Residual Stress In Elasto Plastic Torsion When R Lies Between Constant And R2 Calculator

Formula Used:

\[ \zeta_{ep\_res} = \tau_{nonlinear} - \frac{T_{ep} \times r}{\frac{\pi}{2} \times (r_2^4 - r_1^4)} \]

Yield Shear Stress (non-linear):

Pascal

Elasto Plastic Yielding Torque:

Newton Meter

Radius Yielded:

Meter

Outer Radius of Shaft:

Meter

Inner Radius of Shaft:

Meter

Residual Shear Stress in Elasto Plastic Yielding:

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1. What is Residual Shear Stress in Elasto Plastic Yielding?

Residual Shear Stress in Elasto Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress. It represents the stress that remains in a material after the original cause of the stress has been removed.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \zeta_{ep\_res} = \tau_{nonlinear} - \frac{T_{ep} \times r}{\frac{\pi}{2} \times (r_2^4 - r_1^4)} \]

Where:

\( \zeta_{ep\_res} \) — Residual Shear Stress in Elasto Plastic Yielding (Pascal)
\( \tau_{nonlinear} \) — Yield Shear Stress (non-linear) (Pascal)
\( T_{ep} \) — Elasto Plastic Yielding Torque (Newton Meter)
\( r \) — Radius Yielded (Meter)
\( r_2 \) — Outer Radius of Shaft (Meter)
\( r_1 \) — Inner Radius of Shaft (Meter)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the residual shear stress in elasto-plastic yielding by subtracting the stress component due to applied torque from the yield shear stress.

3. Importance of Residual Stress Calculation

Details: Accurate calculation of residual stresses is crucial for understanding material behavior under load, predicting fatigue life, and ensuring structural integrity in mechanical components subjected to torsional loads.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that the outer radius is greater than the inner radius, and all values are positive. The radius yielded should be between the inner and outer radii.

5. Frequently Asked Questions (FAQ)

Q1: What is elasto-plastic yielding?
A: Elasto-plastic yielding occurs when a material experiences both elastic and plastic deformation simultaneously, with some portions yielding plastically while others remain elastic.

Q2: When is this formula applicable?
A: This formula is specifically applicable when the radius lies between a constant value and the outer radius (r2) in torsional loading scenarios.

Q3: What are typical units for these measurements?
A: Stress is typically measured in Pascals (Pa), torque in Newton-meters (N·m), and radii in meters (m).

Q4: How does residual stress affect material performance?
A: Residual stresses can significantly affect fatigue life, corrosion resistance, and dimensional stability of mechanical components.

Q5: Can this calculator be used for hollow shafts?
A: Yes, this formula and calculator are specifically designed to handle both solid and hollow shafts by accounting for both inner and outer radii.