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

Scope:

ASTM E111 test method is used to determine the stress-strain curve of a material. A stress-strain curve gives the relationship between stress and strain, between load and deformation. These curves reveal many of the properties of a material, such as yield strength and Young’s modulus.

Linear stress-strain curve: 

The solid material will undergo elastic deformation when a small load is applied. Elastic deformation is reversible, meaning that the material returns to its original shape after the load is removed.

At very low stress and strain, the stress-strain curve is linear, and the linear relationship between stress and strain is described by Hooke’s law 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 amount of 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 will 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 nonlinear elastic stress-strain behavior, the value of tangent or chord modulus is useful in estimating the change in strain for a specified range in stress.

Test Procedure:

In the ASTM E111 test, the specimen is cleaned and measured. It is installed on the fixture. A uniaxial force is applied to the test specimen. 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 conditions of either increasing or decreasing forces. 

Video 01: An introduction to stress and strain

Specimen size:

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

Data:

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

Modulus of Elasticity calculation for the ASTM E111 test:

Conclusion:

ASTM E111 test method is used to determine the stress-strain curve of a material.