Commonly Used Testing Techniques in the Biomechanics Core
Uniaxial testingis atest in which a sample is subjected to a uniaxial force until failure. The uniaxial force can be applied as either a tension or a compression. During these tests, the forceapplied to the specimen is recorded as a function of displacement between the grips of the testing machine. Properties that can be directly measured via a uniaxial test are ultimate tensile/compressive strength, change in specimen length,and change in cross-sectional area.From these measurements the stress, strain, and Young’s Modulus (elasticity) of the specimen can be calculated.
The force measurement is used to calculate the stress using the following equation:
where F is the force and A is the cross-sectional area of the specimen.
The following equation is used with this to calculate strain:
where delta Lis the change in length of the specimen; L0is the initial length of the specimen, and L is the final length.
The data points from these calculations can be graphed into a stress-strain curve, and the slope of the linear portion of this curve represents the Young’s Modulus (E) of the material. A typical stress-strain plot for a material that is tested to failure looks like this:
Figure 1: A typical stress-strain curve for a homogenous material that is tested to failure (X). The slope of the linear portion of the curve represents the Young’s Modulus (E).
Uniaxial Tension with Polarized Light:
When examining the tendons of small animals, polarized light can be used during tensile testing to elucidate collagen fiber organization and alignment as a function of load. The birefringence of aligned collagen provides different amounts of illumination when exposed to varying degrees of polarized light. The intensity of illumination can be quantified for the entire tendon, which is correlated to the organization of the collagen within the tendon. Examples of tendons that are exposed to polarized light during tensile testing and under a microscope can be seen above.
Three and Four Point Bending:
Flexural strength, or bend strength, is defined as a material's ability to resist deformation under load. The flexural strength represents the highest stress experienced within the material at its moment of rupture. It is measured in terms of stress. Three and four point bend tests are commonly used to determine the flexural strength of a specimen.
When a specimen is bent, it experiences a range of stresses across its depth. At the edge of the concave face of the specimen (point A), the stress will be at its maximum compressive value. At the convex face of the specimen (point B), the stress will be at its maximum tensile value. Most materials fail under tensile stress before they fail under compressive stress, so the maximum tensile stress value that can be sustained before the specimen fails is its flexural strength. The flexural strength would be the same as thetensile strength if the material were homogeneous. In the case of bones, the complex structure and small defects within the specimen serve to concentrate stresses locally, effectively causing localized weaknesses and lower flexural strength values.
The mechanics that dictate bending tests rely heavily upon the geometry of the specimen. For example, rectangular specimens are treated differently than cylindrical ones. The arrangement of the testing apparatus (three-point or four-point bend, distance between supports, etc.) also influences the calculation of the beam mechanics. For more in-depth detail, click the links below to see step-by-step calculations that are made during bend tests:
In many cases, the mechanical properties of cartilage change, based on its anatomical location. For example, the thickness and elastic modulus of cartilage within the shoulder joint are not uniform throughout. We can elucidate the properties of the tissue with two assays: 1) high frequency ultrasound; and 2) mechanical testing with a spherical probe.
High Frequency Ultrasound: Ultrasound probes used during pregnancy typically have a frequency that ranges between 1.6 -10 MHz. The probes that are used to measure the thickness of cartilage in a small animal must be able to make very fine measurements, and therefore have a much higher frequency, around 55 MHz. In order for measurements to be made, the specimen is submerged into a bath of phosphate buffered saline solution and protease inhibitors, and the specimen is scanned in planes that are 0.25 mm apart. The resulting series of images are then segmented and the thickness of the cartilage can be measured. The images can then be stitched together to create a map of cartilage thickness, as seen in the example below.
Figure 2: An ultrasound map of cartilage thickness in the shoulder of a rat. The regions of the glenoid are outlined as superior (S), anterior superior (AS), posterior superior (PS), central (C), anterior inferior (AI), and posterior inferior (PI).
Compression Testing: Spherical-tipped probes can be used in conjunction with a uniaxial testing machine to determine the elastic modulus of the cartilage of a specimen. Briefly, the probe can be pressed into various regions of the specimen at a constant rate of displacement. The resulting force-displacement curve can be used to determine the local elasticity of the cartilage. The moduli of the cartilage are subject to change based on factors such as anatomical location and amount of loading the joint experiences on a regular basis. An example of probe placement within a rat glenoid can be seen below.
Figure 3: Example of spherical probe locations in a rat shoulder specimen. The regions of the glenoid are outlined as superior (S), anterior superior (AS), posterior superior (PS), central (C), anterior inferior (AI), and posterior inferior (PI).