This paper describes tests to determine if the Bauschinger effect can act as an\ud
additional source of formability, this may possibly explain the enhanced formability observed in incremental sheet forming Small cylindrical products have been made by deep drawing and wall ironing. The upper edges have been necked to various levels of reduction. Tensile test specimens have been cut from the necked upper edges and tested, causing an almost perfect stress/strain reversal. An increase of strain could be observed indeed. The results are discussed using the Considère condition as a guideline

Boogaard, A.H. van den

Emmens, W.C.

English

This paper describes tests to determine if the Bauschinger effect can act as an additional source of formability, this may possibly explain the enhanced formability observed in incremental sheet forming Small cylindrical products have been made by deep drawing and wall ironing. The upper edges have been necked to various levels of reduction. Tensile test specimens have been cut from the necked upper edges and tested, causing an almost perfect stress/strain reversal. An increase of strain could be observed indeed. The results are discussed using the Considère condition as a guideline

van den Boogaard, Antonius H.

University of Twente Research Information

   2 nd  International Conference on New Forming Technology, Bremen, September 20-21, 2007 Formability created by the Bauschinger effect?W. C. Emmensa, A. H. van den BoogaardbaCORUS RD&T, P.O.Box 10.000, 1970 CA IJmuiden, the Netherlands bUniversity of Twente, P.O.Box 217, 7500 AE Enschede, the Netherlands aw.c.emmens@utwente.nl,  bA.H.vandenBoogaard@utwente.nl This paper  describes  tests  to  determine  if  the  Bauschinger  effect  can  act  as  an additional  source of  formability,  this  may possibly  explain  the enhanced formability observed in incremental sheet forming Small cylindrical products have been made by deep drawing and wall ironing. The upper edges have been necked to various levels of reduction. Tensile test specimens have been cut from the necked upper edges and tested, causing an almost perfect stress/strain reversal. An increase of strain could be observed  indeed.  The  results  are  discussed  using  the  Considère  condition  as  a guideline.IntroductionFigure 1. A two-piece can in early production stage, the diameter has been reduced from 66 mm to 62 mm over a large part of the height (body-necked). In  cases  of  classic  stamping  the  formability  of  the  material  is  restricted  by  the occurrence of instabilities that cause fracture. These limits are expressed by the well known Forming Limit Curve (FLC). However situations have been encountered as well where the material could be stretched well above the FLC without fracture. This is for example the case in Incremental Sheet Forming (ISF). A special variant of ISF is the shaping of beer and beverage cans by means of a high pressure water jet, this has been described before in detail [1,2]. 1Formability created by the Bauschinger effect?                                                                                So  far  little  effort  seems  to  be  made  to  find  out  why  in  ISF  the  material  shows enhanced formability. One of the possible mechanisms that has been mentioned is the Bauschinger effect. This paper describes tests that have been carried out to check if this claim is true. As this was done with a background in can shaping, can making techniques and equipment present at Corus have been used throughout.The purpose of  can shaping is  to  give the  can a more  fanciful  shape so that  the consumer  can  distinguish  the  brand  easily  in  the  supermarket.  Normally  this  is achieved by changing the overall contour of the can, and this is done by moving some parts of the wall outwards. A consequence is that the outside dimensions increase but this is limited: a too large increase will make it impossible to handle the can in standard production  lines.  A  possible  solution  put  forward  is  to  initially  decrease  the  can dimensions as shown in figure 1 (this process is called body-necking). In this way a change of overall contour can be achieved without expanding the can too much.Expanding the can after necking causes a stress/strain reversal, and this might evoke the well-known Bauschinger effect. It had been suggested that this effect would also increase the formability of the heavily cold worked can wall but no evidence could be found that supported this. Therefore a preliminary test was carried out by taking some tensile test  samples out  of  the wall  of  a body-necked can and comparing those to samples taken from comparable unnecked cans, the result is shown in figure 2. There is indeed an increase of formability expressed by the fracture strain, this increase may look  very  small  but  it  is  still  relevant.  This  result  was  sufficient  to  start  a  more systematic approach.0.0 0.5 1.0 1.5 2.0 2.5strain (%)02505007501000stress (MPa)normal canbody-necked canFigure 2. Tensile test results (engineering) taken from a body-necked can as in figure 1, and from a comparable standard can; tested in tangential direction.Experimental proceduresBlanks of 136 mm diameter were cut from standard 0.22 mm thick can stock material. The blanks were deep drawn into 66 mm diameter cups. One half of the cups were wall ironed to 160  µm wall thickness (series A), the other half to 110  µm wall thickness (series  B).  All  cups  were  trimmed  to  75  mm height.  The cups  were  subsequently 2   2 nd  International Conference on New Forming Technology, Bremen, September 20-21, 2007 necked  to  different  levels  of  reduction  (meaning  decrease  of  diameter)  using  a standard die-necker. This is always done in small steps to limit the axial load on the cups, and to limit the possibility of wrinkling. From the total collection of cups series were collected with approximately 7%, 12%, 16% and 20% necking reduction; samples are shown in figure 3. The total forming history (calculated) of the upper edge of the cups is presented in figure 4. Figure 3. Products used for the tests made by deep drawing, wall ironing and necking; the diameter is 66 mm. Tensile test specimens were cut from the upper, necked part in tangential direction.-1.0 -0.8 -0.6 -0.4 -0.2 0.00.00.20.40.60.81.01.2εε zφdeep drawingwallironingneckingABFigure 4. Overview of the forming history (calculated) of the upper edge of the products used in the tests. Series A had a final wall thickness of 160 mm, series B of 110 mm. The difference in deep drawing deformation is caused by the fact that for series B a relatively large part of the wall had to be removed to obtain a cup height of 75 mm.Following tensile test samples were cut from the upper part of the cups in tangential direction  and  tested.  Note  that  necking  with  a  die  (contrary  to  necking  with  rolls) creates an almost perfect uniaxial compressive state in the wall. This means that when performing the tensile tests, that also creates a uniaxial state, the stress/strain state is almost perfectly reversed. Due to the relatively large cup diameter (compared to the wall thickness) the strain state is more or less uniform over the material thickness. This presents an ideal situation to study the Bauschinger effect.3Formability created by the Bauschinger effect?                                                                                ResultsTensile specimens where cut from the upper (necked) part  of  all  cups in tangential direction and tested. All tests were performed threefold, the data presented following presents the mean of these three measurements. Figure 5 presents two stress-strain curves (engineering) that are typical. The curve for the unnecked situation is typical for heavily cold worked material like that of the can wall; the amount of hardening is well beyond  the  stability  limit  and  the  material  fractures  immediately  (some  plastic deformation still occurs due to the high level of strain-rate hardening of steel). From all curves the following data were obtained:• the tensile strength (UTS) • the uniform elongation• the total elongation at fracture0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0strain (%)0200400600800stress (MPa)unnecked cup edgenecked cup edgeFigure 5. Two typical stress-strain curves (engineering) taken from the upper part of the products.Ideally the yield stress of the material should be examined to study the Bauschinger effect. However this is difficult to determine from the tensile curves (see figure 5). So the tensile strength has been used instead, this differs only slightly from the yield stress due to the low amount of plastic straining; the results are presented in figure 6. If there would  not  be a  Bauschinger  effect  we  would  expect  the  strength  to  increase with increasing  necking  reduction  as  the  material  has  been  subjected  to  additional deformation,  this  is  shown  with  the  dotted  lines  (the  slope  is  based  on  general assumptions). However we see that the strength decreases instead, and also that the decrease  of  strength  is  larger  for  larger  necking  reductions  with  little  difference between  the  series  A  and  B.  This  observation  that  the  strength  decreases  with increasing reduction is remarkable; it is not known if this is a common result of the Bauschinger effect. It may also be caused by the fact that the necking operation itself causes a change in strain path (see figure 4) and the observed behaviour may still be a remnant of that. 4   2 nd  International Conference on New Forming Technology, Bremen, September 20-21, 2007 0 5 10 15 20 25amount of necking reduction (%)500600700800tensile strength (MPa)series Aseries BFigure 6. Reduction of tensile strength as observed from the tensile tests. The dashed lines indicate the expected strength without the Bauschinger effect.The measured elongations are presented in figure 7. We clearly see an increase of elongation due to the necking process. Note that this increase is basically independent of the necking reduction. The uniform elongation shows little difference between series A and B, only in the total elongation we see a difference the cause of which is unknown (and not investigated). The increase in formability (strain) seems to be an on-off case: the effect is simply there or it is not, independent of the forming history.0 5 10 15 20 25amount of necking reduction (%)01234elongation (%)uniformtotalseries Aseries BFigure 7. Increase of formability expressed as elongation (uniform and total) measured from the tensile tests.DiscussionTo  understand  these  phenomena  we  have  to  look  more  specifically  to  what  the Bauschinger effect in fact is. Figure 8 shows a recorded stress-strain curve for high strength steel that clearly shows the effect. The Bauschinger effect is best known for its reduction  of  the  momentary  yield  stress,  that  effect  can be  seen at  B  in  figure  8 (“Permanent  stress offset”).  However we are more interested in another effect  also shown in figure 8: the stress-strain curve for the reversed state (below the zero line) 5Formability created by the Bauschinger effect?                                                                                does not show a distinct yield point as the original curve, but a more gradual transition from situation A to situation B, this is indicated as the “Transient Bauschinger effect”. This can also be seen in figure 9 that presents stress-strain curves for pre-strained material with varying changes in strain path. For abrupt changes an overshoot is seen, but for more gradual changes in strain path a transient effect is clearly visible as well. This transient effect  can also be noticed in the two curves in figure 5: for stresses above 200 MPa the curve for the necked cup already deviates from the elastic line.Figure 8. Typical phenomena during stress reversal: the Bauschinger effect [3].Figure 9. Stress-strain curves for pre-stressed material showing typical effects [4].6   2 nd  International Conference on New Forming Technology, Bremen, September 20-21, 2007 In  stretching  operations  (including  the  tensile  test)  formability  is  limited  by  the occurrence of instabilities. The so-called Considère condition tells that the tensile test operation is stable as long as: σ>εσdd(1)where  σ and  ε are the true stress and true strain respectively.  This applies to ANY situation  where  the  stress  is  increasing  with  strain,  regardless  of  the  underlying metallurgical  processes.  We can  now understand  what  is  happening:  the  transient effect creates a situation where there is again considerable ‘hardening’ meaning that dσ/dε is large again over a certain range of strain.In figure 8 the range in strain of the transient effect  is approx. 4%, in figure 9 it is approx. 15%. It is not known if these values are typical and comparable to our situation. The observed effect in our tests is much smaller and this may be disappointing to the reader: the uniform elongation increased only from 1% to 2% (figure 7). Although this is a doubling, the absolute size is very small. However this is not unexpectedly. The can wall material is very hard (σ = 700-800 MPa) and the rate of hardening has dropped to low levels (dσ/dε = 150-200 MPa). Comparing this to equation (1) makes it clear that it will  be very difficult  to change the situation in such a way that the condition is met again. It can hardly be expected that the Bauschinger effect will decrease σ sufficiently to  satisfy  (1),  so  we  can  only  expect  the  transient  effect  to  be  effective  if  at  all. Nevertheless an increase of strain is observed, even in these awkward situations. The results of figure 7 suggest that the effect is independent of the forming history, but for the moment this is just speculation. However  in softer  materials  the situation will  be different.  If  a  material  is  stretched somewhat beyond the stability limit (by some means) we have a situation that dσ/dε is not too much smaller than σ. The Bauschinger effect will both increase dσ/dε (maybe considerably,  transient  effect)  and decrease  σ (permanent  effect)  meaning that  the situation  becomes  stable  again.  If  the  material  is  hardened  somewhat  more  the permanent  effect  may  not  be  sufficient  to  lower  σ sufficiently  any  more,  but  the transient  effect  is  always  there.  As  only  a  (relatively)  small  increase  of  dσ/dε is sufficient, the effect is expected to be larger than found in the tests. This implies that for soft material the increase of formability by the Bauschinger effect is expected to be (much) larger than observed in the tests presented here. Nevertheless, we observe that the formability of the can walls does increase and this simply proves that the proposed mechanism does exist.Conclusions• Transient  effects  like  the  transient  Bauschinger  effect  can  create  enhanced formability in materials subjected to changes in strain path in general, and to cyclic bending/unbending operations specifically.• Necking of cylindrical parts allows compression in uniaxial mode, this is ideal for studying the Bauschinger effect. Material to be studied in the undeformed state 7Formability created by the Bauschinger effect?                                                                                can be tested by necking cylinders manufactured by bending and welding as in common 3-piece food cans.References[1]  W.C.  Emmens;  Water  Jet  Forming  of  Steel  Beverage  Cans;  Proceedings  1st ICNFT, Harbin, China, Sept. 6-9, 2004, pp 285-290. Also: Int. J. of Machine Tools & Manufacture, vol 46-11 (2006), pp 1243-1247.[2] W.C. Emmens; Detailed Incremental Forming of Steel Beverage Cans by a High-Pressure Water Jet;  Proceedings 12th Shemet, Palermo, Italy,  April  1-4, 2007,  Key Engineering Materials vol 344(2007), pp 567-574.[3]  T.  Uemori,  T.  Okada,  F.  Yoshida;  Importance  of  Appropriate  Modelling  of  the Bauschinger Effect in Springback Analysis; J. JSTP, vol 43 (2002), no. 498, pp. 639-643 (in Japanese).[4]  M.  van  Riel,  A.H.  van  den  Boogaard;  Stress-strain  responses  for  continuous orthogonal strain path changes with increasing sharpness; accepted for publication in Scripta Materialia.8

Formability created by the bauschinger effect

Detailed Incremental Forming of Steel Beverage Cans by a HighPressure Water Jet;

Importance of Appropriate Modelling of the Bauschinger Effect in Springback Analysis;

Stress-strain responses for continuous orthogonal strain path changes with increasing sharpness; accepted for publication in Scripta Materialia.

Water Jet Forming of Steel Beverage Cans;

http://purl.utwente.nl/publications/59635

Formability created by the Bauschinger effect?

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