REG NACA-TN-2073-1950 Stress and Strain Concentration at a Circular Hole in an Infinite Plate.pdf

1、bthe ayparent discrepancyis probably due in part to thePeculiarities of the stress-straincurve, which permit a slight errorin stress to be enormouslymagnified in strain, and in part to the useof 1/2 for Poissonls ratio.In order to compare the distributionof strain and stress given bythe formulas of

2、this yaper with measured distributions,figures j and 4have been yreyared. Figures 6 and 8 of reference 1, which represent themeasured distrilxztionsof strain and stress perpendicular to the directionof the tension, have been reproduced herein as figures 3 and 4, respec-tively, with the addition of c

3、irculsr points to represent computedvalues at three different stress levels (am = 21, 30, and 37 ksi,corresondingto the net-section-stresslevels of av = 253 35j0and 45 ksiof reference 1) For the strain distribution (fig. 3), the computedpointsed - - . .Provided by IHSNot for ResaleNo reproduction or

4、 networking permitted without license from IHS-,-,-NACA TN 2073 . . .- 3.agree with the measured curves at the hole and at a large distance awayfrom it but fall appreciablybelow the curves between these two places.The disagreementmay be considered as a measure of the namely, G(O) = ()when 20.(Es)mEq

5、uilibrium of stresses.-The equations of equilibria weWhen the assumed stresses are substituted into the equations of equilibrium,the results sre( a21+2 -r2Es)a4 am3rz that is, d shouldbeEs (Eso mma IIIInimum.This expression represents a kind of mean square error inwhich the averaging is weighted hea

6、vily in the vicinity of the hole,since here the variation of the modulus is most rapid. The calculus ofvariations yields the Ner equation for this case as1d “2=. 0,Es Esmm qfrom whichEs =cl+c:where c1 and C2 are constants. From the conditions G(1) = 1 andG(0) = 0, it is found thatCl=lC2=0 ,so thatEs

7、“q.-. - . - .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I?ACATN 2073 7. J?inalstress system.-The final stress system, obtainedby insertingthe expression for G into the assumed expressions for stress, is)4$ + 3%4r4 Cos 2e-1Ha437 Cos 2(3ram Es ( a

8、2 )a4T= - 1+2 - 3 sin 2e2 (Es) r2 r4mStress concentrationfactor.-At the hole ar = T = O; the stressUg is a maximum for e = and has the value .and the stress concentrationfactor is(“O)s,fi/2=1 + 2(ES)a y(/2am(Es)a.-. - -.Provided by IHSNot for ResaleNo reproduction or networking permitted without lic

9、ense from IHS-,-,-._ . . .fromStrain concentrationfactor.- The strains er, ee, and ,7 are foundthe stressesthrough the stress-strain.- The strains are:7=At the hole where%Ue-2E.e Es3T“7=Esrelations( “a2cm 1 -32 ES 3-8$+9: as 2 + (Es)w 2m the strain concentration=“,+2!*2!5242 .(Es)m/( )crm Es ES? a,

10、7(/2wThe strain concentrationdivided by Es)a,7r/2e(Es)m(Es)cu-factor is thus the stress).Cos 28)cos 2efactor isconcentrationfactor-,. . - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2073 9REFERENCES1. Griffith, George E.: EQerimental Inve

11、stigation of the Effects ofPlastic Flow in a Tension Panel with a Circular Hole.NACATN 1705, 1948.2. Timoshenko, S.: Theory of Elasticity. J?irstcd., McGraw-HillBook CO., Inc., 1934, p. 77.“-.-.- . . . .-, - . _ . _ _ . _Provided by IHSNot for ResaleNo reproduction or networking permitted without li

12、cense from IHS-,-,- -. -.10 NACA TN 2073E.I.0.8.64.201 m * 1 1 a 1 to 10 20 30 40 50 60 70stress, ksiS for 24S-T3 aluminum aFigure l.- Values of TLused in reference L.,Ioy .d. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA TN 20739- Experimet

13、i (ref. i) Calculated (present theory) ,/ I- Calculated (elastic theory)7 ,/Strain/,1 /11Concentrationfactors.05 -03 - - - - _ _lo 1020 30 40 50Applied stress, mm, ksi =5=, Figure 2.- Comparison between calcudted stress and strain“ concentration factors and tests of reference 1.-. - -.- . .- . .- .

14、- ._ _. . -.+ - . -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .-. .12 NACA TN 2073distribution12Strain,6 r./ / *am, ksi am,45 378 304L“ v*o”2 4 6 8 10 =Distancefrom edge of h61e,in.Figure 3.- Comparison between palculofed points, for three val

15、uesof applied stress, and experimental strain distribution fromreference 1.ksi _- -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2073 “ .- 13I2C1008060Stress,UT,ksi4020/1 -./applied stress, and experimental#.-./00 2 4 6 8“ 1Distance from ed

16、ge, in.Figure 4.- Comparison between calculated points, for three values ofstress distribution from reference 1. . . . . . . . _ - ._. . . _s. _. _ - . . _ _ _ -_Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.-. . .- _. .,” -NACA TN 2073Tensile stress, Itttl .1 t I L“(r,O)111111 ”11111./Tensile stress,cmFigure 5.- Goordinate system for sheet with .hole.NACA-LW3E7 -4-6-50-1050. - - L_ .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-