Han-Chin Wu

Anisotropic plasticity for sheet metals using the concept of combined isotropic-kinematic hardening

Abstract Hills 1948 anisotropic theory of plasticity (Hill, R., 1948. A theory of yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London A193, 281–297) is extended to include the concept of combined isotropic-kinematic hardening, and the objective of this paper is to validate the model so that it may be useful for analyses of sheet metal forming. Isotropic hardening and kinematic hardening may be experimentally observed in sheet metals, if yielding is defined by the proportional limit or by a small proof strain. In this paper, a single exponential term is used to describe isotropic hardening and Pragers linear kinematic hardening rule is applied for simplicity. It is shown that this model can satisfactorily describe both the yield stress and the plastic strain ratio, the R -ratio, observed in tension test of specimens cut at various angles measured from the rolling direction of the sheet. Kinematic hardening leads to a gradual change in the direction of the plastic strain increment, as the axial strain increases in the tension test; while in the traditional approach for sheet metal, this direction does not change due to the use of isotropic hardening.

Effect of loading-path on the evolution of yield surface for anisotropic metals subjected to large pre-strain

Abstract A theory of plasticity previously formulated by the author to discuss the free-end torsion problem has been extended to the more general case of combined axial-torsion of a thin-walled tube. This paper is devoted to the discussion of evolution of the yield surface due to different (proportional and non-proportional) loading paths with pre-strains in the large strain range. Experimental yield surfaces with axial and torsion pre-strains of magnitudes up to 40 and 45%, respectively, are presented, and theoretical results are compared with the experimental data.

On finite plastic deformation of anisotropic metallic materials

Abstract The classical flow theory of plasticity has been extended to the large strain range for anisotropic metallic materials. The following concepts have been incorporated into the constitutive framework: (1) the convected coordinates and the contravariant true stress, (2) an observer independent yield function, (3) the convected rate for general kinematics of deformation, and (4) the rotation of material texture expressed by a constitutive spin. The theory has been applied to the problem of free-end torsion of a thin-walled tube. The predicted results of shear stress-strain curve, axial strain versus shear strain curve, back stress versus shear strain curve, and initial and subsequent yield surfaces compare favorably with experimental data obtained by the author and his co-workers. It has been shown that the yield function defined by the contravariant true stress can account for the distortion of the yield loci.

Torsion test of aluminum in the large strain range

Abstract A series of experiments was conducted on cast and extruded high purity aluminum material under monotonic large strain torsion condition. Both free-end and fixed-end torsions were studied using tubular specimens of different gage lengths (long, medium and short). The experiments used an axial–torsional extensometer. A procedure of calibration for elevated temperature test was determined. The torque versus angle of twist curves were recorded and converted into true shear stress–strain curves by use of the modified Nadai method developed previously by the authors. The axial extension for free-end torsion and the axial stress developed during fixed-end torsion were recorded. The hoop strain was also measured and was found to be approximately 0.8–0.9 times the axial strain when the shear strain is 150%. The effect of specimen geometry was studied. It was found that the long, thick-walled tubular specimen is suitable for torsion test in the large strain range.

Anisotropic plasticity with application to sheet metals

Abstract Hill’s 1948 anisotropic theory of plasticity is extended to include the concept of isotropic–kinematic hardening. The “anomalous” effect can be accounted for by kinematic hardening. It is shown that the quadratic yield function can be used for sheet metals irrespective of its plastic strain ratio R. It is further shown that effects of thickness reduction due to further rolling may be accounted for by kinematic hardening.

An endochronic theory accounted for deformation induced anisotropy

Abstract An anisotropic quadratic form of plastic strain increment is used to define the intrinsic time in the endochronic theory of plasticity. Based on this new definition, a yield function can be derived. This new version of endochronic theory can describe the expansion, translation, rotation, and distortion of the yield surface. While the initial yielding is in the form of the Mises yield criterion, the distortion of subsequent yield surfaces is expressed by the compression or stretching of the Mises yield surface. The effect of sharp front and blunt rear of the yield surface is considered to be of secondary importance and neglected in the interest of keeping the equations simple. This idealization will not much affect the prediction power of the model, because the plastic strain increment is in the radial direction emanating from the center of the current yield surface and is not normal to the current yield surface. In this theory, the plastic deformation is thus not sensitive to the exact shape of the yield surface. It has been shown that the proposed theory is capable of describing the experimental results of three different metals considered. The test series investigated include several different paths of prestress.

Some considerations in the endochronic description of anisotropic hardening

SummaryExperimental results of Aris Phillips and his co-workers show that both distortion and motion of yield surface are path dependent. These phenomena are attributed to the path-dependent rate of strain-hardening for initially isotropic metallic materials.A version of endochronic theory is shown to describe this effect. Theoretical results are compared with the experimental data. This approach is further demonstrated to lead to improvement in the description of the Bauschinger effect.

Further development and application of an endochronic theory accounted for deformation induced anisotropy

SummaryIn a work by Wu et al. [11], an anisotropic quadratic form of plastic strain increment was used to define the intrinsic time in the endochronic theory of plasticity. Based on this new definition, an anisotropic yield function was derived. This new version of endochronic theory was shown to describe the expansion, translation, rotation, and distortion of the yield surface under loading conditions. In this paper, the previous theory has been extended to include unloading and reloading. A procedure has been established to determine the metric of the anisotropic intrinsic time using information related to the yield surface of a material. An agreement with experimental results has been demonstrated in terms of motion and distortion of yield surfaces and the stress-strain response of tubular specimens subjected to a proportional and a non-proportional path in the axial-torsional plastic strain space. The procedure of calculation is given in detail.

Endochronic description of plastic anisotropy in sheet metal

Abstract It is shown in this paper that an extended form of Hills quadratic yield criterion for anisotropic sheet metal can be derived from an endochronic theory of plasticity. The extended form considers the combined isotropic–kinematic hardening and the anomalous behavior observed in the anisotropic plastic behavior of sheet metals can be accounted for by the concept of kinematic hardening. This form of anisotropic endochronic theory can accommodate the usual requirement of normality between the plastic strain rate and the yield function. In addition, the theory leads naturally to the expressions for back stresses. This work provides an additional example to show that the form of the intrinsic time is directly related to the form of the yield function. It is suggested that the coefficients of the quadratic yield function be determined from the yield stresses obtained from a set of tension tests.

The viscoplastic circular plate—A new solution

SummaryIn a previous paper a theory of viscoplasticity was developed in which the dynamic yield surface is defined as the surface which encloses the quasistatic yield surface and has a constant distance from it. In the present paper, by means of the above theory, the problem of a thin circular plate under uniformly distributed transverse pressure is solved. The material of the plate is assumed to be rigidviscoplastic. The solution is compared with previous solutions of the same problem.ZusammenfassungIn einer vorangeganenen Arbeit wurde eine Theorie der Viskoplastizität entwickelt und die dynamische Fließfläche definiert, eine Fläche, die die quasistatische Fließfläche in konstantem Abstand umgibt. In vorliegender Arbeit wird mit Hilfe dieser Theorie das Problem einer dünnen Kreisplatte unter Gleichlast gelöst. Der Plattenwerkstoff wird als starr-viskoplastisch vorausgesetzt. Die Lösung wird mit anderen desselben Problems verglichen.