Stress Concentrations
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1 Stress Cncentrtins A stress cncentrtin refers t n re in bject where stress increses ver very shrt distnce (i.e., where high stress grdient eists Stress cncentrtins typiclly ccur due t sme lclized chnge in gemetry (ner hles, filets, crners, grves, crcks, etc These chnges in gemetry re ften clled stress risers
2 Stress Cncentrtin Ner Circulr Hle In 898 Ernst Kirsch ( Germn engineer published slutin fr the elstic stresses ner circulr hle in n istrpic infinitely lrge thin plte (the Kirsch slutin is derived in Sec 3.3 f the Shukl nd Dlly tetbk In prctice, thin plte cn be cnsidered t be infinitely lrge if the hle dimeter is smll cmpred t the in-plne plte dimensins (if /D < ~0.05, sy D
3 Stress Cncentrtin Ner Circulr Hle Stresses lng the -is in n infinite plte predicted by the Kirsch slutin: y r yy rr τ τ σ σ σ σ σ σ θ θθ Figure 3.6: Distributin f σ /σ nd σ yy /σ lng the -is
4 Stress Cncentrtin Ner Circulr Hle Stresses t the edge f the hle (t : σ rr σ 0 σ θθ σ yy 3σ τ rθ τ y 0 The stress cncentrtin fctr fr circulr hle in n infinite plte: K t σ σ yy 3 Figure 3.6: Distributin f σ /σ nd σ yy /σ lng the -is
5 Stress Cncentrtin Ner Circulr Hle If /D > 0.05 then the plte is finite nd the Kirsch slutin is n lnger vlid Stress cncentrtin fctrs fr circulr hles in finite pltes hve been mesured eperimentlly fr rnge f /D rtis (usully using phtelsticity, nd tbulted in the frm f curve-fits in reference hndbks required severl yers nd mny cntributrs D
6 Stress Cncentrtin Ner Circulr Hle Emple: Whl, A.M., nd Beeuwkes, R., Stress Cncentrtin Prduced by Hles nd Ntches, Trnsctin f the ASME; Applied Mechnics, Vl 56 (, 930
7 Stress Cncentrtin Ner Circulr Hle Tw different definitins f the stress cncentrtin fctrs re in cmmn use: -bsed n the grss stress : m g σ yy P Kt where σ g σ g t * D (σ g remins cnstnt s increses D P -bsed n the net stress: m n σ yy P Kt where σ n σ n t *( D (σ n increses s increses P
8 Stress Cncentrtin Ner Circulr Hle Emple: frm Rrk s Frmuls fr Stress nd Strin (00: D K n t D 3.67 D.53 D 3
9 Tbulted Stress Cncentrtin Fctrs Stress cncentrtin fctrs fr mny types f stress risers hve been tbulted fr emple: -Yung, W.C., nd Budyns, R.G., Rrk s Frmuls fr Stress nd Strin, 7 th editin, McGrw-Hill, (00 - nline tbultins:
10 Stress Cncentrtin Ner n Ellipticl Hle In 93 Chrles Inglis ( British mthemticin published slutin fr the elstic stresses ner n ellipticl hle in n istrpic infinitely lrge thin plte (the Inglis slutin is discussed in Sec 4. In this cse the stress cncentrtin depends n bth the spect rti f the hle (/b nd n the size f the plte
11 Stress Cncentrtin Ner n Ellipticl Hle Fr n infinite plte the stresses lng the -is (i.e., fr, y 0 re given by: where: 0 ( ( ( ( ( ( ( F F F F y s s yy s s τ σ σ b b m b B m B B s m s m s m s m m s m F m s m F s s ( 3 ( ( ( σ σ
12 Stress Cncentrtin Ner n Ellipticl Hle Fr finite plte: b b C b b C b b C b b C D C D C D C C K n t / 4.0 / / / /.483 / /.000 /
13 Mesuring Stress Cncentrtins Using Strin Gges In generl, even the smllest f cmmercil resistnce strin gges re t lrge t mesure strin cncentrtins ner stress risers:
14 Mesuring Stress Cncentrtins Using Strin Gges
15 Mesuring Stress Cncentrtins Using Strin Gges In generl, even the smllest f cmmercil resistnce strin gges re t lrge t mesure strin cncentrtins ner stress risers: pr eperimentl pprch
16 Mesuring Stress Cncentrtins Using Strin Gges Insted, use cmmercil strip gge nd etrplte eperimentl mesurements t edge f stress riser
17 Pseud Lb #6: Stress nd Strin Cncentrtins
18 Pseud Lb #6: Stress nd Strin Cncentrtins in in (typicl Ail gges M-M gge type SA-3-03PJ-0 Gge fctr., K t.0% in in (typicl Trnsverse gges M-M gge type EA-3-03MF-0 Gge fctr.09, K t.%
19 Crrectins fr Biil Rsettes With Differing Trnsverse Sensitivity Cefficients y t t my t y t m t K K K K K ( ( ε ν ε ν ε y t t m y t t my y t y K K K K K ( ( ε ν ε ν ε m ε my ε, strins mesured in the - nd y- directins y t t K K, Trnsverse sensitivity cefficients fr gges in the - nd y- directins MM Tech-Nte 509 Errrs Due t Trnsverse Sensitivity in Strin Gges
20 Pseud Lb #6: Stress nd Strin Cncentrtins Gls: T cmpre stress distributins mesured ner n ellipticl hle in finite thin plte t thse predicted fr n infinite thin plte, nd T cmpre the stress cncentrtin fctr mesured fr n ellipticl hle in finite thin plte t the vlue epected frm reference hndbk.
21 Pseud Lb #6: Stress nd Strin Cncentrtins Officil Dt Ail Strins 00 Ail Strins 000 Strin (µε Gge A Gge A Gge 3A Gge 4A Gge 5A Gge 6A Gge 7A Gge 8A Gge 9A Gge 0A Applied Ld (lbf
22 Pseud Lb #6: Stress nd Strin Cncentrtins Officil Dt Trnsverse Strins 60 Trnsverse Strins 40 Strin (µε Gge T Gge T Gge 3T Gge 4T Gge 5T Gge 6T Gge 7T Gge 8T Gge 9T Gge 0T -80 Applied Ld (lbf
23 Pseud Lb #6: Stress nd Strin Cncentrtins Gl : Cmpre stress distributins mesured ner n ellipticl hle in finite thin plte t thse predicted fr n infinite thin plte (Suggestin: cmpre nrmlized stresses σ yy /σ net Inglis Slutin Mesured Nte: s mentined during clss lecture, the mesured vlues shwn here re fictitius Psitin lng -is (in
24 Pseud Lb #6: Stress nd Strin Cncentrtins Gl : T cmpre the stress cncentrtin fctr mesured fr n ellipticl hle in finite thin plte t the vlue epected frm reference hndbk. (Suggestin: etrplte curve fit Nrmlized il stress
25 Pseud Lb #6: Stress nd Strin Cncentrtins Gl : T cmpre the stress cncentrtin fctr mesured fr n ellipticl hle in finite thin plte t the vlue epected frm reference hndbk..fit f fictitius dt using nd -rder plynmil: Nrmlized il stress y
26 Pseud Lb #6: Stress nd Strin Cncentrtins Gl : T cmpre the stress cncentrtin fctr mesured fr n ellipticl hle in finite thin plte t the vlue epected frm reference hndbk..fit f fictitius dt using n epnentil: Nrmlized il stress y 5.87e
27 Pseud Lb #6: Stress nd Strin Cncentrtins Gl : T cmpre the stress cncentrtin fctr mesured fr n ellipticl hle in finite thin plte t the vlue epected frm reference hndbk.. fit f fictitius dt using pwer lw Nrmlized Ail Stress y
28 Pseud Lb #6: Stress nd Strin Cncentrtins Gl : T cmpre the stress cncentrtin fctr mesured fr n ellipticl hle in finite thin plte t the vlue epected frm reference hndbk..fit f fictitius dt using n plynmil nd (/nrmlized stress /Nrmlized Ail Stress y
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