Fundamentals of Plane Strain (PST) Testing

Engineering products are designed for more than just looking nice- they often need to be strong enough for the application. But a component can only be as strong as the materials that make it up. Engineers must choose the appropriate materials to build their products, and to do that, they need to know the material properties. This is where material testing comes in.

Materials can be subjected to a wide variety of tests to determine their suitability for applications. This article will focus on a specific type of material test called a plane strain tension (PST) test. We will explore the basics of plane strain testing, including theory, equipment, methods, results, and testing standards.

Definition of Plane Strain

Plane strain is a condition where all deformation (and thus all strain) occurs in a plane. In other words, strain only occurs in two dimensions out of three. This is not the case in most common types of testing. For example, in the popular uniaxial tension test, a long thin “dogbone” specimen is pulled apart along a single axis. The volume of the material does not change during this process, which means that the material must become thinner as it stretches along its length. This thinning effect can easily be observed in soft foods such as taffy and string cheese, but the constant-volume principle applies even to the strongest metals. When stretched, materials tend to become thinner both widthwise and depthwise. Thinning is a negative strain. Thus, a standard tension test involves positive strain along the tensile axis and negative strain in the other two axes. The goal of a plane strain tension test is to minimize thinning along the width of a material sample. This causes all strain to occur along two axes: lengthwise (positive strain/stretching) and depthwise (negative strain/thinning), fulfilling the plane strain condition.

Relevance: Why Plane Strain Testing?

Plane strain tension (PST) is one of three common tensile loading types, along with uniaxial tension (UT) and balanced biaxial tension (BBT). Though some tests, such as FLC, are designed to study material behavior under all these conditions, the plane strain condition can be of particular interest. Most real-world applications of plane strain involve tubes of various kinds being subject to pressure from within. Long pipes filled with pressurized fluid are the most common examples of this. Pressurized pipes are extremely relevant in numerous fields, from the automotive sector to power plant design to air conditioning systems. To ensure the effectiveness of these pipes and the machines that rely on them, engineers must be able to predict how parts will behave under plane strain.

Plane Strain Testing Equipment and Methods

As stated above, plane strain tension testing seeks to minimize thinning along the width of a material sample. Fortunately, this can be done with the same methods and machines as other common tests. The key is to realize that widthwise strain can be minimized simply by changing the shape of the material sample. This allows PST testing to use the same equipment setups as the ubiquitous uniaxial tension and FLC tests. Depending on which equipment is available, either of these setups may be used.

The primary piece of equipment for standard tension testing is the universal tester or pull tester. This machine is oriented vertically, with two grips to hold the material specimen at both ends. The bottom grip is static, while the top grip moves upward during the test, anchored by the crosshead. The crosshead is a beam that can only move up or down; the speed of a test can be expressed by referring to the “crosshead speed.” Crosshead movement is tightly controlled by the machine’s drive system, which in turn is controlled by electronics and dedicated test control software. The control software typically directs the crosshead to move upward at a constant speed, though other control methods such as strain rate control can be used.

In contrast, formability testing requires a machine capable of providing clamping and punching forces. The most common options are the Universal Formability Tester (UFT) and the dual-acting hydraulic press. These are discussed in more detail in our article on Formability Testing.

PST testing can also be performed using hydraulic bulge methods. These replace the mechanical punch in formability testing machines with a fluid pressure chamber, which is compressed by the machine piston. The sample is made to bulge outward through a shaped die because of the increasing pressure in the fluid chamber below it.

Sensors are also crucial for any material test. Though PST testing using the standard tensile setup can utilize traditional extensometers, it is important to verify that widthwise strain is close to zero. However, this task is made very difficult with extensometers due to spatial constraints. For this reason, digital image correlation (DIC) is the best choice for strain sensing for PST.
For DIC, the test piece is painted in a speckle pattern and the entire test is filmed using one or more cameras. The DIC software can compare the later images to the initial “reference” image and calculate the displacement (or strain) over the painted surface. This method also makes it easy to calculate lengthwise and widthwise strain in the same region, a great advantage for PST testing.

Plane Strain Testing Sample Geometry

Sample design is the key to successful PST testing. Depending on the equipment setup used, samples will look very different.
For PST using tension testing machines, the material sample shares some similarity to the standard dogbone shape. However, instead of a long parallel region, the sample features curved notches. During testing, this curvature prevents the notches from thinning in the way a dogbone sample would.

PST with formability testers can utilize several different sample geometries, depending on the type of formability method being used. For testing with a mechanical punch, the usual FLC sample geometries are appropriate. The PST point for an FLC is usually somewhere near the middle of the curve, thus requiring a sample with a middling height-to-width ratio. The exact dimensions vary depending on the material, but these can be determined with a little experimentation.

For hydraulic bulge PST testing, the sample is a simple square sheet of material; instead, the shape of the bulging die is the crucial factor. PST dies are long and narrow, essentially replicating the effect of a pressurized pipe section.

Plane Strain Testing Results

Using data from the test sensors, a PST stress strain curve can be determined for the material. Like the more common tensile stress-strain curve, the PST curve plots the stress in the material at every time during the test against the measured strain at that time.

However, stress-strain curves derived from plane strain conditions will look very different to those derived from uniaxial loading, even for the same material.Knowledge of the relevant Load/Displacement curves can be very useful when engineers work with materials that are expected to undergo plane strain conditions.

Plane Strain Testing Standards

Though no standards currently cover PST testing in full, multiple standards do exist which pertain to the testing methods and setups often adapted for PST. ISO 6892 and ASTM E8 regulate tension testing, ISO 12004 regulates FLC testing, and ISO 16808 regulates hydraulic bulge testing.