Effect of shear angle magnitude on chip formation During orthogonal cutting, what happens when the shear angle is small in terms of shear path length and resulting chip thickness?

Introduction / Context:
The shear angle determines how a material deforms into a chip in orthogonal cutting. It controls chip thickness, cutting forces, and power consumption. Understanding its qualitative effects helps in selecting rake, speed, and lubrication to improve machinability.

Given Data / Assumptions:

• Orthogonal cutting model with a defined rake angle.
• Steady-state cutting without built-up edge for clarity.
• Comparing conditions with relatively smaller shear angles.

Concept / Approach:
Smaller shear angle implies the shear plane is oriented closer to the cutting direction, making the shear plane longer. A longer shear plane increases the area over which plastic deformation occurs, resulting in higher shear work and thicker chips for the same uncut chip thickness. Conversely, a larger shear angle shortens the shear plane and produces thinner chips and lower forces.

Step-by-Step Solution:
Decrease shear angle ⇒ shear plane tilts, path length increases.Increased shear plane length ⇒ greater deformation zone.Outcome ⇒ chip thickness increases while uncut thickness is unchanged.

Verification / Alternative check:
Classic cutting analysis shows chip thickness ratio r = t1 / t2 decreases when shear angle decreases, meaning chip thickness t2 grows for a given uncut thickness t1.

Why Other Options Are Wrong:
Short shear path with thin chip describes a larger shear angle. Short path with thick chip or long path with thin chip are internally inconsistent with the shear plane mechanics.

Common Pitfalls:
Confusing rake angle with shear angle; while related, it is the shear angle that directly governs chip compression ratio.

Final Answer:
Long shear path and thick chip