Molecular dynamics modelling of brittle–ductile cutting mode transition: Case study on silicon carbide

The mechanism of brittle–ductile cutting mode transition has received much attention over the past two decades. Due to the difficulties in directly observing the cutting zone during the brittle–ductile cutting mode transition by experimental techniques, many molecular dynamics (MD) studies have been conducted to investigate the atomicscale details of the phenomena, e.g. phase transformation, stress distribution and crack initiation, mostly under nanoscale undeformed chip thicknesses. A research gap is that direct MD modelling of the transition under practical undeformed chip thicknesses was not achieved in previous studies, due to the limitations in both computation capability and interaction potential. Important details of the transition under practical undeformed chip thicknesses thereby remain unclear, e.g. the location of crack formation and the stress distribution. In this study, parallel MD codes based on graphics processing units (GPU) are developed to enable large-scale MD simulations with multi-million atoms. In addition, an advanced interaction potential which reproduces brittle fracture much more accurately is adopted. As a result, the direct MD simulation of brittle–ductile cutting mode transition is realised for the first time under practical undeformed chip thicknesses. The MD-modelled critical undeformed chip thickness is verified by a plunge cutting experiment. The MD modelling shows that tensile stress exists around the cutting zone and increases with undeformed chip thickness, which finally induces brittle fractures. The location of crack formation and direction of propagation varies with undeformed chip thickness in the MD simulations, which agrees with the surface morphologies of the taper groove produced by the plunge cutting experiment. This study contributes significantly to the understanding of the details involved in the brittle–ductile cutting mode transition.     

Study of the mechanism of nanoscale ductile mode cutting of silicon using molecular dynamics simulation

In cutting of brittle materials, it was observed that there is a brittle-ductile transition when two conditions are satisfied. One is that the undeformed chip thickness is smaller than the tool edge radius; the other is that the tool cutting edge radius should be small enough—on a nanoscale. However, the mechanism has not been clearly understood. In this study, the Molecular Dynamics method is employed to model and simulate the nanoscale ductile mode cutting of monocrystalline silicon wafer. From the simulated results, it is found that when the ductile cutting mode is achieved in the cutting process, the thrust force acting on the cutting tool is larger than the cutting force. As the undeformed chip thickness increases, the compressive stress in the cutting zone decreases, giving way to crack propagation in the chip formation zone. As the tool cutting edge radius increases, the shear stress in the workpiece material around the cutting edge decreases down to a lower level, at which the shear stress is insufficient to sustain dislocation emission in the chip formation zone, and crack propagation becomes dominating. Consequently, the chip formation mode changes from ductile to brittle.     

Crack initiation in relation to the tool edge radius and cutting conditions in nanoscale cutting of silicon

In cutting of brittle materials, experimentally it was observed that there is a ductile–brittle transition when the undeformed chip thickness is increased from smaller to larger than the tool cutting edge radius of the zero rake angle. However, how the crack is initiated in the ductile–brittle mode transition as the undeformed chip thickness is increased from smaller to larger than the tool cutting edge radius has not been fully understood. In this study, the crack initiation in the ductile–brittle mode transition as the undeformed chip thickness is increased from smaller to larger than the tool cutting edge radius has been simulated using the Molecular Dynamics (MD) method on nanoscale cutting of monocrystalline silicon with a non-zero edge radius tool, from which, for the first time, a peak deformation zone in the chip formation zone has been found in the transition from ductile mode to brittle mode cutting. The results show that as the undeformed chip thickness is larger than the cutting edge radius, in the chip formation zone there is a peak deformation depth in association with the connecting point of tool edge arc and the rake face, and there is a crack initiation zone in the undeformed workpiece next to the peak deformation zone, in which the material is tensile stressed and the tensile stress is perpendicular to the direction from the connecting point to the peak. As the undeformed chip thickness is smaller than the cutting edge radius, there is no deformation peak in the chip formation zone, and thus there is no crack initiation zone formed in the undeformed workpiece. This finding explains well the ductile–brittle transition as the undeformed chip thickness increases from smaller to larger than the tool cutting edge radius.     

Cutting process in glass peripheral milling

Peripheral glass milling for trimmings of several devices and touch panels is studied with measuring cutting forces and observing surface damages. Peripheral millings were performed to cut the end faces of 1 mm thick glass plates. In order to discuss the typical cutting force in glass milling, the cutting forces were compared with those of 0.45% carbon steel (AISI 1045) at high feed rates in a large radial depth of cut. The differences of the cutting force in glass milling from that of metal milling are: (1) the change in the cutting force does not correspond to the uncut chip thickness; and (2) the maximum cutting force does not change with the feed rate. A model is proposed to predict the cutting forces in glass millings, which are performed in ductile, ductile/brittle complex and brittle modes. The cutting force depends on the uncut chip thickness in a ductile mode. In a brittle mode, the mean value of the cutting force does not change though the vibration component becomes large. Because the uncut chip thickness changes with the dynamic displacement of the cutting edge, the cutting process is performed in a ductile/brittle complex mode when the cutting mode changes in ductile–brittle transition. The critical uncut chip thickness at the transition from a ductile to a ductile/brittle complex mode and that of the transition from a ductile/brittle complex to brittle mode are determined in the rate of the cutting force change. The force model is verified by the cutting forces in up- and down-cutting milling operations. Then, the surface finishing and crack propagation in up- and down-cutting millings were analyzed to define the cutter path in glass trimming. Cracks propagate to the surface to be finally finished in down-cutting; while cracks propagate to the chip to be removed in up-cutting. The cutter path in up-cutting milling should be selected to finish the fine surfaces.     

Experimental study of surface generation and force modeling in micro-grinding of single crystal silicon considering crystallographic effects

In this study, surface formation mechanism in micro-grinding of single crystal silicon is investigated based on analysis of undeformed chip thickness h_m. A predicting model of grinding force considering crystallographic effects in micro-grinding of single crystal silicon is built. In this model, micro-grinding process of single crystal silicon is divided into two steps by one line on which h_m of single grit equals to lattice constant. Two micro-grinding experiments with different ranges of cutting depths and feed rates have been designed and conducted on single crystal silicon to verify the model this paper proposes. The relationship between micro-grinding parameters and crack length l_c is investigated and the empirical formula of l_c is derived based on analysis of experiment results. Ductile-regime transitions in micro-grinding process of single crystal silicon have been revealed, 20 nm and 100 nm are turned out to be two critical conditions based on analysis of experiment results. It is found that the grinding force has a sudden change when micro-grinding process comes within material's crystal boundary in experiment. The force predicting model this paper proposes has well explained this phenomenon in micro-grinding of single cyrstal silicon. When micro-grinding undeformed chip thickness h_m belows 0.5 nm, micro grinding force doesn't decrease with the decrease of cutting parameters but has a rising tendency, and these experimental measurements also provide a support to the result of model this paper proposes.     

Investigations of yield stress,fracture toughness,and energy distribution in high speed orthogonal cutting

This paper presents a novel prediction method of the yield stress and fracture toughness for ductile metal materials through the metal cutting process based on Williams' Model [38]. The fracture toughness of the separation between the segments in serrated chips in high speed machining is then deduced. In addition, an energy conservation equation for high speed machining process, which considers the energy of new created workpiece surfaces, is established. The fracture energy of serrated chips is taken into the developed energy conservation equation. Five groups of experiments are carried out under the cutting speeds of 100, 200, 400, 800 and 1500 m/min. The cutting forces are measured using three-dimensional dynamometer and the relevant geometrical parameters of chips are measured with the aid of optical microscope. The experiment results show that the yield stress of machined ductile metal material presents an obviously increasing trend with the cutting speed increasing from 100 to 800 m/min while it decreases when the cutting speed increases to 1500 m/min further. Meanwhile, the fracture toughness between the chip and bulk material displays a slightly increasing tendency. In high speed machining, the fracture toughness of the separation between the segments in serrated chips also presents increasing trend with the increasing cutting speed, whose value is much greater than that between the chip and bulk material. In the end, the distribution of energy spent in cutting process is analyzed which mainly includes such four portions as plastic deformation, friction on the tool–chip interface, new generated surface and chip fracture. The results show that the proportion of plastic deformation is the largest one while it decreases with the cutting speed increasing. However, the proportions of energy spent on new created surface and chip fracture increase due to the increasing of both the chip's fracture area and the fracture toughness.     

Fracture behaviour and numerical study of resistance spot welded joints in high-strength steel sheet

Cross tension tests of resistance spot welded joints with varying nugget diameter were carried out using 980 MPa high strength steel sheet of 1.6 mm thickness. In proportion, as nugget diameter increased from 3√t to 5√t (where t is thickness), cross tension strength (CTS) increased while fracture morphology simultaneously transferred from interface fracture to full plug fracture. In cases of interface fracture, circumferential crack initiation due to separation of the corona bond arose at an early stage of loading. The crack opening process without propagation was recognized until just before fracture and then the crack propagated to the nugget immediately in a brittle manner around CTS. In full plug fracture, main ductile crack initiation from the notch-like part at the end of sheet separation occurred with the sub-crack initiated at an early stage. The ductile crack propagated toward the HAZ and base material to form full plug fracture. The mode I stress intensity factor was considered as a suitable fracture parameter because the circumferential crack behaved pre-crack for brittle fracture in the nugget region at the final stage. Based on the FE analysis, the mode I stress intensity factor was calculated as 116 MPa √m at CTS as fracture toughness for the nugget. With respect to full plug fracture, ductile crack initiation behaviour from the notch-like part was expressed by concentration of equivalent plastic strain. On the assumption that the ductile crack arose in critical value of equivalent plastic strain, the value was calculated as 0.34 by FE analysis. Reasonable interpretation for interface fracture and full plug fracture in the resistance spot welded joint was proposed due to first crack initiation by stress concentration, brittle fracture by using mode I stress intensity factor, and ductile crack initiation by using equivalent plastic strain.     

Effect of tilt angle on cutting regime transition in glass micromilling

Recent development in mechanical micromachining technology has increased the realization of micromachining as a feasible manufacturing process of micro-scale components including glass-based devices. It has been found that glass can be machined in a ductile regime under certain controlled cutting configurations. However, favorable ductile regime machining instead of brittle regime machining in micromilling of brittle glass is still not fully understood as a function of cutting configuration. In this study, the effect of tilt angle along the feed direction on cutting regime transition has been studied in micromilling crown glass with a micro-ball end mill. Straight glass grooves were machined in water bath by varying the tool tilt angle and the feed rate, and the resulting surface was characterized using the scanning electron microscope and the profilometer to investigate the glass cutting regime transition. In characterizing the cutting regimes in glass micromilling, rubbing, ductile machining, and brittle machining regimes are hypothesized according to the undeformed chip thickness. It is found that a crack-free glass surface can be better machined in the ductile mode using a 45° tilt angle and feed rates up to 0.32 mm/min. During each milling pass, surface roughness was found to decrease from the entry zone to the groove bottom and then increase to the exit zone regardless of the cutting regime.     

Revisiting the empirical relation for the maximum shearing force using plasticity and ductile fracture mechanics

Combination of plasticity with ductile fracture mechanics in a simple plastic flow model for sheet metal cutting provides a new level of understanding of the empirical relation between the maximum shearing force F_max and the ultimate tensile stress σ_UTS of the workpiece. The constant C in F_max = C σ_UTStL, where t is the sheet thickness and L the total surface length of the cut contour, is shown to be determined either (a) by the load to cause plastic instability in shear with separation (cracking) occurring subsequently or (b) by the load to cause cracking when that occurs at a punch displacement smaller than that at plastic instability in which case no instability occurs. The usually encountered range of empirical values for C, viz.: 0.65 < C < 0.85, is shown to correspond with the load for instability and depends on the work hardening index, with less-ductile materials having C at the lower end of the range. Whether cracking can precede the instability depends on the toughness/strength ratio (R/k₀) of the material and the workpiece thickness, where R is the fracture toughness and k₀ the yield stress in shear. The thicker the sheet and the less ductile the material, i.e. the lower the (R/k₀), promotes ductile fracture at a load smaller than that for plastic instability.     

Energy dissipation in modulation assisted machining

The specific energy in modulation assisted machining (MAM) – machining with superimposed low frequency (<1000 Hz) modulation in the feed direction – is estimated from direct measurements of cutting forces. Reductions of up to 70% in the energy are observed relative to that in conventional machining, when cutting ductile metals such as copper and Al 6061T6. Evidence based on chip structures and strains, stored energy of cold work, recrystallization, and finite element simulation of chip formation, is presented to show that this reduction is due to smaller strain levels in chips created by MAM. A simple geometric ratio of the length to thickness of the ‘undeformed chip’, which can be estimated a priori from MAM and machining parameters, is shown to be a predictor of the transient chip formation conditions that result in the reduction in specific energy and deformation levels.     

A wedge fracture toughness test for intermediate toughness materials: Application to brazed joints

A fracture toughness test for intermediate toughness materials is developed. The test configuration is a wedge-driven double cantilever beam, with design guided by analytical solutions for the energy release rate and compliance. Actual toughness measurements require finite element methods. To promote crack stability, a pre-cracking fixture is employed. The method is illustrated for a brazed joint. Measurements of the fracture resistance used both fractographic and compliance methods to ascertain crack length. The ensuing fracture resistance, Γ_R ≈ 1 kJ m⁻², is significantly greater than that for the intermetallic constituents. Approximately half of the toughening is attributed to plastic stretch of the ductile phase within the eutectic. The remainder is attributed to dissipation within a plastic zone that forms in the primary γ-Ni regions. A rationale for improving toughness is presented.     

The brittle–ductile transition in single-crystal iron

The fracture behaviour of single-crystal pure iron was studied by four-point bending of pre-cracked specimens at temperatures between 77 and 180 K and strain rates between 4.46 × 10⁻⁵ and 4.46 × 10⁻³ s⁻¹. Fracture behaviour changes from brittle to ductile with increasing temperature. The brittle–ductile transition (BDT) temperature increases with increasing strain rate. The relation between BDT temperature and strain rate follows an Arrhenius relation, giving an activation energy for the BDT of 0.33 eV. Dislocation-dynamics simulations of the crack-tip plasticity and resultant shielding of the crack tip were performed using two different variants of the dislocation velocity/stress/temperature relation. The models predict an explicit BDT, and give a good quantitative fit to the experimental transition temperatures.     

Ductilisation of tungsten (W) through cold-rolling: R-curve behaviour

Here we show that cold-rolling of tungsten (W) decreases the stable crack growth onset temperature. Furthermore, we show that stable crack growth is accompanied by crack bridging, which in turn is triggered by dislocation activity. The entire stable crack growth regime shows ductile intergranular fracture.Our ductilisation approach is the modification of microstructure through cold-rolling. In this work, we assess two different microstructures obtained from (i) cold-rolled and (ii) severely cold-rolled tungsten plates. From these plates, single-edge cracked-plate tension (SECT) specimens were cut and tested in the L-T direction. Crack growth resistance (R) curves were obtained using the direct-current-potential-drop method (DCPM). The experiments show the following results: cold-rolled plates are brittle at room temperature (RT), but show stable crack growth at 250 °C (523 K) and a fracture toughness, K_IQ, of about 100 MPa(m)^1/2 at a crack extension, Δa, of 0.6 mm. Severely cold-rolled tungsten plates show stable crack growth at RT and a fracture toughness, K_IQ, of 100 MPa(m)^1/2 at a crack extension, Δa, of 0.3 mm. Scanning electron microscopy (SEM) analyses of the stable crack growth region show intergranular fracture with microductile character.The question of why cold-rolling causes the stable crack growth onset temperature to decrease (or in other words, why cold-rolling causes the brittle-to-ductile transition (BDT) temperature to decrease) is discussed against the background of (i) intrinsic and extrinsic size effects, (ii) crystallographic texture, (iii) impurities and (iv) the role of dislocations. Our results suggest that the spacing between the dislocation nucleation sites (high angle grain boundaries (HAGBs) act as dislocation source) is the most important parameter responsible for the decrease of the stable crack growth onset temperature.     

Experimental study of the brittle–ductile transition in hot cutting of SG iron specimens

The present paper investigates the brittle–ductile transition (BDT) of the primary shear zone during cutting of spheroidal graphite (SG) iron in the austenitization temperature range (around 1000 °C). The experimental tests were performed using a cutting test bench in the cutting speed range of 0.8–1.6 m s^?1. The cut surfaces were studied using optical microscopy and scanning electron microscope (SEM) analysis techniques. The obtained results revealed either consequent deep fractured regions governed by a brittle-cracking regime (BCR) or a crack-free cut surface governed by a ductile-shear regime (DSR) with large plastic deformations.When cutting data were discussed with respect to the influences of cutting parameters and obtained cut surface, the correlation is significantly rich. Both cut surface integrity, cutting force curves and metallographic results show a BDT indicating a change in the dominating hot cutting process mechanism. Such a transition is associated with the dynamic recrystallization promoting strain softening and hot cutting by ductile shearing.     

The role of deformation twins in brittle crack propagation in iron–silicon steel

Crack initiation and propagation in polycrystalline metals and alloys can be characterized by the crack driving force and the resistance to fracture. Interfaces such as grain, sub-grain and interphase boundaries are microstructural features that can resist crack propagation. For iron–silicon polycrystalline steels, brittle fracture occurs predominately by transgranular cleavage but intergranular fracture is enhanced by embrittling heat-treatments. In this paper, we consider the role of deformation twin boundaries on the brittle crack propagation and fracture resistance of poly and single crystals of Fe–3 wt.% Si steel. Three-point bend, impact and miniaturized disc tests have been undertaken at temperatures in the range of 77–273 K. The fractographic features have been characterized with attention being given to (i) the role of the {1 1 2} deformation twins on the propagation of the {0 0 1} cleavage cracks and (ii) the process-zone of the propagating cleavage cracks. The results are discussed with reference to three-dimensional model predictions.     

The relationship between thin film fragmentation and buckle formation: Synchrotron-based in situ studies and two-dimensional stress analysis

Fragmentation and buckling of Ta layers with thicknesses of 50, 100, and 200 nm on polyimide substrates was studied by in situ light microscopy and synchrotron analysis. Buckling indicates the presence of compressive stress, which cannot be explained exclusively by a Poisson ratio mismatch. We extended the classical shear lag model and derived a rigorous analytical solution for the biaxial stress field in a single fragment attached to a uniaxially loaded substrate. The presence of cracks not only gives rise to tensile stress relaxation, but also induces compressive stress in the perpendicular direction, which eventually leads to film buckling. The validity of the model has been confirmed using a synchrotron-based technique for the in situ determination of the biaxial coating stress during uniaxial tensile testing. Taking into account the mean crack distance as a function of the applied strain, the model is utilized to determine the residual stress and fracture toughness of thin films.     

Characteristics of high speed micro-cutting of tungsten carbide

In this study, experiments are carried out to evaluate the characteristics of high speed cutting of tungsten carbide material using a Makino V55 high speed machine tool with cubic boron nitride (CBN) tool inserts. The cutting forces were measured using a three-component dynamometer, the surface roughness of the machined workpiece was measured using a Mitutoyo SURFTEST 301, and the machined workpiece surfaces and the chip formation were examined using a scanning electron microscope (SEM). Experimental results indicate that the radial force F_x is much larger than the tangential force F_z and the axial force F_y. Two types of surfaces of the machined workpiece are achieved: ductile cutting surface and fracture surface. Continuous chips and discontinuous chips are formed under different cutting conditions. Depth of cut and feed rate almost have no significant effect on the surface roughness of the machined workpiece. The SEM observations on the machined workpiece surfaces and chip formation indicate that the ductile mode cutting is mainly determined by the undeformed chip thickness when the tool cutting edge radius is fixed. Ductile cutting can be achieved when the undeformed chip thickness is less than a critical value.     

Observations on chip formation and acoustic emission in machining Ti–6Al–4V alloy

Orthogonal cutting tests were undertaken to investigate the mechanisms of chip formation for a Ti–6Al–4V alloy and to assess the influences of such on acoustic emission (AE). Within the range of conditions employed (cutting speed, v_c=0.25–3.0 m/s, feed, f=20–100 μm), saw-tooth chips were produced. A transition from aperiodic to periodic saw-tooth chip formation occurring with increases in cutting speed and/or feed. Examination of chips formed shortly after the instant of tool engagement, where the undeformed chip thickness is slightly greater than the minimum undeformed chip thickness, revealed a continuous chip characterised by the presence of fine lamellae on its free surface. In agreement with the consensus that shear localisation in machining Ti and its alloys is due to the occurrence of a thermo-plastic instability, the underside of saw-tooth segments formed at relatively high cutting speeds, exhibiting evidence of ductile fracture. Chips formed at lower cutting speeds suggest that cleavage is the mechanism of catastrophic failure, at least within the upper region of the primary shear zone. An additional characteristic of machining Ti–6Al–4V alloy at high cutting speeds is the occurrence of welding between the chip and the tool. Fracture of such welds appears to be the dominant source of AE. The results are discussed with reference to the machining of hardened steels, another class of materials from which saw-tooth chips are produced.