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A study of the strength of carbon–carbon brake disks for automotive applications
Composite Structures 86 (2008) 101–106
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
A study of the strength of carbon–carbon brake disks for automotive applications Do-Wan Lim a, Tae-Hwan Kim a, Jin-Ho Choi a,*, Jin-Hwe Kweon a, Hong-Sik Park b a b
Research Center for Aircraft Parts Technology, School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Republic of Korea DACC, 24-4 Seongju-dong, Changwon, Gyeongnam 641-120, Republic of Korea
a r t i c l e
i n f o
Available online 15 March 2008 Keywords: Carbon–carbon composites Composite joint Maximum stress theory
a b s t r a c t Carbon–carbon composites are often used in high-temperature applications due to their high specific modulus, high specific strength, excellent heat resistance, high thermal shock resistance and chemical inertness. In this paper, the strength of carbon/carbon brake disks for automotive applications were tested and evaluated. The laminate material properties of carbon/carbon composites were evaluated via tension, compression and shear tests. The strengths of mechanically fastened composite joints for brake disks were tested and their failure criterion was established based on the maximum stress theory. Additionally, torsion tests of carbon/carbon brake disks were performed and the results were compared with those from a finite element analysis. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Currently, the most widely used material in brakes, cast iron, requires a very large size to fulfill the challenging requirement for braking performance of modern luxury and sports cars. However, increasing the size of cast iron disks is accompanied by an increased mass in the wheel suspension. This has an impact on the comfort of driving and on the handling of the vehicle. C/C (carbon/carbon) brake disks provide good technical performance with a high specific modulus and high specific strength in addition to their tribological characteristics [1]. Thus, they can offer both improved braking performance and comfort. The excellent wear resistance of these disks offers the additional possibility of a longer vehicle life time. In this paper, the strength of C/C brake disks for automotive use are tested and evaluated. The laminate material properties of C/C composites were evaluated via tension, compression and shear tests. The strengths of the mechanically fastened composite joints for brake disks were tested and their failure criterion was established based on the maximum stress theory. In addition, torsion tests of C/C brake disks were performed and the results were compared with those from a finite element analysis. 2. Mechanical properties of carbon–carbon composites The structural stability of C/C brake disks was evaluated in tests of the mechanical properties and structural analyses. C/C composites are composed of continuous long carbon fiber, chopped fiber and carbon matrix. However, it is unworkable to manufacture a * Corresponding author. Tel.: +82 55 751 6073; fax: +82 55 757 5622. E-mail address: [email protected] (J.-H. Choi). 0263-8223/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2008.03.017
C/C specimen of each fiber type as well as a single-stacking angle specimen at, for example, 0° due to the complexity and cost of the processing involved. As chopped carbon fiber has a random orientation and the stacking sequence of continuous carbon fiber is [0/60/ 60], the C/C brake disk can be considered a quasi-isotropic material. The test specimens extracted from an actual C/C brake disk were manufactured for the evaluation of the mechanical properties, as shown in Fig. 1 [2]. Test specimens of 0°, 10°, 20° and 30° with respect to the reference axis were extracted and the tensile, compression and shear test specimens were created, as shown in Fig. 2. A universal testing machine was used for tests (Model 5582, Instron Co.) and its crosshead speed was fixed at 1 mm/ min. Table 1 shows the experimental mechanical properties of the C/C composites in each test.
3. Joint analysis of a C/C brake disk The C/C brake disk used here has several mechanical joints, as shown in Fig. 3. There are often the weakest parts in the C/C brake disk; therefore, the evaluation of the strength of the composite joint is very important in the design of a C/C brake disk. Failure criteria such as the Tsai–Wu index or the Yamada–Sun index, which can estimate the failures of composites, are based on the ply strength [3]. However, as the only the laminate modulus and strength were measured in the previous chapter, these failure criteria cannot be used in the joint of a C/C brake disk here. The stresses around a hole are generally larger than the material strength due to the stress concentration around a hole when composite joints failed. Therefore, the failure index at a certain point [4–7] or area [8,9] away from the hole of a composite joint can generally be used for a failure load prediction of the joint.
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In this paper, the laminate stresses around a hole were used as the failure criterion of the composite joints. For use as a stress criterion, it is very important to know the level of stress around a hole when composite joints fail. The composite joint of a C/C brake disk consists of two parts: a straight hole and a two-step hole, as shown in Fig. 4. As the stresses around the two-step hole can be more complex compared to those around the straight hole, the composite joints, which have two-step holes and w/d (width to diameter) and e/d (edge to diameter) ratios that are identical to those of a C/C brake disk were machined. Fig. 5 shows the shape and dimension of the manufactured composite joint specimen. The failure loads of the composite joints with the two-step hole were experimentally measured and applied to the finite element model.
Fig. 1. Test specimen extracted from a C/C brake disk.
Fig. 3. Mechanical joints for a C/C brake disk.
Fig. 4. Section of a composite joint.
Fig. 2. Dimensions of the test specimens. (a) Tension specimen (b) compression specimen (c) in-plane shear specimen.
Table 1 Mechanical properties of the C/C composites
EX (GPa) XT (MPa) XC (MPa) EY (GPa) YT (MPa) G12 (GPa) S12 (MPa)
0°
10°
20°
30°
Average
55.2 104.5
44.6 77.3
50.5 81.0
52.4 54.4
36.3 28.3 18.1 87.9
83.3 27.6 22.0 85.2
74.8 31.1 16.6 77.2
48.9 39.4 21.3 80.7
50.7 79.3 263.6 60.8 31.6 19.5 82.8
Fig. 5. Dimension of the manufactured composite joint specimen.
D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
103
3.1. Single-lap joint # 1 A C/C brake disk and metal bush were assembled using several bolts, as shown in Fig. 6. As a single instance of shear force is applied to a composite joint of a C/C brake disk during a braking operation, single-lap joint tests were performed. Fig. 7 shows a schematic diagram of the single-lap joint #1. The bolt head was fixed to the two-step hole and the shear force was applied to the bolt of single-lap joint # 1. Fig. 8 shows the single-lap shear test of the composite joint. The experimental maximum failure load was 8.35 kN and the tensile crack around the hole was observed, as shown in Fig. 9. For the calculation of the stress distribution around the hole, finite element analyses of the single-lap joints were performed. Fig. 9. Fractured single-lap joint # 1.
Fig. 6. Metal bush assembled to C/C brake disk.
Commercial MSC/MARC software was used for the analysis, and a finite element model was created, as shown in Fig. 10. In addition, the average mechanical properties of Table 1 were input into the finite element model. Contact elements were used for nonlinear contact between the hole and bolt, and an experimental failure load (P = 8.35 kN) was applied to the bolt of the composite joint. Fig. 11 shows the stress distributions around the hole. As shown in Fig. 11, it was observed that the stresses reached their maximum around the hole and that the locations of maximum tensile rx and compressive ry were close to the location of the crack. The stress percentage, in which the maximum stress was divided by the material strength, was calculated. The compressive strength in the X-direction was assumed to be identical to that in the y-direction (XC = YC = 263 MPa). The calculated stress percentages are summarized in Table 2. F.I. in Table 2 is the maximum failure index according to the Tsai–Wu criterion under the experimental failure load. 3.2. Single-lap joint # 2
Fig. 7. Schematic diagram of the single-lap joint # 1.
Fig. 8. Single-lap shear test of the composite joint.
Failure of the composite joint of a C/C brake disk can be caused by a compression load on the metal bush under a single shear force. Fig. 12 shows a schematic diagram of single-lap joint # 2 for failure mode resulting from a compression load on the metal bush. As shown in Fig. 12, the bolt head was inversely assembled onto the hole of the composite joint and the single shear force was applied to the end of the bolt. Fig. 13 shows tensile cracking around a hole after a single shear test; the experimental failure load here was 7.5 kN. The stress distribution around the hole is shown in Fig. 14 when the experimental failure load (P = 7.5 kN)
Fig. 10. Finite element model of single-lap joint # 1.
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Fig. 11. Stress distributions of single-lap joint # 1 (a) rx (b) ry.
Table 2 Stress percentage of single-lap joint # 1 Item
Value
Tension (%) Compression (%)
rx/XT 100 ry/YT 100 rx/Xc 100 ry/YC 100
368.3 980.6 173.0 72.5 300.9 48.2
s12/S12 100 F.I.
Fig. 13. Fractured single-lap joint # 2.
Fig. 12. Schematic diagram of the single-lap joint # 2.
was applied in the finite element model. Fig. 14 shows the stress distributions around the hole. As shown in Fig. 14, the stresses reached their maximum around the hole and the location of maximum compressive stress in the y-direction was close to that of the crack. Table 3 shows the calculated stress percentages and the F.I. value.
From the two joint tests described above, the lower stress percentages were used for the prediction of the failure load of the C/C brake disk. Table 4 shows the failure criterion of the C/C brake disk based on the stress percentages. 4. Structural analysis and torsion test of the C/C brake disk The failure load of the C/C brake disk was predicted by the criterion based on the stress percentage shown in Table 4. Fig. 15 shows a 1/11 finite element model of a C/C brake disk using cyclic symmetry. Contact elements were used as nonlinear contacts
Fig. 14. Stress distributions of single-lap joint # 2.
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D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
between the hole, bolt and bush, and normal and shear braking force were applied to the frictional surface of the C/C brake disk. The stresses around the composite joint of the C/C brake disk were relatively high; Fig. 16 shows the rx stress distribution around the hole under the braking force. Table 5 shows the calculated stress percentage when torque of 14,734 N m was applied. As shown in Table 5, the stress percentage of compressive rx reaches that of
Table 3 Stress percentage of single-lap joint # 2 Item
Value
Tension (%) Compression (%)
rx/XT 100 ry/YT 100 rx/XC 100 ry/YC 100
s12/S12 100 F.I.
510.9 1511.9 394.5 134.0 570.4 295.0
Table 4 Failure criterion of C/C brake disk
Table 5 Stress percentages under a torque of 14,734 N m
Item Tension (%) Compression (%)
the failure criterion. The composites were assumed to have failed according to the maximum stress theory if any stress component was equal to or greater than the failure criterion [10]. Therefore, the torque capacity of the C/C brake disk using the stress percentage was considered to be 14,734 N m. Moreover, the torque capacity using the Tsai–Wu failure criterion, F.I. was predicted. The C/C brake disk was assumed to have failed when the F.I. was greater than 48 and when the predicted torque capacity was 21,037 N m. To compare the analysis with the experiments, a torsion test of the C/C brake disk was performed. Fig. 17 shows the jig used in the torsion test of the C/C brake disk. The side edges of the C/C brake were cut into an eleven-polygon shape and eleven shoes in the radial direction were installed to prevent rotation of the C/C brake disk. Additionally, a rubber pad was inserted between the frictional surface and the steel disk. Fig. 18 shows a photograph of the eleven-polygon C/C brake disk and shoes. A torque testing machine by MTS Systems Co. was used with its rotational speed fixed to 0.5 degree/min. Cracks around five holes were observed after the
rx/XT 100 ry/YT 100 rx/XC 100 ry/YC 100
s12/S12 100 F.I.
Value
Item
368.3 980.6 173.0 72.5 300.9 48.2
Tension (%) Compression (%) s12/S12 100 F.I.
rx/XT 100 ry/YT 100 rx/Xc 100 ry/YC 100
Failure criterion
B/D
368.3 980.6 173.0 72.5 300.9 48.2
237.2 427.0 172.6 32.8 207.9 175.0
Fig. 15. 1/11 Finite element model of a C/C brake disk.
Fig. 17. Jig for torsion test of a C/C brake disk.
Fig. 16. rx stress distribution when torque of 14,734 N m was applied.
Fig. 18. Photograph of the eleven-polygon C/C brake disk and shoes.
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D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
Fig. 19. Cracks around the five holes after a torque test.
torque capacity could be predicted within a 40.0% difference using the maximum stress theory. Moreover, the prediction accuracy by the maximum stress theory was superior to that by Tsai–Wu failure criterion.
14000 12000
Torque (N.m)
10000
5. Conclusions
8000
From the testing and analyses of a C/C brake disk for automotive use based on the maximum stress theory, the following conclusions are offered:
6000 4000 2000 0 0
0.5
1
1.5
2 2.5 Degree of angle
3
3.5
4
4.5
Fig. 20. Torque-twisting angle curves.
1. The strength of mechanically fastened composite joints for a brake disk was tested and the failure criterion based on the maximum stress theory was established. 2. The torque capacity could be predicted within a 40.0% difference using the failure criterion based on the maximum stress theory.
25000 Experiment Maximum stress F.I
Acknowledgements
Maximum Torque (N.m).
20000
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005005-J09902) and the 2nd stage BK21 Project.
15000
90.9%
10000 40.0% 5000
0
Fig. 21. Failure load prediction accuracies of the C/C brake disk.
torque test. Enlarged photographs of cracks around the five holes are shown in Fig. 19. Fig. 20 shows the torque-twisting angle curves. As shown in Fig. 20, the measured maximum torque capacities were 8750 N m and 12,297 N m, respectively and their average value was 10,523 N m. The accuracy rates of the failure load predictions of the C/C brake disk are summarized in Fig. 21. As shown in Fig. 21, it the
References [1] Reinhart JJ, editors, Compos ASM Int 1987;1:470–95. [2] Daniel IM, Ishai O. Engineering mechanics of composite materials. Oxford University Press; 1994. p. 312–35. [3] Jones RM. Mechanics of composite materials. McGraw-Hill; 1975. p. 71–82. [4] Whitney JM, Nuismer RJ. Stress fracture criteria for laminated composites containing stress concentrations. Int J Compos Mater 1974;8:253–65. [5] Chang FK, Scott RA. Strength of mechanically fastened composite joints. Int J Compos Mater 1982;16:470–94. [6] Chang FK, Scott RA. Failure of composite laminates containing pin loaded holes-method of solution. Int J Compos Mater 1984;18:255–78. [7] Xiong Y, Poon C, Straznicky PV, Vietinghoff H. A prediction method for the compressive strength of impact damaged composite laminates. Compos Struct 1995;30:357–67. [8] Choi JH, Chun YJ. Failure load prediction of mechanically fastened composite joint. Int J Compos Mater 2003;37(24):2163–77. [9] Ryu CO, Choi JH, Kweon JH. Failure load prediction of composite joints using linear analysis. Int J Compos Mater 2007;41(7):865–78. [10] Lee DG, Suh NP. Axiomatic design and fabrication of composite structures. Oxford University Press; 2006. p. 152–201.
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
A study of the strength of carbon–carbon brake disks for automotive applications Do-Wan Lim a, Tae-Hwan Kim a, Jin-Ho Choi a,*, Jin-Hwe Kweon a, Hong-Sik Park b a b
Research Center for Aircraft Parts Technology, School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Republic of Korea DACC, 24-4 Seongju-dong, Changwon, Gyeongnam 641-120, Republic of Korea
a r t i c l e
i n f o
Available online 15 March 2008 Keywords: Carbon–carbon composites Composite joint Maximum stress theory
a b s t r a c t Carbon–carbon composites are often used in high-temperature applications due to their high specific modulus, high specific strength, excellent heat resistance, high thermal shock resistance and chemical inertness. In this paper, the strength of carbon/carbon brake disks for automotive applications were tested and evaluated. The laminate material properties of carbon/carbon composites were evaluated via tension, compression and shear tests. The strengths of mechanically fastened composite joints for brake disks were tested and their failure criterion was established based on the maximum stress theory. Additionally, torsion tests of carbon/carbon brake disks were performed and the results were compared with those from a finite element analysis. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Currently, the most widely used material in brakes, cast iron, requires a very large size to fulfill the challenging requirement for braking performance of modern luxury and sports cars. However, increasing the size of cast iron disks is accompanied by an increased mass in the wheel suspension. This has an impact on the comfort of driving and on the handling of the vehicle. C/C (carbon/carbon) brake disks provide good technical performance with a high specific modulus and high specific strength in addition to their tribological characteristics [1]. Thus, they can offer both improved braking performance and comfort. The excellent wear resistance of these disks offers the additional possibility of a longer vehicle life time. In this paper, the strength of C/C brake disks for automotive use are tested and evaluated. The laminate material properties of C/C composites were evaluated via tension, compression and shear tests. The strengths of the mechanically fastened composite joints for brake disks were tested and their failure criterion was established based on the maximum stress theory. In addition, torsion tests of C/C brake disks were performed and the results were compared with those from a finite element analysis. 2. Mechanical properties of carbon–carbon composites The structural stability of C/C brake disks was evaluated in tests of the mechanical properties and structural analyses. C/C composites are composed of continuous long carbon fiber, chopped fiber and carbon matrix. However, it is unworkable to manufacture a * Corresponding author. Tel.: +82 55 751 6073; fax: +82 55 757 5622. E-mail address: [email protected] (J.-H. Choi). 0263-8223/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2008.03.017
C/C specimen of each fiber type as well as a single-stacking angle specimen at, for example, 0° due to the complexity and cost of the processing involved. As chopped carbon fiber has a random orientation and the stacking sequence of continuous carbon fiber is [0/60/ 60], the C/C brake disk can be considered a quasi-isotropic material. The test specimens extracted from an actual C/C brake disk were manufactured for the evaluation of the mechanical properties, as shown in Fig. 1 [2]. Test specimens of 0°, 10°, 20° and 30° with respect to the reference axis were extracted and the tensile, compression and shear test specimens were created, as shown in Fig. 2. A universal testing machine was used for tests (Model 5582, Instron Co.) and its crosshead speed was fixed at 1 mm/ min. Table 1 shows the experimental mechanical properties of the C/C composites in each test.
3. Joint analysis of a C/C brake disk The C/C brake disk used here has several mechanical joints, as shown in Fig. 3. There are often the weakest parts in the C/C brake disk; therefore, the evaluation of the strength of the composite joint is very important in the design of a C/C brake disk. Failure criteria such as the Tsai–Wu index or the Yamada–Sun index, which can estimate the failures of composites, are based on the ply strength [3]. However, as the only the laminate modulus and strength were measured in the previous chapter, these failure criteria cannot be used in the joint of a C/C brake disk here. The stresses around a hole are generally larger than the material strength due to the stress concentration around a hole when composite joints failed. Therefore, the failure index at a certain point [4–7] or area [8,9] away from the hole of a composite joint can generally be used for a failure load prediction of the joint.
102
D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
In this paper, the laminate stresses around a hole were used as the failure criterion of the composite joints. For use as a stress criterion, it is very important to know the level of stress around a hole when composite joints fail. The composite joint of a C/C brake disk consists of two parts: a straight hole and a two-step hole, as shown in Fig. 4. As the stresses around the two-step hole can be more complex compared to those around the straight hole, the composite joints, which have two-step holes and w/d (width to diameter) and e/d (edge to diameter) ratios that are identical to those of a C/C brake disk were machined. Fig. 5 shows the shape and dimension of the manufactured composite joint specimen. The failure loads of the composite joints with the two-step hole were experimentally measured and applied to the finite element model.
Fig. 1. Test specimen extracted from a C/C brake disk.
Fig. 3. Mechanical joints for a C/C brake disk.
Fig. 4. Section of a composite joint.
Fig. 2. Dimensions of the test specimens. (a) Tension specimen (b) compression specimen (c) in-plane shear specimen.
Table 1 Mechanical properties of the C/C composites
EX (GPa) XT (MPa) XC (MPa) EY (GPa) YT (MPa) G12 (GPa) S12 (MPa)
0°
10°
20°
30°
Average
55.2 104.5
44.6 77.3
50.5 81.0
52.4 54.4
36.3 28.3 18.1 87.9
83.3 27.6 22.0 85.2
74.8 31.1 16.6 77.2
48.9 39.4 21.3 80.7
50.7 79.3 263.6 60.8 31.6 19.5 82.8
Fig. 5. Dimension of the manufactured composite joint specimen.
D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
103
3.1. Single-lap joint # 1 A C/C brake disk and metal bush were assembled using several bolts, as shown in Fig. 6. As a single instance of shear force is applied to a composite joint of a C/C brake disk during a braking operation, single-lap joint tests were performed. Fig. 7 shows a schematic diagram of the single-lap joint #1. The bolt head was fixed to the two-step hole and the shear force was applied to the bolt of single-lap joint # 1. Fig. 8 shows the single-lap shear test of the composite joint. The experimental maximum failure load was 8.35 kN and the tensile crack around the hole was observed, as shown in Fig. 9. For the calculation of the stress distribution around the hole, finite element analyses of the single-lap joints were performed. Fig. 9. Fractured single-lap joint # 1.
Fig. 6. Metal bush assembled to C/C brake disk.
Commercial MSC/MARC software was used for the analysis, and a finite element model was created, as shown in Fig. 10. In addition, the average mechanical properties of Table 1 were input into the finite element model. Contact elements were used for nonlinear contact between the hole and bolt, and an experimental failure load (P = 8.35 kN) was applied to the bolt of the composite joint. Fig. 11 shows the stress distributions around the hole. As shown in Fig. 11, it was observed that the stresses reached their maximum around the hole and that the locations of maximum tensile rx and compressive ry were close to the location of the crack. The stress percentage, in which the maximum stress was divided by the material strength, was calculated. The compressive strength in the X-direction was assumed to be identical to that in the y-direction (XC = YC = 263 MPa). The calculated stress percentages are summarized in Table 2. F.I. in Table 2 is the maximum failure index according to the Tsai–Wu criterion under the experimental failure load. 3.2. Single-lap joint # 2
Fig. 7. Schematic diagram of the single-lap joint # 1.
Fig. 8. Single-lap shear test of the composite joint.
Failure of the composite joint of a C/C brake disk can be caused by a compression load on the metal bush under a single shear force. Fig. 12 shows a schematic diagram of single-lap joint # 2 for failure mode resulting from a compression load on the metal bush. As shown in Fig. 12, the bolt head was inversely assembled onto the hole of the composite joint and the single shear force was applied to the end of the bolt. Fig. 13 shows tensile cracking around a hole after a single shear test; the experimental failure load here was 7.5 kN. The stress distribution around the hole is shown in Fig. 14 when the experimental failure load (P = 7.5 kN)
Fig. 10. Finite element model of single-lap joint # 1.
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D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
Fig. 11. Stress distributions of single-lap joint # 1 (a) rx (b) ry.
Table 2 Stress percentage of single-lap joint # 1 Item
Value
Tension (%) Compression (%)
rx/XT 100 ry/YT 100 rx/Xc 100 ry/YC 100
368.3 980.6 173.0 72.5 300.9 48.2
s12/S12 100 F.I.
Fig. 13. Fractured single-lap joint # 2.
Fig. 12. Schematic diagram of the single-lap joint # 2.
was applied in the finite element model. Fig. 14 shows the stress distributions around the hole. As shown in Fig. 14, the stresses reached their maximum around the hole and the location of maximum compressive stress in the y-direction was close to that of the crack. Table 3 shows the calculated stress percentages and the F.I. value.
From the two joint tests described above, the lower stress percentages were used for the prediction of the failure load of the C/C brake disk. Table 4 shows the failure criterion of the C/C brake disk based on the stress percentages. 4. Structural analysis and torsion test of the C/C brake disk The failure load of the C/C brake disk was predicted by the criterion based on the stress percentage shown in Table 4. Fig. 15 shows a 1/11 finite element model of a C/C brake disk using cyclic symmetry. Contact elements were used as nonlinear contacts
Fig. 14. Stress distributions of single-lap joint # 2.
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D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
between the hole, bolt and bush, and normal and shear braking force were applied to the frictional surface of the C/C brake disk. The stresses around the composite joint of the C/C brake disk were relatively high; Fig. 16 shows the rx stress distribution around the hole under the braking force. Table 5 shows the calculated stress percentage when torque of 14,734 N m was applied. As shown in Table 5, the stress percentage of compressive rx reaches that of
Table 3 Stress percentage of single-lap joint # 2 Item
Value
Tension (%) Compression (%)
rx/XT 100 ry/YT 100 rx/XC 100 ry/YC 100
s12/S12 100 F.I.
510.9 1511.9 394.5 134.0 570.4 295.0
Table 4 Failure criterion of C/C brake disk
Table 5 Stress percentages under a torque of 14,734 N m
Item Tension (%) Compression (%)
the failure criterion. The composites were assumed to have failed according to the maximum stress theory if any stress component was equal to or greater than the failure criterion [10]. Therefore, the torque capacity of the C/C brake disk using the stress percentage was considered to be 14,734 N m. Moreover, the torque capacity using the Tsai–Wu failure criterion, F.I. was predicted. The C/C brake disk was assumed to have failed when the F.I. was greater than 48 and when the predicted torque capacity was 21,037 N m. To compare the analysis with the experiments, a torsion test of the C/C brake disk was performed. Fig. 17 shows the jig used in the torsion test of the C/C brake disk. The side edges of the C/C brake were cut into an eleven-polygon shape and eleven shoes in the radial direction were installed to prevent rotation of the C/C brake disk. Additionally, a rubber pad was inserted between the frictional surface and the steel disk. Fig. 18 shows a photograph of the eleven-polygon C/C brake disk and shoes. A torque testing machine by MTS Systems Co. was used with its rotational speed fixed to 0.5 degree/min. Cracks around five holes were observed after the
rx/XT 100 ry/YT 100 rx/XC 100 ry/YC 100
s12/S12 100 F.I.
Value
Item
368.3 980.6 173.0 72.5 300.9 48.2
Tension (%) Compression (%) s12/S12 100 F.I.
rx/XT 100 ry/YT 100 rx/Xc 100 ry/YC 100
Failure criterion
B/D
368.3 980.6 173.0 72.5 300.9 48.2
237.2 427.0 172.6 32.8 207.9 175.0
Fig. 15. 1/11 Finite element model of a C/C brake disk.
Fig. 17. Jig for torsion test of a C/C brake disk.
Fig. 16. rx stress distribution when torque of 14,734 N m was applied.
Fig. 18. Photograph of the eleven-polygon C/C brake disk and shoes.
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D.-W. Lim et al. / Composite Structures 86 (2008) 101–106
Fig. 19. Cracks around the five holes after a torque test.
torque capacity could be predicted within a 40.0% difference using the maximum stress theory. Moreover, the prediction accuracy by the maximum stress theory was superior to that by Tsai–Wu failure criterion.
14000 12000
Torque (N.m)
10000
5. Conclusions
8000
From the testing and analyses of a C/C brake disk for automotive use based on the maximum stress theory, the following conclusions are offered:
6000 4000 2000 0 0
0.5
1
1.5
2 2.5 Degree of angle
3
3.5
4
4.5
Fig. 20. Torque-twisting angle curves.
1. The strength of mechanically fastened composite joints for a brake disk was tested and the failure criterion based on the maximum stress theory was established. 2. The torque capacity could be predicted within a 40.0% difference using the failure criterion based on the maximum stress theory.
25000 Experiment Maximum stress F.I
Acknowledgements
Maximum Torque (N.m).
20000
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005005-J09902) and the 2nd stage BK21 Project.
15000
90.9%
10000 40.0% 5000
0
Fig. 21. Failure load prediction accuracies of the C/C brake disk.
torque test. Enlarged photographs of cracks around the five holes are shown in Fig. 19. Fig. 20 shows the torque-twisting angle curves. As shown in Fig. 20, the measured maximum torque capacities were 8750 N m and 12,297 N m, respectively and their average value was 10,523 N m. The accuracy rates of the failure load predictions of the C/C brake disk are summarized in Fig. 21. As shown in Fig. 21, it the
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