When a material is subjected to an external force, it responds by changing its shape or size, a process known as deformation. While the total amount of deformation is a crucial metric, the speed at which this change occurs is often equally important in predicting a material’s performance. The strain rate quantifies the rate of change in an object’s shape.
Understanding Strain and Deformation
Before calculating the speed of deformation, it is necessary to define the deformation itself, which is referred to as strain (\(\epsilon\)). Strain is a measure of the relative change in a material’s dimensions when a force is applied. For simple stretching or compression, it is calculated as the ratio of the change in length to the original length of the material. Because it is a ratio of two lengths, strain is a dimensionless quantity, meaning it has no units.
Strain is the effect of stress, which is the internal force acting within a body per unit of cross-sectional area. Stress is the cause (the external load applied), while strain represents the resulting change in shape. A material can undergo various types of deformation, including tensile strain (stretching), compressive strain (shortening), and shear strain (twisting or sliding).
Calculating the Strain Rate
The strain rate (\(\dot{\epsilon}\)) is defined as the speed at which strain accumulates within a material over time. Mathematically, it represents the time derivative of the strain. The formula for calculating strain rate is therefore expressed using differential calculus as \(\dot{\epsilon} = d\epsilon / dt\).
In this expression, \(d\epsilon\) represents an infinitesimal change in strain, and \(dt\) represents the corresponding infinitesimal change in time over which that strain occurs. Since strain is dimensionless, the unit of strain rate is determined solely by the time component. The standard unit for strain rate in the International System of Units is inverse seconds, denoted as \(s^{-1}\).
For practical engineering measurements over a defined interval, the formula is often simplified to an average rate: \(\dot{\epsilon} = \Delta\epsilon / \Delta t\). Here, \(\Delta\epsilon\) is the total change in strain over a measurable time period, \(\Delta t\). A numerical value of \(0.01\ s^{-1}\), for example, indicates that the material is deforming by 1% of its current size every second.
Physical Significance of Strain Rate Measurement
Measuring the strain rate is important because the mechanical properties of materials are sensitive to how quickly they are deformed. For instance, testing a material at a low strain rate, such as \(10^{-6}\ s^{-1}\), might simulate long-term creep or slow loading.
Conversely, testing at high strain rates, such as \(10^2\ s^{-1}\) or higher, simulates dynamic events like car crashes or explosive impacts. Many materials, including metals like steel and aluminum, exhibit an increase in yield strength when the strain rate is high. This means they require more force to begin deforming plastically, but they may also lose some of their ability to stretch before fracturing.
In some cases, a material that is normally ductile and pliable under slow loading can fail in a brittle manner if the force is applied very quickly. Polymers, for example, might stretch and absorb energy during a slow tensile test, but could shatter during a high-speed impact. Understanding this rate-dependent behavior is necessary for designing components that must withstand both sustained loads and sudden impacts.