Residual Stress In Fully Plastic Torsion Calculator

Formula Used:

\[ \zeta_{f\_res} = \tau_{nonlinear} - \frac{2\pi \cdot \tau_{nonlinear} \cdot r_2^3 \cdot \left(1 - \left(\frac{r_1}{r_2}\right)^3\right) \cdot r}{\frac{3\pi}{2} \cdot (r_2^4 - r_1^4)} \]

Yield Shear Stress (non-linear):

Outer Radius of Shaft:

Inner Radius of Shaft:

Radius Yielded:

Residual Shear Stress in fully Plastic Yielding:

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1. What is Residual Stress In Fully Plastic Torsion?

Residual Stress In Fully Plastic Torsion refers to the stress that remains in a material after it has been subjected to torsion beyond its yield point and then unloaded. This residual stress can significantly affect the material's future performance and fatigue life.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \zeta_{f\_res} = \tau_{nonlinear} - \frac{2\pi \cdot \tau_{nonlinear} \cdot r_2^3 \cdot \left(1 - \left(\frac{r_1}{r_2}\right)^3\right) \cdot r}{\frac{3\pi}{2} \cdot (r_2^4 - r_1^4)} \]

Where:

\( \zeta_{f\_res} \) — Residual Shear Stress in fully Plastic Yielding (Pa)
\( \tau_{nonlinear} \) — Yield Shear Stress (non-linear) (Pa)
\( r_2 \) — Outer Radius of Shaft (m)
\( r_1 \) — Inner Radius of Shaft (m)
\( r \) — Radius Yielded (m)

Explanation: The formula calculates the residual shear stress by subtracting the plastic component from the applied yield stress, accounting for the geometry of the shaft and the extent of yielding.

3. Importance of Residual Stress Calculation

Details: Accurate calculation of residual stress is crucial for predicting the behavior of components under subsequent loading, assessing fatigue life, and ensuring structural integrity in engineering applications involving torsion beyond the elastic limit.

4. Using the Calculator

Tips: Enter all values in consistent units (Pa for stress, m for radii). Ensure 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 the significance of residual stress in torsion?
A: Residual stress affects the shaft's load-carrying capacity, fatigue resistance, and potential for crack propagation in subsequent service.

Q2: How does this differ from elastic torsion calculations?
A: This formula accounts for plastic deformation, where stress redistribution occurs beyond the yield point, unlike elastic calculations which assume reversible deformation.

Q3: When is this calculation most relevant?
A: This is particularly important for components that experience overload conditions or are designed to operate in the plastic range for specific applications.

Q4: Are there limitations to this equation?
A: The equation assumes ideal plastic behavior, homogeneous material properties, and may not account for strain hardening effects in all materials.

Q5: How can residual stress be measured experimentally?
A: Techniques include X-ray diffraction, hole-drilling method, and ultrasonic measurements, though these are more complex than analytical calculations.