TALAT Lecture 3801


    Manufacturing Examples and Fundamentals
                                14 pages, 20 figures

   ...
3801 Manufacturing Examples and Fundamentals


Table of Contents


3801 Manufacturing Examples and Fundamentals .............
The superplastically formed reflector shown in Figure 3801.01.01 has very large
differences in drawing depths, making it d...
Large differences in drawing depth, reentrant corners and slanting body forms lead to
problems during manufacturing with c...
Fundamentals of Superplastic Behaviour

Figure 3801.01.05 shows the grain structure of the alloy AA 5083 in its convention...
with the superplastic forming process. The extremely low straining rate leads to
production times extending from about 5 m...
is not affected by the degree of plastic strain. The equation is then reduced to
 k f = C ⋅ ϕ m , which is given in Figure...
rate. In the case of superplastic forming, this leads to an increase of flow stress in the
necked region. The material flo...
F        v 
                                                              m = ln  A  / ln  2 
                    ...
Methods of Determining the Strain Rate Exponent m

Further calculating methods for determining m have been developed in or...
quotient of the logarithmic ratios of the flow stresses at the points A and C and the local
logarithmic strain rates. Acco...
Effect of Material Cross-Section on the Rate of
                                                            Cross-Sectiona...
Figure 3801.01.19 lists the m values obtained from literature for different forming
temperature ranges. It is to be noted ...
List of Figures


Figure No.   Figure Title (Overhead)
3801.00.01   Superplastic Sheet Shaped Components
3801.01.01   Supe...
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TALAT Lecture 3801: Manufacturing Examples and Fundamentals

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This lecture describes the fundamentals of the superplastic behaviour phenomenon of aluminium alloys and the basic process parameters which govern the manufacturing of superplastic sheet metal parts. General background in production engineering and material science is assumed.

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TALAT Lecture 3801: Manufacturing Examples and Fundamentals

  1. 1. TALAT Lecture 3801 Manufacturing Examples and Fundamentals 14 pages, 20 figures Advanced Level prepared by K.Siegert and T. Werle, Institut für Umformtechnik, Universität Stuttgart Objectives: − to describe the fundamentals of the superplastic behaviour phenomenon of aluminium alloys and the basic process parameters which govern the manufacturing of superplastic sheet metal parts Prerequisites: − General background in production engineering and material science Date of Issue: 1994  EAA - European Aluminium Association
  2. 2. 3801 Manufacturing Examples and Fundamentals Table of Contents 3801 Manufacturing Examples and Fundamentals .......................................2 Superplastic Sheet Shaped Components............................................................. 2 Definition of Superplastic Forming..................................................................... 4 Fundamentals of Superplastic Behaviour........................................................... 5 Methods of Determining the Strain Rate Exponent m .................................... 10 Factors Influencing the Strain Rate Exponent m ............................................ 11 List of Figures...................................................................................................... 14 Note: Literature/References at the end of TALAT Lecture 3805 Superplastic Sheet Shaped Components Superplastic Sheet Shaped Components Source: Superform Metals Ltd. alu Superplastic Sheet Shaped Components 3801.00.01 Training in Aluminium Application Technologies Figure 3801.00.01 gives some examples of superplastically formed aluminium parts of the company Superform Metals Ltd., England. The complex components shown are all fabricated in a low series production. Examples of superplastically formed parts are side panels of aeroplanes, facade elements, heat exchangers, gear boxes, fuel tanks, reflectors etc. TALAT 3801 2
  3. 3. The superplastically formed reflector shown in Figure 3801.01.01 has very large differences in drawing depths, making it difficult to produce the part with conventional sheet forming methods. Furthermore, the part has reentrant form segments at the circumference and a convex base, which can only be produced with additional sets of tooling with standard sheet forming processes. Superplastically Formed Reflector Source: Superform Metals Ltd. alu Superplastically Formed Reflector 3801.01.01 Training in Aluminium Application Technologies Figure 3801.01.02 shows superplastically formed building facade parts with a design which makes it extremely difficult to produce using conventional fabrication methods. The part on the left has two tilted surfaces ending in transverse ribs. A complicated material flow occurs at the transition zone. The extreme stretch forming process occurring here causes problems during cold forming. The high ribs prevent or hinder the transverse flow of material, which is further complicated by the sharp radii. Superplastically Formed Facade Parts Source: Superform Metals Ltd. alu Training in Aluminium Application Technologies Superplastically Formed Facade Parts 3801.01.02 TALAT 3801 3
  4. 4. Large differences in drawing depth, reentrant corners and slanting body forms lead to problems during manufacturing with cold forming methods. The superplastically formed tank shown in Figure 3801.01.03 is a good example of very complex sheet shaped parts. Superplastically Formed Fuel Tank Source: Superform Metals Ltd. alu Training in Aluminium Application Technologies Superplastically Formed Fuel Tank 3801.01.03 Definition of Superplastic Forming The technical definition of superplastic forming as given in Figure 3801.01.04 has been obtained from existing literature. It must be noted here that failure occurs due to a break up of the grain structure and not due to local necking as observed during tensile testing. Technical Definition of Superplastic Forming Superplasticity is that property of materials which makes it possible to obtain extremely large uniform and rupture elongations under pure tension loading. alu Training in Aluminium Application Technologies Technical Definition of Superplastic Forming 3801.01.04 TALAT 3801 4
  5. 5. Fundamentals of Superplastic Behaviour Figure 3801.01.05 shows the grain structure of the alloy AA 5083 in its conventional form and in the superplastic variation. Superplastic quality requires homogeneity, isotropy and extreme fineness of the grain structure, which is not normally achievable in standard sheet metal production Comparison: Conventional - Superplastic of AA 5083 AA 5083 SPF Grain Structure 100 µm 100 µm Source: Superform Metals Ltd. Grain size: µ > 100 µm Grain size: µ < 100 µm alu Grain Structure Comparison: Training in Aluminium Application Technologies Conventional - Superplastic 3801.01.05 The metallurgical requirements of materials for superplastic forming are listed in Figure 3801.01.06. The material must have a high resistance to grain growth and formation of pores. The stability of the grains, i.e. a high resistance to grain growth, is an essential material requirement, since the superplastic forming process for aluminium alloys is carried out at elevated temperatures and thus constitutes a thermally activated process. Metallurgical Requirements of Materials for Superplastic Forming • Very fine grains: 2 < d < 10 (20) µm • High resistance to grain growth • Strain rate has a very pronounced effect on the flow stress kf • High resistance to formation of pores alu Metallurgical Requirements of Materials for 3801.01.06 Training in Alum inium Application Technologies Superplastic Forming The basic process requirements for superplastic forming are summarized in Figure 3801.01.07. These requirements indicate the economical problems associated TALAT 3801 5
  6. 6. with the superplastic forming process. The extremely low straining rate leads to production times extending from about 5 minutes to a few hours. Process Requirements for Superplastic Forming Constant forming temperature TU ≥ 0,5 TS TU = forming temperature TS = melting temperature • Low strain rates 10-2 > ϕ > 10-5 1/s alu Training in Aluminium Application Technologies Process Requirements for Superplastic Forming 3801.01.07 Figure 3801.01.08 underlines the advantages and special technological properties of superplastic materials. Since the flow stress values are low, small forming forces are required which lead to low tool stresses. The potential of large uniform elongation properties provides optimum performance under severe stretch forming conditions. Technological Advantages of Superplastic Materials during Forming Uniform elongation and rupture Extremely small elongation in uniaxial flow stress tensile test of during forming 100 - 800 % kf = (4 -70) N/mm2 ⇓ ⇓ Large straining capacity Low forming forces, during stretch forming Low tool stresses alu Technological Advantages of Superplastic 3801.01.08 Training in Aluminium Application Technologies Materials during Forming Figure 3801.01.09 describes the general material law for plastic deformation according to Ludwik. The Ludwik material law gives the flow stress as a function of the logarithmic value of strain (or true strain), the strain hardening exponent, the log. strain rate and the rate coefficient. It is worth mentioning the fact that almost no strain hardening occurs during warm forming, i.e. the flow stress during superplastic forming TALAT 3801 6
  7. 7. is not affected by the degree of plastic strain. The equation is then reduced to k f = C ⋅ ϕ m , which is given in Figure 3801.01.10. Here, the importance of the exponent ! m for the superplastic forming behaviour of materials becomes obvious. The flow stress depends on the logarithmic strain rate and the strain rate exponent m. If the logarithmic strain rate is kept constant for a forming process, then the flow stress required depends only on the strain rate exponent m. The following figure depicts the principle of the effect on the material flow behaviour. Material Law according to Ludwik • kf = C ϕn ϕm • kf flow stress ϕ logarithmic strain rate C material constant n strain hardening coefficient ϕ logarithmic strain m rate exponent alu Training in Aluminium Application Technologies Material Law according to Ludwik 3801.01.09 Flow Stress according to Ludwik • Kf = C ϕm • kf flow stress ϕ logarithmic strain rate C material constant m rate exponent alu Flow Stress according to Ludwik 3801.01.10 Training in Aluminium Application Technologies Figure 3801.01.11 shows the momentary state of a tensile specimen under constant strain rate. When the local necking starts, different rate conditions become valid. In the necked region 2, the instantaneous local logarithmic strain rate is larger than in the region 1 without necking. Since the logarithmic strain rate is the differential of the logarithmic strain with respect to time, the strain in region 2 is greater than in region 1. The flow stress kf, as explained in Figure 3801.01.10, depends on the logarithmic strain TALAT 3801 7
  8. 8. rate. In the case of superplastic forming, this leads to an increase of flow stress in the necked region. The material flow is, therefore, displaced to the regions outside the necked region. This strain-rate-hardening effect in the necked region balances the necking tendency. Influence of the Start of Necking on the Flow Stress during the Tensile Test l1 1 Normal specimen cross-section ϕ1 = ln l 2 Start of necking 0 l1 l0 • dϕ1 ϕ1 = dt a0 a1 b1 b0 l2 l0 a0 • • dϕ2 > dϕ1, ϕ2 > ϕ1 l2 ϕ2 = ln l a2 0 kf = c ϕm b2 b0 • dϕ2 ϕ2 = kf2 > kf1 dt alu Influence of the Start of Necking on the Flow Stress 3801.01.11 Training in Aluminium Application Technologies during the Tensile Test Besides the logarithmic strain rate ϕ the strain rate exponent m is the second value ! which governs the flow stress in the Ludwik equation. The strain rate exponent depends on various factors listed in Figure 3801.01.12. Each alloy has its own characteristic m- value behaviour. Other factors which play an important role are the average grain size, the forming temperature and the logarithmic strain. A number of methods are available for measuring the rate exponent m. In principle, however, all these methods are based on the tensile test. Figure 3801.01.13 schematically indicates the influence of a sudden increase in drawing rate on the measured drawing force. A specimen is elongated with a drawing rate of v1 till a certain maximum stress is obtained, after which stationary flow begins. Once a defined specimen elongation is reached, the drawing rate is suddenly increased (or decreased) to the value v2. The change ratio v1/v2 lies between 2 to 2,5. Due to the increase in straining rate, a different drawing force level is attained. The points A and B are locations with similar elongations of logarithmic strains, so that these can be related to each other. It is obvious, that the influence of the logarithmic strain is only of minor importance. In this manner, a measuring point m = f(ϕ) can be determined for each tensile test. The force FA is determined by extrapolating the load diagram for the rate v1. According to Backofen, the rate exponent m can be calculated using the equation TALAT 3801 8
  9. 9. F  v  m = ln  A  / ln  2   FB   v1  Factors Influencing the Value of m Grain size Alloy • m m = f ( Alloy, Tu, ϕ, dgrain ) Forming Logarithmic temperature strain rate alu Training in Alum inium Application Technologies Factors Influencing the Value of m 3801.01.12 Effect of Increasing Drawing Rate on Drawing Force A v2 Drawing Force εA = εB v1 B Time alu Training in Aluminium Application Technologies Effect of Increasing Drawing Rate on Drawing Force 3801.01.13 TALAT 3801 9
  10. 10. Methods of Determining the Strain Rate Exponent m Further calculating methods for determining m have been developed in order to overcome the inaccuracy of the extrapolation method according to Backofen (see Figure 3801.01.13). The calculating points for the m values used in the various calculation methods are defined in the detailed force-time diagram, see Figure 3801.01.14, for sudden changes in the logarithmic strain rate from v1 to v2 or v2 to v1. Methods of Determining the Rate Exponent m E A v2 D´ B´ Drawing force F C v1 v1 D B E´ C´ Time alu Training in Aluminium Application Technologies Methods of Determining the Rate Exponent m 3801.01.14 Different Methods for Calculating the Rate Exponent m According to MORRISON ln ( kfA / kfC ) ln ( kfC´ / kfA ) m= or m= • • • • ln ( ϕA / ϕC ) ln ( ϕC´ / ϕA ) According to HEDWORTH and STOWELL ln ( FD´ / FE´ ) ln ( FE / FD ) m= or m= ln ( v2 / v1 ) ln ( v2 / v1 ) According to CUTLER ln ( kfA / kfD ) m= • • ln ( ϕ2 / ϕ1 ) alu Training in Aluminium Application Technologies Different Methods for Calculating the Rate Exponent 3801.01.15 Based on Figure 3801.01.14, the equations for the individual calculation methods are shown in Figure 3801.01.15. According to Morrison, the m value is calculated as the TALAT 3801 10
  11. 11. quotient of the logarithmic ratios of the flow stresses at the points A and C and the local logarithmic strain rates. According to Hedworth and Stowell, m can be calculated from the logarithmic ratios of the force values determined at the points D and E and their drawing rates. It is assumed here that the specimen cross-section immediately before and after the sudden strain rate jump is the same. According to Cutler, the m value is calculated from the logarithmic ratio of the flow stresses at the points A and D and the average strain rate before and after the rate jump. Factors Influencing the Strain Rate Exponent m The m value is shown qualitatively as a function of the logarithmic strain rate ϕ in ! Figure 3801.01.16. The parameters are the forming temperature and the average grain size. Reducing grain size and increasing forming temperatures give more favourable m values. Effect of Forming Temperature and Grain Size on the Rate Exponent m d3 G d2 R T3 T A m m value d1 E I T2 M N V P A T1 E R + S I = L U A Z E T E U R E Logarithmic strain rate Grain size Forming temperature d1 > d2 > d3 T1 < T2 < T3 alu Effect of Forming Temperature and Grain Size 3801.01.16 Training in Aluminium Application Technologies on the Rate Exponent m Figure 3801.01.17 shows the rate of cross-sectional area change dA/dt as a function of the cross-sectional area A for the m values of 1, 0.75, 0.5 and 0.25. For m = 1 (Newtonian flow), dA/dt is independent of A. Thus, an uncontrolled necking in the specimen cross-section does not occur even at high elongations and small specimen cross-sectional areas. The notch sensitivity of the specimen increases with decreasing m values. The effect of m on the flow resistance decreases, the logarithmic strain is locally concentrated and necking starts. TALAT 3801 11
  12. 12. Effect of Material Cross-Section on the Rate of Cross-Sectional Area Decrease m = 0.25 Rate of cross-sectional area decreases dA/dt m = 0.5 m = 0.75 m=1 Cross section A Effect of Material Cross-Section on the Rate of alu 3801.01.17 Training in Aluminium Application Technologies Cross-Sectional Area Decrease Figure 3801.01.18 clearly depicts the correlations between the m value, logarithmic strain rate and rupture elongation. The logarithmic strain rate has a very strong effect on flow stress in zone II. Both elongation at rupture and the m value also have their maxima in this zone. The zone I is rate insensitive, so that m and the attainable rupture elongation have their minimum values here. Similar conditions exist in zone III, i.e. low gradient of the flow stress curve with increasing strain rate. The m value also decreases in this zone. In summary, superplastic forming behaviour does only occur in the region of the rate zone II. Behaviour of Flow Stress, m Value and Fracture Elongation within the Three Rate Zones 103 0.9 Elongation at fracture I II III I II III I II III N/mm² m value 0.6 Flow stress kf 101 0.3 100 -6 0 -6 10 10-4 10-2 10-0 1/s 10 10-4 10-2 10-0 1/s 10-6 10-4 10-2 10-0 1/s Logarithmic strain rate Logarithmic strain rate Logarithmic strain rate Zone I Zone II Zone III Flow stress is almost Strain rate has a Flow stress is almost independent of strain pronounced effect on independent of strain rate, low m values, flow stress, high m values, rate, low m values, only small deformations large deformations possible only small deformations possible possible alu Behaviour of Flow Stress, m Value and Fracture 3801.01.18 Training in Aluminium Application Technologies Elongation within the Three Rate Zones TALAT 3801 12
  13. 13. Figure 3801.01.19 lists the m values obtained from literature for different forming temperature ranges. It is to be noted here, that the flow stress is almost independent of the strain rate at room temperature and increases with increasing temperature. The maximum values for m are obtained in the temperature range for superplastic forming. Rate Exponent and Forming Temperature RT ca. 200°C ca. 350°C ca. 550°C 1 Cold to half Warm forming Superplastic warm forming forming m Value 0.01 < m < 0.15 0.15 < m < 0.3 m > 0.3 0.5 Liquid 0 Temperature alu Training in Aluminium Application Technologies Rate Exponent and Forming Temperature 3801.01.19 TALAT 3801 13
  14. 14. List of Figures Figure No. Figure Title (Overhead) 3801.00.01 Superplastic Sheet Shaped Components 3801.01.01 Superplastically Formed Reflector 3801.01.02 Superplastically Formed Facade Parts 3801.01.03 Superplastically Formed Fuel Tank 3801.01.04 Technical Definition of Superplastic Forming 3801.01.05 Grain Structure Comparison: Conventional - Superplastic 3801.01.06 Metallurgical Requirements of Materials for Superplastic Forming 3801.01.07 Process Requirements for Superplastic Forming 3801.01.08 Technological Advantages of Superplastic Materials during Forming 3801.01.09 Material Law according to Ludwik 3801.01.10 Flow Stress according to Ludwik 3801.01.11 Influence of the Start of Necking on the Flow Stress during the Tensile Test 3801.01.12 Factors Influencing the Value of m 3801.01.13 Effect of Increasing Drawing Rate on Drawing Force 3801.01.14 Methods of Determining the Rate Exponent m 3801.01.15 Different Methods for Calculating the Rate Exponent 3801.01.16 Effect of Forming Temperature and Grain Size on the Rate Exponent m 3801.01.17 Effect of Material Cross-Section on the Rate of Cross-Sectional Area Decrease 3801.01.18 Behaviour of Flow Stress, m Value and Fracture Elongation within the Three Rate Zones 3801.01.19 Rate Exponent and Forming Temperature TALAT 3801 14

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