ASTM E111 Test for Young’s Modulus, Tangent Modulus, and Chord Modulus

Introduction

ASTM E111 determines Young’s modulus, tangent modulus, and chord modulus of structural materials. This test method is limited to materials in which creep deformation is negligible compared to the strain (deformation) produced immediately upon loading. The values are in SI units.

Scope

The ASTM E111 test method determines a material’s stress-strain curve. This curve shows the relationship between stress, strain, load, and deformation and reveals many properties, such as yield strength and Young’s modulus.

Linear stress-strain curve 

When a small load is applied, a solid material undergoes elastic deformation. Elastic deformation is reversible, meaning the material returns to its original shape after removing the load.

The stress-strain curve remains linear at low stress and strain. Hooke’s law describes the linear relationship between stress and strain, which states stress is proportional to strain. The coefficient of proportionality is Young’s modulus. The higher the modulus, the more stress is needed to create the same strain; an idealized rigid body will have an infinite Young’s modulus. Conversely, a very soft material such as fluid would deform without force and have zero Young’s modulus. Not many materials are linear and elastic beyond a small amount of deformation.

Non-linear stress-strain curve

For materials that follow non-linear elastic stress-strain behavior, the tangent or chord modulus value helps estimate the change in strain for a specified range of stress.

Test Procedure

In the ASTM E111 test, the specimen is cleaned and measured. Then, the technicians install the sample on the fixture and apply a uniaxial force. The force and strain are measured either incrementally or continuously. The axial stress is determined by dividing the indicated force by the specimen’s original cross-sectional area. The appropriate slope is then calculated from the stress-strain curve, which may be derived under increasing or decreasing forces.

Specimen Size

For ASTM E111 testing, the specimen length should exceed the minimum requirements for general-purpose specimens. The length ratio to the cross-section of compression specimens should be such as to avoid buckling. The ends should be flat, parallel, and perpendicular to the lateral surfaces for compression specimens.

Advantages and Disadvantages of ASTM E111

The advantages and disadvantages of ASTM E111 are as follows.

Data

The stress-strain diagram for a particular material is reported. Young’s tangent and chord modulus are derived from the stress-strain curve.

Modulus of Elasticity calculation for the ASTM E111 test:

E = modulus of elasticity

Result

The ASTM E111 test method determines a material’s stress-strain curve and provides its modulus of elasticity.

Conclusion

Understanding the stress-strain properties of any material through ASTM E111 testing dramatically improves its quality and durability. Because it accurately measures Young’s modulus, tangent modulus, and chord modulus, this method gives significant information about how a particular material will act under stress, thus allowing for an optimized design and performance of structural components. This information is essential in achieving safety and durability standards, ensuring the material’s reliability in realistic conditions. Additionally, ASTM E111 testing stimulates the innovation of new materials and technologies by providing material selection and design knowledge for progress. It also predicts how materials behave under different stress conditions -including extreme environments- to ensure long-term functionality and integrity.

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