基于全量理论的金属体积成形有限元模拟研究
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摘要
金属体积成形在金属加工制造业中有着不可替代的作用,是涉及到几何、材料和边界条件三重非线性的复杂物理过程。目前基于增量理论的有限元数值模拟技术在体积成形分析研究中被日益广泛的应用。基于增量理论的有限元法,能够准确地追溯成形过程的历史,这一点对于分析具有强非线性的体积成形问题十分重要。但是,这种方法分析模型复杂,计算量大,因此难以快速提供分析结果,也不适合于产品的初期概念设计和加工工艺方案的预分析。
全量理论是增量理论在简单加载条件下的积分,理论意义上一般不能普遍适用,但是由于该理论比较简单,很多人试图将它应用于各种复杂加载情况。大量实际问题的分析表明,对于许多偏离了比例加载路径的问题,采用全量理论可以得到与增量理论相近的结果。全量理论具有推广应用于偏离比例加载问题的潜力,而且在计算的准确性方面也有自己的特点。全量理论已经成功地应用于板料成形的有限元模拟,运用基于全量理论的冲压成形一步和多步模拟方法可以获得与增量有限元法相近的模拟结果,而且分析模型十分简单、计算时间很短。与板料成形相比,体积成形中材料的变形量更大、变形路径的变化更复杂、工件与模具型面的接触难以确定,将全量理论应用于体积成形问题比前者要困难得多,因此尽管全量理论在板料成形模拟中的应用已经取得了很大的进展,但是其在体积成形中的应用研究尚鲜见报道。
本文对全量理论在金属体积成形有限元模拟中的应用进行了较为深入的研究,主要研究内容和结果如下:
提出了一种基于全量理论的金属体积成形有限元方法。在进行大变形情况下应变、应力的度量和全量本构关系描述的基础上,从极值功原理出发,针对刚塑性不可压缩材料,基于约束变分原理在静力平衡条件下使以总塑性功和等效外力功所构成的近似塑性势能取最小化,推导了刚塑性全量有限元的求解列式。
对金属体积成形全量有限元方法所涉及的若干技术处理方法展开了研究。提出了以虚拟滑动约束处理大步计算边界条件的方法;提出了等效外力功的估算方法;采用构形预测和网格映射相结合的方法,解决了初始解确定问题;提出了适合于具有近似刚性区体积成形问题的局部自由度约束技术,旨在增强全量大步长计算的收敛性。
构造了一步全量模拟方案,并开发了一步有限元计算程序。一步模拟忽略了变形的中间历史环节,以一个大计算步在成形过程中的初始和终了构形之间进行有限元求解。构造了多步全量模拟方案,并开发了多步有限元计算程序。多步模拟根据整个成形过程中变形路径和接触状态的变化进行计算步的划分,以多个大增量步进行有限元求解。多步模拟基于全量理论追踪变形全路径的变化,通过近似地考虑成形接触历史变化来提高外力功估算的准确度,使全量有限元方法可以解决更具一般性的体积成形问题。
通过以平面应变、轴对称厚壁筒受内压力成形及平面应变压缩成形过程为算例进行正向一步或多步数值模拟,分析了变形路径、材料硬化和边界条件等因素对全量有限元计算的影响,探讨了全量理论在金属体积成形有限元模拟中的适用性。
对圆柱体镦粗和平板轧制过程进行了正向一步模拟。针对平板轧制的一步模拟,提出了轧制过程中工件与轧辊之间摩擦边界问题的处理方法。将一步有限元法的计算结果与增量有限元法的计算结果和实验数据进行了对比,验证了前者的正确性。
对圆棒正挤压和方坯拔长过程进行了正向多步模拟,并对圆棒正挤压进行了相关实验研究。将多步有限元法的计算结果与增量有限元法的计算结果和实验数据进行了对比,验证了前者的可行性和有效性。
Bulk metal forming plays an important role in metal processing and manufacturing, which is a complicated physical process with ternary nonlinearity of geometry, material and boundary condition. At present, finite element (FE) simulation technique based on incremental theory is widely applied in the study of bulk metal forming. The history of deformation process could be traced accurately in the incremental FE approach, which is very important for analysis of bulk forming problems with intensive nonlinearity. However, incremental FE approach, in which analyzed model is complex and computing effort is considerable, couldn’t provide analyzed results rapidly, which couldn’t be suitable for initial concept design of product and predictive analysis of process technic.
Deformation theory is the integral of incremental theory in the condition of simple loading, which couldn’t be used in general situations theoretically. However, the deformation plasticity solution is preferred for many applications of complex loading problems due to the mathematical simplicity. It is indicated that deformation theory could provide very close results compared with incremental theory for many problems deviating proportional loading path by plentiful analysis of practical problems.
Deformation theory has the potential of applications for problems deviating proportional loading and has its own characters of computation accuracy. Deformation theory has been applied for sheet metal forming FE simulation successfully, by which one-step and multi-step simulation methods could provide results in close agreement with incremental FE predictions with very simple model and very short computing time. Compared with sheet forming processes, the deformation is larger and the deformation path and the contact history of the deformed part are more complicated in bulk metal forming processes. So it is more difficult to apply the deformation theory to bulk forming simulation. Consequently, despite the remarkable progresses that have been achieved in FE approach based on deformation theory for sheet metal forming, the applications of that in bulk metal forming are seldom. The research on application of deformation theory to bulk metal forming FE simulation is carried out in the dissertation, the main works and innovations are:
A bulk metal forming FE approach based on deformation theory is put forward. The strain and stress under large deformation condition and deformation constitutive relationship are defined. This approach is implemented to minimize approximated plastic potential derived from the total plastic work and the equivalent external work in static equilibrium for incompressible rigid-plastic materials based on constraint variational principle under the principle of extremum work. The rigid-plastic deformation FE equations are deduced.
Several key techniques of bulk metal forming deformation FE approach are studied. The fictitious sliding constraint is proposed for dealing with boundary condition of large-step computation. The estimation of equivalent external work is put forward. The initial solution is present by presetting configuration and mapping meshes. The local constraint of freedom is proposed for bulk forming problems with approximate rigid region in order to improve the convergence of deformation large-step computation.
The one-step simulation scheme based on deformation theory is proposed and one-step FE simulation program is developed. One-step simulation, which neglecting deformation history, is performed by FE calculation in one large step between the initial and final configurations of process. The multi-step simulation scheme based on deformation theory is proposed and multi-step FE simulation program is developed. Multi-step simulation, in which the computing step is divided by considering variation of deformation path and contact situation in whole process, is performed by FE calculation in multiple large steps. In multi-step simulation, it is realized to track the variation of entire deformation path by using deformation theory and consider the variation of contact history to improve the accuracy of external work estimation, which result in application of deformation FE approach to bulk forming problems more generally.
The one-step and multi-step numerical simulations are performed by taking plain strain and axisymmetric thick-walled cylinder forming under inner pressure and plain strain compression as examples to analyze the effect of deformation path, material’s hardening and boundary condition on deformation FE calculation. The applicability of deformation theory in bulk metal forming FE simulation is discussed.
The one-step forward simulations of cylindrical upsetting and flat plate rolling are performed. As for one-step simulation of flat plate rolling, the treatment of friction boundary problem between workpiece and roller during process is put forward. The results of one-step simulation are compared with those of incremental simulation and experiment to verify the correctness of the proposed approach.
The multi-step forward simulations of cylindrical bar forward extrusion and rectangular billet elongation are performed. The experiment of cylindrical bar forward extrusion is carried out. The results of multi-step simulation are compared with those obtained by incremental simulation and experiment to verify the feasibility and validity of the proposed approach.
全量理论是增量理论在简单加载条件下的积分,理论意义上一般不能普遍适用,但是由于该理论比较简单,很多人试图将它应用于各种复杂加载情况。大量实际问题的分析表明,对于许多偏离了比例加载路径的问题,采用全量理论可以得到与增量理论相近的结果。全量理论具有推广应用于偏离比例加载问题的潜力,而且在计算的准确性方面也有自己的特点。全量理论已经成功地应用于板料成形的有限元模拟,运用基于全量理论的冲压成形一步和多步模拟方法可以获得与增量有限元法相近的模拟结果,而且分析模型十分简单、计算时间很短。与板料成形相比,体积成形中材料的变形量更大、变形路径的变化更复杂、工件与模具型面的接触难以确定,将全量理论应用于体积成形问题比前者要困难得多,因此尽管全量理论在板料成形模拟中的应用已经取得了很大的进展,但是其在体积成形中的应用研究尚鲜见报道。
本文对全量理论在金属体积成形有限元模拟中的应用进行了较为深入的研究,主要研究内容和结果如下:
提出了一种基于全量理论的金属体积成形有限元方法。在进行大变形情况下应变、应力的度量和全量本构关系描述的基础上,从极值功原理出发,针对刚塑性不可压缩材料,基于约束变分原理在静力平衡条件下使以总塑性功和等效外力功所构成的近似塑性势能取最小化,推导了刚塑性全量有限元的求解列式。
对金属体积成形全量有限元方法所涉及的若干技术处理方法展开了研究。提出了以虚拟滑动约束处理大步计算边界条件的方法;提出了等效外力功的估算方法;采用构形预测和网格映射相结合的方法,解决了初始解确定问题;提出了适合于具有近似刚性区体积成形问题的局部自由度约束技术,旨在增强全量大步长计算的收敛性。
构造了一步全量模拟方案,并开发了一步有限元计算程序。一步模拟忽略了变形的中间历史环节,以一个大计算步在成形过程中的初始和终了构形之间进行有限元求解。构造了多步全量模拟方案,并开发了多步有限元计算程序。多步模拟根据整个成形过程中变形路径和接触状态的变化进行计算步的划分,以多个大增量步进行有限元求解。多步模拟基于全量理论追踪变形全路径的变化,通过近似地考虑成形接触历史变化来提高外力功估算的准确度,使全量有限元方法可以解决更具一般性的体积成形问题。
通过以平面应变、轴对称厚壁筒受内压力成形及平面应变压缩成形过程为算例进行正向一步或多步数值模拟,分析了变形路径、材料硬化和边界条件等因素对全量有限元计算的影响,探讨了全量理论在金属体积成形有限元模拟中的适用性。
对圆柱体镦粗和平板轧制过程进行了正向一步模拟。针对平板轧制的一步模拟,提出了轧制过程中工件与轧辊之间摩擦边界问题的处理方法。将一步有限元法的计算结果与增量有限元法的计算结果和实验数据进行了对比,验证了前者的正确性。
对圆棒正挤压和方坯拔长过程进行了正向多步模拟,并对圆棒正挤压进行了相关实验研究。将多步有限元法的计算结果与增量有限元法的计算结果和实验数据进行了对比,验证了前者的可行性和有效性。
Bulk metal forming plays an important role in metal processing and manufacturing, which is a complicated physical process with ternary nonlinearity of geometry, material and boundary condition. At present, finite element (FE) simulation technique based on incremental theory is widely applied in the study of bulk metal forming. The history of deformation process could be traced accurately in the incremental FE approach, which is very important for analysis of bulk forming problems with intensive nonlinearity. However, incremental FE approach, in which analyzed model is complex and computing effort is considerable, couldn’t provide analyzed results rapidly, which couldn’t be suitable for initial concept design of product and predictive analysis of process technic.
Deformation theory is the integral of incremental theory in the condition of simple loading, which couldn’t be used in general situations theoretically. However, the deformation plasticity solution is preferred for many applications of complex loading problems due to the mathematical simplicity. It is indicated that deformation theory could provide very close results compared with incremental theory for many problems deviating proportional loading path by plentiful analysis of practical problems.
Deformation theory has the potential of applications for problems deviating proportional loading and has its own characters of computation accuracy. Deformation theory has been applied for sheet metal forming FE simulation successfully, by which one-step and multi-step simulation methods could provide results in close agreement with incremental FE predictions with very simple model and very short computing time. Compared with sheet forming processes, the deformation is larger and the deformation path and the contact history of the deformed part are more complicated in bulk metal forming processes. So it is more difficult to apply the deformation theory to bulk forming simulation. Consequently, despite the remarkable progresses that have been achieved in FE approach based on deformation theory for sheet metal forming, the applications of that in bulk metal forming are seldom. The research on application of deformation theory to bulk metal forming FE simulation is carried out in the dissertation, the main works and innovations are:
A bulk metal forming FE approach based on deformation theory is put forward. The strain and stress under large deformation condition and deformation constitutive relationship are defined. This approach is implemented to minimize approximated plastic potential derived from the total plastic work and the equivalent external work in static equilibrium for incompressible rigid-plastic materials based on constraint variational principle under the principle of extremum work. The rigid-plastic deformation FE equations are deduced.
Several key techniques of bulk metal forming deformation FE approach are studied. The fictitious sliding constraint is proposed for dealing with boundary condition of large-step computation. The estimation of equivalent external work is put forward. The initial solution is present by presetting configuration and mapping meshes. The local constraint of freedom is proposed for bulk forming problems with approximate rigid region in order to improve the convergence of deformation large-step computation.
The one-step simulation scheme based on deformation theory is proposed and one-step FE simulation program is developed. One-step simulation, which neglecting deformation history, is performed by FE calculation in one large step between the initial and final configurations of process. The multi-step simulation scheme based on deformation theory is proposed and multi-step FE simulation program is developed. Multi-step simulation, in which the computing step is divided by considering variation of deformation path and contact situation in whole process, is performed by FE calculation in multiple large steps. In multi-step simulation, it is realized to track the variation of entire deformation path by using deformation theory and consider the variation of contact history to improve the accuracy of external work estimation, which result in application of deformation FE approach to bulk forming problems more generally.
The one-step and multi-step numerical simulations are performed by taking plain strain and axisymmetric thick-walled cylinder forming under inner pressure and plain strain compression as examples to analyze the effect of deformation path, material’s hardening and boundary condition on deformation FE calculation. The applicability of deformation theory in bulk metal forming FE simulation is discussed.
The one-step forward simulations of cylindrical upsetting and flat plate rolling are performed. As for one-step simulation of flat plate rolling, the treatment of friction boundary problem between workpiece and roller during process is put forward. The results of one-step simulation are compared with those of incremental simulation and experiment to verify the correctness of the proposed approach.
The multi-step forward simulations of cylindrical bar forward extrusion and rectangular billet elongation are performed. The experiment of cylindrical bar forward extrusion is carried out. The results of multi-step simulation are compared with those obtained by incremental simulation and experiment to verify the feasibility and validity of the proposed approach.
引文
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