Estimation of Actual State of Contact Surfaces in Pressure Testing of Small Pure Aluminum Blocks
論文ID: aem.26-0010
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論文ID: aem.26-0010
Surface topography, which represents the asperities and geometric features of a material surface, has a significant influence on contact conditions between bodies, as well as on wear, friction, lubrication, contact resistance, and heat transfer. For example, in manufacturing processes such as resistance spot welding, where high voltage is applied under pressure, it is well known that the surface topography of the electrode and the sheet material greatly affects the results. However, even in the simple case of pressing two material surfaces together, accurate estimation of the real contact state remains difficult, and related studies continue to be conducted today. In this study, pressure tests were performed using small blocks of pure aluminum, and the height distribution of the contact surfaces before and after testing was measured. Furthermore, a method for estimating the real contact areas from the height distribution was proposed and applied to the tests. By applying the proposed method, it was possible not only to evaluate the contact area ratio as a single metric of the interface, but also to estimate the specific areas that were actually in contact.
The surface topography, which characterizes the asperities and geometry of a material surface, has a significant influence on contact conditions, wear, friction, lubrication, contact resistance, and heat transfer. Resistance spot welding provides a representative example. In this process, a high voltage is applied under pressure, so the surface topography of the electrode and the sheet material strongly affects the fine-scale distribution of real contact areas, the electrical resistance at those interfaces, and consequently the heat generation and melting behavior at the contact. Because spot welding involves a complex interplay of mechanics, electricity, and heat transfer, accurately capturing the phenomenon is far from straightforward [1]. Even in the simpler case where two materials are merely pressed together without any applied current, accurately determining the real contact state remains challenging, and research on this issue continues.
Research on contact surfaces has been conducted for many decades. For example, Pullen et al. analyzed the real contact area using a simple, classical model in which the portions of the surface that are compressed by the rigid plate become flattened, while the remaining regions rise upward without changing their original shape and the volume generated by the rising surface is equal to the displaced (compressed) volume, which is called the uniform rise hypothesis [2]. Based on the uniform rise hypothesis and the volume conservation law, it is demonstrated that the relationship between the real contact area ratio and the compressive load becomes nonlinear under high compressive loads. Kalin et al. pressed a transparent sapphire glass against the surface of metal-cutting steel with different roughness levels to observe the actual contact area and examined how elastic deformation and work hardening contribute to the load-bearing capacity [3]. They demonstrated that, in the early stage where the real contact area is small, the applied compressive load is mainly supported by elastic deformation, whereas in the later stage, where the contact area becomes larger, the resistance arises not only from plastic deformation accompanied by work-hardening but also from hydrostatic bulk stresses. They further clarified that the relative contributions of these mechanisms depend on the surface roughness. Other studies include the work by Yastrebov et al., who examined the evolution of the contact area from the onset of contact to near-complete contact by assuming a self-affine surface and employing probabilistic analysis and numerical simulations [4]. There also exist studies that extend conventional models, where a rough surface is treated as an assembly of many independent asperities, by incorporating asperity interactions and plastic deformation to predict the overall contact behavior of material surfaces [5].
Although many studies have been conducted, it is still difficult to claim that a reliable method has been established for estimating the distribution and precise location of real contact areas between metal surfaces. For example, even at the same nominal contact area ratio, the surface properties, such as friction, are expected to differ depending on whether a few large contact areas or many small contact areas are present. Furthermore, considering the future development of related research, it is important to establish a simulation method capable of predicting the actual contact areas under loading based on the height distribution of the contact surface prior to compression. Motivated by these considerations, this study proposes a method for estimating contact areas from the measured height distribution of the contact surface, and applies the proposed method to compression tests conducted using small blocks of pure aluminum.
Pure aluminum bars with a purity of 99% and a square cross section of 4 mm on each side were used as the test specimens. The bars were cut into 4 mm long pieces by wire electrical discharge machining (EDM) to produce small block specimens, as shown in Fig. 1. Because the pure aluminum bars were manufactured through extrusion and drawing processes, they experienced significant strain hardening and are therefore expected to exhibit a higher yield stress than ordinary pure aluminum. Consequently, even under a relatively large compressive load of 1 kN, which corresponds to an apparent compressive stress exceeding 60 MPa, the specimens showed only macroscopic elastic deformation, and no plastic deformation was observed.
Shape and size of small pure aluminum block specimen
For the contact surfaces of each block, the as-machined surface produced by wire EDM was used as the rough surface, while the machined surface polished with #4000 waterproof abrasive paper followed by 3‑µm and 1‑µm diamond paste was used as the smooth surface. Five rough-smooth pairs of specimens were prepared. The arithmetic mean roughness of the rough surfaces ranged from 2.48 µm to 2.84 µm, whereas that of the smooth surfaces was less than 0.1 µm. Rough-rough pairs of specimens, which are more practical and difficult to analyze, are planned to be reported in a separate paper.
2.2 Pressure test and measurement of surface heightA micro vise (Nihon Automatic Co.), a load cell (Sanei Instruments Co., 9E01-L-42), a dynamic strain amplifier (NEC Sanei Co., AS2103), and a data logger (Graphtec Corp., GL200A) were used for the pressure tests as shown in Fig.2. The two specimens shown in Fig. 1 were aligned so that their contact surfaces faced each other, held in the vise, and then compressed to conduct the test. The applied compressive load was increased in increments of 0.2 kN up to a maximum of 1 kN.
Overview of the pressure testing apparatus
The observation area of 256 µm × 256 µm is set at the center of each contact surface, as shown in Fig.3. The observation and height measurement were performed at each compressive load level using 3D measuring laser microscope (Olympus Corp., LEXT OLS5100). To reduce measurement noise, the data from a 4 × 4 pixel area were averaged to obtain a single pixel value. The microscope used in this study has a function that automatically stitches data from adjacent measurement areas. However, the height-distribution data obtained from a large number of stitched areas did not provide sufficient accuracy. For this reason, the measurements were limited to a single 256 µm × 256 µm area obtained from one scan. The compressive load was increased stepwise in increments of 0.2 kN, and after unloading at each load level, the specimen was removed for observation and measurement of the contact surface. Accordingly, the surface conditions measured in this study correspond to the state in which the elastic deformation during compression had been fully released. The analysis focused on the central region of the contact surface. However, the behavior near the periphery is expected to involve radial material flow originating from the central area, and thus requires further investigation.
Observation area at the center of contact surface
Figure 4 shows an example of the contact surfaces before and after the pressure test. The initial value of arithmetic mean roughness for smooth surface was 0.06 µm and that for rough surface was 2.68 µm. As can be seen from the figure, it is difficult to capture the changes in surface topography from simple observational images alone.
Example of contact surface morphology before and after pressure test
The change in height distribution within the measurement area of the same specimen on the smooth surface is shown in Fig. 5. On the smooth surface, very small depressions are observed in regions that appear to have been indented by the asperity peaks of the rough surface.
Height distribution on smooth surface in pressure test
Figure 6 shows the change in height distribution on the rough surface with compressive load. Although significant surface undulations exist prior to testing, it is difficult to discern changes associated with increasing compressive load. It can be understood from the height distributions on both surfaces that it is difficult to estimate the real contact area by their simple comparison. In this study, a method is proposed and the results will be shown.
Height distribution on rough surface in pressure test
The real contact areas within the contact interface were determined using the following method:
1. The observations of the contact surfaces and measurements of their height distributions were conducted at each compressive load-stage of the pressure testing.
2. For the alignment of the height distributions measured under different compressive loads, it was assumed that the lower portions of the surface experienced negligible contact and deformation. Based on this assumption, the reference levels were adjusted so that the average height of the lowest 10% of the surface profile matched across all measurements. Although the appropriateness of the 10% threshold has not been examined in a strictly rigorous manner, a value that is too low makes it difficult to identify the relevant locations, whereas a value that is too high increases the influence of the deformed areas. It has been confirmed that the 10% threshold adopted in this study is not significantly affected by these issues.
3. The in-plane position is aligned using the alignment function of 3D measuring laser microscope.
4. The difference in the height distribution before and after the test, Dh(x, y), is calculated. The coordinates x and y show the location of pixel in measurement area.
5. A threshold value hth is set for the height distribution before the test, and the regions where the height exceeds this threshold are extracted as g(h(x, y), hth) given by Eq.(1).
| (1) |
6. The threshold value hth is determined so as to minimize the mean squared error, MSEh, defined by Eq.(2) over the entire measurement area.
| (2) |
7. Areas where the height hth is greater than or equal to the threshold hth are defined as real contact areas.
8. Compressive amount u, where compressive displacement from the first contact, is evaluated by Eq.(3).
| (3) |
where hmax is the maximum height in the contact area. The value of u corresponds to the compressive displacement, and because this value is small, it is difficult to measure with high accuracy.
To simplify the estimation procedure, the smooth surface is assumed to be rigid in this study. Both the smooth and rough surfaces were fabricated from blocks of the same pure aluminum. Consequently, when a compressive load is applied, some degree of height variation is expected to occur even on the smooth surface. This point has not been examined in the present study. Improving the accuracy of the estimation results by taking the deformation of the smooth surface into account is currently under investigation.
4.2 Results of actual contact areaAn example of the change in mean squared error MSEh against threshold height hth is shown in Fig.7. This is a case when F=0.6 kN and the value of hth is found to be 6.017 µm. Since the MSEh values exhibited distinct minima at each specified height in the other cases, it was straightforward to determine the threshold based on those values.
Change in mean squared error with threshold height when F = 0.6 kN
Estimated real contact area is shown in Fig.8, where red areas show contact areas predicted by the method mentioned above. In previous studies, the deformation of modeled material surfaces has often been analyzed using numerical and statistical methods to evaluate the real contact area and applied load. Even though the overall state of the contact interface was known, it was not possible to infer which specific areas were actually in contact. In practice, even when the real contact area ratio is the same, the characteristics such as lubrication, contact resistance, and heat transfer are expected to differ between cases where many small contact areas are distributed and cases where only a few large contact areas exist. Therefore, establishing a concrete prediction method that incorporates the actual surface topography of the contact interface is considered essential. In contrast, the method described above makes it possible to identify which parts of the actual contact surface are in contact and to what extent, as well as to distinguish whether the small contact areas are dispersed or whether a few large contact patches dominate. If the height distribution of the contact surface is measured in advance, it should be possible to accurately predict the areas that will actually come into contact and their distribution. Figure 8 shows one example from the five pairs of specimens. For the other specimens as well, the specific distribution of the contact areas has been obtained. To the best of the authors' knowledge, no method has yet been established that can accurately identify the actual contact areas based on the fracture surface condition. Therefore, it is currently difficult to discuss the accuracy of the obtained results, and this issue is left for future work.
Estimated real contact area in pressure test (α [%] represents the real contact area ratio)
Change in contact area ratio a with compressive load F is shown in Fig.9 for all five pairs of specimens. Although some scatter is observed in the results among five pairs, the overall trend shows an increase with increasing compressive load. The variation in the results is considered to arise from the initial height distribution of the rough surface. However, the initial values of arithmetic mean roughness for five rough surfaces were between 2.48 µm and 2.84 µm. Their difference was not very large. Therefore, it is unlikely that the initial roughness is the main cause of the variation in the results. On the other hand, the compressive load F acts on the entire contact surface including the designated measurement area at the center, and therefore is likely to be influenced by the roughness and height distribution outside the measurement area. It is also possible that a slight eccentricity of the compression axis caused a non-uniform distribution of compressive stress over the contact surface. In fact, although no pronounced one-sided contact was observed when examining the entire contact surface, its influence cannot be completely ruled out. Furthermore, material inhomogeneity within the block may also be a contributing factor. A close examination of Fig. 9 shows that, although the real contact area ratio increases almost linearly overall, some results exhibit a slight reduction in the rate of increase. A linear relationship between the real contact area ratio and the compressive load implies that the effective stress required for compression remains constant during the loading test. In the present experiment, the real contact area ratio remains relatively small (below 10%) so each asperity deforms almost independently, which likely leads to this nearly linear behavior. Under higher compressive loads, however, a nonlinear relationship similar to that reported by Pullen is expected to emerge.
Change in real contact area ratio with compressive load in pressure test
Figure 10 shows the change in compressive amount, u, against compressive load, F. In the initial stage under low compressive loads, the compressive amount exhibits a high rate of increase, but as the compressive load continues to rise, the rate of increase in compressive amount gradually decreases. In Fig. 10, a nonlinear relationship is observed between the compressive amount and the compressive load. This indicates that as the compressive amount increases, the load required to produce the same increment of compressive amount also increases. The contact area ratio shown on the vertical axis of Fig. 9 is a quantity proportional to the square of a length, corresponding to the cross-sectional area used for calculating stress. In contrast, the compression displacement shown in Fig. 10 represents a one-dimensional change in length along the loading direction. Considering the deformation of asperities in a simplified manner, a reduction in asperity height is expected to increase the asperity cross-sectional area in proportion to the square root of that height. This difference in dimensionality associated with asperity deformation is reflected in the differing trends observed in Fig. 9 and Fig. 10.
Change in compressive amount with compressive load in pressure test
In this study, pressure tests were conducted using five pairs of small block specimens of pure aluminum, and the real contact areas during loading were estimated based on the measured changes in surface height before and after the testing. The main findings obtained are summarized as follows:
1. The changes in the surface topography of the contact interface caused by the compression of the small block specimens were successfully captured.
2. A method was proposed to estimate the areas that were actually in contact, based on the height distribution of the contact surfaces before loading and the changes in height distribution before and after the pressure test.
3. By using this method, it becomes possible to identify which specific areas of the contact interface were actually in contact, rather than relying solely on global measures of surface condition such as the real contact area ratio.
4. Although a weak nonlinear relationship between the real contact area ratio and the compressive load was observed in some specimens, the overall trend remained nearly linear. This is considered to be because the real contact area ratio in this loading test was at most around 10%, meaning that the microscopic asperities deformed almost independently under compression.
5. The relationship between the compressive amount and the compressive load exhibited a nonlinear trend, in which the rate of increase in compressive amount gradually decreased. The difference between the linear relationship observed for the real contact area ratio versus compressive load and the nonlinear relationship for the compressive amount versus compressive load is considered to arise from whether the deformation of asperities is characterized as a one-dimensional measure or a two-dimensional measure.
F compressive load
h(x, y) surface height at pixel location (x, y)
hth threshold value of surface height
g(h(x, y), hth) height exceeding the threshold
MSEh mean squared error between Dh(x, y) and g(h(x, y), hth)
u compressive amount
α contact area ratio
∆h(x, y) difference of surface height
The authors would like to acknowledge the assistance of Mr. Reiji Nakamura, who was a master's student in the Graduate School of Natural Science and Technology at Okayama University (currently with Sanyo Special Steel Co., Ltd.), and Mr. Haruki Maeda, who is a master's student in the Graduate School of Environmental, Life, Natural Science and Technology, for their support in acquiring the experimental data used in this study.
