Polishing deals with the final surface enhancement process, where the upper layer of the material is modified by means of various techniques like mechanical abrasion, chemical etching, electrolysis, etc. Despite all these techniques, getting a precise ultrafine, defect-free surface without planarity issues is still a huge challenge. The enormous demand for polishing has encouraged the researchers not only to generate a desirable surface finish but also to improve the productivity and efficiency of the polishing process. When mechanical abrasion is involved in a polishing process, loading of the polishing tool is one of the common issues encountered. Soft materials like aluminum and copper get stuck all over the abrasives and make it blunt [2] . The bluntness of the tool consumes more energy and decreases the polishing rate. Hence repeated dressing of the tool is needed, which interrupts the production. In order to address this issue, a polishing technique with the self-dressing provision is required.
Ice Bonded Abrasive polishing (IBAP) is one of the selfdressing polishing techniques which uses frozen slurry as a polishing tool [3] . The IBAP tool is maintained at a temperature near to the melting point of ice. The frictional heat produced during polishing melts the ice matrix and exposes fresh abrasives continuously during the process. The hardness of ice can be controlled with temperature and maintained in such a way that it behaves like a soft polishing pad. The thin layer of water present at the interface due to thawing reduces the coefficient of friction [21] . The higher compressive strength of ice and hexagonal crystal structure creates a suitable environment for polishing.
IBAP encounters both fixed and free abrasives simultaneously during the process. Basically, fixed abrasives slide on the surface whereas free abrasives tend to roll. The involvement of rolling makes the free abrasives present in the
Polishing deals with the final surface enhancement process, where the upper layer of the material is modified by means of various techniques like mechanical abrasion, chemical etching, electrolysis, etc. Despite all these techniques, getting a precise ultrafine, defect-free surface without planarity issues is still a huge challenge. The enormous demand for polishing has encouraged the researchers not only to generate a desirable surface finish but also to improve the productivity and efficiency of the polishing process. When mechanical abrasion is involved in a polishing process, loading of the polishing tool is one of the common issues encountered. Soft materials like aluminum and copper get stuck all over the abrasives and make it blunt [2] . The bluntness of the tool consumes more energy and decreases the polishing rate. Hence repeated dressing of the tool is needed, which interrupts the production. In order to address this issue, a polishing technique with the self-dressing provision is required.
Ice Bonded Abrasive polishing (IBAP) is one of the selfdressing polishing techniques which uses frozen slurry as a polishing tool [3] . The IBAP tool is maintained at a temperature near to the melting point of ice. The frictional heat produced during polishing melts the ice matrix and exposes fresh abrasives continuously during the process. The hardness of ice can be controlled with temperature and maintained in such a way that it behaves like a soft polishing pad. The thin layer of water present at the interface due to thawing reduces the coefficient of friction [21] . The higher compressive strength of ice and hexagonal crystal structure creates a suitable environment for polishing.
IBAP encounters both fixed and free abrasives simultaneously during the process. Basically, fixed abrasives slide on the surface whereas free abrasives tend to roll. The involvement of rolling makes the free abrasives present in the
Polishing deals with the final surface enhancement process, where the upper layer of the material is modified by means of various techniques like mechanical abrasion, chemical etching, electrolysis, etc. Despite all these techniques, getting a precise ultrafine, defect-free surface without planarity issues is still a huge challenge. The enormous demand for polishing has encouraged the researchers not only to generate a desirable surface finish but also to improve the productivity and efficiency of the polishing process. When mechanical abrasion is involved in a polishing process, loading of the polishing tool is one of the common issues encountered. Soft materials like aluminum and copper get stuck all over the abrasives and make it blunt [2] . The bluntness of the tool consumes more energy and decreases the polishing rate. Hence repeated dressing of the tool is needed, which interrupts the production. In order to address this issue, a polishing technique with the self-dressing provision is required.
Ice Bonded Abrasive polishing (IBAP) is one of the selfdressing polishing techniques which uses frozen slurry as a polishing tool [3] . The IBAP tool is maintained at a temperature near to the melting point of ice. The frictional heat produced during polishing melts the ice matrix and exposes fresh abrasives continuously during the process. The hardness of ice can be controlled with temperature and maintained in such a way that it behaves like a soft polishing pad. The thin layer of water present at the interface due to thawing reduces the coefficient of friction [21] . The higher compressive strength of ice and hexagonal crystal structure creates a suitable environment for polishing.
IBAP encounters both fixed and free abrasives simultaneously during the process. Basically, fixed abrasives slide on the surface whereas free abrasives tend to roll. The involvement of rolling makes the free abrasives present in the 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to slurry to produce a smoother surface than the fixed abrasives [10] . When the initial surface has poor surface finish, then free abrasive polishing is preferably followed by the bonded one. But free abrasives are difficult to manage, unlike bonded abrasive processes, as the abrasives are thrown out due to the relative motion and makes the material removal nonuniform. IBAP retains the advantages of both states of abrasives and can be used to reduce the surface roughness to a greater extent. IBAP tool is prepared in a layer by layer manner, hence it is also possible to vary the size of abrasive size across with the tool thickness to make a multi-graded tool. An improved finish has been observed, when coarser abrasives are placed in the upper layer and finer abrasives in the further layers [7] . [1] . But polymers are prone to plasticity at room temperature. At smaller loads, a high rate of deformation is attained, which makes them difficult to polish. Meanwhile, at lower temperatures, polymers accomplish better stiffness which creates a favorable condition for polishing. Similarly, the finely polished surface of Titanium alloy has broad applications in the field of bio-implants. Due to the poor conductivity of the material, heat gets accumulated at the tool-workpiece interface easily, which affects the material properties of both tool and workpiece and makes it difficult to deal with material removal. Many attempts have been made to create a cryogenic environment while dealing with titanium and its alloy [15] . Therefore, application of IBAP will be suitable in these cases to a great extent.
The cryogenic polishing was introduced for brittle materials like glass, silicon wafers, crystals, optical materials [21] [22] [23] and then extended to observe its effects on metal surfaces [3] [4] [5] [6] . The surface finish (Ra) on silicon wafer improved to 1.29nm from 14.87nm in 70 minutes [22] whereas for stainless steel surface finish has been obtained up to 8nm with an improvement of 20-28% [5] . As mentioned above, the tool temperature during the polishing is a crucial parameter as it decides the tool life of the IBAP process. Previously, liquid nitrogen and dry ice have been used, which makes the control over polishing temperature difficult and shortens the tool life too. Rambabu and babu (2017) altered the traditional methods of temperature control by installing a refrigeration unit, which gave proper control over the tool temperature [6] . Although the previous studies have covered the feasibility of the process to produce a finished surface on various materials and development of experimental setup, mechanics behind surface generation is not explored yet. The study of the mechanism for surface generation in the IBAP process will direct to predict the tool behavior, which will be useful to design the tool. The present paper has focused on the experimental investigation of the mechanism of the process and, also an attempt has been made to establish an analytical model to predict the material removal rate for a proper understanding of the process.
Many attempts have been made by the researcher to study the mechanism behind material removal in polishing processes. Aghan and Samuels (1970) proposed three techniques for mirror finish surface generation viz. flow mechanism, mechanical mechanism and molecular mechanism [11] . According to the flow mechanism, the material is melted due to friction at the interface and fills the grooves. But the theory was found infeasible afterward. The second theory considered the abrasives as a single-point cutting tool and material is removed due to shearing. Whereas the third concept explained the molecular level of material removal similar to the mechanical abrasion but defer only in degree due to smaller load and chip formation. For validation, the SEM images of the different scratches formed during mechanical polishing with a soft pad over a ductile material were presented. Komanduri et.al (1998) interpreted the mechanism of the ultrafine finishing process in terms of tool geometry [12] . They considered the abrasive used to have higher negative rake angle and larger edge radii compare to the depth of cut, which is responsible for the generation of hydrostatic pressure at the interface and leads to plastic deformation. Chang et. al (2000) predicted material removal considering two aspects [13] . One is the gap between the chemical mechanical polishing pad and the work surface decides the involvement of two-body and three-body abrasion and the second aspect deals with the critical factor as a function of the material property decides the type of material failure i.e. ductile or brittle. Che et. al (2003) interpreted that the material is removed as a result of the interaction of scratches [14] . With the primary scratch, the material will be piled up to the sides of the trenches and the secondary scratch is responsible for material detachment and chip formation. For the experimental investigation, the performed chemical mechanical polishing over 99% annealed copper surface and showed the evidence in SEM images. Kasai and Bhushan (2008) described the material removal mechanism from a single asperity level and extended to multiple asperities considering statistical distributions [15] . The depth of penetration was considered as a deciding factor for the transition of elastic to fully plastic deformation of the material and hence the failure. IBAP involves the combined effect of abrasives and water at the interface. For a proper understanding of the mechanism, many researchers have attempted to interpret the mechanism as mechanistic models [14, 15, 18] . But the exact mechanism behind any polishing process is still unclear. The models described in works of literature are focused on the material removal in polishing considering the abrasives orientation, but less attention was given to the combined effect of fluid and abrasives, which has been attempted in this study.
The experimental setup of IBAP consists of 3 basic units namely, refrigeration unit, IBAP tool, and workpiece holding as shown in Fig.1 . The refrigeration unit comprises of vapor compression refrigeration cycle (VCR cycle), where R404a is used as a refrigerant and isopropyl alcohol is used as a coolant because of its much lower freezing point compared to water. The total cooling unit is capable to maintain coolant temperatures up to -40 ᵒC. The second unit is the IBAP tool, which is one of the crucial parts to deal with. As mentioned above, the frozen slurry is used as a polishing tool. The first step of tool preparation is the selection of abrasive. The final surface finish depends on the size, hardness, and concentration of abrasives used. Hence according to the requirement of the surface finish, the required amount of abrasives is added to distilled water to acquire required concentration. The prepared slurry is stirred continuously by a magnetic stirrer to avoid settlement of abrasives. Layer by layer freezing of slurry preferred over direct freezing to avoid the non-uniform distribution of abrasives across the thickness of the tool [4] . Hence the small volume of slurry is poured in a mold to freeze and the process is repeated until the total thickness of the tool is obtained. The tool mold is rotated about its axis with the help of a DC motor.
The third unit concerned with the work holding arrangement. The workpiece is placed at an offset from the tool center and rotated about its own axis through a geared DC motor. Polishing loads are applied over the workpiece with the help of dead weights. To study the mechanism behind IBAP surface generation, Titanium alloy (Ti-6Al-4V) was chosen as the workpiece. The material was cut from a long rod through wire-cut EDM to maintain the planarization of the surface. The normal metallography procedure was followed. The wire cut specimen was rub over emery sheets (#400, #600, #800, #1000 respectively) The surface finish obtained was measured in a 3D profilometer (Wyko NT1100) and both 3D plot and 2D analysis of the surface topography were shown in Fig.2(a, b) . The surface finish (Ra) was observed under 3D surface profilometer (Wyko NT1100 ) and recorded as 264.29 nm.
SiC abrasives of average size 8µm were added to distilled water to prepare a slurry of concentration of 15% by weight. The SEM micrograph of abrasives are shown in Fig. 3(a) , which shows the random size distribution and shape of the abrasives. In order to collect more specifications of abrasives, the abrasives were passed through particle size analyzer (PSA) to obtain the distribution. The PSA (Microtrac FLEX10.6.2) is used for observations, where the LASER diffraction method is employed to measure the particle size. The scattered light from abrasives at different angles is used to interpret the particle size as the diameter of spheres having an equivalent volume of the abrasives. The Fig. 3(b) shows the size distribution of abrasives from PSA and which shows the distribution almost follow the normal distribution. As mentioned above, a small amount of slurry was poured into the mold of 200 mm diameter and allowed to freeze and the process was repeated to obtain a tool thickness of 12mm in order to sustain for the longer polishing duration. While tool preparation the coolant temperature was reduced to -35°C for fast freezing. After the tool is being prepared, it is left for a few minutes to attain the polishing temperature i.e. -4°C. The polishing was carried out for 2 hours and the final surface generated was cleaned with acetone in an ultrasonic cleaner and observed under a 3D surface profiler and presented in Fig.2 (c,   d) . The surface finish was reduced to 73.80nm after 2 hours of polishing. For further analysis, the polished surface was observed under the scanning electron microscope (SEM) at a magnification of 100000X and is shown in Fig.4 . The number of scratches and grooves are observed on the polished surface along with redeposited and detached material. The scratch width was found in the range of 100nm-200nm. Materials found to be piled up at the side of the scratches due to plowing action. 
IBAP is similar to the chemical mechanical polishing (CMP) process. In the CMP process, both mechanical abrasion and chemical processes are involved whereas IBAP deals with only mechanical abrasion. Basically, abrasives are allowed to slide, roll and indent quasi-statically on the upper layer of the work surface in order to modify the surface finish.
The irregular shape and random distribution of the size of the abrasives are responsible for the complexity behind model development [8] . Hence statistical approaches are adopted to establish the analytical model. In the current model, material removal due to single abrasive is determined and then extended for multiple abrasives considering Gaussian distribution of abrasive size. The deformation produced over the upper surface of work material is categorized as elastic, elastoplastic and fully plastic depending on the depth of penetration. The applied downforce, as well as meniscus force due to water column present between abrasive and work interface, are taken into account while predicting the deformation. Finally, the material removal rate is predicted for different polishing conditions.
It is quite difficult to interpret the exact geometry of an abrasive. Fig.3 (a) shows the SEM image of the irregularly shaped abrasives. But for ease, the shape is assumed as spherical in the current study. Fig.3 (b) shows that the size at D10 is 4.28µm. At D50, the average mean diameter is obtained as 8.36µm and at D95, the particle diameter is 16.35µm. The distribution pattern, shown in Fig.3 (b) is close to Gaussian. The standard deviation of the abrasive particle was mentioned as 3.95µm and the mean value is 8.94µm. Considering the total span of 6σ, which covers 99.97% of the area under the bell curve, the maximum diameter of the abrasive was found 20.79µm and the minimum diameter is 2.91µm.
As mentioned above IBAP tool is prepared by freezing slurry in a layer by layer manner. By considering the mold dimension, 50 ml of slurry is poured for freezing to form a single layer. For a particular concentration, the mass of abrasive to be added in distilled water to make slurry is determined by the following expressions [3] . Where D is the average diameter of the abrasives. If N l is the line density of abrasive, then volume density of abrasives
The surface density is
hence, the number of abrasives per area is given by [8] .
If A is the apparent area of the workpiece. Number of abrasives per unit area under the workpiece can be determined as
The involvement of both fixed and free abrasives in the IBAP tool mainly contributes to three types of microscopic interactions during polishing. viz (i) ice and workpiece, (ii) fixed abrasives and workpiece and (iii) slurry and workpiece. The model has considered the work surface as flat and tool surface as rough. The presence of abrasives makes the surface rougher than the work surface. Therefore, Greenwood and Williamson's model has been considered to describe interaction [9] . When ice encounters with the work surface, material removal and surface improvement will be negligible because the hardness of ice is much lower than the metallic surface. The second and third type of interaction plays a major role. Abrasives of different diameters are present in the IBAP tool. But only those abrasives having a dimension equal to or greater than the gap between the tool and workpiece will come in contact and the load applied during polishing will be carried by those abrasives as shown in Fig.5(d) . Let's consider a single abrasive having diameter D and the gap between two surfaces is d. Based on the nominal size of the abrasives, three conditions arise viz non-contacting, just touching and penetrating abrasive. The force exerted on each abrasive will be different in each case, which has been interpreted in the following subsections.
In this case, the gap between the abrasive and work surface will be filled with the water column, which will exert meniscus force due to surface tension as shown in Fig.6 (a) . The negative Laplace pressure produce can be represented as [17] .
where ∆p is the Laplace pressure, γ is the surface tension of water and is the meniscus radius. If V is the liquid molar volume, R g is the gas constant, RH is the relative humidity, T is the absolute temperature then the meniscus radius is expressed as m g γV r = R Tln(RH)
The projected meniscus area
where h c is the thickness of the water column and function of the meniscus radius and contact angle. (d -D) represents the separation distance between abrasive and surface. The force exerted due to the water meniscus is
where θ is the contact angle, for water and metallic surfaces, θ ≈ 10. The surface tension of water can be taken as 72.8 mN/m.
This case is also similar to the previous case. As the abrasive is only touching the work surface and will rub against the work surface. The projected area formed around the abrasive due to the meniscus is m c A =πDh (4) The separation distance between abrasive and work surface will be zero. Hence the force exerted due to the meniscus can be given as m m F =ΔpA =2πDγcosθ (5) Fig. 6 . Schematic of (a) non-contacting abrasive, (b) just touching (c) penetrating abrasive
When the diameter of the abrasive is greater than the gap then it will indent into the work surface to counter the applied polishing load. The depth of indentation depends on the force exerted on each abrasive due to the applied downforce and meniscus force due to the water column around the abrasive. Based on the indentation depth, the deformation can be categorized as elastic, elastoplastic and fully plastic. The fully plastic deformation leads to detachment of material. The meniscus force and projected area will be A m =πD(δ + h c -δ)= πDh c Archad's theory explains two cases for contact force between two contacting surfaces [19] . The first case describes that, when the applied load gradually increases, the number of contact increases keeping the real area of contact of each abrasive constant. In such cases, the area of contact will vary linearly with force. The second case describes that the number of contacts remains constant and the contact area of each abrasive increases nonlinearly with the load. The current model adopted the nonlinear relationship between the contact area and force. If a is the contact radius as shown in Fig. 6 , then the real area of contact of abrasive can be represented as
According to the Hertz theory of elasticity, the force requires to produce elastic deformation is
where * is the combined elastic modulus
is the Poisson's ratio, E is Young's modulus, R is asperity radius. The elastic deformation occurs until the pressure exerted is equivalent to 0.4 times hardness of the surface. Therefore, the critical indentation depth to differentiate the elastic region can be obtained by equating the total pressure with 0.4H. e m re m The real area of contact and force required for fully plastic deformation can be presented as 2 rp A =πa =πDδ (10) 
When the pressure exerted is equivalent to the hardness of the surface the plastic deformation will initiate.
The indentation depth between δ e and δ p will lead to elastoplastic deformation.
The material removal rate depends on three prime factors viz the probability that material will be removed, the crosssectional area of the indentation depth and relative velocity between the tool and workpiece [18] . The volume of material removed by single abrasive can be expressed as the product of the cross-sectional area and sliding velocity. The crosssectional area of a single abrasive is very small. Hence crosssection of the trench can be assumed as a triangle with a base length equivalent to contact diameter and height equal to indentation depth as shown in Fig.7(b) . Therefore, the area will be
Volume removed by single abrasive
where a is the radius of contact, δ is indentation depth, V is the sliding velocity and t is the polishing duration. The total volume removed by the process can be obtained by multiplying the number of abrasives under the workpiece and probability that the indentation produced by them will result in plastic deformation. The probability of plastic deformation can be defined as
d is the separation distance between tool and work surface. But it is impractical to involve infinite, hence generally the limit is taken up to 3σ. The volume removed can be explained in a normalized way by dividing the total volume of removal by apparent area of the workpiece. Hence the expression explained in Eq. (15) will give the average depth removed per second.
The above expression was evaluated numerically using MATLAB to predict the material removal rate and influence of different parameters on it. The separation distance (d) between tool and work surface is assumed according to the minimum diameter of the abrasive required to produce plastic deformation. Komanduri et.al (2003) reported that the critical depth of cut required for the cut is 0.05 times of radius of abrasive. The average diameter of the abrasive is obtained as 8.94µm from PSA, which was used to determine the separation distance.
Initially, the fixed abrasives of the ice matrix encounter the work surface. Microscopically, the workpiece contains a number of protrusions. Initially, the larger peaks of the work surface will come in contact with the abrasives. The abrasives are harder than the work surface. Therefore, when the load is applied the peaks will deform to some extent depending on the polishing load. Resistance is created against the applied load due to relative velocity. Stress is produced at the interface of abrasives and the protrusions, which is in a more concentrated form than that for the bulk material as the real area of contact is much smaller than the apparent area. Gradually, the stress exceeds the flow stress of the work material, then the material starts to deform. The deformed material tries to fill the valley and piles up, which seems like a scratch as shown in Fig.4 . The material gets detached in the form of chips due to the interaction of scratches as a result of repetitive sliding. The size of abrasive decides the real area of contact at the interface, which determines the amount of force will transfer. The coarser abrasives held in ice, having dimension more than the gap between tool and workpiece will produce scratches over the surface, which resembles two-body abrasion. Whereas the abrasives present in the slurry will form swallow grooves because of their free movements and resemble three-body abrasion. The ice matrix is in its molten form. Hence it behaves like a flexible soft pad in the chemical mechanical process, which reduces the sudden shock to the work surface and avoids the formation of deep scratches. Due to the repetition of the above process, abrasive will produce a surface with grooves of constant depth and further polishing will not affect the surface finish any more, which can be considered as the endpoint of the polishing. The developed model was used to study the influence of sliding velocity and applied load on MRR for two different material. The material properties used for the model have been tabulated in Table. 1. The normalised material removal rates were predicted for two different materials. Copper is a soft material with higher conductivity and density, whereas Ti alloy has poor conductivity and lower density. Fig. 8 (a) shows the predicted normalised MRR for copper and Titanium alloy in IBAP at 9 m/min of sliding velocity and different polishing load. The predicted MRR implies the average reduction in depth of worksurface. For both materials, MRR increases with applied polishing load. Fig.8 (b) shows the predicted normalised MRR values of Ti alloy for different loads at different sliding velocity. By increasing sliding velocity and applied load the MRR is increasing, obeying Preston's law, which states that the rate of depth produced is directly related to sliding velocity and applied load. From the figure, it is visible that sliding velocity has more impact on MRR compare to load In order to validate the above model, experiments were conducted to find out the material removal rate. Fig. 8 (c) shows a comparison between experimental and predicted values. The predicted value was found to give lower value than the experimental, which may be due to the following reasons. The abrasives were assumed as spherical whereas the shape is irregular hence the depth of indentation produced will be more than the predicted one. The concentration of the abrasive changes continuously due to the repeated evolution of new abrasive from the ice matrix.
The current paper explained the mechanism behind surface generation in IBAP. The scratch patterns on the polished surface shown in SEM images describe the involvement of two-body and three-body abrasion during the process. An attempt was made to develop an analytical model for a proper understanding of the mechanism. The information regarding abrasive shape, size and distribution were obtained by processing the abrasive in particle size analyser. The number of abrasives was obtained from the concentration of the slurry by weight. The deformation produced on the surface was considered due to the force of individual abrasive and meniscus force produced due to the water surrounded by the abrasive. The deformation produced was categorized as elastic, elastoplastic and fully plastic based on indentation depth produced. The developed model was simulated in MATLAB, to study the effect abrasive size and distribution, sliding velocity and applied load on MRR. Experiments were conducted to validate the model. The predicted values were compared with the experimental values.