Spherical indentation method for measuring local mechanical properties of welded stainless steel at high temperature

Materials and Design 52 (2013) 812–820

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Spherical indentation method for measuring local mechanical properties of welded stainless steel at high temperature Akio Yonezu a,⇑, Hirotaka Akimoto a, Shoichi Fujisawa a, Xi Chen b,c,1 a

Department of Precision Mechanics, Chuo University, 1-13-27 Kasuga, Bunkyo, Tokyo 112-8551, Japan Department of Earth and Environmental Engineering, Columbia University, 500 W 120th Street, New York, NY 10027, USA c International Center for Applied Mechanics, SV Lab, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China b

a r t i c l e

i n f o

Article history: Received 26 March 2013 Accepted 8 June 2013 Available online 19 June 2013 Keywords: Welded stainless steel Local mechanical property Indentation method

a b s t r a c t Indentation method was employed to evaluate the local mechanical properties of welded stainless steel at a high temperature of 320 °C. The welding process often changes the mechanical properties (in particular the plastic properties), and make the material property inhomogeneous. An indentation method was proposed to effectively evaluate the stress–strain relationship (approximated by the Ludwick-type hardening law) in the welded SUS316L at 320 °C. Functional relationship between the indention response and plastic property was established using finite element method (FEM). The dimensional function was deduced based on sufficiently-deep indentation, so that it can directly estimate plastic properties up to large uni-axial strain (about 20%). Spherical indentation tests applied to welded SUS316L may enable the evaluation of the distribution of plastic properties, such as the yield stress, plastic strain and tensile strength. The properties around the welded area were estimated to be higher than the base material of SUS316L, owing to the local plastic deformation from welding-induced thermal expansion and construction. Parallel test was conducted to validate the model. The proposed indentation technique can quantitatively evaluate the local mechanical properties at high working temperature, and supply useful information on inhomogeneous property distribution in materials. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Stainless steel is widely used for corrosion resistant structural materials, such as underground pipe for oil well and cooling water piping for nuclear power system. In practice, the engineering components often undergo plastic work (cold work) and welding joint processes. During the welding process, the local heat input leads to local thermal expansion, which induces large local plastic strain – such welding deformation often leads to significant work-hardening and residual stress [1–5]. For instance, Piatti and Vedani showed that the tensile property of welded stainless steel was changed due to local dissimilarities in thermal and mechanical history during welding [1]. Trough micro Vickers hardness measurements around welded area, Song et al., reported that welding induces inhomogeneous mechanical property [5]. Since the inhomogeneous distribution of plastic property often leads to environmental assisted cracking and fatigue fracture [6,7], the distribution

⇑ Corresponding author. Tel.: +81 3 3817 1829; fax: +81 3 3817 1820. E-mail addresses: [email protected] (A. Yonezu), [email protected] (X. Chen). 1 Address: Department of Earth and Environmental Engineering, Columbia University, 500 W 120th Street, New York, NY 10027, USA. Tel.: +1 212 854 3787; fax: +1 212 854 7081. 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.06.015

should be clarified. In other words, for the sake of structural integrity and the optimization, quantitative evaluation of the inhomogeneous distribution of material property is desired for a ‘‘local’’ area (e.g. a limited area of material surface). Note that in some cases (e.g. power plants), the operating temperature is relatively high and the in situ material characterization prohibits the use of conventional testing methods (e.g. uniaxial tension). Indentation is a useful method to probe mechanical property of materials in small volume [8]. In this method, a hard indenter impresses against the specimen surface at a given force and then unloads. The relationship between indentation response (forcepenetration depth relationship) and the elastoplastic property of material can be established through theoretical or numerical analyses, such as finite element method (FEM) simulations. By assigning the indentation responses to the established functions, reverse analysis can be employed to identify the material constants in the constitutive equation [9–15]. Dao et al. [9] [13] introduced the representative strain concept to dimensionless function [16] which can correlate the indentation curve with elastoplastic properties in a simplified way. Following this idea, the uses of plural sharp indenter with different angle [14] and spherical indenter [10,12] were proposed in order to make accurate estimations. An appropriate application of such a framework may enable the evaluation of welding joint or plastic worked materials, such that their local

A. Yonezu et al. / Materials and Design 52 (2013) 812–820

plastic properties can be quantitatively evaluated, thus supplying critical information on ‘‘mapping’’ of inhomogeneously distributed property. One of the practical issues of the indentation method is the uniqueness of reverse analysis, that is, whether there is a one-toone correspondence between indentation response and material constitutive relationship. Previous studies have shown the existence of special sets of materials which have distinct elastoplastic properties, yet whose indentation curves are almost the same [11,17,18]. These materials cannot be effectively distinguished by the indentation method unless very deep spherical indentation tests are carried out [18]. Another important issue is the data scattering from experiments and error sensitivity of reverse analysis. In all cases, experimental verification of the proposed method is required. In addition, most previous studies were focused on materials that obey the power law hardening behavior (sometimes called the Hollomon law); these types of materials involve only two unknown variables for plastic property (the yield stress and work hardening exponent). However, sometimes the power-law hardening behavior is insufficient to describe practical materials, and other constitutive equations (e.g. linearly hardening law, Swifttype, Voce-type, Ludwick-type etc.) may be employed to describe the stress–strain curves in engineering steels. Indeed, appropriate selection of the type of constitutive relationship is a first step for a robust indentation-based reverse analysis. Some studies have reported that the plastic flow behavior of stainless steel is difficult to be expressed by the power law equation (Hollomon law) [1,19,20]. It is suggested that, when the reverse analysis based on power law hardening was experimentally applied to stainless steel, the estimations of plastic behavior may be of poor accuracy [19,21,22]. Thus, Kim et al. emphasized that an appropriate constitutive equation is required a priori for indentation-based estimation [19]. Based on the above considerations, this study aims to develop a robust and effective indentation analysis framework for SUS316L welding joint. We first investigated the plastic constitutive equation of the stress–strain curve of SUS316, so that the present indentation method can be applied to both the as-received and drawn SUS316L. Based on the appropriate constitutive equation, functional relationship between the indentation response and plastic property was next established by extensive FEM simulations of deep spherical indentation tests. The formulations were simplified through the use of the representative strain, which makes it possible for the identification of several materials constants by using one test (single indentation). The indentation framework was applied to the evaluation of the local plastic property in welding stainless steel at 320 °C (operating temperature of power plant). The estimations from the present indentation method were verified by comparing with the stress–strain relationship evaluated from tensile tests at both room temperature and 320 °C. This study also evaluated the local plastic properties of welded stainless steel at 320 °C. The distribution of the properties, including the yield stress, plastic strain and tensile strength, around the welding joint were quantitatively evaluated. Thus, the present method (which can readily evaluate local properties) may be extended to various welded components, plastic worked material and surface hardening treatment (carburizing and peening etc.), which often have inhomogeneous distribution of plastic property.

813

to previous study [23]. One is the as-received material (base material) and the other is cold-drawn material (the reduction area is about 16%). Fig. 1 shows the relationship between true stress and true strain (true stress – true strain curve) of both materials, exhibiting non-linear behavior of plastic flow. Here, the horizontal axis indicates true plastic strain, since this study will use Ludwick law for appropriate constitutive law. It was observed that the flow stress behavior of cold-drawn material was higher than that of based material. The Young’s moduli E was 175 GPa. The yield stresses rY were 260 MPa and 620 MPa. Next, the non-liner regions of plastic flow for both materials (in Fig. 1) were approximated by two constitutive equations, i.e. power hardening law (Hollomon type, Eq. (1)) and Ludwick type hardening law (Eq. (2)). These equations are expressed as follows.

r ¼ Ee for r 6 rY ; and r ¼ K en for r P rY

ð1Þ

r ¼ Ee for r 6 rY ; and r ¼ rY þ K enp for r P rY

ð2Þ

where rY is the yield stress, n is the work-hardening exponent, K is the work-hardening strength and E is the Young’s modulus. Note that in Eq. (1) strain e is total strain, while ep in Eq. (2) is plastic strain. The power hardening law in Eq. (1) is the most-used constitutive equation whose independent parameter is only two (rY and n), when E is known prior, and its elastoplastic property identification through indentation has been widely studied. On the other hand, the Ludwick type hardening law has three independent

2. Materials The material considered in the present study is an austenitic stainless steel and its welding joint. To investigate the appropriate constitutive equation of the plastic flow behavior, stress–strain curves under uniaxial tensile test were first investigated, according

Fig. 1. Stress–strain curve of SUS316L(23); (a) base stainless steel and (b) cold worked one. This compares the fitted curves with Ludwick law and Hollomon law.

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constants (rY, n and K) to express the non-linear behavior of plastic flow. Here, Eq. (2) becomes the linearly hardening law, when n is one. Although the Ludwick type hardening law was reported to be available for stainless steels and high alloy steels [1,19,20]2, the use of such hardening law was rare in the previous indentation studies. In Fig. 1, each experimental curve up to the strain of 30% was fitted by Eqs. (1) and (2), i.e. the materials constants were optimized, when the correlation factors become the highest value. For the fittings by power law hardening (as indicated by dash lines), the approximation appears to be poor whose correlation factors were 0.93 of base material, and 0.88 of cold-drawn material. In contrast, the Ludwick type hardening law (as indicated by solid lines) could well approximate the constitutive behavior with the correlation factors of 0.999 of both base and cold-drawn materials. This indicated that the stress–strain curve of SUS316L can be fitted well by the Ludwick type hardening law rather than the power law hardening one. Therefore, the Ludwick type law should be employed to develop the indentation framework.

Rigid indenter 20 μm

Rigid indenter

Material

Material 100 μm

Fig. 2. Axi-symmetric two-dimensional FEM model for spherical indentation.

3. Indentation framework 3.1. FEM analyses Previous studies have shown that spherical indentation is capable to deduce elastoplastic properties from the measurements at several depths (which mimics the effect of the dual/plural sharp indenter method), yet it requires only one test (single indentation). In the last two decades, there have been many attempts to measure the elastoplastic properties of power law hardening materials based on spherical indentation curve [10,12,24–26]. Among them, the method of stress–strain constraint factor and dimensionless analysis have been widely investigated, in particular the approaches based on the concept of the representative strain were well discussed. The present study extends such an approach for improvement of the method to be available for the Ludwick type material with application to SUS316L. The axisymmetric model of two-dimensional FEM was created to compute the response of spherical indentation. As shown in Fig. 2, the model comprises more than 3000 four-nodes wherein fine meshes were created around the contact region and a mesh convergence study was carried out. The spherical indenter with a tip radius R of 40 lm was assumed to be a rigid body. The computations were performed using the commercial package software, Marc and Mentat (Marc 2005r3 and Marc 2011). The Coulomb’s law of friction was assumed with a friction coefficient l of 0.15, often used for indentation analysis [11,27]. The indenter was impressed on the specimen up to the maximum indentation depth hmax and was released down to h = 0 lm under displacement control for all computations. Here, we assumed that FEM model obeys the macroscopic plastic hardening law (see Eq. (2)). Strain gradient effect and grain plasticity (whose effects are usually faced on in nano/micro indentation experiment) were not taken into account. To ignore such effects, indentation penetration should be deeper [11,28,29]. Indeed, deep indentation with the normalized penetration of h/ R = 0.3 is useful to ensure the unique solution of the identified properties [11,18]. Another advantage is that owing to the non self-similarity, deep penetration curve captures the plastic property up to a large range of stress–strain relationship (approaching the failure strain). Considering the above issues, this study computed deep indentation with h/R 6 0.5. 2 They also reported that similar equation with Eq. (2) can fit the plastic flow behavior better than Eq. (1).

The plastic properties used for extensive FEM computation are listed in Table 1. Here, Poisson ratio m were set to be 0.3, which has minor influence for indentation analysis [11]. The elastoplastic properties for extensive FEM computations were relatively large range which covers base and work-hardened stainless steel, i.e. the Young’s modulus was changed from 100 to 300 GPa, the yield stress from 0.2 to 1.0 GPa, n from 0.3 to 1.0, and K from 0.1 to 1.5 GPa. In total, 81 different combinations were simulated. It is noted that the elastic properties can be evaluated by instrumented indentation using the well-established Oliver–Pharr method [30]. Other techniques such as X-ray diffraction and acoustic wave techniques are also available for this purpose. Furthermore, the Young’s modulus in typical plastic work steels does not vary much. Therefore, our attention is focused on the measurement of plastic properties, i.e. the determination of the three unknown parameters, rY, n and K. 3.2. Estimation method The representative strain er in a uni-axial stress–strain curve is defined as shown in Fig. 3, and it is a function of h/R (which will be discussed later). Correspondingly, the representative stress rr is expressed using Eq. (2).

rr ¼ rY þ K enr

ð3Þ

when h/R is fixed, dimensional analysis leads the value of indentation force to:

F 2

rr h

  E or ¼P

rr

F  2

Eh

¼ P0

r  r

ð4Þ

E

where E is the reduced Young’s modulus, which can be expressed  2 1m2  1m by E1 ¼ Es s  Ei i [31]. Note that for the subscript of E and m (Poisson’s ratio) ‘‘s’’ is that of specimen and ‘‘i’’ is that of indenter.

Table 1 Material property combinations used in the FEM parametric study. E (GPa)

rY (GPa)

n

K (GPa)

100 200 300

0.2 0.6 1.0

0.3 0.5 1.0

0.1 0.8 1.5

v = 0.3 is assumed for all cases.

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computations. Here, the relationships of representative h/R values (= 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5) were plotted in this figure, showing that these can be expressed by a polynomial function which monotonically increases with larger rr/E. These relationships can be fitted by3

F  2

Eh

Fig. 3. Illustration of stress–strain curve of materials that obey Ludwick hardening law. The point of representative strain and stress is plotted.

As expressed in Eq. (4), by introducing the representative strain, it is expected that Eq. (4) may be independent of n and K by optimizing the value of er for a given h/R. Although the former P function has been widely used for dimensional analysis [25], it is reported that the P function is difficult to be complete independent of n at h/R > 0.1 [10]. Therefore, this study investigated the latter function of Eq. (4) (the P0 function has not yet been reported so
far). Fig. 4 shows the relationship between EFh2 and rEr for all

4

2

0

rr E

þ A2

r 0:5 r

E

þ A3

ð5Þ

The coefficients of A1, A2 and A3 are dependent of h/R value. Table 2 shows changes in the coefficients with respected to h/R. The table also includes the correlation factors and maximum/minimum error for the fitting curve. The factors showed relatively high value and the errors were small, which is similar to previous work [32]. The resulting P0 function is apparently independent of n and K up to large h/R (60.5) (by contrast, it was reported that P function was not independent of n in the range of h/R > 0.1 [10]). Table 2 also shows the optimized er value for each h/R, such that the P0 function is independent of n and K. The relationship between er and h/R is shown in Fig. 5. As expected, these er values depend on h/R, indicating that er increases moronically with larger h/ R, i.e. the er – h/R relationship is of one to one correspondence. The relationship can be fitted by the following equation4

 2 h h þ 0:1409 þ 0:0164 R R

er ¼ 0:3242

ð6Þ

This equation can cover the range of h/R 6 0.5. The present method is summarized as follows. We first assumed that the Young’s modulus is known prior and our focus is evaluation of plastic properties. By conducting a spherical indentation test with a given tip radius, the indentation force values at several points of h/R (more than three points) are obtained and then substituted into Eq. (5) to solve the representative stress rr. Furthermore, the representative strain er can be obtained by Eq. (6) for each h/R, so that several representative points of stress– strain are deduced. Finally, these values are substituted to Eq. (2), leading to materials constants (rY, n, K). As expressed in Eqs. (5) and (6), the procedure is straightforward without any additional computational effort. The advantage of deep indentation (up to h/R = 0.5) is also discussed in the following sections (reverse analysis and experimental verifications). 3.3. Reverse analysis

0

0.005

0.01

0.015

0.02

σ

(a)

0.8

0.4

0

¼ A1

0

0.0025

0.005

σ

(b) Fig. 4. Relationship between F/Eh2 and rr/E.

0.0075

Reverse analysis of numerical experiments was carried out to verify the proposed method. Table 3 shows the selected materials for experiments, which were not used for parametric study as shown in Table 1. The estimation error (difference between input and estimation data) is shown in Fig. 6. The yield stress rY, work hardening exponent n and work hardening strength K are shown in Fig. 6a–c, respectively. In those figures, solid black bar corresponds to the estimation of reverse analysis. This suggested that all material cases have error less than 30%, indicating relatively good agreement. We also investigated the robustness of the proposed method. In laboratory experiment, measurement accuracy of testing equip3 This is the polynomial approximation for the proposed dimensionless function of Eq. (4). The exact format of fitting equation (Eq. (5)) does not matter. This equation provides higher correlation factor and simplify reverse analysis (calculate representative stress from Eq. (5)). Indeed, as shown in Fig. 4 and Table 2, this fitting equation is found to be valid for both small and large penetration depth range (i.e. data of small and large h/R). 4 This is a fitting equation, which can be recognized dependent on the geometrical factor (i.e. h/R). Note that this equation is established based on all present data obtained from parametric FEM study, which includes various materials (the materials property range is shown in Table 1). Thus, the limitation (applicable condition) of Eq. (6) is the range of Table 1 (for current study).

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Table 2 Coefficient of A1, A2 and A3 in Eq. (5). h/R

er

A1

A2

A3

|R|

Max error (%)

Min error (%)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.023 0.035 0.046 0.058 0.071 0.087 0.104 0.126 0.147 0.167

35.912 46.647 40.731 37.586 33.796 30.143 26.779 24.428 22.152 20.174

30.766 14.238 8.955 6.035 4.368 3.295 2.593 1.990 1.583 1.259

0.537 0.262 0.173 0.119 0.089 0.069 0.056 0.044 0.036 0.029

0.999 0.999 0.999 0.998 0.998 0.998 0.997 0.997 0.997 0.997

15.11 14.14 15.44 15.40 16.58 16.01 16.82 17.10 17.64 18.07

5.91 7.10 7.43 7.60 7.87 8.23 8.31 8.56 8.65 8.57

0.2

ε

4. Experimental results and discussions 4.1. As-received stainless steel

0.1

0

0

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 5. Representative strain as a function of h/R.

Table 3 Case study for sensitive analysis. Material Material Material Material Material Material

1 2 3 4 5

E (GPa)

rY (GPa)

n

K (GPa)

E/rY

100 150 170 200 250

0.8 0.4 0.6 0.3 0.2

0.4 0.9 0.8 0.7 0.6

0.6 1.4 0.8 1.2 1.5

125 375 283 667 1250

ment, surface roughness of material, and friction may lead to variation of indentation curve. In fact, for deep indentation test, the indentation curve is slightly affected by the friction coefficient, which depends on the experimental condition and material [25]. Thus, how the perturbation of input data affects the estimation is discussed here. According to previous studies [33–35], the perturbation of input data (indentation curve) is set around ±4%. The indentation force data (which was employed with reverse analysis) was changed to +4% and 4%. The estimation error is also shown in Fig. 6 where for all cases considered herein the perturbations were less than 30%. Therefore, it is concluded that our proposed method is relatively robust. As mentioned above, our proposed method is valid for the material range in Table 1 (the present parametric FEM study), and we have given a sensitivity analysis to show the relevant robustness of the proposed method (Table 3 and Fig. 6). In addition, we assume that the material obeys the Ludwick type constitutive equation (Eq. (2)), which can cover various materials, including stainless steel. Thus, these assumptions represent the applicable limitation of our method; that is, as long as materials fall within the current parametric space, our method is directly applicable. Note that the present study focus on the stainless steel (see Section 1 and 2). Thus, we will experimentally prove that our method is valid for stainless steels in the next section.

In order to experimentally verify our method, uni-axial tensile test was conducted. This study prepared as-received specimen of austenitic stainless steel (SUS316) with round bar, whose diameter is 10 mm, gage length is 25 mm and radius of fillet is 45 mm (which is similar to the ASTM: E8 guideline5). Electro-hydraulic servo testing equipment (Shimadzu corp. EHF-EB50KN-10L) was used for uniaxial tensile tests in room temperature (RT) and high temperature (320 °C). The tensile strain was measured by an extensometer, which is available for high temperature. Here, a furnace with resistance heating type was used for specimen heating, and temperature was controlled at 320 ± 1 °C. At both temperatures, the strain rate was set to 0.024%/min up to around 0.2% proof stress (i.e. yield stress), and changed to 2.4%/min (for shortening of testing time). However, for 320 °C test, additional tests were conducted with different strain rates in order to clarify the creep effect (strain rate effect). Namely, other two different tests were conducted, after proof stress the strain rate was changed to 0.024 and 0.24%/min. Thus, the test in RT is once, while that at 320 °C was three times. Fig. 7 shows the true stress and true strain curve for RT and 320 °C. Here, the horizontal axis indicates true plastic strain (which is similar with Fig. 1). As shown in this figure, flow stress in 320 °C is lower than that at RT. Among the data of 320 °C, there is little difference due to the strain rate, indicating that the effect of strain rate on flow stress–strain relationship is minor at the current temperature. For the same specimen, indentation test was carried out using a Dynamic Ultra Micro Hardness Tester (DUH-510S). A spherical diamond indenter with the tip radius of 20 lm was employed. Upon deep impression experiment, the data of indentation force F and penetration depth h curve were recorded continuously. At 320 °C, several trials were performed to explore the appropriate indentation force rate, such that the effect of thermal drift minimizes and the F–h curve becomes stable. The maximum force Fmax was set to 2500 mN and force rate was 41.5 mN/s for all tests. The number of the test in both temperatures is at least more than five times, and the averaged data was studied. Fig. 8 shows the F–h curves at RT and 320 °C. Similar with Fig. 7, it is found that the results depended on ambient temperature, i.e. the specimen at higher temperature was deformable. Based on these data, reverse analysis with our proposed method was carried out to estimate the plastic properties at both temperatures. The estimation (representative stress and strain) is plotted on Fig. 7 with good agreement, which validated the pres5 The present specimen geometry, i.e. gage length, is relatively short, against diameter (10 mm), since the heating furnace is used in this study. Such a short geometry is categorized in the standard tension test for cast iron in ASTM: E8. Our preliminary test confirmed there was little effect of gage length on stress-strain curve.

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40

30

30

20

20

10

10

σ

40

(a)

(b) 40

30

20

10

(c) Fig. 6. Sensitive analysis of reverse analysis; (a) yield stress rY, (b) work-hardening exponent n, (c) work-hardening strength K.

3000

800 2000

σ

600

400

1000

200 0

0

0

0.1

0.2

0

10

μ

0.3

ε

20

Fig. 8. Indentation force F and penetration depth h curves of stainless steel at RT and 320 °C.

Fig. 7. Stress–strain curve at room temperature (RT) and 320 °C. The symbol marks indicates the point of representative stress–strain estimated by indentation method (Fig. 8).

ent method for the evaluation of plastic properties of austenitic stainless steel at RT and high temperature (320 °C). As mentioned above in Introduction, indentation framework based on the Hollomon hardening law of Eq. (1) is not suitable for stainless steel [19,22]. Thus, the result of Fig. 7 indicates our method is perhaps applicable. Upon plastic instability during tensile loading, it is well known that the true strain at the maximum nominal stress (tensile

strength) corresponds to the work-hardening exponent n in the Hollomon type constitutive equation (Eq. (1)). Similarity, Ludwick type equation (Eq. (2)) gives us the tensile strength rB as follows.





rY

rB ¼ rY þ K enpB eðepB þ E Þ

ð7Þ

Here, epB is plastic strain at tensile strength rB, and can be obtained from the following equation.

en1 pB ðn  epB Þ ¼

rY K

ð8Þ

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A. Yonezu et al. / Materials and Design 52 (2013) 812–820

800

3000

(A) (B)

(C)

(A) 600

(B)

σ

2000

400 1000

0

(C)

200

0

5

10

15

0

20

0

0.05

0.1

μ

0.15

0.2

ε

(a)

(b)

Fig. 9. The representative result of indentation test for welded stainless steel; (a) Indentation curves and (b) estimated stress–strain curves.

700

600

σ

500

400

300 30

20

10

0

10

0

(b) 20

σ

ε

500

400

15

300

10

200

5

100 30

20

10

(a)

0

0 30

20

(c)

Fig. 10. The distribution of mechanical properties in welded stainless steels estimated by indentation test; (a) yield stress, (b) tensile strength and (c) plastic strain.

A. Yonezu et al. / Materials and Design 52 (2013) 812–820

The indentation method can estimate plastic properties (rY, n and K) through Eq. (2). Thus, Eqs. (7) and (8) can deduce the tensile strength rB, which at 320 °C (from Fig. 7) is estimated as 518 MPa, which agrees with the value of 504 MPa obtained from uni-axial tensile test. Upon validation of the proposed method, the local plastic properties of welded stainless steel were investigated next.

4.2. Welded stainless steel The specimen used here was an austenitic stainless steel with low carbon (SUS316L) with welding joint. The SUS316L plate (100 mmL  170 mmW  55 mmT) was welded by filler metal of nickel based alloy (690) using tungsten inert gas welding. The multiple pass procedure was chosen because of the large thickness. The width of filler metal was about 10 mm. For indentation testing, the welded specimen was cut in rectangles with 55 mmL  15 mmw  3 mmT across the welding area. Thus, the length of the one side was 27.5 mm. This specimen was mechanically polished to obtain a smooth surface. In addition, electro chemical polishing was carried out to remove the work hardening layer due to the above mechanically polishing. After polishing, we observed clear grain boundary, indicating that the surface metal may have been dissolved electro-chemically. For the present welded specimen, indentation tests were carried out at 320 °C. The testing area was changed along the line from the welding metal to base metal (SUS316L). The impression interval was 0.5 mm. Fig. 9 show the representative three indentation curves. As shown in the insert picture, indented area was below 2 mm from the surface. The origin was set to the center of welding metal. The three curves were obtained from the tested area at 1.3 mm ((A) in welding metal), 8.8 mm ((B) in base material near welding metal) and 22.8 mm ((C) in base material). This indicates that the indentation curve was changed, depending on the distance. Reverse analysis results were shown in Fig. 9b. As expected, the flow stress is higher when the distance is closer to the welding metal, due to hardening caused by welding deformation. Similarly, we evaluated the plastic properties (true stress and true strain curve) inside each area, and deduced the yield stress and tensile strength. Furthermore, plastic strain was also obtained, and compared with the stress–strain curve of base material (SUS316L). These results were shown in Fig. 10. It is found that near the weld metal, the yield stress, tensile stress and plastic strain were higher. In particular, the plastic strain was more than 10% near the weld metal due to welding deformation, i.e. plastic deformation developed in the welding process. Thus, the yield stress and tensile strength were relatively higher. It is well known that the welding process induces local plastic deformation [1,5], because the heat input causes thermal expansion around the welded area. Such thermal expansion induces plastic deformation, leading to residual tensile stress. Reduction and controlling the residual stress and plastic deformation around welded area is important for structural material integrity. Thus, post-weld heat treatment has been well developed in order to improve the local mechanical properties around the welded area. For this technique, the local mechanical properties around the welded area are very important for optimizing and improving the welding technique. However, such local properties are difficult to be evaluated by macroscopic tensile tests [1]. Indentation method can probe local mechanical properties through indentation force and penetration depth (indentation curve). With this method, this study proposed that a simple framework for deducing local plastic properties, even for high temperature working conditions. Thus, the proposed method may be useful for potential diagnostic application for plant operation (e.g. degradation of mechanical

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properties, which may lead to environmentally assisted cracking and fatigue fracture [6,7]).

5. Conclusion This study investigated the ability of spherical indentation method for evaluating local mechanical properties in welded stainless steel at high temperature (320 °C). First, an indentation method was proposed to accurately evaluate the plastic property (i.e. the relationship between stress and strain) in austenitic stainless steel at 320 °C. In this method, the Ludwick-type hardening law which can better describe the plastic flow behavior was employed to establish the functional relationship between indention curve and plastic property, through a parametric study using finite element method (FEM). The dimensional function was established based on sufficiently-deep indentation test (maximum depth/indenter radius h/R = 0.5), so that it can directly estimate the plastic properties up to large uni-axial strain (about 20%). In the numerical experiments, the robustness of our method was verified by error estimation against input perturbation. In parallel experiment, indentation test was conducted for homogeneous as-received stainless steel in order to estimate the plastic properties based on the proposed framework. The result agreed well with those obtained from uni-axial tension at both room temperature and 320 °C. Subsequently, a number of indentation tests were conducted to welded stainless steel (SUS316L), so that the distribution of the plastic properties was evaluated, such as yield stress, plastic strain and tensile strength. The properties around the welded area were estimated to be higher than those of base SUS316L, since it is work-hardened due to thermal expansion and construction during welding process. It is thus revealed that the proposed indentation technique can quantitatively evaluate the local mechanical properties of welded stainless steel at high operating temperature. Acknowledgments The authors are grateful for the computational data and valuable discussion with Mr. Keishi Yoneda (former graduate student at Osaka University, Japan). The work of A.Y. is supported in part of Grant-in-Aid for Young Scientist of (B) (no. 22760077) from the Japan Society for the Promotion of Science, and Research Grant for Science and Technology of SUZUKI Foundation. The work of X.C. is supported by the National Natural Science Foundation of China (11172231), DARPA (W91CRB-11-C-0112), the World Class University program through the National Research Foundation of Korea (R32-2008-000-20042-0), and the National Science Foundation (CMMI-0643726). References [1] Piatti G, Vedani M. Relation between tensile properties and microstructure in type 316 stainless steel SA weld metal. J Mater Sci 1990;25:4285–97. [2] Meola C, Squillace A, Memola F, et al. Analysis of stainless steel welded joints: a comparison between destructive and non-destructive techniques. J Mater Proc Technol 2004;155–156:1893–9. [3] Khoshnaw FM, Hamakhan IA. Determination of the mechanical properties of austenitic stainless steel weldments by using stress strain microprobe. Mater Sci Eng A 2006;426:1–3. [4] Zhang L, Lu JZ, Luo KY, et al. Residual stress, micro-hardness and tensile properties of ANSI304 stainless steel thick sheet by fiber laser welding. Mater Sci Eng A 2013;561:136–44. [5] Song Y, Hua L, Chu D, Lan J. Characterization of the inhomogeneous constitutive properties of laser welding beams by the micro-Vickers hardness test and the rule of mixture. Mater Des 2012;37:19–27. [6] Cheng X, Fisher JW, Prask HJ, et al. Residual stress modification by post-weld treatment and its beneficial effect on fatigue strength of welded structures. Int J Fat 2003;25:1259–69.

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[7] Farrell K, Byun TS. Structural stability and hardness of carburized surfaces of 316 stainless steel after welding and after neutron irradiation. J Nucl Mater 2006;356:178–88. [8] Gouldstone A, Chollacoop N, Dao M, et al. Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater 2007;55:4015–39. [9] Dao M, Chollacoop N, VanVliet KJ, et al. Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater 2001;49:3899–918. [10] Zhao M, Ogasawara N, Chiba N, Chen X. A new approach of measuring the elastic-plastic properties of bulk materials with spherical indentation. Acta Mater 2006;54:23–32. [11] Chen X, Ogasawara N, Zhao M, Chiba N. On the uniqueness of measuring elastoplastic properties from indentation: the indistinguishable mystical materials. J Mech Phys Solids 2007;55:1618–60. [12] Ogasawara N, Chiba N, Chen X. A simple framework of spherical indentation for measuring elastoplastic properties. Mech Mater 2009;41:1025–33. [13] Chollacoop N, Dao M, Suresh S. Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater 2003;51:3713–29. [14] Bucaille JL, Stauss S, Felder E, Michler J. Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater 2003;51:1663–78. [15] Cao YP, Lu J. Depth-sensing instrumented indentation with dual sharp indenters: stability analysis and corresponding regularization schemes. Acta Mater 2004;52:1143–53. [16] Cheng YT, Cheng CM. Scaling approach to conical indentation in elastic-plastic solids with work hardening. J Appl Phys 1998;84:1284–91. [17] Alkorta J, Martinez-Esnaola JM, Sevillano JG. Absence of one-to-one correspondence between elastoplastic properties and sharp-indentation load-penetration data. J Mater Res 2005;20:432–7. [18] Liu L, Ogasawara N, Chiba N, Chen X. Can indentation test measure unique elastoplastic properties? J Mater Res 2009;24:784–800. [19] Kim Y-C, Kang S-K, Kim J-Y, Kwon D. Contact morphology and constitutive equation in evaluating tensile properties of austenitic stainless steels through instrumented spherical indentation. J Mater Sci 2013:48. [20] Singh KK. Strain hardening behavior of 316L austenitic stainless steel. Mater Sci Technol 2004;20:1134–42. [21] Ma D, Ong CW, Lu J, He J. Methodology for the evaluation of yield strength and hardening behavior of metallic materials by indentation with spherical tip. J Appl Phys 2003;94:288–94.

[22] Ogasawara N, Makiguchi W, Chiba N. Plastic properties determination method using triangular pyramid indenters based on elastic solution and rigid/perfectly plastic solution. J Soc Mech Eng A 2005;71: 1406–12. [23] Minoshima K, Yoneda K, Yonezu A, et al. Evaluation method of local mechanical properties using micro tensile testing and its application to coldworked materials. J Soc Mech Eng A 2010;76:493–9. [24] Cao Y, Qian X, Huber N. Spherical indentation into elastoplastic materials: Indentation-response based definitions of the representative strain. Mater Sci Eng A 2007;454–455:1–13. [25] Cao YP, Lu J. A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater 2004;52:4023–32. [26] Lee H, Lee JH, Pharr GM. A numerical approach to spherical indentation techniques for material property evaluation. J Mech Phys Solids 2005;53:2037–69. [27] Bowden FP, Tabor D. The friction and lubrications of solids. Oxford: Oxford University Press; 1950. [28] Saha R, Xue Z, Huang Y, Nix WD. Indentation of a soft metal on a hard substrate: Strain gradient hardening effects. J Mech Phys Solids 2001;49:1997–2014. [29] Xue Z, Huang Y, Hwang KC, Li M. The influence of indenter tip radius on the micro-indentation hardness. J Eng Mater Technol (ASME Trans) 2002;124:371–9. [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;19:3–20. [31] Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 1985. [32] Cao YP, Huber N. Further investigation on the definition of the representative strain in conical indentation. J Mater Res 2006;21:1810–21. [33] Le M-Q. A computational study on the instrumented sharp indentations with dual indenters. Int J Solids Struct 2008;45:2818–35. [34] Le M-Q. Material characterization by dual sharp indenters. Int J Solids Struct 2009;46:2988–98. [35] Yonezu A, Yoneda K, Hirakata H, et al. A simple method to evaluate anisotropic plastic properties based on dimensionless function of single spherical indentation – application to SiC whisker reinforced aluminum alloy – Mater. Sci Eng A 2010;527:7646–57.