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

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

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Residual Shear Stress in Elasto Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress. Check FAQs

ζ ep_res = 𝞽 nonlinear \cdot {(\frac{r}{ρ})}^{n} - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

ζ_{ep_res} - Residual Shear Stress in Elasto Plastic Yielding?𝞽_nonlinear - Yield Shear Stress(non-linear)?r - Radius Yielded?ρ - Radius of Plastic Front?n - Material Constant?T_ep - Elasto Plastic Yielding Torque?r₂ - Outer Radius of Shaft?r₁ - Inner Radius of Shaft?π - Archimedes' constant?

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

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Here is how the Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant equation looks like with Values.

Here is how the Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant equation looks like with Units.

Here is how the Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant equation looks like.

62.11 = 175 \cdot {(\frac{60}{80})}^{0.25} - \frac{2.6E+8 \cdot 60}{\frac{3.1416}{2} \cdot (100^{4} - 40^{4})}

62.11MPa = 175MPa \cdot {(\frac{60mm}{80mm})}^{0.25} - \frac{2.6E+8N*mm \cdot 60mm}{\frac{3.1416}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

62.11 = 175 \cdot {(\frac{60}{80})}^{0.25} - \frac{2.6E+8 \cdot 60}{\frac{3.1416}{2} \cdot (100^{4} - 40^{4})}

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

Follow our step by step solution on how to calculate Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant?

FIRST Step Consider the formula

ζ ep_res = 𝞽 nonlinear \cdot {(\frac{r}{ρ})}^{n} - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

Next Step Substitute values of Variables

∴

ζ ep_res = 175MPa \cdot {(\frac{60mm}{80mm})}^{0.25} - \frac{2.6E+8N*mm \cdot 60mm}{\frac{π}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

Next Step Substitute values of Constants

∴

ζ ep_res = 175MPa \cdot {(\frac{60mm}{80mm})}^{0.25} - \frac{2.6E+8N*mm \cdot 60mm}{\frac{3.1416}{2} \cdot ({100mm}^{4} - {40mm}^{4})}

Next Step Convert Units

∴

ζ ep_res = 1.8E+8Pa \cdot {(\frac{0.06m}{0.08m})}^{0.25} - \frac{257000N*m \cdot 0.06m}{\frac{3.1416}{2} \cdot ({0.1m}^{4} - {0.04m}^{4})}

Next Step Prepare to Evaluate

∴

ζ ep_res = 1.8E+8 \cdot {(\frac{0.06}{0.08})}^{0.25} - \frac{257000 \cdot 0.06}{\frac{3.1416}{2} \cdot ({0.1}^{4} - {0.04}^{4})}

Next Step Evaluate

∴

ζ ep_res = 62109987.3511997Pa

Next Step Convert to Output's Unit

∴

ζ ep_res = 62.1099873511997MPa

LAST Step Rounding Answer

∴

ζ ep_res = 62.11MPa

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

Variables

Constants

Residual Shear Stress in Elasto Plastic Yielding

Residual Shear Stress in Elasto Plastic Yielding can be defined as the algebraic sum of applied stress and recovery stress.

Symbol: ζ_{ep_res}

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Residual Shear Stress in Elasto Plastic Yielding

Yield Shear Stress(non-linear)

Yield Shear Stress(non-linear) is the shear stress above the yield point.

Symbol: 𝞽_nonlinear

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Shear Stress(non-linear)

Radius Yielded

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.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius Yielded

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

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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Material Constant

Elasto Plastic Yielding Torque

Elasto Plastic Yielding Torque is the torque required to initiate plastic deformation in a material, affecting its residual stresses and overall mechanical properties.

Symbol: T_ep

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Elasto Plastic Yielding Torque

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

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

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 to find Residual Shear Stress in Elasto Plastic Yielding

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

ζ ep_res = 𝞽 nonlinear - \frac{T ep \cdot r}{\frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

Other formulas in Residual Stresses for Non Linear Stress Strain Law category

Go Residual Stress in Fully Plastic Torsion

ζ f_res = 𝞽 nonlinear - \frac{2 \cdot π \cdot 𝞽 nonlinear \cdot {r 2}^{3} \cdot (1 - {(\frac{r 1}{r 2})}^{3}) \cdot r}{3 \cdot \frac{π}{2} \cdot ({r 2}^{4} - {r 1}^{4})}

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant using this online evaluator? To use this online evaluator 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.

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

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

The formula of Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant is expressed as 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)). Here is an example- 6.2E-5 = 175000000*(0.06/0.08)^0.25-(257000*0.06)/(pi/2*(0.1^4-0.04^4)).

How to calculate Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant?

With 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) we can find Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant using the formula - 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)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Residual Shear Stress in Elasto Plastic Yielding?

Here are the different ways to Calculate Residual Shear Stress in Elasto Plastic Yielding-

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))

Can the Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant be negative?

Yes, the Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant, measured in Stress can be negative.

Which unit is used to measure 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 is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant can be measured.

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

​GoResidual Stress in Elasto Plastic Torsion when r lies between Constant and r2 Formula

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

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

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

Other Formulas to find Residual Shear Stress in Elasto Plastic Yielding

Other formulas in Residual Stresses for Non Linear Stress Strain Law category

How to Evaluate Residual Stress in Elasto Plastic Torsion when r Lies between r1 and Constant?

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

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