简介概要

Mechanism of size effects in microcylindrical compression of pure copper considering grain orientation distribution

来源期刊：Rare Metals2013年第1期

论文作者：Chuan-Jie Wang Chun-Ju Wang Bin Guo De-Bin Shan Yan-Yan Chang

文章页码：18 - 24

摘要：In microscale deformation, the magnitudes of specimen and grain sizes are usually identical, and sizedependent phenomena of deformation behavior occur, namely, size effects. In this study, size effects in microcylindrical compression were investigated experimentally. It was found that, with the increase of grain size and decrease of specimen size, flow stress decreases and inhomogeneous material flow increases. These size effects tend to be more distinct with miniaturization. Thereafter, a modified model considering orientation distribution of surface grains and continuity between surface grains and inner grains is developed to model size effects in microforming. Through finite element simulation, the effects of specimen size, grain size, and orientation of surface grains on the flow stress and inhomogeneous deformation were analyzed. There is a good agreement between experimental and simulation results.

Rare Metals 2013,32(01),18-24+2

Mechanism of size effects in microcylindrical compression of pure copper considering grain orientation distribution

Chuan-Jie Wang Chun-Ju Wang Bin Guo De-Bin Shan Yan-Yan Chang

School of Materials Science and Engineering, Harbin Institute of Technology

Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology

作者简介：Chun-Ju Wang,e-mail: cjwang1978@hit.edu.cn;

收稿日期：22 February 2012

基金：financially supported by the National Natural Science Foundation of China (Nos. 50835002 and 51105102);

Mechanism of size effects in microcylindrical compression of pure copper considering grain orientation distribution

Abstract：

In microscale deformation, the magnitudes of specimen and grain sizes are usually identical, and sizedependent phenomena of deformation behavior occur, namely, size effects. In this study, size effects in microcylindrical compression were investigated experimentally. It was found that, with the increase of grain size and decrease of specimen size, flow stress decreases and inhomogeneous material flow increases. These size effects tend to be more distinct with miniaturization. Thereafter, a modified model considering orientation distribution of surface grains and continuity between surface grains and inner grains is developed to model size effects in microforming. Through finite element simulation, the effects of specimen size, grain size, and orientation of surface grains on the flow stress and inhomogeneous deformation were analyzed. There is a good agreement between experimental and simulation results.

Keyword：

Microforming; Cylindrical compression; Size effects; Grain orientation; Inhomogeneous deformation;

Received： 22 February 2012

1 Introduction

With a rapid development of microelectromechanical systems,the demand for microparts,such as microscrews,micropins,microcups,microgears,and micro-lead frames,has been increasing.Micromanufacturing methods,such as LIGA(Lithographie,Galanoformung,Abformung),quasiLIGA,etching,micro-EDM(Electrical Discharge Machining),laser technology,microelectrochemical machining,and micromechanical cutting,are unable to satisfy the requirements for products with low price,high efficiency,and large production volumes.Microforming is a manufacturing process that can form microparts with dimensions or structures at least in two-dimensional scale in the submillimeter range[1–3].The magnitudes of specimen and grain sizes are usually identical when the dimensions of specimens are downscaled to microscale.Deformation behavior of these sized specimens exhibits large differences compared to that in macrodeformation,and so-called size effects occur.Much research has been done to understand the microscale deformation behavior well.Geiger et al.[4,5]experimentally investigated flow stress size effect in microcylindrical compression.It was noticed that flow stress decreased with a decrease in specimen dimensions.Chen and Tsai[6]studied the flow stress size effect in microupsetting of brass based on the relationship between hardness and flow stress.Experimental results showed that flow stress decreases with a reduction in specimen size.Chan et al.[7–9]analyzed the deformation behavior in microupsetting using pure copper and aluminum alloy.Again,similar phenomena related to flow stress were observed,and irregular surface topography occurred with increase of grain size.Chen and Ngan[10,11]found that both the tensile elongation and the ultimate tensile strength decreased as the grain size increased for a given wire diameter;in addition,the elongation of the wires decreased as their diameters decreased at a constant grain size in tension of silver microwires.To interpret the decrease of flow stress,Geiger et al.[12]initially proposed the surface layer model.It proved to be adequate for interpreting flow stress reduction as miniaturization.Then,Geiger and colleagues[12,13]developed a mesoscopic model based on the theory of metal physics to simulate the forming behavior of microparts as well as the occurring scatter of the process factors.Shen et al.[14]pided the specimen into the interior grain and grain boundary parts,and the flow stress size effects were analyzed.Kim et al.[15]introduced two parameters,a and b,related to specimen size and grain size,respectively,into the Hall–Petch relationship to analyze the influence of specimen and grain size on flow stress.Lai et al.[16]built a constitutive model to analyze size effects on microforming through introducing a size factor.The previous referenced work shows that size effects in microforming have been investigated experimentally and analyzed by using surface models.However,for modeling size effects,especially the scatter of flow stress and inhomogeneous deformation,less work has been done to investigate the effect of the distribution of grain orientation on size effects in microforming.Grain orientation distribution of surface grains not only has a large influence on mechanical properties but also on the plastic flow behavior in microforming.The aim of this article is to determine the influence of orientation distribution of surface grains on microscale deformation behavior.An experimental study on size effects,such as reduction of flow stress and increase of inhomogeneous deformation,was carried out.A modified model was proposed to characterize size effects in microcylindrical compression,considering the impact of orientation distribution of surface grains,and a good agreement with the experimental results was achieved.

2 Experimental

Cylindrical specimens of pure copper were machined to U0.81 mm 9 1.62 mm,U1.01 mm 9 1.62 mm,U1.54mm 9 1.62 mm,and U 2.8 mm 9 4.2 mm.The specimens were annealed under conditions of 430°C for 1 h,700°C for 8 h,and 700°C for 24 h to modify the grain size L(10,45,and 65 lm).To reduce the size effect of friction in micro compression,machine oil was chosen as lubricant.The strain rate was set up to 0.002 s^-1.Flow stress curves of the specimen(U 0.81 mm 9 1.62 mm)with different grain sizes are shown in Fig.1.Flow stress decreases with the increase of grain size for the given sized specimen.Flow stress curves of different sized specimens with 65 lm in grain size are shown in Fig.2.Flow stress decreases with the decrease of specimen size.These results are consistent with the results in Refs.[4–9].Dislocations moving through grains during deformation pile up at grain boundaries but not at free surfaces.This leads to less hardening and lower resistance against deformation of surface grains.With the decreasing specimen size and increasing grain size,the share of surface grains increases which results in lower overall flow stress.

Fig.1 Variation in flow stresses with grain size

Fig.2 Variation in flow stresses with specimen size

Figures 3 and 4 are the SEM photos of different sized and grain sized specimens after deformation.It is clear that inhomogeneous deformation behavior increases with the increase of grain size and decrease of specimen size.Grains with free surfaces are easily moving toward the free surfaces than the boundaries,which results in rough and uneven on the free surfaces[9].The topography is difficult to predic because of the random distributions of grain size and grain orientation of surface grains.A more irregular surface topography appears with the decrease of specimen dimension or number of grains located through the specimen.

3 Finite element modeling and analysis

3.1 Theoretic analysis

With miniaturization,fraction of free surfaces increases which has dominated influence on the total mechanical properties of material.The effect of free surfaces on the dislocation revolution has been widely studied for single crystals through TEM investigations.The dislocation density is distinctly lower in the surface region than in the interior as a result of the escape of dislocations through the free surfaces[17].The dislocation structures in the vicinity of the free surfaces are found to be softer than in the core regions causing a stress decrease.Keller et al.[18]found that the effect of free surfaces is similar to this observation in single crystals.The grains located at the surface of a specimen are less restricted than grains inside the material.Surface layer models proposed by scholars[2,12–16]have been improved effectively to model size effects in microforming.In this study,a model considering the grain size,initial distribution of orientation,and continuity of mechanical properties is proposed.This model pides a specimen into three parts:surface layer,transition layer,and inner layer region,as shown in Fig.5.Each part was assigned different mechanical properties.Therefore,the overall flow stress of a specimen can be modeled with a composite model as shown below:

Fig.3 Surface topographies(SEM image)of deformed specimens with different sizes:a U0.81 mm 9 1.62 mm and b U2.8 mm 9 4.2 mm

Fig.4 Surface topographies(SEM image)of deformed specimens with different grain sizes:a L=10 lm and b L=65 lm

Fig.5 Partitions of a polycrystalline specimen

where a_Sj,a_Tk,and a_Iare the fractions of the jth surface grain,kth sublayer of transitional grains,and inner grains.r_Sj(e),r_Tk(e),and r_I(e)are the flow stresses of the jth surface grain,kth sublayer of transitional grains,and inner grains.r(e)is the overall flow stresses of the specimen,and n,m and s are numbers of the total grains,surface grains,and transitional grains.

3.2 Constitutive relation

Mechanical properties of each part in the model are assigned based on the analysis in the section above.Surface grains are regarded as single crystals and assigned with different orientations.Three representative crystallographic orientations(C₂₃,C₂₆,and C₃₀as shown in Fig.6)which represent a soft,a medium,and a hard orientation,respectively,were selected in the simulation.The stress–strain curves of C₂₃,C₂₆,and C₃₀are shown in Fig.7[19].The flow stress curves of inner grains are from specimens of U2.8 mm 9 4.2 mm with grain size of 10,45,and65 lm,respectively.The surface grains were assigned with different orientations and mechanical properties from Fig.7.The flow stresses of transitional layer were calculated through mechanical properties of surface grains and inner grains.The flow stresses of each sublayer are expressed as Eqs.(2)–(4):

Fig.6 Three crystallograghic orientations of copper[19]

Fig.7 Stress–strain curves of C23,C26,and C30[19]

where r_single(e)indicates the average flow stress of single crystal,r_poly(e)indicates the flow stress of polycrystalline and r_Tk(e)indicates the flow stress of the transitional layer metal,k=1,2,3.

3.3 Finite element modeling

In this article,the dispersion of grain size is ignored,and the grains are considered constant through the specimen To reduce the computation time and enhance simulation efficiency,only half model of the specimen is analyzed Each part of the specimen was assigned with different mechanical properties according to the analysis in Sect3.2.The initial orientation distribution of surface layer grains was assigned by a random function.This model was built by the finite element code of MSC.Marc,using fournode quadrilateral element to mesh the part,as shown in Fig.8.

3.4 Prediction of flow stress

Figures 9 and 10 show comparisons of flow stresses between experimental and simulation results.It is clearly shown that flow stress calculated by the proposed model decreases with the increase of grain size or decrease of specimen size.There is a good agreement between experimental and simulation results.When the grain size is10 lm or specimen size is U1.54 mm 9 1.62 mm,the two group curves are not in match well.In macroforming surface grains have little influence on the overall mechanical property of a specimen,and the assumption of single crystal for surface grains may introduce overestimated influence of surface grains,which results in the deviation between experimental and simulation results.For specimens with larger grain sizes or smaller dimensions,there is a very good agreement between experimental and simulation results.

Fig.8 Finite element model for microcompression:a partition,b enlarged picture of partial mesh,and c contact condition

Fig.9 Comparison of flow stress for different grain sized specimens between simulation and experimental results

Fig.10 Comparison of flow stress for different sized specimens between simulation and experimental results

In microforming,with the increase of grain size and decrease of specimen size,scatter of flow stress increases,as reported in Refs.[7–9].The scatter of flow stress is mainly caused by the distributions of grain size and orientations.In this study,only grain orientations of surface grains are taken into consideration.Three different distributions are used to characterize the hard preferred distribution,uniform distribution,and soft preferred distribution,and C₂₃:C₃₀:C₂₆are 1.5:1:1,1:1:1,and 1:1:1.5,respectively.The flow stress curves of three specimens with different orientation distributions are shown in Fig.11.Grain orientation distributions have a large influence on flow stress.Flow stress curve of the specimen with homogeneous distribution lies between curves of specimen with hard preferred distribution and soft preferred distribution.In fact,with the increase of grain size and the decease of specimen size,fewer grains in the specimen result in a more inhomogeneous grain orientation distribution and increase of fraction of surface grains,which leads to a greater contribution of surface grains to the overall mechanical property of the specimen.Then,a more distinct scatter of flow stress appears.

Fig.11 Curves of flow stress of specimens with different distribu-tions of grain orientation

3.5 Inhomogeneous deformation behavior

Figures 12 and 13 show contours of deformed parts with different specimens and grain sizes simulated by the proposed model.With the increase of grain size and decrease of specimen size,irregular deformation of surface grains tends to be more distinct.These results are in good agreement with the experiments and results from others[7–9].In contrast to the strength of grain boundaries,free surfaces are so weak that dislocations can move through them,which results in the inner grain part of surface grains moving normal to the specimen and the appearance of irregular topography.The bigger the fraction of surface grains is,the more irregular the topography appeared.

To study the effect of grain orientation distributions on the deformation behavior in microscale,two different distributions are used to characterize hard preferred distribution and soft preferred distribution,and C₂₃:C₃₀:C₂₆are 1.5:1:1 and 1:1:1.5,respectively.The contours of specimen with two different distributions are shown in Fig.14.The soft grains are easily deformed and can easily move normal to the free surfaces compared with the hard grains.When the grain size is large enough,the influence becomes significant.The obviously uneven phenomenon that appears at the surface of specimen indicates that nonuniform deformation increases with grain size,which is consistent with the result of the experiment shown in Figs.3 and 4.

Fig.12 Contours of different sized specimens after deformation:a U0.81 mm 9 1.62 mm and b U1.54 mm 9 1.62 mm

Fig.13 Contours of different grain sized specimens after deformation:a L=10 lm and b L=65 lm

Fig.14 Contours of specimen dependent on grain orientation:a C23:C30:C26=1.5:1:1 and b C23:C30:C26=1:1:1.5

4 Conclusion

In this study,microcylindrical compression of pure copper with different grain and specimen sizes was carried out Experimental results show that,with the increase of grain size and decrease of specimen size,decrease of the flow stress and increase of non-uniform plastic deformation occur.The decrease of flow stress results from the increasing ratio of less hardened surface grains with increase of grain size and decrease of specimen size.In addition,surface grains play a dominant role on the mechanical property when fewer grains across a specimen Increase of inhomogeneous distributions of grain orientation and size between different specimens with the same dimension results in an increase of flow stress scatter and inhomogeneous deformation.The proposed model that considers grain orientations of surface grains not only can analyze the heterogeneity of plastic deformation but also predict the increase of the scatter and reduction of flow stress in microforming.However,to investigate size effects in depth,the combined influence of grain orientation and distribution needs to be considered in the next research This study provides a basis for further investigation of size effects in microforming.