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Chapter 2
2.4 Microcrack formation in the shear zone
2.5 Gross fracture phenomenon ahead of tool-tip
Occurrence of crack or gross fracture in cutting of brittle materials is well accepted [30-31]. Fig. 2.17a shows crack formation during discontinuous chip formation. Similarly, the occurrence and propagation of cracks along the shear plane (see Fig. 2.17b) during formation of serrated chips. Researchers [33-34, 39-40] have also studied the crack formation during cutting of materials such as cast iron, ceramics, composites, etc. However, cracks do occur during cutting of ductile metals under certain cutting conditions. But the traditional studies did not consider crack formation in analytical models as the cracks are usually not evident at the tip of the tool or at the root of chip during cutting of ductile metals [29]. They have assumed that plastic deformation and friction consume most of the energy spent in cutting [49-50].
Kaneeda et al. [35] observed ductile fracture ahead of tool-tip using scanning electron microscope (SEM) during cutting experiments on pure aluminum. Subbiah and Melkote [36] found fracture zones at the root of the chip and ahead of tool-tip during micro-cutting of oxygen-free high-conductivity (OFHC) copper and 2024-T3 aluminum alloy. Fig. 2.18a-c shows evidence of ductile fracture using SEM images with increasing magnification from left to right. Madhavan et al. [73] reported chip formation as an indentation process which is considered to be a result of brittle/ductile fracture just ahead of the tool.
Crack formation is modeled analytically and numerically by several researchers in cutting of ductile and brittle metals using the concepts of fracture mechanics. Ueda et al. [34] observed cracks ahead of tool-tip (see Fig. 2.19a) and studied the type of material removal mechanisms in micro-cutting of engineering ceramics using the concepts of linear elastic fracture mechanics (LEFM) by estimating energy release rate (G). Further, Iwata and Ueda [74] presented a new approach to understand the ductile and brittle regime cutting using J-integral concept which is capable of elastic-plastic fracture mechanics (EPFM). Fig. 2.19b shows FEA simulation model along with contour paths (see Fig. 2.19c) for J-integral ahead of tool-tip during micro-cutting of ceramics.
Chiu et al. [75] predicted crack trajectories (see Fig. 2.20a) during cutting of brittle materials using stress intensity factors KI and KII. They stated that two modes of crack occur as shown in Fig. 2.20b due to loading effects at tool-tip.
Ericson and Lindberg [76] estimated energy dissipation during crack propagation in polymers using the theory of critical fracture energy. Authors further implemented use of instrumented ultra-microtome to measure energy dissipation during cutting of polymers. Recently, Williams et al. [39] calculated energy release rate (G) by establishing a linear relationship between cutting forces and uncut chip thickness. They analyzed the process of cutting using the concepts developed in the fracture analysis of beam specimens.
Fleck et al. [77] performed orthogonal cutting experiments on sintered bronze which is a porous material. Due to porosity of the sintered material, compaction of the workpiece occurs. Fig. 2.21a shows cracks ahead of tool-tip in the work material during chip formation. Representative load cycle in the form of fluctuating waveform is shown in Fig. 2.21b where incomplete scallops are formed. They explained cutting mechanism in four stages as mentioned below:
A. Crack initiation
B. Crack growth
C. Crack extension
D. New crack initiation
Near the peak load, a crack develops from tool-tip and grows towards the free surface as the load drops from A to B. Continued tool travel compacts material, the load increases through point C up to D when the process starts all over again.
Rosa et al. [41] presented an analogy between crack propagation in a deformation zone in a double notched fracture test (see Fig. 2.22a) and plastically deformed thick shear zone during micro-cutting as shown in (see Fig. 2.22b). They suggested that material flow, chip formation, etc. can be obtained qualitatively without considering fracture within finite element models. But modeling of ductile fracture is essential to obtain good estimate of cutting forces and specific cutting energy. It is observed that the specific cutting energy obtained by FEA simulation including fracture is close to the experimental results.
An analytical model based on fracture has been proposed by Atkins [38] in cutting of ductile metals. He studied the role of fracture in metal cutting using specific work of fracture (R) and found that it is a significant component of the total cutting energy under certain conditions. He considered energy spent in cutting of ductile metals for three purposes, that is, plastic deformation, friction at tool-chip interface and formation of new surfaces (or fracture ahead of tool-tip) (see Fig. 2.23).
Above Eq. 2.7 is an equation of a line in which the first term represents the slope of the line, whereas the second term represents its intercept. From the intercept, specific work of fracture (R) can is obtained.
Because of the tool cutting edge radius, a significant amount of energy is involved in the flow of material over the cutting edge. Atkins model [38] described using Eq. 2.7 doesn’t include the effect of the tool cutting edge radius. Therefore, the Atkins’s model overestimates the energy of new surface formation [43]. One of the reasons for the model to overestimate energy of new surface formation is due to the neglect of ploughing energy. However, when the ploughing energy is considered, then the energy of new surface formation would get substantially reduced as given by the model of Karpat [43] below:
Fig. 2.24 shows the slip-line field model used in their study. In this model, a stagnant metal zone in front of the cutting edge was considered. Frictional forces act on tool-chip contact, whereas the ploughing forces act on tool-work interface i.e. the stagnant metal zone. Under sticking conditions at tool-work interface, friction factor (mf) becomes unity, whereas the inclination angle (z1) becomes zero. With these assumptions, Eq. 2.11 can be simplified and is given by Eq. 2.15 which is similar to the Atkins [38] model given by Eq. 2.7. In this model, R is evaluated from the intercept of Eq. 2.15 which includes the effect of ploughing forces.
It was shown that a consideration to the fracture phenomenon in analytical modeling of metal cutting gives better estimate of cutting forces and specific cutting energies. Atkins [29] advocated theory of material separation using specific work of fracture (R) during cutting of biomaterials, metals and non-metals. Further, Atkins model is widely used by various researchers to calculate fracture energy during cutting with sharp tools [29, 39-42] but significant amount of energy is involved in the flow of material over the cutting edge while cutting with rounded edge tools. Atkins model doesn’t include the effect of the tool cutting edge radius. Hence, Karpat [43] proposed another model which includes ploughing energy in addition to the energies considered by Atkins. He showed that when the ploughing energy is considered, the fracture energy would get substantially reduced as shown in Fig. 2.25.
Astakhov and Xiao [44] proposed that energy balance in metal cutting is further complicated and involves several other energies, besides the energies considered by Atkins [38] and Karpat [43]. Therefore, R evaluated using Atkins’s model and Karpat’s model would be higher than that evaluated using the energy balance proposed by Astakhov and Xiao [44]. Therefore, to accurately evaluate the contribution of fracture energy in the total cutting energy, it is understood that some other parameter like J-integral would be necessary as it accurately characterizes fracture energy in the presence of mixed mode, material plasticity and nonlinear behavior conditions prevailing during micro-cutting.
2.6 Workpiece microstructure effect
2.7 Conclusions from the literature review
2.8 Objective and scope of the research
