Experimental and Numerical Study on the Accuracy of Residual Stress Measurement by Incremental Ring-Core Method

Transcription

1 AUT Journl of Mechnicl Engineering AUT J. Mech. Eng., () (08) DOI: 0.060/jme Experimentl nd Numericl Study on the Accurcy of Residul Stress Mesurement by Incrementl Ring-Core Method M. A. Mozm, M. Honrpisheh * Fculty of Mechnicl Engineering, University of shn, shn, Irn ABSTRACT: In this study, the clibrtion constnts of incrementl step method hve been determined by finite element nlysis to clculte the residul stresses by the ring-core method. The clibrtion coefficients hve been determined by simultion the unixil nd bixil loding. It is indicted tht the loding pproch hs not effect on the clibrtion constnts nd they re unique. The unixil condition hs been used to determine the clibrtion coefficients in the experimentl method. To verify the determined constnts, the clibrtion fctors hve been used to clculte the residul stresses in the cse of uniform nd non-uniform residul stresses. The xil nd bixil conditions hve been studied nd the results re in good ccordnce with pplied stresses in simultions. In the unixil loding the mesured residul stresses in finite element model completely ccommodted by the pplied stresses nd presented formul nd clibrtion constnts determined the direction of the mximum principl stress by clernce less thn 0.7%. Clernce of the mesures stresses nd pplied stresses in the non-uniform cse ws bout %. An experimentl test hs been used to show the effectiveness of the obtined clibrtion coefficient by finite element nlysis. Also, it is indicted tht the results of the experimentl test re stisfctory. Review History: Received: 3 Jnury 08 Revised: 5 My 08 Accepted: 4 June 08 Avilble Online: 5 July 08 eywords: Residul stress Ring-Core Clibrtion coefficients Incrementl method - Introduction In the mnufcturing of prts nd equipment the residul stresses re importnt nd this topic is considered nowdys. Control the residul stresses in the prts tht re subjected to the cyclic lods is serious nd in some mnufcturing stndrd mesurement the residul stresses re mndtory. For exmple tension residul stresses on the foot of the rils shll not exceed thn 50 MP []. There re mny different methods for mesuring the residul stresses such s holedrilling [, 3], slitting method [4-7], nd contour method [8, 9], but ech method hs its property nd could be used just in certin conditions. Residul stress mesurement methods could be clssified into three min ctegories nmed destructive, semi destructive nd non-destructive. Stress could not be mesured directly nd usully is clculted by mesuring the strin. The strins could be mesured with electricl strin gges. To determine the residul stresses with strin gge t first the strin gge is bonded on the surfce of the specimen, then the equilibrium of the residul stresses re disturbed by mteril removing process similr mchining. As the result new equilibrium condition is mde nd some deformtions will occur. The strin gges sense the strin due to the deformtions nd by using the pproprite mthemticl reltion the mesured strins re used to mesure the residul stresses. Hole-drilling is known s the most fmous semi-destructive method which used the strin gge to mesure the residul stresses. This method is stndrdized by ASTM [0]. The ring-core method is nother semi-destructive method nd bsed on the sme principl s the hole-drilling. The ring-core method llows for determintion of residul stresses t high depth from the surfce []. In ring-core method by cutting n nnulr groove Corresponding uthor, E-mil: honrpishe@kshnu.c.ir in stressed specimen, the strins will be relxed in the core of the ring. It is possible to estimte the residul stresses before cutting the nnulr groove by use the relesed strins on the surfce of the core []. Sensing the stress chnge inside, the mteril by the sensor ttched t the top of the component is not suitble by using the clssic Hook s lw. Thus, there re three commonly used evlution techniques for residul stress determintion: incrementl, differentil nd integrl [3]. Ech technique hs its bckground nd specific mthemticl formul nd ll of them need to clibrtion coefficients. The clibrtion coefficients of ech technique re unique nd they re not relted to ech other. Clibrtion fctors in ech technique could be determined by experimentl test nd lso by Finite Element (FE) nlysis. In the determintion of the clibrtion fctors process known residul stress field should be used. Unixil tension nd compression field re the best conditions in the uniform cse of the residul stresses nd bending could be used in non-uniform residul stress distribution long the thickness of the specimen. Mris nd Peterson [4] used the bending condition to mke known residul stress distribution. eil [5] determined the clibrtion coefficients of incrementl technique by using the tension test in bulk specimen. Václvík et l. [6] used the FE nlysis to determine the clibrtion coefficients, they lso mesured the residul stresses in bulk forged shft by the ring-core method. Civin nd Vik [7] used FE model for determintion of clibrtion coefficients nd they lso proposed new set of clibrtion fctors. The ring-core method is reltively common to mesure the residul stresses, especilly in cse of bulk mterils similr which mnufctured by csting nd forging. Although the theory of the ring core method is well-known, but the connection between experimentl mesurements nd 37

2 numericl studies is still not sufficient. Residul stress mesurement by the ring-core method needs to dequte clibrtion coefficients. There is not still unique set of clibrtion constnts for ech technique of the ring-core method. Finl element method is the most effective wy to determine the clibrtion fctors. In this reserch n pproprite numericl model hs been studied to determine the clibrtion fctors for the incrementl technique of the ring-core method. Also the required formul to determine the clibrtion constnts in the bixil cse hve been introduced. Effectiveness of the constnts hve been studied by simultion the uniform nd the non-uniform residul stress fields. The results hve been very stisfctory in the cse of the both uniform nd non-uniform residul stresses. Moreover to the FE nlysis n experimentl test hs been devised to indicte the effectiveness of the clibrtion constnts. The results of the experimentl tests re in good ccordnce with the expected results nd conform the FE nlysis. Therefore, the presented clibrtion constnts could be used in experimentl residul stress mesurement by the ring core method s prerequested constnts. The presented constnt improve the finl results in compring with the constnts tht presented by [5]. - Principles of Incrementl Ring-Core Method In the ring-core method smll nnulr groove is mde on the surfce of the specimen nd seprtes the centrl core of the surrounding mteril. This seprtion cuses the relese some prts of the residul stresses [5]. This method ws innovted by Milbert [8] nd modified by severl other reserchers. During the development of the ring-core method, specil strin rosette ws mde. This rosette is bonded on the surfce of the specimen nd the nnulr groove is mde round it. The ring-core rosette is mde of three strin gges nd ech gge is displced by 45 degrees. Fig. indictes the ring-core method strin rosette. As mentioned in the previous section, there re three min techniques to clculte the residul stresses by the ring-core method nmed differentil, integrl nd incrementl. By differentil method, it is possible to mke rpid test nd estimte the vlue of the residul stresses. This technique could be used s workshop qulity control test. In this technique residul stress re clculted by relieving strins tht mesured t two different depths nd step s difference ΔZ consist of two prticulr depths Z i nd Z i, described by Eq. (). Residul stresses re clculted by Eqs. () nd (3) [0]. Z = Z Z = Z Z =,, 3, mm () i i i i σ = A ε B ε () σ = A ε B ε (3) In Eqs. () nd (3), A nd B re clibrtion coefficients nd σ nd σ re principl residul stresses. ε nd ε re clculted by the Eqs. (4) nd (5). ε = ε ε (4) Zi Zi ε = ε ε (5) Zi Zi The integrl method commonly used for hole drilling method nd its constnts described in ASTM E837 stndrd [0]. Ajovlsit et l. [] pplied integrl method to the ring-core. Brsnti et l. [] determined the constnts of integrtionmethod by finite element nlysis. The integrl method is presented by Eq. (6) nd it is ssumed tht ε x (H) relieved on the surfce fter milling the groove of depth H is the integrl of infinitesiml strins due to the residul stresses σ x (Z) cting in whole groove depth []. ε x H H = F H Z x z dz E (6) (, ) σ 0 Becuse this pper dels with the incrementl method, it is described in detil. Residul stresses could be uniform or non uniform in plne of mesurement nd in the depth direction. On the surfce of the specimen the plne stress condition exists nd this is mens tht the stress perpendiculr to the free surfce is zero. Also, it is ssumed tht in the plne of mesurement the mgnitude of the residul stresses is constnt or its vrition is negligible. Thickness of the specimen could be thin of thick, but in the thin cse just uniform cse of residul stresses should be considered. Principles of the ring core method nd incrementl technique is indicted in Fig. [5]. Lyer removl, equl to dz, cuse to relese the residul stresses in this portion of the specimen nd cuse some deformtion in the core. Strin gges will sense the strins on the core surfce. If just the strin gge () is considered, it is possible to introduce the relesed strin ε on the surfce of the core s function of depth by Eq. (7) [5]. dε dz * = z z (7) Fig.. The ring-core strin rosette [9]. In Eq. (7), ϵ * (z) is the mesured strin by the strin gge () in depth (Z). (z) is the clibrtion constnt relted to direction () nd depth (Z). By considering the unixil residul stress condition the Eq. (7) could be written in the form of the Eq. (8). 38

3 If σ pplies in the principl direction (), then the bixil condition could be considered. In this condition the effect of σ should superimposed by σ. Therefore, the mesured strins in principl directions could be presented by Eqs. () nd (3). dε ν = σ σ () dz E E dε ν = σ σ (3) dz E E It is possible to determine the mgnitude of the principl residul stresses by rrnging the Eqs. () nd (3). Eqs (4) nd (5) present the principl residul stresses. E dε z dε σ = + υ dz dz (4) ν E dε z dε σ = + υ dz dz (5) dε dz = σ (8) E In Eq. (8), E is the module of elsticity, (z) is the clibrtion constnt relted to direction () nd depth (Z). It is well-known tht stress σ mkes the strins ε =(/E)σ nd ε =(-ν/e)σ. Therefore, it is possible to predict the mesured strin by strin-gge which is perpendiculr to the stringge, by Eq. (9). dε dz = σ (9) E In Eq. (9), (z) is the clibrtion constnt relted to direction () nd depth (Z). By ttention to mentioned notes, it is possible to determine the clibrtion constnt by using the known principl direction. To determine the clibrtion constnt (z) nd (z) the unixil tension test or simultion the unixil condition could be considered. The clibrtion constnts hve been clculted by Eqs. (8) nd (9) nd presented by Eqs. (0) nd (). Fig.. Used prmeters in the incrementl ring core method [5]. E dε σ dz = (0) E νσ = () dε dz It is possible to extend the Eqs. (4) nd (5) to ny two perpendiculr system. If perpendiculr to c nd b perpendiculr to d then the Eqs. (6) to (9) re confirmed. E dε z dεc σ = + υc (6) c dz dz E dεc z dε σc = + υc (7) c dz dz E dε z dε σ z = z + υ z b d b b d b d dz dz (8) E dεd z dεb σd = b + υd (9) c dz dz From the Mohr s circle, the Eqs. (0) nd () re esily verified. σ + σ = σ + σ = σ + σ (0) c b d dε + dεc = dεb + dεd = dε+ d ε () By substituting the Eqs. (0) nd () to the Eqs. (6) to (9), the Eqs. () nd (3) will be creted. z = z = z () c b d z = z = z (3) 39

4 In the ring-core strin rosette three strin gges exist, therefore, dε d in Eq. () could be written s function of the three other vribles. dε = dε dε + dε (4) d b c By combining the Eqs. (6) to (4), the stress in the direction of the three strin gge would be clculted by Eqs. (5) to (7). E dε z dεc σ = + υ dz dz σ b = E (5) dεb dz dε dεb dεc (6) + υ + dz dz dz E dεc z dε σc = + υ dz dz (7) 3- Determintion of the Clibrtion Constnts If the elstic constnt of the mteril, E nd υ nd lso the clibrtion coefficients (Z) nd (Z) re known, the residul stresses could be clculted by the Eqs. (5) to (9). Therefore, determintion the clibrtion coefficients re pre-required step for experimentl test. The clibrtion coefficients of the incrementl method re determined by the Eqs. (0) nd (). In the clibrtion coefficient determintion process, known field of stress shll be used. It is possible to determine the clibrtion coefficients by experimentl method nd tension or compression test, but in rel mteril lwys vlue of residul stresses exist nd could effect on the finl vlue. Therefore, the finite element method is known s n pproprite wy to determine the clibrtion constnts. In this reserch the ABAQUS finite element pckge hs been used to determine the clibrtion coefficient of the incrementl method. The dimension of the finite element model considered s mm. Due to the symmetry, only qurter of the model hs been modeled (5 5 5 mm) nd indicted in Fig. 4. In the ring-core strin rosette, ech gge is displced by 45 degrees. Therefore, two strin gges re perpendiculr. It is considered tht nd c re perpendiculr nd b is in 45 degrees in counter-clock wise direction respect to the. A typicl Mohr s circle relted to the ring-core strin rosette is indicted in Fig. 3. By ttention to Fig. 3 the principl residul stresses nd lso direction between the gges nd the mximum principl residul stress re mesured by Eqs. (8) nd (9). + σ σ c σ, = ± σb σ + σb σc (8) σ σ σb σ σc = rc tn c Fig. 3. Mohr s circle relted to the ring-core strin rosette. (9) Fig. 4. Finite element model of the ring-core clibrtion. The mteril is considered s liner elstic nd isotropic nd the nnulr groove hs been modeled in 0 equl increments with the size of Z= 0.5mm. Prmeter of the finite element model indicted in the Tble. In the position of the strin rosette the fine mesh hs been used. The mesh sizing study indicted tht pproprite dimension for the mesh of the strin rosette portion is bout 0.7 mm. Figs. 5 nd 6 present the model fter first nd finl Tble. Prmeters of the FEM prmeters Vlue Dimension (mm) Annulr groove (mm) Ø4-Ø8 Elsticity modulus (GP) 00 Poison rtio 0.3 Unixil stress (MP) 50 Element type C3D0 Gge length of strin rosette (mm) 5 40

5 The clibrtion fctors hve been clculted by Eqs. (0) nd (), nd the results hve been indicted in Fig. 8. Fig. 5. Model t the end of the first step. Fig. 8. Clibrtion coefficients in term of the nnulr groove depth. The dt in Fig. 8 hve been obtined from the simultion of the tension test. In theory, it is possible to use the compression stress too. To compre the results between tension nd compression stress, the clibrtion process hs been done under 50 MP compression stress. The relesed strins in principl directions hve been indicted in Fig. 9, but the finl results re exctly the sme s dt in Fig. 8. Fig. 6. Model t the end of the finl step. steps, respectively. Stress contours indicte tht, increse in the depth of the nnulr groove result to stress relese in the core. To clculte the clibrtion coefficients, the strin vlues in principl directions hve been mesured. Fig. 7 indictes the relesed strin in the principl directions. Fig. 9. Relesed strin in principl directions in term of the nnulr groove depth in the compression test. The clibrtion constnt should be unique nd different loding condition should not ffect them. In cse of the bixil stress the clibrtion coefficient could be clculted by Eqs. (30) nd (3). Fig. 7. Relesed strin in principl directions in term of the nnulr groove depth. ( Z ) ( Z ) Eσ dε = σ σ dz dε Z E σ + dz σ σ σ ( Z ) ε Eσ dε Z d Z σ = νσ ( σ ) dz dz σ (30) (3) 4

6 The clibrtion process in the bixil condition hs been simulted by σ =80 MP,nd σ =50 MP nd relesed strins in the principl directions hve been indicted in Fig. 0. The clibrtion constnts hve been clculted by Eqs. (30) nd (3) nd the results hve been indicted in Fig.. ny significnt chnge in the results. Simultion consists of steps. In the first step the loding is simulted nd in the next 0 steps the depth of the nnulr groove incresed by Z= 0.5mm. Fig. 0. Relesed strin in principl directions in term of the nnulr groove depth in the bixil test. Fig.. Relesed strin in strin rosette directions, in term of the simultion steps (t ech step the depth of nnulr grooves increse by 0.5mm). The residul stresses corresponding to the directions of the strin rosette hve been clculted by Eqs. (5) to (7) nd the clibrtion constnts. The results hve been indicted in Fig. 3. Fig.. Clibrtion coefficients in term of the nnulr groove depth. 4- Verifiction of the Clibrtion Coefficients The clibrtion coefficients re vluble if they be verified. To verify the clibrtion coefficient, it is possible to use the experimentl test s well s the finite element method. Similr to the determintion of the clibrtion coefficient severl prmeters such s residul stresses exist in experimentl tests tht could effect on the finl results. To prevent the unexpected problems, the finite element method hs been used for verifiction the clibrtion constnts. In first step the uniform residul stresses hve been simulted. Prmeters of the model re similr to wht explined in the previous section. The unixil tensile stress with σ =50 MP,nd σ =0 hve been considered. The relesed strins in the directions of the strin rosette (Fig. ) hve been mesured nd indicted Fig.. Severl models with different dimensions hve been used, but, there ws not Fig. 3. Clculted residul stresses in strin rosette directions, in term of the nnulr groove depth. The principl residul stresses hve been clculted by Eq. (8) nd indicted in Fig. 4. The ngle between the gges nd the mximum principl residul stress hve been clculted by Eq. (9) nd indicted in Fig. 5. In the uniform cse of the residul stresses, the bixil condition hs been considered by σ =80 MP,nd σ =50 MP. All of the model prmeters except the loding condition were similr to the unixil condition. The relesed strins nd pproprite residul stresses in strin rosette directions hve been indicted in Figs. 6 nd 7. The principl residul stresses nd lso the ngle between the gge nd the mximum principl residul stresses hve been indicted in Fig. 8 nd 9. 4

7 Fig. 4. Clculted principl residul stresses in term of the nnulr groove depth. Fig. 7. Clculted residul stresses in strin rosette directions, in term of the nnulr groove depth- The bixil cse. Fig. 5. Angle between the gge nd the mximum principl residul stress in term of the nnulr groove depth. Fig. 8. Clculted principl residul stresses in term of the nnulr groove depth- The bixil cse. Fig. 6. Relesed strin in strin rosette directions, in term of the simultion steps (in ech step the depth of nnulr groove increse by 0.5mm) of the bixil cse. Fig. 9. Angle between the gge nd the mximum principl residul stress in term of the nnulr groove depth- The bixil cse. 43

8 Addition to the uniform cses of the residul stresses, the unixil non-uniform cse hs been considered. The only chnge in the model ws the loding. After simultion nd extrcting the dt, the principl residul stresses nd lso the ctul pplied stresses long the gge tht is the loding direction, hve been clculted nd indicted in Fig. 0. The ngle between the mximum principl residul stresses nd the gge hs been indicted in Fig.. Fig.. Devised fixture, specimen, cutter nd rosette for experimentl test Fig. 0. The mximum principl residul stresses nd pplied stresses in term of the nnulr groove depth- The non-uniform unixil cse. Fig.. Angle between the gge nd the mximum principl residul stress in term of the nnulr groove depth-the nonuniform unixil cse. 5- Experimentl Test To verify the clibrtion constnt n experimentl test hs been devised. In this test plte is subjected to the unixil tension condition nd then the ring-core method is used to mesure the pplied stress. Devised fixture, specimen, specil cutter for mshing the nnulr groove nd strin rosette for the ring-core method re indicted in Fig.. The fixture is mde from piece of ril nd fter mchining process het treted to obtin 45 HRC hrdness. The specimen is mde of mild steel (S35JR EN 005). The specimen hve been nneled fter mchining nd just slightly polished to mke clen surfce. The fixture is considered s rigid body in compring with the specimen. The specimen hs been subjected to tensile stress by fsten the nuts. The vlue of tensile strins hs been controlled by the strin gge which bonded long the direction of the pplied strin. Then the ring-core process hs been done in 0 equivlent steps (ech depth step=0.5mm). Different prmeters of the test hve been indicted in the Tble nd the test setup is indicted in Fig. 3. Tble. Prmeters of the Experimentl test prmeters Vlue Dimension of the specimen (mm) Elsticity modulus (GP) 00 Poison s rtio 0.3 Unixil Applied strin 86e-6 Unixil stress (MP) 7. Strin rosette Annulr groove (mm) TML-FRA-5- Ø4-Ø8 Depth step (mm) 0.5 Finl depth (mm) 5 After mchining the nnulr groove nd record the relived strin in ech step, the vlue of the stresses hs been clculted ccording to the procedure of the ring-core method. The relived strins fter filtering the noises hve been indicted in Fig. 4. To clculte the stresses the clibrtion coefficients which obtined from the FE nlysis hve been used nd Fig. 5 shows the results. By ttention to the test condition it is possible to clculte the clibrtion coefficients by using the dt of Fig. 4 nd Eqs. (0) nd (). The clculted clibrtion constnt nd lso, the clibrtion constnt by FE nlysis hve been indicted in the Fig Conclusions This pper offers some informtion bout the residul stress mesurement by semi-destructive ring-core method. The bsic formuls hve been presented nd procedure for determining the clibrtion coefficient for certin mteril hs been introduced. The clibrtion coefficients hve been determined by simultion the unixil tension nd compression tests. Also the required formul to determine the clibrtion constnts 44

9 Fig. 5. Clculted principl residul stresses by the ring-core method nd rel pplied stresses in the experimentl test Fig. 3. Setup of the experimentl test Fig. 6. Clibrtion constnts by FE nlysis nd experimentl test Fig. 4. Recorded strins in rosette in term of the nnulr groove depth in the bixil cse hve been introduced. It is indicted tht the clibrtion constnts in unixil nd bixil conditions re the sme. The clibrtion constnts of both unixil nd bixil conditions hve been indicted in the Tble 3. This point shows tht the clibrtion coefficients re independent of loding directions. The clibrtion constnts hve been verified by simultion the uniform nd non-uniform cses of the residul stresses. In the cse of the uniform residul stresses, it is indicted tht the introduced formul nd clibrtion coefficient could clculte the residul stress field. The conformity between the pplied stress in finite element nlysis nd clculted stress ws bout 00%. Also the direction between the mximum principl residul stresses nd gge hve been clculted by clernce bout ±0.7 tht is excellent. The non-uniform cse of residul stresses lso hve been considered nd indicted tht the mximum difference between the pplied nd clculted residul stresses ws bout % tht is very good. An experimentl test hs been devised to show the effectiveness the clculted clibrtion constnt. In this test uniform cse of stresses is formed by creting unixil tensile strins in plte. Compring the clculted nd pplied 45

10 Tble 3. the clibrtion constnts in unixil nd bixl conditions depth (mm) unixil unixil bixil bixil stresses shows tht the results of the ring-core method re cceptble. The clculted clibrtion constnt by experimentl test shows similr trend by the results of the FE nlysis. This note confirms the FE nlysis, but smll vrition in clibrtion constnt cuse to big mistkes in clculting stresses. Moreover, in experimentl test severl uncertinty effects on the results which re not controllble. Therefore the uthors just present the FE nlysis vlues. By ttention to the results it is concluded tht the presented clibrtion coefficients hve enough ccurcy to use s the pre-required constnt in the incrementl ring-core method References [] Europen Stndrd, pren 3674-, Rilwy Applictions- Trck-Ril, Prt : Vignole rilwy rils 46 kg/m nd bove, Nov. 00. [] M. Sedighi, M. Honrpisheh, Experimentl study of through-depth residul stress in explosive welded Al Cu Al multilyer, Mterils & Design, 37 (0) [3] M. Sedighi, M. Honrpisheh, Investigtion of cold rolling influence on ner surfce residul stress distribution in explosive welded multilyer, Strength of Mterils, 44(6) (0), [4] M. Honrpisheh, E. Hghight, M. otobi, Investigtion of residul stress nd mechnicl properties of equl chnnel ngulr rolled St strips, Proceedings of the Institution of Mechnicl Engineers, Prt L: Journl of Mterils: Design nd Applictions (06) org/0.77/ [5] M. otobi, M. Honrpisheh, Uncertinty nlysis of residul stresses mesured by slitting method in equlchnnel ngulr rolled Al-060 strips, The Journl of Strin Anlysis for Engineering Design, 5() (07), [6] M. otobi, M. Honrpisheh, Experimentl nd numericl investigtion of through-thickness residul stress of lser-bent Ti smples, The Journl of Strin Anlysis for Engineering Design, 5(6) (07) [7] M. otobi, M. Honrpisheh,Through-depth residul stress mesurement of lser bent steel titnium bimetl sheets, The Journl of Strin Anlysis for Engineering Design, 53(3) (08) [8] I. Alinghin, M. Honrpisheh, S. Amini, The influence of bending mode ultrsonic-ssisted friction stir welding of Al-606-T6 lloy on residul stress, welding force nd mcrostructure, The Interntionl Journl of Advnced Mnufcturing Technology, 95 (5-8) (08) [9] I. Alinghin, S. Amini, M. Honrpisheh, Residul stress, tensile strength, nd mcrostructure investigtions on ultrsonic ssisted friction stir welding of AA 606-T6, The Journl of Strin Anlysis for Engineering Design, 53(7) (08) [0] ASTM E Stndrd Test Method for Determining Residul Stresses by the Hole-Drilling Strin-Gge Method, (03). [] M. Brsnti, M. Beghini,C. Sntus, A. Benincs,L. Bertelli, Integrl method coefficients nd regulriztion 46

11 procedure for the ring-core residul stress mesurement technique, Advnced Mterils Reserch, 996 (04) [] M. A. Mozm, M. Honrpisheh, Residul Stresses Mesurement in UIC 60 Ril by Ring-Core Method nd Sectioning Technique, AUT J. Mech. Eng., () ( 07) [3] F. Mend, P. Šrg, T. Lipták, F. Trebun, Comprison of different simultion pproches in ring-core method, Americn Journl of Mechnicl Engineering, (7) (04) [4] A. Misr, H. A. Peterson, Exmintion of the ring method for determintion of residul stresses, Experimentl Mechnics, (7) (98) [5] S. eil, Experimentl determintion of residul stresses with the ring-core method nd n on line mesuring, Experimentl Technique, 6(5) (99) 7-4. [6] J. Vclvik, O. Weinberg, P. Bohdn, J. Jnkovec nd S. Holy, Evlution of Residul Stresses using Ring Core Method, 4 th Interntionl Conference on Experimentl Mechnics, (00) -0. [7] A. Civin, M. Vlk, Anlysis of Clibrtion Coefficients for Incrementl Strin Method Used for Residul Stress Mesurement by Ring-Core Method, Applied Mechnics, (00) 5 8. [8].P. Milbrdt, Ring-method Determintion of Residul Stresses, Proc. SESA Sw ng Meeting, Clevelnd (950) [9] Tokyo Sokki enkyujoco, Ltd., TML Strin gge ctloge, Accessed on Aguest 06; jp/e. [0] A. Civin, M. Vlk, Determintion of principl residul stresses directions by incrementl strin method, Applied nd Computtionl Mechnics, 5 (0) 5 4. [] A. Ajovlsit, G. Petrucci,B. Zuccrello, Determintion of nonuniform residul stresses using the Ring- Core method, Journl of Engineering Mterils nd Technology, 8( ) (996) 4-8. [] M. Brsnti, M. Beghini, C. Sntus, A. Benincs, L. Bertelli, Integrl method coefficients for the ring-core technique to evlute non-uniform residul stresses, The Journl of Strin Anlysis for Engineering Design, 53(4) (08) 0-4. Plese cite this rticle using: M. A. Mozm nd M. Honrpisheh, Experimentl nd Numericl Study on the Accurcy of Residul Stress Mesurement by Incrementl Ring-Core Method, AUT J. Mech. Eng., () (08) DOI: 0.060/jme

12