- 8.2 STRENGTH OF PLASTICALLY DEFORMED MATERIALS / 8.3 8.3 ESTIMATING ULTIMATE STRENGTH AFTER PLASTIC STRAINS / 8.4 8.4 ESTIMATING YIELD STRENGTH AFTER PLASTIC STRAINS / 8.8 8.5 ESTIMATING ULTIMATE STRENGTH OF HEAT-TREATED. - 8.6 ESTIMATING ULTIMATE STRENGTH OF HEAT-TREATED LOW-ALLOY STEELS / 8.11. - S u Engineering ultimate strength in tension S y Engineering yield strength, 0.2 percent offset t Time. - The designer needs to know the yield strength of the material at the critical location in the geometry and at con- dition of use.. - It also examines the changes in ultimate strength in heat-treated plain carbon and low-alloy steels.. - 5-35) and surface, ultimate strength can be assessed. - The important strength is that of the part in the critical location in the geometry and at condition of use.. - The sense of the strength: tensile, t. - The direction or orientation of the strength: longitudinal, L. - The sense of the most recent prior strain in the axial direction of the envisioned test specimen: tension, t. - A strength (Su) tLc would be read as the engineering ultimate strength S u , in tension. - In a round e w = max(le r l, Ie 9 I, Ie x I).The largest absolute strain. - Table 8.1 summarizes the strength relations for plastically deformed metals.. - Find, using Datsko's rules, an estimate of the ultimate strength in a direc- tion resisting tooth bending at the root of the gear tooth to be cut in the blank.. - TABLE 8.1 Strength Relations for Plastically Deformed Metals f. - In the first step (cold rolling), the largest strain is axial, and it has a magnitude of (rule 3). - The endurance limit and the ultimate strength resisting tensile bending stresses are (S e. - The endurance limit and the ultimate strength resisting compressive bending stresses are (S' e ) cTt and (S u ) cTt , namely kpsi and 118.5 kpsi, respectively (group 4 strengths). - TABLE 8.2 Summary of Ultimate and Yield Strengths for Groups 1 to 4 for Upset Pinion Blank. - 118.7 kpsi Table 8.2 summarizes the four group strengths.. - Yielding will commence at the weaker of the two strengths. - They give the sense (improved or impaired) of the strength change and a prediction of variable accuracy. - A1040 steel has a ladle analysis as shown in Table 8.3 and a Jominy test as shown in Table 8.4. - The Jominy distance numbers are sixteenths of an inch from the end of the standard Jominy specimen. - TABLE 8.3 Ladle Analysis of a 1040 Steel Element C Mn P S Si Percent . - TABLE 8.4 Jominy Test of a 1040 Steel. - Table 8.5 displays the sequence of steps in esti- mating the softening due to tempering at each Jominy distance of interest.. - A shaft made from this material, quenched in oil (H = 0.35) 1 and tempered for 2 hours at 100O 0 F would have surface properties that are a function of the shaft's diameter. - This means an as-quenched hardness of about 15.9 and a surface ultimate strength of about 105.7 kpsi. - Similar determinations for other diameters in the range 0.1 to 4 in leads to the display that is Table 8.10. - A plot of the surface ultimate strength versus diameter from this table provides the 100O 0 F contour shown in Fig.. - f The quench severity H is the ratio of the film coefficient of convective heat transfer h [Btu/(h-in 2 -°F)]. - to the thermal conductivity of the metal k [Btu/(h-in-°F. - 8.14 as a function of per- cent carbon and grain size of the steel.. - Determine the surface properties of an 8640 steel with average grain size 8 that was oil-quenched (H = 0.35) and tempered 2 hours at 100O 0 F The ladle analysis and the multiplying factors are shown in Table 8.11. - TABLE 8.5 Softening of 1040 Round Due to Tempering at 100O 0 F for 2 Hours. - The ratio of initial hardness (distance 1), denoted IH, to distant hardness (at any other Jominy distance), denoted DH, is available as a function of the ideal critical. - For the 8640 steel the Jominy hard- nesses are estimated as displayed in Table 8.12. - FIGURE 8.12 Variation of surface ultimate strength with diameter for a 1040 steel oil- quenched (//-0.35) from 1575 0 F and tempered 2 hours at 100O 0 R. - SURFACE ULTIMATE STRENGTH S y, kpsi. - TABLE 8.6 Equivalent Jominy Distances for Quenched Rounds at rlR = 1. - TABLE 8.7 Equivalent Jominy Distances for Quenched Rounds at rlR = 0.8. - TABLE 8.8 Equivalent Jominy Distances for Quenched Rounds at rlR = 0.5 Severity of quench //,in". - Table 8.13 shows the tempered hardness and ultimate strength corresponding to the Jominy distances.. - The surface ultimate strength can be estimated for diameters and 4 in. - The surface ultimate strength as a function of diameter of round is displayed in Table 8.14. - The tensile ultimate strength at the surface versus diam-. - TABLE 8.9 Equivalent Jominy Distances for Quenched Rounds at rlR = O Severity of quench //,in". - TABLE 8.10 Surface Ultimate Strength of a 1040 Steel Heat-Treated Round as a Function of Diameter 1. - Note the greater hardening ability of the 8640 compared to the 1040 steel of the previous section. - An estimate of the variation of properties across the section of a round 4 in in diameter will be made. - Thus Table 8.15 may be formed. - TABLE 8.11 Ladle Analysis and Multiplying Factors for 8640 Steel, Grain Size 8. - In addition, the designer needs to know the properties of the critical location in the geometry and at condition of use. - These methods have produced for a 4-in round of 8640, quenched in oil (H = 0.35) from 1575 0 F, and tempered for 2 hours at 100O 0 F, the property estimates displayed as Table 8.16. - Reference [8.6] is a circular slide rule implementation of the multipli- cation method of Grossmann and Fields.. - Probabilistic ele- ments of the predicted Jominy curve are addressed in Ho [8.9].. - TABLE 8.12 Prediction of Jominy Curve for 8640 Steel by Multiplication Method of Grossmann and Fields. - TABLE 8.13 Tempered Hardness and Ultimate Strength at Jominy Distances Due to Softening after Tempering 8640 Steel 2 Hours at 100O 0 F. - TABLE 8.14 Surface Ultimate Strength of 8640 Steel Tempered for 2 Hours at 100O 0 F as a Function of Diameter of Round. - TABLE 8.15 Ultimate and Yield Strength Traverse of a 4-in- Diameter Round of 8640 Steel Tempered 2 Hours at 100O 0 F. - FIGURE 8.20 Variation on surface ultimate strength for 8640 steel oil-quenched (H = 0.35) from 1575 0 F and tempered for 2 hours at 100O 0 F as a function of diameter of round.. - FIGURE 8.21 Variation in surface ultimate strength across a section of a 4-in round of 8640 steel oil-quenched (H = 0.35) from 1575 0 F and tempered for 2 hours at 100O 0 F as a function of radial position.. - TABLE 8.16 Summary of Strength and Hardness Estimates for a 4-in Round of 8640 Steel Quenched in Oil (H = 0.35) from 1575 0 F and Tempered 2 Hours at 100O 0 F. - Property Estimate Surface hardness 270 Brinell Surface ultimate strength 135kpsi Surface yield strength 110.8 kpsi Surface R. - Moore endurance limit 67.5 kpsi Contact endurance strength (QAH kpsif Central hardness 239.6 Brinell Central ultimate strength 119.8 kpsi Central yield strength 89.9 kpsi. - It is possible to program the digital computer to give mean values of the ultimate strength predictions [8.1O]. - An example of a computer-generated worksheet is dis- played as Table 8.17. - For Jominy distances 1 to 32, the Rockwell C-scale hardness is displayed as an ultimate strength as a function of the 2-hour tempering temperature in both IPS and SI units. - For this 1340 steel we can expect for a still-oil quench (H = 0.35) that is tempered 2 hours at 100O 0 F a sur- face ultimate strength on a 3-in round of 121.4 kpsi.The standard deviation is largest at Jominy Station 8 and is about two points on the Rockwell C scale [8.9].. - TABLE 8.17 Computer-Generated Worksheet, CADET Program HTTREAT HEAT TREATMENT UORKSHEETt 1340 STEEL» GRAINSIZE 7*0. - HARDENABILITY DATA FOR TWO HOUR TEMPERING EXPRESSED AS ULTIMATE STRENGTH JOM JOM 40OF 60OF 80OF 100OF 120OF JOM 20OC 30OC 40OC 50OC 60OC STA RC KPSI KPSI KPSI KPSI KPSI RC MPa MPa MPa MPa MPa. - O LOCAL ULTIMATE STRENGTH (KPSI) IN 100OF TEMPERF.U RQUNTiS. - if(fans.eq.'y'.or.fans.eq.'Y')iflag=!. - if(fans.eq.'n'.or.fans.eq.'N')iflag=2 if(iflag.eq.O) go to 1. - if(iflag.eq.l) then write(*,601). - print*,'Enter engineering ultimate strength Su in kpsi' read*,Suo. - If(index.eq.l)Print*,'Enter exponent m' if(index.eq.1)read*,m. - if(index.eq.1)go to 11 m=0.1. - if(iflag.eq.1)open(unit=6,file=filnam,status='new',err=987) if(iflag.eq.l)write(6,899)DAY. - 899 formate CADET Program COLDWORK, Method of Datsko',9X,'DATE:',A9) if(iflag.eq.l)write(6,50)(ew(i),i=l,j). - if(equ(l).le.m)Su(l)=Suo*exp(equ(l)) i f(equ(1).gt.m)Su(1)=sigmao*equ(1)* *m if(k.eq.l.and.equ(l).gt .m) write (*,901). - i f(k.eq.1.and.equ(1).gt.m.and.i f1ag.eq.1)wri t e formatC PRESENCE OF BENDING REQUIRES CRACK TESTS!'). - IF(IFLAG.EQ.1)WRITE(6,902). - if(iflag.eq.l)write(6,17)icount,equ(1),Su(I),eqy(l),Sy(I) write(*,17),icount,equ(1),Su(I),eqy(l),Sy(I). - if(iflag.eq.l)write(6,17)icount,equ(2),Su(2),eqy(2),Sy(2) wri te(*,17),icount,equ(2),Su(2),eqy(2),Sy(2). - if(iflag.eq.l)write(6,17)icount,equ(3),Su(3),eqy(3),Sy(3) write(*,17),icount,equ(3),Su(3),eqy(3),Sy(3). - if(iflag.eq.l)write(6,19)icount,equ(4),Su(4),SytTc write(*,19),icount,equ(4),Su(4),SytTc. - 19 format(2x,12,2x,F5.3,2x,F5.1,9x,F5.1) if(iflag.eq.l)write(6,904). - if (iflag.eq.l)write(6,25)iabc write(*,25),iabc. - if(iflag.eq.l)write(6,905)Syo,offset,Suo write(*,905),Syo,offset,Suo. - Suo=',f6.1,' kpsi') if(iflag.eq.l)write(6,916)AR. - F5.2) if(iflag.eq.l)write(6,906)epsif. - if(iflag.eq.l)write(6,907)sigmao write(*,907),sigmao. - is sigmao =',f6.1,' kpsi') if(index.eq.1.and.iflag.eq.l)write(6/ 908)m. - if(index.eq.l)write(*,908) ,m. - 908 format(' Strain-strengthening exponent is m =',f5.2) if(index.eq.2.and.iflag.eq.1)write(6/909 )m. - if(index.eq.2)write(*,909) ,m. - if(iflag.eq.l)print*,'Output in directory under name. - Ho, "Probabilistic Prediction of the Jominy Curve of Low Alloy Steels from Com- position and Grain Size,"
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