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

✖Yield Shear Stress(non-linear) is the shear stress above the yield point.ⓘ Yield Shear Stress(non-linear) [𝞽_nonlinear]			+10% -10%
✖Radius Yielded is the remaining stress in a material after the original cause of the stress has been removed, affecting its structural integrity and durability.ⓘ Radius Yielded [r]			+10% -10%
✖Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses.ⓘ Radius of Plastic Front [ρ]			+10% -10%
✖Material Constant is a measure of the internal stresses that remain within a material after the original cause of the stress has been removed.ⓘ Material Constant [n]			+10% -10%
✖Elasto Plastic Yielding Torque is the torque required to initiate plastic deformation in a material, affecting its residual stresses and overall mechanical properties.ⓘ Elasto Plastic Yielding Torque [T_ep]			+10% -10%
✖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%
✖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%

✖Residual Shear Stress in Elasto Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress.ⓘ Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant [ζ_{ep_res}]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
ζ_{ep_res} = 𝞽_nonlinear*(r/ρ)^n-(T_ep*r)/(pi/2*(r₂^4-r₁^4))
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Residual Shear Stress in Elasto Plastic Yielding - (Measured in Pascal) - Residual Shear Stress in Elasto 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.
Radius Yielded - (Measured in Meter) - Radius Yielded is the remaining stress in a material after the original cause of the stress has been removed, affecting its structural integrity and durability.
Radius of Plastic Front - (Measured in Meter) - Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses.
Material Constant - Material Constant is a measure of the internal stresses that remain within a material after the original cause of the stress has been removed.
Elasto Plastic Yielding Torque - (Measured in Newton Meter) - Elasto Plastic Yielding Torque is the torque required to initiate plastic deformation in a material, affecting its residual stresses and overall mechanical properties.
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.
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

Yield Shear Stress(non-linear): 175 Megapascal --> 175000000 Pascal (Check conversion here)
Radius Yielded: 60 Millimeter --> 0.06 Meter (Check conversion here)
Radius of Plastic Front: 80 Millimeter --> 0.08 Meter (Check conversion here)
Material Constant: 0.25 --> No Conversion Required
Elasto Plastic Yielding Torque: 257000000 Newton Millimeter --> 257000 Newton Meter (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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ_{ep_res} = 𝞽_nonlinear*(r/ρ)^n-(T_ep*r)/(pi/2*(r₂^4-r₁^4)) --> 175000000*(0.06/0.08)^0.25-(257000*0.06)/(pi/2*(0.1^4-0.04^4))

Evaluating ... ...

ζ_{ep_res} = 62109987.3511997

STEP 3: Convert Result to Output's Unit

62109987.3511997 Pascal -->62.1099873511997 Megapascal (Check conversion here)

FINAL ANSWER

62.1099873511997 ≈ 62.10999 Megapascal <-- Residual Shear Stress in Elasto Plastic Yielding

(Calculation completed in 00.020 seconds)

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< Residual Stresses for Non Linear Stress Strain Law Calculators

Residual Stress in Fully Plastic Torsion

LaTeX 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

LaTeX 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

LaTeX 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 Elasto Plastic Torsion when r Lies between r1 and Constant Formula

LaTeX Go

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 Elasto Plastic Torsion when r Lies between r1 and Constant?

Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant calculator uses 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)) to calculate the Residual Shear Stress in Elasto Plastic Yielding, Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant formula is defined as a measure of the remaining stress in a material after it has been subjected to plastic deformation, which can affect its mechanical properties and behavior. Residual Shear Stress in Elasto Plastic Yielding is denoted by ζ_{ep_res} symbol.

How to calculate Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant using this online calculator? To use this online calculator for Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant, enter Yield Shear Stress(non-linear) (𝞽_nonlinear), Radius Yielded (r), Radius of Plastic Front (ρ), Material Constant (n), Elasto Plastic Yielding Torque (T_ep), Outer Radius of Shaft (r₂) & Inner Radius of Shaft (r₁) and hit the calculate button. Here is how the Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant calculation can be explained with given input values -> 6.2E-5 = 175000000*(0.06/0.08)^0.25-(257000*0.06)/(pi/2*(0.1^4-0.04^4)).

FAQ

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

Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant formula is defined as a measure of the remaining stress in a material after it has been subjected to plastic deformation, which can affect its mechanical properties and behavior and is represented as ζ_{ep_res} = 𝞽_nonlinear*(r/ρ)^n-(T_ep*r)/(pi/2*(r₂^4-r₁^4)) or 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)). Yield Shear Stress(non-linear) is the shear stress above the yield point, Radius Yielded is the remaining stress in a material after the original cause of the stress has been removed, affecting its structural integrity and durability, Radius of Plastic Front is the distance from the center of the material to the point where plastic deformation occurs due to residual stresses, Material Constant is a measure of the internal stresses that remain within a material after the original cause of the stress has been removed, Elasto Plastic Yielding Torque is the torque required to initiate plastic deformation in a material, affecting its residual stresses and overall mechanical properties, Outer Radius of Shaft is the distance from the center of the shaft to its outer surface, affecting residual stresses in the material & 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 Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant?

Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant formula is defined as a measure of the remaining stress in a material after it has been subjected to plastic deformation, which can affect its mechanical properties and behavior is calculated using 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)). To calculate Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant, you need Yield Shear Stress(non-linear) (𝞽_nonlinear), Radius Yielded (r), Radius of Plastic Front (ρ), Material Constant (n), Elasto Plastic Yielding Torque (T_ep), Outer Radius of Shaft (r₂) & Inner Radius of Shaft (r₁). With our tool, you need to enter the respective value for Yield Shear Stress(non-linear), Radius Yielded, Radius of Plastic Front, Material Constant, Elasto Plastic Yielding Torque, Outer Radius of Shaft & 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.

How many ways are there to calculate Residual Shear Stress in Elasto Plastic Yielding?

In this formula, Residual Shear Stress in Elasto Plastic Yielding uses Yield Shear Stress(non-linear), Radius Yielded, Radius of Plastic Front, Material Constant, Elasto Plastic Yielding Torque, Outer Radius of Shaft & Inner Radius of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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