离散单元法在金属粉末高速压制成形过程中的应用研究
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摘要
离散单元法是研究非连续体力学行为的有效数值方法,特别适合求解大变形和不连续结构问题,已广泛应用于工程领域。粉末高速压制成形技术具有压制时间短、压坯密度高、压坯密度分布均匀等特点,由于加工过程中粉末的致密化机理尚不明确,制约了该项技术发展和推广。本论文首次将离散单元法应用于粉末高速压制成形过程和粉末传热过程的研究,根据金属粉末原料及高速压制工艺的特点,基于弹塑性力学和散度空间理论,建立了描述粉末高速压制过程的数学模型,并分析了粉体的变形行为、粉体中应力波传播和热传导规律。
首先,介绍了离散单元法的发展现状及高速压制技术的工艺特点。根据粉末压制中的颗粒粒度分布服从高斯正态分布的特点,应用Box Muller变换得到了满足粉末试样粒径分布条件的颗粒生成方法。对粉末离散单元法的单元搜索方法、计算方法、边界条件进行了分析。考虑到粉末在成形过程中会先后发生加工硬化、加工软化及塑性变形,建立了描述颗粒高应变率、塑性变形的离散元接触模型。
然后,模拟了满足实验条件的松装系统在高速加载条件下的三维成形过程,结果表明压制初期粉末重排及孔隙填充是使压坯密度急剧增加的主要因素,后期粉末变形会使压坯密度进一步提高。所得成型坯密度分布与实验结果吻合,验证了所建立模型的有效性。本文对高速压制粉体内外摩擦系数、压坯高径比、单双向压制条件进行了对比实验,发现颗粒间摩擦系数对压坯最终密度有主要影响,颗粒与模腔间摩擦系数及高径比主要影响压坯密度的分布。
其次,利用散度定理对粉末系统的应力公式进行了离散化处理,建立了压制过程中的应力统计公式,得到了实际实验中难以测得的粉体内部不同高度层的应力波波形,及粉末高速压制过程中应力波的传播过程。分析了铁基及铜基粉末在不同摩擦系数下的应力波传播情况,得出粉末高速压制成形坯的高致密化是应力波反复作用的结果,粉体内部存在明显的应力迟豫现象,加卸载波形呈锯齿状的弹性波形,随着粉体被压实应力传播速度加快。
最后,分析了粉末压坯内部的高温蔓延及温度分布规律。根据温度场与接触力作用场的相似性,将颗粒看作独立热阻,整个粉体看作热阻与热流构成的温度传导网,建立了离散单元热传导模型,热流通过颗粒接触面传导。研究了粉体内颗粒排列、粒径分布、压坯密度对成形坯温度的影响。数值结果表明,粉末压坯的热传导过程与内部的颗粒架构有关,在高速压制过程中粉体内部确实存在着可短时耗散的高温积聚。
Discrete element method (DEM) is an effective numerical approach in simulating force behavior of non-continuous materials. It has established itself as an important simulation technique for engineering applications involving granular and large-deformable systems. High velocity compaction (HVC) is a new technology for fabricating high density powder metallurgy parts with low cost and high production capacity. Its productions permit good characters such as high green density, uniform density distribution, low ejection force and low spring-back etc. In the paper DEM is applied for studying the particle flowing process of dense granular system in High Velocity Compaction. According to the characteristics of metal powder materials and the relevant principles of HVC, the numerical model was established based on mechanics of granular media and theory of elastic-plasticity. The densification behavior, stress wave propagation and heat transfer rule of powder system in the compaction process of HVC were analyzed. The main works are concluded as follows:
Firstly, we summarized the research situation and application of DEM and the principle and characteristic of HVC. Since the distributing features of raw packing material obey to Gaussian distribution, a new specimen generation method based on Box Muller transform was presented. Considering powder presents successively to work Hardening, work softening and plastic deformation in HVC process, a contact force model was deduced to describe the high strain rate and elastic-perfectly plastic of powder material. The element search method, boundary condition and governing equation of particle flow for HVC were also proposed.
Secondly, with the computing program developed based on software Particle Flow Code (PFC), the three-dimensional forming process and density distribution of samples under HVC conditions were simulated. The quantitative capabilities of DEM are provided by comparing numerical models to real experimental data. Numerical results show that the rearranging and porosity filling behavior of metal powder at the early compaction stage have significant influences on green density increasing, at the late stage the densification of particles is mainly in the manner of elastic-plastic deformation. The contrast experiments were performed for different packing fractions, diameter high ratio of compacts and different loading conditions. The simulation results coincide well with experiments in engineering application.
Thirdly, evolution features of compaction force in HVC process was simulated based on the DEM. Because the full process was divided into elastic loading, plastic deformation and elastic unloading, the governing equations were established in three stages respectively. The impacting forces through different layers of powders were obtained, which could not be observed by experiments. The simulation results show obviously delay phenomenon and serrate wave with different gradient at loading and unloading processes. The simulated low-level stress waves are compared to available experimental data, which are consistent with the overall waveform.
Finally, DEM was applied for studying the high temperature spread in a compacted metal particles system. Assuming that thermal transmissions existed only at the contact zones between particles, the general thermal equation based on continuum mechanics was rewritten to a discrete form. Then the interior heat source generated during friction of the motion particles was deduced from kinetic equations. Using the proposed model, the factor which affect the temperature distribution of specimen was investigated including particles arrangement, particle diameter distribution and green density. Temperature profiles at different locations and different moments are given. At a fixed location the temperature rise presents a logarithmic relationship with time. Simulation results show that the geometry distribution of particle materials significantly influences the temperature distribution. Heat transfers fast in the system which is comprised of small and uniform particles.
首先,介绍了离散单元法的发展现状及高速压制技术的工艺特点。根据粉末压制中的颗粒粒度分布服从高斯正态分布的特点,应用Box Muller变换得到了满足粉末试样粒径分布条件的颗粒生成方法。对粉末离散单元法的单元搜索方法、计算方法、边界条件进行了分析。考虑到粉末在成形过程中会先后发生加工硬化、加工软化及塑性变形,建立了描述颗粒高应变率、塑性变形的离散元接触模型。
然后,模拟了满足实验条件的松装系统在高速加载条件下的三维成形过程,结果表明压制初期粉末重排及孔隙填充是使压坯密度急剧增加的主要因素,后期粉末变形会使压坯密度进一步提高。所得成型坯密度分布与实验结果吻合,验证了所建立模型的有效性。本文对高速压制粉体内外摩擦系数、压坯高径比、单双向压制条件进行了对比实验,发现颗粒间摩擦系数对压坯最终密度有主要影响,颗粒与模腔间摩擦系数及高径比主要影响压坯密度的分布。
其次,利用散度定理对粉末系统的应力公式进行了离散化处理,建立了压制过程中的应力统计公式,得到了实际实验中难以测得的粉体内部不同高度层的应力波波形,及粉末高速压制过程中应力波的传播过程。分析了铁基及铜基粉末在不同摩擦系数下的应力波传播情况,得出粉末高速压制成形坯的高致密化是应力波反复作用的结果,粉体内部存在明显的应力迟豫现象,加卸载波形呈锯齿状的弹性波形,随着粉体被压实应力传播速度加快。
最后,分析了粉末压坯内部的高温蔓延及温度分布规律。根据温度场与接触力作用场的相似性,将颗粒看作独立热阻,整个粉体看作热阻与热流构成的温度传导网,建立了离散单元热传导模型,热流通过颗粒接触面传导。研究了粉体内颗粒排列、粒径分布、压坯密度对成形坯温度的影响。数值结果表明,粉末压坯的热传导过程与内部的颗粒架构有关,在高速压制过程中粉体内部确实存在着可短时耗散的高温积聚。
Discrete element method (DEM) is an effective numerical approach in simulating force behavior of non-continuous materials. It has established itself as an important simulation technique for engineering applications involving granular and large-deformable systems. High velocity compaction (HVC) is a new technology for fabricating high density powder metallurgy parts with low cost and high production capacity. Its productions permit good characters such as high green density, uniform density distribution, low ejection force and low spring-back etc. In the paper DEM is applied for studying the particle flowing process of dense granular system in High Velocity Compaction. According to the characteristics of metal powder materials and the relevant principles of HVC, the numerical model was established based on mechanics of granular media and theory of elastic-plasticity. The densification behavior, stress wave propagation and heat transfer rule of powder system in the compaction process of HVC were analyzed. The main works are concluded as follows:
Firstly, we summarized the research situation and application of DEM and the principle and characteristic of HVC. Since the distributing features of raw packing material obey to Gaussian distribution, a new specimen generation method based on Box Muller transform was presented. Considering powder presents successively to work Hardening, work softening and plastic deformation in HVC process, a contact force model was deduced to describe the high strain rate and elastic-perfectly plastic of powder material. The element search method, boundary condition and governing equation of particle flow for HVC were also proposed.
Secondly, with the computing program developed based on software Particle Flow Code (PFC), the three-dimensional forming process and density distribution of samples under HVC conditions were simulated. The quantitative capabilities of DEM are provided by comparing numerical models to real experimental data. Numerical results show that the rearranging and porosity filling behavior of metal powder at the early compaction stage have significant influences on green density increasing, at the late stage the densification of particles is mainly in the manner of elastic-plastic deformation. The contrast experiments were performed for different packing fractions, diameter high ratio of compacts and different loading conditions. The simulation results coincide well with experiments in engineering application.
Thirdly, evolution features of compaction force in HVC process was simulated based on the DEM. Because the full process was divided into elastic loading, plastic deformation and elastic unloading, the governing equations were established in three stages respectively. The impacting forces through different layers of powders were obtained, which could not be observed by experiments. The simulation results show obviously delay phenomenon and serrate wave with different gradient at loading and unloading processes. The simulated low-level stress waves are compared to available experimental data, which are consistent with the overall waveform.
Finally, DEM was applied for studying the high temperature spread in a compacted metal particles system. Assuming that thermal transmissions existed only at the contact zones between particles, the general thermal equation based on continuum mechanics was rewritten to a discrete form. Then the interior heat source generated during friction of the motion particles was deduced from kinetic equations. Using the proposed model, the factor which affect the temperature distribution of specimen was investigated including particles arrangement, particle diameter distribution and green density. Temperature profiles at different locations and different moments are given. At a fixed location the temperature rise presents a logarithmic relationship with time. Simulation results show that the geometry distribution of particle materials significantly influences the temperature distribution. Heat transfers fast in the system which is comprised of small and uniform particles.
引文
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