Constitutive laws commonly used to model friction stir welding have been evaluated, both qualitatively and quantitatively, and a new application of a constitutive law which can be extended to materials commonly used in FSW is presented. Existing constitutive laws have been classified as path-dependent or path-independent. Path-independent laws have been further classified according to the physical phenomena they capture: strain hardening, strain rate hardening, and/or thermal softening. Path-dependent laws can track gradients in temperature and strain rate characteristic to friction stir welding; however, path-independent laws cannot. None of the path-independent constitutive laws evaluated has been validated over the full range of strain, strain rate, and temperature in friction stir welding. Holding all parameters other than constitutive law constant in a friction stir weld model resulted in temperature differences of up to 21%. Varying locations for maximum temperature difference indicate that the constitutive laws resulted in different temperature profiles. The Sheppard and Wright law is capable of capturing saturation but incapable of capturing strain hardening with errors as large as 57% near yield. The Johnson-Cook law is capable of capturing strain hardening; however, its inability to capture saturation causes over-predictions of stress at large strains with errors as large as 37% near saturation. The Kocks and Mecking model is capable of capturing strain hardening and saturation with errors less than 5% over the entire range of plastic strain. The Sheppard and Wright and Johnson-Cook laws are incapable of capturing transients characteristic of material behavior under interrupted temperature or strain rate. The use of a state variable in the Kocks and Mecking law allows it to predict such transients. Constants for the Kocks and Mecking model for AA 5083, AA 3004, and Inconel 600 were determined from Atlas of Formability data. Constants for AA 5083 and AA 3004 were determined with the traditional Kocks and Mecking model; however, constants for Inconel 600 could not be determined without modification to the model. The temperature and strain rate combinations for Inconel 600 fell into two hardening domains: low temperatures and high strain rates exhibited twinning while high temperatures and low strain rates exhibited slip. An additional master curve was added to the Kocks and Mecking model to account for two hardening mechanisms. The errors for the Kocks and Mecking model predictions are generally within 10% for all materials analyzed.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





friction stir welding, constitutive law, modeling, flow stress, stacking fault energy