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Chapter 2

2.1 Material strengthening

Material strengthening is a known phenomenon during the severe plastic deformation that takes place in the primary and secondary deformation zones (PDZ and SDZ) ahead of tool-tip in micro-cutting. It causes the size effect due to a change in flow stress of the work material, which is a function of crystal imperfections, strain, strain rate, strain gradients and temperature.

Backer et al. [5] performed turning experiments on a thin-walled tube made of SAE 1112 steel with uncut chip thickness ranging from 58.4 μm to 294.6 μm using a carbide tool. They observed that as the uncut chip thickness decreases, the specific cutting energy increases due to the presence of crystallographic imperfections in the workpiece. These imperfections increase the flow stress of a material due to anisotropic behavior of the material at an uncut chip thickness that is equivalent to crystalline size of workpiece materials.

Similarly, Shaw [4] suggested that the material imperfections are responsible for the inhomogeneous behavior of a work material. When uncut chip thickness is relatively large, there is a uniform density of imperfections leading to uniform strain and strain hardening. However, as uncut chip thickness approaches micrometer size or the size of imperfections (see Fig. 2.3), the material behavior becomes inhomogeneous and the flow stress of material increases.

The magnitude of strain involved in micro-cutting is several orders higher than those generated from conventional tensile testing [1, 31]. In micro-cutting, strain hardening is caused due to severe plastic deformation which increases the flow stress of the work material. Generally an expression for the flow stress (σ_f ) of a material including strain hardening is as follows:

Besides, strain hardening, the material strengthening is also caused by strain rate hardening. In micro-cutting, strain rates are normally greater than 10⁴s^-1 [31, 55], which increases the flow stress rapidly. The effect of strain rate on flow stress is given by Eq. 2.2:

Larsen [7] suggested that shear strain rate within PDZ is inversely proportional to the uncut chip thickness (t_o) in micro-cutting and is given by Eq. 2.3:

Therefore, at smaller uncut chip thickness, the strain rate increases leading to an increase in the flow stress. Researchers explained the presence of size effect due to material strengthening caused by strain and strain rate effect of the workpiece material [6-11]. Fig. 2.4 shows a plot of specific cutting energy vs. uncut chip thickness of turning tests on plain carbon steel using ceramic tools by Kopalinsky and Oxley [9]. Nonlinear effects are clearly evident at the smaller uncut chip thicknesses, which are attributed to strain rate work hardening caused at high cutting speed of 420 m/min.

Filiz et al. [8] performed micro-cutting experiments at different cutting speeds i.e. 40, 80 and 120 m/min on OFHC copper to study strain rate effects in material strengthening. They observed that material softening is less dominant than strain rate hardening at higher speeds during micro-cutting. Thus, the flow stress of the material increases due to strain rates. Although, the flow stress in micro-cutting is not directly correlated to the cutting speed, it controls two aspects in micro-cutting i.e. strain rate and temperature of deformation zones. Therefore, researchers also observed that the specific cutting energy varies with cutting speed depending on the predominant effect. Childs et al. [56] observed that when the cutting speed is increased, with all other parameters kept constant, the specific cutting energy for many materials decreases due to thermal softening. Boothroyd [1] also observed that the size effect in micro-cutting is higher at a lower cutting speed and a lower uncut chip thickness.

Researchers also offered explanation for the presence of size effect using experimental and numerical studies that include strain gradient plasticity during micro-cutting. According to strain-gradient plasticity, when deformation is large and is constrained spatially to a narrow region, the stress not only depends on strain at a point but also upon the strains in the region surrounding that point. In micro-cutting, strain varies from point to point within PDZ and SDZ leading to large strain gradients. Therefore, Dinesh et al. [12] suggested that the size effect in micro-cutting can also be explained by the theory of strain-gradient plasticity since strain gradients in micro-cutting are very intense. Joshi and Melkote [13] presented an analytical model to capture size effect using strain gradient plasticity in PDZ during orthogonal micro-cutting by considering a simple parallel-sided configuration of the PDZ. In this configuration, they considered a row of elements parallel to the shear plane subjected to a large plastic strain near the tool rake face. They observed that the strain decays away from the rake face towards the outer surface of the chip. Similarly, along the thickness of the PDZ, the strain increases from the lower boundary to its upper boundary. They developed a model for evaluating specific shear energy based on the strain gradients in the PDZ. It is observed that the predicted specific shear energy considering strain gradient plasticity is closer to the experimental value. Recently, Liu and Melkote [3] included strain gradient plasticity in the flow stress equations during FEA simulations of micro-cutting using Abaqus to study the size effect. The study concluded that the strain gradient strengthening contributes significantly to the size effect at a low cutting speed and at a small uncut chip thickness (<10 μm) as shown in Fig. 2.5. Asad et al. [15] performed orthogonal micro-cutting experiments and numerical simulations on Al-alloy to study specific cutting energy. They found that the specific cutting energy values obtained by numerical simulations based on strain gradient plasticity are quite close to the experimental values at very high cutting speeds.

All materials do not behave in an identical way. Some are easily machinable but some are not. Fig. 2.6 shows the size effect in the specific cutting energy during micro-cutting experiments of different materials such as aluminum alloy, Oxygen Free Copper, Germanium, Fluorite (CaF₂) and Acryl resin (PMMA) [57]. It is observed that the size effect is minimal over a range of uncut chip thickness for Al-alloy, Germanium, and Fluorite. These materials appear isotropic even at very low uncut chip thickness. The trend in size effect suggests that PMMA and copper show a prominent size effect and are difficult to finish.