5m 1.: IBRARIES lllll‘lll ll ll Llll Hill 3129 This is to certify that the thesis entitled THE EFFECT OF MICROSTRUCTURE AND TEXTURE ON THE MECHANICAL PROPERTIES OF DOUBLE-REDUCED TINPLATE STEEL presented by Michael Wavid Wood has been accepted towards fulﬁllment of the requirements for Master degree in Materials Science Major professor Cult»- {‘jow? Date (9/74/9é7é 0-7639 MS U is an Afﬁrmative Action/Equal Opportunity Institution LIBRARY Mlchlgan State University PLACE u nsrunu BOX to "limit. vii. Mum your record. ' TO AVOID FINES Mum on or More data duo. DATE DUE DATE DUE DATE DUE Y—_ ’7 L A " f’g‘ﬁ" .. ff,“ ’1 V/ n' a, It I " C THE EFFECT OF MICROSTRUCTU RE AND TEXTURE ON THE MECHANICAL PROPERTIES OF DOUBLE-REDUCED TINPLATE STEEL By Michael David Wood A THESIS Submitted to Michigan State University in partial fulﬁllment of the requirements for the degree of MASTER OF SCIENCE Department of Materials Science and Mechanics 1994 ABSTRACT THE EFFECT OF MICROSTRUCTURE AND TEXTURE ON THE MECHANICAL PROPERTIES OF DOUBLE-REDUCED TINPLATE STEEL By Michael David Wood The inﬂuence of microstructure and crystallographic texture of double-reduced tinplate steel was investigated in order to determine their effect on the mechanical properties. Double-reduced tinplate steel undergoes hot-rolling, cold-rolling, continuous annealing and further cold-rolling during its production, with the parameters of each step having an inﬂuence on the ﬁnal microstructure and texture. Tinplate of two different thicknesses were examined, with both materials exhibiting a fully recrystallized ferritic microstructure. The dominant texture component present in the tinplate steel was the _{ 111} ﬁber texture, with a weak {100}

and {111}<110>; and ii) the { 111} ﬁber texture. A considerable amount of { 100}<011> may also be present due to the grain rotations occuring in the deformed 0t phase. The resultant texture and rrricrostructure of the hot-rolled strip plays an important role in the ﬁnal texture and properties obtained after the cold—rolling and annealing operations. The texture present after the continuous annealing cycle depends on the parameters of the annealing process, and on the texture and microstructure of the cold-rolled material. In 14 turn, the cold-rolling texture and microstructure is dependent on the hot-rolling texture and rrricrostructure. The transformation texture associated with finish rolling above A3 is relatively weak in comparison to the texture formed when finishing occurs in the (y + or) range. However, Vanderschueren, VanHoutte, et. a1. [11] have shown that these transformation-type and defonnation-type hot-rolling textures yield almost identical subsequent cold ~rolling textures, with the exception of a higher intensity at the {001}<110> orientation associated with the deformation-type hot-rolling texture. Cold Working / Cold-rolling is a generic term applied to passing unheated metal through rolls for the purpose of reducing its thickness; producing a smooth, dense surface; and achieving desired mechanical properties, either with or without subsequent heat treatment. Although the metal is unheated, a considerable amount of heat is generated due to the friction involved in the rolling process. The heat is dissipated through the use of oil lubrication jets directed at the rolls, and the resulting temperature falls far below the recrystallization temperature of the metal. Each pass in the cold reduction process must exceed the elastic limit of the material when considering the resultant of the compressive forces imposed by the rolls as well as the tension along the length of the strip between the reels and rolls [12]. The plastic deformation is primarily accomplished by the motion of dislocations and by shearing processes such as twinning. The structures and resulting properties which develop during plastic deformation depend on factors such as the crystal structure of the metal, the amount [of deformation, the composition, the deformation mode, and the deformation rate. As a consequence of the symmetry involved in the cold-rolling operation, deformation textures are formed where certain crystallographic planes rotate and align parallel to the rolling plane, and certain directions align parallel to the rolling direction, which also has a signiﬁcant effect on the resulting properties of the material. The nature of the plastic deformation of a material during an operation such as cold- rolling is dependent upon the crystal structure of the material. Hot-rolled steel strip entering the cold reduction process primarily consists of ferrite, 0t-iron, which has a body- centered cubic crystal structure (bcc), as shown in Figure 5. The predominant process occuring during plastic deformation of metals is slip of adjacent planes of atoms SLIP DIRECTION O SLIP PLANE C Figure 5: Body-Centered-Cubic Unit Cell within the crystal. The crystallographic planes on which dislocations move and the unit displacement of dislocations (Burgers vector) are determined by the crystal structure. A typical <111>{ 110} bcc slip system is depicted in Figure 5. Slip has been reported by glide of dislocations with a Burgers vector of 1/2 <111> on {110}, {211} and {321} planes yielding 48 possible slip systems, however, it is generally considered that slip occurs on any plane containing a slip direction, known as pencil glide. 16 Plastic deformation of polycrystalline materials begins with single Slip in a few grains whose orientation yields a high Schrrrid factor. As deformation continues, single slip is initiated in more grains, which results in increasing misfits at the grain boundaries. The elastic strains created by the grain boundary misﬁt are accomodated in the material in the form of reaction stresses, which give rise to the activation of other slip systems. After a relatively small amount of plastic deformation, a state of polyslip exists in all of the grains. As a result of polyslip, dislocations begin to interact with one another, forming dislocation tangles. The interaction of dislocations, as well as the creation of additional dislocations in the material, raises the stress required to cause additional deformation, which is termed strain hardening. The dislocation tangles formed eventually delineate deformation cell walls [1]. Three-dimensional walls of dislocation tangles form a cell structure around unifome sized areas of nearly perfect lattice. The dislocation walls are often parallel to a slip plane, with the average spacing between the walls decreasing as the strain increases. As the amount of plastic deformation continues to increase, dislocation glide, cell formation and reduction in cell size can no longer describe the resulting microstructure. Deformation within individual grains becomes increasingly inhomogeneous because each grain must conform to the macroscopic shape changes which occur at large deformations. The microstructural features appearing at large deformations include deformation bands, transition bands, kink bands, microbands and shear bands [13]. Deformation bands are regions of diﬁerent orientation within a single grain. Adjacent deformation bands are connected by transition bands, with continuous orientation changes through the thickness of the band. Kink bands are deformation bands separating regions of identical orientation. Microbands are long, straight bands of highly concentrated slip lying on the slip planes of individual grains. Microbands are typically 0.1 to 0.2 pm thick, traverse an entire grain, and correspond to the slip bands seen on the surface of a polished specimen. Shear bands are regions of very high shear strain. During the rolling process, strain bands form at ~ 17 135° to the rolling plane, parallel to the transverse direction. At high strains, strain bands traverse the entire thickness of the rolled sheet material. The microstructural changes which occur as a result of the cold-rolling operation are accompanied by the formation of a deformation texture. Deformation textures have their origins in the crystallographic nature of the deformation processes occuring during deformation. At large Strains, Slip is usually the major factor, however twinning can also have a signiﬁcant contribution because of the massive re-orientations involved. During rolling, the operation of Shear on a slip system causes crystal lattice rotations as a result of the Shape change and the geometrical constraints of the process. The restricted number of slip systems available produces rotations towards a limited number of end-points. Continuing deformation causes additional rotation until eventually stable orientations are reached where rotation is not a requirement for additional slip. The ﬁnal deformation texture consists of the stable orientations (components) which result from all possible initial crystal orientations. The strength of the individual components depends on the proportion of original crystal orientations which rotate to that end point, which is affected by any previous texture existing in the material. During cold-rolling of low carbon sheet Steel, the texture of ferrite becomes progressively stronger and sharper with increasing deformation, however, the main components that develop are almost independent of the material and processing variables. The cold-rolling texture of steel is comprised of two major orientation spreads [14,15]. One component is the yﬁber, with {111} planes parallel to the sheet surface and a continuous spread of orientations from <110> to <211>, depicted as {111} and typically referred to as the cube-on-comer texture. The other major Spread is a partial ﬁber texture with <110> parallel to the rolling direction. encompassing the orientations {001}<110>, {112}<110> and {111}<110>. The {111} and {001}<110> textures are depicted schematically in Figure 6. 18 Rolling Direction (001)1110] (111)1T10] Figure 6: Typical bcc Deformation Textures [16] Annealing The cold reduced Sheet steel is subjected to a continuous annealing stage, which serves the purpose of restoring ductility to the deformed material. The internal stored energy and dislocation structures present in the various deformed grains of the cold-rolled Sheet represent the driving force for recovery and recrystallization on annealing. In the recovery stage, the steel reverts to a condition in which the mechanical and physical properties tend towards the undeforrned state. During the initial stages of recovery, little change occurs to the microstructure and properties of the steel. As recovery continues, the dislocation density decreases while a dislocation network of subgrains is formed [1]. The subgrains which are formed have low-angle boundaries comprised of low-energy dislocation arrays, rather than the dislocation tangles associated with the deformed material. Once the dislocation rearrangement is complete, the cell size increases by either a process of l9 subgrain boundary migration [17] or coalescence [18]. The new subgrain boundaries are higher-angle, higher-energy boundaries, however, the total boundary area and dislocation density have decreased. The subgrains slowly increase in size until they have mobile high-angle boundaries, at which time they can act as the nuclei of recrystallized grains. Recrystallization begins when the high-angle boundary subgrains begin to grow at the expense of neighboring subgrains to form new grains that are relatively free of substructure. The resulting microstructure obtained after the continuous annealing cycle is fully recrystallized ferrite. During the processes of recovery and recrystallization, the deformed material undergoes microstructural changes, and new grains are nucleated and grow at the expense of the deformed matrix. The changes which occur within the material also cause a change in the preferred orientation. Various theories have been proposed as to the mechanism by which the changes in texture occur. Some believe that the annealing texture is established by the formation of nuclei of Speciﬁc orientations, the oriented nucleation theory, and these preferentially oriented nuclei grow without competition from nuclei of diﬁemnt orientations. The oriented growth theory states that nuclei of all orientations are formed, and that some nuclei grow faster than others, depending on their orientation relative to the recovered matrix. According to the literature, the theory which seems to best explain the phenomena of annealing texture formation involves elements of both oriented nucleation and oriented growth [19,20]. During the process of recovery, the individual crystallite orientations are modiﬁed very little, and the deformation texture is retained. In a study conducted by Dillarnore, et a1. [21], it was shown that the relative amounts of stored energy in the components of the rolling texture inﬂuence the formation of the recrystallization texture. The cell size and cell-boundary misorientation measured by transmission electron microscopy in iron cold-rolled to 70% reduction varied in a systematic way according to the deformed grain orientation. Fine cells with large misorientations occurred in the {111} family, while the cells became coarser and more 20 oriented closer to the {001}<110> component. The stored energy of deformation therefore increased in the order { 001} < {112} < {111}. Nucleation by subgrain growth mechanisms within individual deformed grains is most rapid where the stored energy is greatest, and favors nucleation within {111} oriented grains. The recrystallized orientation is also { 111}, however, it should be noted that the recrystallization texture formed is related to the original deformation texture, often by rotations about simple crystallographic directions, but not usually identical. At some point after the { 111 } grains have started to recrystallize, the remaining orientations recrystallize according to their relative amount of stored energy. The recrystallization ordinarily occurs at the as-rolled grain boundaries, and the grains grow by absorbing the remaining unrecrystallized orientations. Therefore, the intensity of the {111} component remains relatively constant in comparison to the deformation texture, or shows a slight increase, while the { 100} components of the rolling texture decrease considerably. Dillarnore and co—workers also showed that { 111} oriented grains tend to form subgrains more readily than { 100} deformed grains. After recrystallization the {100} grains are smaller than the {111} grains, and during the process of grain growth the {100} oriented grains are consumed by the larger {111} grains. As a result, the texture of the annealed sheet steel product retains the { 111} ﬁber texture which was present in the cold reduced material, and the {100}<011> component of the partial ﬁber with <011> parallel to the rolling direction is Si gniﬁcantly reduced in intensity. EXPERIMENTAL PROCEDURES Materials; The material used in this study was double-reduced tinplate steel, conforming to A.S.T.M. A-623, Type L, and was supplied by The United States Can Company. The chemical composition requirements, as stated in A.S.T.M. A-623, for Type L tinplate are listed in Table 1. Table 1: Chemical composition of Double-Reduced Tinplate Steel, Type L Element Composition max. % Carbon 0. 13 Manganese 0.60 Phosphorous 0.015 Sulfur 0.05 Silicon 0.020 Copper 0.06 Nickel 0.04 Chromium 0.06 Molybdenum 0.05 Residuals 0.02 21 22 Double-reduced tinplate steel is produced from continuous cast steel slabs. The cast slabs, ranging in thickness from 4 to 10 inches, are hot-rolled at an elevated temperature to a single continuous length which is coiled. The coiled product is typically 0.070 to 0.100 inches in thickness. The hot-rolled product exits the last ﬁnishing stand at a temperature in the range of 1500 to 1600 °F, is cooled through the use of water jets, and enters the coiler at a temperature of 1100 to 1250 °F. The hot-rolled product is continuously pickled in an acidic solution to remove all of the scale and oxide from the surface and is subsequently oiled prior to cold reduction. The pickled product is cold-rolled 80 to 90 percent on ﬁve-stand or six-stand four-high tandem cold-reduction mills. The cold- reduced product is continuously annealed in a protective atmosphere at approximately 1200 °F in order to soften the material and increase its formability. The annealed strip is cold-rolled an additional 30 to 40 percent, yielding a product with high hardness, yield strength and tensile strength, yet still possessing sufﬁcient formability for a wide range of applications. The ﬁnal reduced product receives an electrolytic tin coating with a thickness in the range of 83 - 275 um, which is melted to give a lustrous appearance. The two materials investigated in this study were 62 #lbase box and 78#/base boxl tinplate steel (0.0068 inch and 0.0086 inch thickness respectively). The difference in end product thickness is achieved at the hot-rolling stage, with thinner gage end products receiving larger hot-rolling reductions. The amount of cold reduction and additional reduction subsequent to the annealing process is typically held constant (Le. 90% cold reduction and 30% additional reduction) in order minimize the variation in properties. l. Tin mill products are ordered to thicknesses expressed in base weight units. The base weight is the weight, in pounds, of one base box (a unit of area equivalent to 112 sheets 14 by 20 in. or 31,360 in.2) which is a measure of the approximate thickness. 23 MetasmrcturalAnalysis The microstructure of the sheet stock materials was characterized by cold mounting specimens using a two-part room temperature curing epoxy resin system. Three specimens for each thickness material were mounted such that the Sheet normal, on-edge in the rolling direction and on-edge perpendicular to the rolling direction microstructures could be observed, as Shown in Figure 7. Sheet Plane Normal V Rolling Di ction On- .d e lleI to Rolling Direction .On-Edgg . . . Perpendicular to ollrng Direction Fr gure 7: Location of Microstructural Characterization Samples The mounted samples were mechanically ground using progressively ﬁner stationary abrasive papers of 240 grit, 320 grit, 400 grit and 600 grit. The samples were thoroughly rinsed between grinding stages to remove residual abrasive. The ground specimens were then polished using Leco VP-150 polishing wheels in conjunction with 600 grit, 5 um, 0.3 um and 0.05 urn A1203 abrasive suspended in distilled water. Once again, the samples were thoroughly rinsed between polishing steps in order to avoid carry over of residual abrasive to subsequent polishing Steps. The polished specimens were etched using a 3% 24 Nital solution (3% Nitric acid, remainder Methanol) for approximately 20 seconds to reveal the sheet steel rrricrostructure. The microstructure of the polished and etched specimens was photographed using an Olympus PME3 optical microscope equipped with the PM-lOAK automatic exposure photomicrographic system and Polaroid camera attachment. The grain Size in the width, height and length of the elongated grains was determined using the line intercept method: L an GS: where: GS = average grain size L = length on intercept line n = number of grains intercepted M = microscope magniﬁcation The number of grains intercepted was determined by drawing 5 lines of equal length in each respective direction, and computing the average number of grains traversed. The magniﬁcation used for the grain size calculation was determined through the use of a marker of ﬁxed length located inside the microscope which appears on the photograph. The marker was manually measured using a scale with 0.01 inch increments to determine the actual magniﬁcation. The aspect ratio of the grains was determined by dividing the average grain width by the average grain height. The average grain volume was calculated using the average width, height and length of a grain in conjunction with the formula for the volume of an ellipsoid: V = ﬂ11’.wlh 3 where: w = width 1 = length h = height 25 The average number of grains through the thickness of the materials was determined by dividing the material thickness by the average grain height. The fracture morphology of 62# and 78# plate materials was characterized using a Hitachi S-2500C Scanning Electron Microscope (SEM). A tensile sample with the tensile axis parallel to the rolling direction was tested to failure, and the failed region of the sample was mounted on an SEM stage using carbon paint. Micrographs of the fracture surface were taken using the polaroid camera attachment of the SEM. ”1.113. The mechanical strength properties of the double-reduced tinplate Steel were determined through the use of several different techniques. Standard tensile tests, high strain-rate tensile tests, r-value tensile tests and three-point bending ﬂexure tests were performed on specimens of varying angle with respect to the rolling direction. Samples for the standard tensile tests were supplied by The United States Can Company. Test samples for the high Strain-rate, r-value and ﬂexure tests were produced from supplied sheet materials. Standard tensile tests were performed on 62# plate and 78# plate specimens oriented at 0, 15, 30, 45, 60, 75 and 90° with respect to the rolling direction in accordance with the ASTM E8-83 testing procedure. Five specimens were tested at each orientation. The testing was performed on an Instron model 4302 bench-top universal testing machine using wedge-action grips and a 2 inch gage length extensometer. Instron series IX data reduction software was used for the calculation of the 0.2% offset yield stress, the peak stress, the Young’s modulus and the percent plastic elongation at break. The strain hardening exponent was determined manually according to ASTM E646. Five equally spaced points were chosen on the stress-strain curve between a location where the curve began to exhibit non-linearity in the elastic region and the peak stress. The stress-strain 26 data pairs were converted to true stress and true strain, their logarithm taken, and the strain hardening exponent, n, determined through linear regression analysis. The angle of fracture with respect to the tensile axis was manually measured on each tensile specimen by tracing the outline of the fracture surface and the gage length region and measuring using a protractor. High strain-rate testing was performed using an MTS series 810 servo-hydraulic testing machine in conjunction with a Nicolet model 4094B digital storage oscilloscope. Tensile specimens with 0.5 inch gauge lengths and 0.5 inch widths having orientations of 0, 15, 30, 45, 60, 75 and 90° with respect to the rolling direction were tested at a strain rate of 1 x 102 sec]. Test specimens were prepared by initially shearing rectangular strips from the steel sheet, then routering the gage length section using a Tensilkut test specimen preparation machine and associated Specimen cutting fixture. The specimen dimensions were taken using calipers with 0.01 inch increments. Real-time displacement and load data was collected by attaching lead wires from the displacement and load transducers of the MTS to the appropriate channels of the oscilloscope. Load vs. displacement data points were taken manually from the storage oscilloscope and converted into stress vs. strain data points and plotted. The value r refers to the plastic strain ratio, which is an estimate of the ratio of plastic strains in the plane of the sheet and perpendicular to the sheet. The plastic strain ratio is a very useful parameter used to determine the deep-drawing capabilities of materials. Press forming and deep drawing are very common methods used to produce parts from sheet materials, and require maximum plastic ﬂow in the plane of the Sheet while providing maximum resistance to ﬂow in a direction perpendicular to the sheet. An estimate of the ratio of strains in the plane of the sheet and perpendicular to the sheet can be obtained in a Simple tension test from a ratio of the true strains in the width and thickness directions according to: 27 where: SW = true width strain at = true thickness strain wo = original width Wf = final width 10 = original length If = ﬁnal length The physical meaning of r is such that r = 1 indicates equal ﬂow strengths in the plane and across the thickness of the Sheet; r > 1 indicates the average strength in the plane of the sheet is lower than across the thickness; and r < 1 indicates higher strength in the plane of the sheet than across the thickness. For deep drawing applications, an r value greater than unity is desirable because the material will resist thinning during the drawing operation. R value determination tests were performed on 0.5 inch gage length tensile specimens oriented at 0, 15, 30, 45, 60, 75 and 90° with respect to the rolling direction. The specimens for the r-value determination tests were produced in the same fashion as those used for the high strain-rate tests. Due to the lack of available material, only one tensile specimen was tested at each orientation. Micro-measurements CEA-06-125UT-350 biaxial strain gages were mounted in the center of the gage length of the specimens, with the foil grids arranged parallel and perpendicular to the tensile axis, as shown in Figure 8. Testing was performed on an Instron model 4302 bench-top testing system. The strain gage was balanced before mounting the specimen in the testing machine, and load was applied to the specimen at a constant rate of 0.05 inch/minute until a strain reading of 0.8% was reached and the test was terminated. The permanent residual strain due to 28 plastic deformation of the test specimen was measured using a Micro-Measurements switch and balance unit, and the strain readings were converted to displacements and used in the calculation of the r-value. \ j ¢ <— 0.5 inches ‘ J 0.5 inches t 0.75 inches biaxial strain gage angle with respect to rolling direction Figure 8: R-value Test Specimen Three-point bending tests were performed on specimens with orientations of 0, 15, 30, 45, 60, 75 and 90° with respect to the rolling direction, according to ASTM E855-84. The specimens were prepared by shearing rectangular strips of the appropriate size from the sheet steel and removing any burrs along the sheared edges with a ﬁle. The tin coating was left intact, assuming that the thickness of the coating would have negligible effect on the ﬂexure strength of the sheet material. The specimen and loading schematic are shown in Figure 9. Flexure testing was performed on an Instron model 4206 universal testing machine. Data collection, stress at yield and ﬂexural modulus calculations were performed using Instron Series IX computer software. 29 i 0.5 inches /angle WRT rolling directiorJ f P = Load i t = thickness 1 r l U o i <———— 150xt ———> Figure 9: Three-Point Bending Test Specimen and Loading Schematic IextureAnalxsis Pole ﬁgure data was collected for 62# and 78# plate using specimens that were sheared from the steel sheet with orientation and dimensions as shown in Figure 10, mechanically ground to remove the tin coating, and polished with 5 um and 0.05 um suspensions of A1203 in distilled water. Measurements of the texture were taken at the surface, as well as grinding the specimen to a reduced thickness and measuring the texture towards the center of the sheet. The pole ﬁgure measurements were performed using a Scintag XRD 2000 X- ray diffractometer with Kat radiation in conjunction with a pole figure goniometer, as pictured in Figure 11. 30 Rolling Direction ‘4— lcm—P‘ Figure 10: Texture Analysis Specimen Figure 11: Scintag XRD 2000 X-Ray Diffractometer 31 The data acquisition system was automated, and consisted of measuring diffracted intensity at background levels on either side of a diffraction peak, and then collecting intensity measurements at the peak angle, with specimen tilt ranging from 0 to 75° at 5° increments and 360° rotation at each tilt angle with 5° increments. Three diffraction peaks were located for each sample by performing a diffraction scan near each peak. A rough approximation for the peak locations was determined using the Powder Diffraction Files compiled by the International Centre for Diffraction Data for or-Fe. The standards book lists d-Spacings for {110}, {200} and {211} planes as 2.03, 1.43 and 1.17 A respectively. The d—spacings were used in conjunction with the wavelength for Kat copper radiation, A = 1.542 A, to determine the peak angles with the Bragg equation: A = 2dsinO where: A = wavelength of radiation (1 = interplanar spacing O = diffraction peak angle The pole figure raw data was reduced using popLA [22], the preferred orientation package from Los Alamos National Laboratories. Defocusing corrections were made using a theoretical algorithm, rather than an experimental defocusing curve, so the corrections were self-consistent, but not absolute. The data was rotated to allow for misalignment of the specimen, symmetrized, and the outer ring was computed using harmonic analysis. The program was used to generate 110, 200 and 211 pole figures; normal direction, rolling direction and transverse direction inverse pole ﬁgures; as well as sample orientation distributions and crystallite orientation distributions. An additional utility program included in the popLA software allows for the conversion of texture components given in generic Miller indices to their appropriate sets of Euler angles, which was used in the interpretation of the texture data. RESULTS MmstmcturaLAnalysis Polishing and etching of the double—reduced tinplate steel revealed a fully recrystallized ferritic microstructure, with pancake-shaped grains elongated in the rolling direction. Three-dimensional representations of the microstructure for 62# and 78# plate materials are shown in Figures 12 and 13, respectively. The grains appear equiaxed when viewed normal to the sheet surface and on-edge in the rolling direction, and are elongated in the rolling direction when viewed on-edge perpendicular to the rolling direction, which is typical for heavily rolled, fully recrystallized plate steel. Grain size, aspect ratio and grain volume data collected on the plate steel specimens are listed in Table 2. Table 2: Microstructural Data Material VVrdth Height Length Aspect Volume # Grains Thru (um) (um) (um) Ratio (m3) Thickness 62# plate 13.6 6.9 25 .4 1.97 1248 25 78# plate 10.6 5.9 17.8 1.80 581 37 While the aspect ratio of the two materials is very similar, the grain size of the 62# plate material is larger and the unit grain volume is signiﬁcantly larger than the 78# plate material. The larger grain size of the 62# plate material translates into a correspondingly lower yield strength and tensile strength. The 62# and 78# plate materials have similar microstructures, both consisting of fully rectrystallized ferrite. Even though the rrricrostructures appear nearly identical, slight differences in the processing parameters 32 Figure 12: Microstructure of 62# Plate in Vlfrdth, Height and Thickness Directions Fr gure 13: Microstructure of 78# plate in Vlfrdth, Height and Thickness Directions. 34 can alter the substructure of the material. However, the difference in thickness between the two plate materials is accounted for in the hot-rolling operation, with both materials experiencing the same amount of cold reduction and additional reduction after annealing. Therefore, the plate materials are expected to have very similar substructures, hence the microscopic substructures of the plate steel was not investigated. The fracture surface morphology of failed tensile test specimens is shown in F1 gures 14 and 15 for 62# and 78# plate, respectively. Figure 14: Fracture Surface of 62# Plate Tensile Specimen 35 Figure 15: Fracture Surface of 78# Plate Tensile Specimen The above rrricrographs clearly Show the failure mode as ductile dimple rupture. Specimens with the tensile axis parallel to the rolling direction were photographed, specimens oriented 90° to the rolling direction were also investigated, with identical failure mode. ”1.11:. Results from the standard tensile tests are shown in Tables 3 — 14, with comparison plots of 62# vs. 78# plate materials being shown in Figures 18 — 22. Typical stress-strain curves for the double-reduced tinplate are shown in Figures 16 and 17. As shown in the comparison plots, the offset yield strength and peak Strength increase as the angle with respect to the rolling direction varies from 0 to 90°. For the 62# plate and 78# plate 36 materials, the increase in both yield strength and peak strength is in the range of 14-16% as the tensile axis varies from 0 to 90° with respect to the rolling direction. While both materials Show a similar trend in strength, the 78# plate material has a strength 8-10% higher than the 62# plate material. The Young’s modulus remains relatively constant as the angle with respect to the rolling direction varies from 0 to 90°, with values for the 62# and 78# plate materials being very sirrrilar. During the tensile testing, a two inch extensometer was used to measure the strain. The standard deviation of the modulus values, listed in Tables 7 and 8, are rather high. The scatter of the measured modulus could be due to several factors, including slippage of the extensometer and factors associated with the thinness of the specimens. The percent plastic elongation to failure, as shown in Figure 21, shows an opposite trend. As the angle with respect to the rolling direction varies from 0 to 90°, the percent plastic elongation decreases for both materials. The 62# plate material exhibited a higher plastic elongation to failure than the 78# plate material, which is consistent with the lower strength of the 62# plate. The strain hardening exponent, 11, increased as the tensile axis with respect to the rolling direction varied from 0 to 90°. The strain hardening exponent is a measure of the increase in strength of a material due to plastic deformation, and for this study was determined from the yield point to the peak stress range of the stress-strain curve. The strain hardening exponent is the slope of the assumed linear relationship between the logarithm of the true stress and logarithm of true strain. The angle of fracture with respect to the tensile axis was also measured, with values ranging from 55 - 61° for both 62# and 78# plate materials. Liiders bands have been shown to form in steel specimens at approximately 55° to the stress axis, and were observed during the tensile testing. Eventual failure of the specimen occured at the location of a Ltiders band, which would explain the observed angle of fracture. Stress (psi) Stress (psi) 80000 37 720004- 64000<> 560000 48000" 40000<~ 320004- 24000? ‘16000‘L 80004 90 deg. 45 deg. \ 0 deg. (18000 c10042 0.0083 ESLradrr 00i25 (irr//irr) 00i67 00005 Figure 16: Stress - Strain Curves for 62# Plate Steel 0.0250 90000 81000» 72000< 63000» 54000¢ 4SOOOT 36000» 270000 18000-1- 9000*- 90 deg \ 45 deg. 0 deg 0. 0.0000 00029 00038 EHA“air1 0.0088 0.0117 (irr//irr) QOT46 Figure 17: Stress - Strain Curves for 78# Plate Steel 0.0175 38 Table 3: 0.2% Offset Yield Strength (psi) -- 62# Plate AnRgée/ 1 2 3 4 5 Avg. 0' 0 65,450 66,150 64,680 65,040 * 65,330 630 15 65,560 65,690 66,830 64,950 66,580 65,920 771 30 68,190 67,250 68,280 69,160 68,290 68,240 676 45 70,200 69,040 69,870 70,310 70,670 70,020 618 60 72,440 73,210 72,270 73,500 72,510 72,790 539 75 74,720 74,910 75,310 74,980 75,190 75,030 268 90 77,850 77,720 77,710 77,820 * 77,780 71 Table 4: 0.2% Offset Yield Strength (psi) -- 78# Plate ADRECI 1 2 3 4 5 l Avg. o 0 71,510 72,880 72,560 73,130 * 72,520 713 15 74,470 73,840 74,520 74,190 * 74,260 309 30 75,760 75,180 74,310 75,130 76,490 75,380 810 45 77,580 * 78,200 78,120 77,730 77,910 301 60 78,400 79,660 79,090 80,220 79,950 79,460 725 75 * 83,600 * 83,490 83,750 83,610 129 90 84,590 84,550 84,740 83,540 * 84,350 546 39 Table 5: Peak Stress (psi) -- 62# Plate Ag“ 1 2 3 4 5 Avg. o 0° 67,690 68,180 67,160 67,220 * 67,560 474 15° 67,880 68,370 68,100 68,230 68,590 68,230 269 30° 69,850 69,860 71,000 70,690 70,390 70,360 508 45° 72,100 72,800 72,240 72,930 72,780 72,570 373 60° 74,450 74,800 73,900 74,710 74,790 74,530 382 75° 76,530 76,350 76,590 76,530 76,590 76,520 112 90° 80,220 80,050 79,950 79,700 * 79,980 217 Table 6: Peak Stress (psi) -- 78# Plate “Rig” 1 2 3 4 5 Avg. o 0° 74,630 74,220 74,480 74,070 * 74,350 252 15° 76,680 75,560 75,820 76,320 * 76,100 504 30° 77,470 77,270 77,550 77,570 77,640 77,500 142 45° 79,870 * 79,630 79,900 80,060 79,860 181 60° 81,720 82,060 81,790 82,120 82,050 81,950 178 75° * 86,470 * 86,130 86,310 86,310 166 90° 86,780 86,690 86,740 86,830 * 86,760 56 02% Yield Stress (psi) Peak Stress (psi) 40 100000 , +62# Plate 90000.. +78# Plate 80000» 70000» d 60000» 50000» 40000» 30000» 20000» 10000» 0 . : ~ 0 15 30 45 60 75 90 Angle With Respect. to Rolling Direction Figure 18: 0.2% Yield Stress 100000 +62# Plate 90000» +78# Plate 50000t 70000: 60000» 50000« 400001 30000» zooooi 10000» O ‘ e e A 0 15 30 45 60 75 90 Angle With Respect to Rolling Direction Figure 19: Peak Stress 41 Table 7: Young’s Modulus (ksi) -- 62# Plate Angle/ RD 1 2 3 4 5 Avg. 0 0° 26,400 27,770 27,120 27,600 * 27,220 613 15° 26,890 27,450 24,550 25,600 25,060 25,910 1,224 30° 25,370 30,250 27,420 27,320 27,580 27,640 1,844 45° 29,280 3 1,650 28,390 28,960 28,410 29,340 1,348 60° 28,990 29,040 3 1 ,040 29,930 28,320 29,460 1,049 75 ° 28,970 26,880 29,450 27,440 27,730 28,260 1,171 90° 31,620 34,250 33,240 29,980 * 32,270 1,872 Table 8: Young’s Modulus (ksi) -- 78# Plate AnRg’ie/ 1 2 3 4 5 Avg. 0 0° 3 1,140 * 29,500 26,770 * 29, 137 2,208 15° 31,690 29,720 28,110 27,980 * 29,370 1,733 30° 29,190 29,960 36,530 32,950 26,440 31,010 3,858 45° 27,990 * 29,130 27,520 31,750 29,100 1,894 60° 28,890 27,470 28,370 28,860 30,790 28,880 1,214 75° * 30,140 * 29,680 30,810 30,210 569 90° 32,070 30,540 29,880 29,310 * 30,450 1,191 Table 9: Percent Plastic Elongation - 62# Plate 42 “11%” 1 2 3 4 5 Avg. 6 0° 2.044 1.973 1.900 2.176 * 2.023 0.117 15° 1.453 1.548 1.538 1.399 1.511 1.490 0.063 30° 1.129 1.143 1.121 * 1.209 1.150 0.040 45° 1.235 1.061 1.072 0.948 1.030 1.069 0.105 60° 0.896 1.152 0.831 0.904 0.821 0.921 0.135 75° 0.915 0.862 0.897 0.892 0.837 0.878 0.035 90° 0.836 0.861 0.896 0.584 * 0.794 0.143 Table 10: Percent Plastic Elongation -- 78# Plate An$el l 2 .3 4 5 Avg. 0' 0° 1.571 1.369 1.598 1.495 * 1.508 0.102 15° 1.145 1.070 1.308 1.206 * 1.182 0.100 30° 0.932 0.984 1.091 ' 1.052 0.992 1.010 0.062 45° 0.941 * 0.886 1.017 0.878 0.931 0.064 60° 0.865 0.858 0.945 0.876 0.888 0.886 0.035 75° * 0.895 * 0.842 0.854 0.864 0.028 90° 0.870 0.892 0.933 0.902 * 0.899 0.026 Young's Modulus (ksi) % Plastic Elongation 43 40000 +62# Plate 36000» +78# Plate 32000» 28000‘» 24000» 20000» 16000» 12000» 8000» 4000» 0 - . - , 0 15 30 45 60 75 90 Angle With Respect to Rolling Direction Figure 20: Young’s Modulus +62# Plate 2,25.. +78# Plate 0.00 ‘v - ¢ ‘ 0 15 30 45 60 75 90 Angle With Respect to Rolling Direction Figure 21: Percent Plastic Elongation 44 Table 11: Strain Hardening Exponent, n -- 62# Plate Angle/RD l 2 3 4 5 Avg. 0° 0.2230 0.2304 0.2315 0.2170 0.2063 0.2216 15° 0.2285 0.2293 0.2376 0.2696 0.2781 0.2486 30° 0.2593 0.2402 0.2602 0.2540 0.2931 0.2614 45° 0.2218 0.2694 0.2867 0.2860 0.2890 0.2706 60° 0.3025 0.2748 0.2547 0.3002 0.2954 0.2855 75° 0.2770 0.3303 0.3016 0.2918 0.2482 0.2898 90° 0.2698 0.2556 0.2759 0.3021 0.2648 0.2736 Table 12: Strain Hardening Exponent, n -- 78# Plate Angle/RD l 2 3 4 5 Avg. 0° 0.2953 0.2079 0.2424 0.2790 0.2163 0.2482 15° 0.2895 0.3100 0.2874 0.3030 0.2770 0.2934 30° 0.2784 0.3214 0.3399 0.2866 0.3056 0.3064 45° 0.3042 0.2905 0.3075 0.2935 0.3226 0.3037 60° 0.3335 0.3190 0.3405 0.3054 0.3246 0.3246 75° 0.3193 0.2765 0.3266 0.3005 0.3356 0.3117 90° 0.3003 0.3510 0.3225 0.3214 0.3604 0.3311 45 0.4000 +62# Plat 03500.. +78# Plate 0 1600» 0.1200» 0.0800» 0.0400» 0.0000 s s ‘ 0 15 30 45 60 75 90 Angle With Respect to Rolling Direction Figure 22: Strain Hardening Exponent, n 46 Table 13: Angle of Fracture With Respect to Specimen Axis -- 62# Plate Angle/RD l 2 3 4 5 Avg. 0° 61° 57° 61° 60° * 60° 15° 60° 58° 61° 59° 58° 59° 30° 58° 55° 60° 59° 57° 58° 45° 52° 51° 58° 56°° 57° 55° 60° 51° 50° 57° 50° 58° 53° 75° 52° 53° 52° 51° 58° 53° 90° 55° 55° 53° 55° * 55° Table 14: Angle of Fracture With Respect to Specimen Axis (degrees) -- 78# Plate AuuﬂeﬂRE) 1 2 3 4 5 .Avg. 0° 60° 62° 61° 60° * 61° 15° 58° 59° 58° 57° 59° 58° 30° 55° 57° 56° 55° 54° 55° 45° 57° 51° 58° 51° 56° 55° 60° 57° 57° 55° 57° 58° 57° 75° 59° 55° 55° 55° 55° 56° 90° 54° 52° 54° 53° 54° 53° 47 High Strain-rate tensile results are given in Table 15 and Figure 23. The values listed are an average of two specimens. Some difﬁculties were experienced during the high strain-rate testing. A hydraulic leak existed on the MTS testing machine between the servovalve and the actuator assembly at the time the testing was performed, which lead to 1 was unachievable, with the several problems. The targeted strain rate of 1 x 102 sec' actual strain rate of the test being approximately 1 x 101 sec'l. As the strain rate of the test was increased, the amount of displacement achieved by the actuator (crosshead) decreased. Therefore, the strain rate had to be compromised in order to develop enough crosshead displacement to plastically deform the test specimen. While the test specimens showed signs of permanent deformation (Liiders bands), the peak stress values listed in Table 15 seem inexplicably low. One would expect the ﬂow stress of the material to increase at high strain-rates because the ability of the material to recover dynamically lags behind the rate of strain hardening. However, the peak stress results obtained during this study are signiﬁcantly lower than those measured during the standard tensile tests, which may be due to the lack of sufﬁcient crosshead travel during the test. Even though the values appear low, the trend of increased strength as the angle with respect to rolling direction increases remains intact. Table 15: High Strain-Rate Testing -- Peak Stress (psi) Material 0° 15° 30° 45° 60° 75° 90° 62# plate 38,509 40,800 40,697 40,800 43,541 45,333 45,799 78# plate 43,514 43,472 44,41 1 44,342 45,521 46,775 48,682 48 60000 ' +62# Plat 54000.. +78# Plate 48000-11- D 42000.;/.—_‘—_—_././.——’—‘ 1 36000» 30000-1» 240001- 18000» Peak Stress (psi) 12000< 6000» 0 - . - - . 0 15 30 45 60 75 90 Angle With Respect’to Rolling Direction Figure 23: High Strain-Rate Test Results Results from the r-value testing are given in Table 16. As seen from the data, several problems were encountered during the testing. In order to obtain an accurate reading of the permanent plastic deformation encountered by the test specimen, the bond between the strain gage and the test specimen must be very strong. Several of the strain gages had very poor bonds to the test specimens, which was discovered after the testing was complete. Another problem was in the geometry of the test specimens used. The ASTM test method speciﬁes a 2 inch gage length test specimen, allowing for very uniform strain in the gage section. Due to the lack of available material, 0.5 inch gage length specimens had to be used. While the strain in the gage section may have been fairly uniform through most of the test, the ﬁnal strain of 0.8% caused the formation of Liiders bands in specimens approaching 90° with respect to the rolling direction. These Liiders bands, whether they fall in the area of the strain gage or not, have a signiﬁcant impact on the test results. 49 Table 16: R-Value Testing Results Material 0° 15° 30° 45° 60° 75° 90° 62 # plate 0.489 0.982 0.530 0.830 * 0.445 0.904 78# plate 0.340 * 0.422 1 .610 1.440 * * Flexure testing results are Shown in Tables 17-20 and Figures 24 and 25. Results from the three-point bending tests Show the same trend as the standard tensile tests, an increase in strength as the angle with respect to the rolling direction increases from 0 to 90°. The yield stress increases approximately 30% from 0 to 90° for the 62# plate steel, and 20% for the 78# plate Steel. Parallel to the rolling direction, the 78# plate steel has a strength 18% higher than the the 62# plate steel, and transverse to the rolling direction the strength is 5% higher than the 62# plate material. AS would be expected, the ﬂexural modulus also increases as the angle with respect to the rolling direction increases. The 62# plate exhibited a 20% increase in modulus, with the 78# plate material exhibiting a 9% increase. The modulus at 0° was 10% higher for the 78# plate, and almost equal at 90°. 50 Table 17: Stress At Yield (psi) -- 62# Plate Angle/RD l 2 3 4 Average 0' 0 91,070 * 98,690 98,520 96,090 4352 15 100,700 101,400 98,840 100,300 100,300 1068 30 112,700 110,200 112,500 116,100 112,900 2452 45 122,800 120,800 122,300 122,800 122,200 941 60 127,800 128,300 131,800 130,200 129,500 1814 75 131,000 138,100 138,500 132,800 135,100 3767 90 137,200 134,500 141,300 141,000 138,500 3254 Table 18: Stress At Yield (psi) - 78# Plate Angle/RD 1 2 3 4 Average 0' 0 116,900 116,700 115,900 116,600 116,500 428 15 121,400 123,200 121,000 121,800 121,900 968 30 128,700 128,300 128,600 129,600 128,800 542 45 133,600 134,200 132,800 134,800 133,800 835 60 136,700 138,200 139,200 142,200 139,100 2346 75 141,800 145,100 141,300 143,300 142,900 1695 90 146,700 146,700 146,600 146,500 146,600 116 51 Table 19: Flexural Modulus (ksi) -- 62# Plate Angle/RD 1 2 3 4 Average 0' 0 26,810 * 25,990 29,370 27,390 1763 15 28,190 28,880 26,370 25,650 27,270 1514 30 28,530 25,800 28,310 31,150 28,450 2184 45 27,800 27,590 27,900 28,530 27,960 4015 60 32,920 30,180 29,950 31,330 31,090 1355 75 30,430 34,080 32,020 3 1,760 32,070 1510 90 35,130 32,650 33,630 32,870 33,570 1121 Table 20: Flexural Modulus (ksi) -- 78# Plate Angle/RD 1 2 3 4 Average 0' 0 3 l ,900 30,080 29,610 30,190 30,440 1003 15 35,170 31 ,450 30,010 39,040 3 1 ,420 2689 30 30,790 30,990 32,550 29,400 30,930 1289 45 31,730 29,510 31,420 31,080 30,930 985 60 30,670 31,140 32,440 32,010 31,570 804 75 31,030 33,420 34,240 32,940 32,910 1364 90 33,280 33,160 33,470 32,740 33,160 309 Peak Stress (psi) Flexural Modulus (ksi) 52 60000 +62# Plate 540004 +78# Plate 48000l———./.——.// P 42000T 1 36000» 30000» 24000» 18000» 12000» 6000» O 5 : A A A 0 15 30 45 60 75 90 Angle With Respect to Rolling Direction Figure 24: Flexure Stress at Yield 40000 +62# Plate 360004 +78# Plate 24000» 20000» 160004 12000» 8000» 4000» O A e t c t 0 15 30 45 60 75 90 Angle With Respect to Rolling Direction Figure 25: Flexural Modulus 53 W The pole ﬁgure diffraction data was input into the popLA software package, and pole ﬁgures, inverse pole ﬁgures, sample orientation and crystallite orientation distributions were generated for samples of 62# plate and 78# plate. (110), (200) and (211) pole ﬁgures for the 62# and 78# plate materials are shown in Figures 27 and 28, respectively. A pole ﬁgure is a stereographic projection showing the density of particular crystallographic poles as a function of orientation, with the sample axes (normal, rolling and transverse directions) as a reference frame. Pole ﬁgures are often very difﬁth to interpret. Textures of rolled sheets are usually given in terms of ideal orientations, such as {111}<01I>. However, an experimentally measured pole figure is quite complex, exhibiting multi- component textures. The actual texture is commonly described as having a “spread” of orientations from one texture component to one or several other texture components. The (110) and (200) pole ﬁgures are typical of severely rolled low-carbon sheet steel. The (200) pole ﬁgures reveal two major orientation spreads. The strongest component is a ﬁber texture with a <111> ﬁber axis parallel to the normal direction, with an orientation spread from {111}<011> to {111}<112>. A partial ﬁber also exists, with the <110> direction parallel to the rolling direction and an orientation spread from {001}<110> to { 111}<1T0>, as shown in Figure 26 RD o-~ TD Figure 26: (100) Pole Figure Showing <110> Fiber Texture [23] Pole Figures - 62! Plate 4.75 4.00 Figure 27: Pole Figures -- 62# Plate Pble Figures - 78! Plate ( l ' 5.48 Figure 28: Pole Figures -- 78# Plate 55 Inverse pole ﬁgures in the normal, rolling and transverse directions for the 62# and 78# plate materials are shown in Figures 29 and 30, respectively. Inverse pole ﬁgures are most useful for the interpretation of true ﬁber textures, such as those produced by wire drawing. Since these figures do not indicate rotations that may occur around the chosen axis, they are less useful for materials which have undergone a deformation process of less symmetry, such as rolling. The ﬁgure uses one quadrant of the standard 001 stereographic projection as a reference frame, and displays intensity contours corresponding to the frequency with which the various directions in the crystal coincide with the specimen axis under consideration. As for the pole figure data, the textures present in the 62# and 78# plate materials are very similar. The normal direction inverse pole ﬁgure indicates a very strong intensity of <111> directions parallel to the normal direction of the sample. This indicates that a high density of {111} planes are parallel to the surface of the sheet, which is consistent with the {111} ﬁber texture mentioned previously. The rolling direction inverse pole ﬁgure shows a high intensity of <011>, with a smaller intensity associated with <1 12>. The {111} ﬁber texture consists of an orientation spread from { 111} to { 111}<112>, which is consistent with the results obtained from the inverse pole ﬁgures. The transverse direction inverse pole ﬁgure also shows intensity peaks located at <011> and <112>. The intensities associated with the transverse direction inverse pole ﬁgure are lower than those for the rolling direction, which is logical since the deformation occurs in the rolling direction, and the directions should be more strongly aligned due to the symmetry of the process. The location of the intensity peaks is also expected since since the and <1 12> directions are orthogonal, and the rolling and transverse directions are also orthogonal. 56 Inverse Pole Figures — 62! Plate (equal—area proJ.) nax.=17.93 1.” 2.83 2.” 1.11 1.“ Figure 29: Inverse Pole Figures -- 62# Plate Inverse Pole Figures —- 78! Plate (equal-area proJ.) nax.=18.% Figure 30: Inverse Pole Figures -- 78# Plate 57 Pole ﬁgures and inverse pole ﬁgures can yield satisfactory qualitative descriptions of the texture present in a sample, however, sample and crystallite orientation distribution plots are much more descriptive and can yield quantitative results. The problem with pole ﬁgures and inverse pole ﬁgures is that a general crystallographic orientation has three degrees of freedom, whereas pole ﬁgures and inverse pole figures specify only two degrees of freedom. Therefore, pole ﬁgures and inverse pole ﬁgures are merely “projections” of the three dimensional orientation distribution function, which is the full description of the texture. The three degrees of freedom associated with a crystallographic orientation correspond to three Euler angles, which relate the crystallographic coordinate system (001, 010 and 100) to the sample coordinate system (rolling direction, transverse direction and normal direction). Since three independent parameters are associated with the relation of two orthogonal coordinate systems, the Euler angles are considered to represent three orthogonal axes which define a volume of orientation space [23]. The definition of the Euler angles, and the symbols which represent these angles, varies among several different conventions developed by workers in the ﬁeld of texture analysis. The method used in this study was the Kocks convention [22], with Euler angles ‘1’, O and o, as shown in Figure 31. 010 Figure 31: Definition of Kock’s Convention Euler Angles [23] 58 The orientation distribution function (ODF) can be calculated using numerical data obtained from several pole figures by a number of different methods. The most common methods of ODF determination involve either an iterative least squares solution or generalized spherical harmonics. The method used by the popLA software package is the WIMV analysis method. The WIMV method involves the use of the most constructive elements of William’s [24] and Irnhof’s [25] least squares ODF reproduction method, as well as the automatic ghost correction suggested by Matthies and Vinel [26], hence the name WIMV [27]. The analysis procedure involves the creation of “pointers” (or “vectors” or “matrices”) which connect each cell in three-dimensional orientation space with all cells on the various pole ﬁgures into which they project [22]. The pole ﬁgure data is stored on a 5° x 5° grid, with one intensity value associated with each grid cell. The orientation distribution (OD) is calculated on a 5° x 5° x 5° three-dimensional grid in orientation Space, with one intensity value assOciated with each grid cell. A set of “pointers” is established which relate each cell in the OD to the cell or cells of the pole ﬁgures into which they project. In general, each OD cell points to several pole ﬁgure cells, and each pole ﬁgure cell is pointed to by several OD cells. An initial estimate of the OD is calculated by assigning to the OD cell the geometric mean of the intensity values in the pole ﬁgure cells to which it points [22]. The estimated OD is then used to recalculate the pole ﬁgures, which is essentially done by reversing the process used to estimate the OD. The recalculated pole ﬁgures usually do not correspond well with the measured pole ﬁgures due to the averaging of intensities in the OD grid cells. Therefore, the ratios of the measured to the recalculated intensity values are averaged and used to calculate a correction factor for each corresponding cell in the OD grid. This procedure is repeated until the solution converges to a stable value. Once a solution to the OD has been obtained, the symmetry between the sample and crystal coordinate systems allows for two equivalent descriptions of the orientation relationship: the sample orientation in terms of the crystal reference frame (sample orientation distribution (SOD)); or the crystal 59 orientation in terms of the sample reference frame (crystallite orientation distribution (COD)). Since these three-dimensional plots are very difﬁcult to generate and interpret, the orientation distributions are usually presented as a series of parallel sections through orientation space. The SOD has constant ‘1’ sections, with O and (b varying from 0 to 90° in each section, while the COD has constant (1) sections, with ‘1’ and O varying from 0 to 90° in each section, as shown in Figure 32. SOD - constant ‘1’ COD - constant 0 Figure 32: SOD and COD Angle Conventions Traditionally, each orientation distribution section is plotted in Cartesian coordinates, yielding a square plot in which equal areas on the plot do not represent equal volumes in orientation space. The method of representing oiientation distributions employed by the popLA software package plots each section in polar coordinates, projecting densities in each section in an equal-area projection. This method of representation has several advantages over the traditional square plots: equal volumes in orientation space correspond to equal areas in the plot; crystal and sample symmetries are clearly displayed, often allowing for quadrant or hemispherical representations; angles can be directly measured from the plot through the use of a net; and the sum of all sections, or the 60 projection, is the normal direction inverse pole ﬁgure in the case of the SOD, or the (100) pole figure in the case of the COD [28]. The SOD’s for the 62# and 78# plate materials are shown in Figures 33 and 34, respectively. As was the case for the pole ﬁgures and inverse pole ﬁgures, the preferred orientation displayed by the SOD’S is very Similar for the two plate materials, and the projection is , in fact, the normal direction inverse pole ﬁgure. The method used to analyze the SOD’S, as well as the COD’s, involved the use of a utility program included with the popLA software package, hk12eul. This program allows the user to input Miller indices in the form (hkl)[uvw], and converts these indices into sets of Euler angles. The listing of Euler angles includes both positive and negative angles from 0 to 360°. Typical rolling and recrystallization textures for steel were input into the program, and the set of Euler angles was pared down to include only positive angles between 0 and 90°, since the SOD sections are quadrants with angles of the same range, and are listed in Table 21. Due to the crystal symmetry involved, indices of lower symmetry require a larger number of Euler angle sets to completely deﬁne all equivalent orientations. Comparing the angles listed in Table 21 with the SOD’S, the most Si gniﬁcant texture component present in the plate steel samples is the ( l l 1)[1I0] cube-on-comer textures. However, each SOD section Shows a signiﬁcant intensity associated with O = 55° and o = 45°, indicating a { 111} ﬁber texture with orientation spreads from {111 }<1T0> to { 111 }d- 11>. In order to compare the the relative strength of the ﬁber textures associated with the plate steel materials, the relative intensity (in arbitrary units) at O = 55° and q) = 45° obtained from the SOD data ﬁles was plotted for each section as ‘1’ ranged from 0 to 90°. This skeleton line associated with the y—fiber texture for the 62# and 78# plate materials is shown in Figure 35. The peak locations for the 62# and 78# plate materials occur in approximately the same location, with the intensity associated with the 62# plate being higher than that for the 78# plate. The increased intensity is due to the additional grain growth experienced by the thinner material during the annealing cycle. During the grain growth process, the more favorably oriented {111}<1I0> grains grow 61 Salple Orientation Distribution -- 63. Plate SDI] PSI= (Read phi Pro. 100 touard 019) Figure 33: SOD -- 62# Plate 62 Sample Orientation Distribution — PSI Plate 801) PSI= (Bead phi Pro- 100 toward 810) log. scale HIM-91 Figure 34: SOD - 78# Plate 63 Table 21: Miller Indices and Their Respective Sets of Euler Angles Orientation ‘1’ O 0 0101110] 30° 55° 45° 90° 55° 45° (111)1211] 0° 55° 45° 60° 55° 45° (112)1110] 39° 66° 63° 90° 35° 45° (100)1011] 0° 0° 45° (100)10011 0° 0° 0° 0° 0° 90° (554)1225] 0° 60° 45° 64° 52° 51° (411)[ﬁ8] 23° 19° 45° 24° 76° 14° 70° 76° 14° 64 at the expense of the less favorably oriented grains, which sharpens the resulting texture. Continued annealing would lead to additional grain growth, and a continued sharpening of the resultant texture. 1500 +62# Plat 1350, +7544 Plate 1200» D 10504 900» 750» q Intensity 600» 300» 150» 0 i5 30 4'5 60 75 90 ‘1’ Figure 35: y - Fiber Skeleton Line The COD’s for the 62# and 78# plate materials are shown in Figures 36 and 37, respectively. Again, the orientation distributions for the two materials are very similar, and the projection of the COD is very similar to the (200) pole ﬁgure. Comparing the COD plots with the Euler angles listed in Table 21, it is clear that the predominant texture component is the (111)[1T0] cube-on-comer orientation, and the intensity maxima located in the ([1 = 45° section at O = 55° is indicative of the {111} complete fiber texture present in the samples. This location of intensity maxima is the same as that shown in the skeleton line plot of Figure 35, viewed from another direction. 65 Crystallite Orientation Distribution —- 62! Plate COD phl= (Bead Psi fro. +1 touard +2) Figure 36: COD -- 62# Plate 66 Crystalllte Orientation Distribution — 78! Plate CODph1= (BeadPs Psi fro. +1 touard +2) Figure 37: COD -- 78# Plate DISCUSSION The common metals of industrial importance are polycrystalline aggregates in which each of the individual grains has an orientation that differs from those of its neighbors. During the manufacture of products such as sheet Steel, processes such as rolling cause rotations of the crystallites as a result of the Shape change and the geometrical constraints due to the imposed stress system. The nature of these rotations is based on the crystallographic nature of the deformation process of slip. The restricted number of slip systems available produce rotations towards a limited number of stable end points, creating a preferred orientation. Upon annealing, the material undergoes the processes of recovery, recrystallization and grain growth. Recovery does not generally affect the deformation texture, however, recrystallization and grain growth are characterized by the movement of high-angle grain boundaries whiCh create changes in the local orientation. The summation of all local orientation changes represents a textural change in the material, which is related to the deformation texture. The existence of sharp crystallographic textures creates pronounced directionality of properties. The anisotropy which exists in the polycrystal is based on the directionality which exists in the Single crystal. In the case of bcc (it-Fe, the strength is highest along the cube diagonal <111>, lower along the face diagonal <110>, and lowest along the cube edge <100>. In fact, the Young’s modulus in the <111> direction is as much as 2.4 times higher than the modulus in the <100> direction [29]. During the course of the current study, directionality in the mechanical properties was observed. The anisotropy is explained by consideration of the effects of the microstructure present, as well as the effects of the preferred orientation which exists in the material. The microstructure of the 62# and 78# double-reduced tinplate steels consisted of a fully recrystallized matrix of ferrite. The grains are elongated in the rolling direction, with the so-called pancake grain structure. Materials which have undergone heavy cold 67 68 reductions often exhibit mechanical ﬁbering, where second phases and inclusions are elongated and aligned in the rolling direction. The ﬁbering is typically associated with anisotropic mechanical properties, because the inclusion stringers hinder plastic ﬂow of the material varying amounts in different directions in the plane of the sheet. The microstructure of the sheet steels did not reveal appreciable mechanical ﬁbering, in fact, the material was relatively free of large sized inclusions. When the sheet steel is ﬁnish rolled above A3 and the coiling temperature is kept low, the resulting rrricrostructure consists of recrystallized ferrite grains with small, evenly distributed precipitates. The rapid heating and cooling rates associated with the continuous annealing process produce a relatively fine grain size, and promote the retention of carbon and nitrogen in ferrite solid solution. The resulting microstructure of the ﬁnal product is relatively “clean,” with small, evenly spaced precipitates. The grain-shape effect, however, does play a role in the observed anisotropic properties. AS the stress‘axis varies from 0 to 90° with respect to the rolling direction, grains elongated in the rolling direction become increasingly constrained by contiguous grains. Due to the elongation of the grains, more barriers to slip exist in the form of grain boundaries, and plastic deformation becomes increasingly difﬁcult, resulting in increased strength. When comparing the strengths of the 62# and 78# plate materials, the smaller grain Sized 78# material exhibited higher strength and reduced plastic elongation to failure. The smaller grain size relates to larger grain boundary area. The grain boundaries act as obstacles to dislocation motion, and a larger number of obstacles to plastic ﬂow in the material results in increased strength. For polycrystals, a condition of compatibility between neighboring grains exists during deformation. This accomodation is realized by multiple slip in the vicinity of the boundaries. The smaller the grain size, the larger will be the total boundary surface area per unit volume. Therefore, for a given deformation the total volume occupied by work-hardened material increases with decreasing grain size, resulting in greater hardening due to dislocation interactions induced by multiple slip. 69 While the microstructural features play a small role in the directionality of mechanical properties, the major cause of anisotropy in rolled steel sheet is attributed to the preferred orientation present in the material. When a material is subjected to large rolling reductions, the individual grains in the polycrystal rotate on their appropriate Slip systems under the constraints of the deforming forces. Eventually, a limited number of stable orientations are reached where further reductions do not cause additional reorientation. The stable orientations reached are dependent on many factors, including the crystal structure and processing parameters, and are such that slip occurs easily. Upon annealing, the texture is altered in a way which is related to the rolling texture. In the case of sheet Steel, the {111} fiber texture is present through hot-rolling and cold-rolling, and is further enhanced by the annealing process. The texture present in the material allows slip to occur easily when the testing axis is aligned with the rolling direction due to the activation of primary slip Systems. Since the orientation difference from grain to grain is minimized due to the preferred orientation, dislocation motion from grain to grain occurs easily. As the testing axis is varied towards 90° with respect to the rolling direction, the applied stress to initiate plastic deformation is increased since secondary slip systems must be activated. Due to the increasing rrrisorientation between neighboring grains, dislocations must change their direction of motion at the grain boundaries, which results in increased strength, reduced ductility and an increase in the strain hardening of the material. During the standard tensile testing, Lt'iders band formation was observed during the latter stages of the deformation, with failure occuring at the location of one of these bands. Liiders bands are caused by inhomogeneous yielding, with yielding occuring within but not outside of the bands. Specimens oriented along the rolling direction exhibited a high degree of Liiders band formation, with the bands eventually propagating to cover the entire reduced gage section. As the off-axis angle increased, the amount of observable Ltiders band formation decreased, reinforcing the theory of the activation of secondary 70 slip systems for specimens with increasing off-axis orientation. The main texture component present in the sheet steel specimens was the {111} fiber texture, with a continuous orientation spread from { 111 }<1 10> to { 111 }<211>. While the two end points of the above orientation spread are orthogonal to one another with a continuous spread, one might conclude that the properties in the plane of the sheet would be relatively isotropic. However, the texture is much sharper in the rolling direction due to the constraints of the rolling process, leading to anisotropy in the plane of the sheet. It should be noted that the processing conditions imposed on the double-reduced tinplate steels are such that the directionality of mechanical properties is minimized. The processing parameters associated with the hot-rolling, cold-rolling and continuous annealing operations produce a product which is fully recrystallized ferrite, and is ductile despite its relative hardness. The preferred orientation present imparts directionality in properties due to the inherent anisotropy in the single crystal. However, as a measure of uniformity, the strength of the material varied less than 15% from 0 to 90° with respect to the rolling direction in the plane of the sheet. Thus, this material represents a high quality product which has been engineered to avoid many undesirable properties. CONCLUSIONS 1. The microstructure of the double-reduced tinplate steel consisted of a fully recrystallized matrix of ferrite grains, with relatively few inclusions and precipitates. While the grain Size and average grain volume was larger for the 62# plate material, the aspect ratios of 62# and 78# plate materials were very similar. The smaller grain size of the 78# plate material lead to increased strength and decreased ductility due to the larger total boundary area which impedes dislocation motion. 2. Mechanical testing showed a trend of increased strength and decreased ductility as the testing axis with respect to rolling direction varied from 0 to 90°. The trend in material strength is explained by considering the effects of the grain shape as well as the contribution of the texture associated with the material. The shape of the grains leads to an increase in the number of grain boundary interactions, and increasing misorientation between neighboring grains due to the texture lead to additional impedance to dislocation motion. 3. The popLA software package proved to be a very useful tool in the analysis of the experimentally determined pole ﬁgure data. Theoretical texture analysis is extremely complex, requiring mathematically sophisticated techniques. The complexity of the mathematics involved has made it operationally inaccessible to the materials user. The popLA software package performs all of the necessary mathematical computations, many of which could only be performed by mainframe computers a short time ago, and is quite user friendly. The program generates all necessary descriptive texture plots, with very good graphics. 71 72 4. Texture analysis results showed the preferred orientation of the sheet steels to consist mainly of a { 111} complete fiber texture. A partial ﬁber texture with <110> directions parallel to the rolling direction encompassing orientations of {001}<110>, {112}<110> and {111}<110> was also present to a much smaller degree. 5. While the textures present in the 62# and 78# plate materials were very similar, the skeleton line along the { 111} y—fiber revealed a slightly stronger intensity associated with the { 111}<110> orientation for the 62# plate material. 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