Measurement of Residual Stress/Strain (Using Strain Gages and the Hole Drilling Method) Summary of Discussion in Section 8.9

Transcription

1 Mesuement f Residul Stess/Stin (Using Stin Gges nd the Hle Dilling Methd) Summy f Discussin in Sectin 8.9

2 The Hle Dilling Methd Is Bsed On: () Stess tnsfmtin equtins τ x' x' y' y' x' y' xx xx cs sin sin cs τ τ cs sin cs sin ( ) ( ) cs sin τ cs sin yy xx yy yy xy xy xy

3 The Hle Dilling Methd Is Bsed On: () Stess tnsfmtin equtins lbel the new xes nd (insted f x' nd y') τ xx xx cs sin sin cs τ τ cs sin cs sin ( ) ( ) cs sin τ cs sin yy xx yy yy xy xy xy

4 The Hle Dilling Methd Is Bsed On: (b) Stesses in Unifmly-Lded Thin Plte

5 The Hle Dilling Methd Is Bsed On: (b) Stesses in Unifmly-Lded Thin Plte The stte f stess is identicl t ll pints within the plte (igning pssible stess cncenttins ne the lded ends)

6 The Hle Dilling Methd Is Bsed On: (b) Stesses in Unifmly-Lded Thin Plte Define n x-y cdinte system t the cente f the plte: xx 0 yy τ xy 0 y x

7 The Hle Dilling Methd Is Bsed On: (b) Stesses in Unifmly-Lded Thin Plte Rtte the stess element lng the cicumfeence f n (imginy) cicle f dius

8 The Hle Dilling Methd Is Bsed On: (b) Stesses in Unifmly-Lded Thin Plte Rtte the stess element lng the cicumfeence f n (imginy) cicle f dius t ny ngle : τ xx xx cs sin sin cs τ τ cs sin cs sin ( ) ( ) cs sin τ cs sin yy xx yy yy xy xy xy y x Since xx τ xy 0, yy sin τ cs cs sin

9 The Hle Dilling Methd Is Bsed On: (b) Stesses in Unifmly-Lded Thin Plte Using tig identities: sin cs cs sin ( cs ) ( cs ) sin The stess cmpnents cn be witten: ( cs ) ( cs ) τ sin eqs (e), pg 69 eqs (8.44), pg 44 y x

10 x y The Hle Dilling Methd Is Bsed On: (c) The Kisch Slutin (Deived in sectin.): The stesses induced t ny pint (, ) in n infinitely lge thin plte with hle f dius, subjected t emte unixil stess, e given by (whee ): eqs (.4) τ sin cs cs 4 4

11 ( n Aside..) Stess Cncenttin Ne Cicul Hle Stesses lng the x-xis in n infinite plte pedicted by the Kisch slutin: xy yy xx x x x x τ τ Figue.6: Distibutin f xx / nd yy / lng the x-xis

12 ( n Aside ) Stess Cncenttin Ne Cicul Hle Stesses t the edge f the hle (t x ): xx 0 yy τ τ xy 0 The stess cncenttin fct f cicul hle in n infinite plte: K t yy Figue.6: Distibutin f xx / nd yy / lng the x-xis

13 The Hle Dilling Methd Assume: A unixil esidul stess exists in thin plte (Nte unixil esidul stess field is unusul will genelize this discussin lte )

14 The Hle Dilling Methd Assume: A unixil esidul stess exists in thin plte (Nte unixil esidul stess field is unusul will genelize this discussin lte ) Hle-dilling Pcedue: ) Specil -element stin gge sette bnded t the plte Nte: - gge elements nged t cnstnt dius in cicul ptten - gge cicuits e blnced in this cnditin since esidul stesses e pesent, the mesued ze stin des nt cespnd t ze stess y c b x

15 The Hle Dilling Methd Assume: A unixil esidul stess exists in thin plte (Nte unixil esidul stess field is unusul will genelize this discussin lte ) Hle-dilling Pcedue: ) Specil -element stin gge sette bnded t the plte Nte: - gge elements nged t cnstnt dius in cicul ptten - gge cicuits e blnced in this cnditin since esidul stesses e pesent, the mesued ze stin des nt cespnd t ze stess - A hle with dius is dilled thugh the cente f the sette, elesing the esidul stesses tht existed in the hle vlume

16 The Hle Dilling Methd The stin gges espnd t the chnge in the stess field, which is given by: (eqs.4) (eq 8.44) Mking the substitutin nd pefming lgebic simplifictins, the stess field tht the stin gges espnd t is given by: eqs (8.45) τ sin cs cs 4 unifm stess plte with hle

17 The Hle Dilling Methd The chnge in dil nd tngentil stins cused by (ceful!) dilling f the hle cn be btined by substituting the chnge in stess (i.e., eqs 8.45) int Hke s Lw f plne stess: Mking this substitutin nd pefming lgebic simplifictins: eqs (8.46) ( ) ( ) E E ν ν ν ν ν ν ν cs 4 cs ) ( 4cs cs ) ( E E

18 The Hle Dilling Methd The chnge in dil nd tngentil stins cused by (ceful!) dilling f the hle cn be btined by substituting the chnge in stess (i.e., eqs 8.45) int Hke s Lw f plne stess: Mking this substitutin nd pefming lgebic simplifictins: eqs (8.46) ( ) ( ) E E ν ν ν ν ν ν ν cs 4 cs ) ( 4cs cs ) ( E E Rdil stins mesued by the -element sette, if esidul stess is unixil nd ligned with y-xis

19 The Hle Dilling Methd Pcticl Applictin The esidul stess field is usully bixil, invlving: tw unknwn pincipl esidul stesses unknwn ienttin f pincipl xis, R R nd ( ) Figue 8.

20 The Hle Dilling Methd Pcticl Applictin The pedicted stins induced by unixil stess (eqs 8.6) cn be used t septely clculte: stins induced by pincipl stess R R R stins induced by pincipl stess (cting t 90º w//t )

21 The Hle Dilling Methd Pcticl Applictin The pedicted stins induced by unixil stess (eqs 8.6) cn be used t septely clculte: stins induced by pincipl stess stins induced by pincipl stess (cting t 90º w//t ) Applying the pincipl f supepsitin, using Hke s lw nd the stin tnsfmtin equtins we find: R R R ( ) ( ) ( ) ( ) ν ν ν 4 tn E C E C C C C C A C C B A c B B A C A R c B B A C A R eqs (8.5)

22 Fig 8.4: Residul Stess (Stin) Gges pduced by Mic- Mesuements

23 Residul Stess (Stin) Gges pduced by Mic-Mesuements Refeences: () ASTM E87: Stndd Test Methd f Detemining Residul Stesses by the Hle- Dilling Stin-Gge Methd () M-M TN-50: Mesuement f Residul Stesses by the Hle Dilling Stin Gge Methd

24 Alignment nd Hle-Dilling Setup f Residul Stess/Stin Mesuement

25 (Fme) ME556 Lb Expeiment: Residul Stess Mesuement

26 Ovell View f Set-up: Welded Ht Rlled Mild Steel Plte (ASTM A6), Residul Stin Gge Rsettes, P-500 Stin Gge Amplifie, SB- 0 Ten-Chnnel Switch nd Blnce Unit

27 Specimen : Welded Ht Rlled Steel Plte (Intended Rsette Ptten) 4 inch 4 Uppe Rsette Bnding Line inch Lwe 4 Welding #Cente Symmetic Psitin # # # #4 #5 #6 #7 #8

28 Rsettes: Befe (n Right) nd Afte (n Left) Cente Hle is Dilled Definitin f gge element,, nd Element numbe: