MAN TECH 3MF3: Metal Cutting Mechanics and Process Parameters

A comprehensive vocabulary review of orthogonal metal cutting mechanics, shear zone theories, tool geometry, milling configurations, Merchant's force circle, and thermal equations.

Plastic Flow Stress Equation

An empirical constitutive relationship given by $\sigma = [A + B \varepsilon_{pl}^n]$, where $\sigma$ is the plastic flow stress, $A$ is the yield strength or hardness equivalent, $B$ is the strain hardening coefficient, $n$ is the strain hardening index, and $\varepsilon_{pl}$ is the plastic strain.

Austenitic Stainless Steel

A high strain-hardening material with a face-centered cubic (FCC) crystal structure that is unstable at room temperature and transforms into martensite under high pressure and rapid cooling rates during cutting.

Negative Rake Angle Tool

A tool configuration characterized by a negative rake angle ($-\text{ve}$) that exhibits excellent cutting edge strength to withstand high mechanical stresses due to a larger wedge angle between the rake and clearance faces, typically paired with hard and brittle materials such as cemented tungsten carbide and polycrystalline cubic boron nitride.

Positive Rake Angle Tool

A tool configuration characterized by a positive rake angle ($+\text{ve}$) that generates lower cutting forces and shear plane areas but has poorer cutting edge strength, typically used on low $A$-value materials and paired with soft, tough tool materials like high-speed steel.

Cutting Ratio ($r$)

The dimensionless ratio of undeformed chip thickness ($t$) to deformed chip thickness ($T$), represented as $r = \frac{t}{T}$, which is strictly less than $1$ ($r < 1$) because $t < T$.

Recovery Depth

The sub-surface depth from a newly machined surface at which material hardness recovers back to its initial bulk hardness; materials with higher strain-hardening sensitivity produce a deeper recovery depth.

Down Milling (Climb Milling)

A milling configuration in which undeformed chip thickness starts from thick to thin ($t_1 > t_2 > t_3$) and tool rotation matches the workpiece feed direction at minimum chip thickness; cutting edges engage material near bulk hardness, reducing initial engagement stress for high strain-hardening materials.

Up Milling (Conventional Milling)

A milling configuration in which undeformed chip thickness starts from thin to thick ($t_1 < t_2 < t_3$) and tool rotation opposes the workpiece feed direction, forcing the cutting edge to engage material work-hardened by the previous pass.

Ploughing Condition

The cutting threshold occurring when the undeformed chip thickness is less than one-third of the tool cutting edge radius ($t < \frac{R}{3}$), causing the tool to burnish and displace workpiece material without chip formation.

Stagnation Point

A stationary boundary point along the cutting edge radius where the shear stress drops to zero ($\tau = 0$) and the compressive normal stress reaches its absolute maximum ($\sigma = \sigma_{\max}$).

Primary Shear Zone (PSZ)

The narrow shear plane region where plastic strain reaches up to $3$ ($300\%$) due to combined compressive and shear loading and extreme heating rates ($\approx 2 \times 10^9\,^\circ\text{C/s}$), terminating in material fracture at the cutting edge.

Secondary Deformation Zone (SDZ)

The high-temperature zone located along the tool-chip interface where the chip material experiences pure plastic deformation without fracture, reaching strains up to $7$ ($700\%$).

Sticking Region

The contact portion of the secondary deformation zone closest to the cutting edge where shear stress reaches a constant maximum ($\tau = \tau_{\max}$) and heat generation originates entirely from plastic deformation.

Sliding Region

The contact portion of the secondary deformation zone where shear stress obeys Coulomb friction ($\tau = \mu \sigma$), generating heat through both material plastic deformation and sliding friction against the rake face.

Trochoidal Milling

A circular tool path machining strategy used in slotting operations when the slot width is at least $20\,\text{mm}$.

Strain Rate Sensitivity

The degree to which the deformation rate ($\text{s}^{-1}$) increases the material flow stress; materials with high strain-rate sensitivity require narrow, lower cutting speed operating windows.

Knee Temperature

The critical temperature on a yield-strength-versus-temperature curve above which material yield strength drops precipitously due to thermal softening.

Merchant's Circle

A circular diagram used in orthogonal cutting analysis where cutting force ($F_p$), feed force ($F_q$), rake face forces ($F_c$, $N_c$), and shear plane forces ($F_s$, $N_s$) are represented with resultant force $R$ as the diameter.

Friction Angle ($\beta$)

The angle formed between the resultant cutting force $R$ and the normal to the tool rake face, defined mathematically by $\tan(\beta) = \frac{F_c}{N_c} = \frac{F_p \tan(\alpha) + F_q}{F_p - F_q \tan(\alpha)}$.

Merchant's Shear Angle Model

An analytical model based on the minimum work assumption stating that the shear angle establishes itself such that cutting force ($F_p$) is minimized, formulated as $\phi = \frac{\pi}{4} - \frac{\beta}{2} + \frac{\alpha}{2} = 45^\circ - \frac{\beta}{2} + \frac{\alpha}{2}$.

Lee and Shaffer Shear Angle Model

An analytical model employing Mohr's circle and slip-line field theory to predict shear angle as $\phi = \frac{\pi}{4} - \beta + \alpha = 45^\circ - \beta + \alpha$, which is valid exclusively for positive rake angle tools ($\alpha \ge 0$).

Thermal Diffusivity ($H$)

A thermophysical property quantifying heat conduction relative to heat storage capacity, expressed as $H = \frac{k}{\rho c}$, where $k$ is thermal conductivity ($\text{W/(m}\cdot\text{K)}$), $\rho$ is density ($\text{kg/m}^3$), and $c$ is specific heat capacity ($\text{J/(kg}\cdot\text{K)}$).

Shear Plane Velocity ($V_s$)

The kinematic velocity of the workpiece material shearing along the primary shear plane, calculated as $V_s = \frac{V \cos(\alpha)}{\cos(\phi - \alpha)}$, where $V$ is the cutting speed.

Primary Shear Strain ($\gamma$)

The total shear strain imparted to the material within the primary shear zone, defined analytically as $\gamma = \frac{\cos(\alpha)}{\cos(\phi - \alpha) \sin(\phi)}$.

Jaeger's Heat Partition Ratio ($R_1$)

The proportion of total thermal energy generated in the primary shear zone that flows into the chip (typically between $60\%$ and $80\%$), derived from Jaeger's moving heat source theory as $R_1 = \frac{1}{1 + 1.328 \left(\frac{H \gamma}{V t}\right)^{1/2}}$.