The dynamics of chip formation during high-speed orthogonal machining (planing) is examined. Merchant’s vector diagram of the forces acting upon the continuous chip free body is expanded to include inertial force components. Expressions are developed for cutting force and pressure. Energy balances are used to show that Merchant’s classical equation relating shear angle φ to rake angle α and friction angle τ applies, independent of cutting speed. Apparent differences between experimental observations of shear angle φ and Merchant’s prediction are attributed to workpiece material anisotropies, tool wear, built-up edge, and inaccurate measurement of the friction coefficient at the tool–chip interface. It is shown that good experimental values of the shear angle and friction coefficient may be obtained by measuring cutting pressure, utilizing dynamic material properties data, and invoking Merchant’s relation to resolve the energy balance. Continuous and segmented chip formation are contrasted. Melting in the tool–chip interface is verified.

Dynamic plastic behavior of materials is influenced by internally generated temperature gradients. These gradients are a function of thermophysical properties as well as strain rate and shear strength. Criteria are presented for the prediction of catastrophic shear in materials. Catastrophic shear occurs when the local rate of change of temperature has a negative effect on strength which is equal to or greater than the positive effect of strain-hardening. Catastrophic slip is an influential deformation mechanism during high-speed machining and ballistic impact. Structural failure may occur during dynamic loading of components which are designed without regard to the specific sensitivity of certain materials to catastrophic shear.

Analytical equations of the types required to define ballistic perforation dynamics are developed. These equations concern both blunt and sharp-nosed fragments, perforating plates normally and at oblique impact angles. Residual velocities are defined in terms of magnitude and direction. Analytical models and confirming experimental data, which are presented here, specifically concern the ballistic velocity-impact range to about 25 percent of the velocity of longitudinal sonic waves in the impacting materials.