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**Young’s Modulus Decrease After Cold Forming in High Strength Steel (HSS)**

Supervised By: Eisso atzema Pascal Kommelt Presented by: Abdul Haleem Oral Introduction of work: In automotive sheet metal forming with High Strength Steel, springback plays an important role. Springback is found higher for HSS with increase in strength and decrease in thickness. In prediction of Springback with FE analysis, Young’s modulus is assumed constant which is not accurate. My work will focus on this decrease of Young’s Modulus during sheet metal deformation.

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Contents Introduction to the Problem Theory Experimental Procedure Results Conclusions

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory HSS In Automotives Reduction in car weight and hence fuel economic Solution: Light Weight Design Improvement on Safety Solution: High Strength Design Relationship between fuel mileage and automotive weight, Source: Fukizawa(2000)

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory HSS In Automotives The soln is use of High Strength Steel (HSS), Advanced High Strength Steel(AHSS) and Ultra High Strength Steel (UHSS) with thinner gauges Alternative materials like Aluminium Alloy are more expensive Mass Market Remains that of Steel Source: “Structural Material in Automotive Industries: Application and Challenges” GM R&D Center As can be seen from the graph, usage of low carbon decreased from 95% in 1992 to 10% in Medium and high strength steel will constitute 90% in Automotive applications.

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**Sheet Metal Forming Techniques**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Sheet Metal Forming Techniques Car body parts are made of steel sheet mainly by the following processes Bending Hydro Forming Deep Drawing Others Stamping: Using a set with the desired shape to stamp the flat sheet into shape .Bending: Die Set with no Part Shape, Necessry components Pressure Pad, Punch and a die .Hydro/Explo/Incr. Forming: One die is missing Edge or Wipe Bending

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**Sheet Metal Forming Techniques**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Sheet Metal Forming Techniques Deep Drawing (DD) a main forming technique for automotive sheet metal forming. Deep Drawing: Most widely used technique in automotive sheet metal forming. Necessary components are a punch, die and a blank holder. The blank holder needs to hold the sheet flat. Source: CORUS

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback Weight Saving Achieved But at the expense of higher springback. An elastic driven change of shape during load removal Governed by the stress state obtained at the end of deformation SB is a geometrical defect in Sheet Metal Forming Springback can be defined as an elastic driven change of shape that takes place during removal of the external load. Springback is undesireable because it produces deviation from the design specification of components. It is a complex physical phenomenon which is mainly governed by the stress state obtained at the end of a deformation. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback Bending Animation

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback Bending Animation

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback Bending Animation

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback Bending Animation

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback Bending Animation Springback

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback For bending, springback is [Burchtiz, 2008] M: App. Bending Moment, t: Thickness, E: Young’s Modulus ρ,θ: Circumferential radius and direction We can see that stresses near the neutral axis are lower than the outer surfaces. In fact, in those regions the elastic limit has not yet crossed while the outer surfaces have crossed the plastically deformed region. In the outer surface, there is a tensile stress and strain while the inner fibre is under compressive stress and strain. Due to elastic region aroung NA, there is a elastic driven shape change at the end of deformatio process. After load removal, the sheet will springback to a different shape to reach a new equilibrium. The mathematical relation give some basic idea of dependence of SP on material properties and thickness. More on next sheet. Stress and Strain Profile in plane bending strain, Source: Burchitz(2008) 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Springback In general, Spring Back ↑ with ↑ in Yield Strength ↑ with ↓ in Thickness of the material For HSS, both (1) & (2) are there, so higher SB ↑ with ↓ in Young’s Modulus e.g. Aluminium Alloy Also depends on the Hardening of the material Elastic and Plastic deformation zones for a general strength material (b) More Springback with higher Yield stress and hence a large elastic deformation zone around neutral axis (c) More Springback with the same material as in (a) but with a thinner gauge with effect of relatively same elastic deformed zone as with a thicker gauge. In modern automotives, high strenght steel is used with thinner gauge to achieve the goal of light weight and improved safety. This means with application of HSS, AHSS and UHSS the magnitude of springback is much higher.

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**Prediction of Springback**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Prediction of Springback Living with SB is acceptable as long as it can be predicted correctly Prediction is possible by the use of CAE and FE Prediction is important because we can -compensate springback in the tooling design -save labour of reworking -Reduce design to production time Implimentation of CAE helps in producing the “first time right” product.` Unfortunately, the prediction with FE at the moment is not very accurate

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**Prediction of Springback**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Prediction of Springback The above figure is result of extensive research of the inaccurate prediction of SB with FE. Several material, process and numerical factros influences the results of FE simulation. For accurate prediction, FE needs an accurate model that accurately addresses all of the above mentioned factors. In this study, I will focus on the variation of E modulus when sheet metal is subjectd to prestraining. Source: Burchitz[2008]

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**Prediction of Springback**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Prediction of Springback Young’s modulus reduces before saturation during plastic deformation One of the reasons for under prediction of springback is assumption of constant E-modulus in FE Analysis. For XC38 steel, Source: Morestin, 1996 Source: Corus Internal Report

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Contents Introduction to the Problem Theory Experimental Procedure Results Conclusions

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Theory of Degradation In addition to elastic strain, there is a dislocation strain caused by deformation. Effective E modulus is then, ;where σ=applied stress εel= Elastic Strain εdis = Dislocation Strain The mechanical energy of a vibrating solid is rapidly dissipated into heat, even if the body is completely isolated from its surrounding. This is called damping or internal friction. (In vibrating string model, dislocation is considered as an elastic string pinned at its end by impurities and which bows out under the influence of an applied stress. Koehler (Imperfections in nearly perfect crystals, Wiley-New York, 1952,p 197) presents an anlogy between this string and a forced damped vibration of a string and calculated change of modulus and internal friction due to movement of dislocation. In hysteretic model of dislocation, the breakaway of weak intermediate point causes the degradation. Therefore, in addition to elastic strain, there is an additional dislocation strain and this causes the decrease of E modulus.

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Theory of Degradation Literature suggests modulus degradation a function of loop length and dislocation density Lems[1963] proposed the model Nowick[1972] suggested the model ρ:Dislocation density; ℓ: loop length, G: shear Modulus E: Young’s Modulus

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Theory of Recovery Degradation of E modulus disappears with time Effect of prestraining and heat treatment for DP/TRIP is shown in figure This offers opportunity to validate the mechanism by experiments Source: Baumer [2007]

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Theory of Recovery From literature, it has been found that recovery in E modulus is characterized by three stages Snoek Relaxation Cottrell Atmosphere Formation Carbide Precipitates Among them Cottrell atmosphere is the most important in recovery of E modulus Diffusion of interstitials in Cottrell atmosphere is temp dependent 1)The Snoek ordering is a local ordering of the impurities when present in the stress field of the dislocation. This ordering involves only single atomic jumps and therefore does not lead to any migration to the dislocations. 2) When prestrained, a dislocation introduces local volume change. Below the line of a positively oriented edge dislocation, local tensile stresses exist while above the defect line, local compression stresses are present. Changes in the stress field of the dislocation are the driving force for the migration of impurity atoms to the dislocations. These carbon atoms hence pin the dislocation and cause reduction in the loop length. 3) Precipitation of carbides occurs at dislocations during ageing. As the process of ageing continues, more interstitials arrive at dislocations and dense atmosphere form around dislocation which act as nuclei for precipitation. The process results in formation of clusters and finally the precipitation. It is postulated that the carbides in the form of coherent particles are cut by dislocations

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Bake Hardenable Steel Selection of Bake Hardenable (BH) steel Good Formability and low initial yield strength Increased Final yield Strength in the product Excellent Dent Resistance Young’s Modulus do not show decrease after baking treatment. Source: The US steel Automotive Group Bake hardening is defined as the difference between lower yield point after pre-straining ad ageing and the proof stress at the prestrain level Source: Elsen,Hougardy[1993]

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Contents Introduction to the Problem Theory Experimental Procedure Results Conclusions

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Experimental Procedure Sample prestrained to different level. Samples heat treated in silicon based oil bath for required temp and time. E Modulus is measured by a static method i.e. Tension and a dynamic Method (i.e. Impulse Excitation Tech(IET).) Scheme of experiments Temperature Uni-axial Pre Strain by Tensile Machine Baking Time Room Temp 0,2,4,6,8,10,14,18% - 160°C 0,2,6,10,14,18% 10 and 20 min 180°C 11 and 20 min 200°C 12 and 20 min 230°C 13 and 20 min All samples were prestrained in RD. Heat Treatment was given by an oil bath in which the samples were friend for the required time of baking. Time

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory IET Setup Pre Strained Samples were transported to TU Delft for measurement with IET Measurement velocities from few micron/sec to 1km/sec and vibration frequency from 0.01 Hz to few MHz is possible. IET Set Up Laser Vibrometer Pre strained sample from Corus Plant were transported to TU Delft for measurement with IET as the facility of IET is not available in Corus. The reason for this description is an important result, which will be describe in the coming slides. Since dynamic method is new method, therefore, I wanted to explain a little about it. Specimens of elastic material including steel posses specific mechanical resonant frequencies of a suitable geometry (rectangular in this case). Dynamic E modulus is measured using resonant frequencies in flexural mode of vibration. For measurement of frequencies, a non contact laser vibrometer was used. The laser vibrometer is based on the principle of Laser Doppler Principle and evaluates the light scattered back from a moving/vibrating object. LDV consists of a two beam laser interferometer which measures the frequency or phase differences between an internal reference beam and a test beam. LDV is coupled with Siglab acquistion system for display of measuremed of frequency and amplitude. Non-contact vibration measurements with very high spatial resolution are possible with such a scanning system and can lead to significant improvements in the accuracy and precision of experimental modal models. Commercial instruments can measure velocities ranging from a few μm s−1 to 1000 mm s−1 for vibration frequencies from 0.01 Hz to a few MHz. The most common type of laser in LDV is Helium Neon Laser

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory IET Setup(2) Modified Setup of Support Norms used ASTM E and NEN-EN 843-2 Modified setup included the support system thorough Rubber bands. It was done because some sheet metal samples were not perfectly flat and hence gave problem when they were hit by impulsere on the knife edged supports. Further, the boundary condition may differ when the supports are not in touch at all points along the nodal line.

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Data Analysis for Tensile Test E Modulus is calculated from the static tenisle test from stress-strain curve as shown below from the stress-strain data, maximum stress (σmax ) is found for strain ranging from 0 to 1%. Now stress strain diagram is drawn for the stress strain in the range of 5% σmax to 40% σmax. E modulus is now found from the linear regression of the calculated stress strain curve. This is done because in most loading systems and test specimens, effects of backlash, specimen curvature, initial grip alignment, etc, introduce significant errors in the extensometer output when applying a small force to the test specimen. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Data Analysis for IET E Modulus is calculated from Dynamic Measurement as[ASTM standard] For (L/t)≥20 Where m=Mass of the sample in gram ff=fund. Resonant frequency of the samples measured in flexure;Hz L=Length of the samples,mm t=thickness of the samples, mm b= breadth of the samples, mm T1=Correction factor

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Contents Introduction to the Problem Theory Experimental Procedure Results Conclusions

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**No Heat Treated(HT) Samples**

Introduction to the Problem Conclusions Results Experimental Procedure Theory No Heat Treated(HT) Samples No degradation observed (10 to 20% Decrease was expected) What was wrong? Strange results 2nd Feb 2009

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**No Heat Treated(HT) Samples[2]**

Introduction to the Problem Conclusions Results Experimental Procedure Theory No Heat Treated(HT) Samples[2] True stress true strain data revealed existence of strain ageing phenomenon beyond 2% prestrain level. Prestrain samples were kept in between Ice blocks and were placed in an insulated bag during transportation to Delft and back. Still, the strain ageing phenomenon took place which shows the high sensitivity of recovery to ageing. Even with care for not ageing during transportation, strain ageing took place. Retesting needed for Non Heat treated samples 2nd Feb 2009

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**No HT Samples (Retested)**

Introduction to the Problem Conclusions Results Experimental Procedure Theory No HT Samples (Retested) Re testing with only tension test for two conditions prestrained only and prestrained and aged for 24 hours at Room Temperature. At 2% and higher, 11.5% reduction in E modulus from 192 GPa to 170 Gpa Gradual restoring in E modulus in aged samples (Quicker than expected) The retesting results proved degradation. Aged samples shows high sensitivity of recovery to ageing especially after prestraining. A degradation of 11.5% from 192 Gpa to 170 Gpa when prestrained to 2% and hihger . Aged samples shows higher sensitivity of recovery to ageing especially after prestraining which showed full recovery when prestrained to 10% and higher. The design of aged sample was included in the retesting to approximate the condition during transportation. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory HT Samples (IET) Results for 20 and 10 minutes baking times Average E modulus results for a specific temperature and time Heat Treatment restored E modulus. The effect of heat treated E modulus is clear from non heat treated sample. However, the effect of different heat treatments is within standard deviation bars and is hardly distinguishable. Baking time dependence is also not clear. Since E seems to be independent on prestrain, therefore averaging per strain was allowed. The Average E mod against temperature shows a small continuous increase in E mod with temperature. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory HT Samples (TT) Static Tensile Test results for 20 and 10 minutes baking times Average E modulus results for a specific temperature and time Again, like IET results, TT showed Heat Treatment has restored E modulus. The effect of heat treated E modulus is clear from non heat treated sample. However, the effect of different heat treatments is within standard deviation bars and is hardly distinguishable. Baking time dependence is also not clear. Small continous linear trend is found for av.E modulus in the same range as that of IET. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Discussion Calculated dislocation density for different prestrain levels through following relation where σf=Flow stress; σ0= back stress; b=2.5x10-10 m(burger’s vector) G= 7.8x104 MPa (shear Mod) Minimum Dislocation Density required for effective bake hardening Pre Strain ρ [1012 m-2] 0% 1[ Cottrell 1949] 2% 10.98 4% 24.96 6% 36.41 8% 45.18 10% 51.26 14% 58.68 18% 61.49 Condition T [°C] Time[sec] Diffusion (micron) ρ [1012 m-2] 24 hours at RT 20 86400 0.02 3400 160°C+10 min 160 600 0.29 12 160°C+20 min 1200 0.41 6 180°C+10 min 180 0.47 4.5 180°C+20 min 0.67 2.3 200°C+10 min 200 0.74 1.8 200°C+20 min 1.04 0.92 230°C+10 min 230 1.35 0.55 230°C+20 min 1.91 0.27 Dislocation density calculated from flow stress equation. Only at 2% prestrain level, the calculated dd is less than the minimum dislocation density at 160°C for 10 minutes. This seems the reason of observation of non ageing behaviour of our initial experiment. Shown on slide 36. Another interesting observation is that for 24 hrs the min DD is 3400x1012 m-2 which shows at 10% prestrain level for 24 hrs aged samples.the bake hardeining was not effective and still we observed full recovery. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Discussion Loop Length calculated from Lems model[ 1963] Dislocation density calculated from flow stress equation. The decrease of loop length with prestrain is in contrast to the theoretical model presented in the theory section We have come out with the conclusion that when DD is increased by prestraining, Dislocation itself will reach to interstitials and cause a decrease in the loop length which can be seen beyond 2% prestrain level. In the theory it was mentioned that beyond breakaway stress, weak intermediate point will collapse which will result in the increase of the loop length. It is concluded that at 6% and higher prestrain level decrease in dislocation loop length caused by increase of dd is equal to increase in dislocation loop by breakaway. If there were no breaking of weak intermediat points, we would see the red curve or may be a curve continously decreasing as see from 2 to 4% prestrain level. 2nd Feb 2009

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**Comparison of measurement methods**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Comparison of measurement methods Dynamic IET Method Lower Standard Deviation Dimensions and Mass Dependent Non destructive method. Non contact Laser vibrometer with high accuracy Our experiment’s measurement resolution was 0.06Hz. Higher resolution is possible easily Shearing not a good option. Less St.Deviation compared to T.T Result dependent on accuracy of dimensions, mass and frequency. Percent error in the output can be seen by 0.1% error in the measuremnt of input parameters Unlike traditional contact vibration transducers, laser-based vibration transducers requires no physical contact with the test object. Non-contact vibration measurements with very high spatial resolution are possible with such a scanning system and can lead to significant improvements in the accuracy and precision of experimental modal models Shearing of the samples is not a good option. A better alternative could be teh punched samples. 2nd Feb 2009

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**Comparison of measurement methods**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Comparison of measurement methods Static Tensile Test Method For lower standard deviation in E modulus, 3 samples are not sufficient. Destructive Method More information per one set of test. More Accuracy emphasized. Lack of standardization( Only ASTM standard, No European Standard exists) Some factors responsible for inaccuracy in E modulus are conditions of clamps, extensometers, test conditions e.g. pre load, temperature, stress rate, way of finding linear regression, material condition etc. Due to high st. deviations in tension test for E mod, 3 samples r not sufficient. At least 5 or 6 samples should be used. Destructive method and hence the samples cannot be used for further testing. More info like Rp, Rm, n, r, Ag etc unlike IET Need of higher resolution is still there. Lack of standardization for E modulus calculation form stress strain data. At present, No European norm exists for E modulus except the american ASTM E111. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Contents Introduction to the Problem Theory Experimental Procedure Results Conclusions

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Conclusions 10% to 12 %Reduction in E modulus on prestraining Heat treatment restores the original E modulus of the material after prestrain Recovery in E modulus is more sensitive to ageing than the yield strength increment Cottrell atmosphere formation by the carbon diffusion is the main mechanism of recovery The effect of prestrain on recovery is visible before restoration of E modulus as for aged samples. No baking time dependence is found. E modulus is a function of dislocation density and av.loop length between pinning points. . 1)Young’s Mod reduces to 10 to 12% on prstraining 2) Recovery in E mod is more sensitive to ageing than the yield strength increment 3)Carbon diffusion to the stress fields of dislocation is the main mechanism of recovery 4)Effect of prestrain is visible before full restoration as for aged samples. As after restoration, we have not seen any dependence of prestrain even with the heat treatment. 5)Baking time dependence is not found. 6) E mod is a function of l and DD. 7) Max. extent of E mod is full restoration. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Conclusions Increase/Recovery of E modulus after prestraining by heat treatment is bound by physical constraint Dynamic IET is more reproducible and adoption of higher resolution is easier. With one test of T.T, more info is possible unlike IET. Dynamic IET is more reproduciable while more informatino is possible from TT. 2nd Feb 2009

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**Experimental Procedure**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Recommendations Loop Length as a function of prestrain should be found for other grades of steel. The need of more accurate E mod measurement is still there and can be done by high resolution in (a) IET of LDV and (b) of extensometer in T.T. For BH material, a non heat producing tech. should be adopted for cutting/shearing and tension samples. Measurement time of IET can be reduced if all samples are of same size and dimension. For distorted sheet metal samples, band supports are more convenient than the rigid knife edged supports. To cater for anisotropic nature of sheet metal, it should be measured along other directions than the RD. Development of loop length model for other grades of steel is recmendede. For accurate measurement of loop length, accuracy of both test method has to increased. For BH material, a non heat producing method should be adopted. At least,temperature/time history should be known. Individual time of measurement in IET can be reduced significantly if all samples are of the same size and dimension. Therefore, shearing is not a good option as it fails to produce exactly same dimension samples. A punched sample seems better option for this purpose. Since boundary condition can differ for distored samples when used with rigid knife supports, therefore, rubber band support system should be used in that case. Due to anisotropic nature of sheet metal, it should be measured in different direction relative to RD by accurate methods like Ultrasonic Pulse Echo Mehtod and Resonant Ultrasound Spectroscopy 2nd Feb 2009

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**Ultimate Goals of the Research**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Ultimate Goals of the Research Better Springback Prediction First Time Accurate Production of stamping dies and tooling Labour of Reworking reduced Design to Production Time Reduced All of above, results in reduction of production costs The ultimate goal of the research will make the production of first time right product possible through better predictio of SB. This will serve automotives in the reduction of design time to production time when new dies and tolling has to be introduced. Labor will be saved and production costs can be reduced significantly.

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**Thank You for Your Attention Questions/Comments?**

Introduction to the Problem Conclusions Results Experimental Procedure Theory Thank You for Your Attention Questions/Comments?

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FIGURE 5.1 Potentiometric displacement sensor.

FIGURE 5.1 Potentiometric displacement sensor.

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