggested that microcracks on the 

 surface and in the bulk of a solid could cause loss of strength. A 

 useful analogy here is to imagine the cracks acting as levers to separate 

 the atoms, the cracks becoming more effective the longer their lengths. 

 Griffith, in experiments on glass, was able to show that the strength 

 was in fact related to the depths of cracks which he artificially added 

 to the glass. 



The size of the microcracks sufficient to explain a practical strength 

 for glass of 20,000 p.s.i. when its theoretical strength is 100 times higher 

 turns out to be very small; cracks of length 1 or 2 microns (10~*cm.) 

 and widths of a few angstroms (lA=10"^cm.) are sufficient. It is not 

 surprising, therefore, that even with modern electron microscopes 



