How to Measure True Strain and Engineering Strain Using Strain Gauges: Understanding Stress and Strain in Solid Mechanics

In the field of solid mechanics, understanding the behavior of materials under stress is crucial for engineering design and analysis. One of the key measurements in this process is strain, which can be measured using strain gauges. This article delves into the methodology of measuring true strain and engineering strain through the use of strain gauges, highlighting the importance of accurate measurement in the realm of stress and strain analysis.

Introduction to Strain Gauges and Their Function

Strain gauges are small devices that are used to measure the deformation or strain of a material when an external force is applied. They are essentially resistive transducers that convert mechanical strain into an electrical signal, which can then be measured and analyzed. The principle behind strain gauges is quite simple, yet their applications are extensive across various industries, including aerospace, automotive, and civil engineering.

Basic Principle of Strain Gauge Operation

When a strain gauge is bonded to a material, the deformation caused by an applied load results in a change in the physical dimensions of the gauge. This change in dimensions, in turn, causes a change in the resistance of the gauge. The change in resistance can be quantified and used to determine the strain in the material. The relationship between strain and change in resistance can be expressed by the following equation:

Strain (ε) ΔR/R k * εe

Where:

ε is the strain ΔR is the change in resistance R is the original resistance value k is the gauge factor (a measure of the change in resistance per unit strain) εe is the engineering strain

True Strain vs. Engineering Strain

While both true strain and engineering strain are measures of deformation, they are calculated differently and are used in different contexts. Engineering strain is a simpler concept and is used in most practical applications. However, true strain is more accurate and provides a better representation of the material's deformation under varying conditions.

Engineering Strain

Engineering strain, often denoted as εe, is a straightforward measure of strain that is commonly used in practical applications. It is defined as the change in length divided by the original length, as shown:

εe (ΔL/L0) / L0

Where:

ΔL is the change in length L0 is the original length

Engineering strain is useful in many practical applications due to its simplicity and ease of calculation. However, it does not account for the effects of plastic deformation and can lead to inaccuracies under certain conditions.

True Strain

True strain, denoted as εt, is a more accurate and comprehensive measure of deformation that takes into account the logarithmic change in length. It is defined as:

εt ln(L / L0)

Where:

L is the current length L0 is the original length

True strain is preferred in cases where the material undergoes significant deformation and where accounting for plastic strain is important. It provides a more accurate representation of the material's behavior under various loading conditions.

Measuring Strain Using Strain Gauges

The process of measuring strain using strain gauges involves several steps, including the application of the gauge to the material, the measurement of resistance changes, and the interpretation of the results.

Application of the Strain Gage

Gluing a strain gauge to the material is the first step. This is typically done using a specialized adhesive that ensures the gauge remains securely bonded to the material. The gauge is placed at strategic points on the material to capture the desired strain measurements. The orientation and placement of the gauge can significantly impact the accuracy of the results, making it crucial to choose the appropriate location.

Measurement of Resistance Changes

Once the strain gauge is installed, the resistance across the gauge is measured using a Wheatstone bridge circuit. The change in resistance is a direct measurement of the strain in the material. This is achieved by connecting the strain gauge to a strain measuring device, which can be a simple multimeter or a more sophisticated electronic strain measurement system.

Data Interpretation and Analysis

The resistance changes are converted into strain values using the gauge factor and other relevant parameters. The strain data can then be analyzed to obtain engineering strain or true strain, depending on the specific requirements of the application. This data can be used to understand the behavior of the material under different loading conditions and to predict its structural integrity.

Using Strain Rosettes for Comprehensive Strain Measurement

To gain a complete picture of the strain state in a material, it is often necessary to measure both normal and shear strains. For this purpose, strain rosettes are used. A strain rosette consists of a group of three strain gauges bonded to the material, typically placed at 45° or 60° to each other. By measuring the strain in multiple directions, these rosettes provide a more comprehensive understanding of the strain state in the material.

Types of Strain Rosettes

There are two common types of strain rosettes:

45° Strain Rosette: In this configuration, the three strain gauges are placed at 45° to each other, allowing for the measurement of both normal and shear strains. 60° Strain Rosette: In this configuration, the three strain gauges are placed at 60° to each other, also capable of measuring both normal and shear strains.

Interpreting Strain Rosette Data

The data from a strain rosette can be used to calculate the strain state at the rosette location. This involves using the three measured strains to solve for the principal strains and the angle of rotation. The principal strains and the angle of rotation can then be used to determine the complete state of strain in the material. This information is invaluable for understanding the structural behavior and predicting the failure of the material under various loading conditions.

Conclusion

Measuring strain using strain gauges is a fundamental technique in solid mechanics and engineering. Whether in the context of true strain or engineering strain, accurate strain measurement is essential for ensuring the structural integrity of materials. By understanding the principles behind strain gauge operation and strain rosette configurations, engineers can make informed decisions and design reliable structures that withstand various loading conditions.

For more information on advanced applications and methodologies in stress and strain analysis, refer to the resources provided below.