Elastic–Plastic and Inelastic Characteristics of High Strength Steel Sheets under Biaxial Loading and Unloading

Abstract

p ϭ0.02 are measured from the biaxial loading, unloading and reloading experiments. The moduli of elasticity at reloading were lower by 9 to 17 % than those at initial loading. The amount of strain recovery along the rolling direction (RD) is more than that along the transverse direction (TD) for uniaxial unloading, as well as for biaxial unloading. An exponential decay model is proposed that provides good reproduction of the unloading stress-strain relations, (s/s u )-De/(s u /E 2 ), of both materials under different stress ratios.KEY WORDS: biaxial tension; contours of plastic work; anisotropic yield function; unloading; inelastic strain recovery; cruciform specimen; instantaneous tangent modulus. 613© 2010 ISIJ relations of both materials for different stress ratios is proposed. Experimental Method Test MaterialsTwo types of high strength steel alloy test materials were used in this study: 0.7 mm thick BH340 and 1 mm thick DP590. BH and DP denote bake-hardenable and dualphase, respectively. The numbers indicate the tensile strength of the materials. The work hardening characteristics and the r-values of the test materials are listed in Table 1. Test SpecimensFigures 1(a), 1(b) and 1(c) show the geometry of the specimens used in this study. Figure 1(a) is the specimen for the uniaxial tensile test . Figure 1(b) is the specimen for the biaxial tensile test of sheet metals, which was originally proposed by Kuwabara et al.,13) and is the same as those used for the biaxial tensile tests of steel alloys, [14][15][16][17] aluminum alloys, 14,18) austenitic stainless steel SUS304 19) and pure titanium. 20) Figure 1(c) is the specimen for the combined tension-compression test of sheet metals, which was originally proposed by Kuwabara et al. 21) The x and y-axes are in the rolling (RD) and transverse directions (TD) of the materials, respectively. Seven slits have been fabricated in the arms of the specimens at intervals of 7.5 mm in order to exclude geometric constraint on the 60ϫ60 mm square gauge section.The normal strain components, e x and e y , were measured for the specimens shown in Figs. 1(a) and 1(b) using uniaxial strain gauges (Tokyo Sokki Kenkyujo, YFLA-2). A biaxial strain gauge (Tokyo Sokki Kenkyujo, FCA-11-1L) was used at the center of the specimen shown in Fig. 1(c). Figure 2 shows the biaxial testing apparatus used in this study. It was originally designed and fabricated by Kuwabara et al. 13) The hydraulic pressure of each pair of hydraulic cylinders is servo-controlled independently, so that the stress-paths or strain-paths applied to a specimen can be arbitrarily controlled using a closed-loop circuit. The displacements of the rams of the opposing hydraulic cylinders are equalized using the pantograph-type link mechanism proposed by Shiratori and Ikegami,22) so that the centre of the specimen is always maintained at the centre of the testing apparatus during the tests. A load cell is included in each loading direction. Biaxial strain components in the RD and TD of the specimen are measured con...

Development and application of the material constitutive model in springback prediction of cold-bending

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Non-linear Deformation Behavior during Unloading in Various Metal Sheets

“…This tendency is the same as that reported in the literature. 18,20) In case of the Al alloy sheet, such rapid decrease at the beginning hardly occurs and the gradient decreases very gradually from the beginning of unloading. Therefore, the difference in the gradients between the beginning and the end of unloading is smaller in the Al alloy sheet than the mild steel sheet.…”

Multiaxial Stress Tests for Metal Sheets and Tubes for Accurate Material Modeling and Forming Simulations

“…It should be noted that the biaxial tensile test method using a cruciform test piece has proven to be useful for accurately detecting and modeling the deformation behavior of sheet metals under biaxial tension and consequently improves the predictive accuracy of FEA for springback in stretch-bending [11], hole expansion in HSS sheet [12][13], surface deflection in automotive body panels [14], and hydraulic bulge forming of 6000 series aluminum alloy sheets [15]. A cruciform test piece is useful for biaxial load-unload tests of sheet metals [16] [17]. Successful FEA simulations of springback require suitable constitutive models that can capture the nonlinear strain recovery measured in these tests.…”