Minimum weight axisymmetric shell structures

The membrane approximation was used to determine the shapes and thickness distributions for axisymmetric shell structures that can support specified loads with minimum material. A Lagrange multiplier technique was employed. It resulted in Euler field equations and associated boundary conditions for the optimum shells. It also generated expressions for the multipliers directly in terms of the shell geometry. Specific solutions were obtained for the cases where the prescribed forces were uniform pressure, uniform vertical load and the weight of the shell itself. Both the Mises and the Tresca yield condition were used, and the optimum shells were shown to be in a state of yielding everywhere. The optimum shells, however, differed in general from equal strength shells which also satisfied yielding everywhere.     

板料屈服行为及强化规律的研究进展

研究板料塑性成形的理论基础是屈服准则、强化规律以及本构模型。随着新材料、新工艺的不断出现,温度和应变速率对塑性成形过程中的影响也不容忽视,原有的塑性理论已无法满足研究和工程应用的需求。从板料屈服准则研究、包辛格效应与强化模型研究、屈服强化规律试验方法研究以及涉及应变速率和温度的板料屈服强化研究4个方面阐述板料屈服行为及强化规律的研究进展,指出常用屈服准则的特点和不足,说明各种强化模型中组合强化模型仍然是研究重点。试验方法主要从研究屈服轨迹的双向拉伸试验及确定强化模型参数试验的2个方面进行介绍。此外,指出针对板料在复杂应力状态下应力张量与应变张量之间的涉及应变率和温度的屈服准则和相应的流动准则的本构关系还有待研究。提出随着新材料、新工艺的不断出现,涉及应变速率和温度的屈服准则和强化规律、试验方法以及在有限元模拟中的应用等研究将是未来的研究热点。     

Ideal forming—II. Sheet forming with optimum deformation

A method is proposed for the design of ideal forming processes. The objective is to directly determine ideal configurations for both the initial and the intermediate stages that are required to form a specified final shape. At the start, it is assumed that formability of local material elements is optimum when they deform in minimum work paths. The ideal global process is then defined as the one having such local deformations optimally distributed in a final shape. Mathematical procedures for implementing these conditions are derived. Primary emphasis is placed upon forming of sheet (membrane) materials under plane-stress conditions, although many of the ideas are applicable to more general forming processes. Sample results illustrate optimum process parameters which the ideal forming theory can provide.     

弹性圆柱壳的稳定性优化设计

研究任意轴对称边界条件下和受均布法向载荷作用圆柱壳的稳定性优化设计问题，即极大化屈曲临界载荷。利用能量原理分析轴对称变厚度圆柱壳的分支点屈曲，将求解屈曲临界载荷变成求解广义特征值方程，使圆柱壳稳定性优化设计成为极大化最小特征值问题。实际算例验证了本方法的有效性。研究结果可用于圆柱壳的加肋优化设计。     

Anisotropic plasticity with application to sheet metals

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.     

Forming limit investigation of friction stir welded sheets: influence of shoulder diameter and plunge depth

The main aim of the present work is to analyze the influence of shoulder diameter and plunge depth on the formability of friction stir welded sheets. The base material used for welding and forming was AA6061-T6. Formability evaluation was performed through limiting dome height tests. The forming limit curve, FLC (only in the stretching region), thickness distribution, and strain hardening exponent of the weld region were monitored during formability studies. It is found from the work that the forming limit of friction stir welded sheets is better than unwelded sheets. In general, with an increase in shoulder diameter and plunge depth, the forming limit is found to improve considerably. With a decrease in thickness gradient severity and an increase in strain hardening exponent (n) of the weld region, the forming limit is found to increase. The increase in n value of the weld region is believed to occur because of the reduction in dislocation density. The maximum thickness difference is higher in the retreating side, rather than in the advancing side, of the weld. This is due to the differential straining and hardness levels attained by both sides during friction stir welding.     

Bifurcation analysis of wrinkling formation for anisotropic sheet

Surface distortions in the form of localized buckles and wrinkles are often observed in the sheet metal forming process. In many cases the presence of wrinkles in the final praduct is unacceptable for the purposes of assembly. Because of the trend in recent years towards thinner gauges and higher strength, wrinkling is increasingly becoming a more common and troublesome mode of failure in sheet metal forming. In this study, a numerical analysis for evaluating a wrinkling limit diagram (WLD) for an anisotropic sheet subjected to biaxial plane stress is presented. Here the scheme of plastic bifurcation theory for thin shells based on the Donnell-Mushtari-Viasov shell theory is used. The effects of the various material parameters (yield stress, strain hardening coefficient and normal anisotropy parameter) and geometric parameters on WLD are investigated numerically and compared with Kawai's and Havranek's experiment(1975).     

在材料厚度临界值时封头设计厚度的选取

阐述了材料力学性能随板厚范围变化而变化的问题；举例说明当考虑封头加工成形减薄量而增加板厚时，在相同设计温度条件下，由于板厚的增加有些材料许用应力会相应降低，导致封头成形后的最小厚度不能满足强度要求。总结了当封头设计厚度处于相应材料厚度临界值时，设计人员应适当增加最小设计厚度、工艺人员应考虑尽量减小成形减薄量，以保证封头成形后的最小厚度仍能满足强度要求。     

Molecular dynamics simulation of deformation behavior in amorphous polymer: nucleation of chain entanglements and network structure under uniaxial tension

In order to clarify the mechanical behavior of molecular chains in amorphous polymers, a molecular dynamics simulation is conducted on a nanoscopic specimen of amorphous polyethylene under uniaxial tension. The specimen involves 3542 random coil molecular chains composed of 500–1500 methylene monomers with about two million methylene groups. The stress–strain curve shows a linear elastic relationship at the initial stage of _zz0.03 at . Then the material “yields” by elongating without stress increase up to the strain of 1.5, where strain hardening appears. Careful investigation of changes in dihedral angle and morphology of all molecular chains reveals that the gauche→trans transition takes place during yielding, generating a new network-like structure composed of entangled molecular clusters and oriented chains bridging them. The strain hardening is due to the directional orientation and stretching of molecular chains between entanglements in the nucleated structure.     

基于三剪统一强度准则的厚壁圆筒自增强分析

基于三剪统一强度准则,考虑材料应变强化效应、包辛格效应、拉压异性及中间主应力的影响,采用双线性强化材料模型对厚壁圆筒进行自增强分析,得到了厚壁圆筒加载应力、残余应力和工作应力的解析解,提出了最佳自增强压力的计算方法,探讨了拉压比、强度准则变化参数的影响,比较了自增强处理和非自增强处理及双线性强化模型和理想弹塑性模型厚壁圆筒的应力分布差异。研究结果表明：厚壁圆筒的最佳自增强压力随半径比和强度准则参数的增大而增大;工作时的最大等效应力随半径比和强度理论参数的增大而减小,随拉压比的增大而增大;自增强等效应力的最大值在弹塑性分界面处,且应力沿壁厚的分布较均匀;与理想弹塑性模型相比,双线性强化模型所对应的弹塑性分界面半径和残余应力较小,且随着自增强压力的增大,两种模型的差值越来越大;等效应力随半径比的变化规律可为厚壁圆筒选择合理的壁厚提供一定的参考;自增强技术可改善厚壁圆筒工作时的实际应力分布,提高其极限承载能力。     

Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet

Forming limit curves at neck and at fracture have been experimentally determined, and surfaces of fractured dome specimens have been observed optically and in the SEM, for an automotive AA6111-T4 sheet material. Various continuum ductile fracture criteria from the literature along with the assumptions of power law hardening, Hill’s quadratic yield criterion, and proportionality of stress and strain paths have been utilized for prediction of forming limit curve at fracture and compared with the experimental curve to assess the applicability of the different fracture criteria. The maximum shear stress criterion by Tresca predicts reasonably well the fracture limits of AA6111-T4 sheet material for a range of strain ratios, and is consistent with the microstructural observations. The criterion can be used to predict fracture limit curves from uniaxial tensile data and plane strain limit at fracture. A methodology for incorporating such a ductile fracture criterion into FE simulations of sheet stampings for prediction of fracture is discussed.     

Numerical and experimental analysis of wall thickness variation of a hemispherical PMMA sheet in thermoforming process

In thermoforming, a heated plastic sheet is stretched into a mold cavity by applying pressure, eventually assisted by direct mechanical loading. Since upon its contact with the cold surface of the mold the sheet is prevented from undertaking any further deformation, the forming sequence induces a thickness variation in the final part. This fundamental inherent defect of thermoforming technology highly affects the optical characteristics of optical products. Therefore, the more uniform the wall thickness, the less chance optical defects will occur. In this research, the production process of a hemispherical transparent PMMA sheet as an optical product was numerically simulated. The simulated process is a two-step process comprising a combination of free forming and plug-assisted forming. In the simulation, the acrylic sheet is assumed to undergo a nonlinear and large elastic deformation which merits application of hyperelastic models. Mooney–Rivlin hyperelastic model is used as the constitutive equation. The obtained numerical results are validated with those achieved from the experiments. Different combinations of free forming and plug-assisted forming methods are studied based on what percentage of total height of the final part is produced by each method. Finally, an optimum combination of the two-step forming process is proposed. With this optimum combination, satisfactorily uniform wall thickness and minimal mold marks on the product surface will be achieved.     

内压圆筒厚度计算公式分析讨论

GB 150—2011中采用的是弹性失效准则,规定对设计压力p≤0.4[σ]t的内压圆筒厚度按中径公式进行设计。JB 4732—1995中规定对设计压力p≤0.4[σ]t的内压圆筒厚度按中径公式进行设计,设计压力p>0.4[σ]t时按Tresca全屈服压力进行设计。比较研究表明:基于弹性失效准则时,中径公式算出的厚度最薄;基于塑性失效准则时,中径公式算出的厚度最厚;当径比较小时,按Tresca全屈服压力和中径公式算出的内压圆筒厚度相差很小,在工程设计中,可以统一采用Tresca全屈服压力计算内压圆筒壁厚。     

奥氏体不锈钢应变强化工艺及性能研究

针对奥氏体不锈钢延性好但屈服强度低的问题,提出采用应变强化工艺来提高材料屈服强度。分析应变强化工艺中两个关键工艺参数——应变速度和应变量对材料力学行为的影响,指出应变速度不宜过慢,否则会出现锯齿形屈服行为,对材料性能造成不利影响。经应变强化后的奥氏体不锈钢在显著提高强度的同时,仍能保持较好的韧性。通过金相组织分析、马氏体体积分数测定等结果表明,将应变量控制在10%以下,强化后奥氏体组织仅发生少量的α′马氏体相变,对材料的力学性能影响不大,且材料的微观组织也没有明显变化。研究结果表明,采用应变强化技术在大幅提高奥氏体不锈钢屈服强度的同时,对材料的其他力学性能均不造成大的影响,从而为压力容器的安全运行提供有力保证,可实现压力容器的轻型化设计,经济和社会效益显著,应用前景广阔。     

A simplified analysis of the effect of microstructure gradient on the stress relief of aluminum plates and extrusions

Many bulk forms of metal products are quenched after heat treatment in order to preserve material characteristics. Rapid quenching results in large thermal stress gradients that lead to high levels of residual stress. For products such as plates and extrusions, stretching by a few percent can reduce these stresses, but the stresses are not completely relieved. This report presents a simplified analytical model of the stress relief process illustrating the effects of through-thickness property gradients on residual stress after stretching. The basic conclusion is that for plates with uniform yield surface shapes through the thickness, the through-thickness residual stress range after stress relief is equal to the strength range in the direction of stretch. In extrusions, the bow after stress relief is proportional to this strength range. Cases are also considered in which the yield surface shapes range from isotropic to anisotropic through the thickness. Plastic anisotropy can perturb the effect of strength range on residual stress.     

基于ANSYS的铝制错列锯齿翅片成形回弹研究

以铝制错列锯齿翅片为研究对象,利用ANSYS/LS-DYNA非线性动力有限元求解功能,模拟了翅片成形过程与卸载后回弹变形的全过程,得到了成形过程中任意时刻各处的应力、应变和卸载后板料的回弹结果。研究翅片成形过程中压边力、板料厚度、冲压速度、刀具齿形组合、刀具圆角半径等对回弹的影响。利用回弹规律进行模具补偿设计,以此优化专用翅片成形机及模具的结构参数和工艺参数,从根本上提高铝制错列锯齿翅片的制造精度,为翅片的结构优化设计提供了可靠的依据。     

圆筒形件拉深失稳及各因素影响分析

对板料成形中圆筒形件拉深的破裂失稳及产生破裂失稳的临界压边力进行研究.由于凸、凹模圆角及其间隙的存在,圆筒形件拉深的筒壁区实际为凸、凹模圆角之间的公切线部分.根据Mises-Hill屈服函数及Tresca准则求出凸缘变形区、凹模圆角区和筒壁区的应力分布,得到危险断面处的应力表达式,从而求出不产生破裂失稳的临界压边力的解析表达式,并进一步分析获得拉深比、硬化指数、厚向异性系数、摩擦因数以及径向推力等因素对临界压边力的影响规律.采用液压压边与周缘加径向推力的拉深模具对08Al板料进行拉深试验,试验结果与理论计算结果具有很好的一致性.     

应变时效对双相钢和低合金高强钢屈服强度及应变硬化率的影响

通过力学性能测试和显微组织观察研究了应变时效对双相钢和低合金高强钢屈服强度及应变硬化率的影响。结果表明:经过2%预应变之后,双相钢的屈服强度提高了106MPa,低合金高强钢的屈服强度提高了28MPa;预应变之后再经历烘烤,双相钢的屈服强度提高了149MPa,而低合金高强钢的屈服强度只提高了66MPa;预应变或烘烤硬化之后,两种钢的应变硬化率均降低,但双相钢仍然具有很强的应变硬化能力,其应变硬化率接近于低合金高强钢未预应变条件下的;铁素体马氏体组织赋予了双相钢比低合金高强钢更强的应变硬化能力。