The primary objective of this research sub-task was to investigate the total effect of magnetic pulse forming on the limit strains of aluminum sheets with various levels of prestrain in essentially the plane strain region. The test parameters and data, as described hereafter is sufficient to insure control and repeatability of overall performance tests. The data is not sufficient to attempt a formulation of any basic constitutive relation. The test data will be presented in a manner that is deemed conducive to providing insight about the material behavior during a MT-EM process to an application engineer.

The deformation velocity and material temperature key variables needed to produce a more fundamental understanding of the material behavior could not be independently controlled or precisely observed. The peak deflection velocity can be only be indirectly controlled by the amount of energy discharged from the capacitor bank. Deformation velocity and

acceleration histories are determined by the over all response of the specimen to the magnetic pressure pulse generated by the capacitor discharge. The discharge energy also indirectly controls the sample temperature through adiabatic heating due to rapid plastic work and the joule heating of the large transient currents passing through the part. The part temperature cannot, therefore, be held constant at any specific level. The strain, strain rate, magnetic pressure and deformation velocity vary somewhat with position on the specimen. The center portion of the specimen will experiences a fairly uniform magnetic pressure distribution across its width but varies along the length, the nominal major strain direction. The strain distribution roughly follows the pressure distribution as will be detailed in the following sections. Finally, the flow stress cannot be directly calculated as is possible in tensile tests, from load cell data. An average flow stress in the coupons could only be estimated by the free form velocity-time information. Fortunately, flow stress data is not required for the prime objective of these tests.

Much of the predicted advantage of the hybrid forming concept applies to large parts where the ability to draw-in most of the part geometry inducing minimal strain can be coupled to the capability of achieving extended plasticity at high deformation rates over more localized areas of the part. It is therefore not necessary that the MT-EM process generate useful deformations greater than a fully dynamic process. It is only necessary to demonstrate by these small sample tests that the hybrid process can reliably generate useful plastic deformation greater than the conventional quasi-static process alone. Returning to Figure 1.3, the diagram shows both low and high rate data along with a standard FLD for 6061-T4 material. Note that the high rate data plotted in Figure 1.3 are only illustrative of the extended ductility available at high deformation velocities and cannot be rigorously included in a "forming diagram" since the deformation velocities are not known. It has been shown that the limit stain for many materials, is a function of the deformation velocity [44, 6, and 52]. Therefore FLD type plots for high rate or hybrid forming will need to include a deformation velocity parameter. If the limit strain of different strain states is a strong function of velocity, separate plot would be required for each average dynamic velocity range . In effect, the FLD curve becomes a surface for deformation velocities above some threshold at which the inertia effect becomes significant. If the limit strain is shown to be insensitive to velocities above the inertia threshold then all data might be presented on a single plot with the minimum velocity specified.
 

3.1 Experimental Determination of the Effect of Static Prestrain and Eddy Currents on Limit Strains

To establish the efficacy of hybrid forming methods it is first necessary to investigate the relationship between quasi-static prestrain levels and subsequent limit strains available by high velocity deformation. Specifically, small-scale coupon experiments were conducted to determine a general relationship between allowable prestrain and available dynamic strain under near plane strain boundary conditions.

The plane strain boundary condition is chosen for several reasons. First, plane strain is a limiting sheet forming condition since the single strain component in the plane of the sheet must be matched by an equivalent thickness reduction. On a forming limit diagram (FLD), the plane strain condition lies on the minor strain axis and is invariably the lowest point on the FLD curve. (see FLD Figure 1.3 ) Secondly, large pan type parts can have significant areas of deformation at or near the plane strain condition. Generating a true plane strain condition in a small scale, laboratory coupon is difficult except for very low aspect ratio gage sections. A rule of thumb for tensile specimens is that the coupon width should be 8-10 times the gage length. To obtain a gage length of fairly uniform strain of 2.5 cm (1.0 in.) the coupon is at least 20 cm (8. in) wide. It was considered that maintaining a uniform tension over such wide coupons would be problematic and that small negative minor strains would be measurable until the coupon width became too wide to be practical with the available equipment. The coupon size was therefore based on the greatest width that could be accommodated and reliably, uniformly strained in the quasi-static mode. Figure 3.1 is the schematic of the test coupon geometry used.

To keep the hardware requirements simple, it was decided to conduct the coupon experiments in two separate phases, quasi-static and dynamic. First the coupons were all quasi-statically strained to specific levels in a standard tensile test machine as depicted by Figure 3.2. The actual prestrain of the central 1.0 in. gage section of each labeled coupon was measured and recorded. The coupons were then clamped in the coil fixture, as shown in Figure 3.3, and subjected to an electro-magnetic pulse centered on the gage section. A schematic of the coupon EM pulse forming system is shown in Figure 3.4. The current and voltage probes depicted in Figure 3.4 were used in conjunction with the two-channel digital storage scope to capture the coil current and voltage traces. The traces for each coupon were then available to check actual pulse energy levels and uniformity of the discharges. The coupling of the coil and coupon inductance determines the strength of the eddy currents induced and efficiency of the conversion of the electromagnetic energy to the initial kinetic energy of the coupon bulging. The coupling can theoretically be calculated from the geometry and electrical properties of the coil fixture and coupon assembly. This calculation is quite tedious and sensitive to geometry approximations [35, 36]. Therefore, the coupling was measured at various pulse energy levels by threading the flexible "worm" pick-up coil of the current sensor through holes in the coupon, fixture and restraining plate such that a coil leg and eddy current path was encircled. In this way only the net magnetic flux induces a current in the pick-up coil. The difference between the net current signal and the current signal measured without the coupon in place provides a measure of the eddy current. The term coupling, applied to the coilóworkpiece system, used in this document is therefore defined as the ratio of the coupon current to the coil current. This ratio will change continually as the work sheet moves away from the coil during EM forming. However, if the work coil inductance is smaller than the rest of the system, as it is for the coupon coil, the coupling ratio can be considered as a constant for the first current cycle of the bulging event. The majority of the energy is transferred during the first half cycle in most cases. Figure 3.5 shows a typical coil input, net flux and calculated coupon currents from a clamped coupon coupling test. With reference to Fig. 3.5 and the method described above, the coupling between the coupon and coil was found by subtracting the coupon+coil+base first peak value from coil+base first peak value and dividing the result by the first peak value of the coil current. This ratio was found to be 0.435, +/- .03 for the energy levels in the range of the coupon tests. Since the direct measurement of the coupling was only possible with a unique, thin flexible sensing coil, a more detailed description is appropriate.

The flexible current probe listed in the schematic of Fig. 3.3 and used in most all the experiments described in this document is a type of Rogowski current sensing coil. The instrument grade coils of this general design are available from several manufactures but only as rigid, iron cored, metal shielded torus configurations. Experiments, such as the one used to measure the actual electromagnetic coupling as well as most others in this work, required a current sensing probe which could be passed through narrow opening in order to measure currents in subsections of the work coils. No such devices were found in the literature of current sensor manufacturers. However, a brief Design Note published by P. N. Murgatroyd et al. [56] described the basic design, construction and electrical characteristics of a flexible Rogowski type sensing coil made from an arbitrarily long length of the inner part of standard electrical instrument coaxial cable. The coil is formed by treading the outside of the polyethylene core containing the positive conductor with a standard screw thread cutting die and then winding the thread groove with a small gage, coated magnet wire. The magnet wire is soldered to the center conductor at one end and the entire coil is covered and secured with a length of shrink tube. The coil output is passed though an attenuation resistor and integrating capacitor before being feed into the digital storage scope. A major advantage of this worm coil is that it can be placed almost anywhere in the discharge circuit by simply looping the coil around the conduction path of interest. Since the coil has a quite small minor diameter, centering and perpendicular orientation with the current path being sensed it not required. Worm coils are also quite inexpensive to build and are easily designed to any desired sensitivity. The major disadvantages of worm coils are that they are a bit noisy and not as linear as commercial iron cored Rogowski coils. The general response of the worm coil was calculated from its physical parameters, for design purposes and a direct comparison against a factory calibrated Pearson Rogowski coil was used to establish the worm coil gain. Figure 3.6 is a graph of the Pearson coil and scaled worm coil output signals for one of the several different bank energy levels applied. The calibration factor for the worm coil was determined by the visual best fit between the scaled worm and Pearson waveforms. More detail information of the coupon coil fixture and test system instrumentation is provided in Appendix A.

The energy levels of the discharges for each coupon test group were determined by trial and error. The minimum level needed to be high enough to just crack the coupon as a baseline. Additional tests were then conducted, with coupons from the same group, at energy levels approximately 50% greater in order to investigate the relationship between velocity and failure strain.

The elapse time between the quasi-static and dynamic phases varied up to two weeks for any group of coupons during which time they were store at or slightly below room temperature. The aluminum alloys used in the experiments are adequately stable in the prestrained levels and storage temperatures so that the results are considered to be indicative of the behavior of the alloys in a continuous MT-EM process.

 

Figure 3.2: Coupon Prestrain Method
 
 
 
 

Figure 3.3: Coupon Coil Fixture

(arrows indicate coil current flow)
 
 
 
 
 

Figure 3.4: Test Coupon, Electromagnetic Forming System Schematic
 
 
 

 
 

Figure 3.5: Current-Time history for a 12 kJ discharge, coupon restrained by a non-metallic plate
 

Figure 3.6: Comparison calibration of Worm coil with

Pearson coil (1000. amps/volt); Worm gain = 5000. amps/volt

The experiments were restricted to alloys having properties representative of those of most interest to the automotive industry. Specifically, the two alloys that currently fall into this class are 6111-T4, a

precipitation hardening alloy and 5754-0. Restriction to these two particular alloys should not limit the generalization of the experimental results to other aluminum alloys of similar metallurgical characteristics. Another consideration was to keep the number of experiments require for this research effort to a reasonable level. Moreover, at the present state of the technology it would be unwarranted to investigate other than a few materials of central interest to the target industry.

The primary variables of interest in the coupon tests are as follows:

1) Quasi-static strain level measured over a 2.54 cm (1.00 in) gage

length at the center of the coupon.

2) Coupon grain orientation

3) Energy level of the EM pulse

4) Maximum local major strain at failure

1) Impressed coil current as a function of time.

2) Impressed coil voltage as a function of time.

3) Coupon deformation velocity average at the mid plane.

4) Minor strain at the maximum major strain location.

The intense magnetic field pulse applied to the coupon in the coil fixture, induced an eddy current in the coupon and as a result, a narrow, high pressure area across the transverse mid plane of the coupon. This in turn produced high velocity deformation and strains through the gage section of the coupon with securely clamped ends. The resultant bulging motion of the coupon was such as to generate an essentially tensile stress state in central gage section at the time of failure. A typical coupon deformation time sequence as captured by a high speed digital array camera and strobe system is shown in Figure 3.5. The figure shows an illuminated free edge of a coupon at five, 50 microsecond, intervals during the pulsed EM deformation event. The average vertical displacement velocity of the coupon at its mid plane is 200 M/sec. However, inspection of Figure 3.7 reveals that the major portion of the deformation is completed within the first three exposures (1.5E-4 sec) over which the velocity average is 230 M/sec. Therefore, velocity reported, for all test coupons, will be the average calculated for the first two or three images. The long axis of the work coil is perpendicular to the plane of the image, at the midpoint. It and fixture are indistinguishable in the figure since they are painted black in order to enhance the contrast of the deforming coupon edge images. The image sequence is generated by overwriting a 768(H) x 493(V), CCD array producing the same effect as a multiple exposure on film. The adjustable exposure and delay times of the camera ranges from one microsecond to one millisecond. Up to ten exposures can be captured in a single frame providing a virtual high speed frame rate from 500 to 500,000 frames per second. The "exposure" on time used for the coupon experiments varied from 3 to 10 microseconds. At such short exposures, adequate illumination required the use of a 5000. watt quartz spot lamp or a high intensity photographic flash unit. A quartz spot lamp was first used but was abandoned as it tended to melt the plastic sheets used to insulate the coupons from the work coil. The photographic flash unit that replaced the spot lamp was triggered along with the camera by a simple alarm circuit that sensed the high tension pulse from the control ignitron of the capacitor bank. The control ignitron simultaneously fired the main ignitrons of the capacitors generating the bank discharge. The camera system work well with the exception that the heat-up time of the flash unit precluded capturing the initial 20 microseconds of coupon deformation. Although the flash delay had no serious impact on the coupon tests, it could have been remedied by the use of an overlord trigger circuit which independently controls the bank master ignitron as well as the camera and flash unit. With the appropriate flash lead time, the bank and camera could be triggered to capture the deform event during the peak photon flux of the flash unit. The complete specification of the Cooke Corp. FlashCam camera, flash unit and capacitor bank can be found in Appendix A.

Figure 3.8 is a photograph of a coupon subjected to an electromagnetic pulse slightly less than that required to produce failure and shows more clearly the approximate coupon geometry at minimum energy failure.

Figures 3.7 and 3.8 show that the dynamic strain induced in the coupons is approximately along the same path as the quasi-static strain. The slight transverse bulging of the coupons during the EM pulse resulted in total minor strains remaining the same or moving closer to zero than the minor prestrain for most coupons. The bulging and the down turned free edges of the coupons were both due to the eddy current paths in the coupon. The coupon currents formed two narrow counter rotating circuits, opposite to the coil current, traversing the coupon width and turning short of the free edges. Since the coil extended beyond the coupon width, there was not a coil current near enough to interact with the outer turn path of the eddy currents to produce significant acceleration forces near the free edges.

For all coupons, the maximum major strain reported were measure by the greatest deformed circle of three chosen by visual inspection from the grid area next to the failure fracture. Care was exercised in selecting only grid marks that were in the neck affected zone but not in or across an actual neck that displayed greater strains but are considered fully failed. This convention was adopted from the generally accepted criterion for generating the forming limit curves on forming limit diagrams (FLD) (Mielnik 1991). The criterion is the same as used by one coupon material supplier, ALCOA, in generating the static FLD for the 6111-T4 . It is assumed that the 5754-0 FLD supplied by ALCAN was generated similarly. The vendor supplied FLDís are reproduced in summary in Fig. 3.9. Additional detailed material data is provided in Appendix B.

Figure 3.10 shows a fragment of a typical high energy failed coupon with numbers indicates the grid marks chosen for measurement.
 
 

An expected conclusion from inspection of Figures 3.7, 3.8 and 3.10 is that the strain produced by the EM pulse is not uniform along the length of the coupon. In fact, it is not. The dynamic strain is always greatest in the area of the coupon that experiences the greatest magnetic pressure pulse. For the 3-bar coil used in most of these coupon tests, the maximum pressure on the coupon occurs directly over the center bar of the coil that carries the maximum current. Maximum strains therefore occur along a transverse strip, approximately 1cm wide, at the middle of the coupon (see Fig. 3.10). Figure 3.11 is a plot of the total engineering strain versus distance from the middle of the coupon for two coupons that did not fail during EM pulse bulging. The fact that the highest strains are centrally localized is an artifact of the 3-bar coil design. The 3-bar configuration generates the greatest pressure between the center leg and the work sheet since it carries the greatest current. Consequently, thermal softening effects will also be greatest at this location.

The slightly wider distribution for coupon 10D of Fig. 3.11 is due to the effect of a 0.1mm insulated copper foil shield interposed between the coil and the coupon. The foil acted as a driver sheet absorbing most of the magnetic field in the process and thus reducing the eddy current heating of the coupon. Note however, that the non-uniform strain distribution is largely due to the concentrated pressure, for coupon 10D is only slightly less peaked that the unshielded 8D coupon.

The coupon strain distribution shown in Fig . 3.11 is fairly typical and considered to be acceptable for these coupon tests in which only the maximum strain is of interest. More uniform strain distributions are possible with different coil designs, as implied by the foil effect which will be discussed further in chapter 5.

The results of the coupon experiments will be presented in two ways. First the maximum dynamic strain was calculated for each coupon by subtracting the coupon prestrain from the total strain measured for each coupon. The coupons were grouped together according to material type and the level of minor total strain. The dynamic strain was plotted against the prestrain for each group along with lines indicating the failure limits from the static FLD for the minor strain range of the group. The maximum major total stain for each coupon plotted can be simply calculated by adding the dynamic and prestrain coordinates of the coupon. The coupons are further segregated into three sub-groups, on each of the dynamic Vs prestrain plots, identified by different icons, according to the relative energy level of the electromagnetic pulse. Low medium and high pulse energy categories are used to consolidate the results of all coupon tests The first series were run at a wide variation of energy levels to obtain an overview of coupon behavior in the initial phase of this investigation. From the early coupon results, a two level, fractional factorial experiment was conducted which included two specific energy levels. This experiment will be discussed in detail later in this chapter. The three energy levels referred to in the graphical figures to follow correspond to actual bank setting ranges of 14.4 to 19.4 kJ for the low category, 21.6 to 26.4 for the medium category and 28.8 to 36 kJ for the high energy category.

Figures 3.12a, 3.12b, 3.13a and 3.13b present the general results of the four series of coupon test. Two each for the alloys; 6111-T4 (D & G) and 5754-0 (E & G5). All data in the following figures represent only fully failed coupons, one per data marker. Each figure also presents the quasi-static strain limits in the form of two diagonal lines, one for each minor strain FLD value that brackets the final strain state of the coupons. The displacement of a coupon data marker to the upper right of the graph, from the quasi static line is a measure of the additional plastic deformation provided by the MT-EM process.

Average deformation velocity at failure varied within each category with the amount of prestrain as well as actual energy level. For any specific electromagnetic pulse energy level the coupons with higher levels of prestrain tended to fail earlier and therefore at higher velocities and strain rates. Moreover, by the principle of conservation of energy and momentum, the earlier the coupon failed, the higher the velocities of the fragments. Although, fragment velocities as high as 550. m/sec. were recorded, the maximum coupon deformation velocity reliably measured was 350. m/sec. Measuring the average deformation velocities from the multiple exposure images was further complicated by the fact that the fragments of the coupons which failed early would distort in a downward U shape and occlude the previous image(s) from which the true forming velocity could be obtained. At the highest energy and prestrain levels arcing between the coupon fragments occurred most likely a result of fractures developing before the eddy currents were dissipated by the resistivity of the coupon material. In most of the tests in which a coupon arc occurred, the camera image was largely obliterated by over exposure and no reliable velocity information could be extracted. Figure 3.14 illustrates both problems of fragment occlusion and arcing at fracture. The image is not completely obliterated most likely because the fracture and arc happened to occur at the end of the 7.0 msec. exposure window and dissipated during the 43. msec delay.

Due to the problems with obtaining high energy deform velocities and the relatively few coupons tested at these levels, only reliable velocities can be reported for the low and medium energy categories. For the low energy category, the mean vertical center section velocity was 173. m/sec with a standard deviation of 26. m/sec. The medium energy category has a mean center section velocity of 258. m/sec with a standard deviation of 52. m/sec. A very approximate average forming velocity for the high-energy category may be estimated by noting that the mean velocity change is roughly proportional to the energy change. One would expect a proportional variation between the energy and the square of the velocity but there are many intervening factors at work that could easily distort this elementary kinetic relation. Accepting this argument, it would be reasonable to estimate a mean high-energy deformation velocity of approximately 340 m/sec.

Note that as previously stated the major dynamic strains of the 3. 12 and 3.13 figures are not failure strains in a neck area but are the largest recorded in the immediate adjacent area termed the neck affected zone. Clear from an inspection of the figures is that large majority of the coupons, the total strain for the hybrid MT-EM process lies beyond the limit for a quasi-static process.

Also apparent in the figures is the general trend of maximum dynamic reduction with increasing prestrain levels. However the downward trend is slower than the decrease in total static strain as indicated by the lines representing the static minor limits. The process design implication is that greater overall formability may be achieved by pushing the pre-form fairly close to the quasi-static material limit. Another trend easily seen in the figures is that the 5754-0 alloy appears to out perform the 6111-T4 alloy in the MT-EM process in terms of total major strain attainable at any prestrain level.

An obvious question to arise from the discussion of the coupon bulge forming concerns the coupon strain rates attendant to the bulge velocities. Accurate estimation of the distribution of strain rates experienced by a coupon during the electromagnetic pulse bulging requires a dynamic three dimensional simulation program as will be discussed in Chapter 4. However, a simple analysis can be used to estimate the lower bound of the strain rate at the center of the coupon during the first 50 to 75 m sec. of bulge formation. The simplified analysis is based on the fact that the early bulge shape evolution of the coupon is approximately elliptical along the major coupon axis and fairly straight in the transverse direction, along the coil centerline. Returning to Figure 3.5, the two ellipses with the same major diameter are superimposed on the multiple coupon deformation image to illustrate the approximation being considered. During the initial period of bulging, the major diameter of the ellipse remains approximately constant and roughly equal to the width of the coil. If one also assumes a plain strain approximation, simple analytic relations for strain and strain rates can be developed as follows. Letting 2a be the major diameter and 2b the minor diameter of the ellipse the perimeter of an ellipse can be approximated by:

The engineering strain is then

and the true strain is

Assuming ( a ) is constant, the time differential gives the strain rate as

or true strain rate as

Where  is the vertical velocity of the coupon center section measured at the minor diameter of an ellipse which corresponds to the center of the first image. Referring to the larger ellipse drawn on Figure 5, a=31mm, b= 14.1mm,  = 245.m/sec which gives an estimated strain of 0.20 and strain rate of 3500/sec. The final dynamic strain measured at the center of coupon 32D is [.26, -.0067] while the average for the 1.0 inch gage section is [.19, 0.0]. For a lower velocity coupon (19D), which had a prestrain level of 17.5%, the estimated strain and strain rate is 0.16 and 1960/sec. for  = 164.m/sec. The measured final dynamic strain was [.27, -.05] local and [.15, -.07] over the gage section. These results indicate that the uniform strain distribution assumed by the analysis is not valid, as can be expected. However, the errors are not so large as to reject the analysis as a first approximation for the initial strain rates. By this simple model, the initial strain rates of the test coupons, in general, range in value from 1000/sec. to 5000/sec.
 

3.2 Thermal effects in coupon electromagnetic bulging

The primary usefulness of the simple strain rate analysis is to verify that the coupon deformation applied in these tests was inducing strain rates of the same general level as reported in the literature for other high rate forming investigations. Also, most all (~95%) of the energy of plastic deformation of metals is finally converted to heat. When the deformation is as fast or faster than the heat conduction rate of the material, a near adiabatic condition exists in the deformation zone. This can lead to significant changes in the local flow behavior of the material due to the elevated local temperature. The coupon strain rates calculated by the simplified analysis presented, are sufficiently high that adiabatic deformation heating is indicated. in the center section during the first 50 to 75 microseconds of bulging. The local temperature rise due to high rate plastic work is given by Meyers [52] as:

Using the Johnson- Cook constitutive equation;

Meyers gives the following relation for metals with m =1 applied to T*

The readily available Johnson - Cook coefficients for 2024-T351 and the strain and strain rate values determined for coupon 32D, were used for an approximate calculation of the temperature rise in a representative coupon test. The approximate temperature rise for the initial strain and strain rate of the 32D coupon is estimated to be 32 . This coupon is a lower energy example. However, tripling the strain rate and doubling the strain would exceed all coupon tested (and the regime of electromagnetic pulse forming in general) for which the estimated temperature rise is less than 100 . Alone, adiabatic shear heating should not have a major effect on the plastic behavior of the coupons or, more importantly, any real application of the MT-EM process. However, compounding the effects of whatever adiabatic shear heating is locally produced is the joule heating of the same coupon area due to the induced eddy currents. In addition, there is the possible "electron wind" or the electroplastic (EP) effect proposed by some as a non-thermal cause of observed reduction in flow stress in plastic deformation performed under high current density conditions. The literature on the EP effect was investigated and summarized in two Ph.D. thesis conducted by students of Dr. Hans Conrad at U. NC Raliegh [63, 22]. Sprecher determined that his experimental results supported an electron wind contribution of 0.1 to 1.0 MPa to the thermal component of the flow stress for aluminum and copper which is 1% or less of the total for these metals. In view of the reported level of the EP effect, it is assumed that simple thermal softening would be chiefly responsible for any difference in plastic behavior of aluminum sheet directly attributable to the eddy currents. Except for the very brief time scale involved, any localized softening could be due to well known mechanisms of dislocation relaxation and/or partial solutionizing of hardening precipitates.

J. C. Benedyk, in a two part paper, [11, 12] describes a rapid induction heating and quenching process for softening 6XXX-T6 extrusions immediately prior to an aggressive forming operation. The time scales and temperatures reported by Benedyk to obtain effective softening in his process are less than 2 seconds at 650 F. which is both much shorter and cooler that standard solutionizing practice. This process termed Retrogression Heat Treatment has the additional characteristic of recovering most of the original hardness and strength after a few days at room temperature. Table 3.1 reproduced from [11], shows the general trend of softening observed for 6XXX-T6 for the retrogression process and that there appears to be a temperature threshold between 600 and 650 F.
 
 

The relative hardness changes with retrogression temperatures for the specimens of tables 3.1 and 3.2 show good agreement with the 423 oF coupon, which was held for 180 seconds. The increase in hardness for this specimen can be attributed to the initiation of precipitate growth of the artificial aging process. Except for the time scale, this result should be expected at a 423 oF

(217 oC) bath temperature. Tables 3.1 and 3.2 reveal that solutionizing effects are obtainable at temperatures and holding times well below the standard. From the preceding, it was not obvious that a similar solutionizing/ softening effect would be encounter at holding times four orders of magnitude shorter than the shortest salt bath test. Another unknown was the actual transient temperature experienced by the coupons during the EM bulging phase of the test. The entire heating and cooling cycle was estimated at a few milliseconds at most which alone eliminated most thermocouple systems. A very fast thermocouple system would still be severely hindered by the high voltage potential of the coupon during the eddy current flow. These factors, along with the very high pressures generated during the discharge, made direct temperature measurement with a thermocouple very difficult so that an indirect calculation method was used to estimate local coupon temperature rise due to eddy current heating.

The resistance heating of the coupon sections that are carrying the eddy currents can be rather easily approximated since we can accurately measure the coil current and initial coil-coupon magnetic coupling and assuming an adiabatic process. The coil currents recorded during the coupon tests varied with the discharge energy level of the capacitor bank. The peak current varied with the square root of the energy level, generally following the classical relation between current, inductance and energy given by:

The current traces recorded were, except for peak levels, all very similar in appearance to the one shown in Figure 3.4 for a 12 kJ discharge against a clamped coupon. The current traces are nearly ideal representations of the transient output of a classic series RLC circuit inductively coupled to an RL circuit. Figure 3.12 is the schematic of the ideal circuit.

Excluding the circuit charging transformer (T), the differential equations describing the circuit of Figure 3.12 can be found in any good electric circuits text and can be written as,

where L1, R1 and C1 are the lumped induction, resistance and capacitance of the bank and work coil. L2 and R2 are the inductance and resistance of the

work piece (coupon) and M is the mutual inductance between the coil and work piece. M is related to L1 and L2 by:  where k < 1, is the coupling factor.

The induction of the coupon coil is small compared to the internal induction of the bank and bus work. For such work coil systems, the motion of the work sheet does not significantly change the ringing frequency. The waveform of the current is about the same as the shorted bank alone. A nearly constant ringing frequency also implies a nearly constant resistance of the coil and workpiece. Actually, the resistivity of the system must be increasing during a discharge since most metals show linear variation with temperature. For the short term temperature rise expected in the coil and coupon, a doubling in resistivity would not be unreasonable. Including temperature effects couples the entire system eliminating any closed form approximation. However, the damped frequency of these systems are dominated by the inductance and capacitance terms (otherwise they would not ring) so doubling of the resistance results in minor changes the frequency, as will be shown. Therefore, using judiciously chosen, average parameter values, closed form temperature predictions useful as checks of the simulations results are obtained. In using the following analytic expressions, the limitations of such approximations must be kept in mind.

Allowing the coupon current traces to be represented by the differential equations of a elementary serial RCL circuit with the work piece, coil and bank parameters lumped together. The well-known differential equation of the elementary circuit is written as:

I(t), the solution of 3.10 is also familiar.

where

at t=0 , . Since  is the basic relationship between inductor voltage and current,  is given by,

where V0 is the initial charge voltage across the bank capacitors. However, the capacitor bank setting is usually give in terms of initial stored energy , where . K1 can then be written in term of bank energy by,

and for small R by:

(3.13c)

Assuming adiabatic conditions, the temperature rise due to resistive heating in the coupon is estimated by equating the eddy current energy with the internal thermal energy capacitance of the volume of coupon material supporting the current. This simple relation is given in differential form by

where U is the internal energy, the material density, the specific resistance, V the affected material volume,  the material specific heat, J is the instantaneous current density and T is the material temperature. In order to change 3.14 into a form contain the measured coil current, the substitution,  is made where A is the cross sectional area of the eddy current path,  is the coil current and k is the experimentally determined coupling gain previously described. Separating the variables and assuming ,  and  are approximately constant, the integration of 3.14 yields the temperature rise estimation equation,

By substituting equation 3.11 for  in equation 3.15 along with assuming a true sinusoidal current and performing the indicated integration, a closed form approximation for  can be written as,

where 

where R, L and  can be roughly estimated from physical parameters of the bank-coil system or by direct measurement. Direct measurement is preferred since accurate calculations of system resistance R and inductance L are frequency as well as temperature dependent. Estimates of system parameters based on a direct current assumption will contain additional errors further reducing the usefulness of the approximations given above [10, 34].

Time integration limits for equations. 3.15 and 3.16 correspond to about the first half cycle of the coil current or as long as the coil-coupon coupling gain remains valid. For the clamped coupon tests, the upper integration limit extends to where the current is largely damped out which will produce the greatest temperature rise for a given discharge energy level.

Equations 3.7 to 3.13 can be used to verify the results obtained by direct measurement of coupon test system voltage and current-time data. The temperature rise was not directly measured but can be estimated by equation 3.16. However, since the above equations contain several simplifying assumptions, direct numerical calculations with the digital format test data were used in estimates of resistance heating effects.

The mutual induction coupling gain (k) was determined to have an average value of 0.435 for the first two cycles (see Figure 3.5). Peak coil currents varied from 250. to 500 kilo amps which, using the clamped coupon coupling gain , implies peak eddy current levels between 88. and 175 kilo amps. The path of the eddy current in a coupon directly reflects the path of the impressed coil current but counter to the direction. Were the coil extends beyond the coupon, the eddy current turns within the coupon to follow the outer coil legs (refer to Fig. 3.4). The highest current density occurs opposite the center coil leg that is 10. mm wide. The current depth is a function of the ringing frequency and a uniform equivalent depth, termed the skin depth  is defined as

given the system ringing frequency in radians/sec and material conductivity and permeability. For the coupons,=44.4 for Al and< 7.5E4 so that >.8 mm which is the equal to the coupon thickness. The eddy current can be taken to be uniform though the coupon thickness giving a path cross sectional area of 8.0 mm2 .

Using the presented temperature estimation method in a spreadsheet software package with coil current sensor-time data, coupon center strip temperature rise was calculated for several coupons. Figure 3.13 presents the calculation results for three clamped coupons exposed to discharges of increasing energy levels. Referring to Figure 3.13, the major temperature gain occurs within 100 microseconds (one current cycle). The threshold softening temperature, approximately 320 0C, is predicted for the 19.2 kJ coupon at 95 m sec and for 26.4 kJ to occur at 60 m sec. Both coupons are predicted to experience temperature rise sufficient to initiate solutionizing within the first current cycle. As discussed previously, the current coupling gain can be considered approximately constant for the first half cycle period of the coupon bulging. It is therefore predicted that local softening of work hardening should be measurable for clamped coupons subjected to discharges of 10 kJ and partial solutionizing of precipitation alloys at discharge energies of about 16kJ. Eddy current softening of free bulged coupons can not be directly measured due to strain re-hardening. However, bulged coupons are certain to experience some level of thermal softening at unshielded discharges of 12kJ or more.

The clamped, Z coupon test sequence was conducted for the express purpose of isolating the eddy current thermal solutionizing-softening effect. A series of 6111-T4 and 5754-0 coupons with and without prestrain were subjected to increasing discharge levels while being clamped to the coil and restrained from deforming by a 25 mm thick G-10 composite plate. The coupons were quickly removed from the coil fixture after the discharge and placed in an ice water bath until the superficial hardness scan was performed. The ice bath storage period was never more than two hours. The coupons were then stored at room temperature between successive hardness scans.

AA 6111-T4 coupons subjected to 19% quasi-static tensile strain, exhibited superficial hardness on the Rockwell 15T (HR 15-T) scale of 84 +/- 2 units. The alloy as received exhibited hardness reading of 74 +/- 1 units. Figure 3.14 is a plot of the successive hardness scans of a 19%, 6111-T4 coupon after being subjected to a 18 kJ discharge in the clamped-down mode. The estimated peak center strip temperature for this discharge level is 585 0C. Coupon hardness was reduced to 61. +/- 2 units above the main (center) bar of the coil. The hardness of this center section recovered to about 70 units within 24 hours. After 10 days at room temperature, the center section hardness had recovered another 4 units that implied a return to the unstrained, T4 condition. The area of Figure 3.14 between the abscissa points (+/-) 20 and 30mm, are above the outer bars of the coil where no reduction in hardness is indicated. Also, note that as would be expected, the strain-induced hardness at the center section was not recovered. Figure 3.14 is representative of all the 6111-T4, Z coupons subjected to similar discharge energy levels.

The absence of eddy current induced softening above the outer coil bars is directly linked to the 3-bar coil design were the outer coil bars each carry half the current of the center bar and thus experience only about 25% () of the temperature rise of the center section. The lack of softening at the outer coil bars is therefore a manifestation of the temperature threshold seen in data of tables 3.1 and 3.2.

To further define the temperature softening threshold as manifested in the MT-EM process under study, 19% prestrain coupons were subjected to discharges beginning at 3.6 kJ and increasing by steps of 1.8 kJ until softening was detected. Measurable softening occurs in these coupons between 7.2 and 9.0 kJ as shown in Figure 3.15. As an additional check, a copper foil shield, 0.08 mm thick, insulated by 0.10 mm thick sheets of Mylar was interposed between the coil and a 19% prestrain coupon and clamped with the G-10 plate. The coupon and shield were subjected to a 18 kJ discharge. No change in coupon hardness was detected.

It is apparent by inspection of Fig. 3.12 that the joule heating of coupon 18Z was only sufficient to remove the work hardening of the center section. The reduced hardness of 76 units is about the level of the "as received", T-4 coupons.

At the high discharge levels, 25 kJ and above, the predicted temperature rise of the clamped coupon center section reaches 72% of the melting point of the coupon alloys (see Figure 3.13). If the actual center temperature of coupons subjected to the high discharge levels was much greater than predicted, one would expect to find some evidence of grain boundary melting in a micrograph. To examine this possibility, a specimen was taken from the highest current density path of a clamped 6111-T4 coupon subjected to a 25 kJ discharge. Figure 3.16 is an optical photo micrograph taken at the sheet center of the specimen. The micrograph shows no sign of thickened grain boundaries that would indicate the initial phase of melting.
 
 

a) High current density; center of coupon (18 kamps/mm²⁾                  b) No current; clamp area

The lack of any clear sign, in Fig. 3.16, of changes do to high temperatures implies that the analysis does not seriously underestimate the coupon temperature. It should be further noted that the temperature rise predictions are sensitive to the coupon-coil coupling constant (k) which is in turn dependent on the repeatability of the worm coil current transducer.
 

3.3 Factorial Experiment on MT-EM Process Parameters

In order to gain a more organized view of the MT-EM process parameters including a general ranking of importance, a two level, half fraction factorial experiment of four factors was conducted. The factors investigated were discharge energy, grain direction, prestrain level and eddy current level. The measured effect was the maximum major total strain of the coupon as described in section 3.1. Other metrics could have been used as the principle effect such as effective strain that would have explicitly taken the minor stain level into account also. Using the effective or flow strain as the principal effect would likely have produced the same conclusions but would have been less easily compared to conventional forming limit analysis. A measure of the coupon strain distribution or variation might be another useful measured effect. However, the major effects of the chosen variables would be quite different and ultimately useful in designing a MT-EM process. But, not comparable to the most of the conventional forming limit data.

Two level half-fraction factorial experimental design was chosen to investigate the effect level and interaction of the main process factors because of the coupon test system only approximates an actual MT-EH. Consequently only the major characteristics of the process can be discovered. A higher resolution experimental method or even a full two-level factorial design would not be efficient at this point of process development. The details of the

factorial experimental design and analysis method will not be presented here as they can be found in any good text on statistical design of experiments such as Box, Hunter and Hunter [16].

Separate experiments were conducted for the 6111-T4 and 5754-0 materials. The actual levels of factors were chosen to span the MT-EM process operating space to the extent possible with the coupon test system. Energy level is the only really independent variable of the MT-EM process since prestrain and grain direction are significantly more restricted by the desired part geometry. However, a minimum energy level was dictated by the necessity of obtaining coupon fracture for all runs. The low energy and therefore deformation velocity, level was 19.2 kJ, the minimum discharge required to fracture the low prestrain level coupons. The high energy level, 26.4 kJ, was restricted by the structural limitations of the coupon coil fixture. This variation in discharge energy provided for an adequate spread in deformation velocity (see section 3.1).

The eddy current level can not be controlled independent of discharge energy level unless shielding/driver sheets are used as described in the last section. For the purposes of the factorial coupon experiments, 0.08 mm thick copper foil sheets provided a convenient means of eliminating eddy currents in the coupon and thus the localized thermal softening/retrogression effects in the coupon. The use of shielding or driver sheets are quite effective in experimental work but may not be attractive as part of a real process as will be discussed further in Chapter 5. The data for the two experiments of 8 runs with replication is presented in Tables 3.3 and 3.4.
 
 

The commercially available, statistical analysis software program, MINITAB was used to analyze the data of tables 3.3 and 3.4. For each material the main effect of each factor was calculated along with the forward and backward interactions. A linear model was generated for each set of data. The normal plot of effects, for the full model of each material data set was then examined to determine the most influential main and two-way interacting factors. Reduced models were constructed to illustrate which of the factors considered in these coupon tests might be safely ignored as inactive effects in the design of a real MT-EM process. The graphical results of the MINITAB analysis are presented in Figures 3.17 to 3.24.

Figure 3.21: Half fraction factorial experiment; 5754-0 main effects

Figure 3.22: Half fraction factorial experiment; 6111-T4 interactions

Figure 3.23 Half fraction factorial experiment; 5754-0 interactions

Visual analysis of the interaction plot matrices can be summarized as the follows.

To investigate this conjecture a bit more, MINITAB was used to generate linear regression models from the two level half-factorial experimental data.

Figure 3.21 and 3.22 each contain four subplots that describe the appropriateness of the linear assumption of both full and reduced models for each material. The full models are a linear combination of all the factors and all two-way interactions not totally confounded. The relationship is written:

where  through  are the coefficients generated by MINITAB. Any value in the range of the model can be input for the numeric factors. Only -1 and 1 can be used for those so represented in the model generation data. The Reduced models represent the result of several iterations of generating and analyzing models based on subsets of the main and two-way interacting factors. The objective of the reduction exercise was to find the minimum set of factors whose linear regression model still adequately represents the experimental data. From examination of the reduced model for the free bulging coupon experiments, insights into the effect of the test factors on real process applications are sought. Figure 3.21 and 3.22 indicate that a linear regression model is an acceptable representation of the coupon data. The normal plot of residuals lie nearly on a straight line for both materials although 6111-T4 less so than the 5754-0 data. Significant deviation from a straight line would indicate that factors other than those considered in the model are influencing the output results. The remaining residual plots of the Figures 3.21 and 3.22 are also generally representative of good models. Specifically, the histogram should approximate a normal distribution about zero. The I-Chart, which is sensitive to time dependent effects, should show an approximate random distribution of points as should the plot of Residuals Vs Fits.

Figure 3.25: Half fraction factorial experiment; 5754-0 full model

The best efforts in reducing the number of factors in the full models of the two materials are summarized by the residual sub plots of Figures 3.23 and 3.24.

For both the 6111-T4 and 5754-0 materials one of the main factors, grain direction (GrnDir), could be eliminated from the models. All the two-way interactions of the 5754-0 coupons were found to be inactive and removed. However the (Energy * Pstrain) interaction was required in the 6111-T4 model.

The reduced model factors-results relation is given by equation 3.21 for the 6111-T4 coupons and by equation 3.22 for the 5754-0 coupons. Note that in both equations the prestrain term carries the largest positive coefficient. The second largest coefficient is carried by the energy term for 5754-0 coupons and the foil term for 6111 coupons.

Some generalizations can be made about real MT-EM process from consideration of the effects and reduced models of the two-level fractional factorial experiments. One is that the greatest total plastic strain is usually obtained at the greatest prestrain levels. Other is that precipitation-hardening materials such as 6111-T4 may not responded with increased plasticity, to energy levels above some threshold. Overdriving such 6111-T4 alloys may, in fact be counter productive, due to an active negative interaction between prestrain and energy levels. The softening/ solutionizing effect of the induced eddy currents will definitely increase the maximum obtainable strain in the local region of the current path. In general, 5754-0 type alloys will exhibit greater and more linear response to increases in the main process inputs of energy and prestrain than 6111-T4 type materials . The use of a driver/ shielding sheet reduced the eddy current levels and was shown to lower the peak strain even at slightly higher energies. However, the high strain region in shielded coupons was slightly wider than the unshielded coupons. It is shown that the strain distribution is more directly related to the pressure distribution with the local softening as a secondary effect.
 

3.4 Summary of Coupon Experiment Results

Free form coupon experiments have been shown to support the fundamental premise for the utility of the MT-EH process. The results of the experiments indicate that the two component processes, quasi-static tensile elongation and high velocity bulge stretching have a synergistic effect on total plastic strain. The plastic strains are produced by the combined process are larger than those produced by either component process. The near plane strain condition produced in the test coupons allow that the experimental results are applicable to actual applications using matched tool performing. The principle aspect of a real MT-EM application absent in the coupon experiments is the effect of the high-speed impact of the work sheet on the form tool surface. Research effort of others, discussed in the preceding chapters have presented evidence that the high speed tool face impact produces an ironing type effect in the work sheet leading to plastic strain levels even greater than those reported here. This ironing effect can be fully gainfully utilized through proper design of a MT-EM process.

The following statements summarize the possible extrapolations of the coupon tests results to real MT-EM processes.