Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation

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Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation Yu Liu, Xiaohui Zhao, Dongpo Wang

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S0921-5093(14)00128-2 http://dx.doi.org/10.1016/j.msea.2014.01.096 MSA30755

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Materials Science & Engineering A

Received date: 11 November 2013 Revised date: 25 December 2013 Accepted date: 31 January 2014 Cite this article as: Yu Liu, Xiaohui Zhao, Dongpo Wang, Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation, Materials Science & Engineering A, http://dx. doi.org/10.1016/j.msea.2014.01.096 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation Yu Liu1, Xiaohui Zhao2*, Dongpo Wang3 1 School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China 2 Key Laboratory of Automobile Materials, School of Materials Science and Engineering, Jilin Univers ity, Changchun 130025, China 3 School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China (* Corresponding author: Dr. Xiaohui Zhao, Tel. +86-0431-85094687, Fax: +86-0431-85094687) [email protected]

Abstract Ultrasonic surface rolling process (USRP) is a novel surface nanocrystallization technique based on severe plastic deformation (SPD). The combination of static extrusion and dynamic impact generates intensive plastic deformation, which leads to the strengthening of material surface. The present paper aims to investigate the mechanical properties of material surface after USRP. For this purpose, nano-indentation tests were adopted to obtain the load P and penetration depth h. Dimensional analysis of test results (P-h curves) was then performed for determining the microplasticity of treated material locally. The values of yield strength and strain hardening exponent of surface layer were calculated and verified by finite element simulation. Good agreement was obtained between experimental curves and simulated ones. The microstructural evolution of the surface treated by USRP was discussed to interpret the mechanism of surface strengthening. Finally, effects of USRP parameters including static force, vibration amplitude and repeated processing numbers on the variation of plastic parameters in surface layer were discussed.

1

Keywords:

Nano-indentation;

Ultrasonic

surface

rolling

process;

Surface

nanocrystallization; Plastic property 1. Introduction Severe plastic deformation based surface nanocrystallization technique is being increasingly used to improve the resistance of mechanical components to fatigue, corrosion, friction and wear [1-3]. This is due to the gradually refined surface grain layer generated by SPD, which has no apparent interface with base material and yet has the same chemical composition with base material [4]. A variety of surface nanocrystallization processes have emerged in recent years, such as ball drop, shot peening,

ultrasonic

shot

peening,

high-energy

shot

peening,

surface

nanocrystallization and hardening, deep rolling and diamond burnishing, ultrasonic cold forging technology, etc. [5-10]. On the basis of these methods, Wang [11] proposed the ultrasonic surface rolling process method, shown as Fig. 1. Alternating current of 20 kHz generated by ultrasonic power supply is converted to mechanical vibration in the same frequency through the USRP tool fasten on the feed mechanism of CNC machining centre. The processing tip is a rotatable ball and thus impacts the surface of specimen with static force while rolling on the specimen surface under certain CNC parameters. The combination of ultrasonic vibration and static force applied by spring fixed at the bottom of USRP tool produces large elastic and plastic deformation in the surface layer of material. As a result, grains in surface layer are refined with hardness, roughness etc. remarkably improved. It can be seen that in this way the imperfection of surface integrity induced by high-energy balls or

2

shots bombarding under improper processing parameter can be overcome [12]. Meanwhile, the ubiquitous lack of service life in ultrasonic cold forging technology is ameliorated in USRP by means of changing sliding friction to rolling friction [10,11]. For a new surface nanocrystallization process, the mechanical properties of material surface after treatment are particularly concerned. Conventional test methods for mechanical properties are apparently not applicable. The nano-indentation technique is then adopted for determining the microplasticity of treated material locally. This testing technique is able to measure the force and displacement in an extremely sensitive way through a small-scale indenter [13]. Straightforward measurement results are load-displacement curves. The mechanical properties need to be derived from nano-indentation data. A few studies have been carried out to obtain the local elastic-plastic properties quantitatively [14-18]. One frequently-used method among these studies is the dimensional analysis of nano-indentation, which provides the basic relations between the elastic-plastic properties of the indented materials and their indentation load-penetration depth measurements [13]. The early acknowledged dimensional analysis was done by Dao et al. They performed a parametric study of 76 cases with various elastic-plastic parameters using finite element analysis and found out that the loading curvature C can be normalized independently of the strain hardening exponent n at the representative strain

H r of 0.033 [14]. Based on this, they

established a set of dimensionless functions that can predict the indentation response from the elastic-plastic properties. Yet the sensitivity to the data (P-h curve) and

3

experimental errors should be minimized. Recently, Jungmin Lee et al. [19] have proposed a reverse analysis of nano-indentation accomplished by using various representative strains in a generalization of the loading curvatures and adopting only C and Wp/Wt as the independent parameters representing P-h curve in establishing a series of dimensionless functions. The general procedure of this method was based on the work of Dao et al. [14]. The present work adopts the method of Jungmin Lee et al. for determining the plastic properties of materials treated by ultrasonic surface rolling process. For most pure metals and alloys, the uniaxial stress-strain relation of material can be estimated by power law constitutive equation. Thus, the power law relationship is often used for expressing the plastic behavior of material during nano-indentation test [13]. The stress-strain relation is shown as follows [20]:

V

EH ( V d V y )

(1)

V

KH n ( V ! V y )

(2)

This constitutive model includes two independent material parameters, which are yield stress V y and strain hardening exponent n, respectively. K is the strength coefficient. Before the stress reaches y, only elastic deformation occurs. When the stress exceeds this limiting value, plastic deformation also appears (see Fig. 2). Assuming the yield strain as H y corresponding to the initial yield stress, then:

Vy

EH y

KH yn

(3)

If H p denotes plastic strain, the total strain can be presented as [21]:

H

Hy Hp 4

(4)

Combine formula (1) ~ (4), the flow stress beyond yield stress is:

V

· § E V y ¨¨1  H p ¸¸ ¹ © Vy

n

(5)

Clearly, the plasticity of material is determined in case of V y and n solved out. In order to accomplish this, dimensional analysis of the loading-unloading processes based on the experimental nano-indentation curves is carried out and the fundamental relation between plastic parameters and load-displacement curves can be acquired. A critical issue in dimensional analysis of indentation response is to ascertain the representative strain H r , so that the normalized curvity C in loading stage could be unaffected by the strain hardening exponent. That is the yield stress and strain hardening exponent can be obtained independently. For Vickers indenter and Berkovich indenter, a variety of representative strain values are given in existing literature, for example 0.076, 0.029, 0.033, etc. [14,22,23]. Recent studies have concluded that r changes between 0.0115 and 0.042 due to the difference of E r / V r [17,24]. r is 0.033, 0.025, 0.023 respectively, corresponding to the range of Er/r as ~800, ~1500, ~3300 [24]. Yet, these results against r are less specific. Jungmin Lee et al. have reported the details about r, shown in Fig. 3 [19]. As can be seen from Fig. 3, r decreases with the increase of Er/r. The function of the fitted curve in Fig. 3 is [19]:

Hr

§ · 166 .7 ¸ exp¨¨  3.91  E r V r  177 .3 ¸¹ ©

(6)

In general, the indentation load P is the function of variables including indentation depth h , elastic modulus E , poisson ratio Q , elastic modulus of

5

indenter Ei , poisson ratio of indenter Q i , V y and n, represented as [19]:

P

Ph, E,Q , Er ,Q r ,V y , n

(7)

The elastic modulus of material E has a relation with that of indenter as [13]:

1 Er

1 Q 2 1 Q i2  E Ei

(8)

where E r is the composite modulus. Combine formula (7) with (8):

P

Ph, Er , V y , n

(9)

Meanwhile, P can be presented by V r H r , then

P

P h, E r , V r , n

(10)

According to the 3 theorem of dimensional analysis, E, H , V r and n can be expressed by a set of dimensionless functions [14]. With formula (5), the yield stress and strain hardening exponent of material can be uniquely decided. The concrete solving steps of the above variables are [19]: 1) The loading stage of nano indentation curve is denoted as:

P Ch 2

(11)

Also, the elastic work We , plastic work W p and total work Wt can be extracted from the curve in loading stage, corresponding to the area under unloading curve, the area bounded by loading curve and unloading curve, the area under loading curve, respectively shown as Fig. 4. The utilization of Wp and Wt reduces the error brought by the calculation of parameters through residual depth after unloading. C ,

Wp and Wt are directly obtained from the nano indentation curve. 2) Elasticity modulus is solved as:

6

§Wp 3 2 ¨¨ © Wt

C Er

§Wp 2.107  2.1092 ¨¨ © Wt

· ¸¸ ¹

· ¸¸ ¹

(12)

The elasticity modulus here is the composite modulus and will used for the solution of latter formulas. 3) The representative stress V r is solved as:

C

Vr

§E · 3 1 ¨¨ r , n ¸¸ ©Vr ¹

ª §E 0.00656 «ln¨¨ r ¬ ©Vr

ª §E  1.47864 «ln¨¨ r ¬ ©Vr Then,

3

ª §E ·º ¸¸»  0.17093«ln¨¨ r ¹¼ ¬ ©Vr

·º ¸¸» ¹¼

2

(13)

·º ¸¸»  0.42932 ¹¼

H r can be calculated with the known r and E r .

4) The nano-indentation hardness is solved as: §Wp 3 4 ¨¨ © Wt

H Er

§Wp 0.244  0.245¨¨ © Wt

· ¸¸ ¹

· ¸¸ ¹

0.78908

(14)

5) The strain hardening exponent is solved as:

C H

§E · 3 3 ¨¨ r , n ¸¸ ©Vr ¹

0.00802 n  0.02194 n  0.00677 n  0.00858 ª«ln§¨¨ E r ¬ ©Vr

·º ¸¸ » ¹¼

3

ª §E  0.11401n  0.17866 n  0.0163 n  0.20838 «ln ¨¨ r ¬ ©Vr

·º ¸¸ » ¹¼

2

3

2

3

2

ª §E   1.06707 n 3  0.57297 n 2  0.56114 n  1.68803 «ln ¨¨ r ¬ ©Vr  0.97574 n 3  1.20917 n 2  0.02855 n  0.09175

(15)

·º ¸¸ » ¹¼

6) The yield stress is solved through:

Vr

· § E V y ¨¨1  H r ¸¸ © Vy ¹

n

(16)

With Er, r, r and n ascertained, the yield stress V y is finally determined. After the plastic parameters of the material surface with the USRP processes were 7

quantified, effect of USRP on mechanical properties were discussed. A detailed microstructural characterization of the surface treated material was presented, and correlated with the measured local mechanical properties to interpret the mechanism of surface strengthening. The overall study was aimed at enriching the knowledge of USRP. 2. Experimental 2.1 Ultrasonic surface rolling treatments The specimens examined in this study were treated by ultrasonic surface rolling before nano-indentation tests. As a novel surface nanocrystallization method, USRP principally treats surface of plane or rotational parts with the aid of a numerically controlled lathe. Considering the accessibility and accuracy of nano-indentation tests, plane specimen, as-supplied 40Cr steel (according to the Chinese nomenclature), was chosen for USRP. Its chemical composition is presented in Table 1. The processing tip used in this paper was 15mm in diameter and made of carboloy metal. USRP parameters adopted for processing were divided into two groups generally representing two types of typical fabrication intensity. For low processing strength, the USRP parameters including spindle speed, feeding rate, static force, ultrasonic vibration amplitude and repeated processing numbers were 246r/min, 10mm/min, 200N, 6m, 3 and 6 times, respectively, while for high processing strength parameters were 246r/min, 10mm/min, 600N, 10m, 3, 6 and 12 times, respectively. The spindle speed was set at the maximum radius in the contact zone and gradually changed to keep the circumferential speed constant. The entire

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treatment was carried out at ambient temperature with coolant poured around the machining area. 2.2 Nano-indentation tests Cube samples (8 mm×8mm×8mm), one side of which had been processed by USRP, were cut from 40Cr specimens using wire-electrode cutting. With the purpose of investigating the variation of mechanical parameters from material surface to matrix, the nano-indentation measurements were performed on sections perpendicular to the treated surface, schematically shown as Fig. 5. The cut surfaces to be tested were carefully prepared by mechanical grinding using SiC paper down to 2000 grit followed by orderly polishing with 3.0-0.5m K-type aluminum suspension. All the nano-indentation measurements in the present work were performed using a Nano Indenter XP with displacement resolution of 0.01nm and loading resolution of 50nN. This instrument is equipped with a standard Berkovich indenter whose total displacement range is 2mm. The maximum testing load was 300mN, and the holding time corresponding to this maximum load was 30s, while load and displacement were recorded as a function of time. Besides, the loading rate and unloading rate were both 10mN/s. In order to avoid the overlapping of stress field caused by adjacent indentations, the distance between adjacent indentation centers should be longer than 400m for all the experiments. For each test condition, the procedure was repeated several times in different positions and the average value was finally adopted. 3. Analysis of experimental results

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3.1 Load-penetration depth curves The output load-displacement curves recorded during loading-unloading tests are given in Fig. 6 to Fig. 10 for different groups of processing parameters. Apparently, all the curves present a parabolic shape in loading stage and a horizontal straight line in load holding stage. After unloading, the indentation depth is slightly reduced for all the cases as a result of material elastic recovery. Moreover, it can be found that the maximum displacement and residual displacement together decrease as the indentation location gets close to the treated surface, which indicates that the strengthening effect tends to be obvious with the distance from surface reduces. Furthermore, comparing Fig. 6 with Fig. 7, values of maximum displacement and residual displacement for each testing position in Fig. 7 are less than those for the same testing position in Fig. 6. Meanwhile, the curves in Fig. 7 are easy to distinguish, while the curves representing load-displacement response deeper than 90m from the processed surface in Fig. 6 are difficult to distinguish. This means the strengthened layer is thicken by the increase of repeated processing numbers. 3.2 Stress-strain curves Using the equations referred in the previous section, the material parameters calculated were listed in table 2-6. Based on the calculated material parameters, the stress-strain curves of treated material representing the power law relationship are shown from Fig. 11 to Fig. 15 for diverse process parameters. From Fig. 11 to Fig. 15, we can see that after ultrasonic surface rolling processing, the yield strength of material surface layer is highly improved. For 40Cr steel with

10

yield strength of 443.3MPa, the value of surface has been raised to 700.5MPa after 3 USRPs when static force is 200N and vibration amplitude is 6m. As the depth from surface reaches 200m, the yield strength gets close to that of matrix. When the repeated processing number increased to 6, the surface yield strength has been boosted to 817.0MPa. With the increasement of static force and vibration amplitude, material reinforcement effect is more apparent. Subjected by 12 USRPs (static force 600N and vibration amplitude 10m), the yield strength of material surface has been enhanced to 970.0MPa, which is twice as much as the matrix. It is thus clear that the effect of ultrasonic surface rolling process on the strengthening of surface layer is limited in certain material thickness, while processing parameters profoundly affect the enhance degree. 3.3 Finite element validation The indentation processes were simulated using the ABAQUS/Standard implicit finite element code under the conditions of finite deformation kinematics. Since Berkovich indenter was applied in the tests, the finite element model for indenter should be a triangular pyramid, exactly like Berkovich indenter in shape and dimension. However, such a 3D pyramidal shape with sharp edges is not suitable for computation not only because it produces a large stress range in the indented region due to the stress concentrations near the pyramid edges, but also because it has been proved to be highly computationally expensive [20]. Therefore, equivalent modeling approach was adopted. Considering the fact that Berkovich indenter has the same contact area projection functional form with a perfect cone indenter, a conical tipped

11

indenter was used instead of the standard indenter. For Berkovich indenter, the contact area as a function of critical indentation depth hC is given as A cone indenter, the function is A

24.56 hC2 , while for

ShC2 tan 2 T , where  is half the included angle of the

indenter [14,20]. When  is equal to 70.3°, the cone indenter will have the same area to depth ratio as the Berkovich indenter [14,20]. The indenter, made of diamond, was assumed as a rigid body. As axisymmetric conditions were used, the indenter was represented by a line deviated from axis with an angle of 70.3° degrees, shown in Fig. 16. For the tested material, an elastic-plastic model with an isotropic hardening was adopted and the material parameters were derived from the strain hardening law established in the previous section. The geometric dimensions of the indented material (see Fig. 16(a)) were large enough to protect the plastic deformation area (Fig. 16(b)) from boundary effect. Since plastic deformation of 40Cr steel is not very sensitive to thermal activation, no strain rate dependence was included in this model [20]. The indented material was meshed by quadrilateral four-node elements with a gradual refinement near the contact zone. For boundary conditions, the x displacement of the nodes along the symmetry axis was prescribed to be nil and the y displacement together with the x displacement of those nodes on the bottom face of material were fixed. No displacement conditions were imposed on the lateral and upper faces of the material. Comparisons between the results obtained with and without friction force between the indenter and the tested material indicated that the friction force does not

12

introduce any significant deviation in the results [25]. Therefore, the contact area was assumed to be frictionless. The loading-unloading processes were realized in the form of a prescribed force on the reference point of the indenter. Comparison between the experimentally measured indentation load-displacement curves and the simulated ones are shown in Fig. 17 for a series of USRP parameters. The test position for them is the material surface (0m from the surface). It can be seen that the simulated curves correspond well with the experimental data, especially under low processing parameters which is confirmed whether in loading stage or in unloading stage. When static force is 600N and vibration amplitude is 10m, deviation appears in loading stage as the indentation load gets maximum value. Meanwhile, the horizontal section of the load-displacement curve is artificially added to keep consistent with the experimental curves since the rate-independent elastic-plastic model used could not display a "creep" response. In general, all the comparisons clearly demonstrate the soundness of the plastic parameters calculated through theoretical equations and the validity of the finite element model developed for predicting the nano-indentation response. 4. Discussion 4.1 Mechanism of surface strengthening After USRP treatments, severe plastic deformation is generated in the surface layer of material. In consequence, the microstructures of surface layer will be changed, and this change is gradual from the surface to the matrix as stated before. To observe this gradient change, a cross-sectional observation of 40Cr steel treated by 12 USRPs

13

(246r/min spindle speed, 10mm/min feeding rate, 600N static force, 10m ultrasonic vibration amplitude) through optical microscope (OM) is shown in Fig. 18. It is clear that evidences for severe plastic deformation can be seen in the surface layer. Grains in the plastic flow region are severely distorted from equiaxed shape to long striped shape. The severity of grain deformation presents a gradient distribution from the surface to the matrix. The extruding direction of grains close to surface is almost perpendicular to the impact direction of processing tip. As observed from Fig. 18, the apparent plastic flow region reaches 150m in depth after 12 USRPs, yet there are no obvious deformed marks in the region deeper than 200m from the top surface, schematically noted as the dashed line. Grain boundaries and phases could not be clearly identified in OM observations. TEM was then used for observing the variation of grain morphology by depth in the surface layer. Relevant TEM observations of 40Cr steel treated under exactly the same USRP parameters as those in present work were done by other researchers of our team [11], as shown in Fig. 19. The observation positions correspond to the red markers in Fig. 18. It is clear that a nanocrystal surface layer is formed in surface layer. The microstructure of the top surface is characterized by ultrafine equiaxed grains in even size of about 3~7nm with random crystallographic orientations, as indicated by the bright-field image and the selected area electron diffraction (SAED) pattern (Fig. 19 (a)). All diffraction rings in the SAED pattern are identified as ferrite, and the cementite particles which are visible in the metallograph of matrix do not already exist in nano-structured surface. Fig. 19 (b) shows typical TEM plane-view of the

14

layer at about 30m deep from the top surface, where grains grow to 10nm and are still even in size. It can be seen in the electron diffraction pattern that the diffraction ring formed by cementite is fuzzy visible, indicating the existence of cementite in this layer, but the particles are very small and the severe plastic deformation produced during USRP may induce dissolution of the cementite phase into the ultrafine ferrite matrix. At the depth of about 60m, as shown in Fig. 19 (c), grain size continues to grow to 15nm, accompanied by the increase of cementite. Yet, in the layer of 90m deep from surface (Fig. 19 (d)), grains are different in size and most of them are not equiaxed but irregular-shaped. This layer is a transition region and grain size is still nanoscale. In the layer of 140m from the top surface (Fig. 19 (e)), grains rapidly increase to more than 100nm, or in micron-sized. The grain shape is irregular with grain boundaries clearly seen. A lot of strain rest in the interior of grains, though effect of USRP on grain refinement is unapparent. With the deepening of the test position, we found that a small amount of strain still appears in grains. However, grain itself scarcely deforms (see Fig. 19 (f) and Fig. 20 (g) (h)). The severe plastic deformation leading to grain refinement is ascribed to dislocation, since 40Cr has a body-centered cubic (bcc) lattice structure and a high stacking fault energy (SFE) of about 250 mJ/m2. Under the action of static force and dynamic impact, strain keeps increasing. Consequently, dislocation walls and dislocation tangle are formed through slip, accumulation, interaction, annihilation and recombination of dislocations. These dislocation walls and dislocation tangle divide original grains into relatively small dislocation cells, as presented in Fig. 19 (f) and

15

Fig. 20 (g) (h). As strain increases, dislocation density continually grows. In order to reduce the energy of the system, these high-density dislocations annihilate and recombine near the dislocation walls and dislocation tangle, which as a result develop into subboundaries, like Fig. 19 (e). When deformation gets severer, more dislocations emerge and annihilate at subboundaries, making the misorientation on both sides of grain boundaries increasing. Crystallographic orientations tend to be random, shown as Fig. 19 (d). Moreover, dislocation walls and dislocation tangle are also generated in subgrains and grain interior. Hence, these subgrains and grains will be further fragmented following the same mechanism. When the dislocation multiplication rate is balanced by the annihilation rate, the increase of strain does not reduce the subgrain size any further, and the grain size reaches a stabilized value, as the status in Fig. 19 (a) (b) and (c) . Compared microscopic observations with Fig. 15, it can be found that the yield strength is improved as gets closer to the surface where grains get smaller. In fact, the grain refinement greatly enhances the mechanical properties of material, because fine grains could disperse plastic deformation into more grains than coarse grains, which makes the plastic deformation more uniform, thus reducing stress concentration. Besides, the refined grains increase the area of grain boundaries and make the grain boundaries more tortuous, thus impeding the crack propagation. The refined crystalline strengthening is apparent near the top surface since grains in that region achieve nanoscale. For the depth of 200m, 300m and 500m, the tested yield strength values are close, yet still larger than that of matrix. This is because the

16

microstructure in the layer of 200m, 300m and 500m is micron-sized, which means grains there are not refined, but dislocation tangle is much more than that of matrix. Therefore, the yield strength is a little bit higher than that of matrix. 4.2 Effect of USRP parameters on mechanical characteristics As stated in the previous section, the material is strengthened under USRP treatment and dislocation movement induced grain refinement plays a very important role in surface strengthening. Yet what extent does the grain size reduction affect the surface strengthening, and what extent is the dislocation density increasing the strength of surface layer material was not discussed in detail and related with the USRP parameters. Thus, to show a deeper link between the microstructural change after USRP and the indentation-measured stress-strain properties, the relationship of yield stress vs. grain size and strain hardening exponent vs. grain size are presented in Fig. 21 and Fig. 22. On the whole, yield stress reduces as grains get larger for all the experiment conditions. The variation trend of these curves falls broadly into three stages: rapid decline stage, steady decline stage, smooth stage. With 12 USRPs under 600N static force and 10m ultrasonic vibration amplitude, grains from the surface within 100m completely reach nanoscale. In this region, the nano-sized grains have a stable size and random orientation. Also, the dislocation multiplication rate is balanced by the annihilation rate without further plastic deformation, which lowers the energy of the system. In consequence, the boost of yield stress is primarily due to grain size reduction. As observed in Fig. 21, yield stress decreases quickly as grain size

17

increases, indicating that the magnitude of yield stress is very sensitive to grain size, especially when the grain size is less than a dozen nanometers. While in the area where most grains exceed 100nm but still less than 600nm, the yield stress reduces uniformly with the growth of grains. Although no distinct nanocrystal is generated, dislocation density in this area is extremely high. In the layer of 100m deep from surface, the dislocation density almost causes grains to be refined. Such high dislocation density undertakes the effect of strength enhancement. The external load produces relatively even reduction of dislocation density, resulting in steady decline of yield stress. With the test position continues deep to substrate, the dislocation density is insufficient to resist plastic deformation, correspond to the smooth stage in Fig. 21. The influencing mechanism of yield stress after 6 USRPs under 600N static force and 10m ultrasonic vibration amplitude is similar to the case of 12 USRPs. For nanocrystalline area, the dominant factor determining yield stress is still grain size. It is worth noting that though grains in this area are in nanoscale, they are obviously greater than grains of the same test position generated by 12 USRPs. However, for identical grain size, the yield stress of the former is higher than that of the latter. This is because for the same grain size, grains of the former is very close to material surface, but grains of the latter are at a certain distance from the surface, which leads to discrepant residual stress state of two cases. As we have known that the maximum residual compressive stress after 12 USRPs is a little larger in magnitude and depth than that after 6 USRPs, nonetheless for the region within 100m from surface, the

18

residual compressive stresses of two cases are basically the same. Consequently, grains close to surface are more able to resist plastic deformation with the help of residual compressive stress. As to the steady decline stage, it can be seen that the two curves overlap in this part, illustrating that the distributed situation of dislocation density for them is similar. Refined grains in surface layer already improve the strength of material, thus the subsequent external load is hard to make internal material deformed, so as the situation in smooth stage. With 3 USRPs (600N static force, 10m ultrasonic vibration amplitude), 6 USRPs (200N static force, 6m ultrasonic vibration amplitude) and 3 USRPs (200N static force, 6m ultrasonic vibration amplitude), grains in surface layer are all not up to nanoscale, still rest in micro-scale. Larger USRP parameters create higher dislocation density, and the variation trend of dislocation density can also be characterized as three stages: rapid decline stage, steady decline stage, smooth stage. Therefore, these curves show a homologous shape. Moreover, material within 100m from the surface is significantly strengthened not only owing to high dislocation density but also owing to residual compressive stress. As shown in Fig. 22, strain hardening exponent generally increases with the increase of grain size for one type of experimental conditions. When grains are in nanoscale, the strain hardening exponent reduces dramatically as the grains refined, while within micro-scale, the strain hardening exponent has a relatively even increment as grain size grows and dislocation density decreases. Analogously, residual compressive stress lowers the strain hardening exponent of the same sized-grain area

19

which is closer to surface. Fig. 23 and Fig. 24 provide explicit variation of y accompanied by the distance from impacted surface. Fig. 23 shows the y values of surface layer under 3 and 6 USRPs respectively with the static force of 200N and vibration amplitude of 6m. Fig. 24 shows the y values of surface layer under 3, 6 and 12 USRPs respectively with the static force of 600N and vibration amplitude of 10m. It is clear that the value of y generally increases with the increase of repeated processing numbers. The repeated processing numbers have significant effect on superficial y, while hardly affect the thickness of strengthened layer. This is because the repeated processing exacerbates the plastic deformation in surface, resulting in finer grains, which enhances the yield strength of material. As the initial processing already produces dislocation walls and dislocation tangle which become a disadvantage for further plastic deformation, the top surface absorbs most of the energy in the following process. Hence, grains in surface layer relatively far from the top surface bear insufficient plastic deformation, thus unable to be refined. As observed from Fig. 23, the y is close to that of base material when the distance from surface exceeds 200m. In contrast, increasing static force and vibration amplitude not only enhances the y of surface layer but also deepen the strengthened layer due to apparently larger single processing power. It can be seen from Fig. 24, for the case of 600N static force and 10m vibration amplitude, the strengthened layer is 300m in thickness. The penetration depth is still increasing in the constant load holding stage of nano-indentation test, which means material creeps in this section. Due to grain

20

refinement, the creep portion alters under diverse test positions and USRP parameters. The penetration depth occurred in constant load holding stage as a function of depth from surface is shown as Fig. 25. Creep displacement increases as test position deep to the substrate for all groups of USRP parameters. With 12 USRPs, 600N static force and 10m ultrasonic vibration amplitude, the creep displacement of surface is down to 33.2nm, while that of 500m from surface is 42.8nm. The creep displacement values of surface and 500m from surface (3 USRPs, 200N static force and 6m ultrasonic vibration amplitude) are 40.6nm and 50.4nm, respectively. It is apparent that larger USRP parameters produce finer grains, which leads to higher strength, thus enhances the creep resistance. Besides, larger USRP parameters also deepen the thickness of strengthened layer against creep deformation. 5. Conclusions This paper investigates the mechanical properties of material surface after ultrasonic surface rolling process which is a new surface nanocrystallization process. Nano-indentation tests were carried out and dimensional analysis of test results (P-h curves) for determining the microplasticity of treated material locally was performed. Results show that the yield strength of material surface layer is highly improved after USRP. For 40Cr steel with V y of 443.3MPa, the surface V y has been raised to 970.0MPa by 12 USRPs (static force 600N and vibration amplitude 10m), which is twice as much as the matrix. The strengthening of surface layer is attributed to grain refinement and high dislocation density for different depth of surface layer. Meanwhile, residual compressive stress is in favor of against indentation load. The

21

USRP treatments also improve the creep resistance. It is worth noting that the static force, vibration amplitude and repeated processing numbers have significant effect on superficial V y , but unlike static force and vibration amplitude, the repeated processing numbers hardly affect the thickness of strengthened layer. The overall work enriches the knowledge about the performance of USRP.

Acknowledgement The authors acknowledge the financial support by the National Science Foundation through grant no. 51305160 and the Youth Scientific Research Fund of Jilin province through grant no. 20130522184JH.

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[11] Wang Ting, Wang Dongpo, Liu Gang, et al. Investigations on the nanocrystallization of 40Cr using ultrasonic surface rolling processing. Applied Surface Science, 2008, 255: 1824~1829. [12] Leon L. Shaw, Jia-Wan Tian, Angel L. Ortiz, et al. A direct comparison in the fatigue resistance enhanced by surface severe plastic deformation and shot peening in a C-2000 superalloy. Materials Science and Engineering A, 2010, 527: 986~994. [13] A.C. Fischer-Cripps. A review of analysis methods for sub-micron indentation testing. Vacuum, 2000, 58: 569~585. [14] M. Dao, N. Chollacoop, K. J. Van Vliet, et al. Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta mater, 2001, 49: 3899~3918. [15] L.M. Farrissey, P.E. McHugh. Determination of elastic and plastic material properties using indentation: Development of method and application to a thin surface coating. Materials Science and Engineering A, 2005, 399: 254~266. [16] M. Toparli, N.S. Koksal. Hardness and yield strength of dentin from simulated nano-indentation tests. Computer Methods and Programs in Biomedicine, 2005, 77: 253~257. [17] N. Ogasawara, N. Chiba, X. Chen. Measuring the plastic properties of bulk materials by single indentation test. Scripta Materialia, 2006, 54: 65~70. [18] Hongzhi Lan, T.A. Venkatesh. Determination of the elastic and plastic properties

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of materials through instrumented indentation with reduced sensitivity. Acta Materialia, 2007, 55: 2025~2041. [19] J.M. Lee, C.J. Lee, B.M. Kim. Reverse analysis of nano-indentation using different representative strains and residual indentation profiles. Materials and Design, 2009, 30: 3395~3404. [20] L.M. Farrissey, P.E. McHugh. Determination of elastic and plastic material properties using indentation: Development of method and application to a thin surface coating. Materials Science and Engineering A, 2005, 399: 254~266. [21] I.S. Choi, M. Dao, S. Suresh. Mechanics of indentation of plastically graded materials-I: Analysis. Journal of the Mechanics and Physics of Solids, 2008, 56: 157~171. [22] K.L. Johnson. Contact mechanics. UK: Cambridge University Press; 1985. [23] A.E. Giannakopoulos, S. Suresh. Determination of elastoplastic properties by instrumented sharp indentation. Scripta Mater, 1999, 40:1191~8. [24] N. Ogasawara. Representative strain of indentation analysis. J Mater Res, 2005, 20:2225~34. [25] H. Elghazal, G. Lormand, A. Hamel, et al. Microplasticity characteristics obtained through nano-indentation measurements: application to surface hardened steels. Materials Science and Engineering A, 2001, 303: 110~119.

25

Tables Table 1 Chemical composition of 40Cr steel (wt%) Table 2 Plastic parameters obtained under 3 USRPs (200N, 6m) Table 3 Plastic parameters obtained under 6 USRPs (200N, 6m) Table 4 Plastic parameters obtained under 3 USRPs (600N, 10m) Table 5 Plastic parameters obtained under 6 USRPs (600N, 10m) Table 6 Plastic parameters obtained under 12 USRPs (600N, 10m)

26

Table 1 Chemical composition of 40Cr steel (wt%) C

Si

Mn

Cr

S

P

Ni

0.37-0.45

0.17-0.37

0.50-0.80

0.10-0.80

0.01

0.021

0.12

27

Table 2 Plastic parameters obtained under 3 USRPs (200N, 6m) Distance from the surface (m)

C (GPa)

W p / Wt

V y (MPa)

n

0

83.63

0.89175

700.5

0.092

30

77.16

0.90011

612.0

0.103

60

69.90

0.89906

569.1

0.120

90

65.02

0.90730

525.3

0.126

140

64.22

0.91705

483.5

0.127

200

63.63

0.92054

457.8

0.130

300

63.05

0.92204

449.3

0.133

500

62.48

0.91988

443.6

0.135

29

Table 3 Plastic parameters obtained under 6 USRPs (200N, 6m) Distance from the surface (m)

C (GPa)

W p / Wt

V y (MPa)

n

0

96.71

0.89054

817.0

0.089

30

89.14

0.89286

729.4

0.098

60

82.14

0.90051

623.5

0.115

90

78.28

0.90406

566.1

0.122

140

72.02

0.90784

510.9

0.126

200

66.70

0.90975

468.5

0.128

300

63.47

0.90930

456.0

0.130

500

62.13

0.90664

453.6

0.131

31

Table 4 Plastic parameters obtained under 3 USRPs (600N, 10m) Distance from the surface (m)

C (GPa)

W p / Wt

V y (MPa)

n

0

91.14

0.89169

764.0

0.091

30

83.44

0.89602

683.5

0.096

60

76.73

0.90232

589.9

0.111

90

73.48

0.90909

532.2

0.120

140

69.30

0.91836

529.0

0.125

200

65.28

0.91629

488.6

0.127

300

63.55

0.91927

468.1

0.127

500

62.15

0.91815

454.0

0.129

33

Table 5 Plastic parameters obtained under 6 USRPs (600N, 10m) Distance from the surface (m)

C (GPa)

W p / Wt

V y (MPa)

n

0

104.68

0.89544

873.0

0.086

30

90.94

0.90204

746.9

0.091

60

81.81

0.90642

636.5

0.104

90

74.95

0.89814

579.8

0.112

140

70.13

0.90765

522.5

0.116

200

66.97

0.90833

497.1

0.117

300

64.27

0.89905

466.0

0.122

500

63.12

0.90586

464.5

0.121

34

Table 6 Plastic parameters obtained under 12 USRPs (600N, 10m) Distance from the surface (m)

C (GPa)

W p / Wt

V y (MPa)

n

0

116.89

0.90168

970.0

0.087

30

99.30

0.88766

850.5

0.087

60

88.72

0.90536

713.0

0.095

90

80.66

0.91151

609.7

0.109

140

72.68

0.90967

546.3

0.112

200

68.82

0.90825

510.0

0.117

300

64.65

0.91202

471.5

0.118

500

62.09

0.91011

457.8

0.121

36

Figures Fig. 1 Schematic of USRP working Fig. 2 The power law stress-strain behavior of metals Fig. 3 Variations of representative strain H r as a function of E r / V r [19] Fig. 4 The schematic diagram of indentation work Fig. 5 Schematic of nano-indentation measuring position on section perpendicular to the treated surface Fig. 6 Load-displacement responses for specimen treated by 3 USRPs (200N, 6m) Fig. 7 Load-displacement responses for specimen treated by 6 USRPs (200N, 6m) Fig. 8 Load-displacement responses for specimen treated by 3 USRPs (600N, 10m) Fig. 9 Load-displacement responses for specimen treated by 6 USRPs (600N, 10m) Fig. 10 Load-displacement responses for specimen treated by 12 USRPs (600N, 10m) Fig. 11 Stress-strain curves of different depth from surface obtained under 3 USRPs (200N, 6m) Fig. 12 Stress-strain curves of different depth from surface obtained under 6 USRPs (200N,6m) Fig. 13 Stress-strain curves of different depth from surface obtained under 3 USRPs (600N,10m) Fig. 14 Stress-strain curves of different depth from surface obtained under 6 USRPs (600N, 10m)

26

Fig. 15 Stress-strain curves of different depth from surface obtained under 12 USRPs (600N, 10m) Fig. 16 Finite element model for nano-indentation tests Fig. 17 Comparison between experimental and computed load as a function of displacement for cases of (a) static force 200N, vibration amplitude 6m, 3 USRPs, (b) static force 200N, vibration amplitude 6m, 6 USRPs, (c) static force 600N, vibration amplitude 10m, 3 USRPs, (d) static force 600N, vibration amplitude 10m, 6 USRPs Fig. 18 Cross-sectional metallographic observation of 40Cr subjected to 12 USRPs Fig. 19 TEM images and the corresponding SAED patterns at depth less than 200m of 40Cr sample treated by 12 USRPs [11] Fig. 20 TEM images and the corresponding SAED patterns at depth of 300m and 500m of 40Cr sample treated by 12 USRPs Fig. 21 The relationship between yield stress and grain size Fig. 22 The relationship between strain hardening exponent and grain size Fig. 23 y values of different depth from surface (200N, 6m) Fig. 24 y values of different depth from surface (600N, 10m) Fig. 25 The creep displacement occurred in constant load hold stage as a function of depth from surface

27

Fig. 1 Schematic of USRP working

28

Fig. 2 The power law stress-strain behavior of metals

29

Fig. 3 Variations of representative strain H r as a function of E r / V r [19]

30

Fig. 4 The schematic diagram of indentation work

31

Fig. 5 Schematic of nano-indentation measuring position on section perpendicular to the treated surface

32

Fig. 6 Load-displacement responses for specimen treated by 3 USRPs (200N, 6m)

33

Fig. 7 Load-displacement responses for specimen treated by 6 USRPs (200N, 6m)

34

Fig. 8 Load-displacement responses for specimen treated by 3 USRPs (600N, 10m)

35

Fig. 9 Load-displacement responses for specimen treated by 6 USRPs (600N, 10m)

36

Fig. 10 Load-displacement responses for specimen treated by 12 USRPs (600N, 10m)

37

Fig. 11 Stress-strain curves of different depth from surface obtained under 3 USRPs (200N, 6m)

38

Fig. 12 Stress-strain curves of different depth from surface obtained under 6 USRPs (200N, 6m)

39

Fig. 13 Stress-strain curves of different depth from surface obtained under 3 USRPs (600N, 10m)

40

Fig. 14 Stress-strain curves of different depth from surface obtained under 6 USRPs (600N, 10m)

41

Fig. 15 Stress-strain curves of different depth from surface obtained under 12 USRPs (600N, 10m)

42

(a) Finite element mesh

(b) Deformation area around indenter Fig. 16 Finite element model for nano-indentation tests

43

Fig. 17 Comparison between experimental and computed load as a function of displacement for cases of (a) static force 200N, vibration amplitude 6m, 3 USRPs, (b) static force 200N, vibration amplitude 6m, 6 USRPs, (c) static force 600N, vibration amplitude 10m, 3 USRPs, (d) static force 600N, vibration amplitude 10m, 6 USRPs

44

Fig. 18 Cross-sectional metallographic observation of 40Cr subjected to 12 USRPs

45

Fig. 19 TEM images and the corresponding SAED patterns at depth less than 200m of 40Cr sample treated by 12 USRPs [11]

46

Fig. 20 TEM images and the corresponding SAED patterns at depth of 300m and 500m of 40Cr sample treated by 12 USRPs

47

Fig. 21 The relationship between yield stress and grain size

48

Fig. 22 The relationship between strain hardening exponent and grain size

49

Fig. 23 V y values of different depth from surface (200N, 6m)

50

Fig. 24 V y values of different depth from surface (600N, 10m)

51

Fig. 25 The creep displacement occurred in constant load hold stage as a function of depth from surface

52