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A vision-integrated tension test for use in sheet-metal formability studies
Journal of Materials Processing Technology 118 (2001) 238±245
A vision-integrated tension test for use in sheet-metal formability studies K.P. Rao*, Emani V.R. Mohan Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Abstract In the prediction of formability of sheet metals, it is necessary to determine the material properties which are normally evaluated based on the data obtained by performing a simple tension test. Anisotropy is width strain over thickness strain, and the change in width traditionally measured by using an extensometer is not always acceptable. Also, as it is impractical to measure the change in the thickness of the sheet metal, it is normally estimated indirectly by measuring the extension of the specimen. Generally, this measurement is unable to establish the longitudinal strain accurately since the exact portion of the specimen that actually contributes to extension is uncertain, i.e. extension is not limited to the gauge length alone. In this paper, a new vision-integrated methodology has been introduced for the estimation of material properties through a uniaxial tension test. The required experimental data can be obtained by integrating the simple tensile test with a visionbased system that offers a most direct, continuous, non-interfering and accurate way of measuring the surface strains involved. Thus, with the establishment of actual strains, it is now possible to estimate the stress accurately. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Tensile test; Stress±strain curve; Anisotropy
1. Introduction The forming limit curves (FLCs) are normally used as diagnostic tools to assess the formability limits of sheet metals in industry. However, the FLC is constructed using a large number of critical major and minor strain combinations obtained experimentally, and the FLC depends on the material properties, processing conditions as well as the strain history [1±6]. As a result, their prediction using analytical approaches [7±11] has assumed importance since the FLCs obtained experimentally pose several limitations, while the former provides a high level of ¯exibility in adopting a variety of conditions. Several attempts have been made to model the formability on the basis of mechanical properties obtained through a simple test. In principle, a uniaxial test is preferred even though this state of deformation is not solely involved in metal-forming processes. Favorably, investigations have indicated [12] that the ¯ow curves obtained from uniaxial test and simulation tests involving drawing mode of deformation are equivalent for several materials. On the other hand, some discrepancies on the stress±strain curves obtained under uniaxial and multiaxial loading conditions have been reported [13], and the effect of prestrain cannot be ignored. Nevertheless, the simple tension test continues to play an *
Corresponding author. Tel.: 852-2788-8409; fax: 852-2788-8423. E-mail address: [email protected] (K.P. Rao).
important role in providing the mechanical properties needed for analytical modeling of FLCs. It is necessary to determine the material properties such as strain hardening index (n), strength coef®cient (K) and plastic anisotropy (R) of the material under a wide range of processing conditions so that their use in analytical modeling of sheet-metal forming is justi®able. These properties can be obtained within a narrow range of testing conditions following the well-established standard testing methods [14,15] for uniaxial tension. The ratio of width strain (ew) to thickness strain (et) is commonly accepted as a measure of plastic anisotropy and has been widely used as a standard practice [15]. The early investigators measured width and thickness strain directly near the limit of uniform elongation. Alternatively, others had employed compound or multiple extensometers to measure the width and thickness strains over a speci®ed gauge length. However, strain values determined by such direct methods are particularly sensitive to errors of thickness measurement. To overcome this dif®culty with direct measurement of thickness, the strain ratios are now commonly estimated [16±22] from the measurements of the length and width strains by assuming constancy of volume throughout the straining process. Hence, the anisotropy may be estimated following: R
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 9 3 3 - 5
ln w0 =wf ln wf lf =w0 l0
e2 e1 e2
(1)
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
where l0 and lf are initial and final lengths, w0 and wf are initial and final widths, e1 and e2 are longitudinal and transverse strains, respectively. Kim [21] used a camera and two extensometers simultaneously Ð one along the length and another along the width of the specimen Ð to determine anisotropy, and has called it as automatic strain measurement. Even this measurement has some limitations in assessing the longitudinal strain accurately since the exact portion of the specimen that actually contributes to extension is uncertain since extension is not limited to the gauge length alone. Such inaccuracies affect the estimation of anisotropy value, and in turn constrains the prediction accuracy of analytical models for establishing the true forming limits. Other main limitations of such test procedures include: (i) test speeds being much lower than those involved in actual forming; (ii) dif®culty in measuring width strains along the entire specimen length (mainly due to the type of sensors used); (iii) interruptions during the test to facilitate measurements in some cases; (iv) instantaneous and simultaneous recording of various parameters with a single reference, etc. To overcome the limitations mentioned above, a new vision-integrated methodology has been developed in this study for the estimation of material properties through a uniaxial tension test. The required experimental data can be obtained by integrating the simple tensile test with a visionbased system that offers a most direct, continuous, noninterfering and probably more accurate way of measuring the surface strains involved. Through appropriate analysis of the recorded test data, the mechanical properties of sheet metals can be evaluated for a wide range of test and process conditions that are relevant to modeling of metal-forming processes.
239
Fig. 1. Schematic diagram of a vision-integrated set-up (hardware and software) for conducting a uniaxial tension test for evaluating various material properties.
at the selected time intervals, and converts them into digital output for the chosen variables. Important variables to be recorded through this route include load and stroke. It should be noted that calibration of the various sensors and instruments involved in the test set-up is essential. The grid distortions represent the nature of actual deformation and are evaluated by analyzing the recorded image
2. Vision-integrated tension test The set-up and the procedure for conducting an integrated tension test are represented as a schematic diagram in Fig. 1. As shown in the ®gure, the testing as well as the recording of relevant parameters will be initiated by the controller (in the present case, it is Dartec M9500 controller) of the computer-controlled testing machine. A servohydraulic testing machine is preferable as it can provide a wide range of test speeds. Several parameters, like load, stroke, grid distortion, etc., can be recorded and processed using ASAME (automated strain analysis and measurement environment), supplied by CamSys, USA. Signals from the controller are sent to ASAME through a Bit¯ow Raptor frame-grabber and an A/D board. The frame-grabber board (Bit¯ow Raptor PCI PAL frame-grabber has been used in this study), which is connected to a video camera, converts the video signal from the camera into a digital photograph. Another A/D board (Keithley Metrabyte A/D board has been used in this study) receives the signals from different sensors (e.g. load-cell) of the testing machine through the controller
Fig. 2. Grid-marked tensile specimen (only the parallel reduced width region shown) employed for strain measurement Ð (a) specimen before the test, (b) specimen after the test.
240
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
frame using ASAME software, which provides a data ®le (which is spreadsheet compatible). This data ®le contains a variety of estimated geometric parameters such as major strain, minor strain, effective strain, direction of strain, etc., both at the level of elements and nodal points. Anisotropy can be easily evaluated using this information. In addition, these strain values provide an accurate estimate of the instantaneous cross-section area of the specimen to facilitate the calculation of stress±strain curve without relying on the stroke recorded through the testing machine controller (which obviously include machine compliance and other errors). Fig. 2 shows typical instantaneous images captured at the start and end of a tensile test with the latter indicating the grid distortions and the fracture of the specimen. 3. Experimental The experimental plan included a series of tensile tests on commercial 60:40 brass sheet of 1.5 mm thickness to evaluate its ¯ow curves and anisotropy values under several imposed test conditions, as listed in Table 1. Standard size 200 mm 12:5 mm 1:5 mm specimens with a gauge length of 50 mm, following ASTM E8 M speci®cations [14], were used for the tensile tests. Fig. 3 shows the typical test specimen employed with its important dimensions. Grids of 4:5 mm 4:5 mm were marked, as per the scheme shown in the ®gure, over the reduced width region (includes the entire gauge length) using a numerically controlled milling machine along with an indigenously developed plotting accessory. This programmed marking allowed the grids to be uniformly positioned on all the tested specimens. It may be noted that the accuracy of strain measurement depends mainly on the grid size as well as the quality of marking, such as line thickness and contrast. Though smaller grid sizes can provide strain distribution in greater detail, Table 1 Conditions employed for the tension tests on brass sheet Test direction with reference to rolling direction (8)
Test speed (mm/s) Speed #1
Speed #2
Speed #3
0 45 90
0.021 0.021 0.021
0.21 0.21 0.21
2.1 2.1 2.1
Fig. 3. Dimensions of the test specimen for conducting uniaxial tension tests, and the grid pattern employed for strain analysis.
loss of resolution that may lead to larger relative errors should be a problem of concern. Hence, the optimum grid size depends on the capabilities of associated hardware. Specimens were selected in three directions and load-elongation recordings were obtained under uniaxial tensile conditions to determine the various mechanical properties. The test machine employed was a servo-hydraulic computer-controlled Dartec universal testing machine. The test conditions, like speed and stroke, were programmed using its software and the various test parameters were controlled and recorded through its M9500 controller. Both stress± strain curves and anisotropy values were estimated using the processed data obtained from ASAME software. The estimation of plastic anisotropy over a wide range of test speed and strain in different directions of the sheet metal was carried out. 4. Results and discussion The mechanical properties of the material were evaluated from the recordings of various parameters for the conditions employed in testing. The stress±strain curves determined using the instantaneous strains of the captured images are presented in Figs. 4±6. The ¯ow curves determined using the conventional method, i.e. based on recorded elongation through LVDT and 50 mm gauge length, are also shown for comparison. As the remaining reduced parallel region outside the gauge length is also likely to have some contribution to the overall elongation of the specimen, the ¯ow curves are also estimated based on this overall initial length of 57 mm. The results obtained are also presented in the same ®gures. The anisotropy values obtained are presented in Figs. 4±6 as a function of longitudinal or major strain. These values are based on the strains obtained from the captured images using ASAME. The average anisotropy values are presented in Table 2. The ¯ow curves obtained using different methods clearly indicate that the conventional approach underestimates the ¯ow stress as a result of the inclusion of machine and tool compliance in the measured stroke. Though there are remedies [14] to reduce such contributions, accuracy is dependent on the consideration of all the factors that contribute them. Extensometers are usually limited by their mechanical structure and construction, and are not generally suitable for high-speed tests or for large elongation. Also, they can provide only average results over their application range. The vision-integrated test, on the other hand, provides instantaneous graphic image of the specimen facilitating a detailed analysis of the strains involved at any stage of the test and over a wide range of test conditions. Without any corrections, one can estimate the strains involved and estimate the stress±strain curve more accurately. The similarity of the ¯ow curves at different test speeds indicates that the material showed no perceptible strain rate sensitivity over the range of test conditions involved. It can
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
241
Fig. 4. Flow curves obtained at different test speeds in the rolling direction on the basis of grid distortions captured through video image and conventional approach using 50 and 57 mm as reference gauge lengths. Variation of anisotropy is also shown.
242
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
Fig. 5. Flow curves obtained at different test speeds in the 458 direction on the basis of grid distortions captured through video image and conventional approach using 50 and 57 mm as reference gauge lengths. Variation of anisotropy is also shown.
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
243
Fig. 6. Flow curves obtained at different test speeds in the transverse direction on the basis of grid distortions captured through video image and conventional approach using 50 and 57 mm as reference gauge lengths. Variation of anisotropy is also shown.
244
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
Table 2 Anisotropy (R) values obtained for different testing speeds and orientations Test direction with reference to rolling direction (8)
Test speed (mm/s) 0.021
0.21
2.1
0 45 90
0.648 0.845 0.638
0.689 1.019 0.706
0.508 0.940 0.606
also be seen that the ¯ow curves obtained in the rolling and transverse directions are very similar. However, the ¯ow curves obtained in the 458 direction (to the rolling direction) are about 10% lower in magnitude. This may be due to the orientation of texture along the natural shear direction in tension test, and the textured grains easily slip over each other in this orientation. The anisotropy values obtained followed a similar trend as far as test speed is concerned, with slightly higher values at the intermediate test speed (see Table 2) for any given orientation. The anisotropy values somewhat scatter around a mean value. The scatter is mostly due to errors in the estimation of strains. Anisotropy being a ratio of two strains, the effect of error pronouncedly shows up. The trend indicates that strain has no signi®cant effect on anisotropy in this material. Again, as in the case of ¯ow curves, the material exhibited similar anisotropy values in the rolling and transverse directions. The values in the 458 direction are signi®cantly higher than the other two directions. This can be explained by the fact that the lower resistance to ¯ow in the 458 direction leads towards larger ¯ow along the shear plane (along the strongly textured plane), i.e. larger strains in the width direction compared to thickness. To test the validity of analytical predictions, the grid strains measured near the fracture can be conveniently used. For this purpose, the analytical predictions made on this material [23], following a prediction model [11], have been used. The FLCs are shown in Fig. 7 along with the strains
measured at the fractured grids. It can be seen that the measured strains in the nine specimens (representing three test speeds in three orientations) lie very close to the predicted limit band. It should be remembered that the measured strains depend on the size of the selected grid, and the results shown here are based on somewhat larger-sized grids. This could only yield strains that would be somewhat smaller than actual strains at fracture. 5. Conclusions A new vision-integrated methodology has been introduced for the estimation of material properties through a uniaxial tension test. The required experimental data was obtained by integrating the simple tensile test with a visionbased system that offered a most direct, continuous, noninterfering and accurate way of measuring the surface strains involved. Tensile tests were conducted on sheet specimens of brass that were selected in three important directions with reference to the original sheet rolling direction. With the establishment of strains based on the actual image of the deformed grids of the specimen, it is now possible to estimate the stress and anisotropy accurately over a range of testing conditions. While the stress±strain curves obtained in the rolling and transverse directions were higher than those obtained in the 458 direction, the anisotropy values in the latter direction were higher than in the former cases for brass. Such detailed mechanical data will contribute towards a better prediction of sheet-metal formability. The grid strains obtained around the region of failure will also serve the purpose of validating any analytical formability predictions. Acknowledgements The ®nancial assistance provided by the Research Grants Council through Project No. 9040307 (CityU1135/97E) is gratefully acknowledged. The authors would like to thank Mr. C.H. Yuen, Materials Processing Laboratory, Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, for his cheerful assistance in the experimental work. References
Fig. 7. FLCs predicted for brass [23], based on the mechanical properties obtained in tension. Experimental strains in the vicinity of fracture in a dome-shaped cup and a tensile test are included for comparison.
[1] S.P. Keeler, Understanding sheet metal formability Ð Part 1±6, Sheet Met. Ind. 48 (1971) 357±364, 440±449, 511±517, 589±618, 687±699, 739±745. [2] H.J. Kleemola, M.T. Pelkkikangas, Effect of predeformation and strain path on the forming limits of steel, copper and brass, Sheet Met. Ind. 54 (1977) 591±599. [3] C.C. Chu, An investigation of the strain path dependence, Int. J. Solids Struct. 18 (1982) 205±215. [4] J. Gronostajski, Sheetmetal forming-limit for complex strain paths, J. Mech. Work. Technol. 10 (1984) 349±362.
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245 [5] H.M. Shang, G.S. Tan, W.C.M. Tan, Effects of prestrain with strain gradient present on sheet metal formability, J. Eng. Mater. Technol. 107 (1985) 298±306. [6] A. Graf, W. Hosford, Effect of changing strain paths on forming limit diagrams of Al2008-T4, Metall. Trans. A 24 (1993) 2503±2512. [7] R. Arrieux, Determination and use of the forming limit stress diagrams, J. Mater. Process. Technol. 53 (1995) 47±56. [8] S.N. Rasmussen, Theoretical prediction of strain-path dependence of limit strains in sheet materials, Ann. CIRP 30 (1) (1981) 179±184. [9] Z.H. Lu, D. Lee, Prediction of history-dependent forming limits by applying different hardening models, Int. J. Mech. Sci. 29 (1987) 123±137. [10] L. Zhao, R. Sowerby, M.P. Sklad, A theoretical and experimental investigation of limit strains in sheet metal forming, Int. J. Mech. Sci. 38 (1996) 1307±1317. [11] W.M. Sing, K.P. Rao, K. Swaminathan, Influence of limit stress states and yield criteria on the prediction of forming limit strains in sheet metals, Metall. Mater. Trans. A 28 (1997) 2323±2333. [12] D.W.A. Rees, Instability limits to the forming of sheet metals, J. Mater. Process. Technol. 55 (1995) 146±153. [13] E.G. Thomsen, F.D. Negroni, A review of recent experimental results of stress±strain curves at large plastic strains, Trans. NAMRI/SME 20 (1992) 91±95. [14] ASTM E 8M, Standard Test Methods for Tension Testing of Metallic Materials (Metric), ASTM, USA, 1993.
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[15] ASTM E 517, Standard Test Method for Plastic Strain Ratio r for Sheet Metal, ASTM, USA, 1993. [16] D.V. Wilson, R.D. Butler, The role of cup-drawing tests in measuring drawability, J. Inst. Met. 90 (1961±1962) 473±483. [17] M. Atkinson, Assessing normal anisotropic plasticity of sheet metals, Sheet Met. Ind. 44 (1967) 167±178. [18] H. Hu, The strain-dependence of plastic strain ration (rm value) of deep drawing sheet steels determined by simple tension test, Metall. Trans. A 6 (1975) 945±947. [19] Y.C. Liu, On the R-value measurements, Metall. Trans. A 14 (1983) 1199±1205. [20] R.W. Logan, D.J. Meuleman, W.F. Hosford, in: A.K. Sachdev, J.D. Embury (Eds.), Formability and Metallurgical Structure, The Metallurgical Society, Warrendale, PA, 1987, pp. 159±173. [21] I. Kim, The evaluation of automatic measurement of plastic strain ratio, Presented at the Third Asia-Pacific Symposium on Advances in Engineering Plasticity and Its Applications, Hiroshima, Japan, August 1996. [22] J.-J. Park, Predictions of texture and plastic anisotropy developed by mechanical deformation in aluminum sheet, J. Mater. Process. Technol. 87 (1999) 146±153. [23] K.P. Rao, Emani V.R. Mohan, Simple prediction of sheet metal forming limit stresses and strains, in: M.Y. Demeri (Ed.), Sheet Metal Forming Technology, Proceedings of a Symposium at the TMS Annual Meeting, The Metallurgical Society, Warrendale, PA, 1999, pp. 205±231.
A vision-integrated tension test for use in sheet-metal formability studies K.P. Rao*, Emani V.R. Mohan Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Abstract In the prediction of formability of sheet metals, it is necessary to determine the material properties which are normally evaluated based on the data obtained by performing a simple tension test. Anisotropy is width strain over thickness strain, and the change in width traditionally measured by using an extensometer is not always acceptable. Also, as it is impractical to measure the change in the thickness of the sheet metal, it is normally estimated indirectly by measuring the extension of the specimen. Generally, this measurement is unable to establish the longitudinal strain accurately since the exact portion of the specimen that actually contributes to extension is uncertain, i.e. extension is not limited to the gauge length alone. In this paper, a new vision-integrated methodology has been introduced for the estimation of material properties through a uniaxial tension test. The required experimental data can be obtained by integrating the simple tensile test with a visionbased system that offers a most direct, continuous, non-interfering and accurate way of measuring the surface strains involved. Thus, with the establishment of actual strains, it is now possible to estimate the stress accurately. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Tensile test; Stress±strain curve; Anisotropy
1. Introduction The forming limit curves (FLCs) are normally used as diagnostic tools to assess the formability limits of sheet metals in industry. However, the FLC is constructed using a large number of critical major and minor strain combinations obtained experimentally, and the FLC depends on the material properties, processing conditions as well as the strain history [1±6]. As a result, their prediction using analytical approaches [7±11] has assumed importance since the FLCs obtained experimentally pose several limitations, while the former provides a high level of ¯exibility in adopting a variety of conditions. Several attempts have been made to model the formability on the basis of mechanical properties obtained through a simple test. In principle, a uniaxial test is preferred even though this state of deformation is not solely involved in metal-forming processes. Favorably, investigations have indicated [12] that the ¯ow curves obtained from uniaxial test and simulation tests involving drawing mode of deformation are equivalent for several materials. On the other hand, some discrepancies on the stress±strain curves obtained under uniaxial and multiaxial loading conditions have been reported [13], and the effect of prestrain cannot be ignored. Nevertheless, the simple tension test continues to play an *
Corresponding author. Tel.: 852-2788-8409; fax: 852-2788-8423. E-mail address: [email protected] (K.P. Rao).
important role in providing the mechanical properties needed for analytical modeling of FLCs. It is necessary to determine the material properties such as strain hardening index (n), strength coef®cient (K) and plastic anisotropy (R) of the material under a wide range of processing conditions so that their use in analytical modeling of sheet-metal forming is justi®able. These properties can be obtained within a narrow range of testing conditions following the well-established standard testing methods [14,15] for uniaxial tension. The ratio of width strain (ew) to thickness strain (et) is commonly accepted as a measure of plastic anisotropy and has been widely used as a standard practice [15]. The early investigators measured width and thickness strain directly near the limit of uniform elongation. Alternatively, others had employed compound or multiple extensometers to measure the width and thickness strains over a speci®ed gauge length. However, strain values determined by such direct methods are particularly sensitive to errors of thickness measurement. To overcome this dif®culty with direct measurement of thickness, the strain ratios are now commonly estimated [16±22] from the measurements of the length and width strains by assuming constancy of volume throughout the straining process. Hence, the anisotropy may be estimated following: R
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 9 3 3 - 5
ln w0 =wf ln wf lf =w0 l0
e2 e1 e2
(1)
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
where l0 and lf are initial and final lengths, w0 and wf are initial and final widths, e1 and e2 are longitudinal and transverse strains, respectively. Kim [21] used a camera and two extensometers simultaneously Ð one along the length and another along the width of the specimen Ð to determine anisotropy, and has called it as automatic strain measurement. Even this measurement has some limitations in assessing the longitudinal strain accurately since the exact portion of the specimen that actually contributes to extension is uncertain since extension is not limited to the gauge length alone. Such inaccuracies affect the estimation of anisotropy value, and in turn constrains the prediction accuracy of analytical models for establishing the true forming limits. Other main limitations of such test procedures include: (i) test speeds being much lower than those involved in actual forming; (ii) dif®culty in measuring width strains along the entire specimen length (mainly due to the type of sensors used); (iii) interruptions during the test to facilitate measurements in some cases; (iv) instantaneous and simultaneous recording of various parameters with a single reference, etc. To overcome the limitations mentioned above, a new vision-integrated methodology has been developed in this study for the estimation of material properties through a uniaxial tension test. The required experimental data can be obtained by integrating the simple tensile test with a visionbased system that offers a most direct, continuous, noninterfering and probably more accurate way of measuring the surface strains involved. Through appropriate analysis of the recorded test data, the mechanical properties of sheet metals can be evaluated for a wide range of test and process conditions that are relevant to modeling of metal-forming processes.
239
Fig. 1. Schematic diagram of a vision-integrated set-up (hardware and software) for conducting a uniaxial tension test for evaluating various material properties.
at the selected time intervals, and converts them into digital output for the chosen variables. Important variables to be recorded through this route include load and stroke. It should be noted that calibration of the various sensors and instruments involved in the test set-up is essential. The grid distortions represent the nature of actual deformation and are evaluated by analyzing the recorded image
2. Vision-integrated tension test The set-up and the procedure for conducting an integrated tension test are represented as a schematic diagram in Fig. 1. As shown in the ®gure, the testing as well as the recording of relevant parameters will be initiated by the controller (in the present case, it is Dartec M9500 controller) of the computer-controlled testing machine. A servohydraulic testing machine is preferable as it can provide a wide range of test speeds. Several parameters, like load, stroke, grid distortion, etc., can be recorded and processed using ASAME (automated strain analysis and measurement environment), supplied by CamSys, USA. Signals from the controller are sent to ASAME through a Bit¯ow Raptor frame-grabber and an A/D board. The frame-grabber board (Bit¯ow Raptor PCI PAL frame-grabber has been used in this study), which is connected to a video camera, converts the video signal from the camera into a digital photograph. Another A/D board (Keithley Metrabyte A/D board has been used in this study) receives the signals from different sensors (e.g. load-cell) of the testing machine through the controller
Fig. 2. Grid-marked tensile specimen (only the parallel reduced width region shown) employed for strain measurement Ð (a) specimen before the test, (b) specimen after the test.
240
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
frame using ASAME software, which provides a data ®le (which is spreadsheet compatible). This data ®le contains a variety of estimated geometric parameters such as major strain, minor strain, effective strain, direction of strain, etc., both at the level of elements and nodal points. Anisotropy can be easily evaluated using this information. In addition, these strain values provide an accurate estimate of the instantaneous cross-section area of the specimen to facilitate the calculation of stress±strain curve without relying on the stroke recorded through the testing machine controller (which obviously include machine compliance and other errors). Fig. 2 shows typical instantaneous images captured at the start and end of a tensile test with the latter indicating the grid distortions and the fracture of the specimen. 3. Experimental The experimental plan included a series of tensile tests on commercial 60:40 brass sheet of 1.5 mm thickness to evaluate its ¯ow curves and anisotropy values under several imposed test conditions, as listed in Table 1. Standard size 200 mm 12:5 mm 1:5 mm specimens with a gauge length of 50 mm, following ASTM E8 M speci®cations [14], were used for the tensile tests. Fig. 3 shows the typical test specimen employed with its important dimensions. Grids of 4:5 mm 4:5 mm were marked, as per the scheme shown in the ®gure, over the reduced width region (includes the entire gauge length) using a numerically controlled milling machine along with an indigenously developed plotting accessory. This programmed marking allowed the grids to be uniformly positioned on all the tested specimens. It may be noted that the accuracy of strain measurement depends mainly on the grid size as well as the quality of marking, such as line thickness and contrast. Though smaller grid sizes can provide strain distribution in greater detail, Table 1 Conditions employed for the tension tests on brass sheet Test direction with reference to rolling direction (8)
Test speed (mm/s) Speed #1
Speed #2
Speed #3
0 45 90
0.021 0.021 0.021
0.21 0.21 0.21
2.1 2.1 2.1
Fig. 3. Dimensions of the test specimen for conducting uniaxial tension tests, and the grid pattern employed for strain analysis.
loss of resolution that may lead to larger relative errors should be a problem of concern. Hence, the optimum grid size depends on the capabilities of associated hardware. Specimens were selected in three directions and load-elongation recordings were obtained under uniaxial tensile conditions to determine the various mechanical properties. The test machine employed was a servo-hydraulic computer-controlled Dartec universal testing machine. The test conditions, like speed and stroke, were programmed using its software and the various test parameters were controlled and recorded through its M9500 controller. Both stress± strain curves and anisotropy values were estimated using the processed data obtained from ASAME software. The estimation of plastic anisotropy over a wide range of test speed and strain in different directions of the sheet metal was carried out. 4. Results and discussion The mechanical properties of the material were evaluated from the recordings of various parameters for the conditions employed in testing. The stress±strain curves determined using the instantaneous strains of the captured images are presented in Figs. 4±6. The ¯ow curves determined using the conventional method, i.e. based on recorded elongation through LVDT and 50 mm gauge length, are also shown for comparison. As the remaining reduced parallel region outside the gauge length is also likely to have some contribution to the overall elongation of the specimen, the ¯ow curves are also estimated based on this overall initial length of 57 mm. The results obtained are also presented in the same ®gures. The anisotropy values obtained are presented in Figs. 4±6 as a function of longitudinal or major strain. These values are based on the strains obtained from the captured images using ASAME. The average anisotropy values are presented in Table 2. The ¯ow curves obtained using different methods clearly indicate that the conventional approach underestimates the ¯ow stress as a result of the inclusion of machine and tool compliance in the measured stroke. Though there are remedies [14] to reduce such contributions, accuracy is dependent on the consideration of all the factors that contribute them. Extensometers are usually limited by their mechanical structure and construction, and are not generally suitable for high-speed tests or for large elongation. Also, they can provide only average results over their application range. The vision-integrated test, on the other hand, provides instantaneous graphic image of the specimen facilitating a detailed analysis of the strains involved at any stage of the test and over a wide range of test conditions. Without any corrections, one can estimate the strains involved and estimate the stress±strain curve more accurately. The similarity of the ¯ow curves at different test speeds indicates that the material showed no perceptible strain rate sensitivity over the range of test conditions involved. It can
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
241
Fig. 4. Flow curves obtained at different test speeds in the rolling direction on the basis of grid distortions captured through video image and conventional approach using 50 and 57 mm as reference gauge lengths. Variation of anisotropy is also shown.
242
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
Fig. 5. Flow curves obtained at different test speeds in the 458 direction on the basis of grid distortions captured through video image and conventional approach using 50 and 57 mm as reference gauge lengths. Variation of anisotropy is also shown.
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
243
Fig. 6. Flow curves obtained at different test speeds in the transverse direction on the basis of grid distortions captured through video image and conventional approach using 50 and 57 mm as reference gauge lengths. Variation of anisotropy is also shown.
244
K.P. Rao, E.V.R. Mohan / Journal of Materials Processing Technology 118 (2001) 238±245
Table 2 Anisotropy (R) values obtained for different testing speeds and orientations Test direction with reference to rolling direction (8)
Test speed (mm/s) 0.021
0.21
2.1
0 45 90
0.648 0.845 0.638
0.689 1.019 0.706
0.508 0.940 0.606
also be seen that the ¯ow curves obtained in the rolling and transverse directions are very similar. However, the ¯ow curves obtained in the 458 direction (to the rolling direction) are about 10% lower in magnitude. This may be due to the orientation of texture along the natural shear direction in tension test, and the textured grains easily slip over each other in this orientation. The anisotropy values obtained followed a similar trend as far as test speed is concerned, with slightly higher values at the intermediate test speed (see Table 2) for any given orientation. The anisotropy values somewhat scatter around a mean value. The scatter is mostly due to errors in the estimation of strains. Anisotropy being a ratio of two strains, the effect of error pronouncedly shows up. The trend indicates that strain has no signi®cant effect on anisotropy in this material. Again, as in the case of ¯ow curves, the material exhibited similar anisotropy values in the rolling and transverse directions. The values in the 458 direction are signi®cantly higher than the other two directions. This can be explained by the fact that the lower resistance to ¯ow in the 458 direction leads towards larger ¯ow along the shear plane (along the strongly textured plane), i.e. larger strains in the width direction compared to thickness. To test the validity of analytical predictions, the grid strains measured near the fracture can be conveniently used. For this purpose, the analytical predictions made on this material [23], following a prediction model [11], have been used. The FLCs are shown in Fig. 7 along with the strains
measured at the fractured grids. It can be seen that the measured strains in the nine specimens (representing three test speeds in three orientations) lie very close to the predicted limit band. It should be remembered that the measured strains depend on the size of the selected grid, and the results shown here are based on somewhat larger-sized grids. This could only yield strains that would be somewhat smaller than actual strains at fracture. 5. Conclusions A new vision-integrated methodology has been introduced for the estimation of material properties through a uniaxial tension test. The required experimental data was obtained by integrating the simple tensile test with a visionbased system that offered a most direct, continuous, noninterfering and accurate way of measuring the surface strains involved. Tensile tests were conducted on sheet specimens of brass that were selected in three important directions with reference to the original sheet rolling direction. With the establishment of strains based on the actual image of the deformed grids of the specimen, it is now possible to estimate the stress and anisotropy accurately over a range of testing conditions. While the stress±strain curves obtained in the rolling and transverse directions were higher than those obtained in the 458 direction, the anisotropy values in the latter direction were higher than in the former cases for brass. Such detailed mechanical data will contribute towards a better prediction of sheet-metal formability. The grid strains obtained around the region of failure will also serve the purpose of validating any analytical formability predictions. Acknowledgements The ®nancial assistance provided by the Research Grants Council through Project No. 9040307 (CityU1135/97E) is gratefully acknowledged. The authors would like to thank Mr. C.H. Yuen, Materials Processing Laboratory, Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, for his cheerful assistance in the experimental work. References
Fig. 7. FLCs predicted for brass [23], based on the mechanical properties obtained in tension. Experimental strains in the vicinity of fracture in a dome-shaped cup and a tensile test are included for comparison.
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