Fundamentals of Plane Strain Testing (PST)

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.

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.

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.

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 stress-strain curves can be very useful when engineers work with materials that are expected to undergo plane strain conditions.