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Recovery Elasto Plastic Torque Formula

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Recovery Elasto Plastic Torque is the torque required to recover the elastic deformation of a material after plastic deformation, indicating residual stresses. Check FAQs

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})))

T_rec - Recovery Elasto Plastic Torque?𝝉₀ - Yield Stress in Shear?ρ - Radius of Plastic Front?r₁ - Inner Radius of Shaft?r₂ - Outer Radius of Shaft?π - Archimedes' constant?

Recovery Elasto Plastic Torque Example

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Here is how the Recovery Elasto Plastic Torque equation looks like with Values.

Here is how the Recovery Elasto Plastic Torque equation looks like with Units.

Here is how the Recovery Elasto Plastic Torque equation looks like.

-257526821.7903 = - (3.1416 \cdot 145 \cdot (\frac{80^{3}}{2} \cdot (1 - {(\frac{40}{80})}^{4}) + (\frac{2}{3} \cdot 100^{3}) \cdot (1 - {(\frac{80}{100})}^{3})))

-257526821.7903N*mm = - (3.1416 \cdot 145MPa \cdot (\frac{{80mm}^{3}}{2} \cdot (1 - {(\frac{40mm}{80mm})}^{4}) + (\frac{2}{3} \cdot {100mm}^{3}) \cdot (1 - {(\frac{80mm}{100mm})}^{3})))

-257526821.7903 = - (3.1416 \cdot 145 \cdot (\frac{80^{3}}{2} \cdot (1 - {(\frac{40}{80})}^{4}) + (\frac{2}{3} \cdot 100^{3}) \cdot (1 - {(\frac{80}{100})}^{3})))

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Recovery Elasto Plastic Torque Solution

Follow our step by step solution on how to calculate Recovery Elasto Plastic Torque?

FIRST Step Consider the formula

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})))

Next Step Substitute values of Variables

∴

T rec = - (π \cdot 145MPa \cdot (\frac{{80mm}^{3}}{2} \cdot (1 - {(\frac{40mm}{80mm})}^{4}) + (\frac{2}{3} \cdot {100mm}^{3}) \cdot (1 - {(\frac{80mm}{100mm})}^{3})))

Next Step Substitute values of Constants

∴

T rec = - (3.1416 \cdot 145MPa \cdot (\frac{{80mm}^{3}}{2} \cdot (1 - {(\frac{40mm}{80mm})}^{4}) + (\frac{2}{3} \cdot {100mm}^{3}) \cdot (1 - {(\frac{80mm}{100mm})}^{3})))

Next Step Convert Units

∴

T rec = - (3.1416 \cdot 1.5E+8Pa \cdot (\frac{{0.08m}^{3}}{2} \cdot (1 - {(\frac{0.04m}{0.08m})}^{4}) + (\frac{2}{3} \cdot {0.1m}^{3}) \cdot (1 - {(\frac{0.08m}{0.1m})}^{3})))

Next Step Prepare to Evaluate

∴

T rec = - (3.1416 \cdot 1.5E+8 \cdot (\frac{{0.08}^{3}}{2} \cdot (1 - {(\frac{0.04}{0.08})}^{4}) + (\frac{2}{3} \cdot {0.1}^{3}) \cdot (1 - {(\frac{0.08}{0.1})}^{3})))

Next Step Evaluate

∴

T rec = -257526.821790267N*m

Next Step Convert to Output's Unit

∴

T rec = -257526821.790267N*mm

LAST Step Rounding Answer

∴

T rec = -257526821.7903N*mm

Recovery Elasto Plastic Torque Formula Elements

Variables

Constants

Recovery Elasto Plastic Torque

Recovery Elasto Plastic Torque is the torque required to recover the elastic deformation of a material after plastic deformation, indicating residual stresses.

Symbol: T_rec

Measurement: TorqueUnit: N*mm

Note: Value can be positive or negative.

Formulas to find Recovery Elasto Plastic Torque

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

Radius of Plastic Front

Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses.

Symbol: ρ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Plastic Front

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

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

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 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})})

Go Residual Angle of Twist for Elasto Plastic Case

θ res = \frac{𝝉 0}{G \cdot ρ} \cdot (1 - (\frac{4 \cdot ρ}{3 \cdot r 2}) \cdot (\frac{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}}{1 - {(\frac{r 1}{r 2})}^{4}}))

How to Evaluate Recovery Elasto Plastic Torque?

Recovery Elasto Plastic Torque evaluator uses Recovery Elasto Plastic Torque = -(pi*Yield Stress in Shear*(Radius of Plastic Front^3/2*(1-(Inner Radius of Shaft/Radius of Plastic Front)^4)+(2/3*Outer Radius of Shaft^3)*(1-(Radius of Plastic Front/Outer Radius of Shaft)^3))) to evaluate the Recovery Elasto Plastic Torque, Recovery Elasto Plastic Torque formula is defined as a measure of the residual stress-induced torque that occurs in a material after it has undergone plastic deformation, providing a way to quantify the internal stresses that remain in the material after deformation has ceased. Recovery Elasto Plastic Torque is denoted by T_rec symbol.

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

FAQs on Recovery Elasto Plastic Torque

What is the formula to find Recovery Elasto Plastic Torque?

The formula of Recovery Elasto Plastic Torque is expressed as Recovery Elasto Plastic Torque = -(pi*Yield Stress in Shear*(Radius of Plastic Front^3/2*(1-(Inner Radius of Shaft/Radius of Plastic Front)^4)+(2/3*Outer Radius of Shaft^3)*(1-(Radius of Plastic Front/Outer Radius of Shaft)^3))). Here is an example- -257526821790.267 = -(pi*145000000*(0.08^3/2*(1-(0.04/0.08)^4)+(2/3*0.1^3)*(1-(0.08/0.1)^3))).

How to calculate Recovery Elasto Plastic Torque?

With Yield Stress in Shear (𝝉₀), Radius of Plastic Front (ρ), Inner Radius of Shaft (r₁) & Outer Radius of Shaft (r₂) we can find Recovery Elasto Plastic Torque using the formula - Recovery Elasto Plastic Torque = -(pi*Yield Stress in Shear*(Radius of Plastic Front^3/2*(1-(Inner Radius of Shaft/Radius of Plastic Front)^4)+(2/3*Outer Radius of Shaft^3)*(1-(Radius of Plastic Front/Outer Radius of Shaft)^3))). This formula also uses Archimedes' constant .

Can the Recovery Elasto Plastic Torque be negative?

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

Which unit is used to measure Recovery Elasto Plastic Torque?

Recovery Elasto Plastic Torque 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 Elasto Plastic Torque can be measured.

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Recovery Elasto Plastic Torque Formula

Recovery Elasto Plastic Torque Example

Recovery Elasto Plastic Torque Solution

Recovery Elasto Plastic Torque Formula Elements

Other formulas in Residual Stresses For Idealized Stress Strain Law category

How to Evaluate Recovery Elasto Plastic Torque?

FAQs on Recovery Elasto Plastic Torque

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