The validation of the upper-bound elemental technique (UBET) in the prediction of strain distributions in forgings

Journal of Matermls Processing Technology, 30 (1992) 231-244

231

Elsevier

The validation of the upper-bound elemental technique (UBET) in the prediction of strain distributions in forgings B O Oyekanml Natmnal Metal Research and Development Centre, Jos, N~germ

A N Bramley and F H Osman School of Mechanwal Engmeenng Unwerslty of Bath, UK (Received March 27, 1991, accepted July 23, 1991 )

Industrial Summary Many researchers have been developing predictive methods in order to establish the behawour of metals at the onset of plastic flow and the upper-bound elemental technique (UBET) is a partmularly suitable practical method whmh has been developed by the authors This paper presents a comparison between the strata d~stmbutlon predicted by UBET with those obtained by an experimental metallographm technique It describes an experimental evaluation of strain distributions within a moderately complex amsymmetnc forged component, using an established microstructural evaluation technique The resultant analysis is then applied to validate the simulated forging and strain distribution obtained by UBET, for the same component The potential of the UBET for practical apphcation and academic enhancement ~s demonstrated thereby

1. I n t r o d u c t i o n

The need for greater efficiency in plant and material utilization in the forging industry cannot be over emphasized, from both the economm and productquahty considerations To facilitate this need, adequate understanchng and effective simulation is required of tool forces and metal flow, which are the important parameters characteristic of a particular forging process In recent years the developments in dlgntal computing, theories and numerical methods have afforded the potential of providing detailed studies of deformation m metal-forming, including the internal strain distribution within the workpmce It is difficult, however, to provide experimental evidence of their validity, due to the lack of experimental data Computer-aided methods for forging design are becoming more popular, as they offer rapid information processing, mcluchng graphic layouts and the

232

evaluatmn of comparative designs, leading to better declsmns being made The use of a computer-atded forging-analysis therefore appears consistent w~th these industrial developments and can exploit the full potential of the power of the computer and the decrease in capital outlay for modern lnstallatmns The upper-bound approach has been used extensively m process analysis and has shown considerable potentml m application to real situations In recent years it has been used also to predict the metal flow and the forging loads at any stage of axlsymmetnc forging-processes [1] The techmque has the potentml of being qutck to use, apphcable to many shapes, and requiring minimal skilled knowledge or previous experience In this way it offers considerable advantages over the fimte-element based methods, although the latter are intrinsically capable of greater accuracy The UBET is an lnteracttve computer package which was developed to simulate the forging-process metal-flow and load from the initial billet, through to the finished component, m an incremental manner Apphcatmn of thxs technique ts already being made by the forging industry The facility for predmtmn of strata distributions m forglngs using the UBET, whxch has not as yet been well utilized, would equally be of great xmportance for the forging process and also for the understanding of the process mechamcs Th~s provides sufficient justlficatmn to explore the effectiveness of the UBET generally, for possible refinement and further wldemng of ~ts scope of apphcatmn 2. The basis and development of U B E T

The UBET is a plastmlty based interactive procedure, adapted from the upper-bound approach As a method of load prediction m metal-forming operatlons, it ~s known that the upper-bound procedure determines an upper hmlt of the load required to deform the metal Thxs ensures that a particular operation can actually be carrmd out without exceeding the predicted load Based on minimizing the power dxsslpated during plastm deformation, the upperbound power is computed in terms of the internal homogeneous deformation throughout the deforming volume, the power dissipated due to chscontlnultms along internal surfaces and the friction losses over the tool-material interface The best solution xs obtained by mm~m~zmg the power w~th respect to the velocity field inside the deforming region. The UBET has been under development over the past twenty years, and has been used to predmt metal flow and forging loads McDermott and Bramley [ 2 ] reported a development of an early version, whmh was a manual procedure based on the dlvlsmn of a forging cross-sectmn mto a number of elemental regions or rings of rectangular and triangular section They introduced also a range of elements capable of being linked to enable the analysis of forgings w~th appreciable curvature The elemental analysis was partially computer-

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:sed, which facilitated the use of the method by industry for the pre&ctlon of forging load and optimum flash geometry [ 3 ] Further refinement in(hcated that the pre(hctmn of metal flow should be capable of showing how the (he cavltms are filled and the role of the flash m that respect Slmphficatmn of the applicatmn to axmymmetmc operatmns was prov:ded, and expemmental shapes were chosen to illustrate typmal (he cawtms encountered m industry [4 ]. Osman and Bramley [5 ] further implemented an internal incremental procedure, m whmh a grM generally (10 × 10 points) is imposed on the component cross-sectmn, and the points incremented accordmg to the optlmlsed velocity-field An incremental effectlve-strmn procedure was apphed, with the assumptmn that the materml will deform along the flowhnes supemmposed on the mesh points. Thin represents the flowhne approach, which allows for the pre(hctmn of the amount of strata expermnced by each element The UBET analysis has been used m mvestlgatmns which included the effects of frmtlon, draft angle, strata rate and temperature, on load and metal flow [3] It has been used also to investigate the effects of varmus parameters on the degree of filhng, and led to a proposal of a general procedure for optimum billet geometry, and optimum flash (hmensmns and designs [6] A more comprehenmve rewew of the development of the techmque has been given by Bramley [1], who also presented further results illustrating the apphcatmn of UBET for the pre(hction of forging loads, metal flow, surface profiles and local (he-pressure, with benefits m terms of press selectmn, die design and preform demgn. 3. Implementation of UBET

The UBET is based on the concept of sub(hv:ding the plast,cally deforming shapes into a seines of singly connected elements of triangular and rectangular cross-sections In each of these standard regmns, the flow charactenstms are descmbed by a velocity field chosen in a form that ensures contmmty of flow through the entire volume of the component The metal flow ~s described by the boundary veloc:tles of the elements, which are determined by an optlmlsmg routine m order to estabhsh the set of velocltms that would g~vethe minimum overall rate of energy (hssipatmn The theoretmal details, the layout of the programme designs, and the associated computer programs have been given by Osman [7]. The initial (he-and-workpmce configuration is described by a series of straight hnes whmh generally result m an apprommatlon of the shapes, and a "squared off"' appearance of the simulations, necessary to keep the computational time down to a level at whmh interactive use would be possible After the shape apprommatmn, the cross-sectmn is sub-(hv:ded into elemental regmns automatmally, but arranged to satisfy the requirements that the elements be singly connected, that the number of elements generated are within the available computer capacity and that the boundaries of the deforming re-

234 glon coincide with the grid mtersectmn points The elemental sub-dlwsmn can also be adjusted to produce a reasonable number of elements at any stage of the process The mltml chmensmns of the workpmce and dins are defined by a set of coordinates whmh describe the cavity outhnes, and the size and positron of the billet at the commencement of the process The data points for the billet, top or bottom dins, have the same format the points are specified by their radml and axml positrons, and numbered sequentmlly starting from the lowest points on the centre hne Other data requirements include the fnctmn factor (m), assumed constant for all dm-materml interface boundaries, the dm velocity, and the materml flow property defined by the flow stress m terms of the power law stram-hardenmg behavlour of the material for a cold-forming operatmn and as a strata-rate sensttlve materml for hot forging. Flow slmulatmn proceeds by analysmg the mltml configuratmn of the dins and workpmce (either a billet or preform), and then allowing the ches to move through an approprmte increment of displacement, determined from the penetratmn distance and the total number of mcrements For each time increment, the free boundarms are chsplaced according to the velocity field determined from the optlmlsatmn procedure At the beginning of each increment the resultant flow is assumed under steady-state conditions when the displacement field advances through the cross-sectton During deformatmn, slmulatmn of the metal flow ]s presented by a wsual display, which can show the gross filhng of the cavttms and the flow reside the deforming regmn The mcrementatmn process is carrmd out automatically until dm closure The grid dlstortmn and local strata values are obtained from the mesh imposed on the forging cross-sectmn The total accummulated strams are obtained also from the summatmn of the strata experienced at each increment and the strata h~story of each element 4. Forging simulation

A reasonably complex axlsymmetrm component shape was selected for the forging investigations and is shown m Fig 1, along with the U B E T model of the component shape illustrating the sub-division into a set of rectangular and tmangular elements The dm was designed and manufactured and appropmate measurements were obtained to enable the identification of the coorehnates reqmred for the U B E T input data, as described earher Estimates of the billet d~menslons were obtained also from cons~deratmn of the component stze derived from the dm configurations In addition to the billet and dm coordinates, spec~ficatlons were given to charactemze the specimens using the flow-stress relatmns estabhshed from some plane-strata compression tests The constants m the power law equation a = a~e '~, were specified to define the flow behavlour

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of the samples and the process was carried out cold In order to evaluate the response of the simulations to different frictional conditions, different values of the friction factor (m) were used m the analysis The influence of strain rate was not utdised as the workpiece was cold worked and hence msensitwe to the strain rate induced during deformation [8] Ten incremental steps were used, and full optlmlsatlon was obtained to the most possible accuracy for each step Different levels of sub-dwlsions with the different number of regmns were examined also for each incremental step For each of the combination of conditions, outputs were obtained for the forging loads, the mesh distortion and the strain d l s t n b u t m n These were expected to be comparable with, or at least gwe an indication of, the experimental situation, the filling characteristics and the final forging load, from the c o m b m a t m n of the conditions used One example has been selected and was further analysed for comparisons w~th the experimental forging analysis 5. The microstructural e v a l u a t i o n technique

The mmrostructural evaluation procedure developed recently [9] is an experimental techmque for chrect evaluation of strata dmtnbutlons and accummulatlon within a workptece, and for general application m deformation studIes of forming processes It requires the determination of a calibration curve of annealed gram size against the a m o u n t of prior plastm strata whmh was obtained using a series of plane-strata compression-test specimens The most sensitive characteristic curve is determined by conducting a series of test sequences using chfferent annealing treatments The gram-s~ze dmtnbutlon in

236

an annealed forging can then be interpreted from the cahbratlon curve as a dlstnbutton of accumulated strain m the forging The technique has been demonstrated in the analysis of various amsymmetric forged components incorporating web and flash features [10], and a hub shape with a short wide shaft, typical of an extrusion forging process [9 ] It has been shown by Oyekanml [11] to be highly consistent, and capable of prowdmg a facility for assessing the vahdlty of existing analytmal methods It has been selected therefore to validate the analysis of the axlsymmetrlc component obtained from the UBET procedure described earlier 6. Material characteristics and experimental forgings

Cyhndrlcal bar stock of commercially pure alummmm was used for the investigations The as-received materials were homogemzed chemically and structurally, by a charactensatlon procedure described elsewhere [9] 150

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Test specimens were characterlsed by the flow-stress relations established from plane-strain compression tests The calibration curve of the recrystalhsed grain size m terms of strain was obtained by anneahng specimens taken from a series of compression tests. A cylindrical billet of 50 0 mm diameter × 70 0 mm length was machined for the forging of the axlsymmetrlc component shapes After forgang, the component was subjected to the experimental annealing procedure and the gram-size determination technique described in Ref. [9] 7. Results and discussion The stress data from the plane-strain compression tests are presented In the form of an equivalent stress-equivalent strain curve in Fig 2 The flow constants in the power-law stress equation were determined from log-log plots as I

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al = 137 7 MPa and n = O 248 The constants are used as inputs m the U B E T modelhng program Figure 3 Is the typical recrystalhsatlon diagram whmh has been used for the analysis of the component. It Is essentially hyperbohc, showing a continuous monotomc decrease of the recrystalhsed grain size with the pre-stram. Figure 4 illustrates the load-dmplacement charactenstms of the axmymmetnc component-shape determined experimentally and from U B E T models at different friction factors The typical upsetting, filling, and the complete filling or finlshmg stages can be identified easily Figure 5 Is the experimental map of recrystalhsed grain size distributions m the component and Fig. 6 is the corresponding strata dmtnbutlons obtained by using a cahbratmn curve from Fig 3 The rachal strata chstnbutmns at different positions m the forging are shown m Fxgs 7-9 Fxgure 7 shows the variations m the regions parallel to the surface

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F~g 6 Correspondingstrata dmtnbutmn to Fig 5 on the top (he, at z-- 23 5 mm, as mchcated by the component shape m Fig 5 The regions exhibit a generally high strata {above 1 0) obtained by the mlcrostructural technique, with a gentle rise m the strain values from the centre hne to the outer edge of the component. The m~crostructural techmque lnchcates higher values than the theory over the entire range, but their s~mflanty

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m trend is notable at the generally high-strata values Figure 8 shows the variations m the regions in the central boss z = 38.5 mm shown in Fig 5 Theory predicts a constant value of the stratus in these regions, whereas the experimental method mchcates a sharp rise at the che corner It is notable also that the U B E T falls to prechct the low-strained and the hlgh-stramed regions mdmated by the experimental method. Figure 9 represents the variation in the regions close to the parting hne The trends and values shown by both methods are s~mllar to those indicated m Fig 7, which represents similarly strained regions The highest strata values for the lntermechate lower regions, represented by Fig 9, have been mchcated to be chrectly below the the corner and

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243

the surrounding regions, by both techmques, whmh also indicate a gradual decrease from this maximum to a lower value, towards the outer edge F~gures 10 and 11 illustrate the ax:al distributions near the central and outer regmn of the forging, respectively, m a section through the boss In both cases a generally similar trend ~s observed for both techmques, although the prechcted values are on average lower than indmated by the mmrostructural techtuque Figure 12 :s a graphical representatmn of all the strain values evaluated from the component, and correlated between the theoretmal and the experimental techmques. The figure suggests that at low strain the UBET predmtmns are high and wce versa at high stratus, but that overall the general level is correct 8. Conclusions

The analyses provided by the mmrostructural-evaluatlon techmque has indicated and quantified quite sensitively regmns of severe- and hght-deformatmns ahke rather consistently, as would be expected m practice Although the UBET has failed to pred:ct very accurately the extreme levels of stratus, the average levels and trends have correlated quite well. Whilst the UBET solutions could be considered generally approximate, the experimental verifications have shown that the facility for the predmtlon of strata &stnbutlons in axlsymmetnc forgmgs has a great deal of potentml. The hmlted correlatmn is probably due to the way m wh:ch the tool-workpmce interface friction is handled in the UBET It is only accommodated in a scalar fashion and as such only affects the loads, whereas m reality the effect on metal flow can be qmte slgmficant A new element formulation being developed currently may enable th~s limitation to be overcome Acknowledgment

The authors appreciate profoundly the provision of the faclhtms for this research by Professor J Nutting at the Umverslty of Leeds where much of the work was carned out, and the award of the study fellowship through the Government of the Federal Repubhc of Nlgerm to one of them

References 1 A N Bramley, Computer aided forging design, Ann CIRP, 36 (1987) 135-138 2 R P McDermott and A N Bramley, Proc 15th Int Machine Tool Design and Research Con[, Birmingham, September 1974, MacMillan, London, 1975, pp 437-443 3 M N Islam and A N Bramley, MetaUurgm, {1983) 181-184 4 A N Bramley and J T Thornton, Proc 6th North American Metalworkmg Res Con/, Socmty of Manufacturing Engnneers, Gamsvllle, 1978, pp 96-102

244 5

6 7 8 9

10 11

F H Osman and A N Bramley, m J F T Plttman, R D Wood, J M Alexander and 0 C Zlenkmwlcz (Eds), Proc Conf on Numertcal Methods ~n Industrml Forming Processes, Swansea, 1982, Pmendge, Swansea, pp 333-342 M I Ghobnal, Computer aided analysis for axlsymmetnc forging, PhD Thesis, 1985, Umverslty of Leeds F H Osman, Computerlsed simulation of forging processes, PhD Thesis, 1981, Umverslty of Leeds A M Sabroff, F W Boulger and H J Hennmg, Forging Matermls and Practices, Reinhold, New York, 1968 B 0 0 y e k a n m l , T A Hughes and A N Bramley, A mmrostructural evaluation techmque for deformation studms m metalformmg processes, J Mater Process Technol, 21 (1990) 7589 B O Oyekanml, T A Hughes and A N Bramley, Proc EUROMAT '89, European Con/ on Advanced Matermls and Processes, November 22-24, 1989 B 0 0 y e k a n m l , The determination of strata distributions m forgnngs, PhD Thesm, 1988, Umverslty of Leeds