Nanoindentation size effects of mechanical and creep performance in Ni-based superalloy

Abstract

Nanoindentation technique was adopted to study indentation size effects of physical-mechanical and creep performance with various depths (200–2000 nm) in GH901 utilising sharp and spherical tip. Residual impressions of both indenters with pile-up patterns are discussed. Nanohardness, reduced modulus and elastic recovery rates curves versus maximum displacement of two tips are obtained and nanohardness size effects are discussed with different models for Berkovich tip. The data obtained with spherical indentation are analysed separately by establishing stress–strain diagram. The creep results using Berkovich tip indicate that creep strain rate declines while creep stress exponent first decreases and then increases with the increasing depth; the creep stress exponent (n) values, 2.39–7.35, imply the dominant creep deformation mechanism is dislocation control.

Keywords

Nanoindentation indentation size effect physical and mechanical properties creep performance Ni-based superalloy

Introduction

Nanoindentation technology can detect load and depth real-timely and get the corresponding curves, and can be utilised to measure the physical-mechanical properties [1,2] such as yield strength [3], strain hardening capacity, creep activation energy [4] and strain rate sensitivity [5], and residual stress [6]. Due to the high displacement resolution of the sensor, nanoindentation technique can reach an indenting depth in a range of nano-scale, 0.1–100 nm, so it has been used widely in ultrathin layers and micro-regions [7]. Nanoindentation has been employed by some researchers to study Ni-based superalloys. For instance, Kommel et al. [8] researched micromechanical properties change of different phases as a result of alloying elements moving at interdiffusion by nanoindentation in single crystal Ni-based superalloy ZS32-vi. Schöberl et al. [9] measured morphology and nanomechanical properties of two ternary Ni-based superalloys with various precipitate volume fraction and annealing time combing the results obtained by atomic force microscope and nanoindentation device, and they found out that the hardness of matrix and precipitates shows a declining trend with indenting depth increases. Nickel-based superalloys are developed for applications involving severe mechanical stress at elevated temperatures, so Sawant et al. [10] conducted nanoindentation studies with respect to creep compliance, hardness and modulus of single crystal CMSX-4 oriented in the 〈001〉and 〈110〉 directions from 303 to 673 K, and the results were further incorporated into the contact mechanics analyses to calculate the elastic modulus of CMSX-4 as a function of temperature.

GH901 is Fe–Ni–Cr-based superalloy showing excellent elevated temperature strength and corrosion resistance, and has been utilised to manufacture turbine disks, shafts and rotors in aerospace field, nuclear engineering and gas turbine industry [11 -13]. Welding technology and surface treatment techniques are commonly employed when manufacturing mechanical parts with GH901 in power plants, which will result in microstructural variations in a narrow region of micro scale. With the development of measurement technology and the increase in required accuracy, it has been found out that even at a lower temperature (T/T_m < 0.2) like room temperature many engineering components can undergo creep when subjected to a constant load, which can cause microstructural changes, crack sprouting and expansion and final material failure [14]. The failure resulted from creep is a significant failure mode for components which are manufactured utilising Ni-based superalloys [15]. Nanoindentation technique has been adopted by Zhang et al. [16] to analyse room temperature creep resistance of DD407, and the creep mechanism is diffusion controlled based on the stress exponent. Bulk/uniaxial creep testing method is difficult to accurately measure the properties of each micro zone of the welded joints or treated surface, while nanoindentation technology has shown unique advantages in characterising the mechanical properties of micro zones. The triangular pyramid Berkovich diamond indenter is used to press into the surface of the sample to reach a certain load and keep it for a certain time. Because the applied stress is usually several to dozens of GPa, most materials, including ceramics, can experience a creep phenomenon similar to that occurring in the range of tensile creep from 0.5T_m to the melting point temperature at room temperature [17].

However, the indentation size effect (ISE) cannot be ignored when adopting nanoindentation technology to evaluate properties. It has been observed and reported in Ni-based superalloys and other alloys that material properties like hardness tend to increase with the drop of penetration depth, which is termed as the indentation size effect [18 -20]. As the hardness of the material is closely related to other mechanical properties such as elastoplasticity, strength and wear resistance of the material, so in this research we adopted two most commonly used indenting tips, Berkovich and spherical indenter, to determine physical-mechanical properties like hardness and module and analyse the size effects produced by the Berkovich indenter base on the Meyer model [21] and Nix-Gao model [22]. The size effects of indentation creep behaviour such as creep rate, strain rate and stress exponent with various maximum penetration loads during dwell stage lasting 120 s are also explored. The above research aims to provide a theoretical foundation for the scientific and engineering applications of the welded joints and components and parts after surface strengthening treatment of GH910 or other similar materials.

Experimental and procedures

The material utilised in this research is forged Fe-43Ni-12Cr based superalloy GH901 after a heat treatment of 1070°C for 3 h followed by water cooling. The chemistry is listed in Table 1. The samples were submitted to the standard polishing procedure route utilising sandpapers and diamond paste to reach a mirror surface with a root-mean-square smoothness of approximately 0.01 µm. The microhardness was measured using a Vickers hardness tester with a test force of 200 gf, a load-hold of 15 s, and repeated eight times. The mechanical properties at 25°C were measured by means of nanoindentation with NanoTest Vantage platform (Micro Materials, Wrexham, UK) on samples. The indentations were carried out with a sharp Berkovich triangular pyramid indenter with a tip containing an apex radius of around 200 nm and a spherical indenter with a radius of 5 µm, with six indenting depths 200, 400, 800, 1200, 1600 or 2000 nm for a holding time of 10 s. The rate of both loading and unloading is set to be 1 mN/s. In addition, nanoindentation testing with a holding time of 120 s after reaching the target depth was implemented with Berkovich tip to study the effects of penetration depth on local creep properties. To reduce the measurement error, eight independent valid measurements were carried out under the same experimental parameters, and the interval between two adjacent indents was at least 30 µm.

Table 1

Chemical composition of GH901 (wt. %).

C	Cr	Ni	Mo	Al	Ti	Fe	B	Mn	Si	P	S	Cu
0.073	12.68	41.95	5.76	0.18	2.71	Bal.	0.019	0.29	0.18	0.01	0.007	0.02

Figure 1 displays residual impressions of (a1-a6) Berkovich and (b1-b6) spherical indenter with six indenting depths 200, 400, 800, 1200, 1600 or 2000 nm with a magnification of 15,000 using scanning electron microscope. When projected on XY coordinate plane, Berkovich indenter leads into an equilateral triangle shape and spherical tip exhibits a rounded square shape, but Z-coordinate is not constant. Furthermore, it can be seen from the figure that the indentation of spherical indenter shows crushed and peeling material and the surface of the pit is rough compared with Berkovich indenter. Berkovich indenter which is self-similar (geometrically) is further chosen in this study to research the creep behaviour under different maximum pressed depths.

Figure 1

Residual impressions of (a1-a6) Berkovich and (b1-b6) spherical indenter for six indenting depths 200, 400, 800, 1200, 1600 or 2000nm, 15,000×.

Results and discussions

Microstructural information and residual imprint morphology

Figure 2 demonstrates SEM micrograph of carbides which are situated in grains and at grain boundaries in alloy 901. The EDS spectra from the observed carbides indicate that elements Mo and Ti are present in carbides and (Ti, Mo)C carbide was also reported in the same alloy [23] and other superalloys such as U-500 and Rene 77 [12]. Annealing twinnings, one of the microstructural features of this alloy, are also illustrated in Figure 2. It is worth noting that γ′ precipitates could not be detected at the magnifications of SEM, since this family of alloys exhibit an ultrafine precipitate in nanometric size in face-centered cubic (FCC) matrix [13]. According to previous study [23], the increase of carbon content of 901 can lead to a higher amount of carbide sizes, meanwhile it can give slight rise to the mismatch between γ and γ′ phases, which are beneficial to the alloy in the first place, and then big blocky carbides become crack initiation sites, because of the incoherent interface of MC and matrix. The average grain size (equivalent circular diameter) is around 100 µm and most precipitates’ size is several micrometers, Figure 2, while the maximum indenting depth is set to be 200 to 2000 nm and the corresponding maximum indentation size (equivalent circular diameter) is between 2 and 10 µm as shown in Figure 1. So, there is no doubt that the precipitates, grain size and orientation can affect the measured nanohardness and creep data in this study. To better understand such effects, further study on factors like dislocation movements, interaction between geometrically necessary dislocations and statistically stored dislocations, the impediment of twin boundaries and precipitates on dislocation motion, the indentation being located in one or more grains with different orientations is needed. And in this research, the discrete data generated by indenting on the precipitates are eliminated and the testing data of repeated measurements with good repeatability are obtained and averaged to improve reliability and precision.

Figure 2

SEM micrograph showing carbides of alloy 901.

Kucharsiki et al. [24] gave a schematic of sample and indenter surface in loaded and unloaded state for isotropic material that exhibit sink-in (or pile up) pattern in their study of the size effect in single crystal copper examined with spherical indenters. Figures 3 and 4 show the three-dimensional residual imprint morphology and the indenting profiles of three cross sections for Berkovich indenter and spherical indenter obtained by utilising atomic force microscopy (AFM). It can be seen that the residual indentation of GH901 alloy exhibits pile-up pattern. In the observation of the indentation depth of 200 to 2000 nm, it is found that all the residual indentation shows the pile-up phenomenon, and the pile-up degree increases when the indentation depth increases. In general, some materials with a low strain-hardening tendency [25] such as strain-hardened Cu [26] will produce pile-up around residual indentations, while residual indentations around materials with a high work-hardening tendency generally exhibit sink-in phenomena. In addition, the penetration depth measured for spherical indenter is smaller than that for Berkovich for a particular set indenting depth, probably because two indenters with different geometry are utilised and they bring in different residual indentation morphology and different deformation and recovery mechanism, which needs further research. For instance, when 2000 nm is chosen as indenting depth, the residual depth is approximately 1850 and 1681 nm for Berkovich and spherical indenter respectively.

Figure 3

3D residual imprint morphology of (a) Berkovich indenter and (b) spherical indenter obtained by atomic force microscopy.

Figure 4

Indenting profiles of three cross sections of six pressed depths from 2000 to 200 nm of (a) Berkovich indenter and (b) spherical indenter obtained with atomic force microscopy.

Nano-indentation results employing spherical and Berkovich indenter

Table 2 lists nano-indentation results of maximum load (P_max ), maximum indenting depth (h_max ), contact depth (h_c ), residual depth (h_f ), reduced elastic module (E_r ) and nanoindentation hardness (H) employing spherical indenter and Berkovich indenter with a dwell time of 10 s. The nano-indentation hardness is given by using the equations from Oliver and Pharr method [27]: (1)

where P _max is the maximum normal load and A is the projected contact area at the maximum load. The reduced modulus of the indented material E_r can be calculated from the following equation [7]: (2)

where E_i and ν_i are the indenter's elastic modulus and Poisson's ratio, 1140 GPa and 0.07, respectively, and ν (0.30) is the Poisson's ratio of the fused quartz silica [28]. The elastic modulus is 201 GPa and the Poisson ratio is 0.29 for the tested alloy.

Table 2

The nano-indentation results of maximum load (P_max ), maximum indenting depth (h_max ), contact depth (h_c ), residual depth (h_f ), reduced elastic module (E_r ), and nanoindentation hardness (H) and elastic recovery rate (R) employing spherical indenter (SI for short) and Berkovich indenter (BI for short).

	200		400		800		1200		1600		2000
Depth/nm	SI	BI	SI	BI	SI	BI	SI	BI	SI	BI	SI	BI
P_max	22.84	7.15	51.78	22.74	105.29	73.43	158.34	149.41	209.29	242.60	257.58	354.33
h_max	209.28	204.05	428.51	397.97	847.33	786.02	1242.52	1164.62	1660.09	1545.58	2052.78	1909.53
h _c	163.88	181.68	351.34	361.25	728.48	723.42	1070.49	1077.50	1459.15	1441.64	1818.11	1777.59
h_f	100.36	152.88	241.49	298.64	569.47	634.85	817.53	917.55	1078.53	1238.83	1272.74	1506.22
H	4.51	6.61	4.86	6.08	5.00	5.28	5.27	4.97	5.34	4.66	5.51	4.42
E_r	148.59	197.77	136.80	206.33	121.27	203.83	111.78	201.49	110.75	206.81	106.81	193.90
R	0.277	0.123	0.219	0.101	0.174	0.086	0.160	0.080	0.137	0.072	0.129	0.074

Load versus depth with spherical and Berkovich indenter under six different maximum indenting depths, 200, 400, 800, 1200, 1600 and 2000 nm, are shown in Figure 5(a). The load-depth curves commonly contain load, dwelling, and unload stages, and the duration plateau for dwelling stage is not obvious as a result of short time of 10 s. The loading curves coincide well, indicating the whole testing process has a good reproducibility. The maximum load increases linearly with the required maximum penetration depth for spherical indenter, while the relationship between the two is close to parabola for Berkovich tip, see Figure 5b. During unloading process, the depth decreases from the maximum depth to a fixed value indicates a local permanent plastic deformation emerging in the tested area, as shown in Figure 5(a), Figures 3 and 4.

Figure 5

(a) Load versus depth curves during indenting process and (b) maximum loads for different maximum indentation depths of spherical and Berkovich indenter.

Indentation size effects of nanohardness employing Berkovich indentation

Figure 6 displays (a) indentation hardness-depth, (b) reduced modulus-depth, and (c) elastic recovery rates-depth curves measured with Berkovich indenter. The elastic reduced modulus values change little with the increasing indention depth. The high value of elastic recovery rate under small indentation displacement implies that the contribution of the elastic deformation for shallow indentation is more significant than that for deep indentation. The hardness (or stress) varies at different displacement (or load) for Berkovich indentation, which means that the indenting size effect exists in the data, and ISE for Berkovich indenter has been observed in previous researches on other alloys [29 -31]. Based on classic plasticity theory, the hardness should be independent of the indenting depth, so the early ISE observations have been attributed to the experimental artefacts such as surface conditions and indenter tip imperfections, thus the underlying physical mechanisms was ignored over a period of time. Then, atomic and molecular dynamics models and dislocation dynamics theories were established to explain the ISE phenomenon [29 -34]. Indentation data will be analysed, and load-independent hardness, i. e. characteristic nanohardness, will be evaluated from the analysis of data exhibiting ISE with various models such as Nix-Gao model [22] in the following text.

Figure 6

(a) Hardness-depth curves; (b) reduced modulus-depth curves; (c) elastic recovery rates-depth curves for different maximum indentation depths by Berkovich indenter.

Meyer model

The Meyer equation based on the energy balance method is the most widely utilised method to describe the size effects [21]; it describes the relationship between the maximum load P_max and the indentation contact depth h_c ; see the following: (3) where A and n are constants in relation to material. When n = 2, there is no indentation size effects; when n < 2, ISE exists; when n > 2, there is inverse ISE. Figure 7 shows the double logarithmic plot of maximum load as a function of contact depth which was linearly fitted to Equation (3). The exponent of Meyer equation is 1.685, which is lower than 2, which is consistent with the significant size effect in this research. The equation is usually utilised as an empirical formula which can reflect the ISE condition of the material, but the underlying physical meaning of A and n is undefined and the hardness or the relationship between load and pressure depth cannot be obtained from the formula.

Figure 7

Fitting curves of ln P_max and ln h_c based on Meyer model.

Proportional specimen resistance (PSR) model

Li and Bradit [35] proposed a PSR model which considers both the elastic resistance of the material and frictional effects between the indenter facet and specimen interface during indenting. As the model indicates, the resistance caused by the friction between specimen and indenter has been offset by part of the load due to the elastic deformation of the material during loading. The expression for this model is: (4) where P_max is the maximum load, h _c is contact depth, and b ₁ and b ₂ are constants for a given material and the former coefficient relates to the proportional resistance of the test specimen and the latter is a constant with units of stress. For Berkovich indenter, the hardness of material can be calculated based on Oliver–Pharr theory [27]: (5) The values of 111.78 and 2.44 for b ₁ and b ₂ respectively are obtained from the fitting of the plot (Figure 8), and the indentation hardness 4.55 GPa is further calculated.

Figure 8

Fitting curves the experimental results of P_max and h_c based on PSR model.

Energy balance model

Gong et al. [36] and Mukhopadhyay et al. [37] argued that PSR model is only applicable to data in a narrow range of loads, so they proposed correction to the PSR model, multiplying both sides of the Equation 4 in Section Energy balance model by the contact depth (h _c), and the energy balance model is given as follows: (6) where P is the maximum load, H₀ is the true hardness of the material, b and β is constant, is the energy consumed to produce a new surface, and is the work done to produce permanent deformation. When η is used to denote the error of the load force P generated by the instrument, δ denotes the error of the indentation size h_c , then the Equation (6) can be expressed as: (7) where , , , and b₀ reflects the systematic error and the residual stress of the specimen. For Berkovich indenter, the hardness of material can be calculated based on Oliver–Pharr theory: (8) The values of 4.23, 11.71 and 104.05 for b₀ , b₁ and b₂ respectively are obtained from the fitting of the plot as shown in Figure 9, and the indentation nanohardness 4.23 GPa can be further calculated from Equation (8).

Figure 9

Fitting curves the experimental results of P_max and h_c based on energy balance model.

Nix–Gao model

The model proposed by Nix and Gao [22] based on the theory of gradient strain of Fleck and Hutchinson [38] is a milestone of the models, which neglected the interaction between geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs), and assumed the total dislocation density (ρ) is simply the summation of SSDs (ρ_S ) and GNDs (ρ_G ); the variation of indentation hardness (H) as a function of the indention depth (h) is given by: (9) where H ₀ is the hardness due to SSDs and h* is the observable depth of the size effect, which is also known as the microscopic size characteristic length of the material. H, H ₀ and h* can be described as follows: (10) (11) (12) where G is the shear modulus, α is a material constant, b is Burgers vector, tan(θ) is the ratio between indentation depth and contact radius. Figure 10 displays nonlinear fitting curve of H−h based on Nix−Gao model [22]. The hardness decreases with the growth of the indentation depth and becomes stable under great indentation depth and the characteristic length (h*) is 297.49 nm and the hardness due to SSDs (H ₀) based is 4.36 GPa, with a confidence coefficient of 0.911. Feng and Nix [39] have observed that Nix–Gao model cannot capture the size effect for small indentation depths below 200 nm, and they believed three reasons may result in the failure: indenter tip bluntness, effect of Peierls stress and dislocation pattern underneath the indenter. Since the minimum penetration depth in the research is set to be 200 nm, our results are consistent with the Nix-Gao model.

Figure 10

Nonlinear fitting curve of H−h based on Nix−Gao model [22].

Analysis on data obtained from spherical indentation

As observed in Figure 11, the hardness measured by spherical indenter increases with the increment of maximum indenting depth, while the reduced modules and elastic recovery rate values drop and level off with the load growth. The above load-dependent hardness for spherical indenter has also been reported by other researchers [24,40,41]. When adopting the self-similar (geometrically) Berkovich indenter, the stress varies at various load/displacement for indentation though the strain remains constant due to the self-similar geometry, indicating the existence of the indenting size effect. However, for spherical indenter, the strain is continuously varying so the stress required will also vary, which should not be confused with ISE. Herein, the part of spherical indenter is not included when dealing with ISE and is analysed separately with stress–strain diagram in this section.

Figure 11

(a) Hardness-depth curves; (b) reduced modulus-depth curves; (c) elastic recovery rates-depth curves for different maximum indentation depths by spherical indenter.

Figure 12 displays the relationship between hardness and 0.2a/R for the spherical indenter used in this study, where R is indenter radius and a is contact radius. For the spherical indenter, Johnson [42] has shown that by using a strain of 0.2a/R, the indentation data can be compared to the tensile data. It is known that the values of hardness are related to local elastic and plastic deformation [43]. The measured hardness increases rapidly as a result of the transition from elastic-dominated deformation to plastic dominated [42]; and the growth rate levels off with the growth of the indenting displacement. And such variation of hardness with strain for spherical indenter is not an indentation size effect as discussed above. Unlike sharp indentation, Swadener et al. [44] and Kucharski et al. [24] have found out that the hardness increases with the decrease of indenter's own size (radius) when the indenter's shape remains spherical and the maximum indenting depth keeps the same. It has been reported that the spherical indenter does not show depth dependence in hardness but show a dependence on the radius of the sphere, i.e. H²∼1/R relationship, where R* is material length scale [44], and that qualitatively agrees with H²∼1/h proposed in previously discussed Nix–Gao model. In this research, we do not carry out nanoindentation testing with spherical indenters of different sizes, so the H²∼1/R relationship cannot be justified. The hardness due to SSDs based (H₀ ), 4.36 GPa, is predicted by Nix–Gao model with a confidence coefficient of 0.911 and the hardness measured by spherical indenter at the smallest a/R = 0.26 is 4.68 GPa. The microhardness value is measured to be approximately 4.15 GPa (424 HV) employing Vickers indenter, which agrees with the above experimental nanoindentation results in the same order of magnitude.

Figure 12

Stress-strain diagram: relation between hardness and strain (0.2a/R) for the spherical indenter (•); experimental hardness values and their fitting curve for Berkovich indenter (▴ and dotted line); microhardness measured by Vickers (solid straight line).

Analysis of indentation size effects for indenting creep behaviour

In this section, we discuss the size effects in the case of indentation creep, that is, the influence of different indenting depths on the detected creep behaviours. The typical peak load-sensitive P−h curves with different depths 200, 400, 800, 1200, 1600 and 2000 nm for 120 s employing Berkovich tip are displayed in Figure 13. The loading curves are overlapped for all P−h curves, implying a good repeatability. A plateau can be observed for all curves, whose width represents the creep depth and height indicates the maximum load, and the plateau depth and indenting load during creep both increase with the growth the setting depth. The plateau data during dwell stage are utilised to research the creep behaviour of the alloy.

Figure 13

Typical peak load-sensitive P−h curves for six different setting depths with Berkovich tip.

Figure 14 displays (a) the creep depth versus time (h-t) and (b) creep depth rate versus time (h-t) under different stationary loads corresponding to the setting depths. h is the indentation depth during the holding stage. is creep rate and can be calculated by fitting h-t curve during holding time with the following empirical law [45]: (13) The fitting parameters of the data shown in Figure 14(a) using the above equation are displayed in Table 3, and the confidence coefficients for all fitting are over 0.98. As shown, the creep depth increases with the setting indenting depth, and it increases to a maximum value of 120 for 2000 nm. For each testing, the creep depth grows dramatically for initial creep stage and the creep rate is tending towards stability with time increasing; the steady creep rate is greater when the set depth is deeper.

Figure 14

(a) Nonlinear fitting curves of creep depth−time and the fitting parameters are listed in Table 3; (b) creep rate–time curves under different maximum depths.

Table 3

Fitting parameters by Equation (13) at various maximum depths.

h_max (nm)	h₀	t₀	A	b	K	R²
200	197.52067	6.49403	2.43963	0.39634	−0.01022	0.98581
400	391.39234	19.78337	3.41252	0.43013	0.09622	0.99939
800	762.51498	57.03079	8.97035	0.26925	0.32044	0.99988
1200	1145.06051	106.66481	5.13945	0.47676	0.36443	0.99992
1600	1513.41995	160.83017	6.5931	0.46749	0.44739	0.99996
2000	1912.71938	220.94008	4.88255	0.59205	0.37327	0.99996

For Berkovich indenter, creep strain rate [46] and indentation contact stress or nanoindentation hardness (σ) [7] can be expressed respectively as follows: (14) (15) where h is instantaneous indentation depth, is creep rate, P is holding load, A_c is projected contact area. The calculated creep strain rate and hardness as a function of dwell time for different indenting depths are displayed in Figure 15. The variation tendency of creep strain rate versus dwell time is similar to creep rate of Figure 14(b), but the nanoindentation of the deepest indenting depth exhibits the smallest creep strain rate. It is obvious that it takes longer time for 200 and 400 nm depth to reach the steady creep strain rate stage. Overall, the instantaneous hardness declines as a function of dwell time for a specific set depth, and the hardness values are greater for small depths.

Figure 15

(a) Creep strain rate and (b) hardness as a function of dwell time for different indenting depths.

Figure 16

Double logarithmic plot of creep strain rate vs. instantaneous stress and variations of creep stress exponent for different set depths.

Figure 16 demonstrates double logarithmic plot of creep strain rate vs. hardness and variations of creep stress exponent at different set depths. The relationship between strain rate and the applied stress (σ) can be established upon the power law equation [47]: (16) where A is the material constant, and n is the exponent of power-law creep that can reflect the mechanism of creep. The value of n (creep stress exponent) is the slope of the double logarithmic plot of and σ under isothermal conditions: (17)

Creep stress exponent n is an important parameter to study material's creep behaviour, which reflects the stability of creep resistance; meanwhile, it can reflect the deformation mechanism for the dwell stage of indenting testing. The diffusion creep is dominant when n values is below 1, when n is between 1 and 2 the main creep deformation mechanism is grain boundary diffusion control or lattice diffusion control, and when creep stress exponent is greater than 3, the creep mechanism is associated with dislocation movement such as dislocation glide (n ≈ 3) and dislocation climb (n > 4) [48,49]. Zhang et al. [16] measured the creep stress exponents of signal crystal Ni-based superalloy DD407 under different loading rates and applied peak loads, which are between 3.82 and 7.10, implying a dislocation controlled deformation. The apex radius of indenter tip is around 200 nm, so the contact area is small, resulting into very high stresses in nanoindentation compared to those developed during uniaxial tensile/compressive tests [50], which allows dislocations to glide through the lattice and obstacles by either passing or shearing them. Also, according to the deformation mechanism map given by Frost and Ashby [51], the dominant mechanism is dislocation glide plasticity under room temperature around 298 K. So, it is reasonable that the dominant deformation mechanism is dislocation glide during loading stage at room temperature in this research. The slope values of the curves in Figure 16 are different for different points, and the creep stress exponent is obtained at the steady-state creep, ranging from 2.39 to 7.35, which indicates the creep mechanisms are dominated by dislocation control.

As displayed in Figure 17(a), the creep stress exponent (n) ranges from 2.39 to 7.35, it decreases with depth for shallow indentations, then it grows up as indenting depth increases; and the smallest n value occurs at the depth of 800 nm. The trend of n value decreasing with depth has been reported by references [16,52], meanwhile n increasing with depth has also been observed in references [45,53,54]. For shallow indentations 200 and 400 nm, it takes longer time to reach the stable creep stage (Figure 15a), and thus large n values are obtained. With the increment of depth, the change rate of creep strain rate with respect to time remains constant in steady state creep stage, and the rate of variation for hardness becomes smaller for large depths, also see Figure 15, which results into an increasing creep stress exponent versus depth. So, Sambhava et al. [53] proposed equation to calculate n, in which K is a constant correlated with indentation size effect. The creep strain rate, creep rate, and hardness are also displayed in Figure 17(a) and (b), with which their dependency on depth of impression, i.e. size effect, can been clearly demonstrated. The creep strain rate and hardness increase with depth whereas a contrary trend was observed for the creep rate and creep stress exponent. The stored elastic strain energy during constant loading rate stage grows with the maximum indenter load, and it releases in constant creep stage, and thus the corresponding maximum creep displacement will increase with indenting depth and leads into larger creep rate with same creep time scope. But creep strain rate still shows a downtrend with maximum load because large creep displacement values for deeper indentation would appear in the denominator in the calculation.

Figure 17

The variations of (a) creep stress exponent and creep strain rate and (b) hardness and creep rate, as a function of maximum indenting depths.

Conclusions

In this study, we employed nanoindentation technology to study the indentation size effect of GH901 concerning mechanical properties and creep performance with different maximum indenting depths varying from 200 to 2000 nm with Berkovich and spherical indenter. The main results are as follows:

The hardness tends to decrease and the reduced module rarely changes with increased depth for Berkovich indenter, and the hardness increases with the growth of the depth while the reduced module changes in the opposite direction for spherical tip.

Indentation size effect for hardness is observed for Berkovich indenter, and it is further analysed by different models. The exponent of Meyer equation is 1.685, lower than 2, implying a significant normal size effect. Based on PSR model, the values of for b ₁ and b ₂ are 111.78 and 2.44 respectively and the indentation hardness 4.55 GPa is calculated, while the hardness obtained based on the energy balance model is 4.23 GPa. The hardness due to statistically stored dislocations is 4.36 GPa with a characteristic length (h*) of 297.49 nm employing Nix-Gao model.

The hardness measured by spherical indenter increases with the increment of maximum indenting depth; previously proposed H²∼1/R relationship for spherical tip can't be verified, because nanoindentation testing with spherical indenters of different sizes is not implemented in this research. The hardness due to SSDs based (H ₀) 4.36 GPa is predicted by Nix-Gao model with a confidence coefficient of 0.911 and the hardness measured by spherical indenter at the smallest a/R = 0.26 is 4.68 GPa. The microhardness value is measured to be 4.15 GPa (424 HV) employing Vickers indenter, which agrees with the above experimental nanoindentation results.

The creep performance of different indenting depths sustaining for 120 s are obtained with Berkovich indenter. The results indicate a negative relationship between hardness and depth, and between creep strain rate and depth; the creep stress exponent decreases firstly and then increases with the depth increasing. The creep mechanisms are dominated by dislocation based on the calculated creep stress exponents, in a scope of 2.39–7.35.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

References

Ahn

Kwon

Micromechanical estimation of composite hardness using nanoindentation technique for thin-film coated system. Mater Sci Eng, A. 2000;285(1-2):172–179.

Ruud

Jervis

Spaepen

Nanoindentation of Ag/Ni multilayered thin films. J Appl Phys. 1994;75(10):4969–4974.

Jacq

Lormand

Nelias

On the influence of residual stresses in determining the micro-yield stress profile in a nitrided steel by nano-indentation. Mater Sci Eng, A. 2003;342(1-2):311–319.

Kral

Dvorak

Zherebtsov

Effect of severe plastic deformation on creep behaviour of a Ti–6Al–4 V alloy. J Mater Sci. 2013;48(13):4789–4795.

Das

Albert

Bhaduri

Understanding room temperature deformation behavior through indentation studies on modified 9Cr–1Mo steel weldments. Mater Sci Eng, A. 2012;552:419–426.

Zhu

L-N

B-S

Wang

H-D

Microstructure and nanoindentation measurement of residual stress in Fe-based coating by laser cladding. J Mater Sci. 2011;47(5):2122–2126.

Oliver

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.

Kommel

Kimmari

Viljus

Phases micromechanical properties of Ni-base superalloy measured by nanoindentation. Mater Sci. 2012;18(1):28–33.

Schöberl

Gupta

Fratzl

Measurements of mechanical properties in Ni-base superalloys using nanoindentation and atomic force microscopy. Mater Sci Eng, A. 2003;363(1-2):211–220.

10.

Sawant

Tin

High temperature nanoindentation of a Re-bearing single crystal Ni-base superalloy. Scr Mater. 2008;58(4):275–278.

11.

Reed

RC.

The superalloys: fundamentals and applications. New York: Cambridge University Press; 2006.

12.

Sims

Stoloff

Hagel

WC.

Superalloys II. London: Applied Science Publishers; 1981.

13.

Donachie

SJ.

Superalloys: a technical guide. 2nd ed. Materials Park, Ohio: ASM international; 2002.

14.

Nie

Zhao

Room temperature creep and its effect on flow stress in a X70 pipeline steel. Mater Lett. 2008;62(1):51–53.

15.

Coakley

Frost

Lattice strain evolution and load partitioning during creep of a Ni-based superalloy single crystal with rafted γ′ microstructure. Acta Mater. 2017;135:77–87.

16.

Zhang

Effects of loading rate and peak load on nanoindentation creep behavior of DD407Ni-base single crystal superalloy. Trans Nonferr Metal Soc China. 2022;32(1):206–216.

17.

Machaka

Derry

Sigalas

Room temperature nanoindentation creep of hot-pressed B6O. Mater Sci Eng A. 2014;607:521–524.

18.

Durst

Franke

Böhner

Indentation size effect in Ni–Fe solid solutions. Acta Mater. 2007;55(20):6825–6833.

19.

Feng

Nix

WD.

Indentation size effect in MgO. Scr Mater. 2004;51(6):599–603.

20.

Guzman

Neubauer

Flinn

The role of indentation depth on the measured hardness of materials. Mrs Proc. 1993;308:613–618.

21.

Babini

Bellosi

Galassi

Characterization of hot-pressed silicon nitride-based materials by microhardness measurements. J Mater Sci. 1987;22(5):1687–1693.

22.

Nix

Gao

Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids. 1998;46(3):411–425.

23.

Dodangeh

Shahri

Abbasi

SM.

The effects of carbon content on the microstructure and 650°C tensile properties of Incoloy 901 Superalloy. High Temp Mater Processes. 2015;34(8):821–826.

24.

Kucharski

Woźniacka

Size effect in single crystal copper examined with spherical indenters. Metall Mater Trans A. 2019;50(5):2139–2154.

25.

Alcala

Barone

Anglada

The influence of plastic hardening on surface deformation modes around Vickers and spherical indents. Acta Mater. 2000;48(13):3451–3464.

26.

Wang

Raabe

Klüber

Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals. Acta Mater. 2004;52(8):2229–2238.

27.

Oliver

Pharr

GM.

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res. 1992;7:1564–1583.

28.

Tiwari

Hihara

LH.

Effect of inorganic constituent on nanomechanical and tribological properties of polymer, quasi-ceramic and hybrid coatings. Surf Coat Technol. 2012;206(22):4606–4618.

29.

Feng

Ngan

Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J Mater Res. 2002;17(3):660–668.

30.

Warren

A model for nano-indentation creep. Acta Metall Mater. 1993;41(10):3065–3069.

31.

Takagi

Fujiwara

Kakehi

Measuring Young's modulus of Ni-based superalloy single crystals at elevated temperatures through microindentation. Mater Sci Eng, A. 2004;387-389:348–351.

32.

Oyen

Cook

RF.

Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials. J Mater Res. 2003;18(1):139–150.

33.

Ngan

AHW

Wang

Tang

Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation. Int J Solids Struct. 2005;42(5-6):1831–1846.

34.

Ngan

AHW

Tang

Viscoelastic effects during unloading in depth-sensing indentation. J Mater Res. 2002;17(10):2604–2610.

35.

Bradt

RC.

The microhardness indentation load/size effect in rutile and cassiterite single crystals. J Mater Sci. 1993;28(4):917–926.

36.

Gong

Guan

Analysis of the indentation size effect on the apparent hardness for ceramics. Mater Lett. 1999;38(3):197–201.

37.

Mukhopadhyay

Paufler

Micro- and nanoindentation techniques for mechanical characterisation of materials. Int Mater Rev. 2006;51(4):209–245.

38.

Fleck

Hutchinson

JW.

A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids. 2001;41(12):1825–1857.

39.

Gang

Nix

WD.

Indentation size effect in MgO. Scr Mater. 2004;51(6):599–603.

40.

Lim

Chaudhri

MM.

The effect of the indenter load on the nanohardness of ductile metals: an experimental study on polycrystalline work-hardened and annealed oxygen-free copper. Philos Mag A. 1999;79(12):2979–3000.

41.

Durst

Göken

Pharr

GM.

Indentation size effect in spherical and pyramidal indentations. J Phys D: Appl Phys. 2008;41(7):074005.

42.

Johnson

KL.

The correlation of indentation experiments. J Mech Phys Solids. 1970;18(2):115–126.

43.

Chen

P-S

Chen

H-W

Duh

J-G

Characterization of mechanical properties and adhesion of Ta–Zr–Cu–Al–Ag thin film metallic glasses. Surf Coat Technol. 2013;231:332–336.

44.

Swadener

George

Pharr

GM.

The correlation of the indentation size effect measured with indenters of various shapes. J Mech Phys Solids. 2002;50(4):681–694.

45.

Ngan

AHW.

Size effects of nanoindentation creep. J Mater Res. 2004;19(2):513–522.

46.

Poisl

Oliver

Fabes

BD.

The relationship between indentation and uniaxial creep in amorphous selenium. J Mater Res. 1995;10(08):2024–2032.

47.

Herbert

Sohn

Measurement of power-law creep parameters by instrumented indentation methods. J Mech Phys Solids. 2013;61(2):517–536.

48.

Abzianidze

Eristavi

Shalamberidze

SO.

Strength and creep in boron carbide (B4C) and aluminum dodecaboride (α-AlB12). J Solid State Chem. 2000;154(1):191–193.

49.

Han

Lavernia

Mohamed

FA.

Dislocation structure and deformation in iron processed by equal-channel-angular pressing. Metall Mater Trans A. 2004;35(4):1343–1350.

50.

Wang

Mukai

Nieh

TG.

Room temperature creep of fine-grained pure Mg: a direct comparison between nanoindentation and uniaxial tension. J Mater Res. 2009;24(5):1615–1618.

51.

Atkins

AG.

Deformation-mechanism maps (the plasticity and creep of metals and ceramics). J Mechl Work Technol. 1984;9(2):224–225.

52.

Zhao

Indenter load effects on creep deformation behavior for Ti-10V-2Fe-3Al alloy at room temperature. J Alloys Compd. 2017;709:322–328.

53.

Sambhava

Nautiyal

Jain

Model based phenomenological and experimental investigation of nanoindentation creep in pure Mg and AZ61 alloy. Mater Des. 2016;105:142–151.

54.

Nautiyal

Jain

Agarwal

Study of nanoindentation induced creep in pure Mg. The10th International Conference on Magnesium Alloys and Their Applications. 2015.