Young’s Modulus, Tangent Modulus, and Chord Modulus

This blog post covers the description and determination of Young’s modulus, tangent modulus, and chord modulus. These properties, commonly used for product and material specification, can be calculated by subjecting a specimen to uniaxial force, measuring its stress and strain properties, and generating a stress-strain curve. The accuracy of the modulus determination depends on the precision of the load and strain measurements. A testing machine equipped with the appropriate grips and fixtures and a strain measurement device is required to measure Young’s modulus, tangent modulus, and chord modulus. Read the full blog post here.

Definitions

Chord modulus- Slope of the chord drawn between any two specified points on the stress-strain curve below the maximum stress a material can withstand without permanent strain upon release of the stress (elastic limit). Chord modulus calculations are recommended for non-linear materials.

C

Tangent modulus- Slope of the stress-strain curve at any specified stress or strain. Like chord modulus, tangent modulus calculations are recommended for non-linear materials.

T

Young’s modulus (E)- Ratio of tensile or compressive stress to the corresponding strain below the maximum stress a material can withstand without deviation from proportionality of stress to strain (proportional limit). Note that Young’s modulus in tension is different from Young’s modulus in compression.

Test Procedure

A simplified test procedure includes the steps below:

1. Prepare the test specimens following the steps in a standardized test method of choice.

2. For tension testing, mount the sample into the tensile grips and clamp the extensometer or the strain measurement device.

3. For compression testing, a compressometer may be used (see ASTM C469).

4. For bend testing, place the sample on a bend fixture with the strain measurement device of choice.

5. Start the test. The speed of testing should be low enough to avoid thermal effects of adiabatic expansion or contraction and should be high enough that creep will be negligible.

6. Record and graph stress versus strain (include specimen number, test data, rate, and other pertinent information).

Test Standards

Modulus calculations can be performed by running static tests, dynamic tests, wave propagation methods, as well as nanoindentation. The obtained modulus value will differ based on the method used. This blog post covers static testing. Common test standards to measure modulus include:

• ASTM A370 – Standard Test Methods and Definitions for Mechanical Testing of Steel Products
• ASTM C469 – Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression
• ASTM D638 – Standard Test Method for Tensile Properties of Plastics
• ASTM D790 – Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials
• ASTM D7291 – Standard Test Method for Through-Thickness Flatwise Tensile Strength and Elastic Modulus of a Fiber-Reinforced Polymer Matrix Composite Material
• ASTM E8 – Standard Test Methods for Tension Testing of Metallic Materials
• ASTM E111 – Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus
• ISO 6892-1:2019 Metallic materials — Tensile testing — Part 1: Method of test at room temperature

Points to Consider

• Measurement Accuracy and Test Equipment
  • When selecting test equipment, make sure a testing system with closed-loop control as well as a high-quality strain measurement device is selected for accurate modulus calculations.
  • Ensure measurement devices are properly calibrated and that the calibrated range covers the range that is used in the test.
  • Read more about ADMET ASTM Calibration How-To’s here.
• Specimen Selection & Size
  • Most often, larger specimens are required for modulus calculations which may be hard to obtain.
  • Standardized test methods can be used for specimen selection criteria, specimen preparation, and the recommended dimensions.
• Linear Portion of the Stress-Strain Curve
  • The straight-line or the linear part of the stress-strain curve, which is used to measure the modulus in a tensile test, may be hard to determine for some materials such as materials with high tensile residual stress with very low proportional limits.
  • Advanced testing systems with material testing software is available to automatically collect data from the linear portion of the stress-strain curve.
• Test Method to Follow
  • There are multiple standardized test methods to choose from to run modulus testing. The scope of each test method should be taken into account first prior to committing to a test. For example, ASTM E8 covers tensile testing of metallic materials in room temperature only while ASTM E111 covers both tensile and compressive testing in room temperatures, elevated, and sub-zero temperatures.
  • In addition, as mentioned earlier, although this post covers static testing, there are other test types such as dynamic testing, wave propagation and the nanoindentation technique to measure modulus values. Calculated values will be different even if the same sample is tested. As an example, the modulus of elasticity values obtained will usually be less than the modulus derived under a dynamic test given other test conditions being the same.
• Modified Environment Testing
  • Some methods require modification of the environment the specimen is loaded at. For example, if testing is run at high temperatures, it is important to ensure that an accurate value of the high-test temperature is kept constant throughout the testing.

Conclusion

The value of Young’s modulus is a material property useful in design for calculating compliance of structural materials that follow Hooke’s law when subjected to uniaxial loading. 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. There are a variety of test methods that can be followed to measure modulus values. These methods often require different test equipment. For a discussion on recommended equipment options, full blog post can be accessed here.