FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Residual Stress in Fully Plastic Torsion Formula

Fx Copy

LaTeX Copy

Residual Shear Stress in fully Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress. Check FAQs

ζ f_res = 𝞽 nonlinear - \frac{2 \cdot π \cdot 𝞽 nonlinear \cdot {r 2}^{3} \cdot (1 - {(\frac{r 1}{r 2})}^{3}) \cdot r}{3 \cdot \frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

ζ_{f_res} - Residual Shear Stress in fully Plastic Yielding?𝞽_nonlinear - Yield Shear Stress(non-linear)?r₂ - Outer Radius of Shaft?r₁ - Inner Radius of Shaft?r - Radius Yielded?π - Archimedes' constant?

Residual Stress in Fully Plastic Torsion Example

With values

With units

Only example

Here is how the Residual Stress in Fully Plastic Torsion equation looks like with Values.

Here is how the Residual Stress in Fully Plastic Torsion equation looks like with Units.

Here is how the Residual Stress in Fully Plastic Torsion equation looks like.

40.5172 = 175 - \frac{2 \cdot 3.1416 \cdot 175 \cdot 100^{3} \cdot (1 - {(\frac{40}{100})}^{3}) \cdot 60}{3 \cdot \frac{3.1416}{2} \cdot (100^{4} - 40^{4})}

40.5172MPa = 175MPa - \frac{2 \cdot 3.1416 \cdot 175MPa \cdot {100mm}^{3} \cdot (1 - {(\frac{40mm}{100mm})}^{3}) \cdot 60mm}{3 \cdot \frac{3.1416}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

40.5172 = 175 - \frac{2 \cdot 3.1416 \cdot 175 \cdot 100^{3} \cdot (1 - {(\frac{40}{100})}^{3}) \cdot 60}{3 \cdot \frac{3.1416}{2} \cdot (100^{4} - 40^{4})}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Plasticity » fx Residual Stress in Fully Plastic Torsion

Residual Stress in Fully Plastic Torsion Solution

Follow our step by step solution on how to calculate Residual Stress in Fully Plastic Torsion?

FIRST Step Consider the formula

ζ f_res = 𝞽 nonlinear - \frac{2 \cdot π \cdot 𝞽 nonlinear \cdot {r 2}^{3} \cdot (1 - {(\frac{r 1}{r 2})}^{3}) \cdot r}{3 \cdot \frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

Next Step Substitute values of Variables

∴

ζ f_res = 175MPa - \frac{2 \cdot π \cdot 175MPa \cdot {100mm}^{3} \cdot (1 - {(\frac{40mm}{100mm})}^{3}) \cdot 60mm}{3 \cdot \frac{π}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

Next Step Substitute values of Constants

∴

ζ f_res = 175MPa - \frac{2 \cdot 3.1416 \cdot 175MPa \cdot {100mm}^{3} \cdot (1 - {(\frac{40mm}{100mm})}^{3}) \cdot 60mm}{3 \cdot \frac{3.1416}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

Next Step Convert Units

∴

ζ f_res = 1.8E+8Pa - \frac{2 \cdot 3.1416 \cdot 1.8E+8Pa \cdot {0.1m}^{3} \cdot (1 - {(\frac{0.04m}{0.1m})}^{3}) \cdot 0.06m}{3 \cdot \frac{3.1416}{2} \cdot ({0.1m}^{4} - {0.04m}^{4})}

Next Step Prepare to Evaluate

∴

ζ f_res = 1.8E+8 - \frac{2 \cdot 3.1416 \cdot 1.8E+8 \cdot {0.1}^{3} \cdot (1 - {(\frac{0.04}{0.1})}^{3}) \cdot 0.06}{3 \cdot \frac{3.1416}{2} \cdot ({0.1}^{4} - {0.04}^{4})}

Next Step Evaluate

∴

ζ f_res = 40517241.3793103Pa

Next Step Convert to Output's Unit

∴

ζ f_res = 40.5172413793103MPa

LAST Step Rounding Answer

∴

ζ f_res = 40.5172MPa

Residual Stress in Fully Plastic Torsion Formula Elements

Variables

Constants

Residual Shear Stress in fully Plastic Yielding

Residual Shear Stress in fully Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress.

Symbol: ζ_{f_res}

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Residual Shear Stress in fully Plastic Yielding

Yield Shear Stress(non-linear)

Yield Shear Stress(non-linear) is the shear stress above the yield point.

Symbol: 𝞽_nonlinear

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Shear Stress(non-linear)

Outer Radius of Shaft

Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material.

Symbol: r₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Shaft

Inner Radius of Shaft

Inner Radius of Shaft is the internal radius of a shaft, which is a critical dimension in mechanical engineering, affecting stress concentrations and structural integrity.

Symbol: r₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Radius of Shaft

Radius Yielded

Radius Yielded is the remaining stress in a material after the original cause of the stress has been removed, affecting its structural integrity and durability.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius Yielded

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Residual Stresses for Non Linear Stress Strain Law category

Go Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant

ζ ep_res = 𝞽 nonlinear \cdot {(\frac{r}{ρ})}^{n} - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

Go Residual Stress in Elasto Plastic Torsion when r lies between Constant and r2

ζ ep_res = 𝞽 nonlinear - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

How to Evaluate Residual Stress in Fully Plastic Torsion?

Residual Stress in Fully Plastic Torsion evaluator uses Residual Shear Stress in fully Plastic Yielding = Yield Shear Stress(non-linear)-(2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)*Radius Yielded)/(3*pi/2*(Outer Radius of Shaft^4-Inner Radius of Shaft^4)) to evaluate the Residual Shear Stress in fully Plastic Yielding, Residual Stress in Fully Plastic Torsion formula is defined as a measure of the remaining stress in a material after it has been subjected to plastic deformation, specifically in the context of torsion, where the material is twisted beyond its elastic limit. Residual Shear Stress in fully Plastic Yielding is denoted by ζ_{f_res} symbol.

How to evaluate Residual Stress in Fully Plastic Torsion using this online evaluator? To use this online evaluator for Residual Stress in Fully Plastic Torsion, enter Yield Shear Stress(non-linear) (𝞽_nonlinear), Outer Radius of Shaft (r₂), Inner Radius of Shaft (r₁) & Radius Yielded (r) and hit the calculate button.

FAQs on Residual Stress in Fully Plastic Torsion

What is the formula to find Residual Stress in Fully Plastic Torsion?

The formula of Residual Stress in Fully Plastic Torsion is expressed as Residual Shear Stress in fully Plastic Yielding = Yield Shear Stress(non-linear)-(2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)*Radius Yielded)/(3*pi/2*(Outer Radius of Shaft^4-Inner Radius of Shaft^4)). Here is an example- 4.1E-5 = 175000000-(2*pi*175000000*0.1^3*(1-(0.04/0.1)^3)*0.06)/(3*pi/2*(0.1^4-0.04^4)).

How to calculate Residual Stress in Fully Plastic Torsion?

With Yield Shear Stress(non-linear) (𝞽_nonlinear), Outer Radius of Shaft (r₂), Inner Radius of Shaft (r₁) & Radius Yielded (r) we can find Residual Stress in Fully Plastic Torsion using the formula - Residual Shear Stress in fully Plastic Yielding = Yield Shear Stress(non-linear)-(2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)*Radius Yielded)/(3*pi/2*(Outer Radius of Shaft^4-Inner Radius of Shaft^4)). This formula also uses Archimedes' constant .

Can the Residual Stress in Fully Plastic Torsion be negative?

Yes, the Residual Stress in Fully Plastic Torsion, measured in Stress can be negative.

Which unit is used to measure Residual Stress in Fully Plastic Torsion?

Residual Stress in Fully Plastic Torsion is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Residual Stress in Fully Plastic Torsion can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Residual Stress in Fully Plastic Torsion Formula

Residual Stress in Fully Plastic Torsion Example

Residual Stress in Fully Plastic Torsion Solution

Residual Stress in Fully Plastic Torsion Formula Elements

Other formulas in Residual Stresses for Non Linear Stress Strain Law category

How to Evaluate Residual Stress in Fully Plastic Torsion?

FAQs on Residual Stress in Fully Plastic Torsion

Variable Name