thermalstress

Thermal stress is the internal force that develops in a material when its temperature changes in a restrained state or when temperature is nonuniform across the body. If a material is free to expand or contract, no stress results; however, fixed supports, bonded interfaces, or geometric constraints prevent free strain, generating stress.

Causes and mechanisms include uniform temperature changes under constraint, leading to a stress proportional to the material’s elastic properties; nonuniform temperature distributions that create gradients and bending or warping; and differential thermal expansion between bonded materials or coatings, which creates interfacial stresses. In composites and multilayer structures, mismatches in the coefficient of thermal expansion (CTE) are a common source of thermal stress.

Theory and modeling often use the thermal strain epsilon_th = alpha * deltaT, where alpha is the coefficient of thermal expansion and deltaT is the temperature change. The total strain is the sum of mechanical and thermal strains, epsilon = epsilon_mech + epsilon_th, and stress follows constitutive relations (for linear isotropic materials, sigma = E * epsilon_mech). In fully constrained cases, epsilon_mech is zero and sigma ≈ E * alpha * deltaT. Real-world cases with gradients or complex geometries are analyzed with finite element methods or diagnostic experiments.

Implications include distortion, cracking, delamination, and altered fatigue life. Thermal stress is a consideration in ceramics and glass due to low fracture toughness, and in metals during rapid heating or cooling. Mitigation strategies include matching CTEs, designing with expansions in mind, controlled heating and cooling, and stress-relief annealing.