稀有金属(英文版) 2019,38(09),824-831

Determination of mechanical properties of pure zirconium processed by surface severe plastic deformation through nanoindentation

Yao-Mian Wang Wei Zhuang Huan-Ping Yang Cong-Hui Zhang

作者简介：Yao-Mian Wang e-mail:ymwang@xauat.edu.cn;

收稿日期：2 November 2018

基金：financially supported by the National Natural Science Foundation of China (Nos. 51674187 and 51671153);the Science and Technology Department of Shaanxi Province(No.2017GY-115);the Education Department of Shaanxi Province(No. 16JK1466);

Determination of mechanical properties of pure zirconium processed by surface severe plastic deformation through nanoindentation

Yao-Mian Wang Wei Zhuang Huan-Ping Yang Cong-Hui Zhang

School of Metallurgical Engineering,Xi'an University of Architecture and Technology

Abstract：

Commercially pure zirconium was processed by the surface mechanical attrition treatment(SMAT),and the microstructure observation showed that a gradient structure was induced.Nanoindentation measurements were taken to obtain the load-displacement curves at different depths below the treated surface.Using dimensional analysis,the local yield stress,hardness,strain hardening exponent,and elastic modulus at the corresponding depths were derived.The results showed that the yield stress and hardness varied with depth,while the strain hardening exponent and elastic modulus were approximately invariable.The finite element method was used to simulate nanoindentation at different depths below the treated surface to verify the derivation of the local elastic-plastic constitutive relationship.Stressstrain curves were computed for the treated samples through the rule of mixtures,and they agreed well with the experimental results.The analysis showed that the surface and subsurface hardening layers as well as the transition layer shared a high load applied to the samples,even though their volume fraction was small.

Keyword：

Mechanical property; Severe plastic deformation; Gradient microstructure; Nanoindentation; Finite element method;

Received： 2 November 2018

1 Introduction

Gradient nanostructured metalmmaterials,showing contin—uous variation in grain size,from nanoscale in the surface layer to microscale in the interior,exhibit high hardness,strength,and fatigue performance as well as wear resistance [ 1, 2, 3, 4, 5] .Several surface severe plastic deformation treatment processes,such as surface mechanical attrition treatment (SMAT) [ 6] ,surface mechanical rolling treatment (SMRT) [ 7] ,surface mechanical grinding treatment(SMGT) [ 8] ,ultrasonic shot peening (USSP) [ 9] ,high-energy shot peening (HESP) [ 10] ,ultrasonic surface rolling process (USRP) [ 11] ,ultrasonic nanocrystal surface modification (UNSM) [ 12] ,and rotational]y accelerated shot peening (RASP) [ 13] ,have been proposed to prepare metal materials with a gradient nanostructure.During processing,severe plastic deformation occurred in the surface layer.As the distance from the treated surface increased,the plastic strain gradually decreased.A gradient microstructure was obtained that corresponded to the gradient distribution of the plastic deformation.This led to a grain size strengthening effect which was obvious near the surface and weak in the interior.In addition,a significant work hardening effect was induced in the surface layer because of the high dislocation density.The work hardening effect decreased as the distance from the treated surface increased.These two strengthening mechanisms are believed to contribute to the improvement in strength [ 14, 15] .Following the rule of mixtures (ROM),the strength of the treated samples was estimated,and the predicted results agreed well with the measured ones [ 16, 17] .In contrast,research conducted by Tsai et al. [ 18] demonstrated that the ROM prediction was much lower than the experimental data.A synergetic strengthening effect has been found in some gradient structure materials [ 4, 19] .This is caused by the macroscopic stress gradient and biaxial stress generated by mechanical incompatibility between the different layers [ 19] .Therefore,further research is needed to elucidate the mechanical behavior of gradient nanostructured materials.

Nanoindentation has proven to be a powerful technique for estimating the mechanical properties of materials [ 20, 21, 22, 23] .The local mechanical properties of gradient nanostructured materials have also been characterized by nanoindentation tests [ 24, 25] .By using dimensional analysis,the elastic-plastic behavior of a material can be determined from the nanoindentation load versus depth curve [ 26, 27] .Even though the local elastic-plastic response of gradient nanostructured materials has been determined using this method [ 24] ,the correlation between the local mechanical response and total mechanical properties has rarely been investigated.In the present study,nanoindentation tests and dimensional analysis were employed to characterize the local elastic-plastic deformation behavior of commercially pure zirconium processed by SMAT.The ROM was used to find a correlation between the local elastic-plastic response and the total mechanical behavior.A comparison of the predicted and the experimental results was conducted,and the strengthening mechanism was also discussed.

2 Experimental

Annealed commercially pure zirconium plate was used in the present study,and its chemical composition is given in Table 1.Samples with dimensions of 100 mm×100mm×4 mm were machined and polished before treatment.The SMAT was performed in vacuum at room temperature with zirconium oxide balls with 3 mm in diameter at a vibration frequency of 20 kHz.The processing duration was 45 min.Only one face of the plate was treated.

Nanoindentation measurements were taken using a nanoindenter (Agilent Nano Indenter G200) equipped with a Diamond Berkovich Indenter.A maximum load of49 mN was used in the tests.During the measurement,the load was increased to its maximum in 15 s,kept constant for 10 s to account for creep,and then unloaded.The nanoindentation tests were carried out on the cross section perpendicular to the treated surface.Different positions along the depth direction were indented at least 20μm apart in order to avoid interaction of the stress field.

  下载原图

Table 1 Chemical composition of commercially pure zirconium(wt%)

Tensile tests were carried out to evaluate the mechanical properties of the samples before and after the surface severe plastic deformation.The samples with a gage length of 10 mm,width of 3 mm,and thickness of 4 mm were stretched on a universal testing machine (INSTRON 1195)at an initial tensile rate of 0.5 mm·min^-1.Stress-strain curves were obtained for the samples.

A cross section of the treated sample was ground using silicon carbide sandpaper from 200 to 1500 grit.This was followed by electrolytic polishing in a solution with the volume ratio of HF/HNO₃/H₂O=2:9:9.The microstructure was then observed using an optical microscope (OM,ZEISS Axio Scope.A1).

3 Theoretical description

Figure 1 shows a typical curve for the indentation load (P)against the penetration depth (h) for an elastic-plastic material during sharp indentation.According to Kick’s law,the relationship between P and h during loading can be described by:

where C is the curvature.Furthermore,h_m is the maximum penetration depth corresponding to the maximum indentation load (P_m),and h_r is the residual penetration depth after complete unloading.The total work done by the load P during indentation is W_t,the released elastic work during unloading is W_e,and the stored plastic work is W_p=W_t-W_e.

The typical uniaxial elastic-plastic deformation behavior of many pure metals and alloys is shown in Fig.2.The stress-strain relation during plastic deformation can be described by a power law equation.Thus,the true stresstrue strain behavior can be expressed as:

Fig.1 Schematic illustration of a typical P-h curve

Fig.2 Typical elastic-plastic stress-strain behavior of metals

whereσis true stress,εis true strain,E is the Young’s modulus,K is the strength coefficient,n is the strain hardening exponent,andσ_y is the initial yield stress.Considering the yield strain asε_y corresponding to the initial yield stress,then:

When the total strainεexceedsεy,it consists of two parts,ε_y and the nonlinear part (ε_p);hence,

Combining Eqs.(2),(3),and (4),the stress-strain relation beyondσ_y can be written as:

Clearly,the elastic-plastic behavior of the material is completely determined by the parameters E,σ_y,and n and Poisson's ratio (v).

Using dimensional analysis,Dao et al. [ 26] constructed dimensionless functions to estimate the elastic-plastic properties of a material from one complete P-h curve.

1.Considering the elasticity effects of an elastic indenterand an elastic—plastic solid,a reduced elastic modulus(E^*) is introduced:

where E_i and v_i are the Young’s modulus and Poisson’s ratio for the indenter.For the diamond indenter,E_i=1100 GPa and v_i=0.07 [ 26] .Poisson’s ratio (v)for the zirconium is taken as 0.3 [ 28] .Thus,E^*can be solved using the dimensionless function∏₆ given by:

where is the initial unloading slope of the P-h curve and P_u is the unloading force.For a Berkovich indenter,c^*=1.2370 for large deformation,and the projected contact area (A_m) is given by:

2.The hardness (P_ave) of the material is found throughdimensionless function∏₄,which is given by:

3.Defining the representative strain (ε_r) and thecorresponding stress (σ_r),a representative strain ofε_r=0.033 was used based on comparisons of the computational results with different values ofε_r [ 26] .The representative stress (σ_0.033) withε_r=0.033 is solved through dimensionless functionsП₁ as:

4.The strain hardening exponent (n) is determined by thedimensionless function∏₂ as

5.The initial yield stress (σ_y) is solved using:

with E,σ_y,and n obtained using equations givenabove;the local elastic-plastic behavior of the treated commercially pure zirconium can be fully determined.

4 Finite element simulation of nanoindentation

The finite element method was used to simulate the elasticplastic response of the sample during nanoindentation and to verify the results of dimensional analysis.An axisymmetric deformable two-dimensional 10μm×10μm planar model was established.A mesh,fine near the contact region and gradually coarser further away,was employed to ensure numerical accuracy and calculation efficiency.A total of 6696 linear quadrilateral elements of CAX4 were generated.The Berkovich indenter was modeled as a rigid body with an apex angle (θ) of 70.3°.The finite element model is shown in Fig.3.

The elastic and plastic properties of the materials used in the calculation were obtained using the dimensional analysis described in Sect.3.Contact between the indenter and the sample was frictionless in the simulation.A concentrated force of 50 mN was applied to the reference point in the general static analysis step.

Once the calculation was completed,the variation of the displacement with load for the reference point was obtained.Thus,the simulated nanoindentation P-h curve during loading was achieved.The creep behavior of the material was not considered,so the elastic-plastic response during holding and unloading was not simulated.

Fig.3 Finite element model for nanoindentation test

Fig.4 P-h curves of treated sample at different depths

5 Results and discussion

In this study,more than twenty points along the depth direction were indented.Figure 4 shows eight P-h curves at different depths.It shows that the C value of the loading section decreased with the distance from the top surface,while h_m and h_r increased.This means that the surface layer was hardened by the severe plastic deformation.

The finite element simulation P-h curves for the loading section of the treated sample at different depths are shown in Fig.5.It can be seen that the simulated and experimental curves agreed well except where the indentation load exceeded 40 mN.This indicates that the elasticplastic behavior derived by the dimensional analysis method is reasonable.

The hardness,calculated through Eq.(9),is shown in Fig.6a.The hardness of surface layer was approximately3.0 GPa.As the distance increased,the hardness decreased until it stabilized at approximately 1.6 GPa between 250and 300μm.The hardness value shows some differences from our previous research [ 29] ,which used a different calculation method [ 30] ,but the variation with distance was similar.

The calculated yield stress is shown in Fig.6b.Similar to the hardness,the yield stress was the highest at the surface,exceeding 1000 MPa at a depth of 6μm.As the distance from the surface increased,the yield stress decreased gradually.At a depth of 300μm,it was approximately 400 MPa.The yield stress was still higher than that of the as-received sample,which was less than300 MPa.This means that the material at this depth was hardened during the surface severe plastic deformation.Our previous research indicated that nanoscale crystallite and high-density dislocation could be induced in the surface layer [ 31] .These features lead to hardening of the surface layer of the sample.

The Young’s modulus and strain hardening exponent of the sample are shown in Fig.6c and d,respectively.Although the results show some dispersion,it can be seen that the Young’s modulus and strain hardening exponent are approximately invariable with the distance.This indicates that the severe plastic deformation method used in this study has little effect on the modulus and hardening exponent.

Fig.5 Comparison of simulated and experimental P-h relation during loading at different depths:a 16μm,b 65μm,c 114μm,and d 254μm

Following the determination of the yield stress,Young’s modulus,and strain hardening exponent of the material at different distances,and assuming that the material has a layer structure,the elastic-plastic deformation behavior of the gradient nanostructured material as a whole can be estimated using the ROM expressed by

whereσ_t is the average stress of the whole material,N represents the number of layers,σ_i is the stress of the ith layer,and w_i is the corresponding weight determined by the volume fraction.Assuming that the strain in the different layers is equal when the material is subjected to uniaxial loading,Eq.(13) gives the average stress of the gradient material.

The material treated by SMAT can be considered as a gradient structure consisting of different layers with distinctive microstructures and mechanical properties.Figure 7 shows the gradient micros truc ture of the treated sample.In this study,for simplification four layers were considered,i.e.,the surface hardening layer,subsurface hardening layer,transition layer,and matrix layer.

The surface hardening layer,with depth of less than100μm,showed a fine microstructure resulting from the severe plastic deformation.During the processing,highdensity dislocation occurred and twins formed.The dislocation slip and twining contributed to the refinement of the microstructure.Nanometer-sized crystallites have also formed in the top surface layer [ 31, 32] .Owing to the fine microstructure and high-density dislocation,the top surface layer possessed high hardness and yield stress,as shown in Fig.6a and b.

Beneath the surface hardening layer,the subsurface hardening layer was mainly characterized by twins,as shown in Fig.7,but the density of the twins was lower than that in the surface hardening layer.Here,the hardness and yield stress still improved significantly compared with the unaffected matrix.This layer was less than 250μm in depth.In addition,the compressive residual stress of this layer was very high [ 31] ,which contributed to the hardening effects.

Fig.6 Variation of a hardness,b yield stress,c Young’s modulus,and d strain hardening exponent with distance from top surface

Fig.7 Gradient OM image of treated sample (1-surface hardening layer,2-subsurface hardening layer,3-transition layer,and 4-matrix)

The transition layer lies between the subsurface hardening layer and the matrix.Its microstructure is similar to that of the matrix,but it contains some occasional twins.By extrapolating the variation in hardness and yield stress in Fig.6,it is concluded that the transition layer was less than 400μm in depth.

The scatter of the measurement results meant that a representative stress-strain curve was used to illustrate the elastic-plastic behavior of the corresponding layers.Three stress-strain curves,which correspond to the three distinctive layers,are shown in Fig.8.Using the three calculated stress-strain relations and a stress-strain relation measured for the untreated sample,as shown in Fig.9,the stress-strain relation for the treated sample was computed through Eq.(13);and Fig.9 shows the result.An experimental stress-strain relation for the treated material is also shown in Fig.9.It can be seen that the calculated and experimental results agreed well.

Fig.8 Stress-strain curve for different layers

Figure 9 clearly shows that the material is strengthened after the surface severe plastic deformation.Although the thickness of the hardening layer is very small compared with the matrix,it shows obvious hardening effects.This can be explained by the load sharing mechanism of composite materials [ 33] :

Fig.9 Computed and experimental stress-strain curves

where F represents the load sharing fraction of the ith layer at a certain strain.Figure 10 illustrates the load sharing effect of the hardening and transition layers.It can be shown that the load sharing fractions of the three layers increased with the strain and remained approximately stable as they all deformed plastically.It also shows that the subsurface hardening layer shares 8.5%of the load applied to the material,which is twice its volume fraction.The three layers share approximately 20%of the applied load,even though their volume fraction is only 9.5%.The hardening and transition layers exhibit higher initial yield and flow stress due to the refined microstructure and work hardening effect;hence,they can share more load in the treated samples.Therefore,the treated materials were strengthened.

The microstructure and the local mechanical behavior of gradient structure materials change as the depth from the top surface increases;therefore,it can be concluded that the underlying dislocation mechanism during plastic deformation is distinctive at different depths.In the biaxial tension-torsion fatigue experiment,the dislocation configuration varied from the surface to the interior [ 2] .In addition,the equal strain assumption was used to calculate the average stress of the treated samples in this study,but a lateral strain gradient may exist during uniaxial straining.For this reason,the dislocation evolution and synergetic effect between the layers should be examined in the future.

Fig.10 Load sharing for different layers

6 Conclusion

Commercially pure zirconium was processed by the SMAT method.A nanoindentation test and dimensional analysis were carried out to evaluate the local mechanical behaviors.It was shown that the hardness and yield stress in the surface layer of the samples increased significantly after treatment.The elastic modulus and strain hardening exponent remained approximately stable at different depths.By using the ROM,a correlation between the local elastic-plastic response and the whole elastic-plastic deformation behavior of the treated materials was approximated.The calculated and experimental results showed good agreement.Even though the volume fraction was smaller than that of the unaffected matrix,the calculation results showed that the hardening and transition layers share a relatively high load applied to the sample.Therefore,the improved strength of the treated samples can be explained by the load sharing mechanism.

Acknowledgements This study was financially supported by the National Natural Science Foundation of China (Nos.51674187 and51671153),the Science and Technology Department of Shaanxi Province (No.2017GY-115) and the Education Department of Shaanxi Province (No.16JK1466).

参考文献

[1] Zhang CH,Yu F,Wang YM,He XM.Fatigue property of commercial pure zirconium subjected to surface nanocrystallization.Chin J Rare Met.2017;41(3):284.

[2] Xin C,Sun QY,Xiao L,Sun J.Biaxial fatigue property enhancement of gradient ultra-fine-grained Zircaloy-4 prepared by surface mechanical rolling treatment.J Mater Sci.2018;53(17):12492.

[3] Li YF,Chen C,Ranabhat J,Shen YF.Formation mechanism and mechanical properties of surface nanocrystallized Ti-6Al-4V alloy processed by surface mechanical attrition treatment.Rare Met.2017.https://doi.org/10.1007/s12598-017-0988-4.

[4] Chen HL,Yang J,Zhou H,Moering J,Yin Z,Gong YL,Zhao KY.Mechanical properties of gradient structure Mg alloy.Metall Mater Trans A.2017;48(9):3961.

[5] Li YS,Li LZ,Nie JF,Cao Y,Zhao YH.Microstructural evolution and mechanical properties of a 5052 A1 alloy with gradient structures.J Mater Res.2017;32(23):4443.

[6] Lu K,Lu J.Nanostructured surface layer on metallic materials induced by surface mechanical attrition treatment.Mater Sci Eng,A.2004;375-377(1):38.

[7] Huang HW,Wang ZB,Lu J,Lu K.Fatigue behaviors of AISI316L stainless steel with a gradient nanostructured surface layer.Acta Mater.2015;87:150.

[8] Li WL,Tao NR,Lu K.Fabrication of a gradient nano-micro-structured surface layer on bulk copper by means of a surface mechanical grinding treatment.Scripta Mater.2008;59(5):546.

[9] Tao NR,Sui ML,Lu J,Lu K.Surface nanocrystallization of iron induced by ultrasonic shot peening.Nanostruct Mater.1999;11(4):433.

[10] Liu G,Wang SC,Lou XF,Lu J,Lu K.Low carbon steel with nanostructured surface layer induced by high-energy shot peening.Scripta Mater.2001;44(8-9):1791.

[11] Wang T,Wang DP,Liu G,Gong BM,Song NX.Investigations on the nanocrystallization of 40Cr using ultrasonic surface rolling processing.Appl Surf Sci.2008;255(5):1824.

[12] Cherif A,Pyoun Y,Scholtes B.Effects of ultrasonic nanocrystal surface modification(UNSM)on residual stress state and fatigue strength of AISI 304.J Mater Eng Perform.2010;19(2):282.

[13] Wang X,Li YS,Zhang Q,Zhao YH,Zhu YT.Gradient structured copper by rotationally accelerated shot peening.J Mater Sci Technol.2017;33(7):758.

[14] Bahl S,Suwas S,Ungar T,Chatterjee K.Elucidating microstructural evolution and strengthening mechanisms in nanocrystalline surface induced by surface mechanical attrition treatment of stainless steel.Acta Mater.2017;122:138.

[15] Ye C,Telang A,Gill AS,Suslov S,Idell Y,Zweiacker K,Wiezorek JMK,Zhou Z,Qian D,Mannava SR,Vasudevan VK.Gradient nanostructure and residual stresses induced by ultrasonic nano-crystal surface modification in 304 austenitic stainless steel for high strength and high ductility.Mater Sci Eng,A.2014;613:274.

[16] Fang TH,Li WL,Tao NR,Lu K.Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper.Science.2011;331(6024):1587.

[17] Xin C,Xu W,Sun QY,Xiao L,Sun J.Effect of SMRT on microstructure and mechanical properties of Zr-4 alloy.Rare Met Mater Eng.2017;46(7):1954.

[18] Tsai MT,Huang JC,Tsai WY,Chou TH,Chen CY,Li TH,Jang JSC.Effects of ultrasonic surface mechanical attrition treatment on microstructures and mechanical properties of high entropy alloys.Intermetallics.2018;93:113.

[19] Wu XL,Jiang P,Chen L,Zhang JF,Yuan FP,Zhu YT.Synergetic strengthening by gradient structure.Mater Res Lett.2014;2(4):185.

[20] Li Y,Kang RK,Gao H,Wang JH,Lang YJ.Nanomechanical behaviors of(110)and(111)CdZnTe crystals investigated by nanoindentation.Rare Met.2009;28(6):570.

[21] Amiri S,Chen X,Manes A,Giglio M.Investigation of the mechanical behaviour of lithium-ion batteries by an indentation technique.Int J Mech Sci.2016;105:1.

[22] Yang GY,Peng H,Guo HB,Gong SK.Deposition of TiN/TiAIN multilayers by plasma-activated EB-PVD:tailored microstructure by jumping beam technology.Rare Met.2017;36(8):651.

[23] Dhakar B,Chatterjee S,Sabiruddin K.Measuring mechanical properties of plasma-sprayed alumina coatings by nanoindentation technique.Mater Sci Technol.2017;33(3):285.

[24] Liu Y,Zhao XH,Wang DP.Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation.Mater Sci Eng,A.2014;600:21.

[25] Huang L,Lu J,Troyon M.Nanomechanical properties of nanostructured titanium prepared by SMAT.Surf Coat Technol.2006;201(1-2):208.

[26] Dao M,Chollacoop N,Van Vliet KJ,Venkatesh TA,Suresh S.Computational modeling of the forward and reverse problems in instrumented sharp indentation.Acta Mater.2001;49(19):3899.

[27] Lee J,Lee C,Kim B.Reverse analysis of nano-indentation using different representative strains and residual indentation profiles.Mater Des.2009;30(9):3395.

[28] Zhang RY,Daymond MR,Holt RA.A finite element model of deformation twinning in zirconium.Mater Sci Eng,A.2008;473(1-2):139.

[29] Zhang CH,Wang YM,He XM.Nanomechanical properties of zirconium processed by means of surface mechanical attrition treatment.In:TMS 2013 Annual Meeting and Exhibition,Supplemental Proceedings:Linking Science and Technology for Global Solutions.San Antonio;2013.579.

[30] Oliver WC,Pharr GM.Measurement of hardness and elastic modulus by instrumented indentation:advances in understanding and refinements to methodology.J Mater Res.2004;19(1):3.

[31] Wang YM,Yang HP,Zhang CH,Yu F.Analysis of the residual stress in zirconium subjected to surface severe plastic deformation.Met Mater Int.2015;21(2):260.

[32] Zhang L,Han Y,Lu J.Nanocrystallization of zirconium subjected to surface mechanical attrition treatment.Nanotechnology.2008;19(16):165706.

[33] Wang YM,Zhang CH,Zong YP,Yang HP.Experimental and simulation studies of particle size effects on tensile deformation behavior of iron matrix composites.Adv Compos Mater.2013;22(5):299.