Mechanical Stress
Mathematical construct describing the three-dimensional deformation of a material caused by temperature changes. The thermal strain tensor captures the expansion or contraction in all directions as a function of the coefficient of thermal expansion and the temperature gradient. It provides a complete map of internal displacement for structural analysis.
Calculation Matrix
Integration of the local temperature change with the material properties yields the individual components of the matrix. A thermal strain tensor for an anisotropic material, such as a carbon fiber composite, shows different expansion rates along each axis. These values are used to predict the warping or cracking of components during thermal cycling.
Measurement Verification
Optical strain gauges and digital image correlation verify the predicted deformations in a laboratory setting. Because the thermal strain tensor is sensitive to the rate of heating, the test environment must be carefully controlled to prevent transient thermal gradients. Comparison with the theoretical model reveals inconsistencies in material density or bonding.
Plastic Boundary
Plastic deformation occurs when the thermal load exceeds the elastic limit of the material. In this regime, the thermal strain tensor no longer returns to zero when the temperature is restored to the reference state. Residual stresses remain locked in the structure, potentially leading to premature failure in high-precision sensor housings or semiconductor packages.
