Numerical analysis of superplastic bulging for cavity-sensitive materials

A simulation of the thinning development until fracture for superplastic material bulging deformation under hydrostatic pressure is realized by the rigid-viscoplastic finite-element method by introducing a model of cavity growth. The deformation and the failure are considered as a combination and interaction process between the inhomogeneous geometric thinning development and the internal cavity evolution, which are controlled by the strain-rate sensitivity and the cavity growth-rate of the material.     

在电场下的超塑变形

介绍在强电场下进行的超塑性拉伸实验，揭示了外加强电场及超塑变形条件对超塑性的影响。实验结果表明，电场降低了材料流动应力和应变硬化指数，提高了拉伸延伸率和应变速率敏感性指数，同时电场使空洞化速率减慢。还介绍了硬铝ＬＹ１２ＣＺ在强电场下超塑变形时的合理工艺参数。     

Blank optimization for free bulging of Inconel 718 to maximize bulged height at high temperatures

Thickness profiled blank is designed via the optimization technique to maximize the bulged height in free bulging for Inconel 718. The thickness of the blank is described by the Bezier curve by using four control points. The location of each control points is used for the design variables of optimization. The material parameters for the flow stress equation of Inconel 718 are obtained from the free bulging test at constant pressure condition by using a flat blank and verified via numerical analysis. The objective function and constraints for optimization are the maximization of the bulged height within a limited strain range. The equivalent static load method for non-linear static response structural optimization with a move limit scheme is used for optimization. The result of optimization shows 21.95% increased bulged height and uniformly distributed strain after bulging. The free bulging test using blank with optimized profile is conducted to verify the optimization process. The results of bulged height and deformed shape are compared with those from numerical analysis, and the comparison shows good agreement.     

A quantitative model of the blow-forming of spherical surfaces in superplastic sheet metal

The blow-forming of a flat superplastic metal sheet to a spherical surface is analysed with a mathematical model based on the classical theory of liquid bubbles. The model enables a quantitative account to be given of the effect of the strain-rate sensitivity, flow stress and temperature of the metal on the rate of blow-forming and the replication of detail. Formulae are derived which enable the superplastic flow stress and strain-rate sensitivity to be calculated from simple blow-forming tests.     

Influence of material parameters on the hydrostatic bulging of a circular diaphragm

The plastic bulging of pressurized circular membranes is examined with particular attention to the effect of material parameters on the inherent inhomogeneity of the test. A rigid-viscoplastic behaviour based on flow-theory of plasticity is considered for materials with transversely isotropic properties. The numerical calculations display the effects of strain-hardening, strain-rate hardening and yield surface shape on the bulging pressure, the strain-distribution and the bulge shape. Comparisons with available experimental data are also presented.     

Rigid viscoplastic finite element analysis of the gas-pressure constrained bulging of superplastic circular sheets into cone disk shape dies

This paper describes the development of a rigid viscoplastic finite element formulation for analysing the gas-pressure constrained bulging processes of superplastic circular sheets in cone disk shape dies. In this formulation, the effects of strain hardening and strain-rate sensitivity of materials are included, and the boundary friction condition is introduced into the formulation in the form of friction functional. The finiteelement model based on the membrane theory is developed, and then applied to simulate superplastic constrained bulging processes. The solutions by the rigid viscoplastic finite element method are compared with existing experimental data. The influences of the geometrical parameters of the dies, the friction factor in the friction functional, the strain hardening and the strain-rate sensitivity on the inhomogeneity of thickness distribution are studied in detail.     

Plastic bulging of sheet metals at high strain rates

The biaxial bulge test is a material test for sheet metals to evaluate formability and determine the flow stress diagram. Due to the biaxial state of stress induced in this test, the maximum achievable strain before fracture is much larger than in the uniaxial tensile test. A new dynamic bulge testing technique is simulated and analyzed in this study which can be performed on a conventional split Hopkinson pressure bar (SHPB) system to evaluate the strain-rate dependent strength of material at high impact velocities. Polyurethane rubber as pressure carrying medium is used to bulge the OFHC copper sheet. The use of hyperelastic rubber instead of fluid as a pressure medium makes the bulge test simple and easy to perform. The input bar of SHPB is used to apply and measure the bulging pressure. The finite element simulation using ABAQUS/explicit and analytical analysis are compared and show good correlation with each other. The results clearly show that as the strain-rate increases, the strength of the OFHC copper increases. From the study, a robust method to determine the material behavior under dynamically biaxial deformation conditions has been developed.     

高温超塑胀形实验装置

超塑变形具有很强的结构敏感性，其变形规律与应力状态和变形路径有关，因此在处理二维胀形问题时，不能直接引用一维拉伸的实验数据，胀形实验装置便成为理论研究和制定工艺方案的重要手段。设计了高温超塑胀形实验装置，并针对实验装置进行了程序设计。该实验装置具有氩气净化、炉外加热、温度和压力闭环控制，能同时施加正压、背压并按设定的恒压、恒极点胀形速度和应变速率进行实验，同时可以无接触地记录胀形件极点高度与时间的关系，并观察其形貌变化过程。     

Plastic deformation analysis of strain-rate sensitive materials under plane strain conditions

The two-dimensional plane strain equation of plastic flow in accordance with the Levy-Mises constitutive relation is expressed in terms of stream functions of complex variables. Expressions for the stress, strain-rate and velocity are derived, assuming the stream function in the forms of both the summation and product of conjugate flow functions, for plastic flow in a nonlinear viscous (strain-rate sensitive) medium. The plastic states are also derived using a mixed mode solution expressed in terms of non-separable, independent conjugate complex variables. Application of the summation form solution is illustrated through the block indentation problem. Calculations are made on the effect of variation of the strain-rate sensitivity exponent on the contact stress. The predicted behavior of the contact stress suggests the possibility of the development of a specially instrumented plane strain block indentation test for the rapid determination of the strain-rate sensitivity of real materials. By reducing the results of the indentation of a perfectly plastic material it is found that the contact stress is uniform and the external load is constant. The stress on the contact surface obtained using the present analysis is identical to that available from a slip line solution to the problem.     

Damage evolution in creep bulging of thin sheet metal

The creeping motion of thin sheet metal, damaged by artificial cavities is observed in bulging tests and simulated ‘semi’-analytically. The sheet metal satisfies Norton’s Law for secondary creep and is subjected to a bi-directional stretch. The stretch is produced by creep bulging through elliptical dies with the virtue of sustaining nearly uniform background stress ratio for each aspect ratio of the die axes. In order to reach large deformations with significant shape evolution of the cavities, the tests were conducted at superplastic conditions. The sheet is double layered (only one layer is cavitated) made of Tin–Lead (50–50 Pb–Sn). The measured damage growth is compared to an approximate simulation. The simulation of the damage evolution, throughout its time history, makes repeated use of a so-called “Green-function solution” for the motion of a single isolated cavity in an infinite viscoplastic continuum. The solution is modified from Muskhelishvili’s elastic solution by replacing the elastic shear modulus by a “viscous-like” variable (“plastic shear modulus”) which depends (non-linearly) on the evolved average strain-rate. Similarly, the stresses in the ligaments between cavities were averaged to approximate the local stress concentrations. Due emphasis is given to the rotation of each elliptical cavity, beside its expansion (contraction) and elongation.     

Deformation analysis of plastic strain rate hardening material using stress function under plane strain condition

The two-dimensional plane strain equation of plastic flow in accordance with the Levy-Mises constitutive relation is expressed in terms of stress functions of complex variables. Expressions for the stress, strain rate and velocity are derived for plastic flow in a non linear viscous medium assuming the stress function in the form of both the summation and product of conjugate stress functions. The plastic states are derived, also using a mixed mode solution expressed in terms of non-seperable, independent conjugate complex variables.The analysis of the block indentation associated with a nonlinear viscous (strain rate hardening) material under plane strain condition using the product form solution is performed. The effect of the variation in the strain-rate hardening exponent on the contact stress is investigated. The predicted behavior of the vertical component of the contact stress suggests the possibility of the development of a specially instrumented plane strain block indentation tests, for the rapid determination of the strain-rate sensitivity of the real material. The vertical contact stress and strain-rate obtained from the product of the complex conjugate stress function are compared with those obtained from the summation form of the complex conjugate stream function.     

Fatigue behaviour of a commercial zinc-aluminium eutectoid alloy

Constant-amplitude, flexural-fatigue tests have been carried out over the frequency range 8–100 Hz and the temperature range 293–373°K on a commercial zinc-aluminium alloy of basically eutectoid composition. This alloy is highly superplastic at 530°K, when the strain-rate sensitivity of the flow stress index, m, 0·5. At 293°K some residual superplasticity exists and this manifests itself as a frequency effect in the fatigue behaviour. This effect is almost certainly the result of room-temperature, strainrate sensitivity; it is shown by the fact that when the superplastic microstructure is destroyed, the frequency effect disappears. Finally, it is shown that the model proposed by Morrow successfully predicts the fatigue life of this alloy.     

拉伸变形应变速率敏感性指数的力学涵义及其规范测量

鉴于建立超塑性变形定量力学解析理论的重要性,从分析Backofen超塑性拉伸的本构方程出发,讨论了方程中的材料参数k和应变速率敏感性指数m的力学涵义。提出了恒应变ε、恒速度υ和定载荷F三种典型变形路径条件下应变速率敏感性指数的规范测量公式。对每种变形路径又提出应变速率敏感性指数的传统测量方法和计算机模拟精确测量方法,并作了精度对比分析。给出了典型超塑Zn-5%Al合金在常态（18℃）和超塑状态（340℃）时三种变形路径下应变速率敏感性指数m ε、m υ和m F的实测结果。由于三者之间不但存在大的偏差,而且随ε的变化规律也各异。这就从试验上判明,即使在相同的应力状态下,应变速率敏感性指数也与变形路径密切相关。由此便向力学理论提出新的问题,要求从理论上解答偏差和变化规律不同的原因,进而揭示其力学本质。     

Plastic behavior of superplastic material moving between two coaxial rotating cylinders

A one-dimensional stationary boundary problem is solved and the related plastic behavior is analyzed for a superplastic material moving between two coaxial rotating cylinders. The well-known relationship for a non-linear viscous material is used as a constitutive relation, which reduces the problem to an ordinary differential equation. The effects of the strain-rate sensitivity and geometrical factor on the kinematics and stress-strain distribution are analyzed. From this analysis it is found that as the value of m decreases, the deformation gradient increases, and localization of the deformation in the vicinity of the interior cylinder takes place. It is shown that the solution obtained fully coincides with the known one for the Couette flow of a Newtonian viscous fluid as a special case.     

Influence of strain-hardening and strain-rate sensitivity on the permanent deformation of impulsively loaded rigid-plastic beams

A simple method is presented for estimating the combined influence of strain-hardening and strain-rate sensitivity on the permanent deformation of rigid-plastic structures loaded dynamically. A study is made of the particular case of a beam supported at the ends by immovable frictionless pins and loaded with a uniform impulse. The results of this work indicates that considering strain-hardening alone when appropriate or strain-rate sensitivity alone gives permanent deformations which are similar to those predicted by an analysis retaining both effects simultaneously.     

Characterization of double strain-hardening behavior using a new flow of extremum curvature strain of Voce strain-hardening model

The traditional flow models with an emphasis on Voce family flow models are criticized using a typical monotonic strain-hardening material and a double strain-hardening (DSH) material. The DSH behavior is quantitatively expressed in detail using SUS304. They are, however, negatively evaluated especially for the DSH material that simultaneously experiences wide ranges of strain (e.g., during cold forging). After characterizing the Voce strain-hardening model (VSHM) with an emphasis on not only asymptotic stress but also a new concept of extremum curvature strain (ECS), the Voce-Ludwik model coupled with ECS is presented to describe the DSH flow behavior, based on the mathematical characteristics of VSHM. It has been found that the proposed Voce-Ludwik model can reflect DSH behavior using the nature of the strain at the ECS, which has the distinct advantage of modeling thermoviscoplastic flow behaviors of the DSH materials including stainless steels, copper alloys, aluminum alloys, etc.

     

On the measurement of friction coefficient utilizing the ring compression test

The main objective of this research was to investigate whether generalized friction calibration curves, as recommended in the literature for use with ring compression tests, are applicable to all types of materials and test conditions. Specifically, the effects of material properties, strain-rate sensitivity, and “barreling” on the behavior of friction calibration curves were investigated. To this end, a series of ring compression tests were conducted in order to determine the magnitude of the friction coefficient, μ, as well as the corresponding calibration curves for two types of modeling materials, white and black Plasticine. The experiments were first conducted using the Physical Modeling Technique (PMT) and then simulated via an elastic–plastic finite element code (ABAQUS). In contrast to the results available in the literature, where the same friction calibration curves are recommended for all types of materials and test conditions, the results of this investigation showed that friction calibration curves are indeed affected by the material properties and test conditions and every material possesses its own distinctive friction calibration curve.     

Investigation of deformation and collapse mechanism for magnesium tube in axial crushing test

This paper demonstrates the quasi-static axial compression and high-speed axial compression tests of extruded magnesium alloy circular tubes for evaluating the crash and fracture behavior of mg parts. To capture the buckling and fracture behavior of Mg tube during the axial compression tests, FE simulation adopts different types of flow curves depending on the deformation mode such as tension and compression with LS-DYNA software. The Mg tube undergoes compressive plastic strain prior to buckling while according to the model based on Hill yield criterion only bulging along the radial direction is predicted. Due to the tension-compression asymmetry of Mg alloys, diameter of Mg tube expands largely at the initial plastic strain before having bulging or folding while only a bulging mode typical for materials with cubic crystal structure can be predicted. Simulation results such as punch load and deformation mode are compared with experimental results in the axial crushing test with AZ61 alloy.     

RETRACTED ARTICLE: Determination of the radial inertia-induced transition strain-rate in split Hopkinson pressure bar tests

The transition strain-rate represents the start of significant contributions from radial inertia-induced lateral confinement to the axial compressive strength of the tested materials. However, it has been misinterpreted for decades by many studies as the start of significant strain-rate effect on the dynamic uniaxial compressive strength of the tested materials. Based on the dimensional analysis and numerical and experimental data, a semi-empirical formula to determine the transition strain-rates for various engineering materials is proposed. Errors in SHPB tests due to the contribution of the lateral confinement effect are estimated. It is found that, except for metals, transition strain-rates of concrete-like, rock-like and polymeric materials are unfortunately located in the valid range of SHPB tests that has been commonly accepted by research communities. Thus SHPB tests cannot be treated as valid measurements under uniaxial stress state when strain-rates are greater than the transition strain-rate.     

H13钢超塑成形性能研究

对 H13钢的超塑性能进行了试验研究 ,得出了变形温度和应变速率对 H13钢超塑性能的影响规律。结果表明 :H13钢经 10 0 0℃三次循环淬火后 ,晶粒度可达 13级 ;在温度为 840℃ ,应变速率为 1.6× 10 - 4 s- 1的条件下拉伸 ,其最大延伸率为 185 % ,流变应力为 31MPa,m值为 0 .2 6。本研究为 H13钢的超塑性成形工艺提供了最佳工艺参数。