Numerical and experimental investigation on shot-peening induced deformation. Application to sheet metal forming.

Transcription

1 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN Numerical and exerimental investigation on shot-eening induced deformation. Alication to sheet metal forming. Florent Cochennec 1, Emmanuelle Rouhaud 1, Lionel Roucoules 1, Bruno Flan 2. 1 University of technology of Troyes, Charles Delaunay Institute FRE 2848, Laboratory of Mechanical Systems and Concurrent Engineering. 12, rue Marie Curie BP26 11 TROYES Cedex FRANCE. 2 Sisson Lehmann Wheelabrator grou. 24, rue Camille Didier BP39 8 Charleville- Mezieres Cedex FRANCE. ABSTRACT The een forming rocess is commonly used in the aeronautical industry to form large wing skin anels. This rocess resents many advantages in terms of cost, roduction time, and beneficial induced residual stresses. Setting the accurate rocess arameters to form a given attern requires however a certain exerience and sometimes many trials and errors. The authors roose to model the shot eening induced deformations by elastically equilibrating the real lastic strain gradient resent in the whole structure. A comlete numerical and exerimental rotocol is roosed to determine the lastic strain gradient assuming the knowledge of some exerimental data. The roosed aroach consists in determining the lastic strain field by inverse calculation based on exerimentally measured residual stresses fields. A second aroach is based on the inverse calculation of shot eening induced lastic strains knowing the global deformation of the treated sheet. A comarison between the roosed aroaches alied to artially treated sheets is resented along with exerimental data. The numerical results are in good agreement with exerimental data and show the strong influence of the eening ath on the resulting global deformations of the treated samles. INTRODUCTION Shot-eening rocesses have been used for more than fifty years to imrove the mechanical behaviour of mechanical comonents. It consists in imacting the surface of the treated art with many steel shots, which induces a lastic strain flow and a corresonding comressive residual stress state under the surface of the comonent (Lu et al., 1991). The induced residual stresses are not suosed to modify the geometry of the art, because it is confined to the surface but it can nevertheless imly a distortion of the structure deending on its geometry, due to the global equilibrium of stresses. The een forming rocess itself is alied to metal sheets to form comlex metallic anels with local reeated imacts of shots on the surface (O Hara, 22). It is mainly used to form large wing skin anels in the aeronautic industry. This forming rocess offers many advantages: the manufacturing requires no dies or resses, comlex sheets metal can be treated and beneficial mechanical erformance can be obtained (Baughman, 1984). While its alication to form aeronautical comonents dates from over fifty years, the choice of eening arameters still deends on the manufacturing oerator knowledge and trial and

2 This document was resented at the Denver X-ray Conference (DXC) on Alications of X-ray Analysis. Sonsored by the International Centre for Diffraction Data (ICDD). This document is rovided by ICDD in cooeration with the authors and resenters of the DXC for the exress urose of educating the scientific community. All coyrights for the document are retained by ICDD. Usage is restricted for the uroses of education and scientific research. DXC Website ICDD Website -

3 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN error tests (Yamada et al., 22). Numerical models have also been roosed to redict the effects of shot-eening on the geometry of the treated arts (Levers and Prior, 1998). These models are generally based on an exerimental calibration of a user-defined equivalent load that is able to model the final distortion of the shot-eened art. The scoe of the resented work is to investigate the lastic strain field in shot-eened metallic lates in different treatment cases. A numerical rocedure based on the introduction of initial lastic strain gradients is roosed to model the deformations of shot-eened lates. Aluminum alloy lates have been shot-eened and the measurement of the resulting residual stresses and distortions has been carried out for comarison with numerical modeling. After the definition of exerimental cases, this aer deals with numerical identification of lastic strain fields along the treated samles. Finally, the numerical results are comared for validation to exerimental measurements. EXPERIMENTAL DATA 224T3 aluminum alloy laminated lates of different thicknesses have been shot-eened without constrain under the same eening conditions. All the eened lates have been cut out from the same material batch. The eening treatment was erformed with air comressed eening machine. The lates have been totally or artially shot eened. The lates deflections have been measured using a three dimensional measurement machine. The geometry of the treated lates and the defined eening aths are given in Figures 1.a and 2.a for artially and totally shot-eened cases. The resulting distortions are lotted in Figures 1 and 2. These distortions resent an imortant variation in the toology itself deending on whether the lates are thick or thin. The distortions show that for thick totally shot-eened lates, the eening ath has no influence on the toology of the shae while for thin lates the shae deends strongly on the eening ath direction. 2 mm Peening direction 5 mm 3 mm a. Illustration of the geometries of the artially shot-eened lates.

4 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN , Deth (mm) -,2 -,4 -, , -,5-1, -1,5-2, -,8-1, Measured - Normal to eening direction -1,2-2,5-3, -3,5 Measured - Normal to eening direction -4, b. 5 mm thick shot-eened late. c. 2 mm thick shot-eened late. Figure 1. Illustration of the artially shot-eened cases and resulting distortions. 2 mm -1, a. Illustration of the geometries of the totally shot-eened lates , -,5 3 mm ,5-2, -2, , -3,5-4, Measured - Normal to eening direction Measured - Normal to eening direction b. 5 mm thick shot-eened late. c. 2 mm thick shot-eened late. Figure 2. Illustration of the totally shot-eened cases and resulting distortions. The in-deth residual stress rofiles were measured using the incremental hole-drilling method and have been comleted by surface measurements of the stresses by X-ray diffraction in the eening ath direction. The microstrains induced by the drilled hole have been measured with strain gages and a finite element rocedure has been secifically develoed to comute the residual stresses. This finite element treatment relies on the numerical introduction of an initial lastic strain field in order to simulate the real comlete residual stress state of the structure. Then, the drilling is simulated on the modeled structure submitted to an unknown lastic strain field and the microstrains induced by the drilling are calculated. Then, an inverse calculation is made to comute the lastic strain field that induced the measured microstrains rofiles. This rotocol insures that the comuted residual stresses resect the equilibrium conditions of the whole structure. This is esecially imortant for calculating the correct residual stresses field in the artially shot-eened lates.

5 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN The X-ray diffraction analysis has been done using the classical sin²(ψ) method, the diffracted lattice lane being the {3 1 1} lane. The in-deth residual stresses rofiles are given in Figure 3 for the eening cases defined above. The residual stresses measured in the artially shot-eened relatively thick secimen (see Figure 3.a) show a similar form between eening and normal to eening directions while those measured in relatively thin secimen (see Figure 3.b) show a strong difference between these two directions, which confirms the observations made on the distortions of these lates. The microstrains evaluated with the drilling of the 5 mm thick totally shot-eened secimen resented an indeendence are the same in all the direction on the surface. The comutation of the residual stresses has thus been done under an axisymmetric assumtion (see Figure 3.b). Residual stress (MPa) 1 5, , -2, -3, -4, Normal to eening direction Peening direction Deth (mm) Peening direction - Xray diffraction -5, Residual stress (MPa) , -,5-1, -1,5 Normal to eening direction Peening direction Deth (mm) Xray difraction - Peening direction a. 5 mm thick artially shot-eened late. b. 2 mm thick artially shot-eened late. Residual stress (MPa) 2-2, Deth (mm) Post-treated in-lane isotroic stress X-ray diffraction c. 5 mm thick totally shot-eened late. Figure 3. Residual stresses measured for the different eening cases. NUMERICAL IDENTIFICATION OF PLASTIC STRAIN GRADIENTS The scoe of the numerical study is to comute the deflections associated to the material accommodation of the incomatible lastic strain field induced by the rocess. The lastic strain field is suosed to be unchanged after shot-eening, i.e. no lastic flow occurs after releasing the samles. The roblem can then be treated in elasticity and the knowledge of the geometric domain, the residual stresses and the elastic characteristics of the samle rovides the existence and uniqueness of the solution (Bérest et al., 23).

6 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN Let us consider a structure with a free surface of normal z that resents a suerficial lastic zone induced by shot-eening. The lastic strain tensor is assumed to take the form: ε xx ~ ε = ε (1) yy ( ε + ε ) xx yy T The total strain tensor ~ ε can be decomosed additively in its elastic and lastic arts: ~ T e ε = ~ ε + ~ ε (2) The ~ lastic flow induced by the reeated imacts, reresented by the strain tensor field ε, and the total strain field ~ ε T are taken as the unknown of the roblem. The generalized Hooke s law lets us exress the elastic tensor field in function of the residual stresses under the following form: ~ R T ~ T σ = λ tr( ~ ε ) I + 2µε~ 2µ ~ ε (3) The total strain tensor must resect the comatibility equations which are, in the case of a numerical resolution using a finite element method, imlicitly verified by the condition of connectivity of the nodes describing the structure. The comatibility conditions, accomanied by the knowledge of residual stresses in the structure, are then sufficient to determine the lastic strain tensor and the resulting total strain tensor. The ~ equivalent roblem is treated as an initial strain roblem. The lastic strain field ε induced by the reeated imacts is numerically introduced in a z-olynomial form: 2 ε = ( z ).( A z + A z + A ) xx ε = ( z ).( B z + B z + B ) yy 2 1 ε = ε ε zz xx yy (4) Where is the lastic deth and A, A 1, A 2, B, B 1, B 2 are real coefficients. The secified boundary conditions are only symmetry conditions. The gravity is neglected in all cases. While little strains assumtion is made, the roblem is treated by using corotational reference frames in order to take large dislacements into account. A unique relation exists between the incomatible art of the lastic strains and the residual stresses, so the coefficients, A, A 1, A 2, B, B 1, B 2 can be identified by inverse calculation while comaring the simulated and measured residual stresses. Another way to comute the in-lane reartition of lastic strains is to iteratively comare the simulated and measured deflections under some assumtions. The relationshi between the distortion of the late and residual stresses being not unique, it is necessary to fix some of the coefficients of the z-olynomial form. The choice has been made to fix seudo-arbitrarily the real coefficients, A 1, A 2, B 1, B 2 of equation (4). The inverse calculation of the A and B coefficient can then be made by comaring the

7 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN simulated and measured distortions. The identified lastic strains are, in such a case, qualitatively interesting for the investigation of the in-lane direction deendency of the lastic strains induced by shot-eening. RESULTS The lastic strain gradients have been identified with the measured residual stresses rofiles. The identified lastic strains rofiles are not deending of the in-lane directions for the 5 mm thick artially shot-eened cases while strong differences are observed for the 2 mm thick secimen. The resulting simulated deflections are lotted in Figure 4 and comared with the measured deflections. The lastic strains gradients identified from the distortion measurement of the lates are lotted in Figure 5 for the 5 mm and 2 mm thick artially shot-eened cases , Deth (mm) -,2 -, ,6-6 -,8 Measured - Normal to eening direction -1, Simulated - Normal to eening direction -1,2-8 Simulated - Normal to eening direction -1 Measured - Normal to eening direction -12 a. 5 mm thick artially shot-eened late. b. 2 mm thick artially shot-eened late , -,5-1, -1,5-2, -2,5-3, -3,5-4, Measured - Normal to eening direction Simulated - Normal to eening direction c. 5 mm thick totally shot-eened late. Figure 4. Comarison of the measured and simulated distortions for the different eening cases. Inverse calculation based on measured residual stresses.

8 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN Plastic strain,7,6 Simulated - Normal to eening direction Plastic strain,12,1 Simulated - Normal to eening direction,5,8,4,3,6,2,4,1,2,,1,2,3,4 Deth (mm),, -,1 -,2 -,3 -,4 Deth (mm) a. 5 mm thick artially shot-eened late. b. 2 mm thick artially shot-eened late. Figure 5. Identified lastic strains gradients. Inverse calculation based on measured distortions. DISCUSSION The resented numerical model gives good results for thick shot-eened lates. In this case the same lastic strains gradients exists in all directions of the lane, the curvatures and residual stresses being deendent of the geometrical characteristics of the samles and of the eening treatment. The results obtained for thin shot-eened lates differ from the exerimental observations. The identified lastic strains rofiles lotted in Figure 5.b show indeed a strong difference between eening direction and normal to eening direction. Such a trend is observed while identifying lastic strains by comaring measured distortions or measured residual stresses. The deflections shown in Figure 4.b are calculated with lastic strains that are directly identified to the measured residual stresses. This leads to large errors committed on the simulated distortions. In Figure 5.b, the lastic strains are directly identified to the measured distortions under the assumtion of the form of its gradients along the deth of the late. This leads to large errors on the estimation of the in-lane stress reartition along the surface of the late. The exerimental observations that can be made on thin totally shot-eened lates show that the lastic flow is largely oriented in the normal to eening direction (see Figure 2.c). Then, it can be assumed that the lastic strains identified from the measurement of the residual stresses in the deth of the late are satisfying. The hyothesis of homogeneity of the lastic strains along the eening stri has then to be revised by further exerimental and numerical investigations. CONCLUSION A ertinent numerical model has been established for the simulation of the distortions induced by shot-eening. The numerical results are in good agreement with exerimental measurements for relatively thick secimens. It shows that such lates resent an in-lane isotroic behavior in terms of lastic strains, residual stresses and curvatures. The results obtained for relatively thin lates are in oor agreement with exerimental measurements. It shows nevertheless a strong biaxiality of the mechanical fields induced by the reeated imacts. Cylindrical shaes have indeed been obtained while eening such thin lates

9 Coyright JCPDS-International Centre for Diffraction Data 29 ISSN without constraining devices. Further numerical and exerimental investigations will be run in order to evaluate the gradient of lastic strain that can exist along the eening stris, which could lead to a bad rediction of the final distortion of the treated lates. The numerical model will be alied to more comlex sheet geometries to show its alicability to real een forming industrial roblems. ACKNOLEDGEMENT This Ph-D research work was suorted in art by Conseil Régional Chamagne- Ardenne (district grant) and the Euroean Social Fund. REFERENCES Baughman D. L. (1984) An overview of een forming technology. Proceedings of the ICSP2, Chicago. Bérest, P., Vouille G. (23). C. R. Mecanique Korsunski A.M., Regino G., Nowell D. (24). Variational determination of eigenstrain sources of residual stress. Proceedings of the Intl. Conf. on Comutational and Exerimental Engng and Sci, Madeira. Korsunsky A.M. (25). On the Modelling of Residual Stresses Due to Surface Peening Using Eigenstrain Distributions. Journal of Strain Analysis, 4 (8) Lu J., Flavenot J.F., Lieurade H.P. (1991) Intégration des notions de contraintes résiduelles dans les bureaux d études, démarche globale. In Les contraintes résiduelles au bureau d études. Senlis : CETIM. ISBN Levers A., Prior A. (1998) Finite element analysis of shot eening. In Journal of Materials Processing Technology. 8: O Hara P. (22) Peen-forming A develoing technique. Proceedings of the ICSP8, Garmisch-Partenkirchen. Yamada T., Takahashi T. et al. (22) Develoment of Shot Peening for Wing Integral Skin for Continental Business Jets. In Mitsubishi Heavy Industries Technical Review. 39 (2):