An approximate machining theory is described in which account is taken of the temperature and strain-rate dependent properties of the work material. A feature of the theory is that the strain rates in the zones of intense plastic deformation in which the chip is formed and along the tool/ chip interface are determined as part of the solution. The theory is applied to make predictions for two plain carbon steels and a range of cutting conditions by using flow stress data obtained from high speed compression tests and excellent agreement is shown, for example, between predicted and experimental cutting forces. The values of tool/chip interface plastic zone thickness predicted by assuming a minimum work criterion are shown to agree well with experimental values, both experiment and theory indicating a marked decrease in thickness with increase in cutting speed. It is also shown how the temperatures and strain rates in this zone can be used to determine the conditions that cause a built-up edge to be formed on the cutting tool and good agreement is again shown with experimental results.

A theory is given for calculating chip geometry, cutting forces, etc., from fundamental work material properties and cutting conditions. The flow stress properties of the work material (0·16 per cent carbon steel) used in the analysis are taken from high-speed compression test results. The theory predicts the main trends observed in machining experiments and a limited comparison with experimental results shows good quantitative agreement. A possible explanation for the occurrence of a built-up edge, involving the dynamic strain ageing (blue-brittleness) of the chip along the tool-chip interface, is considered and found to be consistent with the results.

In previous applications of an approximate machining theory in which account is taken of the strain rate and temperature dependence of the work material flow stress properties it has been found necessary to use an empirical relation to determine the maximum value of the maximum shear strain rate in the chip formation zone. In this paper the machining theory is further developed so that this strain rate can be obtained as part of the solution. Predicted values found in this way are shown to be in excellent agreement with the rather limited number of experimental strain rate results which are available. The paper ends by showing that if the work material is allowed to approach the ideal constant flow stress material usually assumed in slip-line field theory then the predicted strain rates become extremely large. However, it is still found necessary in calculating the corresponding hydrostatic stresses to use the stress equilibrium equations for a variable flow stress material as the variable flow stress terms do not diminish as rapidly as might have been expected.

An approximate theory of machining is described in which the average shear flow stress in the plastic zone in the chip adjacent to the tool/chip interface, which is allowed to vary with strain rate and temperature, is used as the friction parameter and this is shown to be far more effective than the normally used average coefficient (or angle) of friction. It is proposed that the average thickness of the tool/chip interface plastic zone is determined by a minimum work criterion, its value being such that for given cutting conditions the average shear flow stress within the plastic zone will be minimized, thus minimizing both the frictional and total work done in chip formation. A comparison is made between results predicted by assuming minimum work and experimental results.

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