稀有金属(英文版) 2018,37(12),1082-1090

Size effects on springback behavior of H80 foils

Zhen-Wu Ma Zi-Yang Cao Jin-Bin Lu Yuan-Jing Zhang Wei Liu Zhen Yin

College of Mechanical Engineering, Suzhou University of Science and Technology

Suzhou Key Laboratory of Precision and Efficient Machining Technology

作者简介：*Zi-Yang Cao,e-mail: dukeczy@nuaa.edu.cn;

收稿日期：9 July 2018

基金：financially supported by the Foundation of Suzhou University of Science and Technology (No. XKQ2017005);

Size effects on springback behavior of H80 foils

Zhen-Wu Ma Zi-Yang Cao Jin-Bin Lu Yuan-Jing Zhang Wei Liu Zhen Yin

College of Mechanical Engineering, Suzhou University of Science and Technology

Suzhou Key Laboratory of Precision and Efficient Machining Technology

Abstract：

Size effects make traditional bending theories infeasible in analyzing the springback behavior of H80 foils in the similarity bending experiment. It is observed that there is a certain critical thickness value, which pides the change trend of springback amount of foils into two opposite parts. In order to reveal the reason for size effects on the springback behavior of H80 foils, the method of hardness increment characterization was applied to describe the deformation distribution of foils. The competition between strengthening effect of geometrically necessary dislocations and weakening effect of surface grains determines the change trend of springback amount with foil thickness. When the thickness of foils is large, the weakening effects dominate the material behavior, resulting in that the springback amount decreases with the decrease in foil thickness. However, when the foil thickness is small, the strengthening effects dominate the springback tendency, leading to a sharp increase in the springback amount. Furthermore, the deformation distribution is disturbed due to the enhanced effects of inpidual grain heterogeneity with the decrease in the thickness of foils, leading to the large scatter of springback angle after unloading.

Keyword：

Foil bending; Springback behavior; Size effects; Hardness increment characterization;

Received： 9 July 2018

1 Introduction

With the explosion of miniaturization in unmanned aerial vehicle and micro-electrical mechanical equipment manufacturing,the demand for various bending parts such as corrugated sheet and integrated circuit (IC) pins has trended to be miniaturized and mass-produced,which brings new challenges to modern manufacturing technology [ 1, 2] .Compared to the micro-manufacturing technology including LIGA (lithographie,galvanoformung,abformung) and micro-machining,foil bending is the most widely adopted technology due to its comprehensive features such as high efficiency and net forming [ 3, 4, 5, 6, 7, 8, 9] .However,with the reduction in geometric size of bending parts,the springback behavior of foils including the amount and the scatter of springback shows a strong dependence on its geometric size,that is,the size effect phenomenon [ 10, 11, 12, 13, 14, 15] .Because of size effects,the mature bending theory becomes infeasible in analyzing the springback behavior of foils.Therefore,the reason that induces the size effects on springback behavior of foils should be studied.

To address this issue,numerous experimental and theoretical studies on the bending of foils have been implemented.Liu et al. [ 16] researched the springback behavior of copper foils with the three-point bending experiment and found that the springback amount decreases with the decrease in the thickness of foils.They believed that the enhancement of weakening effect of surface grains causes the reduction in springback amount.In order to eliminate the interference of tool geometry and forming conditions,Koca da and Prejs [ 17] designed a pure moment bending device to carry out pure moment bending tests on copper foils and also proved that the smaller the foil thickness is,the smaller the springback amount will be.However,Li et al. [ 18] observed an opposite experimental result that the springback amount increases with the reduction in the thickness of brass foils.They proposed that there exist extra geometrically necessary dislocations to coordinate the change of crystal lattice curvature in the bending of foils,and geometrically necessary dislocations have a strengthening effect on the springback behavior of foils [ 19, 20, 21, 22] .In addition,in the bending test of pure Ni foils,Stolken and Evans [ 23] also revealed that as the foil thickness decreases,the springback amount has the"smaller thickness,stronger springback"material behavior.

From the above review it can be seen that with the decrease in foil thickness,there are two kinds of springback behavior in the bending of foils,which are"smaller thickness,weaker springback"and"smaller thickness,stronger springback".However,in most current theories and experiments,these two springback behaviors are often studied separately.In fact,in the foil bending process,the effects of surface grain weakening and geometry necessary dislocation strengthening exist simultaneously.Diehl et al. [ 24] proposed for the first time that these two factors have coupling effects on the springback behavior of foils,but they only conducted phenomenological analysis without in-depth experimental investigation.As to the research on the scatter of springback angle,Ma et al. [ 25] revealed that the scatter of springback angle increases with the reduction in the thickness of foils,but they made an inadequate explanation only with the finite element method.Therefore,in this paper,H80 foils with a wide range of thickness dimensions were studied by the bend forming experiment which was developed based on the principle of similarity and then the method of hardness increment characterization was used to reveal the reason for size effects on the springback behavior of foils.

2 Experimental

H80 foils with a purity of 99.85%and a thickness of30-400μm were selected as the research materials.In order to eliminate the rolling hardening and obtain the desired grain size parameters,H80 foils were recrystallized and annealed in a vacuum furnace with a vacuum degree of1.5×10^-3 Pa at different combinations of temperatures and time,and then the recrystallized H80 foils were inlaid,polished and etched.Then,the microstructures of recrystallized H80 foils were observed with an optical microscope (OM,Novel MR5000) and the average grain size of foils was measured by transversal method.Foils with similar grain sizes (～35μm) were selected and collected to study the impact of thickness on the springback behavior of foils.Related annealing conditions and corresponding case parameters are listed in Table 1.The analysis ofmicrostructure indicates that the fiber grain pattern produced during the rolling process disappears,and the main difference between foils with different thicknesses is the number of grains in the foil thickness direction.As an example,the typical metallographical micrographs of foil specimens with a thickness of 50 and 30μm are shown in Fig.1.

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Table 1 Annealing conditions and material parameters of H80 foils

a:μ=t/d,number of grains in thickness direction;b:N_S,being number of surface grains

Fig.1 OM images of foil specimens with a thickness of a 50μm and b 30μm

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Table 2 Scheme for bend forming experiment of H80 foils

Fig.2 Experimental device for foil bend forming experiment

In order to ensure the same deformation condition of all foils and eliminate the influence of process parameters,a bend forming experiment was designed based on the principle of similarity [ 8] .All the parameters that related to bending including the diameter of the die (D_d),the diameter of the punch (D_p),the clearance (C) between punch and die,and the movement speed (v) of the punch were adjusted according to scaling factor (λ) which is the similarity ratio.The value of scaling factor (λ) ^is proportional to the thickness of foils.The scaling factor (λ) of H80 foils with a thickness of 100μm was set as 1,so the other scale factors of foils were then obtained according to the ratio of thickness to 100μm.The bending angles of all the specimens were taken as 90°.The experimental scheme is shown in Table 2.

Fig.3 Photographs of representative foil specimens after bending

In order to ensure the accuracy of the configuration of experimental parameters for each group,a foil bend forming device shown in Fig.2 was designed.The bending device was connected to a universal material testing machine (MST) with a connector.The mandrel is a smooth stainless-steel cylinder.The mandrel diameter,die diameter and clearance between punch and die can be changed according to experimental requirements.Tensioning bolts were used to tension the mandrel during the experiment,and the support block guarantees the rigidity of the mandrel.The length and width of the bending specimen are 25and 10 mm,respectively.The springback amount of foils was obtained by averaging the data of six tests for each group.After the bending experiment,foil specimens shown in Fig.3 were photographed using an Olympus E-M1digital camera and their angles were measured using AutoCAD software with an accuracy of 0.01°as illustrated in Fig.4.The springback angle was calculated by subtracting the bending angle (90°) from the measure angle of foils after springback.

The mechanical properties of H80 foils were measured via uniaxial tensile tests.Based on the ASTM-E8 standard,the initial measuring length and width for all specimens were kept constant at 50.0 and 12.5 mm,respectively.The strain rate was in the order of 1×10^-3 s^-1 to ensure that all specimens were deformed under a quasi-static condition and the influence of strain rate could be neglected.The true stress strain curves of H80 foils were obtained by averaging the data of three tests for each group.

Fig.4 Angle measurement of foil specimens after bending with AutoCAD software

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Table 3 Setting parameters of microhardness test points

The Vickers hardness of specimens was measured by microhardness tester (HMAS-C1000SZA) with a method of pressure maintaining for 10 s under a load of 0.1 N.The distribution of test points for each foil specimen is shown in Table 3.The parameter setting of the test is illustrated in Fig.5a,and a representative schematic illustration of the distribution of test points in foils with a thickness of400μm (Novel MR5000) is shown in Fig.5b.The hardness increment was calculated by subtracting the initial hardness of foils from the hardness value of foils after bending.

Fig.6 Change of springback behavior with thickness

3 Results and discussion

3.1 Springback behavior of H80 foils

The springback behavior of H80 foils is shown in Fig.6,demonstrating that the springback amount shows different change trends in different thickness intervals.When the thickness of foils is larger than 100μm,the springback amount gradually decreases with the decrease in foil thickness (from 6.93°at 400μm to 6.65°at 200μm).When the thickness value is 100μm,the springback amount is the minimum,which is 5.97°.However,as the foil thickness further decreases,the springback amount shows the opposite increasing trend.When the foil thickness reduces to 30μm,the springback amount increases dramatically to 16.71°.In addition,the scatter of springback angle increases with the decrease in foil thickness.These results reveal that the springback behavior of H80foils exhibits strong size effects.

Fig.5 a Parameter setting and b schematic illustration of distribution of test points

Fig.7 Change of flow stress with thickness

Fig.8 Comparison between calculated and experimental results of foil springback amount

It is known that the material mechanical properties of foils can be explained by the surface grain theory [ 6, 7, 8] .Finite element simulation technology was used to examine whether the springback behavior of the foils can also be explained by the surface grain theory.If the predicted springback behavior of foils is consistent with the variation of flow stress with thickness,the springback behavior of foils can be explained by the surface grain theory;otherwise,other factors should be considered.The springback amount of H80 foils with different thicknesses was calculated by ABAQUS with the cell type of CPE4R.The flow stress of foils with different thicknesses (Fig.7) was used to describe the material mechanical properties in the calculation.The calculated and experimental values of springback amount of H80 foils are compared in Fig.8.The calculated springback amount of H80 foils by ABA-QUS keeps monotonously decreasing with the decrease in foil thickness.Moreover,when the thickness of foils ranges from 400 to 200μm,the calculated values of springback amount are very close to their experimental results.Gradually,when the foil thickness reduces from 200 to 100μm,the calculated foil springback amount gradually deviates from their experimental results.However,as the thickness of foils further decreases,there is a dramatic deviation between the calculated and experimental results of springback amount of H80 foils.

The"smaller thickness,weaker springback"phenomenon that occurs when the thickness of foils ranges from 400 to 200μm can be interpreted with the weakening effect of surface grains.The surface grain theory holds that compared to internal grains,surface grains have less constraint due to the presence of free surface [ 26, 27, 28] ,so the deformation of surface grains is much easier than that of internal grains.As shown in Table 1,the proportion of surface grains (N_s/μvalue) increases as the thickness of foils decreases.In the similarity bending experiment,all H80 foil specimens are under the same deformation condition.Therefore,the smaller the foil thickness is,the larger the proportion of plastic deformation zone will be,eventually leading to smaller foil springback amount.However,when the foil thickness is less than 100μm,the springback amount of foils shows the opposite trend of"smaller thickness,stronger springback",which is in stark contrast to the results calculated by ABAQUS.The deviation between the simulation and experimental results shows that the springback behavior of H80 foils cannot be explained only with the surface grain theory when the foil thickness is less than 100μm.It can be hypothesized that in the bending of foils,there must be a strengthening factor in addition to the weakening effect of surface layer grains.Moreover,as the foil thickness decreases,this kind of strengthening effect is greatly enhanced,which ultimately leads to a significant increase in the springback amount of foils.

3.2 Distribution of bending deformation

The hardness increment of foils has a positive correlation with the degree of strain hardening,which can reflect the degree of dislocation slip and entanglement.In order to reduce the influence of adjacent test points and sample boundaries on the test results,the minimum sample boundary distance and minimum adjacent point distance are specified according to the Vickers hardness test standard.In order to visually represent the hardness increase distribution of specimens after bending deformation,the distribution maps of hardness increment for foils were drawn by MATLAB software.However,only one test point can be laid out along the thickness direction of foils with thicknesses of 50 and 30μm,so the acquired data volume is insufficient to plot the distribution map of hardness increment.Therefore,the following discussion mainly focuses on the overall bending deformation distribution characteristics of foils with thicknesses of 400,200and 100μm.

Fig.9 Distribution map of hardness increment for foils with a thickness of a 400μm,b 200μm and c 100μm

Figure 9a is the distribution map of hardness increment for foils with a thickness of 400μm,where 0 in the thickness direction represents the geometric neutral layer,negative values represent the compressive deformation portion,and positive values represent the tensile deformation portion.It can be observed that the foil hardness is evenly increasing along the thickness direction with clear delamination,and the hardness increment near the neutral layer is the smallest.The distribution of hardness increment for the compression and tension portions is approximately symmetrical.Moreover,the hardness increment at 0 in the length direction (punch vertices) is the largest,which is consistent with the description of deformation distribution in the bending theory.

As shown in Fig.9b,the hardness increment of foils with a thickness of 200μm is still evenly distributed along the thickness direction and in accord with the deformation distribution characteristics of bend forming.However,compared to the hardness increment of 400-μm-thick foils,the proportion of low hardness region near the neutral layer for 200-μm-thick foils is significantly reduced,showing the phenomenon that high hardness regions migrate inwards.

Compared to the foils with thicknesses of 400 and200μm,the hardness increment distribution of 100-μmthick foils is disorderly in both thickness and length directions,presenting the non-uniformity of deformation distribution.As shown in Fig.9c,the low hardness increment region near the neutral layer disappears and the high hardness region does not appear at the vertex of punch but appears randomly.Since there are only three grains in the thickness direction of 100-μm-thick foils,the deformation distribution is greatly affected by the inpidual grain heterogeneity (specificity of shape,position and orientation).If the grain located at the punch vertex is in a hard orientation,the deformation of this grain is difficult and the degree of dislocation entanglement is at a low level,so the hardness increment is small at this location.However,if the grain located at a certain distance from the punch vertex is in a soft orientation,the deformation of this grain is easier,so the degree of dislocation entanglement is high,resulting in a greater hardness increment.

Besides,as shown in Fig.1a,b,the grain numbers in foils become less with the further decreases in foil thickness.Therefore,the impact of inpidual grains which own unique shape orientation and position intensifies,and the uneven degree of deformation distribution increases,ultimately leading to the large scatter of springback angle when foils are unloaded to the equilibrium state.This is the reason why the scatter of springback angle increases with the decrease in foil thickness (Fig.6).

In order to uniformly compare the hardness increment distribution of foils with different thicknesses,the relative position of test points in the thickness direction is represented by the normalized position (the distance from the test point to the neutral layer pided by half the thickness).Negative values represent compressive deformations,and positive values represent tensile deformations.The representative value of hardness increment is calculated as the arithmetic mean of hardness increments of all test points in a certain bending layer of bending region(Fig.5b) [ 29] .The hardness increments of foils with thicknesses of 400,200 and 100μm are shown in Fig.10.It can be seen that the hardness increment of foils with a thickness of 400μm changes drastically along the thickness direction,and there is a significant nadir near the neutral layer region.In contrast,the overall change is relatively gentle for 200-μm-thick foils and its increment nadir is higher than that of 400-μm-thick foils.However,the hardness increment of 100-μm-thick foils does not show an obvious decreasing tendency near the neutral layer but maintains at a high level.

Fig.10 Normalized hardness increments for foil specimens with different thicknesses

In the bending process,the maximum strain appears on the surface of foils.As the deformation increases,the surface strain will transmit to the interior of specimen by means of dislocation slip.The grain boundary region acts as a barrier to prevent the transmission of dislocation slip between neighbor grains.When the thickness of foils is small,there are a small number of grains along the thickness direction,resulting in smaller proportion of grain boundary regions.Therefore,there is little resistance for dislocation slip continuously transmitting inward,so the surface deformation can easily"penetrate"into the interior of foil specimens,leading to a great hardness increment in the region near the neutral layer.

For foils with thicknesses of 30 and 50μm,the microhardness tests can only be performed in the neutral layer region,so their hardness increments cannot be made normalized comparisons like foils with thicknesses of 100,200and 400μm.Therefore,the hardness increments of 30-and50-μm specimens are averaged according to the method in Ref. [ 30] .When the thickness of bending foils is t,the average hardening rate HV_t can be calculated as:

where HV_iA is the hardness value of the ith test point after the specimen is bent,HV_iB is the hardness value of theith test point before the specimen is bent,and n is the number of test points.

The average hardening rates are 131%±9%and116%±6%for foils with thicknesses of 30 and 50μm,respectively.In terms of the values of average hardening rate,it can be revealed that that the average hardening rate markedly increases as the foil thickness decreases from 50to 30μm.However,foils with thicknesses of 50 and30μm both have 100%proportion of surface grains(Table 1),so the inward transmission of dislocation slip is insufficient to explain the significant increase in average hardening rate.

The strain gradient of foils with small thickness is bigger than that of foils with large thickness.Large strain gradients require numerous geometrically necessary dislocations to coordinate the change of lattice curvature during deformation [ 20, 21, 22] .The relationship between geometrically necessary dislocation density (ρg) and strain gradient(η) is [ 18] :

where b denotes the length of Burger's vector and is3.6×10^-7 mm for H80 foils.For the foil bend forming,the strain gradient (η) can be calculate as:

whereε_s is the surface strain,t is the thickness of the foils,R is the radius of the curved neutral layer,and k is the bending curvature.

The geometrically necessary dislocation density of H80foils can be calculated from Eq.(2).As shown in Fig.11,the geometrically necessary dislocation density increases with the decrease in foil thickness.Especially when the thickness of foils is smaller than 100μm,the geometrically necessary dislocation density has a sharp increase.During the deformation process,geometrically necessary dislocations can pin somewhere as strengthening factors,hinder the dislocation slip and make the dislocations tangle at this location [ 20, 21, 22] .The larger the geometry necessary dislocation density is,the stronger the degree of dislocation slip and entanglement will be,resulting in the strong material hardening behavior,greatly increasing the springback amount of foil specimens.

Therefore,the competition between the strengthening and weakening factors that induce dislocation slip and entanglement causes the size effect phenomenon that the springback amount of foils exhibits an opposite trend in different thickness intervals.When the thickness of foils is large,the proportion of grain boundary regions is large,so the surface deformation can hardly"penetrate"into the interior of foils.Meanwhile,the geometrically necessary dislocation density is still at a low level.The weak transmission ability for surface dislocations to migrate inward and inadequate numbers of geometrically necessary dislocations to increase dislocation slip and entanglement result in the limited strengthening effect of strengthening factors.Moreover,the weakening effect of surface grains increases with the decrease in foil thickness,gradually dominating the springback tendency,so the springback behavior of foils exhibits the"smaller thickness,weaker springback"phenomenon.However,with the further decrease in foil thickness,almost all grains become surface grains,so the enhancement of weakening effect of surface grains is underpowered.Meanwhile,the geometrically necessary dislocation density increases rapidly and then leads to drastic dislocation slip and entanglement.Besides,the surface deformation can easily"penetrate"into the interior of foils because of the small proportion of grain boundary regions,which further promotes the slip and entanglement of dislocations.Therefore,the strengthening effect of geometrically necessary dislocations dominates the springback tendency,resulting in the"smaller thickness,stronger springback"phenomenon.

Fig.11 Variation of geometrically necessary dislocation density with foil thickness

4 Conclusion

In this research,the size effects on the springback behavior of H80 foils were studied by the similarity bending test and the microhardness test.It is observed that there is a certain critical value of thickness,which pides the change trend of foil springback amount into two opposite parts.The method of hardness increment characterization was applied to describe the deformation distribution of foils.It is concluded that the competition between the strengthening effect of geometrically necessary dislocations and weakening effect of surface grains determines the change trend of springback amount with foil thickness.When the thickness of foils is large,the weakening effects dominate the material behavior,resulting in that the springback amount decreases with the decrease in foil thickness.However,when the foil thickness is small,the strengthening effects dominate the springback tendency,leading to a sharp increase in springback amount.The deformation distribution is disturbed due to the enhanced effects of inpidual grain heterogeneity with the decrease in the thickness of foils,leading to the large scatter of springback angle after unloading.

参考文献

[1] Xu J, Guo B, Wang C, Shanac D. Blanking clearance and grain size effects on micro deformation behavior and fracture inmicro-blanking of brass foil. Int J Mach Tool Manuf. 2012;60(1):27.

[2] Ma ZW, Tong GQ, Chen F. Deformation behavior of materials in micro-forming with consideration of intragranular heterogeneities. Trans Nonferrous Metal Soc. 2017;27(3):616.

[3] Han D, Xia Y, Yokota S, Kim JW, Han D, Xia Y. UV-LIGA technique by back UV exposure with self-alignment for ECF(electro-conjugate fluid)micropumps. J Micromech Microeng.2017;27(12):125008.

[4] Garg RK, Singh KK, Sachdeva A, Sharma VS, Ojha K, Singh S.Review of research work in sinking EDM and WEDM on metal matrix composite materials. Int J Adv Manuf Technol. 2010;50(5-8):611.

[5] Creighton E, Honegger A, Tulsian A, Mukhopadhyay D. Analysis of thermal errors in a high-speed micro-milling spindle. Int J Mach Tool Manuf. 2010;50(4):386.

[6] Kals TA, Eckstein R. Miniaturization in sheet metal working.J Mater Process Technol. 2000;103(1):95.

[7] Mahabunphachai S, Koc M. Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales. Int J Mach Tool Manuf. 2008;48(9):1014.

[8] Engel U, Eckstein R. Microforming—from basic research to its realization. J Mater Process Technol. 2002;125(2):35.

[9] Chan WL, Fu MW, Yang B. Experimental studies of the size effect affected microscale plastic deformation in micro upsetting process. Mater Sci Eng, A. 2012;534(2):374.

[10] Wang CJ, Shan DB, Zhou J, Guo B, Sun LN. Size effects of the cavity dimension on the microforming ability during coining process. J Mater Process Technol. 2007;187-188(12):256.

[11] Wang Y, Dong PL, Xu ZY, Hua Y, Wu JP, Wang JJ. A constitutive model for thin sheet metal in micro-forming considering first order size effects. Mater Des. 2010;31(2):1010.

[12] Lai X, Peng L, Hu P, Lan SH, Ni J. Material behavior modelling in micro/meso-scale forming process with considering size/scale effects. Comput Mater Sci. 2008;43(4):1003.

[13] Chan WL, Fu MW, Lu J, Liu JG. Modeling of grain size effect on micro deformation behavior in micro-forming of pure copper.Mater Sci Eng, A. 2010;527(24):6638.

[14] Chan WL, Fu MW, Yang B. Study of size effect in micro-extrusion process of pure copper. Mater Des. 2011;32(7):3772.

[15] Ma ZW, Tong GQ, Chen F. Tensile properties and fractographs of Ti-2.5Al-1.5Mn foils at different temperatures. Rare Met.2017;36(4):247.

[16] Liu JG, Fu MW, Lu J, Chan WL. Influence of size effect on the springback of sheet metal foils in micro-bending. Comput Mater Sci. 2011;50(9):2604.

[17] Kocanda A, Prejs T. Experimental analysis of the effect of grain size on the mechanical behaviour of thin copper sheet in pure moment bending. Proc Inst Mech Eng L J Mater. 2003;217(217):249.

[18] Li HZ, Dong XH, Shen Y, Diehl A, Hagenah H, Engel U,Merklein M. Size effect on springback behavior due to plastic strain gradient hardening in microbending process of pure aluminum foils. Mater Sci Eng, A. 2010;527(16):4497.

[19] Zaami A, Shokuhfar A. Scale-dependent crack modeling for investigation the effect of geometrically necessary dislocations in micro/nano grain size of copper. Adv Eng Forum. 2016;15:1.

[20] Gao H, Huang Y, Nix WD, Hutchinson JW. Mechanism-based strain gradient plasticity—Ⅰ. Theory. J Mech Phys Solids. 1999;47(6):1239.

[21] Huang Y, Gao H, Nix WD, Hutchinson JW. Mechanism-based strain gradient plasticity—Ⅱ. Analysis. J Mech Phys Solids.2000;48(1):99.

[22] Huang Y, Qu S, Hwang KC, Li M, Gao H. A conventional theory of mechanism-based strain gradient plasticity. Int J Plast.2004;20(4-5):753.

[23] Stolken JS, Evans AG. A microbend test method for measuring the plasticity length scale. Acta Mater. 1998;46(14):5109.

[24] Diehl A, Engel U, Geiger M. Influence of microstructure on the mechanical properties and the forming behaviour of very thin metal foils. Int J Adv Manuf Technol. 2010;47(1-4):53.

[25] Ma Z, Tong GQ, Chen F, Wang Q, Wang S. Grain size effect on springback behavior in bending of Ti-2.5Al-1.5Mn foils.J Mater Process Technol. 2015;224:11.

[26] Geiger M, GeiBdorfer S, Engel U. Mesoscopic model:advanced simulation of microforming processes. Prod Eng. 2007;1(1):79.

[27] Wang GC, Zheng W, Wu T, Jiang H, Zhao GQ, Wei DB, Jiang ZY. A multi-region model for numerical simulation of micro bulk forming. J Mater Process Technol. 2012;212(3):678.

[28] Zhi J, Yang H, Peng F. Constitutive modeling of compression behavior of TC4 tube based on modified Arrhenius and artificial neural network models. Rare Met. 2016;35(2):162.

[29] Parasiz SA, Vanbenthysen R, Kinsey BL. Deformation size effects due to specimen and grain size in microbending. J Manuf Sci Eng. 2010;132(1):327.

[30] Diehl A, Engel U, Geiger M. Mechanical properties and bending behaviour of metal foils. Proc Inst Mech Eng B-J Eng. 2008;222(1):83.