Recovery Torque in Fully Plastic Case Calculator

✖Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material.ⓘ Outer Radius of Shaft [r₂]			+10% -10%
✖Yield Stress in Shear is the yield stress of the shaft in shear conditions.ⓘ Yield Stress in Shear [𝝉₀]			+10% -10%
✖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.ⓘ Inner Radius of Shaft [r₁]			+10% -10%

✖Fully Plastic Recovery Torque is the torque required to recover the plastic deformation of a material, indicating the residual stresses present in the material.ⓘ Recovery Torque in Fully Plastic Case [T_{f_rec}]

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Recovery Torque in Fully Plastic Case Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
T_{f_rec} = -(2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Fully Plastic Recovery Torque - (Measured in Newton Meter) - Fully Plastic Recovery Torque is the torque required to recover the plastic deformation of a material, indicating the residual stresses present in the material.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material.
Yield Stress in Shear - (Measured in Pascal) - Yield Stress in Shear is the yield stress of the shaft in shear conditions.
Inner Radius of Shaft - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_{f_rec} = -(2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3)) --> -(2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3))

Evaluating ... ...

T_{f_rec} = -284251.303296805

STEP 3: Convert Result to Output's Unit

-284251.303296805 Newton Meter -->-284251303.296805 Newton Millimeter (Check conversion here)

FINAL ANSWER

-284251303.296805 Newton Millimeter <-- Fully Plastic Recovery Torque

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Plasticity » Residual Stresses » Mechanical » Residual Stresses For Idealized Stress Strain Law » Recovery Torque in Fully Plastic Case

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< Residual Stresses For Idealized Stress Strain Law Calculators

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

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

LaTeX Go Residual Shear Stress in Shaft = 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)))

Recovery Elasto Plastic Torque

LaTeX 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

LaTeX 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 Formula

LaTeX 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))
T_{f_rec} = -(2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3))

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 Torque in Fully Plastic Case?

Recovery Torque in Fully Plastic Case calculator 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 calculate 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 calculate Recovery Torque in Fully Plastic Case using this online calculator? To use this online calculator 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. Here is how the Recovery Torque in Fully Plastic Case calculation can be explained with given input values -> -284251303296.805 = -(2/3*pi*0.1^3*145000000*(1-(0.04/0.1)^3)).

FAQ

What is Recovery Torque in Fully Plastic Case?

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 and is represented as T_{f_rec} = -(2/3*pi*r₂^3*𝝉₀*(1-(r₁/r₂)^3)) or 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)). Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material, Yield Stress in Shear is the yield stress of the shaft in shear conditions & 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.

How to calculate Recovery Torque in Fully Plastic Case?

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 is calculated using 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 calculate Recovery Torque in Fully Plastic Case, you need Outer Radius of Shaft (r₂), Yield Stress in Shear (𝝉₀) & Inner Radius of Shaft (r₁). With our tool, you need to enter the respective value for Outer Radius of Shaft, Yield Stress in Shear & Inner 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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