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Recovery Torque in Fully Plastic Case Formula

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Fully Plastic Recovery Torque is the torque required to recover the plastic deformation of a material, indicating the residual stresses present in the material. Check FAQs

T f_rec = - (\frac{2}{3} \cdot π \cdot {r 2}^{3} \cdot 𝝉 0 \cdot (1 - {(\frac{r 1}{r 2})}^{3}))

T_{f_rec} - Fully Plastic Recovery Torque?r₂ - Outer Radius of Shaft?𝝉₀ - Yield Stress in Shear?r₁ - Inner Radius of Shaft?π - Archimedes' constant?

Recovery Torque in Fully Plastic Case Example

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Here is how the Recovery Torque in Fully Plastic Case equation looks like with Values.

Here is how the Recovery Torque in Fully Plastic Case equation looks like with Units.

Here is how the Recovery Torque in Fully Plastic Case equation looks like.

-284251303.2968 = - (\frac{2}{3} \cdot 3.1416 \cdot 100^{3} \cdot 145 \cdot (1 - {(\frac{40}{100})}^{3}))

-284251303.2968N*mm = - (\frac{2}{3} \cdot 3.1416 \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{3}))

-284251303.2968 = - (\frac{2}{3} \cdot 3.1416 \cdot 100^{3} \cdot 145 \cdot (1 - {(\frac{40}{100})}^{3}))

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Recovery Torque in Fully Plastic Case Solution

Follow our step by step solution on how to calculate Recovery Torque in Fully Plastic Case?

FIRST Step Consider the formula

T f_rec = - (\frac{2}{3} \cdot π \cdot {r 2}^{3} \cdot 𝝉 0 \cdot (1 - {(\frac{r 1}{r 2})}^{3}))

Next Step Substitute values of Variables

∴

T f_rec = - (\frac{2}{3} \cdot π \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{3}))

Next Step Substitute values of Constants

∴

T f_rec = - (\frac{2}{3} \cdot 3.1416 \cdot {100mm}^{3} \cdot 145MPa \cdot (1 - {(\frac{40mm}{100mm})}^{3}))

Next Step Convert Units

∴

T f_rec = - (\frac{2}{3} \cdot 3.1416 \cdot {0.1m}^{3} \cdot 1.5E+8Pa \cdot (1 - {(\frac{0.04m}{0.1m})}^{3}))

Next Step Prepare to Evaluate

∴

T f_rec = - (\frac{2}{3} \cdot 3.1416 \cdot {0.1}^{3} \cdot 1.5E+8 \cdot (1 - {(\frac{0.04}{0.1})}^{3}))

Next Step Evaluate

∴

T f_rec = -284251.303296805N*m

Next Step Convert to Output's Unit

∴

T f_rec = -284251303.296805N*mm

LAST Step Rounding Answer

∴

T f_rec = -284251303.2968N*mm

Recovery Torque in Fully Plastic Case Formula Elements

Variables

Constants

Fully Plastic Recovery Torque

Fully Plastic Recovery Torque is the torque required to recover the plastic deformation of a material, indicating the residual stresses present in the material.

Symbol: T_{f_rec}

Measurement: TorqueUnit: N*mm

Note: Value can be positive or negative.

Formulas to find Fully Plastic Recovery Torque

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

Yield Stress in Shear

Yield Stress in Shear is the yield stress of the shaft in shear conditions.

Symbol: 𝝉₀

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Stress in Shear

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

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 Idealized Stress Strain Law category

Go Recovery Elasto Plastic Torque

T rec = - (π \cdot 𝝉 0 \cdot (\frac{ρ^{3}}{2} \cdot (1 - {(\frac{r 1}{ρ})}^{4}) + (\frac{2}{3} \cdot {r 2}^{3}) \cdot (1 - {(\frac{ρ}{r 2})}^{3})))

Go Residual Shear Stress in Shaft when r Lies between r1 and Material Constant

ζ shaft_res = (𝝉 0 \cdot \frac{r}{ρ} - ((\frac{4 \cdot 𝝉 0 \cdot r}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})}) \cdot (1 - \frac{1}{4} \cdot {(\frac{ρ}{r 2})}^{3} - \frac{3 \cdot r 1}{4 \cdot ρ} \cdot {(\frac{r 1}{r 2})}^{3})))

Go Residual Shear Stress in Shaft when r Lies between Material Constant and r2

ζ shaft_res = 𝝉 0 \cdot (1 - \frac{4 \cdot r \cdot (1 - ((\frac{1}{4}) \cdot {(\frac{ρ}{r 2})}^{3}) - ((\frac{3 \cdot r 1}{4 \cdot ρ}) \cdot {(\frac{r 1}{r 2})}^{3}))}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})})

Go Residual Shear Stress in Shaft for Fully Plastic Case

ζ f_res = 𝝉 0 \cdot (1 - \frac{4 \cdot r \cdot (1 - {(\frac{r 1}{r 2})}^{3})}{3 \cdot r 2 \cdot (1 - {(\frac{r 1}{r 2})}^{4})})

How to Evaluate Recovery Torque in Fully Plastic Case?

Recovery Torque in Fully Plastic Case evaluator uses Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)) to evaluate the Fully Plastic Recovery Torque, Recovery Torque in Fully Plastic Case formula is defined as the torque required to recover the residual stresses in a fully plastic case, which is a critical parameter in understanding the mechanical behavior of materials under various loading conditions, particularly in the context of residual stresses. Fully Plastic Recovery Torque is denoted by T_{f_rec} symbol.

How to evaluate Recovery Torque in Fully Plastic Case using this online evaluator? To use this online evaluator for Recovery Torque in Fully Plastic Case, enter Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Inner Radius of Shaft (r₁) and hit the calculate button.

FAQs on Recovery Torque in Fully Plastic Case

What is the formula to find Recovery Torque in Fully Plastic Case?

The formula of Recovery Torque in Fully Plastic Case is expressed as Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)). Here is an example- -284251303296.805 = -(2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3)).

How to calculate Recovery Torque in Fully Plastic Case?

With Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Inner Radius of Shaft (r₁) we can find Recovery Torque in Fully Plastic Case using the formula - Fully Plastic Recovery Torque = -(2/3*pi*Outer Radius of Shaft^3*Yield Stress in Shear*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)). This formula also uses Archimedes' constant .

Can the Recovery Torque in Fully Plastic Case be negative?

Yes, the Recovery Torque in Fully Plastic Case, measured in Torque can be negative.

Which unit is used to measure Recovery Torque in Fully Plastic Case?

Recovery Torque in Fully Plastic Case is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Recovery Torque in Fully Plastic Case can be measured.

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Recovery Torque in Fully Plastic Case Formula

Recovery Torque in Fully Plastic Case Example

Recovery Torque in Fully Plastic Case Solution

Recovery Torque in Fully Plastic Case Formula Elements

Other formulas in Residual Stresses For Idealized Stress Strain Law category

How to Evaluate Recovery Torque in Fully Plastic Case?

FAQs on Recovery Torque in Fully Plastic Case

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