Endochronic description of plastic anisotropy in sheet metal

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.     

A non-associated flow rule for sheet metal forming

An improved model of material behavior is proposed that shows good agreement with experimental data for both yield and plastic strain ratios in uniaxial, equi-biaxial, and plane-strain tension under proportional loading for steel, aluminum and possibly other alloys. This model is based on a non-associated flow rule in which the plastic potential and yield surface functions are defined by quadratic functions of the stress tensor. The plastic potential aspect of the model is identical to that proposed by Hill for a quadratic anisotropic plastic potential defined in terms of measured r values. The new model differs in that the yield surface, although also defined by a quadratic function of the stress tensor, is defined independently of the plastic potential in terms of measured yield stresses. The model is developed and implemented in an FEM code that is based on a convected coordinate system. Since the associated flow rule, which assumes equivalency between the plastic potential and yield functions, is commonly accepted as a valid law in the theory of plastic deformation of most metals, the arguments for the associated flow rule are also discussed.     

覆盖件冲压仿真中的网格形态优化技术

覆盖件冲压仿真计算模型中网格密度分布的合理性与网格单元形态的优劣,对仿真结果的准确性有很大的影响.提出了一种改进的全四边形网格细分方法,使网格的密度分布适于覆盖件冲压分析计算要求,可保证细分后网格的协调性,并将算法推广以处理非结构化四边形网格和三角形四边形混合网格的细分.提出的网格细分策略,有助于提高细分后网格的质量.提出了适用于细分后四边形网格和非结构四边形网格的拓扑形态优化操作,可有效的提高网格模型的形态质量.     

金属板料成形的快速有限元分析

研究了基于形变理论的金属板形成快速有限元分析的方法－反向方法,并实现了计算程序。通过实例的计算结果和实验以及增量方法进行了比较,表明此方法能够定性地分析成形工件中的变形情况。由于计算速度快、建立分析模模型简单,此方法可用于设计早期估计零件的可成形性,以及部分工艺参数对形的影响。     

Path-dependence of the forming limit stresses in a sheet metal

The effect of changing strain paths on the forming limit stresses of sheet metals is investigated using the Marciniak–Kuczyński model and a phenomenological plasticity model with non-normality effects [Kuroda, M., Tvergaard, V., 2001. A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity. J. Mech. Phys. Solids 49, 1239–1263]. Forming limits are simulated for linear stress paths and two types of combined loading: a combined loading consisting of two linear stress paths in which unloading is included between the first and second loadings (combined loading A), and combined loading in which the strain path is abruptly changed without unloading (combined loading B). The forming limit stresses calculated for combined loading A agree well with those calculated for the linear stress paths, while the forming limit curves in strain space depend strongly on the strain paths. The forming limit stresses calculated for the combined loading B do not, however, coincide with those calculated for the linear stress paths. The strain-path dependence of the forming limit stress is discussed in detail by observing the strain localization process.     

FE-analysis of sheet metal forming processes using continuous contact treatment

Discrete meshes cause stepwise propagation of the contact nodes of a sheet despite the fact that the contact region in the actual forming process is altered very smoothly. This can cause problems of convergence and accuracy in contact-sensitive processes, such as a bending process. In this study, a scheme for a continuous contact treatment is proposed in order to consider the more realistic behavior of the contact phenomena during the forming process. For verification of the proposed method, the contact pressures and forming load are evaluated during the compression forming of a tube. The analysis of a hemispherical dome formed without a blank holder is also presented in order to investigate the effects of the proposed algorithm. The results show that the precise deformation mode is predicted by the utilization of the proposed method.     

A finite element formulation based on non-associated plasticity for sheet metal forming

In the present paper, a finite element formulation based on non-associated plasticity is developed. In the constitutive formulation, isotropic hardening is assumed and an evolution equation for the hardening parameter consistent with the principle of plastic work equivalence is introduced. The yield function and plastic potential function are considered as two different functions with functional form as the yield function of Hill [Hill, R., 1948. Theory of yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. A 193, 281–297] or Karafillis–Boyce associated model [Karafillis, A.P. Boyce, M., 1993. A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids 41, 1859–1886]. Algorithmic formulations of constitutive models that utilize associated or non-associated flow rule coupled with Hill or Karafillis–Boyce stress functions are derived by application of implicit return mapping procedure. Capabilities in predicting planar anisotropy of the Hill and Karafillis–Boyce stress functions are investigated considering material data of Al2008-T4 and Al2090-T3 sheet samples. The accuracy of the derived stress integration procedures is investigated by calculating iso-error maps.     

Marciniak–Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal

The Marciniak–Kuczynski (MK) forming limit model is extended in order to predict localized necking in sheet metal forming operations in which Through-Thickness Shear (TTS), also known as out-of-plane shear, occurs. An example of such a forming operation is Single Point Incremental Forming. The Forming Limit Diagram (FLD) of a purely plastic, isotropic hardening material with von Mises yield locus is discussed, for monotonic deformation paths that include TTS. If TTS is present in the plane containing the critical groove direction in the MK model, it is seen that formability is increased for all in-plane strain modes, except equibiaxial stretching. The increase in formability due to TTS is explained through a detailed study of some selected deformation modes. The underlying mechanism is a change of the stress mode in the groove that results in a delay of the onset of localized necking.     

薄板冲压成型中板料起皱的临界应力分析和预测

针对薄板冲压成型中起皱这一常见的材料失效形式，运用板料压缩失稳理论，提出虚拟刚度变量的概念和板料产生起皱的临界应力计算方法，并借助于计算机仿真技术和有限元计算方法，搜寻并计算得到反映板料各处发生起皱难易程度的临界因子，生成起皱云图来观察材料各部分的稳定状态，预测可能出现起皱的部位，为修改冲压工艺和修模提供依据，通过分析起皱云图得出的结论与实际情况非常接近。     

Initiation and growth of wrinkling due to nonuniform tension in sheet metal forming

An experimental investigation was conducted on the initiation and growth of wrinkling due to nonuniform tension using the Yoshida buckling test. The initiation of wrinkling was detected by strain gages mounted on both surfaces of the samples in the loading and transverse directions. The bifurcation of aluminum auto body sheets appeared to be smooth and much less abrupt than that observed in a steel sheet. A special fixture was designed to, perhaps for the first time, continuously measure the in situ growth of the buckle heights so that the rates of buckle growth were monitored as functions of strain and stress in the loading direction. In contrast to what is commonly believed, it was found that the buckle height is not predominantly determined by the material yield strength, and lower averager value does not increase the rate of buckle growth. Crystallographic texture components and pole figures of the test materials were also measured, and the relationship of plastic anisotropy with wrinkling behavior was investigated by experiments with specimens aligned in the rolling direction, the transverse direction and 45-deg to the rolling direction of the sheet materials.     

Investigation of advanced strain-path dependent material models for sheet metal forming simulations

Sheet metal forming processes often involve complex loading sequences. To improve the prediction of some undesirable phenomena, such as springback, physical behavior models should be considered. This paper investigates springback behavior predicted by advanced elastoplastic hardening models which combine isotropic and kinematic hardening and take strain-path changes into account. A dislocation-based microstructural hardening model formulated from physical observations and the more classical cyclic model of Chaboche have been considered in this work. Numerical implementation was carried out in the ABAQUS software using a return mapping algorithm with a combined backward Euler and semi-analytical integration scheme of the constitutive equations. The capability of each model to reproduce transient hardening phenomena at abrupt strain-path changes has been shown via simulations of sequential rheological tests. A springback analysis of strip drawing tests was performed in order to emphasize the impact of several influential parameters, namely: process, numerical and behavior parameters. The effect of the two hardening models with respect to the process parameters has been specifically highlighted.     

Applications of planar anisotropic yield criteria to porous sheet metal forming simulations

Planar anisotropic yield functions, with rounded vertexes especially near the equal-biaxial direction of the corresponding yield loci, appropriate for some structure metals are employed for the matrix surrounding voids in the present study. The widely adopted Hill anisotropic yield functions are also implemented into the matrix for comparisons. Mechanisms of the void growth, void nucleation, and void coalescence are simultaneously considered here. Effects of the yield function of the corresponding matrix on the sheet metal under two typical sheet forming operations, a hemispherical punch stretching operation and a cup drawing operation, are investigated via a finite element analysis. Thickness strains in various orientations of the sheet are then evaluated. Simulation results show that the yield function of the corresponding matrix plays important roles on the strain distribution and the strain localization as well. Early localization would be found for the sheet with relatively small initial void volume fraction in two operations. Yield functions of the matrix rather influence the earing phenomenon under the cup drawing procedure even similar displacement profiles of the outer boundary could be observed.     

A new method for circular grid analysis in the sheet metal forming test

Computer vision systems are employed to determine the major and minor lengths of deformed elliptic grids while determining a sheet metal's workability. The existing method identifies the ellipse using the least squares analysis. It suffers two drawbacks: assumptions in direct conflict with the observed real-world processes and an undesirable property of orientation dependence. For the remedy, this paper presents a new method that, in addition to achieving the desired property of orientation invariance, discards assumptions that conflict with real-world processes. The proposed method is implemented and tested using simulated and real-world data. Results are reported and compared with those obtained by the existing method.     

On the beneficial effect of rotor suspension anisotropy on viscous-dry hysteretic instability

The destabilizing influence of the internal friction on the supercritical rotor whirl can be efficiently counterbalanced by other external dissipative sources and/or anisotropic suspension systems. The theoretical approach may take the internal dissipation into consideration either by dry or viscous models. Nevertheless, several numerical results and a new perturbation technique of the averaging type prove that similar rotor motions and stability limits are achievable by both models, whence the linear viscous assumption appears preferable. Thus, the internal hysteretic force may be expressed by the product of an equivalent viscous coefficient and the rotor centre velocity relative to a reference frame rotating with the shaft end sections. After calculating the natural frequencies and the response to dynamic imbalances, the stability of the steady motion is checked by the Routh-Hurwitz criterion, focusing the analysis on the individual influence of several characteristic properties, like the gyro structure, the stiffness anisotropy of the supports and their asymmetry, and searching for the external damping level needed for stability. A?fairly interesting result is that the benefit of the suspension anisotropy is most effective for a symmetric rotor mounted at the shaft mid-span and decreases significantly on increasing the configuration asymmetry, even moderately. It is also observed how the stability may somehow be associated with the coupling between progressive and retrograde precession motions.     

A plasticity model for interface friction: application to sheet metal forming

Successful numerical simulations of forming operations require robust and accurate tool-workpiece interface friction models. In this paper we extend the rate-independent, isotropic, isothermal interface friction model proposed by Anand (Anand, L., 1993. A constitutive model for interface friction. Computational Mechanics 12, 197–213) to a rate-dependent formulation. Material parameters in the friction model are determined for lubricated interfaces between Al6111-T4 sheet and D2 tool steel. The lubricants used are MP404 and boric acid; the MP404 lubricant is currently used in industry, whereas boric acid has recently been proposed as a solid-film lubricant for sheet forming by Erdemir (Erdemir, A., 1991. Tribological properties of boric acid and boric acid-forming surfaces. Part i: crystal chemistry and mechanisms of self-lubrication of boric acid. Lubrication Engineering 47, 168–173). The interface friction model is implemented in the finite element code ABAQUS/Explicit (ABAQUS Reference Manual., 1999. Providence, RI), and the finite element program is used to simulate two sheet forming operations: axisymmetric cup-drawing and square pan-drawing. The predictions from the finite element simulation are shown to be in very good agreement with experimental results.     

Analytical and numerical analysis of sheet metal instability using a stress based criterion

Strain based Keeler–Goodwin diagrams are widely used in forming processes to predict onset of local necking. Plastic instability is determined once the forming limit strain is exceeded. Use of these diagrams requires proportional strain paths, which is not necessarily the case in sheet metal forming operations. In many forming processes, the strain path changes during deformation. This may change the forming limit curve significantly. In the paper, a stress based forming limit criterion is adopted to deal with strain path non-linearities. Comparisons with earlier published work on forming limits are made through analytical considerations. Furthermore, the criterion is implemented into the finite element code LS-DYNA and verified numerically against results from large scale bulge tests.     

Texture development and plastic anisotropy of B.C.C. strain hardening sheet metals

A Taylor-like polycrystal model is adopted here to investigate the plastic behavior of body centered cubic (b.c.c.) sheet metals under plane-strain compression and the subsequent in-plane biaxial stretching conditions. The <111> pencil glide system is chosen for the slip mechanism for b.c.c. sheet metals. The {110} <111> and {112} <111> slip systems are also considered. Plane-strain compression is used to simulate the cold rolling processes of a low-carbon steel sheet. Based on the polycrystal model, pole figures for the sheet metal after plane-strain compression are obtained and compared with the corresponding experimental results. Also, the simulated plane-strain stress—strain relations are compared with the corresponding experimental results. For the sheet metal subjected to the subsequent in-plane biaxial stretching and shear, plastic potential surfaces are determined at a given small amount of plastic work. With the assumption of the equivalence of the plastic potential and the yield function with normality flow, the yield surfaces based on the simulations for the sheet metal are compared with those based on several phenomenological planar anisotropic yield criteria. The effects of the slip system and the magnitude of plastic work on the shape and size of the yield surfaces are shown. The plastic anisotropy of the sheet metal is investigated in terms of the uniaxial yield stresses in different planar orientations and the corresponding values of the anisotropy parameter R, defined as the ratio of the width plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial tensile loading. The uniaxial yield stresses and the values of R at different planar orientations from the polycrystal model can be fitted well by a yield function recently proposed by Barlat et al. (1997b).