2018 Volume 59 Issue 4 Pages 602-611
A newly established in situ Brinell indentation technique was conducted to investigate the plastic deformation behavior of pure Mg and Mg-Y alloy single crystals under complex stress conditions. The deformation morphology on the upper surfaces of the specimen around the indent could not be sufficiently observed using the previously reported in situ indentation methods with an optically transparent indenter due to the refraction of rays at the indenter/air interface. In this study, the gap between the indenter and the specimen surface is filled with immersion liquids such as silicone oil and kerosene. This technique enables observation of the specimen surface during indentation. Application of the in situ Brinell indentation to pure Mg and Mg-Y alloy single crystals revealed that the shape of the indents is not circular but elliptical, even during loading. The aspect ratio of the indents decreases with increasing Y content. Moreover, the occurrence of plastic deformation around the indents and beneath the indenter could be observed during the loading and unloading processes using the in situ Brinell indentation method.
This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 81 (2017) 198–205.
Fig. 2 In situ images of (a) pure Mg, (b) Mg-1.3 at% Y and (c) Mg-2.3 at% Y single crystals during loading process (nr/ni = 0.85). (d) In situ image processed to measure the major and the minor diameters of the indent on pure Mg single crystal under a load of 9.8 N.
Mg alloys that exhibit high specific strength are attracting attention as candidate materials for vehicles and aircraft.1,2) However, Mg alloys have poor plastic deformability at room temperature. One of the reasons for this is that the relative activity of each plastic deformation mechanism is significantly different from each other.3–16) In Mg alloys, $\{ 0001\} \langle 1\bar{2}10\rangle $ basal slip and $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ twinning, for which the critical resolved shear stress (CRSS) is relatively small, are favorable, while CRSS for non-basal plastic deformation mechanisms is significantly larger. On the other hand, the CRSS for non-basal plastic deformation mechanisms decreases with increasing deformation temperature,15,16) resulting in an improvement of the plastic deformability of Mg alloys by fulfilling the von Mises criterion.17) The von Mises criterion cannot be fulfilled in polycrystalline materials; therefore, a stress concentration arises in the vicinity of grain boundaries, which is one of the reasons for crack initiation in Mg alloys.18–22) The activation of non-basal slip systems is considered to be effective for alleviation of such stress concentration at grain boundaries. Even in a conventional Mg alloy (AZ61), transmission electron microscopy (TEM) observations show the occurrence of non-basal plastic deformation mechanisms, which are relatively less active, in the vicinity of grain boundaries to alleviate the stress concentration.23) Therefore, an understanding of the plastic deformation behavior at room temperature is necessary for discussion of the plastic deformability of Mg alloys.
Polycrystalline Mg-Y solid-solution alloys exhibit higher room-temperature ductility than other Mg alloys.24) Y addition leads to high solid-solution strengthening for basal slip and $\{ 10\bar{1}2\} $ twinning,4,13) and solid-solution softening for prismatic slip.3) Therefore, the relative activity of non-basal plastic deformation mechanisms increases with increasing Y content. This indicates that the von Mises criterion can be fulfilled more easily in Mg-Y alloys at room temperature than in other Mg alloys. Therefore, it is expected that homogeneous plastic deformation in Mg-Y alloys can be attained and the stress concentration in the vicinity of grain boundaries can be alleviated. This is one of the reasons for improvement of the ductility of polycrystalline Mg-Y alloys.4) However, complex deformation attributed to the stress concentration, which is difficult to understand based only on the results of uniaxial mechanical tests, may be introduced in the vicinity of grain boundaries during the deformation of polycrystalline materials. Therefore, it is necessary to establish a mechanical testing method that provides useful information to estimate plastic deformability under complex deformation conditions.
Indentation is a suitable method to investigate plastic deformation behavior under complex deformation conditions. During indentation, materials deform into a shape similar to that of the indenter. Thus, indentation with a symmetrically shaped indenter on a single-crystal specimen with crystallographic symmetry that is different from that of the indenter provides information on the deformation behavior under various loading conditions simultaneously along crystallographically non-equivalent orientations. The use of ex situ indentation enables plastic deformation behavior during indentation to be deduced from the results of specimen surface observations after testing. However, an understanding of the relationship between applied loads, the order that the plastic deformation mechanisms occur, and the indent shape is necessary to discuss the actual plastic deformation behaviors more precisely. In some previous studies on ex situ Brinell indentation and Vickers indentation of pure Mg single crystals with a loading axis along $[1\bar{2}10]$, an anisotropic indent shape for which the diameter or a diagonal line along [0001] was observed to be significantly longer than that along $[10\bar{1}0]$.25–27) Note that pseudoelastic behavior associated with twinning-detwinning has been reported in various polycrystalline Mg alloys,28–32) and it is difficult to investigate the effect of the pseudoelastic behavior on the anisotropic indent by ex situ observations. In situ observations of the specimen surface during the loading-unloading process of indentation are thus expected to provide valuable information on the extending process of the anisotropic indent and the evolution of various plastic deformation mechanisms.
For such purposes, various in situ indentation methods have been established previously.33–41) Recently, optical indentation microscopy (OIM) was established as an in situ indentation method to determine the contact area between an indenter and a material.39–41) In OIM, the contact area at each step of the indentation testing is determined using an optically transparent indenter made of sapphire or diamond. However, the refractive index of an indenter for OIM is significantly larger than that of air. Consequently, the area on the upper surface of the specimen around the contact area visible by OIM is quite limited due to the significantly large refraction of rays at the indenter/air interface. In situ observations of the specimen surface around the contact area during indentation are necessary to understand the relationship between the applied load, the order that the plastic deformation mechanisms occur, and the indent shape.
In this study, a new in situ indentation method with the use of an optically transparent indenter is established by the addition of an immersion liquid between the indenter and the specimen surface. This enables simultaneous observation of the contact area between the indenter and the specimen, and also the specimen surface around the contact area. The newly established in situ Brinell indentation method was used in an attempt to understand the plastic deformation behavior of pure Mg and Mg-Y alloy single crystals under complex deformation conditions. Brinell indentation was employed because of the symmetrical indenter shape.
In this study, an optically transparent hemispherical indenter (radius: r = 500 µm) based on Brinell indentation defined by the International Organization for Standardization (ISO 6506-2) was selected. Figure 1 shows (a) photographs of the in situ indentation equipment, (b) a schematic diagram of the in situ indentation setup, and (c) a schematic of the ray paths during in situ indentation using a confocal laser microscope. A laser scanning confocal microscope (1LM21H, Lasertech Ltd., Japan) with a He-Ne laser (laser wavelength: λ = 632.8 nm) and a long-focus objective lens (focal length: 200 mm) were employed for observations. A specimen set on a driving part was pushed up by a piezo actuator (NEXLINE®, High-Load Piezo Nanopositioning Drive, N-214, PI-tech, Germany) to penetrate the indenter set above the specimen. The applied load during indentation was measured by a force sensor (9193, Kistler Instrumente AG), and 10 signals per second were recorded by a digital data acquisition system.
(a) In situ indentation jig, (b) schematic diagram of the in situ indentation setup, and (c) schematic of the ray paths with a confocal laser microscope.
In previously established OIM,39–41) rays are significantly refracted at the interface between the optically transparent indenter and the air, and the visible area of the specimen surface around the contact area is quite limited because the refractive indices of the optically transparent indenter and the air are significantly different. Therefore, to expand the area of the specimen surface around the contact area visible through the optically transparent indenter, it is necessary to control the refractive index ratio nr/ni to be close to unity. Here, nr and ni represent the refractive index of the medium filling the gap between the indenter and the specimen surface and that of the optically transparent indenter, respectively. For this purpose, the gap between the indenter and the specimen surface in the newly established in situ indentation method is filled with an immersion liquid with a refractive index close to that of the optically transparent indenter. Details of the optical model for this method are presented in Appendices A and B.
Liquids that satisfy the following requirements are selected as candidates for the immersion liquid; A refractive index close to that of the optically transparent indenter, optically transparent, low volatility, non-toxic, no reaction with the optically transparent indenter and the specimen, stable under testing conditions and easily available. In this study, a silicone oil with nr = 1.5142) (TO-SP10-N, TRUSCO) and kerosene with nr = 1.4343) (Junsei Chemical Co., Ltd.) were selected as immersion liquids that satisfy the specified requirements. Indenters that satisfy the following requirements are selected as candidates for the optically transparent indenter; A refractive index close to that of the immersion liquid, optically transparent, high hardness, non-toxic, no reaction with the immersion liquid and the specimen, stable under testing conditions and easily available. In this study, sapphire with ni = 1.7744) and silica glass with ni = 1.4644) (Edmund Optics) were selected as optically transparent indenter materials that satisfy the specified requirements.
In previously established OIM, an optically transparent diamond indenter was employed due to its very high hardness, while the gap between the indenter and the specimen surface was filled with air. The refractive indices of diamond and air are ni = 2.42 and nr = 1.00, respectively, and the corresponding refractive index ratio is nr/ni = 0.41. Consequently, the area of the specimen surface visible around the contact area during indentation is quite narrow due to significantly large refraction at the indenter/air interface. The combinations of optically transparent indenter and immersion liquid, along with the corresponding nr/ni for each combination are listed in Table 1. Here, “air” indicates there is no immersion liquid. The refractive index ratios nr/ni for each combination listed in Table 1 are closer to unity than nr/ni between the diamond indenter and air (nr/ni = 0.41). Comb. 3 was selected for in situ Brinell indentation of Mg single crystals in this study because nr/ni is close to unity and the hardness of sapphire is sufficiently high for an indenter.
Single-crystal ingots of pure Mg, Mg-1.3 at% Y and Mg-2.3 at% Y alloys were grown in a high purity graphite crucible by a Bridgman method.3) The ingots were mechanically polished using emery papers and colloidal silica (particle size: 0.04 µm) for determination of the crystallographic orientation using field emission scanning electron microscopy (FE-SEM; JSM 6500F, JEOL) and electron backscatter diffraction (EBSD). The alloying content of Mg-Y alloy single-crystal specimens was confirmed by fluorescent X-ray analysis (JSX-3220Z, JEOL). All specimens were sealed in glass tubes filled with Ar gas and subjected to cyclic annealing (373–423 K, 4 h per cycle, 18 cycles) to remove the strain introduced during specimen preparation. For the Mg-Y alloy specimens, solution treatment was also conducted at 773 K for 72 h after the cyclic annealing, followed by quenching. In situ Brinell indentation was conducted at room temperature with the loading axis parallel to $[1\bar{2}10]$ on single-crystal specimens. Comb. 3 (sapphire-silicone oil, nr/ni = 0.85, r = 500 µm) was selected as the best indenter-immersion liquid combination. The penetration rate of the indenter was 1 µm/s and the maximum applied load was 9.8 N. All the deformation processes were recorded with a video recorder. Slip trace analyses were conducted based on FE-SEM observations and EBSD analysis of the specimen surface after indentation.
Figure 2 shows in situ images of (a) pure Mg, (b) Mg-1.3 at% Y and (c) Mg-2.3 at% Y single-crystal specimens. In addition, Fig. 2(d) shows an in situ image of a pure Mg single crystal indented with an applied load of 9.8 N after image processing using software (ImageJ ver. 1.45l) to clarify the contact area of the indents. In situ Brinell indentation revealed that the indent on the pure Mg single crystal was distorted and approximated an ellipsoidal shape, although the indenter was hemispherical. The major and minor axes of the indents are parallel to [0001] and $[10\bar{1}0]$, respectively, regardless of the alloying content. The occurrence of basal slip and $\{ 10\bar{1}2\} $ twinning was observed in situ during the loading process for all specimens. It is noteworthy that the areal fraction of $\{ 10\bar{1}2\} $ twins decreases with increasing Y content. Similar tendencies were previously reported for ex situ Brinell indentation and Vickers indentation measurements.25–27) Figures 2(a–c) show that the anisotropy of the indent shape by Brinell indentation decreases with increasing Y content, which is a similar tendency to that observed with Vickers indentation.26) Hereafter, the difference in the diameters of indents is referred to as the anisotropy of the indent shape, which is evaluated using the lengths of the major and minor axes of the approximated ellipsoid.
In situ images of (a) pure Mg, (b) Mg-1.3 at% Y and (c) Mg-2.3 at% Y single crystals during loading process (nr/ni = 0.85). (d) In situ image processed to measure the major and the minor diameters of the indent on pure Mg single crystal under a load of 9.8 N.
Figure 3 shows the major axis length dL along [0001] and the minor axis length dS along $[10\bar{1}0]$ for the indents on pure Mg, Mg-1.3 at%Y and Mg-2.3 at%Y single crystals as a function of the applied load. Figure 4 shows the ratios between dL and dS for the indents (dL/dS) on each single-crystal specimen as a function of the applied load. A dL/dS ratio close to unity indicates that the anisotropy of the indent shape is small, i.e., the material deforms homogeneously. Figure 3 shows that both dL and dS for each applied load decrease with increasing Y content. This is attributed to solid-solution strengthening by Y addition. Moreover, the dL/dS ratio for each applied load shown in Fig. 4, comes close to unity by Y addition, which indicates a decrease in the anisotropy of the indent shape with Y addition. Note that the differences in the dL/dS ratios between that under loading (at 9.8 N) and that after unloading (at 0.0 N) were sufficiently small for all specimens. From this result, it can be concluded that the effect of pseudoelastic behavior by detwinning on the indent shape is sufficiently small. Basal slip and $\{ 10\bar{1}2\} $ twinning were revealed to occur during in situ Brinell indentation of both pure Mg and Mg-Y alloy single crystals, and the areal fraction of $\{ 10\bar{1}2\} $ twins decreased with Y addition (Fig. 2). These results are in good agreement with previously reported results.26,27) In the previous work with ex situ Vickers indentation of Mg-Y single crystals, slip traces of prismatic slip were observed around indents.26) It was noted that Y addition causes a decrease in the anisotropy of the Vickers indent shape and a decrease of the areal fraction of $\{ 10\bar{1}2\} $ twins; therefore, it was concluded that the decrease in the anisotropy of the Vickers indent shape by Y addition is due to activation of not only $\{ 10\bar{1}2\} $ twinning but also non-basal slips such as prismatic slip, which has a significant contribution to the plastic deformation to extend the Vickers indents on Mg-Y alloy single crystals. It is expected that the decrease in the anisotropy of the Brinell indent shape with increasing Y content could be attributed to the same reasons.
Major axis length dL along [0001] and minor axis length dS along $[10\bar{1}0]$ for indents on various single crystals as a function of the applied load.
Ratio of the major axis dL to the minor axis dS for indents (dL/dS) on various single crystals as a function of the applied load.
Figures 5(a–c) show schematics of the anisotropic indent. The penetration depth h, which is assumed to be the same as the displacement of the piezo actuator, on the pure Mg single-crystal specimen at 9.8 N was h = 28 µm. The relationship between the Brinell indent diameter d, and h without sink-in and pile-up on the specimen surface is expressed geometrically by the following equation.
| \begin{equation} d = 2r\mathit{cos} [\mathit{Arcsin}\{(r - h)/r\}], \end{equation} | (1) |
(a–c) Schematics of the Brinell indent along $[1\bar{2}10]$ based on the Nix-Gao model, together with crystallographic orientation information, and (d) magnified in situ image of pure Mg single crystal at 9.8 N.
The anisotropy of the indent shape with pure Mg and Mg-Y alloys single crystals is discussed based on the plastic flow model of indentation proposed by Nix and Gao (Nix-Gao model45)), combined with CRSS for various plastic deformation mechanisms. Figures 5(a–c) show schematics for the Nix-Gao model applied to a Mg single crystal with the loading axis along $[1\bar{2}10]$. According to the Nix-Gao model, the occurrence of plastic deformation mechanism(s) that introduce $(0001)[1\bar{2}10]$ shear strain is required to increase the diameter of the Brinell indent toward the [0001] direction. Similarly, the occurrence of plastic deformation mechanism(s) that introduce $(10\bar{1}0)[1\bar{2}10]$ shear strain is required to increase the diameter of the Brinell indent toward the $[10\bar{1}0]$ direction. The shear strains of $(0001)[1\bar{2}10]$ and $(10\bar{1}0)[1\bar{2}10]$ are principally introduced by the single occurrence of basal slip and prismatic slip, respectively. However, it is noteworthy that $\{ 10\bar{1}2\} $ twinning contributes to an increase in the diameter of the Brinell indent for both directions. In particular, $\{ 10\bar{1}2\} $ twinning mainly contributes to the increase in the diameter of the Brinell indent toward the $[10\bar{1}0]$ direction in pure Mg single crystals because the CRSS for prismatic slip is much higher than that for $\{ 10\bar{1}2\} $ twinning. However, the addition of Y has been reported to lead to high solid-solution strengthening for both basal slip and $\{ 10\bar{1}2\} $ twinning,4,13) and solid-solution softening for prismatic slip.3) Consequently, there is less difference among the relative activities of basal slip, $\{ 10\bar{1}2\} $ twinning and prismatic slip in Mg-Y alloys than in pure Mg. Although no slip trace of prismatic slip was observed near the Brinell indents, the decrease of the areal fraction of $\{ 10\bar{1}2\} $ twins caused by Y addition, as shown in Fig. 2, strongly suggests the occurrence of prismatic slip in Mg-Y alloys single crystals by taking into account the occurrence of prismatic slip in Vickers indents observed after testing.26) Therefore, the decrease in the anisotropy of the indent shape in Mg-Y alloy single crystals is attributed to less differences among the relative activities of the various plastic deformation mechanisms.
Figure 6 shows (a) in situ images of a pure Mg single crystal during the unloading process, (b) an FE-SEM image and an inverse pole figure (IPF) of the Brinell indent, and (c) magnified images of each. In Figs. 6(b) and (c), the black boundaries in the IPF express boundaries between the matrix and $\{ 10\bar{1}2\} $ twins. Figure 6(a) shows the surface reliefs recognized beneath the indenter by in situ observation during the unloading process. These surface reliefs are also observed by FE-SEM/EBSD analysis (Fig. 6(b)). EBSD analysis revealed that the regions of the surface reliefs have the same crystallographic orientation as the matrix. Thus, these surface reliefs are attributed to the detwinning of $\{ 10\bar{1}2\} $ twins during the unloading process, and detwinning of $\{ 10\bar{1}2\} $ twins occurs during Brinell indentation, which introduces complex deformation to the material. A number of experimental works on compression and tension testing of polycrystalline Mg alloys revealed the occurrence of detwinning of $\{ 10\bar{1}2\} $ twins.46–49) However, there have been no reported in situ observations of detwinning of $\{ 10\bar{1}2\} $ twins during indentation. The plastic deformation behavior of the specimen surface around the contact area was successfully observed during the loading and unloading processes using the in situ Brinell indentation method.
(a) In situ images of pure Mg single crystal during the unloading process, (b) FE-SEM image and the IPF of a pure Mg single crystal after indentation, and (c) magnified images from (b).
A newly established in situ Brinell indentation method was employed to investigate the plastic deformation behavior of pure Mg and Mg-Y alloy single crystals under complex stress conditions. An immersion liquid was introduced to obtain a refractive index ratio (nr/ni) close to unity, so that the present technique enables observation of the contact area between the indenter and the specimen, and the specimen surface around the contact area during the loading and the unloading process. In situ Brinell indentation of pure Mg and Mg-Y alloy single crystals enabled observation of the anisotropic indent formation process during loading. The anisotropy of the indent shape decreases with increasing Y content because the difference in the relative activities among various plastic deformation mechanisms decreases with increasing Y content. Moreover, detwinning of $\{ 10\bar{1}2\} $ twins was observed by in situ Brinell indentation during the unloading process. This result indicates that detwinning of $\{ 10\bar{1}2\} $ twins occurs under complex deformation such as indentation, although it does not contribute to the anisotropy of the indent shape.
The authors would like to thank Assoc. Prof. K. Ikeda and Dr. S. Takizawa for useful discussions. This work was partially supported by Toyota Motor Corp. and The Amada Foundation.
The optical model of in situ indentation for in situ observation of the specimen surface around the contact area during indentation is described here. For simplicity of calculation, it is assumed that the specimen surface is maintained as a flat surface during indentation, although the specimen surface shows “sink-in” or “pile-up” around the contact area. In the previously established optical indentation microscopy (OIM),39–41) it was difficult to observe the specimen surface around the contact area during indentation because incident rays are significantly refracted at the indenter/air interface. This is attributed to the significant difference in the refractive index of the optically transparent indenter and the medium filling the gap between the indenter and the specimen surface. Snell’s law is applied to obtain the relationship between the incidence angle θ1 and the refracted angle θ2 as follows:
| \begin{equation*} n_{1} \times \mathit{sin}\,\theta_{1} = n_{2} \times \mathit{sin}\,\theta_{2}, \end{equation*} |
| \begin{equation} \mathit{sin}\,\theta_{1} = n_{2}/n_{1} \times \mathit{sin}\,\theta_{2}, \end{equation} | (A1) |
| \begin{equation} \mathit{sin}\,\theta_{0} = n_{2}/n_{1}. \end{equation} | (A2) |
Schematic diagrams of (a) Snell’s law and (b) the relationship between incidence angle and positions. The value n represents the refractive index.
Table 1 lists the refractive index ratios nr/ni employed in this study, which are closer to unity than nr/ni in previously established OIM (nr/ni = 0.41).39–41) According to ISO 6506-2 (JIS B 7724), the hardness of a Brinell indenter should be not less than 1500 HV. The hardness of sapphire is 2000 HV50,51) and that of silica glass is 1200 HV.52,53) Although the hardness of silica glass is less than 1500 HV, the use of silica glass (comb. 4) leads nr/ni closer to unity than that of any other optically transparent indenters, as listed in Table 1. Therefore, in situ indentation with comb. 4 (silica glass-kerosene) on soft materials enables wider observation of the specimen surface around the contact area.
An attempt was made to compare simulated in situ images with experimentally observed in situ images. The ray paths during in situ Brinell indentation were simulated using each combination of optically transparent indenter and immersion liquid listed in Table 1. As shown in Fig. 1(c), there are various incident ray paths, and the angle between the specimen surface and the incident rays can be calculated using the numerical aperture NA (NA = 0.16 in this study) of the objective lens. Chromatic aberration does not occur in laser microscopy observations because the laser is monochromatic. Thus, the focal position could be in agreement with the specimen surface in the optical field of view if the gap between the objective lens and the specimen surface were filled with a medium having a homogeneous refractive index. However, in this method, the rays pass through the air, the optically transparent indenter, and the immersion liquid with different refractive indices, which results in refraction of the incident rays at the two interfaces. Consequently, it is expected that the focal positions at each observed point are different from each other (Fig. A2(a) ). The degree of this difference was calculated using the refractive index ratio nr/ni of comb. 4 (silica glass-kerosene, nr/ni = 0.98) for which nr/ni is the closest to unity among the combinations listed in Table 1. Here, Ray 1 is defined as the ray that passes through the center of the objective lens and Ray 2 is defined as the ray that passes through the edge of the objective lens on the same side as the viewing position (Fig. A2(a)). Note that there are rays other than Ray 1 and Ray 2, nevertheless, the combination of Ray 1 and Ray 2 was selected to calculate the focal position which is shifted from the specimen surface because the distance between the focal position f and the specimen surface for this combination is the longest among the combinations of rays. The horizontal (parallel to the specimen surface) distance between the viewing position and the initial contact point between the specimen surface and the indenter tip is expressed as w (Fig. A2(a)). Figure A2(b) shows the focal position f as a function of w. The focal position f = −500 µm indicates focus on the specimen surface. The distance between the focal position f and the specimen surface (f = −500 µm) increases with increasing w. A certain optical image is detected using rays from two different viewing positions on the specimen surface because of the shift of the focal position from the specimen surface (Fig. A2(a)). The distance between these two different viewing positions is expressed as dw. Figure A2(c) shows dw as a function of w; dw increases with increasing w. According to the Rayleigh criterion, the resolution of two point-like objects δ, is expressed as:
| \begin{equation} \delta = 0.61 \times \lambda/\mathit{NA}. \end{equation} | (A3) |
(a) Schematic diagram of ray paths, and the (b) focal positions f and (c) dw as a function of the position w with nr/ni = 0.98.
(a) Schematic diagram of laser ray refraction, and the relationship between x and a under each indenter-immersion liquid combination with penetration depths of (b) h = 0 µm and (c) h = 10 µm. The dotted lines in (b) and (c) indicate x = a, i.e., nr/ni = 1.
Rays are refracted at the interface between two media with different refractive indices. Moreover, the incidence angle θ1 is greater than the critical angle θ0, so that the incident rays undergo total reflection at the interface between two media. Calculations based on the optical model and experimental observations by in situ Brinell indentation of pure Ag were conducted to discuss the effects of these phenomena on the observed in situ images. Pure Ag was selected for observations because it has low hardness and good oxidation resistance. In addition, it is expected that pure Ag, which has a face-centered cubic (FCC) structure, deforms homogeneously.
The following calculations based on the optical model were conducted for comparison with observed in situ images. The horizontal (parallel to the specimen surface) distance between the viewing position and the initial contact point between the specimen surface and the indenter tip is expressed as x. The horizontal distance between the detected imaging position and the contact point is expressed as a. The relationships between x and a were calculated under each condition based on eq. (A1), and the results are shown in Figs. B1(b) and (c). A laser wavelength of λ = 632.8 nm for the He-Ne laser was applied in the present calculations. The position x equals the position w (Fig. A2(a)) because the gap between the objective lens and the specimen surface was filled with a medium having a homogeneous refractive index. Note that x is approximately equal to w (x ≈ w) because nr/ni is sufficiently close to unity. The dotted lines in Figs. B1(b) and (c) indicate that x equals a, i.e., the incident ray is not refracted (nr/ni = 1). Figure B1(b) shows that x becomes close to a (i.e., the solid line is close to the dotted line) with nr/ni close to unity. Moreover, if a exceeds a certain value (e.g., a = 279 µm with comb. 1), an optical image cannot be observed due to total reflection. According to eq. (A2), nr/ni close to unity leads the critical angle θ0 close to 90°, which results in a decrease of the invisible area caused by total reflection (Fig. A1(b)). Therefore, the combination of an optically transparent indenter and an immersion liquid with nr/ni close to unity is effective to decrease the invisible area. The visible area for each combination can be estimated by the maximum value of x; for example, the maximum values of x for comb. 1 and comb. 4 are 206 µm and 441 µm, respectively (Fig. B1(b)). Moreover, two a values that correspond to a certain x value are calculated for each combination (Fig. B1(b)). This indicates that a certain position on the specimen surface corresponds to images observed at different positions in the in situ image. However, as shown in Fig. A2(b), the distance between the focal position f and the specimen surface (f = −500 µm) increases with increasing w. Consequently, the specimen surface cannot be observed sufficiently near the indenter edge (the details will be described later). Therefore, it is not recognized that a certain position on the specimen surface is imaged at different positions in the present in situ image.
It is expected that the relationship between x and a changes during penetration of the indenter into the specimen because the distance between the specimen surface and the indenter changes. Figure B1(c) shows x as a function of a with a penetration depth of h = 10 µm. Here, h = 0 indicates the initial contact between the indenter tip and the specimen surface, and h > 0 indicates penetration of the indenter into the specimen. Comb. 4 (silica glass-kerosene, nr/ni = 0.98) was chosen for the calculation shown in Fig. B1(c). The dashed line indicates Δx = x10 − x0 as a function of a. x10 and x0 indicate the value of x at h = 10 µm (solid line in Fig. B1(c)) and h = 0 µm (solid line for comb. 4 in Fig. B1(b)), respectively. The maximum value of Δx was calculated as Δx = 1.73 µm; therefore, it is concluded that this difference does not have a significant effect on observations.
In this section, the calculated results are compared with the experimental results of in situ Brinell indentation of pure Ag. As-cast pure Ag ingots were mechanically polished using emery papers and alumina slurry (particle size: 0.1 µm). The grain size was determined by the EBSD method. The following combinations of optically transparent indenters and immersion liquids listed in Table 1 were selected. Here, “air” indicates there is no immersion liquid. In situ Brinell indentation was conducted at room temperature with a penetration rate of 1 µm/s. The maximum applied load was 4.9 or 9.8 N. Figure B2 shows in situ images for each combination under various loading conditions. The grain size determined by the EBSD method was larger than 1 mm. Figure B2 shows that the diameter of the indent at 9.8 N is approximately 240 µm; therefore, the grain size is sufficiently larger than the diameter of the indents. This newly established in situ indentation method enables observation of not only the contact area between the indenter and the specimen, but also the specimen surface around the contact area during indentation. During the loading process of indentation, the specimen surface may be distorted slightly by sink-in or pile-up, and this distortion becomes smaller at positions distant from the contact area between the indenter and the specimen surface.54) Although the specimen surface is curved slightly by sink-in or pile-up, the specimen surface can be observed sufficiently almost over the entire visible area, as shown in Fig. B2. Therefore, sink-in or pile-up has a small effect on the in situ observations of pure Ag; this means that the assumption that the specimen surface is flat during indentation is reasonable for this discussion. In comb. 1 (nr/ni = 0.56), the specimen surface around the contact area cannot be observed sufficiently, while the visible area extends with an increase in nr/ni toward unity. These experimental results are consistent with the calculated results.
In situ images of various combinations of indenter and medium filling the gap between the indenter and specimen (pure Ag) surface, i.e., air and immersion liquids.
The distortion of the experimentally observed image of the specimen surface caused by refraction of the incident rays is discussed with respect to a calculated image based on the optical model. To calculate the distortion of the image, an array of marked points placed at 25 µm intervals on the specimen surface was assumed (Fig. B3(a) ). For this calculation, comb. 4 (silica glass-kerosene, nr/ni = 0.98) was selected as the indenter-immersion liquid combination because nr/ni for this combination is the closest to unity among the candidate combinations listed in Table 1. A laser wavelength of λ = 632.8 nm for the He-Ne laser was employed. The values of x and a (Fig. B3) are defined in Fig. B1. The value of x is approximately equal to w (x ≈ w) because nr/ni is close to unity. Figures B3(b) and (c) show calculated images of the specimen surface with the marked points. The penetration depth of the indenter is expressed as h, as defined in Fig. B1. The distortion in the calculated image, which is estimated using the difference between x (Fig. B1(a)) and a (Figs. B1(b) and (c)), becomes larger at the points farther from the contact area between the specimen and indenter. Moreover, the marked points near the indenter edge (500 µm away from the initial contact point between the indenter and specimen surface) disappear due to total reflection at the interface between the indenter and immersion liquid. These results are consistent with Fig. B1. The calculated results are compared with the experimental results for in situ Brinell indentation of pure Ag.
Theoretical images of (a) the initial state, and at (b) h = 0 and (c) h = 10h = 10. (d) Experimentally observed in situ image of pure Ag with nr/ni = 0.98. The marked points were placed at 25 µm intervals.
An array of nanoindents as marked points placed at 25 µm intervals on the pure Ag specimen was prepared using a nanoindenter (TI950 TriboIndenter, Hysitron). Comb. 4 (silica glass-kerosene, nr/ni = 0.98) was selected for comparison with the calculated results. In situ Brinell indentation was conducted at room temperature with a penetration rate of 1 µm/s. Figure B3(d) shows an experimentally observed in situ image. White dashed lines are drawn every 50 µm in Fig. B3(d) for comparison with the calculated image shown in Fig. B3(c). The displacement of the marked points in the experimentally observed in situ image had a similar tendency with that in the calculated image (Fig. B3(c)); therefore, the experimental results are consistent with the calculated results.
Figure B3(d) shows that the experimentally observed in situ image beneath the indenter becomes gradually dark closer to the indenter edge. Two phenomena are attributed to this change in the observed images. One is the total reflection of the incident rays with various incidence angles θ1, such as Ray 3 (Fig. B1(a), vertical incident ray), Ray 1 and Ray 2 (Fig. A2(a)). The position of a at which each incident ray undergoes total reflection differs because the incidence angles θ1 of the various rays differ from each other. According to eq. (A2), The positions of a at which Ray 3 (Fig. B1(a), vertical incident ray) and Ray 2 (Fig. A2(a)) undergo total reflection are calculated to be 489 µm and 459 µm, respectively. Consequently, the rays that reach the detector of the laser microscope decrease with the distance to the indenter edge because some of the incident rays undergo total reflection near the indenter edge; therefore, the in situ image beneath the indenter becomes gradually dark. The region at which the in situ image beneath the indenter gradually becomes dark is consistent with the region at which some of the incident rays undergo total reflection. The second reason is the change of the focal position. As shown in Fig. A2(b), the distance between the focal position f and the specimen surface (f = −500 µm) increases as the distance to the indenter edge decreases. The surface of the pure Ag specimen was observed with different focal positions f to investigate the effect of the distance between the focal position f and the specimen surface for an observed image, and the results are shown in Fig. B4 . The gap between the objective lens and the specimen surface was filled with only air, i.e., the indenter and the immersion liquid were not used. Moreover, Fig. B4(b) shows the results of a quantitative intensity analysis of the observed images measured using ImageJ ver.1.45l. Brighter and darker images indicate higher and lower intensities, respectively. The intensities measured for each focal position f were normalized according to that at f = −500 µm. Figure B4 shows that the observed image becomes dark and the normalized intensity decreases with an increase in the distance between f and the specimen surface (f = −500 µm). The specimen surface was not observed at f = −300 µm (normalized intensity If/I−500 ≈ 0.5). Figure A2(b) shows that f is equal to −300 µm as w = 459 µm with nr/ni = 0.98 (comb. 4). This position, w = 459 µm, is consistent with the region at which the in situ image beneath the indenter gradually becomes dark (Fig. B3(d)) because x is approximately equal to w (x ≈ w) with nr/ni close to unity. These are therefore the reasons for the gradual darkening of the in situ image beneath the indenter with a decrease in the distance to the indenter edge.
(a) Laser micrographs of pure Ag under various focal positions and (b) normalized intensity of experimentally observed images as a function of the focal position f, estimated using ImageJ software.
