Elastic deformations are usually so small that delicate instruments are required in measuring them. Fig. 3 shows in bare principle several types of extensometers or extension-measurers; for more detailed in formation consult the works by Martens, John son and Unwin cited above, and also Morrow, 'Measurement of Strains' (in Proc. Inst. Mech. Eng., April 1904) ; Dalby's photographic ex tensometer is described in the references al ready given. In the direct form, Fig. 3, two brackets are clamped to the specimen bar at a fixed distance apart. The stretch of this length is found by noting the separation between the end of a micrometer screw on the upper clamp and the end of a fixed rod on the lower. In Ewing's extensometer the stretch is read through a small telescope focused on a scale at tached to the lower clamp; multiplying levers (not shown here) are used so that readings may be taken to a precision of one part in 50,000. The displacement of the end of the lever in Goodman's instrument is read on a circular scale. The form devised by Martens is ex tremely delicate and precise but correspondingly difficult to calibrate and to use. A double knife-edge carrying a mirror M is supported between the test piece and a stationary or idle rod; relative motion due to stretching tilts the mirror and the angular deflection of a ray of light reflected by it is measured on a scale. Several recording extensometers have been used but the best is that of Dalby.
Shape of Test Elastic properties and strength depend on the shape and size of the test specimen for several reasons. Local stresses due to clamps and grips have greater disturbing effects on small pieces than on large; rolling, machining, etc., produce a surface layer which, like the capillary film on liquids, has properties different from those within the material; blow-holes, minute cracks and par ticles of foreign substance are relatively larger in smaller specimens; stress tends to concen trate itself at corners, edges, abrupt changes in section and internal cavities so that in a test piece having such peculiarities it is difficult to learn what stress really acts; the planes or surfaces of separation between the molecular crystal groups which are known to exist in even the most homogeneous metals are oriented differently throughout the mass as a result of which two specimens cut from the same body show somewhat different properties. The differences which have been observed between the strengths of long and short round bars cut from the same stock are due largely to lack of homogeneity. Chaplin (in Van Nostrand's Engineering Magazine, December 1880 and in Proceedings Engineers Club, Philadelphia, March 1882) has calculated them by means of the theory of probabilities. It is evident, there fore, that tests give comparative results at best. The American Society for Testing Materials accordingly specifies a piece about 18 inches long and two inches in diameter, the middle nine inches being turned to a diameter of one and a half inches and the three cylinders thus formed running smoothly— without shoulders —into one another. The British Standards Committee recommends a cylindrical bar of a length equal to nine times its diameter, ex tension to be measured on a middle length of not less than eight diameters. Numerous ex periments, especially those by Bauschinger and Martens, have shown that the relations be tween shape and strength follow closely the law suggested by Barba (Memoirs de to Society des Ingenieurs Civil, 1880, I, p. 682) :
Under identical conditions geometrically similar bodies of the same material suffer similar de formations under the same stresses. 'Identical conditions' are difficult to realize in practice. An approximation to Barba's law will obtain if the ratio of the length of a bar to the square root of its section area is constant; a length of 20 to an area of would be convenient as a standard but is considered to be too expensive to prepare for use in commercial tests.
Stress-strain Diagrams.— Hooke's law is only a partial statement of stress-strain rela tions and sometimes does not apply at all. The behavior of wrought iron and structural steel under tension in the testing machine is ex hibited graphically in Fig 4 which is exag gerated in order to show characteristic peculiarities. Compression tests are not satis factory from a strictly scientific standpoint: long specimens tend to bend or buckle and in short blocks the local strains produced at the ends manifest themselves too strongly even when the compression plates are well lubricated — as they usually are not. Up to a certain point P stress is proportional to strain and the graph is a straight line of which the modulus E is the slope; the slope seems to be unaffected by cold-working the material whence Rosenhain concludes that E depends more on the nature of the atoms themselves than on their arrange ment. P is the proportionality limit and marks the point beyond which Hooke's law ceases to hold; the material may or may not be perfectly elastic within this region or beyond it. The limit of perfect elasticity—briefly, the elastic limit — depends on the accuracy with which small extensions can be measured and very largely on the previous history of the material. (Consult the discussion by Bairstow, Phil. Trans. Roy. Soc. 1912). For practical purposes P may be regarded as coincident with the elastic limit. At P, which of course is not a sharply marked point, the locus begins to curve downward until Y, the yield point, is reached; Y is always beyond the elastic limit. All the strains up to Y develop simultaneously with the stresses; beyond Y they do not attain their full values until considerable time has elapsed. This plastic flow or slow growth of strain under constant stress has been called by Ewing; when the stress is removed the strain creeps back but does not wholly disappear. This lagging in the diminution of strain is named hysteresis and belongs to the group of phenomena associated with the elastic after effect; see the reference above. Plastic flow occurs with hardly any increase of volume; during elastic strain the cross sections change according to Poisson's law. The serrated part of the curve, Y to A, occurs only in wrought Iron and mild steel; it indicates unstable re adjustments in crystal grouping. Real ductile distortion begins at A, and a waist of hour glass shape starts to form near the middle of the test piece. If the stresses are calculated by dividing the load by the original the curve runs through M to R the point of rupture. This gives nominal stresses; the actual stresses determined by using the actual area of section—must be computed as they cannot be plotted by automatic recorders.