Art. 22 



DUCTILITY AND PLASTICITY. 



23 



point. Timber and brittle materials like hard steel, cast iron, 

 and stone, do not have a yield point, and for them the limit of 

 proportionality is determined from stress-deformation diagrams. 

 The vertical ordinates of the stress-deformation diagram 

 measure the unit stresses accompanying the deformations meas- 

 ured by the corresponding absiccas. Thus EE' is the unit stress 

 when OE' is the unit elongation. AA' is the unit stress at the 

 elastic limit, and this is what is usually meant by the elastic 

 limit; OA' is the corresponding elongation. It will be observed 

 that the elastic deformation is very small part of the total OD ' 

 CC' is the ULTIMATE STRENGTH or maximum unit stress shown in 

 the test ; it is not the unit stress at the point where rupture takes 

 place. DD' is the unit stress just before rupture takes place; this 

 is less than the ultimate strength because the area of the cross 

 section of the test piece decreases. The stresses in the diagram 

 are per unit of original area which is what the engineer wants. 

 The actual intensity of stress increases up to the point of 

 rupture 1 . 



Since E = ^-, the tangent of the ans^le which A makes with 

 o 



OD' represents the modulus of elasticity. Since the elastic 

 resilience per unit volume is equal to y 2 s 8 (19), it is represented 

 by the area of the triangle OAA'. The total resilience per cubic 

 inch is represented by the area of OABECDD', and is approxi- 

 mately AA'XOD'+% (CC f AA') OD/ 



Testing machines are sometimes fitted with appliances for 

 automatically drawing stress-deformation diagrams 2 . 



22. Ductility and Plasticity. After the yield point is 

 passed (Fig. 15), the metal seems to harden, and it again requires 

 an increase of stress to increase the deformation, but a given 

 increase of stress will produce a much greater elongation (time 

 being a factor) than when the stress is below the elastic limit. 

 The deformation is now chiefly permanent, and the test piece is 

 more or less uniformily elongated throughout its length, and its 

 cross section is diminished ; it is very ductile. 



When the ultimate strength is reached, a local contraction 



iUnwin's The Testing of the Materials of Construction, or Good- 

 man's Mechanics Applied to Engineering. 



2 For complete tensile and compressive stress-deformation diagrams 

 of steel, iron, cast-iron, and timber see Johnson's Materials of Construc- 

 tion. Chapter II, or Johnson's Modern Framed Structures, Chapter VIII. 



