Downloaded from https://www.everyspec.com PROPERTIES OF MATERIALS dx du i . - -[d- ~~dx dyj L (a) NORMAL STRAIN du SHE.A STRAIN -. I dx =dx Figure 2-2. Disfortion of an Elernenst by Nos-mal vdSIear Strains 2-1.2. Propart'onal Limit. Notwithstanding spring constant or Young's Modulus can be the relotively simple nature of" the test that assumed to be independent of both pesition yields the stress-strain curves of Figure 2-1, and direction within the material. Clearly, some of the most useful and basic properties there0vre, this one physical property is of of the material are deduced from it.
It will be major importance to the structural designer noted that both curves exhibit an initial when the design criterion is a rigidity linear relationship between stress and strain, requirement. The value of the stress corre-sponding to the 2-I.4. Y'ield. Consider a simn!;'e tensile end of this linear relationship is called the specield. Conde a im i te ~rroortina hmt. rovied he tresesye- specimen loaded beyond the elastic limit to proportional lim it. Provided the stresses re- a s r s o r -p n i g t o n n F g main below thel , a stress corresponding to point B in Fi- rial remains elastic, i.e., it assumes its origi- ure 2-1a.
Upon the reo d of the load, the nal shape upon the removal of the load. stress decr;ses approximately linearly with Further, the material is linearly elastic. It strain as illustrated by line BC because only Furter, he mteril i linarlyelasic.i ne elastic part of the deformations can be might be well to point out that in reality, t nereaic par t e tiosc n e mateialcanbe sresed bovethe~i~or- regained. A permanent set is observed when material can be stressed above the r-opor- tionai limit and still remain elastic. However, the load is completely removed. The unload- for most engineering materials, the propor- ing line BC is approxi.:
ely parallel to the straight line OA whose slope is equal to tional and elastic limits are relatively close s lus. O f he sltei e pr -o each other and are in fact frequently used Young's Modulus. If the miaterial were per. interchangeably by engineers. fectly elastic, it would have unloaded along the original loading line OAB. For materials 2-1.3.. Young's Modulus. The slope of the whose stress-strain curve has the charocter- stress-strain curve, that is the rate of change istics shown in part (a) of tne figure, t:p of the stress with increasing strain in the yield strpss ii defined that value of the linear region is calied Young's Modulus.
stress c.arre.ipwndirg to an offnet, c,, of 0.002 Physically, it may be considered a spring -ur materials whose -tress-strain curves are constant because Young's Moduius is propor- similar to that shown in part (b) of the fig- tional to the force per unit elongation. ure, the first point of horizontal tangency is Although the stress-strain curve gives the taken as the yield point. value of the spring constant in only ornu di- rection, most engineering material, Are fairly 2-1.5. Ultimate Stress. The maximum value homogeneous and isotropic, and hence the of the stress reached in the simple tensile 9