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The determination of AlLi crystal orientation by indentation
Materials N'ience and Engineering, AI50 (1992) L 11 - L 12
L 11
Letter
The determination of AI-Li crystal orientation by indentation S. C. Chang I)elmrtmenl olMaterials Science and Engineering, National 7~ing Ihm Univerfft)'. Itsinchu. l~dwan (('hina)
T. S. Sheu lhTmrtment of Mechanical Engineering, ('httng ('hetzg Institute oj' gk'chmdogy. 7~u~youn. l}livcan (('hina) iRcceixcd Jul', 8. 1991;in revised form Septembcr 11, 1991 )
with the indentation plane, a one-to-one correspondence exists between the angular relationship among slip lines and the orientation of the indentation plane. As shown in Fig. 1, when a Knoop indentation was made on the (001) plane, two mutually perpendicular families of slip lines were observed. One family of the slip lines w_e_realong_ the [11 ()j direction and were the traces of ( 111 ) and ( 11 ] ) planes; the other family of slip lines were along the [1 i 0] direction and were the traces of ( 111 ) and ( 111 ) planes. Figure 2 shows the indentation made by a 1/16 in ball on an ++unknown" specimen surface. Four sets of
Abstract A method of determining the orientation of a single crystal is describcd. By studying the slip lines formed around a hardness indentation, the orientation of an AI-Li single crystal could be determined quite rapidly and accurately.
The determination of the orientation of a crystal is required in many research efforts and practical applications. Various methods have been developed for this purpose [1, 2]. Among them, the backreflection Laue method is the most widely used because it can be applied to bulk specimens and it needs no special preparation of the specimen. However, in addition to requiring X-ray facilities, the procedure of obtaining the crystal orientation from the Laue photograph involves trial and error and can be time consuming even with the help of a personal computer. The determination of orientation by etch pits was developed and used by many researchers about half a century ago [ 11. It is quite rapid and fairly accurate. The disadvantages of the etch pit method are the necessity of mounting the specimen on a goniometer or similar apparatus and the technical difficulty of developing etch pits with plane faces accurately parallel to crystalIographic planes. Recently, the authors produced single crystals of aluminium and AI-Li alloys in the form of a bar 15 mm in diameter 13J. In hardness measurements, slip lines were observed around the indentation. It is noted that, when indented by any of the regular hardness indenters, slip on all four {11 1 } slip planes in the f.c.c, crystal was necessary to satisfy the condition of plastic compatibility. Since the slip lines on the indentation plane were the lines of intersection of the {1 1 1} slip planes 0921-5093/92/S5.00
Fig. 1. A Knoop indentation (load, 5(I(t g) on the (0(111 plane of an A l - g i crystal. Two mutually perpendicular families of slip lines were observed ahmg [110j and i i 10] respectively.
11 Fig. 2. The indentation made by a 1,/16 in ball (load, 1 kg) on an AI-Li specimen surface. Four sets of slip lines were observed. The angles between each two sets of them were: angle 1 = 1(t7°; angle 2 = 1(16.5°; angle 3 = 5(1°, angle 4 = 96.5 °. © 1992 - Elsevier Sequoia. All rights reserved
L 12
Letter
Fig. 3. The backreflection Laue photograph of the specimen surface shown in Fig. 2. slip lines were observed and marked as a, b, c and d. By assuming that the specimen surface normal S lies in the [001]-[011]-[111] unit stereographic projection triangle and that the normals of the four slip planes in the crystal are [111], [i 11], [] i 1] and [1 i 1], the slip line and the slip plane normals. There are certain conditions to be met by the angles between each two sets of slip line vectors. For example, the angle between the slip line vectors formed by slip on (111) and (111) planes is always an obtuse angle while that by slip on ( ] 11 ) and ( 1 ] 1) planes is always an acute angle. Based on the analytical conditions discussed above, a per-
sonal computer program was developed to get the normalized Miller indices of the specimen surface normal and the slip line vectors from the measured angles between each of two sets of slip lines. Details of the analytical process and the program will be reported by the authors in another paper. For the case shown in Fig. 2, the normalized Miller indices of the specimen surface normal were found to be S=]0.1274 0.4400 0.8889]. The indices of the directions of the slip lines were found as a = [0.7673 - 0 . 5 8 6 8 0.1805], b = [ - 0 . 7 6 7 3 - 0 . 4 3 9 7 0.3267], c=[0.2592 - 0 . 4 3 9 7 0.1805] and d = [ - 0 . 2 5 9 2 -0.5868 0.3276]. The backreflection Laue photograph of the same specimen surface is shown in Fig. 3. The normalized Miller indices of the surface plane normal obtained from the Laue spots were L=[0.140 0.441 0.886]. The discrepancy between the orientations S and L is less than 1°, which is within the accuracy of measurement of S and L. In summary, by measuring the angles between the slip lines formed by hardness indentation with simple facilities in a metallurgical laboratory, the orientation of A1-Li crystals could be determined rapidly with an accuracy close to that of the backreflection Laue method. The authors are grateful for the support of this research by the National Science Council, China, under grant NSC79-0405-E007-15.
1 C.S. Barrett and T. B. Massalski, Structure of Metals, 3rd edn., McGraw-Hill, New York, NY, 1980. 2 B. D. Cullity, Elements of X-Ray Diffraction, 2nd edn., Addison-Wesley,London, 1978. 3 T. S. Sheu and S. C. Chang, Mater. Sci. Eng., 147(1991) 81.
L 11
Letter
The determination of AI-Li crystal orientation by indentation S. C. Chang I)elmrtmenl olMaterials Science and Engineering, National 7~ing Ihm Univerfft)'. Itsinchu. l~dwan (('hina)
T. S. Sheu lhTmrtment of Mechanical Engineering, ('httng ('hetzg Institute oj' gk'chmdogy. 7~u~youn. l}livcan (('hina) iRcceixcd Jul', 8. 1991;in revised form Septembcr 11, 1991 )
with the indentation plane, a one-to-one correspondence exists between the angular relationship among slip lines and the orientation of the indentation plane. As shown in Fig. 1, when a Knoop indentation was made on the (001) plane, two mutually perpendicular families of slip lines were observed. One family of the slip lines w_e_realong_ the [11 ()j direction and were the traces of ( 111 ) and ( 11 ] ) planes; the other family of slip lines were along the [1 i 0] direction and were the traces of ( 111 ) and ( 111 ) planes. Figure 2 shows the indentation made by a 1/16 in ball on an ++unknown" specimen surface. Four sets of
Abstract A method of determining the orientation of a single crystal is describcd. By studying the slip lines formed around a hardness indentation, the orientation of an AI-Li single crystal could be determined quite rapidly and accurately.
The determination of the orientation of a crystal is required in many research efforts and practical applications. Various methods have been developed for this purpose [1, 2]. Among them, the backreflection Laue method is the most widely used because it can be applied to bulk specimens and it needs no special preparation of the specimen. However, in addition to requiring X-ray facilities, the procedure of obtaining the crystal orientation from the Laue photograph involves trial and error and can be time consuming even with the help of a personal computer. The determination of orientation by etch pits was developed and used by many researchers about half a century ago [ 11. It is quite rapid and fairly accurate. The disadvantages of the etch pit method are the necessity of mounting the specimen on a goniometer or similar apparatus and the technical difficulty of developing etch pits with plane faces accurately parallel to crystalIographic planes. Recently, the authors produced single crystals of aluminium and AI-Li alloys in the form of a bar 15 mm in diameter 13J. In hardness measurements, slip lines were observed around the indentation. It is noted that, when indented by any of the regular hardness indenters, slip on all four {11 1 } slip planes in the f.c.c, crystal was necessary to satisfy the condition of plastic compatibility. Since the slip lines on the indentation plane were the lines of intersection of the {1 1 1} slip planes 0921-5093/92/S5.00
Fig. 1. A Knoop indentation (load, 5(I(t g) on the (0(111 plane of an A l - g i crystal. Two mutually perpendicular families of slip lines were observed ahmg [110j and i i 10] respectively.
11 Fig. 2. The indentation made by a 1,/16 in ball (load, 1 kg) on an AI-Li specimen surface. Four sets of slip lines were observed. The angles between each two sets of them were: angle 1 = 1(t7°; angle 2 = 1(16.5°; angle 3 = 5(1°, angle 4 = 96.5 °. © 1992 - Elsevier Sequoia. All rights reserved
L 12
Letter
Fig. 3. The backreflection Laue photograph of the specimen surface shown in Fig. 2. slip lines were observed and marked as a, b, c and d. By assuming that the specimen surface normal S lies in the [001]-[011]-[111] unit stereographic projection triangle and that the normals of the four slip planes in the crystal are [111], [i 11], [] i 1] and [1 i 1], the slip line and the slip plane normals. There are certain conditions to be met by the angles between each two sets of slip line vectors. For example, the angle between the slip line vectors formed by slip on (111) and (111) planes is always an obtuse angle while that by slip on ( ] 11 ) and ( 1 ] 1) planes is always an acute angle. Based on the analytical conditions discussed above, a per-
sonal computer program was developed to get the normalized Miller indices of the specimen surface normal and the slip line vectors from the measured angles between each of two sets of slip lines. Details of the analytical process and the program will be reported by the authors in another paper. For the case shown in Fig. 2, the normalized Miller indices of the specimen surface normal were found to be S=]0.1274 0.4400 0.8889]. The indices of the directions of the slip lines were found as a = [0.7673 - 0 . 5 8 6 8 0.1805], b = [ - 0 . 7 6 7 3 - 0 . 4 3 9 7 0.3267], c=[0.2592 - 0 . 4 3 9 7 0.1805] and d = [ - 0 . 2 5 9 2 -0.5868 0.3276]. The backreflection Laue photograph of the same specimen surface is shown in Fig. 3. The normalized Miller indices of the surface plane normal obtained from the Laue spots were L=[0.140 0.441 0.886]. The discrepancy between the orientations S and L is less than 1°, which is within the accuracy of measurement of S and L. In summary, by measuring the angles between the slip lines formed by hardness indentation with simple facilities in a metallurgical laboratory, the orientation of A1-Li crystals could be determined rapidly with an accuracy close to that of the backreflection Laue method. The authors are grateful for the support of this research by the National Science Council, China, under grant NSC79-0405-E007-15.
1 C.S. Barrett and T. B. Massalski, Structure of Metals, 3rd edn., McGraw-Hill, New York, NY, 1980. 2 B. D. Cullity, Elements of X-Ray Diffraction, 2nd edn., Addison-Wesley,London, 1978. 3 T. S. Sheu and S. C. Chang, Mater. Sci. Eng., 147(1991) 81.