Downloaded from https://www.everyspec.com 0 STRUCTURES where T. is a reference temperature. The efficient of linear expansion. Coefficients of uvit elongailM can be easily calculated after thermal expansion for some engineering ma- . is computed arid plotted ws a function of terials are given in the tables and graphs at temperature from the end of this chapter. e=a-=. 1.) (2 12) If the unit elorgation is required for a tern- 2-4. SELECTED DATA ON PROPERTIES OF perature rise other than from the reference MATERIALS OF CONSTRUCTION temperature, say T, to T., then Collected in the pages that follow are :
a,..(T..- 1.) - a,,,(T - '') selected data on material properties pertinent (2 13) to missile design. Data are included on ma- Consider the case of a slender rod of origi- terials that appear to have promise for appli- nal length 4.,, heated to a temperature T, cation in designs of the future. These data from a reference temperature value T., The have been gleaned from a number of refer- increase in the length of the rod due to the ences which are listed in the bibliography. effects of thermal expansion is required. One of the principal reasons for collecting Taking T, - T,.
= T = 100 0 F as the tern- the information has been to give the reader a perature rise, L,, = 1 ft, and assuming L, quantitative feeling for the order of magni- for the material ha i value of 10 - 7-, the unit tude of the physical properties involved. in elongation from (2-12) is sore instances, the variations in these physi- cal properties for different alloys of the same The e a of -he rod'~) is 10-~ 1material are presented, but this is not con- The elongation of the rod is AL L. = 10 - 2 ft (2-14) sidered of paramount interest.
In addition to It might be well to point out the implicit the objetive mentioned, th curves are set I assumption that the rod is not subject to any up to afford an easy comparison between one external oastraint. If the rod is constrained material and another, The frequency with extrna ~~isrants I th ro i coisraied which~ time and temperature appear as pa- to remain at its original length, then the temperature rise would produce normal rameters may be noted. Another objective in the presentation of stresseqire te rodcesanpeqondi top- the data is to point up the form of presenta- stress required to produce an equal and op- tion which finds favor with the missile de- posite unit elongation.
The value of this tion w nd s avoryth th m isilces (thermal) stress is obtained by multiplying signer and stress analyst. in many instances the unit elongation by Young's Modulus: datc of a particular kind are shown only for one alloy of one material. This is particularly a = Ee (2-15) true in the graphical presentation of creep Hence if Young's Modulus for t1be rod used data, and stress-strain and tangent modulus in the above example is 107 psi, the stress curves as functions of temperature. can easily be calculated:
Tables 2-1 through 2-5 cover several alloys = 101(10 - 1) = 10,000 psi each of steel, aluminum, titanium, magne- Partial restraints at the ends of the rod pro- sium, and a few ceramics. In this compilation duce thermal stresses which are between the the room temperature mechanical properties Values of zero thermal stress for unre- are given for each alloy and for a selected strained ends and the thermal stress calcu- form and condition. Young's Modulus, yield lated above for fully restrained ends. and ultimate strengths are presented on the Expansion of the rod in the lateral direc- basis of tensile test data. The yield stress is tions may be calculated in a similar manner.
based upon a 0.2%. permanent offset condi- The coefficient of thermal expansion is usu- tion. The elongation is the percent change in ally assumed to be independent of direction. length measured over 2 inches of a test Since most engineering material3 can be con- specimen. sidered isotropic, the assumption is fairly Table 2-6 summarizes the physical prop- good. The quantity a is also called the co- erties of various materials: density, melting 16