Battery knowledge · Thermal management and heat transfer

Thermal stress

Mechanical stress caused by a temperature change when a part cannot expand freely or is joined to a material that expands differently. A fully restrained aluminium bar warmed by 50 K would carry about 80 MPa. Repeated cycles fatigue welds, solder joints and adhesive bonds, which is what thermal shock testing sets out to provoke.

Unit
Pa
Relationship
σ = E·α·ΔT

Example

Compare free and constrained expansion

An illustrative fully constrained linear elastic material with E = 2 GPa, expansion coefficient 50×10⁻⁶/K and ΔT = 20 K has EαΔT = 2 MPa. A freely expanding part does not develop this stress from uniform heating alone.

Explore the graph

A fully restrained linear elastic bar develops stress proportional to temperature change.

Restrained stress magnitude
Restrained stress magnitudeTemperature-change magnitude (K) versus Stress magnitude (MPa). Elastic full-restraint estimate. Interpretation follows the graphs.0032.22064.44096.66012980Temperature-change magnitude (K)Stress magnitude (MPa)
Elastic full-restraint estimate

A 50 K change gives 80.5 MPa in this ideal fully restrained model.

|σ| = E α |ΔT| for full uniaxial restraint

Illustrative model. Constant E and α, small strain, no yielding or relaxation. Heating creates compression and cooling tension in a fully restrained bar.

Use in Lemonergy

Select spatial detail for the question.

This is a reference concept. No executable Lemonergy block has been verified for this term.

References & further reading

Further reading on this topic

These sources provide broader context; they are not presented as citations for every statement in this entry.

  1. A General Energy Balance for Battery Systems

    Dawn Bernardi, Ellen Pawlikowski, John Newman · Journal of The Electrochemical Society · 1985

    Topic background · Battery energy balance and irreversible and reversible heat contributions. Reduced thermal models require explicit assumptions and current-sign conventions.

  2. University Physics Volume 2, §1.6: Mechanisms of Heat Transfer

    OpenStax, Rice University

    Topic background · Conduction, convection, radiation and thermal resistance.