Specimen Dimension and Grain Size Effects on Deformation Behaviorin Micro Tensile of SUS304 Stainless Steel Foil

Jie Xu1,2,+, Bin Guo1, Debin Shan1, Mingxing Li1 and Zhenlong Wang1,2

1Key Laboratory of Micro-Systems and Micro-Structures Manufacturing of Ministry of Education, Harbin Institute of Technology,Harbin 150080, China2The Post-doctorate Research Station of Mechanical Engineering, Harbin Institute of Technology, Harbin 150001, China

Size effects are the main problem in micro-forming process and material behavior with miniaturization of feature size. In the paper, sizeeffects of grain size and foil thickness on deformation behavior and fracture were investigated by using micro tensile test of SUS304 foil. Theresults show that the yield strength of SUS304 stainless foil increases with the decrease of foil thickness and grain size in micro tensile tests.Meanwhile, the fracture mechanism of SUS304 foil changes from ductile fracture with lots of dimples to ductile fracture with slip separationwith the decrease of foil thickness. A compound material model by considering grain size, foil thickness and surface effects is proposed andconstitutive relation of SUS304 foil is established. The calculation curves well match with experimental results.[doi:10.2320/matertrans.M2013016]

(Received January 11, 2013; Accepted March 7, 2013; Published April 26, 2013)

Keywords: size effect, deformation behavior, fracture, micro tensile, stainless steel foil

1. Introduction

With the development of micro-electromechanical system(MEMS), micro-forming is one of suitable approaches tofabricate micro-parts due to the advantages of highproductivity, low cost, near-net-shape and excellent mechan-ical properties.1) However, when the feature size of micro-parts is reduced from macro-scale to micro-scale, the plasticdeformation behavior is determined by only a few grainslocated at the deformation regions and size effects occur.2)

The conventional material models are no longer valid in theanalysis of deformation behavior of micro-forming.3)

In order to investigate size effects in micro-forming, a lotof researches have been conducted. Geiger et al.4) presented akeynote paper on micro-forming in 2001 and conducted acomprehensive review of micro-forming technology. Kalsand Eckstein5) studied the size effects in tensile test, airbending and micro blanking of sheet metal by means ofminiaturization methods according to similarity theory.Further research of Raulea et al.6) showed that the yieldstrength is related with the ratio of grain size to specimenthickness and a strong increase of variation occur with theincrease of grain size. Shan et al.7) investigated the sizeeffects of foil thickness and grain size on material behavior inmicro-bending. Eckstein et al.8) established surface layermodel to explain the size effect of flow stress in micro sheetforming. In addition, Geißdörfer et al.9) proposed a meso-scopic model by considering the grain boundary conditionand anisotropic material behavior to simulate the size effectin micro forming. Peng et al.10) established an uniform sizedependence constitutive model to investigate the size effectin thin sheet micro-forming process. Wang et al.11) proposeda new constitutive model considering the first order sizeeffects for micro sheet metal forming combining theHollomon equation and Hall­Petch relationship. Chan andFu12) presented a dislocation density models considering theinteractive effect of specimen and grain size on fracture stress

and strain. Liu13) investigated the surface atomic relaxationproperties of sphalerite by using first principle. Zhao et al.14)

described the size effect on fracture behavior based on thecomposite model concerning the grain boundary and graininterior. Xu et al.15,16) investigated the size effects of grainsize and foil thickness on deformation behavior and fracturein micro-blanking and the results showed that the ultimateshearing strength was decided by the ratio of clearance tograin size. Among the prior studies, there is a lack of in-depth study on the interactive influence of specimen andgrain size on the deformation behavior and fracture in microsheet metal forming process.

Stainless steel is a popular material for MEMS componentsdue to its excellent properties as regards strength, goodplasticity and corrosion resistance. In this paper, micro tensiletests of SUS304 stainless steel foils were conducted to studythe size effect on the deformation and fracture behaviors inmicro forming.

2. Experimental Material and Procedure

2.1 MaterialStainless steel SUS304 foil is selected as the testing

material due to its wide application in MEMS devices. Thechemical compositions are shown in Table 1.

The as-received SUS304 foil thicknesses are ranged from20 to 100 µm. In order to obtain different grain sizes, thespecimens were put into a vacuum glass tube with 10¹3 Paand then were annealed in heat treatment apparatus at thetemperature ranging from 900 to 1100°C kept for from 15 to60min. The heat-treated foils were etched with a solutionof 20ml HF, 10ml HNO3 and 70ml H2O for 30 s. Themicrostructures of cross-section of 80 µm in thickness were

Table 1 Chemical compositions of SUS304 foil (mass%).

Element Cr Ni Mn Si Fe

Content 18 10 2 1 Residue+Corresponding author, E-mail: xjhit@hit.edu.cn

Materials Transactions, Vol. 54, No. 6 (2013) pp. 984 to 989©2013 The Japan Institute of Metals and Materials

observed by optical microscopy (OM) and the grain size wasmeasured by the intercept and planimetric methods accordingto the standard of ASTM E112-10. The grain sizes of 80 µmthickness of SUS304 foil were 17.7, 23.2, 30.5 and 45.4 µmas shown in Table 2 for the heat treatment with thetemperature of 900, 950, 1000 and 1100°C, respectively.The microstructure distributions across the direction of foilthickness are shown in Fig. 1 and the results show that thereare only two or three grains in the cross-section of thicknessdirection.

2.2 ProcessThe stainless steel foil was cut to dog bone shape by

electrical discharge machine (EDM) for micro tensile test andthe dimensions were shown in Fig. 2. The measuring lengthof tensile specimen is 25mm and the free specimen length is70mm. The transition radius R is 7.5mm to reduce the stressconcentrations. Electro-polishing process parameters with avoltage of 4.8V and a current of 0.7A were adopted with thesolution of 60ml HNO3, 25ml H2SO4 and 15ml H2O formicro tensile specimens due to the dirty surface and coursecross-section after EDM.

The micro tensile tests were conducted at room temper-ature in the material testing apparatus with a non-contactstrain measurement by video extensometer,17) which issuitable for the micro tensile testing of foil specimen. Sincethe deformation behavior of SUS304 is sensitive to strainrate, a low tensile velocity of 2mm/min for all the specimenswas used in the paper. It is assumed that the strain rate effectcould be neglected.

3. Results and Discussions

Figure 3 shows the relationship between the true stress andtrue strain with the different foil thickness after the heattreatment of 900°C. From the picture, we can see that theflow stress trends to increase when the foil thicknessdecreases from 100 to 20 µm and the results demonstratethe phenomenon of “much thinner and much stronger”. Thesimilar results were found in micro tensile tests of foils afterother heat treatments. The tendency was also observed fordifferent materials such as Cu and Al foil.18)

The size effect of specimen geometrical dimension onmicro-tensile test can be explained by into the Swift model,19)

·k ¼ Kð¾0 þ �¾Þn: ð1Þ

Table 2 Grain size of 80µm thickness SUS304 stainless foil with differentanneal temperature.

Temperature (°C) 900 950 1000 1100

Grain size (µm) 17.7 23.2 30.5 45.4

Fig. 1 Microstructure of stainless foil (t = 80µm) at different annealing temperature: (a) 900, (b) 950, (c) 1000, (d) 1100°C.

Fig. 2 Micro tensile specimen dimensions (unit: mm).

0.0 0.1 0.2 0.3 0.4 0.5 0.60

200

400

600

800

1000

1200

t = 100 μm

t = 80 μm

t = 50 μmT

rue

stre

ss σ

/MPa

True strain ε

t = 20 μm

SUS304RT, 2 mm/min

Fig. 3 Curves of true stress and true strain with the different foil thickness.

Specimen Dimension and Grain Size Effects on Deformation Behavior in Micro Tensile of SUS304 Stainless Steel Foil 985

Where, K is hardening index, ¾0 is initial strain and n isworking hardening index. The material parameters related tothe Swift model for each thickness are presented in Table 3and Fig. 4. The results show that the elongation ¤, K and nincrease with increasing of foil thickness. The calculatedvalues are consistent with the experimental curves of microtensile test of stainless steel foil of 100, 80 and 50 µm inthickness. However, the calculated value is lower than theexperimental curve due to ignoring the effects of surfacelayer.

Figure 5 shows the effect of grain size on flow stress ofmicro tensile of 80 µm thickness stainless steel. The resultsshow that the flow stress decreases with the increasing ofgrain size, which can be explained with the surface grain

weakening model.8) The grain grew up and strengthdecreased with increasing of heat treatment temperature.According to the surface layer theory, with the increase ofgrain size while keeping the foil thickness constant, the shareof surface grains increases, which results in the decreasing offlow stress.

From the results of Figs. 3 and 5, size effects ofdeformation behavior in micro tensile of SUS304 stainlesssteel were not only related with foil thickness, but also relatedwith grain size and the properties of grains in the surfacelayer of metal foil, which result from the joint effect ofthickness, grain size and surface properties. To explain thesize effect of deformation behavior in micro tensile ofSUS304 foil, a mixed material model proposed by Laiet al.20) based on surface layer model was adopted with asurface grain factor £,

£ ¼ Ns

Nð2Þ

here, Ns is the number of surface grains and N is the totalnumber of grain size in SUS304 foil. The material modelwas expressed by a size independent term · ind and a sizedependent term ·dep.

·y ¼ · ind þ ·dep

· ind ¼ M¸R þ kd�12

·dep ¼ £ðm¸R �M¸R � kd�12Þ

8><>: ð3Þ

where ·y is the yield strength; the term · ind is describedby a polycrystal material model considering surface grainproperties, whereas it is not related with featured size; theterm ·dep is a dependent model related with the size factor£; ¸R is the critical shear stress of a single crystal; M(M = 3.06 for FCC crystal) and m ðm � 2Þ are constant;k is the intensified stress to propagate general yield acrossthe polycrystal grain boundaries and d is the grain size.Therefore, the eq. (3) can be used to describe size effectin micro tensile with a conventional polyscrystal materialsmodel.

In order to analysis the effects of strain gradientstrengthening and surface grain weakening in one materialmodel, surface layer geometrical model was established bydividing surface grains and internal grains as shown in Fig. 6.The number of surface grains can be expressed as

Ns ¼wt� ðw� 2dÞðt� 2dÞ

Sð4Þ

Table 3 SUS304 parameters for Swift model.

Thickness/µm K/MPa ¾0 nElongation,

¤/%

20 1472 0.039 0.579 16.2

50 1686 0.057 0.60 28.2

80 1903 0.064 0.61 36.9

100 1548 0.056 0.64 51.1

0.0 0.1 0.2 0.3 0.4 0.50

200

400

600

800

1000

1200

Tru

e st

ress

σ /M

Pa

True strain ε

100 μm 80 μm 50 μm 20 μm

Experimental data

Theroretical curves

SUS304RT, 2 mm/minThickness

Fig. 4 Contract results of foil thickness effects on micro tensile behaviorbetween theoretical values and experimental results.

0.0 0.1 0.2 0.3 0.40

200

400

600

800

1000

1200

d=45.5 μm

d=30.5 μm

d=23.2 μm

Tru

e st

ress

σ/M

Pa

True strain ε

d=17.7 μm

SUS304RT, 2 mm/s, 80 μm

Fig. 5 Effect of grain size on flow stress in micro tensile of stainless steelfoil (t = 80µm).

Fig. 6 Surface grains and internal grains in metal foil.

J. Xu, B. Guo, D. Shan, M. Li and Z. Wang986

where w is the width of metal foil, t is the thickness of metalfoil and S is the area of single grain.

The total number of grain size N ¼ wtS . Thus £ can be

expressed as

£ ¼ 2d

t1þ t

w� 4d

w

� �: ð5Þ

In micro tensile test, the foil width w is much larger thanthe thickness t ðw � tÞ and the width is also much largerthan the grain size d ðw � dÞ. Therefore, the eq. (2) can beexpressed as

£ ¼ 2d

t: ð6Þ

Combined the eqs. (3) to (6), the yield strength of SUS304foil can be described by

·y ¼ · ind þ ·dep

· ind ¼ 3:06¸R þ kd�12

·dep ¼ �2d

tð1:06¸R þ kd�

12Þ

8>><>>: ð7Þ

here, m is taken the minimum value of 2 and M is taken3.06.

According to the experimental results, the ¸R and k ofSUS304 stainless foil can be obtained by least squares fittingmethod as follows,

¸R ¼ 211þ 57¾0:71

k ¼ �21þ 119¾0:71

(: ð8Þ

Thus, the constitutive relation of SUS304 foil can besimplified with eqs. (7) and (8),

·y ¼ Aþ B¾n: ð9ÞHere n is working hardening exponent, n = 0.71. A and B areconstants related with grain size and foil thickness.

A ¼ 645:7� 21ffiffiffid

p� 42

ffiffiffid

p

t� 447:3

d

t

B ¼ 174:2þ 119ffiffiffid

pþ 238

ffiffiffid

p

t� 120:8

d

t

8>><>>: : ð10Þ

Figure 7 shows the relationship of flow stress of SUS304foil with different grain size in micro tensile. The calculationcurves by using the compound materials model match verywell the experimental results, which verified the materialmodel validity by considering the effects of the grain size andthickness.

The effects of foil thickness and grain size on micro tensilebehavior of stainless steel foil can be explained by the surfacelayer theory. There are a few grains along the direction of foilthickness with the thickness decreasing of stainless steel foilwith fine grain as shown in Fig. 8(a). However, there is apassivation layer in the surface of stainless steel foil and theeffects on mechanical behavior also can’t be ignored whenthe foil thickness is decreased to micro-scale. The effects ofstrain gradient strengthening by passivation layer with muchhigher strength are much larger than that of surface grainweakening in micro tensile test of stainless steel foil.Therefore, the passivation layer as the dislocation blockleads to a higher flow stress with decreasing of foilthickness.4,21) However, when the stainless foil is annealed

at high temperature, the grain size becomes larger and thematerial property is softened. Thus, there are only a fewgrains along the thickness direction for the stainless steel foilof 80 µm in thickness as shown in Fig. 8(b). And thepassivation layer thickness is much thinner compared withthe large grain size and its effects can be ignored. From themetal physics theory it is known that free surface grains showless hardening compared to the internal grains due to thedifferent mechanisms of dislocation movement and pile-up.The surface grains are less subjected to compatibilityrestrictions and the flow stress decreases with the increasingof grain size.

In order to investigate the fracture mechanism of microtensile of SUS304 stainless steel foil, the fracture morphol-ogy of specimen was observed by SEM. Figure 9 demon-strates the SEM fracture photographs of micro-tensile testsamples with the foil thickness of 100, 80, 50 and 20 µm. Theresults show that the number of dimple in fracture surfacedecreases with decreasing of foil thickness and there is nodimple found in the case with the foil thickness of 20 µm andthe slip band and the typical knife edge rupture can be clearlyobserved on the fracture surface.

The results indicate that the fracture mechanism changesfrom ductile fracture with lots of dimples to ductile fracturewith slip separation with the decreasing of foil thickness,which is consistent with fractograph of the tested coppersamples in the report of the reference.22) The reason has beenanalyzed and the facts show that there are one or two grainsin the thickness direction when the foil thickness is reducedto 20 µm. The decrease of grain number leads to the localizeddeformation at the fracture region. The different grainorientation in the cross section leads to shear deformationand coordination much more difficultly and cross-slip is easyto form because the grains are constrained and hamperedamong the grains. With the increasing of foil thickness, thegrain number and grain boundaries increase. The grainboundaries act as an obstacle to dislocation movement. Theshear stress concentrates at the grain boundary regions andcauses the parabolic dimple formation during micro tensileprocess. Thus the dimples increase with the increasing offoil thickness. These fracture size effects also can be foundin micro-blanking of metal foils.15)

0.0 0.1 0.2 0.3 0.4 0.50

200

400

600

800

1000

1200

SUS304RT, 2 mm/s, 80 μm

17.7 μm 23.2 μm 30.5 μm 45.5 μm

Theoretical results

Tru

e st

ress

σ/M

Pa

True strain ε

Experimental results

Grain size

Fig. 7 Contract results of grain size effects on micro-tensile behaviorbetween theoretical values and experimental results.

Specimen Dimension and Grain Size Effects on Deformation Behavior in Micro Tensile of SUS304 Stainless Steel Foil 987

4. Conclusions

(1) The yield strength of SUS304 stainless foil increaseswith the decrease of foil thickness and grain size in microtensile tests.

(2) A compound material model by considering grain size,foil thickness and surface effects is proposed and constitutiverelation of SUS304 foil is established. The calculation curveswell match with experimental results.

(3) With the decrease of foil thickness, the fracturemechanism of SUS304 foil changes from ductile fracturewith lots of dimples to ductile fracture with slip separation.

Acknowledgments

This work was supported by the Postdoctoral ScienceFoundation of China under Grant No. 2011M500659 and

No. 2012T50324. Partial support was provided by theNational Basic Research Program of China under the GrantNo. 2012CB934100 and the National Natural ScienceFoundation of China under Grant No. 51105102.

REFERENCES

1) U. Engle and R. Eckstein: J. Mater. Process. Technol. 125­126 (2006)35­44.

2) M. Geiger, F. Vollertsen and R. Kals: CIRP. Ann. Manuf. Technol. 45(1996) 277­282.

3) F. Vollertsen, D. Biermann, H. N. Hansen, S. Jawahir and K. Kuzmank:CIRP. Ann. Manuf. Technol. 58 (2009) 566­587.

4) M. Geiger, M. Kleiner, R. Eckstein, N. Tiesier and U. Engel: CIRP.Ann. Manuf. Technol. 50 (2001) 445­462.

5) T. A. Kals and R. Eckstein: J. Mater. Process. Technol. 103 (2000)95­101.

6) L. V. Raulea, L. E. Goijaerts and F. P. T. Baaijens: J. Mater. Process.Technol. 115 (2001) 44­48.

Fig. 9 Effect of foil thickness on fracture mechanism: (a) 20, (b) 50, (c) 80, (d) 100µm.

(a) (b)

Fig. 8 Surface model of specimen dimension and grain size effects: (a) Specimen thickness size effect. (b) Grain size effect.

J. Xu, B. Guo, D. Shan, M. Li and Z. Wang988

7) D. B. Shan, C. J. Wang, B. Guo and X. W. Wang: T. Nonferr. Metal.Soc. 19 (2009) s507­s510.

8) R. Eckstein, M. Geiger and U. Engel: Proc. 7th Int. Conf. on SheetMetal, Bamberg, Germany, (1999) pp. 529­536.

9) S. Geißdörfer, U. Engel and M. Geiger: Int. J. Mach. Tools. Manuf. 46(2006) 1222­1226.

10) L. F. Peng, X. M. Lai, H. J. Lee, J. H. Song and J. Ni: Mater. Sci. Eng.A 526 (2009) 93­99.

11) Y. Wang, P. L. Dong, Z. Y. Xu, H. Yan, J. P. Wu and J. J. Wang: Mater.Des. 31 (2010) 1010­1014.

12) W. L. Chan and M. W. Fu: Mater. Sci. Eng. A 528 (2011) 7674­7683.13) J. Liu, S. M. Wen, Y. J. Xian, S. J. Bai and X. M. Chen: Int. J. Miner.

Metall. Mater. 19 (2012) 775­781.14) Y. H. Zhao, Y. Z. Guo, Q. Wei, T. D. Topping, A. M. Dangelewicz,

Y. T. Zhu, T. G. Langdon and E. J. Lavernia: Mater. Sci. Eng. A 525

(2009) 68­77.15) J. Xu, B. Guo and D. B. Shan: Int. J. Adv. Manuf. Technol. 56 (2011)

515­522.16) J. Xu, B. Guo, C. J. Wang and D. B. Shan: Int. J. Mach. Tools. Manuf.

60 (2012) 27­34.17) B. Guo, J. Zhou, D. B. Shan and H. M. Wang: Acta Metall Sin. 44

(2008) 419­422.18) H. Hoffmann and S. Hong: CIRP. Ann. Manuf. Technol. 55 (2006)

263­266.19) J. F. Michel and P. Picart: J. Mater. Process Technol. 141 (2003) 439­

446.20) X. M. Lai, L. F. Peng, P. Hu, S. H. Lan and J. Ni: Comput. Mater. Sci.

43 (2008) 1003­1009.21) Y. Xiang and J. J. Vlassak: Acta Mater. 54 (2006) 5449­5460.22) M. W. Fu and W. L. Chan: Mater. Des. 32 (2011) 4738­4746.

Specimen Dimension and Grain Size Effects on Deformation Behavior in Micro Tensile of SUS304 Stainless Steel Foil 989