CALIBRATION OF DUCTILE FRACTURE PROPERTIES OF TWO CAST ALUMINUM ALLOYS

Transcription

1 CALIBRATION OF DUCTILE FRACTURE PROPERTIES OF TWO CAST ALUMINUM ALLOYS Hiroyuki Mae*, Xiaoqing Teng**, Yuanli Bai**, Tomasz Wierzbicki** * Honda R&D Co., Ltd., ** Massachusetts Institute o Technology * 4630 Shimotakanezawa, Haga-machi, Haga-gun, Tochigi , Japan * hiroyuki_mae@n.t.rd.honda.co.jp ABSTRACT Cast aluminium alloys have ound wide application to manuacture lighted-weight components o complex shape in automotive and aerospace industries. To improve the strength and ductility o cast aluminium alloys, it is necessary to study their racture properties by conducting a series o tests. This study will address calibration o ductile racture o two cast aluminium alloys made with two dierent casing techniques: sand and metal molds. The secondary dendrite arm spacing (SDAS) made by sand molding is larger than that o metal molding. 12 round bar specimens and 12 butterly specimens were machined rom real components. The tensile tests on the smooth and notched round bar specimens were perormed to calibrate the racture strain in the rage o high positive stress triaxialities. The combined loading tests on the butterly specimens were carried out using a uniquely designed Universal Biaxial Testing Device. These tests cover the racture properties in the rage o low and negative stress triaxialities. Detailed inite element models o all the tests were developed. The true stress-strain curves or these two aluminum alloys were determined. The racture loci in the space o the eective plastic strain to racture and the stress triaxiality were constructed in a wide rage rom -1/3 to 1.0. It was ound that material ductility sharply decreases with the stress triaxiality. In addition, the material ductility is strong dependent on the microstructure o the cast aluminium alloy, such as SDAS. Large spread o data was observed or those tests repeated on the same loading coniguration. Clearly, statistical analysis o the racture processes should be perormed with many more specimens and tests. Such a research program is currently undergoing. Introduction The microstructures o aluminum casting alloys in this study consist o an aluminum matrix strengthened by MgSi and Si precipitates, dispersing eutectic silicon particles and Fe-rich intermetallics. These microstructures are aected by chemical compositions, solidiication time and heat treatment. The eects o those actors on the microstructure were examined [1, 2, 3, 4]. It is well known that the ductility o the gravity die casting aluminum alloys depends on the secondary dendrite arm spacing (SDAS) [5, 6]. Wang el al. [7, 8] examined the role o the microstructural eatures such as SDAS in the tensile properties and racture behavior o the A356/357 alloys. The above investigations give an insight to ductile racture micromechanisms but are limited to one particular stress triaxiality o about 1/3. The authors measured and characterized the ductile racture properties o a low pressure die casting aluminum alloy at the stress triaxility rom -1/3 to +1.0 [9]. The attempt o the present study is made to calibrate the racture properties in the wide range o stress triaxiality in two types o gravity die casting aluminum alloys made by sand molding and metal molding techniques leading to the small and large SDAS values. A number o racture criteria have been proposed to describe the material ductility. The ductility is understood here as an intrinsic ability o a material to undergo a certain amount o plastic deormation without racture. Wierzbicki et al. [10, 11, 12] critically evaluated a number o ductile racture models in the space o the eective plastic strain to racture and the stress triaxiality would be able to show a good correlation with a variety o experiments. Such a racture locus can be expressed, in a general orm, as σ m ε = ( η) = (1) σ where ε is the eective plastic strain to racture and η is the stress triaxility deined by the ratio o the mean stress σ m to the equivalent stress σ. In the present study, a racture locus is developed or gravity die casting aluminum alloys with two dierent mean SDAS values by combining coupon tests with corresponding inite element analysis. It is expected that such a racture criterion would be able to correctly predict the racture response o real structural components under complex loading.

2 Specimen Preparation and Test Procedure The material used or a gravity die casting aluminum component was studied in the present research. The castings were made o an Al-Si-Fe-Cu-Mg-Mn alloy in sand and metal moldings under gravity, respectively. The metal molds would give rise to a aster solidiication velocity and lead to superior ductility or the cast alloy than sand moldings because o better heat conduction ability, e.g. see Shabestari and Moemeni [13]. Table 1 Chemical composition o the gravity die casting aluminum alloy (wt%) Cu Si Mg Fe Mn Ti Sn Ni ~0.2 ~0.05 ~0.05 Dozens o metallographic sections in the critical regions o the components were prepared to characterize the microstructure o the prototype o gravity die casting aluminum alloys. The typical graphs taken by a scanning electron microscope (SEM) are displayed in Figs. 1 showing normal aluminum-rich dendrites separated by eutectic regions containing silicon particles. The average SDAS o the present alloy made by sand molding is about 60 micrometer while that made by metal molding is about 40 micrometer. It is clear that the size o silicon particles in sand-molding cast aluminum alloy is larger than that o metalmolding cast aluminum alloy, as shown in Fig. 2. A small value o the SDAS usually indicates a good ductility. A total o six round bars and six butterly specimens were machined rom the cast aluminum components. Figure 1. Micrograph o the microstructure o the casing aluminum alloy made by sand molding and metal molding To construct an empirical racture locus that covers a wide range o stress states, one has to careully design specimens and experimental procedures. In this research, two types o test were considered: conventional tensile tests on notched and unnotched round bars, and biaxial loading tests on lat butterly-like specimens. The ormer provides inormation on the racture properties under tension, represented by high positive triaxialities. The eective plastic strains to racture in the range o low and negative stress triaxialities were obtained rom the biaxial loading experiments. Three types o round bars including one smooth specimen and two notched specimens were proposed to cover racture properties in the range o high positive stress triaxialities. For each type, two identical specimens were prepared rom the sand and metal molding components, respectively. The coniguration and size o three types o specimens are given in Fig. 2(a)-(c). As a complementary to the tensile tests o the round bars, biaxial loading tests on butterly lat specimens were carried out to characterize racture properties o the cast aluminum alloys in the rage o negative and low stress triaxialities. This new type o lat specimens were developed by Bao et al. [14] and have been successully applied to calibrate the racture loci o A710 steel and 2024-T351 aluminum alloy. This type o specimens has a complex, double curvature geometry in the gauge section such that cracks would initiate in the central region in most o the loading cases. A detailed discussion on the development o this type o specimens can be ound in Re. [14]. The major geometrical size o the new specimens is given in Fig. 2(d). To ensure that a crack irst occurs at the center o the gauge section, the central region has the minimal thickness o 1.0 mm, much smaller than the thickness o the shoulder region 3.0 mm. This is an advantage over conventional lat specimens, in which a crack is oten generated at the boundary, particularly under shear. To hold the specimen securely, two long shoulders are designed to provide suicient gripping area.

3 (d) Butterly specimen Figure 2. Dimensions o the round bar specimens and butterly specimen (unit: mm) To ensure that a crack irst occurs at the center o the gauge section, the central region has the minimal thickness o 1.0 mm, much smaller than the thickness o the shoulder region 3.0 mm. This is an advantage over conventional lat specimens, in which a crack is oten generated at the boundary, particularly under shear. To hold the specimen securely, two long shoulders are designed to provide suicient gripping area. The advantage o the new specimen is ully exploited by working with a custom-made Universal Biaxial testing Device (UBTD). Figure 3 illustrates a butterly lat specimen mounted in the UBTD with the orientation angle 10 degree. By suitably changing the orientation o the specimen with respect to the loading direction, dierent stress states would develop rom pure tension, combined tension and shear, pure shear, combined compression and shear, all the way to pure compression. With the UBTD, one would be able to construct a racture locus in a wide range o stress triaxialities using one type o specimens. Five loading conditions were considered rom combined compression and shear, pure shear, to combined tension and shear. The orientation angles o the specimens range rom -10 degree to 20 degree. Two pure shear tests were perormed to examine the repeatability o experimental data. It is expected that obtained average stress triaxialities would be evenly distributed rom -1/3 to +1/3. These two data correspond to uniaxial compression and tension, respectively. Figure 3. A butterly specimen with the orientation 10 degree mounted in the Universal Biaxial Testing Device (UBTD)

4 Calibration o plasticity and racture properties The true stress-strain curve up to racture, which is basic input data in inite element analysis, need to be irst determined rom the tests. A trial-and-error method is adopted here by orcing a numerically predicted load-displacement curve to closely match experimental data. In this study, all the tests were modeled numerically with ABAQUS/Standard. For the round bar specimens, two-dimensional inite element models were generated using axisymmetric, our-noded, reduced integration elements (CAX4R), see Figs. 4(a)-(c). In all the three models, the elements o 0.1 mm x 0.1 mm are deined in the gauge section where necking and subsequent racture occurs. One end o the models is deined with ixed boundary conditions and a tensile displacement is prescribed at the other end. For the butterly specimens, a three-dimensional inite element model was built with eight-noded brick, reduced integration elements (C3D8R), see Figs. 4(d)-(e). The total element number is 39,760. The inest elements o 0.1 mm x 0.1 mm x 0.1mm are located in the central region o the gauge section. Figure 5 shows the calibrated true stress-strain curves or both the sand- and metal- molding. These true stress-strain curves describe strain hardening evolution or a simple isotropic, J 2 plasticity model. (d) Butterly specimen (e) Magniied central portion Figure 4. Finite element models o the round bar and butterly specimens. 450 Equivalent stress (MPa) Sand-molding Metal-molding Eective plastic strain Figure 5. True stress-strain curves or sand- and metal- molding casting aluminum alloys with the elastic modulus o E = 86.0 GPa and the Poisson s ratio o The tests provide the instant at the point o racture, represented by the critical displacement o the gauge section. The corresponding inite element analyses give the evolution o stresses and strains o the critical points. By combining the tests and the numerical simulations, one would be able to construct empirical racture envelopes o materials. In the tensile tests on the round bar specimens, racture usually initiates at the center o the necking zone. For the biaxial loading tests on the butterly specimens, it is not clear whether cracks iniate in the middle thickness o the gauge section or on the outer suraces. Bao et al. [14] compared damage accumulation o both sites and concluded that there was not much dierence. Figures 6 and 7 show the evolution o the stress triaxiality and the eective plastic strain o the critical points up to racture or the round bars and the butterly specimens made by sand- and metal molding, respectively. It appears that the stress

5 triaxialities vary in a certain range o each test. Without resorting to the damage accumulation rule, the average value o the stress triaxiality is deined in the range (0, ε ): σ m 1 ε σ m = dε pl. (2) σ ε 0 av σ The racture strain ε, determined rom the numerical simulation, is the eective plastic strain corresponding to the measured displacement to racture u.. Since the stress triaxialities in all these tests vary in a rather narrow range, the deinition o the average value would not introduce large errors. This is exactly what the butterly specimens were designed or. For practical applications, it would be preerable to use an analytical curve to it the racture test data. An exponential unction relating the eective racture strain to the stress triaxiality is commonly used: ε = D1 + D2 exp( D3η), (3) where three coeicients: D 1, D 2 and D 3 need to be determined. This unction was irst developed by Rice and Tracey [15] rom theoretical analysis o enlargement o a spherical void. Hancock and McKenzie [16] modiied the expression on experimental results o round bar tensile tests. Note, that Eq. (3) is better known as the Johnson-Cook racture criterion [17]. Figure 6. The eective plastic strain versus the stress triaxiality or the critical points in round bars. Figure 7. The eective plastic strain versus the stress triaxiality or the critical points in butterly specimens. All the racture points were plotted in Fig. 8 with the stress triaxiality as an independent variable. It appears that the material ductility sharply decreases with the increasing stress triaxiality. The experimental result obtained in the sand molding shows the eective racture strain reaches 0.56 in the case dominated by compression while the eective racture strain is as low as at the stress triaxiality o On the other hand, the eective racture strain reaches 1.06 in the case dominated by compression while the eective racture strain is as low as 0.02 at the stress triaxiality o Clearly, the ductility o the metal molding is much higher than that o sand molding in the stress triaxiality ranging rom -1/3 to It is considered that the

6 smaller SDAS value o metal-molding cast aluminum alloy makes more ductile characteristics compared to the sand-molding cast aluminum alloy. The optimization gives the ollowing material coeicients or the Johnson-Cook racture loci: D 1 = 0.0, D 2 = 0.27 and D 3 = or sand-molding cast aluminum alloy, D 1 = 0.0, D 2 = 0.65 and D 3 = or metal-molding cast aluminum alloy, respectively. Figure 8. Fracture loci o the cast aluminum alloy made by sand molding and metal molding Conclusions In this study, ductile racture properties o two cast aluminum alloys made by sand molding and metal molding were characterized in the orm o a racture locus using a combined experimental-numerical approach. A total o twelve tests were perormed including six tensile tests on the round bars and six biaxial loading tests on the lat butterly specimens or sandand metal-molding cast aluminum alloys, respectively. Corresponding inite element analysis was conducted and the evolution o stresses and strains o the critical points was determined. The ductile racture loci were ormulated in the space o eective plastic strain to racture and the stress triaxiality. It appears that there is a very strong dependency o the material ductility o the stress triaxiality on both sand- and metal-molding cast aluminum alloys. The ductility o sand-molding cast aluminum alloy is much lower than that o metal-molding cast aluminum alloy in the wide range o stress triaxiality ranging rom -1/3 to +1. It is considered that the secondary arm spacing should have a strong eect on the ductility in the wide range o stress triaxiality. A large spread o racture data was observed. This may be caused by randomly distributed pores. It would be necessary to describe ductile racture properties o the present cast aluminum alloys in a statistical way. This issue is a subject under going. Reerences 1. M. C. Flemings, Solidiication Processing., McGraw-Hill, New York, NY, (1974). 2. R. E. Spear and G. R. Gardner, AFS Trans., 71, (1963). 3. D. Apelian, S. Shivkumar and G. Sigworth, AFS Trans., 97, (1989). 4. Z. Shan and A. M. Gokhale, Acta Mater., 49, (2001). 5. S. F. Frederick and W. A. Bailey, Trans. TMS-AIME, 242, 2063 (1968). 6. K. J. Oswalt and M. S Misra, AFS Trans., 88, (1980). 7. Q. G. Wang, Metallurgical and Materials Transactions A, 34, (2003). 8. Q. G. Wand, C. H. Caceres and J. R. Griiths, Metallurgical and Materials Transactions A, 34, (2003). 9. H. Mae, X. Teng, Y. Bai, T. Wierzbicki, Materials Science and Engineering A, To be accepted. 10. Y. Bao and T. Wierzbicki, Journal o Engineering Materials and Technology, 126, 3, (2004). 11. T. Wierzbicki, Y. Bao, Y. W, Lee, and Y. Bai, International Journal o Mechanical Sciences, 47, 4-5, (2005). 12. X. Teng and T. Wierzbicki, Engineering Fracture Mechanics, 73, (2006). 13. S. G. Shabestar and H. Moemeni, Journal o Materials Processing Technology, 153, (2004). 14. Y. Bao, Y. Bai and T. Wierzbicki, Technical Report, 135, Impact and Crashworthiness Lab, MIT, Cambridge, MA (2005). 15. J. R. Rice and D. M. Tracey, Journal o the Mechanics and Physics o Solids, 17, (1969). 16. J. W. Hancock and A. C. Mackenzie, Journal o the Mechanics and Physics o Solids, 24, (1976). 17. G. R. Johnson and W. H. Cook, Engineering Fracture Mechanics, 21, 1, (1985).