Lamb Wave
Fundamental symmetric mode of ultrasonic vibration propagates through the plane of a thin material by expanding and contracting the thickness. The s0 mode is used in paper testing to measure the in-plane elastic properties such as the Young modulus and the shear modulus. It is characterized by particle motion that is primarily parallel to the direction of wave travel.
This wave type is less sensitive to surface conditions than other modes.
Material Property
Speed of this specific vibration remains relatively constant at low frequencies, making it a reliable indicator of fibre bonding. In a laboratory setting, the s0 mode is generated by a non-contact laser or a dry-coupled transducer to avoid damaging the paper sample. The velocity of the wave is directly proportional to the square root of the ratio of stiffness to density.
By measuring the speed in various directions, researchers can map the orientation of the fibres and the anisotropy of the sheet. Because the wave occupies the entire thickness, it provides a volumetric average of the material strength rather than just a surface measurement. This is particularly useful for heavy boards where the internal structure might differ from the liners.
The data collected helps in predicting how the box will perform under stacking loads.
Defect Detection
Interruptions in the wave path indicate the presence of internal flaws such as cracks, holes, or regions of low density. The s0 mode travels long distances with minimal energy loss, allowing for the inspection of large areas of a paper web. It can identify delamination in multi-ply boards where the layers have failed to bond correctly.
This early detection prevents the production of sub-standard material that would fail during the printing or converting process.