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In previous work on the thermo-mechanical fatigue (TMF) of compacted graphite iron (CGI), lifetimes measured under total constraint were confirmed analytically by numerical integration of Paris' crack-growth law. In current work, the results for CGI are further validated for spheroidal cast iron (SGI), while TMF tests at different constraint levels were additionally performed. The Paris crack-growth law is found to require a different C P a r i s parameter value per distinct constraint level, indicating that Paris' law does not capture all physical backgrounds of TMF crack growth, such as the effect of constraint level. An adapted version of Paris' law is developed, designated as the local strain model. The new model considers cyclic plastic strains at the crack tip to control crack growth and is found to predict TMF lifetimes of SGI very well for all constraint levels with a single set of parameters. This includes not only full constraint but also over and partial constraint conditions, as encountered in diesel engine service conditions. The local strain model considers the crack tip to experience a distinct sharpening and blunting stage during each TMF cycle, with separate contributions to crack-tip plasticity, originating from cyclic bulk stresses in the sharpening stage and cyclic plastic bulk strains in the blunting stage. [ABSTRACT FROM AUTHOR]