Fracture mechanics-based model of abrasive waterjet cutting for brittle materials

Advanced engineering ceramic materials such as silicon carbides and silicon nitride have been used in many engineering applications. The abrasive waterjet is becoming the most recent cutting technique of such materials because of its inherent advantages.In the present study, two elastic-plastic erosion models are adopted to develop an abrasive waterjet model for cutting brittle materials. As a result, two cutting models based on fracture mechanics are derived and introduced. The suggested models predict the maximum depth of cut of the target material as a function of the fracture toughness and hardness as well as the process parameters.It is found that both models predict the same depth of cut within a maximum of 11%, for the practical range of process parameters used in the present study. The maximum depth of cut predicted by the suggested models are compared with published experimental results for three types of ceramics. The effect of process parameters on the maximum depth of cut for a given ceramic material is also studied and compared with experimental work. The comparison reveals that there is a good agreement between the models' predictions and experimental results, where the difference between the predicted and experimental value of the maximum depth of cut is found to be an average value of 10%.Nomenclature C abrasive efficiency factor, see equation (16) - C₁,C₂ c₁/4/3, c₂/4/3 - c₁,c₂ erosion models constants, see equations (1) and (2) - d_a local effective jet diameter - d_j nozzle diameter - d_S infinitesimal length along the kerf - f₁ (_E) function defined by equation (7) - f₂ (_E) function defined by equation (8) - f₃ (_e) function defined by equation (14) - g₁ (_E) f₁(_e)/f₃²(_e) - g₂ (_e) f₂(_e/f₃²(_e) - H Vickers hardness of the target material - h maximum depth of cut - K_c fracture toughness of target material - k kerf constant - M linear removal rate, dh/dt - m mass of a single particle - abrasive mass flow rate - water mass flow rate - P water pressure - Q total material removal rate, see equation (11) - R abrasive to water mass flow rates - r particle radius - S kerf length - u traverse speed - V material volume removal rate (erosion rate) - V idealised volume removal by an individual abrasive particle - particle impact velocity - ₀ initial abrasive particle velocity - x,y kerf coordinates - local kerf angle, Fig. 1 - _E jet exit angle at the bottom of the workpiece, Fig. 1 - particle density - _w water densityOn leave from: Mechanical Engineering Department, Suez Canal University, Egypt.On leave from: Mechanical Power Engineering Department, Alexandria University, Egypt.