微弯曲成形中应变梯度硬化效应的研究
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摘要
金属塑性微成形在微型零件的生产制造过程中显得越来越重要,并受到广大研究者的重视。但随着微型零件几何尺寸的缩小,其微观晶粒尺寸和表面粗糙度等材料参数却保持不变,从而导致材料的塑性变形行为发生变化,其力学性能等与尺寸大小相关,这些不同于宏观尺寸零件成形时的现象称为尺寸效应现象。传统的塑性成形技术和理论中由于不包含材料尺度量而不能直接应用于塑性微成形工艺中。为研究微成形中的尺寸效应现象,在考虑传统应变硬化的基础上,引入了应变梯度对材料硬化的影响,进而将成形零件的几何尺寸量引入控制方程中,使应变梯度硬化理论能够用于描述微成形中的尺寸效应现象。本文基于金属微成形实验中的尺寸效应现象,采用应变梯度塑性理论研究金属塑性微成形过程中表现出的与尺寸相关的现象。
本文研究了厚度为25μm~500μm的纯铝(99.5%)和CuZn37黄铜薄板材料的单向拉伸实验,结果表明:纯铝的的屈服强度表现出随板料厚度减小而降低的“越小越弱”的尺寸效应现象,这是由于具有脆性氧化膜的纯铝,材料表面层晶粒中的位错更容易滑移出表面并且表面层晶粒所占比例随厚度的减小而增加,进而引起小尺寸材料的软化;CuZn37黄铜的屈服强度却显示出了随板料厚度减小而增强的“越小越强”的尺寸效应现象,这与其表面的韧性氧化膜有关,它的存在阻碍了表面层晶粒中位错的滑出,从而使薄试样的强度增加。这两种材料在表面层应变相同的微弯曲实验中均表现出了明显的“越小越强”的尺寸效应现象,即回弹角随试样板料厚度的减小而增大。微弯曲变形区侧表面微硬度分布表明,厚度较大的细晶粒试样变形区侧表面存在明显的低硬度中心层,而粗晶粒试样变形区中心层不明显。传统的塑性模型不能描述实验中与尺寸相关的现象,需采用包含成形材料尺寸量的应变梯度塑性理论来解释。
采用应变梯度塑性理论对微弯曲实验中存在的尺寸效应现象进行了分析研究。结果表明:包含高阶应力的Fleck-Hutchinson应变梯度硬化模型和基于Taylor关系式而不包含高阶应力的Nix-Gao模型能够显示出微弯曲变形中的尺寸效应现象。但FH应变梯度塑性理论模型需要引入与高阶应变功共轭的高阶应力和特殊的边界条件,其中的内禀尺寸量为根据实验数据拟合得到的保持量纲平衡的量。而在NG应变梯度塑性理论中,不需要引入高阶应力,并且内禀尺寸量具有一定的物理意义,但在分析微弯曲实验时,存在内禀尺寸计算值与根据实验拟合得到的内禀尺寸值不相符的问题;同时考虑到内禀尺寸与晶粒尺寸或晶粒相对尺寸之间的关系,因此我们对NG应变梯度模型进行了修正,以解释弯曲回弹实验中表现出的尺寸效应现象。结果表明:修正的Nix-Gao应变梯度硬化模型给出了更好的计算结果。材料内禀尺寸是应变梯度硬化模型的关键参数之一。为了更准确的描述应变梯度对材料硬化的影响,将厚度方向晶粒数引入到了内禀尺寸表达式中,计算得到的内禀尺寸值和采用实验拟合得到的内禀尺寸值比较接近。进一步说明了厚度方向晶粒数越少由几何必需位错引起的应变梯度对硬化的影响越显著,相反厚度方向晶粒数越多由统计存储位错所反映的均匀变形应变引起的硬化作用越显著,这与采用Hall-Petch关系式对屈服的描述相一致。
极薄试样(如厚度为25μm)的微弯曲实验结果显示出很大的波动性,其微观结构金相照片表明厚度方向仅有单层晶粒,同时又存在明显的尺寸效应现象,因此在晶体塑性理论中引入应变梯度对硬化的影响,在考虑晶粒方位对硬化影响的同时考虑微成形过程中的尺寸效应现象。针对应变梯度晶体塑性理论中求解剪应变梯度的关键核心问题提出了新的简化算法,采用计算点近邻域的方法求得该点与相邻点之间的剪应变梯度。对微压痕成形的模拟结果显示压痕载荷与实验结果较接近,其他结果与研究者的模拟结果比较接近,验证了应变梯度晶体塑性理论模型及剪应变梯度的简化算法的准确性;对微弯曲成形进行了模拟计算:由于晶粒方位的不同导致硬化的各向异性,从微观机制上解释了较薄试样弯曲实验中结果误差波动性较大的原因。
Metal plastic microforming is becoming an important manufacturing process for metal micro parts and is investigated by more and more researchers recently. In metal microforming process, some material parameters, such as crystal microstructure, surface roughness etc. are the same as ones in macro scale material forming process, but its macro geometrical dimensions, such as foil thickness, wire diameter and indentation depth, are very small, in finally, the metal plastic forming behaviours are changed. The properties of metal material are different from macro scale forming and related with the macro geometrical dimensions, which is referred to as size effect. The conventional metal forming technology and theory in macro scale cannot be applied directly to metal plastic microforming through scale down the specimen and tooling size due to the lack of the material length scale in their constitutive models. In order to study on the size effects in microforming process, the strain gradient plasticity theory is developed, in which the conventional strain hardening and the strain gradient hardening are included together and the material intrinsic length is present in the constitutive relation. In present dissertation, the plastic stran gradient theories are studied to explain the size effects in metal microforming. The research results are summarized as following:
The uniaxial tensile tests are investigated using 25μm~500μm thickness foils for pure aluminium (99.5%) and CuZn37 brass. The results show that there is a size effect“smaller is weaker”, i.e. the yield strength of pure aluminium decreases with the foil thickness decreasing, and which is attribute to the dislocations in the surface grains might slip easily with brittle oxidation film and the share of surface grains in the overall volume increases with decreasing thickness. For the brass foils, the yield strength increases with the foil thickness decreasing, that is to say, there is a size effect“smaller is stronger”. The reason is that there exists the passivated and ductility oxidation film to block the dislocation slip out of the surface of brass and the ratio of the thickness of oxidation film to the brass foil increases with the brass foil thickness decreasing. In the microbending experiments for these two metal materials, the springback angle increases with decreasing foil thickness, indicating obvious size effects of“smaller is stronger”. The hardness distribution in bended area shows that there is an obvious middle layer for fine grain structure samples and no middle layer for coarse structure samples. The size effects in microbending process are investigated with strain gradient theories.
The analysis results show that Fleck-Hutchinson’s strain gradient plasticity theory with higer-order stress tensor and Nix-Gao’s strain gradient plasticity theory based on the Taylor relation can catch these size effects, but the springback angles or the microbending moment based on the modified Nix-Gao strain gradient plasticity theory are in better agreement with the experimental data. The material intrinsic length is one of the important factors in plastic strain gradient plasticity theory and originally proposed for dimensional consistency. In the Nix-Gao’s srain gradient theory, the material intrinsic lengths calculated from its equation are different from the ones fitted by the experimental data. In present dissertation, the material intrinsic length is related to material properties and average grain numbers along the characteristic scale direction of part to improve the strain gradient hardening effects. The calculated results of material intrinsic length are closed to the fitting results from experiment data. The less the grain numbers across the foil thickness is, the larger the strain gradient hardening based on the geometrically necessary dislocation is. On the contrary, the more the grain numbers across the foil thickness is, the larger the uniforming strain hardening based on the statistically stored dislocation is, which is in accordance with the Hall-Petch relation.
The error of springback angle is larger for thinner foils in microbending experiments, in which there is only one grain across the thinner foils. Therefore, the anisotropic properties of material are more and more highlights together with the size effects phenominon. The anisotropic properties of single crystal together with the shear strain gradient hardening are expressed in the strain gradient crystal plasiticity theory, in which the shear strain gradient hardening is introduced directly into the evolutionary equations of the slip resistence. The new simple numerical algorithm to obtain the shear strain gradient is proposed, in which the concept of the closed neighbour domain of integration points are used to calculated the shear strain gradient between the present integration point and neighbour points in the range of predefined domain. Two examples are provided to illustrate the present theory, including a single crystal subject to microindentation and microbending deforming processes. The FE analysis results of microindentation on a single crystal copper show that the indentation load is closed to the experimental data for the same indentation depth and other results are good agreement with the simulation results from published papers. The accuracy of the strain gradient crystal plasticity theory and simplified numerical algorithm of shear strain gradient is verified. The significant fluctuates of the error for thinner foils in microbending experiments are better attributed to the anisotropic properties of single crystal in microbending simulation of different orientation. The thinner foils are single crystal through the thickness but many grains across the thicker foils; therefore the later is approach to the material isotropic properties.
本文研究了厚度为25μm~500μm的纯铝(99.5%)和CuZn37黄铜薄板材料的单向拉伸实验,结果表明:纯铝的的屈服强度表现出随板料厚度减小而降低的“越小越弱”的尺寸效应现象,这是由于具有脆性氧化膜的纯铝,材料表面层晶粒中的位错更容易滑移出表面并且表面层晶粒所占比例随厚度的减小而增加,进而引起小尺寸材料的软化;CuZn37黄铜的屈服强度却显示出了随板料厚度减小而增强的“越小越强”的尺寸效应现象,这与其表面的韧性氧化膜有关,它的存在阻碍了表面层晶粒中位错的滑出,从而使薄试样的强度增加。这两种材料在表面层应变相同的微弯曲实验中均表现出了明显的“越小越强”的尺寸效应现象,即回弹角随试样板料厚度的减小而增大。微弯曲变形区侧表面微硬度分布表明,厚度较大的细晶粒试样变形区侧表面存在明显的低硬度中心层,而粗晶粒试样变形区中心层不明显。传统的塑性模型不能描述实验中与尺寸相关的现象,需采用包含成形材料尺寸量的应变梯度塑性理论来解释。
采用应变梯度塑性理论对微弯曲实验中存在的尺寸效应现象进行了分析研究。结果表明:包含高阶应力的Fleck-Hutchinson应变梯度硬化模型和基于Taylor关系式而不包含高阶应力的Nix-Gao模型能够显示出微弯曲变形中的尺寸效应现象。但FH应变梯度塑性理论模型需要引入与高阶应变功共轭的高阶应力和特殊的边界条件,其中的内禀尺寸量为根据实验数据拟合得到的保持量纲平衡的量。而在NG应变梯度塑性理论中,不需要引入高阶应力,并且内禀尺寸量具有一定的物理意义,但在分析微弯曲实验时,存在内禀尺寸计算值与根据实验拟合得到的内禀尺寸值不相符的问题;同时考虑到内禀尺寸与晶粒尺寸或晶粒相对尺寸之间的关系,因此我们对NG应变梯度模型进行了修正,以解释弯曲回弹实验中表现出的尺寸效应现象。结果表明:修正的Nix-Gao应变梯度硬化模型给出了更好的计算结果。材料内禀尺寸是应变梯度硬化模型的关键参数之一。为了更准确的描述应变梯度对材料硬化的影响,将厚度方向晶粒数引入到了内禀尺寸表达式中,计算得到的内禀尺寸值和采用实验拟合得到的内禀尺寸值比较接近。进一步说明了厚度方向晶粒数越少由几何必需位错引起的应变梯度对硬化的影响越显著,相反厚度方向晶粒数越多由统计存储位错所反映的均匀变形应变引起的硬化作用越显著,这与采用Hall-Petch关系式对屈服的描述相一致。
极薄试样(如厚度为25μm)的微弯曲实验结果显示出很大的波动性,其微观结构金相照片表明厚度方向仅有单层晶粒,同时又存在明显的尺寸效应现象,因此在晶体塑性理论中引入应变梯度对硬化的影响,在考虑晶粒方位对硬化影响的同时考虑微成形过程中的尺寸效应现象。针对应变梯度晶体塑性理论中求解剪应变梯度的关键核心问题提出了新的简化算法,采用计算点近邻域的方法求得该点与相邻点之间的剪应变梯度。对微压痕成形的模拟结果显示压痕载荷与实验结果较接近,其他结果与研究者的模拟结果比较接近,验证了应变梯度晶体塑性理论模型及剪应变梯度的简化算法的准确性;对微弯曲成形进行了模拟计算:由于晶粒方位的不同导致硬化的各向异性,从微观机制上解释了较薄试样弯曲实验中结果误差波动性较大的原因。
Metal plastic microforming is becoming an important manufacturing process for metal micro parts and is investigated by more and more researchers recently. In metal microforming process, some material parameters, such as crystal microstructure, surface roughness etc. are the same as ones in macro scale material forming process, but its macro geometrical dimensions, such as foil thickness, wire diameter and indentation depth, are very small, in finally, the metal plastic forming behaviours are changed. The properties of metal material are different from macro scale forming and related with the macro geometrical dimensions, which is referred to as size effect. The conventional metal forming technology and theory in macro scale cannot be applied directly to metal plastic microforming through scale down the specimen and tooling size due to the lack of the material length scale in their constitutive models. In order to study on the size effects in microforming process, the strain gradient plasticity theory is developed, in which the conventional strain hardening and the strain gradient hardening are included together and the material intrinsic length is present in the constitutive relation. In present dissertation, the plastic stran gradient theories are studied to explain the size effects in metal microforming. The research results are summarized as following:
The uniaxial tensile tests are investigated using 25μm~500μm thickness foils for pure aluminium (99.5%) and CuZn37 brass. The results show that there is a size effect“smaller is weaker”, i.e. the yield strength of pure aluminium decreases with the foil thickness decreasing, and which is attribute to the dislocations in the surface grains might slip easily with brittle oxidation film and the share of surface grains in the overall volume increases with decreasing thickness. For the brass foils, the yield strength increases with the foil thickness decreasing, that is to say, there is a size effect“smaller is stronger”. The reason is that there exists the passivated and ductility oxidation film to block the dislocation slip out of the surface of brass and the ratio of the thickness of oxidation film to the brass foil increases with the brass foil thickness decreasing. In the microbending experiments for these two metal materials, the springback angle increases with decreasing foil thickness, indicating obvious size effects of“smaller is stronger”. The hardness distribution in bended area shows that there is an obvious middle layer for fine grain structure samples and no middle layer for coarse structure samples. The size effects in microbending process are investigated with strain gradient theories.
The analysis results show that Fleck-Hutchinson’s strain gradient plasticity theory with higer-order stress tensor and Nix-Gao’s strain gradient plasticity theory based on the Taylor relation can catch these size effects, but the springback angles or the microbending moment based on the modified Nix-Gao strain gradient plasticity theory are in better agreement with the experimental data. The material intrinsic length is one of the important factors in plastic strain gradient plasticity theory and originally proposed for dimensional consistency. In the Nix-Gao’s srain gradient theory, the material intrinsic lengths calculated from its equation are different from the ones fitted by the experimental data. In present dissertation, the material intrinsic length is related to material properties and average grain numbers along the characteristic scale direction of part to improve the strain gradient hardening effects. The calculated results of material intrinsic length are closed to the fitting results from experiment data. The less the grain numbers across the foil thickness is, the larger the strain gradient hardening based on the geometrically necessary dislocation is. On the contrary, the more the grain numbers across the foil thickness is, the larger the uniforming strain hardening based on the statistically stored dislocation is, which is in accordance with the Hall-Petch relation.
The error of springback angle is larger for thinner foils in microbending experiments, in which there is only one grain across the thinner foils. Therefore, the anisotropic properties of material are more and more highlights together with the size effects phenominon. The anisotropic properties of single crystal together with the shear strain gradient hardening are expressed in the strain gradient crystal plasiticity theory, in which the shear strain gradient hardening is introduced directly into the evolutionary equations of the slip resistence. The new simple numerical algorithm to obtain the shear strain gradient is proposed, in which the concept of the closed neighbour domain of integration points are used to calculated the shear strain gradient between the present integration point and neighbour points in the range of predefined domain. Two examples are provided to illustrate the present theory, including a single crystal subject to microindentation and microbending deforming processes. The FE analysis results of microindentation on a single crystal copper show that the indentation load is closed to the experimental data for the same indentation depth and other results are good agreement with the simulation results from published papers. The accuracy of the strain gradient crystal plasticity theory and simplified numerical algorithm of shear strain gradient is verified. The significant fluctuates of the error for thinner foils in microbending experiments are better attributed to the anisotropic properties of single crystal in microbending simulation of different orientation. The thinner foils are single crystal through the thickness but many grains across the thicker foils; therefore the later is approach to the material isotropic properties.
引文
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