Deformation-Induced Roughening by Contact Compression in the Presence of Oils with Different Viscosity: Experiment and Numerical Simulation

During deformation, initially smooth metal surfaces are subject to strain induced roughening. Strain induced steel surface roughness is common in many engineering applications. This phenomenon is an undesirable feature that worsens the surface reflectance and the mechanical properties responsible for the location of plastic deformation under load. This change in surface roughness can lead to production problems in particular. It can have a detrimental effect on the surface finish of the sheet, change the coefficient of friction, reduce wear and corrosion resistance. Finally, it can lead to undesirable local phenomena which, in turn, may cause damage or the local delamination process of sandwich or coating structures. This is especially the case in the industrial production of food and cans, canisters or sheet metal metallurgy.

For this reason, the deformation-induced roughening process has become the subject of many experimental, theoretical and numerical modeling works. Early research has shown that this process depends on the materials, grain size deformation and surface texture.

Osakada and Oyane [1] were among the first who presented the quantitative and theoretical study of the roughening of free surface during deformation. They showed that surface roughness increases with strain and is affected by grain size and the lattice structure of the metal. Dai and Chiang [2] investigated the plastic deformation-induced surface roughening mechanism of aluminum sheets The average grain rotation and grain size are found to be the dominant contributor to the surface vertical characteristics such as the root-mean-square roughness. The surface horizontal characteristic such as the correlation length is found to be mainly determined by the average grain size.

Some authors have found deviations from such linearity, which is relevant for larger deformations. Wilson, et al. [3] examining the heterogeneous deformation of copper sheets subjected to biaxial stress, noticed strong surface roughening. The relationship between the Ra parameter describing the roughness profile and the strain was up linear to a certain strain, and above the critical value became strongly non-linear and grew faster. The dependence of the described curve on the grain size in the copper sheet was also clear: the smaller the grain, the earlier the deviation from linearity occurred.

Generally, the relationship between the parameters describing the average height of asperities (such as \(R_{{\text{a}}}\), \(R_{{\text{q}}}\)) can be presented as follows:where ε is the deformation value of the sample, d is the average grain size and C is a constant depending on the material being tested and the determined parameter.

Mahmudi and Mehdizadeh [4] investigating brass sheets under uni- and equi-biaxial stretching showed that, although they obtained linear dependence of roughness parameters on strain and grain size, the slope and location of these curves also depends on the method of sheet metal treatment: fast or slow heating. The increase in roughness is smaller for the fast heating process and the difference increases as the deformation increases.

Wouters et al. [5] examined the relationship between the roughness forming on the surface of samples with Al–8.5% Mg uniaxially tensioned, and the grain size that varied from 30 to 90 μm. Their test results revealed a linear dependence of roughness on the strain value and grain size.

Romanova et al. [6] proposed a three-dimensional model of the material with a hardened layer of varying thickness and strength compared to the initial material. A numerical analysis was carried out by the finite difference methods. It was found that internal stresses appearing at the layer boundary and bulk material are responsible for surface roughness which gets larger as the hardened layer gets thinner. It was observed that the local increase in irregularities is due to the movement of connected grains.

Wang and Abe [7] investigated pure aluminum with very large grains. The samples with rain size changes up to 1 mm, corresponding to ½, ¼, and 1/3 of sample thickness, were tensioned. The R_a relationship also increases linearly for all the samples with an increase of deformation applied. In this work an expanded version of Eq. (1) has been proposed:

It is thought that when n = 1, the surface roughness caused by non-uniform deformation is completely dependent on grain size. At the same time, if n = 0, the value of roughness is caused by factors independent of grain size. The value of n can be determined from the relationship between the rate of change of surface roughness \(R_{{\text{a}}} /\varepsilon\) and the average grain size d in the double logarithmic scale. The slope of a straight line obtained from the fitting by the least squares method allows us to determine the value of n in Eq. (2). For the test samples in the calculated value of n = 0.88, which means that only a small part of the roughness is caused by factors independent of particle size, such as, for example, slip bands.

Song et al. [8] conducted a plastic deformation measurement using a confocal laser scanning microscope of aluminum sheets deformed uniaxially. They showed that the roughness of sheets after deformation is primarily affected by grain rotation, which is greater in the surface layer than inside the material, as well as by locally heterogeneous grain deformation. Thanks to the measuring technique used, it was possible to study the relationship between the deformation of individual grains and the roughness curve resulting from this deformation.

Zhou and Su [9] investigated the surface topography of aluminum and titanium alloys after plastic deformation in the longitudinal and transverse directions using white-light interferometry and a fractal method of analysis. Initially, the homogeneous geometric surface structure changed in different ways depending on the measurement direction in relation to the deformation direction, creating a new, anisotropic structure. This structure was different for aluminum and titanium. Fractal analysis showed that length correlation is in the same order as the size of the grains, but it varies depending on the direction of measurement and the tested material. The standard 3D roughness parameter (\(S_{q}\)) measured for the tested surface grew linearly with the given deformation.

Shia et al. [10] presented a numerical simulation of surface roughness during the tube blow forming process. Simulation data were available from the measurement of electronic backscatter diffraction (EBSD). The roughness of formed aluminum bottle is linked to the difference between the orientation of the neighboring grains, and to the initial texture. The roughness of the formed aluminum bottle is associated with the difference between the orientation of adjacent grains and also with the initial texture.

Cai et al. [11] present an interesting approach (the trapezoidal tensile aluminum alloy sample) to obtaining a continuous strain distribution on the sample after one deformation. Using a specially designed stage, it was possible to measure changes in surface roughness using an electron scanning microscope (SEM) in situ for increasing tensile load. The surface microstructure was also determined using the EBSD. The results presented differed from those generally accepted: the dependence of Ra on deformation increased non-linearly to 7% level, then slightly decreased. From the SEM results it was concluded that the appearance of roughness was caused by a heterogeneous deformation between and within the grains. The increased number of slip bands launched has resulted in uniform deformation and a slight reduction in roughness above the critical value.

Romanova and her team have carried out a series of works on titanium research in recent years (2016–2020) [12‐15]. This articles addresses the problem of multiscale surface roughening in titanium subjected to uniaxial tension. Based on the experimental data obtained, 3D polycrystalline models with explicit consideration of grain structure were generated and implemented in finite element calculations. The experimental and numerical results obtained have shown that a series of multiscale surface undulations are formed on the free surface of the specimen subjected to tension. Larger displacements are associated with relative grain motion. The main conclusion drawn from the experimental and numerical results is that it is the mesoscale that will furnish a clue to prediction of plastic strain localization and fracture of materials far in advance of the macroscale manifestation of these processes [12]. The influence of a texture on the mesoscale deformation-induced surface roughening in titanium polycrystals was studied using direct microstructure-based simulations [13]. The grain constitutive behavior was described in terms of crystal plasticity, with the grain orientations being assigned randomly or representing a basal texture. The mesoscale roughness parameter was shown to grow non-linearly with the plastic strain of the evaluated mesoscale regions. The basal texture was shown to significantly affect the plastic strain localization and roughness patterns. In [14, 15] the three-dimensional numerical analysis was performed of the deformation-induced roughening in polycrystalline specimens with and without surface-hardened layers. Three-dimensional microstructure-based constitutive models are developed, using crystal plasticity, and employed in finite element calculations of uniaxial tension. Grain structure is shown to be responsible for free surface roughening under uniaxial loading. The surface-hardened layer moves the grain structure away from the free surface, smoothing out the microscale folds formed due to displacements of individual grains, while the mesoscale surface undulations remain clearly visible. This study allowed distinguishing between the grain size and texture effects.

Kucharski and Starzynski [16] in their earlier paper present an experimental study of the opposite problem: initially rough surfaces have been compressed by smooth flat counter sample in the presence of lubricant and in dry state. The results of widely analyzed 3D changes in roughness parameters as a function of sample deformation are presented. The trend to the asymptotic state was noted for the lubrication case and its absence for the dry sample. The observed stabilized state was explained by the hydrostatic reaction of the lubricant.

The opposite problem will be presented and analyzed herein—the creation and evolution of a new structure of smooth surface during contact compression. Available literature provides the results of research on surface roughening due to plastic deformation of materials that relate primarily to tensile samples with a free surface. In this work we investigate the roughening of a surface subjected to contact compression in the presence of oil film. The relationships between changes in the roughness are caused not only by the deformation of the sample, but also by the viscosity of oil in the contact area. It has been shown that normal contact loading with the participation of oil initially leads to an increase in surface roughness, then the surface gets smoother.

Available literature provides the results of research on surface roughening due to plastic deformation of materials that relate primarily to tensile samples with a free surface. What has not been analyzed so far the FSI (fluid–structure interaction) analysis considered an oil layer on the steel surface of the sample. The analysis requires the preparation of two separate models: for a solid and a liquid and marking the friction contact surfaces between which the interaction will take place. FSI (fluid–structure interaction) analysis allowed for the oil layer on the steel surface of the sample to be taken into account. Finite element calculations were performed taking into account physical non-linearities (plasticity) and geometric non-linearities (large strains). The changes in the structure of the smooth surface resulting from compression in the presence of oil are caused by the rotation and deformation of surface grains. The roughness of this structure is dependent on the viscosity of oil: the more viscous the liquid is, the rougher texture is formed. Moreover, the developed experiment allowed to show the influence of the oil film viscosity on the formation of roughness and to find the critical point of deformation, above which the surface structure begins to flatten.

For the experiment, two steels have been chosen: H18N9 austenitic stainless steel and S235 steel with characteristic strength shown in Fig. 1. The yield strengths of these steels are very similar (approx. 300 MPa), while the further characteristic varies considerably. Austenitic steel monotonically strengthens, while S235 steel, after an area of instability in the early plasticity, strengthens slightly and above the strain 0.15 begins to weaken and crack before the deformation of 0.30.

Because, as shown in the introduction, deformation-induced roughness depends, among others, on the grain size, the samples were chosen so that the size of grains in the both steels were as close as possible (Fig. 2). The average grains size are 30–40 μm.

Initially, flat discs (approx. 50 mm in diameter) were cut out from the tested steels, then subjected to grinding and fine polishing. As a result of such treatment, almost a mirror surface was obtained, having a roughness S_a of the order of several nanometers. The circle samples (8 mm diameter) were then cut out from the discs so that highly reproducible surfaces of individual samples have been obtained. To study the effect of oil viscosity on the condition of surface subjected to contact compression, we selected two oils, for which the dependence of viscosity on temperature was well examined by the oil company (see Table 1).

The experiment was carried out on circular samples with a thickness of approx. 3 mm and a diameter of 8 mm, which were compressed in the modernized test apparatus for normal contact. Kucharski and Starzynski [17] described the experimental set in details. Operation of the device is based on a hydraulic press that is capable of producing large normal forces. The samples were placed between very smooth, flat plates of a very hard material (WC—tungsten carbide). Oil was placed between the surface of the sample and the WC plate, so the sample was loaded through the thin oil film formed on the surface of the sample and the WC plate (Fig. 3).

The compressive tests have been executed in the presence of two oils having very different viscosity—AN 22 and SP 680 (see Table 1). The load was applied in two ways: (i) direct load to a predetermined force—the following samples showed relative deformation 0.033, 0.087, 0.197, 0.333. In comparative diagrams there is no additional load description in the legend, (ii) the loading up to predetermined forces was performed on one sample, in seven steps, and the following deformations were obtained: 0.0330 → 0.087 → 0.157 → 0.197 → 0.267 → 0.333 → 0.37. After successive deformation, the sample was removed from the device, washed and measured with a profilometer, then again the next step of loading was applied. In the legend of the comparative diagrams this method of loading is described as "steps".

It can be stated in general that as a result of mutual contact loading of the smooth polished surfaces with different oil films between them a new geometric structure is created on the surface. This structure is completely different from the structure before loading and varies for highly viscous oil (SP 680) and an oil of low viscosity (AN 22). To characterize this structure, two parameters have been compared: the amplitude S_a (arithmetic mean deviation of the surface from the mean plane) and the horizontal P_sm (average distance of the asperities in the profile, which may be called the profile wavelength. Parameter P_sm was referred to the profiles, because there is no equivalent parameter for the surface. As the parameter varied a lot from profile to profile, the value shown in the diagrams is the average of all (100) of the measured profiles of the examined surface. A comparison of the peak height distributions of new surface structures is also made.

The compression of smooth polished samples in the presence of oil forms a new structure on the surface of samples. The roughness of this structure is dependent on the viscosity of oil: the more viscous the liquid is, the rougher texture is formed. The structure appears beyond the yield point, and is homogeneous and isotropic. Three phases of surface deformation can be clearly seen to change its structure: 1—below the yield point—no change in surface roughness, 2—the new structure of surface resulting from rotation and deformation of surface grains is generated up to a critical point, 3—beyond certain critical point the roughness is reduced, because the surface is crushed by a counter sample.

There is a critical point below which compression causes further increase in roughness and above which the asperities get crushed. Critical points are between 20 and 30% of the total deformation of the sample and depend on the loading history and sample material. This point is different for various materials and is mainly associated with the number of generated asperities. The tests involving step increments of loads allow us to estimate that the average roughness S_a above which asperities will be crushed, and below which they will still be formed. For austenitic steels and oil SP680 it is 0.24 μm, while for S235 steel the estimated value is 0.4 μm.

With large deformations (above 0.3), the difference between roughness for different oils disappears, especially for horizontal parameter P_sm. It is related to the dominance of flattening of previously built asperities by a counter sample. Further deformation causes the structure to stabilize at 30 μm for H18N9 austenitic steel and 45 μm for S235 carbon steel.

The problem of formulating roughening by contact compression in the presence of oil has been clarified using FE numerical calculations. The changes in the structure of the smooth surface are caused, as in the case of tension, by the rotation and deformation of surface grains.

In the research carried out and presented in this work, changes in the structure of the smooth surface resulting from compression in the presence of oil are caused, as in the case of tension, by the rotation and deformation of surface grains. This has been shown in the numerical model. In addition, during compression with oil, the viscosity of the fluid affects the surface structure formed.