Residual Stress in Fully Plastic Torsion Calculator

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Residual Stresses for Non-Linear stress strain Law

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Residual Stresses in Plastic Bending

✖Yield Shear Stress(non-linear) is the shear stress above the yield point.ⓘ Yield Shear Stress(non-linear) [𝞽_nonlinear]			+10% -10%
✖Outer Radius of Shaft is the external radius of shaft.ⓘ Outer Radius of Shaft [r₂]			+10% -10%
✖Inner Radius of Shaft is the internal radius of shaft.ⓘ Inner Radius of Shaft [r₁]			+10% -10%
✖Radius Yielded is the yielded portion of shaft under load.ⓘ Radius Yielded [r]			+10% -10%

✖Residual Shear Stress in fully Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress.ⓘ Residual Stress in Fully Plastic Torsion [ζ_{f_res}]

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Formula

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Residual Stress in Fully Plastic Torsion

Formula

`"ζ"_{"f_res"} = "𝞽"_{"nonlinear"}-(2*pi*"𝞽"_{"nonlinear"}*"r"_{"2"}^3*(1-("r"_{"1"}/"r"_{"2"})^3)*"r")/(3*pi/2*("r"_{"2"}^4-"r"_{"1"}^4))`

Example

`"40.51724MPa"="175MPa"-(2*pi*"175MPa"*("100mm")^3*(1-("40mm"/"100mm")^3)*"60mm")/(3*pi/2*(("100mm")^4-("40mm")^4))`

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Residual Stress in Fully Plastic Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
ζ_{f_res} = 𝞽_nonlinear-(2*pi*𝞽_nonlinear*r₂^3*(1-(r₁/r₂)^3)*r)/(3*pi/2*(r₂^4-r₁^4))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Residual Shear Stress in fully Plastic Yielding - (Measured in Pascal) - Residual Shear Stress in fully Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress.
Yield Shear Stress(non-linear) - (Measured in Pascal) - Yield Shear Stress(non-linear) is the shear stress above the yield point.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.
Inner Radius of Shaft - (Measured in Meter) - Inner Radius of Shaft is the internal radius of shaft.
Radius Yielded - (Measured in Meter) - Radius Yielded is the yielded portion of shaft under load.

STEP 1: Convert Input(s) to Base Unit

Yield Shear Stress(non-linear): 175 Megapascal --> 175000000 Pascal (Check conversion here)
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion here)
Inner Radius of Shaft: 40 Millimeter --> 0.04 Meter (Check conversion here)
Radius Yielded: 60 Millimeter --> 0.06 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ_{f_res} = 𝞽_nonlinear-(2*pi*𝞽_nonlinear*r₂^3*(1-(r₁/r₂)^3)*r)/(3*pi/2*(r₂^4-r₁^4)) --> 175000000-(2*pi*175000000*0.1^3*(1-(0.04/0.1)^3)*0.06)/(3*pi/2*(0.1^4-0.04^4))

Evaluating ... ...

ζ_{f_res} = 40517241.3793103

STEP 3: Convert Result to Output's Unit

40517241.3793103 Pascal -->40.5172413793103 Megapascal (Check conversion here)

FINAL ANSWER

40.5172413793103 ≈ 40.51724 Megapascal <-- Residual Shear Stress in fully Plastic Yielding

(Calculation completed in 00.020 seconds)

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< 3 Residual Stresses for Non-Linear stress strain Law Calculators

Residual Stress in Fully Plastic Torsion

Go 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))

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

Go Residual Shear Stress in Elasto Plastic Yielding = Yield Shear Stress(non-linear)*(Radius Yielded/Radius of Plastic Front)^Material Constant-(Elasto Plastic Yielding Torque*Radius Yielded)/(pi/2*(Outer Radius of Shaft^4-Inner Radius of Shaft^4))

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

Go Residual Shear Stress in Elasto Plastic Yielding = Yield Shear Stress(non-linear)-(Elasto Plastic Yielding Torque*Radius Yielded)/(pi/2*(Outer Radius of Shaft^4-Inner Radius of Shaft^4))

Residual Stress in Fully Plastic Torsion Formula

How residual stresses are generated in shafts?

When a shaft is twisted, it starts yielding once the shear stress crosses its yield limit. Torque applied may be elasto-plastic or fully plastic. This process is called LOADING. When the shaft so twisted is applied with a torque of same magnitude in the opposite direction, then the recovery of stress takes place. This process is called UNLOADING. The process of UNLOADING is always assumed to be elastic following a linear stress-strain relation. But for a plastically twisted shaft, the recovery doesn’t take place fully. Therefore some amount of stresses are left over or locked. Such stresses are called the residual stresses.

How to Calculate Residual Stress in Fully Plastic Torsion?

Residual Stress in Fully Plastic Torsion calculator 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 calculate the Residual Shear Stress in fully Plastic Yielding, The Residual Stress in fully plastic torsion formula is defined as the algebraic sum of applied stress and recovery stress. Residual Shear Stress in fully Plastic Yielding is denoted by ζ_{f_res} symbol.

How to calculate Residual Stress in Fully Plastic Torsion using this online calculator? To use this online calculator 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. Here is how the Residual Stress in Fully Plastic Torsion calculation can be explained with given input values -> 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)).

FAQ

What is Residual Stress in Fully Plastic Torsion?

The Residual Stress in fully plastic torsion formula is defined as the algebraic sum of applied stress and recovery stress and is represented as ζ_{f_res} = 𝞽_nonlinear-(2*pi*𝞽_nonlinear*r₂^3*(1-(r₁/r₂)^3)*r)/(3*pi/2*(r₂^4-r₁^4)) or 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)). Yield Shear Stress(non-linear) is the shear stress above the yield point, Outer Radius of Shaft is the external radius of shaft, Inner Radius of Shaft is the internal radius of shaft & Radius Yielded is the yielded portion of shaft under load.

How to calculate Residual Stress in Fully Plastic Torsion?

The Residual Stress in fully plastic torsion formula is defined as the algebraic sum of applied stress and recovery stress is calculated using 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 calculate Residual Stress in Fully Plastic Torsion, you need Yield Shear Stress(non-linear) (𝞽_nonlinear), Outer Radius of Shaft (r₂), Inner Radius of Shaft (r₁) & Radius Yielded (r). With our tool, you need to enter the respective value for Yield Shear Stress(non-linear), Outer Radius of Shaft, Inner Radius of Shaft & Radius Yielded 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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