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and cracks are not propagated regardless of the size of the indenter and pressure On the contrary, in the case of indentation on brittle materials, initiation and propagation of cracks become remarkable When the tip radius of the indenter is large (of the order of mm), the so-called cone crack is initiated Indentation with a small radius tip initiates and propagates median as well as lateral cracks when the pressure is high For the initiation of the aforementioned cracks, pre-existing flaws in the material are assumed, with the distance being smaller than the stress field The crack is assumed to initiate at some dominant flaw in the material It is generally believed that all metals contain defects such as grain boundaries, missing and impurity atoms [17] In line with this hypothesis, Taniguchi [18] presented the defect distribution mode in materials and explained how they affect the type of processing energy required in machining ductile and brittle materials (Figure 334) As the chip thickness becomes smaller corresponding to the depth of cut, the amount of energy required becomes higher This is known as the size effect As indicated in Figure 334, the atomic lattice range is between 02 and 04 nm, and the point defect range is from 1 to 100 nm Theoretically, as the depth of cut is reduced to the sub-nanometre level, which is close to the atomic lattice distance, the cutting tool encounters fewer defects existing in this region, and thus the distribution of movable dislocations in the metal crystals approaches zero At this particular condition, an extremely high energy is needed to overcome the very large atomic lattice bonding forces for shearing to take place Compared to atomic processing, micromachining
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Fig 334: Distribution of pre-existing defects in materials, which influences the types of processing: (a) nanometric
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processing with point defects, (b) micromachining in ductile mode with dislocations, (c) micromachining in brittle mode with microcracks and (d) combined ductile-brittle mode machining with grain boundaries [18]
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Mechanics of Materials Cutting
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requires less energy at this level as the tool encounters dislocations of grains and pre-existing flaws in the respective materials, which in turn helps to dislodge materials as chips The aforementioned indentation and pre-existing defect models attribute material removal in brittle materials to microfracture There are cases where brittle materials exhibit ductile behaviour without undergoing any microfracture when subjected to high hydrostatic pressures Komanduri et al [35] have cited the work of Bridgman and Johnson to explain the mechanism of material removal of brittle materials when there is no microfracture involved, which is based on the plasticity theory According to this theory, the yield strength of a material is determined by the magnitude of the hydrostatic stress state, which determines the extent of plastic deformation prior to fracture At room temperature, a high value of the hydrostatic pressure is a prerequisite for plastic flow to occur in brittle materials Such conditions generally exist at light loads under the indenter in indentation testing as shown in Figure 335 Below the indenter, the material is considered to behave as a radially expanding core , exerting a uniform hydrostatic pressure on its surroundings; encasing the core in an ideally plastic region within which flow occurs according to some yield criterion; the elastic matrix lies beyond the plastic region According to this model, the state of the stress determines whether fracture will occur or not Fig 335: A model of the elastic plastic indention of The resulting stress, which acts on the surface, brittle materials in which the dark region depends on the geometry of the tool or the represents the hydrostatic core, the shaded region denotes the plastic region and the abrasive grain (indenter) and the depth of cut surrounding region denotes the elastic and workpiece material properties Komanduri matrix [35] et al [35], Tabor [36][37], and Puttick and Hosseini [38] reported that the tendency of subsurface microcracks to develop in brittle materials decreases with the decrease in the undeformed chip thickness It appears that a significant deformation underneath the tool is necessary to provide adequate hydrostatic pressures for enabling plastic deformation of the workpiece material to occur Figure 336 illustrates various tools used for machining with their associated cutting force components and their chip formation ahead of the tool Apart from conventional cutting, other tools have a very large negative rake, which is typically necessary to provide hydrostatic pressures on the workpiece In ultra-precision machining, at depths of cut smaller than the tool edge radius, the tool presents a large negative rake angle to the workpiece material, and the radius of the tool edge acts as an indenter Similar behaviour is shown in the case of indentation sliding where the tool functions as a blunt indenter across the workpiece In grinding, although a definite rake angle cannot be identified as it is unknown and varies continuously due to wear and a self-sharpening action, it is generally
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