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Chapter 2

Literature Review

2.1 Material strengthening

2.2 Subsurface deformation

2.3 Tool geometry

2.4 Microcrack formation in the shear zone

2.5 Gross fracture phenomenon ahead of tool-tip

2.6 Workpiece microstructure effect

The process of micro-cutting involves uncut chip thicknesses that are comparable to the tool edge radius (r) and the grain size in work material. As shown in Fig. 2.26, a combination of grain size and tool edge radius affects the micro-cutting mechanics and has a significant effect on the size effect [48]. The grain size of work material typically ranges from 100 nm to 100 μm [47]. According to Hall-Petch [78-79] relation, the strength of the material is inversely proportional to the square root of the grain size and given by Eq. 2.16:

Since a large number of grains are encountered during macro-scale cutting processes, an averaged effect from the workpiece microstructure is experienced, and the material can usually be assumed to behave isotropically. Due to this reason, analysis of conventional metal cutting typically ignores the effect of microstructures. But, the process of micro-cutting involves uncut chip thicknesses that are in the micrometer or sub-micrometer regime.

In past, researchers confirmed that workpiece microstructure affects various responses during micro-cutting using analytical, experimental and numerical studies. The following aspects of microstructure mainly composition, size, orientation and density, influence micro-cutting responses:

· Grain

· Grain boundary

As cutting takes place at a grain level, the workpiece material cannot be assumed as homogeneous and isotropic during micro-cutting. Therefore, to consider workpiece microstructure effects in micro-cutting, different assumptions are required which include behavior of grain and grain boundaries. Many researchers have studied the effect of crystallographic orientations on micro-cutting characteristics of workpiece materials [80-82]. Ueda et al. [80] investigated the effect of crystallographic orientations on cutting performance in diamond cutting of b-brass. They observed that the shear angle variation occurs from 15° to 60° with changes in crystallographic orientations. The cutting forces and surface roughness values were also observed to depend on material anisotropy. Moriwaki et al. [81] observed crystallographic orientation effects on the shear angle and the cutting force during micro-cutting experiments inside a SEM on a single crystal copper. They performed cutting experiments in various cutting directions at 120 mm/min cutting speed and at 0.1 to 5 mm uncut chip thickness.

Lawson et al. [83] performed orthogonal micro-cutting experiments on single crystal aluminium using a diamond tool to study the effect of crystallographic anisotropy on cutting force, specific cutting energy, shear angles, chip morphology, etc. They examined six crystallographic orientations at uncut chip thicknesses ranging from 5-20 mm and cutting speeds ranging from 5-15 mm/s. Fig. 2.27 shows the effect of crystallographic orientation on specific cutting energy. The highest and the lowest specific energies were obtained when cutting the (3 2 0) and (6 7 0) facets, respectively.

Plastic deformation in metals is a result of the motion of line defects called dislocations on particular planes, called slip planes, in particular directions, called slip directions. The motion of dislocations does not result in the volume change of the material, consequently, plastic deformation is an iso-volume process. In general, the applied plastic strains are accommodated by the material through combination of slipping action on multiple slip systems. In particular, any arbitrary strain can be achieved by a combination of slip systems. Depending on the orientation of the grains, the amount of work required in deforming microstructures can vary significantly [84]. The presence of grain boundaries oriented in different positions relative to one another serves as an effective barrier to the movement of dislocations. Gao and Huang [85] proposed a Taylor based non-local theory of plasticity to account for the size dependence of plastic deformation in the submicron length scales. Conrad [86] reviewed two models for grain size dependence from millimeters to nanometers on flow stress for copper. One model is based on the concept of dislocation pile-up while the other is based on dislocation density. Li et al. [87] also reported that the flow stress is proportional to the average misorientation and the grain size at low strains. Hughes and Hansen [88] proposed a model to determine the effect of microstructure on flow stress based on dislocation theory.

Simoneau et al. [51, 89] suggested that the when grain size is comparable to the undeformed chip thickness, the cutting edge tries to fracture a single grain of a workpiece material during micro-cutting. This influences cutting forces, chip formation and quality of machined surface. Bissacco et al. [48] stated that limited scalability of material grain size and tool edge radius manifest size effect at the micro-scale. Venkatachalam et al. [49] proposed analytical force model to capture the effects of grain size, grain boundaries, and crystallographic orientations during micro-cutting of brittle materials. They investigated initial bulk material microstructure experimentally and used as an input to evaluate the flow stress. The obtained flow stress is therefore used in the prediction of the cutting forces.

Park et al. [90] developed a mechanistic cutting force model and calibrated the model via microstructure-level FEA simulations during micro-cutting of ferrous materials containing graphite, ferrite, and pearlite grains. Predicted forces using the calibrated model are in good agreement with their experimental results. Takafumi et al. [91] performed experiments to study the effect of ultra-fine grain size on cutting force and surface finish during micro-milling of stainless steel. They observed that the cutting force ratio of the ultra-fine grained steel is higher than that of the normal grain steel. Vogler et al. [50] performed finite element based micro-cutting simulations to study the levels of cutting forces during micro-cutting of pearlite and ferrite microstructures, respectively. FEA simulations were validated through experiments and fine-tuned the analytical model of force prediction. Simoneau et al. [51] performed micro-cutting experiments and developed heterogeneous finite element model of orthogonal micro-cutting to study chip formation and quality of machined surface. Fig. 2.28a shows actual microstructure of workpiece. They approximated the workpiece to consist of two materials (A and B) representing the microstructure of AISI 1045 steel as shown in Fig. 2.28b. Material A is three times stronger than material B and their behavior is described by a Johnson-Cook (J-C) plasticity model. Fig. 2.28c shows chip formation obtained using FE simulations during micro-cutting of heterogeneous workpiece. It also shows chip obtained through corresponding experiments. Chuzhoy et al. [53] developed microstructure-based FEA model of micro-cutting to predict the cutting forces accurately than the prediction based on the homogeneous material model (see Fig. 2.29). They also found that the simulated cutting forces in micro-cutting using multiphase material is larger than that obtained using simulations with single phase material.

Most of the past studies have either used phenomological models to predict work material properties or developed approximate multi-phase models without taking into account actual nature, size and distribution of grains along with grain boundaries. Moreover, several researchers studied effect of microstructure on cutting forces, machined surface quality, etc. using analytical, experimental and numerical approaches. It is further understood that the microstructures have a significant impact on specific cutting energy during micro-cutting depending on the cutting conditions. Therefore, it is necessary to evaluate the contribution of the grain size in the specific cutting energy as the scale of process reduces under different cutting conditions.

Table 2.1 summarizes experimental, analytical and numerical studies explaining causes of size effect in micro-cutting under different cutting conditions. It also lists tool and work materials, and processing parameters used during the micro-cutting experimentation and or simulation.