Determination of mechanical properties of pure zirconium processed by surface severe plastic deformation through nanoindentation
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
Nanoindentation has proven to be a powerful technique for estimating the mechanical properties of materials
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.
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,hm is the maximum penetration depth corresponding to the maximum indentation load (Pm),and hr is the residual penetration depth after complete unloading.The total work done by the load P during indentation is Wt,the released elastic work during unloading is We,and the stored plastic work is Wp=Wt-We.
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,andσy is the initial yield stress.Considering the yield strain asεy corresponding to the initial yield stress,then:
When the total strainεexceedsεy,it consists of two parts,εy and the nonlinear part (εp);hence,
Combining Eqs.(2),(3),and (4),the stress-strain relation beyondσy can be written as:
Clearly,the elastic-plastic behavior of the material is completely determined by the parameters E,σy,and n and Poisson's ratio (v).
Using dimensional analysis,Dao et al.
1.Considering the elasticity effects of an elastic indenterand an elastic—plastic solid,a reduced elastic modulus(E*) is introduced:
where Ei and vi are the Young’s modulus and Poisson’s ratio for the indenter.For the diamond indenter,Ei=1100 GPa and vi=0.07
where
2.The hardness (Pave) of the material is found throughdimensionless function∏4,which is given by:
3.Defining the representative strain (εr) and thecorresponding stress (σr),a representative strain ofεr=0.033 was used based on comparisons of the computational results with different values ofεr
4.The strain hardening exponent (n) is determined by thedimensionless function∏2 as
5.The initial yield stress (σy) is solved using:
with E,σy,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 hm and hr 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
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
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
whereσt is the average stress of the whole material,N represents the number of layers,σi is the stress of the ith layer,and wi 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
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
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
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
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).
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