Modulus of resilience Calculator

✖Yield strength can be defined as follows, a straight line is constructed parallel to elastic portion of stress–strain curve at strain offset of 0.002.ⓘ Yield Strength [σ_y]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%

✖Modulus of Resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.ⓘ Modulus of resilience [U_r]

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Modulus of resilience

Formula

`"U"_{"r"} = "σ"_{"y"}^2/(2*"E")`

Example

`"4.1E^7MPa"=("35N/mm²")^2/(2*"15N/m")`

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Modulus of resilience Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Resilience = Yield Strength^2/(2*Young's Modulus)
U_r = σ_y^2/(2*E)
This formula uses 3 Variables

Variables Used

Modulus of Resilience - (Measured in Pascal) - Modulus of Resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.
Yield Strength - (Measured in Pascal) - Yield strength can be defined as follows, a straight line is constructed parallel to elastic portion of stress–strain curve at strain offset of 0.002.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

STEP 1: Convert Input(s) to Base Unit

Yield Strength: 35 Newton per Square Millimeter --> 35000000 Pascal (Check conversion here)
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_r = σ_y^2/(2*E) --> 35000000^2/(2*15)

Evaluating ... ...

U_r = 40833333333333.3

STEP 3: Convert Result to Output's Unit

40833333333333.3 Pascal -->40833333.3333333 Megapascal (Check conversion here)

FINAL ANSWER

40833333.3333333 ≈ 4.1E+7 Megapascal <-- Modulus of Resilience

(Calculation completed in 00.004 seconds)

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Home » Engineering » Materials Science » Mechanical Behaviour and Testing » Failure Testing in Materials » Modulus of resilience

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Created by Hariharan V S

Indian Institute of Technology (IIT), Chennai

Hariharan V S has created this Calculator and 25+ more calculators!

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< 12 Failure Testing in Materials Calculators

Fracture toughness

Go Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length)

Critical stress for crack propagation

Go Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length))

Percent cold work

Go Percent cold work = 100*(Cross-sectional Area-Area after deformation)/Cross-sectional Area

Percent reduction in area

Go Percent reduction in area = (Cross-sectional Area-Fracture area)*100/Cross-sectional Area

Percent elongation

Go Percent elongation = (Fracture Length-Initial Length)*100/Initial Length

Stress concentration factor

Go Stress Concentration Factor = 2*sqrt(Crack Length/Radius of curvature)

Mean stress of stress cycle (fatigue)

Go Mean Stress of Stress Cycle = (Maximum Tensile Stress+Minimum compressive stress)/2

Maximum stress at crack tip

Go Maximum Stress at Crack Tip = Stress Concentration Factor*Applied stress

Range of stress (fatigue)

Go Range of stress = Maximum Tensile Stress-Minimum compressive stress

Stress ratio (fatigue)

Go Stress ratio = Minimum compressive stress/Maximum Tensile Stress

Modulus of resilience

Go Modulus of Resilience = Yield Strength^2/(2*Young's Modulus)

Stress amplitude (fatigue)

Go Stress Amplitude = Range of stress/2

Modulus of resilience Formula

Modulus of Resilience = Yield Strength^2/(2*Young's Modulus)
U_r = σ_y^2/(2*E)

Resilience

Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered.The associated property is the modulus of resilience. Materials with high modulus of resilience are used in spring applications.

How to Calculate Modulus of resilience?

Modulus of resilience calculator uses Modulus of Resilience = Yield Strength^2/(2*Young's Modulus) to calculate the Modulus of Resilience, Modulus of resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. Modulus of Resilience is denoted by U_r symbol.

How to calculate Modulus of resilience using this online calculator? To use this online calculator for Modulus of resilience, enter Yield Strength (σ_y) & Young's Modulus (E) and hit the calculate button. Here is how the Modulus of resilience calculation can be explained with given input values -> 40.83333 = 35000000^2/(2*15).

FAQ

What is Modulus of resilience?

Modulus of resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding and is represented as U_r = σ_y^2/(2*E) or Modulus of Resilience = Yield Strength^2/(2*Young's Modulus). Yield strength can be defined as follows, a straight line is constructed parallel to elastic portion of stress–strain curve at strain offset of 0.002 & Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

How to calculate Modulus of resilience?

Modulus of resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding is calculated using Modulus of Resilience = Yield Strength^2/(2*Young's Modulus). To calculate Modulus of resilience, you need Yield Strength (σ_y) & Young's Modulus (E). With our tool, you need to enter the respective value for Yield Strength & Young's Modulus 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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