Recovery Elasto Plastic Torque Calculator

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Residual Stresses

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Residual Stresses For Idealized Stress Strain Law

Residual Stresses for Non-Linear stress strain Law

Residual Stresses for Non-Linear Stress Strain Relations

Residual Stresses in Plastic Bending

✖Yield Stress in Shear is the yield stress of the shaft in shear conditions.ⓘ Yield Stress in Shear [𝝉₀]			+10% -10%
✖Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.ⓘ Radius of Plastic Front [ρ]			+10% -10%
✖Inner Radius of Shaft is the internal radius of shaft.ⓘ Inner Radius of Shaft [r₁]			+10% -10%
✖Outer Radius of Shaft is the external radius of shaft.ⓘ Outer Radius of Shaft [r₂]			+10% -10%

✖Recovery Elasto Plastic Torque can be defined as Recovery torque is equal and opposite to the applied torque.ⓘ Recovery Elasto Plastic Torque [T_rec]

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Formula

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Recovery Elasto Plastic Torque

Formula

`"T"_{"rec"} = -(pi*"𝝉"_{"0"}*("ρ"^3/2*(1-("r"_{"1"}/"ρ")^4)+(2/3*"r"_{"2"}^3)*(1-("ρ"/"r"_{"2"})^3)))`

Example

`"-257526821.790267N*mm"=-(pi*"145MPa"*(("80mm")^3/2*(1-("40mm"/"80mm")^4)+(2/3*("100mm")^3)*(1-("80mm"/"100mm")^3)))`

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Recovery Elasto Plastic Torque Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
T_rec = -(pi*𝝉₀*(ρ^3/2*(1-(r₁/ρ)^4)+(2/3*r₂^3)*(1-(ρ/r₂)^3)))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Recovery Elasto Plastic Torque - (Measured in Newton Meter) - Recovery Elasto Plastic Torque can be defined as Recovery torque is equal and opposite to the applied torque.
Yield Stress in Shear - (Measured in Pascal) - Yield Stress in Shear is the yield stress of the shaft in shear conditions.
Radius of Plastic Front - (Measured in Meter) - Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically.
Inner Radius of Shaft - (Measured in Meter) - Inner Radius of Shaft is the internal radius of shaft.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.

STEP 1: Convert Input(s) to Base Unit

Yield Stress in Shear: 145 Megapascal --> 145000000 Pascal (Check conversion here)
Radius of Plastic Front: 80 Millimeter --> 0.08 Meter (Check conversion here)
Inner Radius of Shaft: 40 Millimeter --> 0.04 Meter (Check conversion here)
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_rec = -(pi*𝝉₀*(ρ^3/2*(1-(r₁/ρ)^4)+(2/3*r₂^3)*(1-(ρ/r₂)^3))) --> -(pi*145000000*(0.08^3/2*(1-(0.04/0.08)^4)+(2/3*0.1^3)*(1-(0.08/0.1)^3)))

Evaluating ... ...

T_rec = -257526.821790267

STEP 3: Convert Result to Output's Unit

-257526.821790267 Newton Meter -->-257526821.790267 Newton Millimeter (Check conversion here)

FINAL ANSWER

-257526821.790267 Newton Millimeter <-- Recovery Elasto Plastic Torque

(Calculation completed in 00.004 seconds)

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< 7 Residual Stresses For Idealized Stress Strain Law Calculators

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

Go Residual Shear Stress in Elasto Plastic Yielding = (Yield Stress in Shear*Radius Yielded/Radius of Plastic Front-(((4*Yield Stress in Shear*Radius Yielded)/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))*(1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)))

Residual Angle of Twist for Elasto Plastic Case

Go Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Radius of Plastic Front)*(1-((4*Radius of Plastic Front)/(3*Outer Radius of Shaft))*((1-1/4*(Radius of Plastic Front/Outer Radius of Shaft)^3-(3*Inner Radius of Shaft)/(4*Radius of Plastic Front)*(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))

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

Go Residual Shear Stress in Elasto Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-((1/4)*(Radius of Plastic Front/Outer Radius of Shaft)^3)-(((3*Inner Radius of Shaft)/(4*Radius of Plastic Front))*(Inner Radius of Shaft/Outer Radius of Shaft)^3)))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))

Residual Angle of Twist in Fully Plastic Case

Go Residual Angle of Twist = Yield Stress in Shear/(Modulus of Rigidity*Inner Radius of Shaft)*(1-(4*Inner Radius of Shaft)/(3*Outer Radius of Shaft)*((1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)/(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))

Recovery Elasto Plastic Torque

Go 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)))

Residual Shear Stress in Shaft for Fully Plastic Case

Go Residual Shear Stress in fully Plastic Yielding = Yield Stress in Shear*(1-(4*Radius Yielded*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3))/(3*Outer Radius of Shaft*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^4)))

Recovery Torque in Fully Plastic Case

Go 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))

Recovery Elasto Plastic Torque Formula

What is recovery torque?

Recovery torque is equal and opposite to the applied torque. when the load is removed it tries to recovers it's original shape.

How to Calculate Recovery Elasto Plastic Torque?

Recovery Elasto Plastic Torque calculator 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 calculate the Recovery Elasto Plastic Torque, The Recovery Elasto plastic Torque formula is defined as Recovery torque is equal and opposite to the applied torque. Recovery Elasto Plastic Torque is denoted by T_rec symbol.

How to calculate Recovery Elasto Plastic Torque using this online calculator? To use this online calculator 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. Here is how the Recovery Elasto Plastic Torque calculation can be explained with given input values -> -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))).

FAQ

What is Recovery Elasto Plastic Torque?

The Recovery Elasto plastic Torque formula is defined as Recovery torque is equal and opposite to the applied torque and is represented as T_rec = -(pi*𝝉₀*(ρ^3/2*(1-(r₁/ρ)^4)+(2/3*r₂^3)*(1-(ρ/r₂)^3))) or 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))). Yield Stress in Shear is the yield stress of the shaft in shear conditions, Radius of Plastic Front is the difference between the outer radius of shaft and depth yields plastically, Inner Radius of Shaft is the internal radius of shaft & Outer Radius of Shaft is the external radius of shaft.

How to calculate Recovery Elasto Plastic Torque?

The Recovery Elasto plastic Torque formula is defined as Recovery torque is equal and opposite to the applied torque is calculated using 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 calculate Recovery Elasto Plastic Torque, you need Yield Stress in Shear (𝝉₀), Radius of Plastic Front (ρ), Inner Radius of Shaft (r₁) & Outer Radius of Shaft (r₂). With our tool, you need to enter the respective value for Yield Stress in Shear, Radius of Plastic Front, Inner Radius of Shaft & Outer Radius of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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