Friction Behavior under Creep in High-Temperature Pressure Gas Forming Applications

Superplastic forming (SPF) forming is used in the production of a wide range of aerospace structures. However, one pressing concern is the ability to quantitatively model the SPF process in order to effectively design tooling. Current finite element method (FEM) simulations for SPF generally do not include the evolutionary nature of friction under creeping conditions nor model proper constitutive behavior. The presence of creep strain leads to junction growth and saturated contact areas at longer time scales than conventional metal forming. Therefore, friction models that ignore creep-induced strains will underpredict asperity contact and friction levels.

In this work, micro-contact models of a single asperity that follows a power law profile in contact with a rigid flat tool are modeled using an elastic-creep constitutive model. A design of experiment methodology is used to characterize the main parameters that affect asperity contact, and through the incorporation of a physics-based analytical model, a new contact area expression is established based on a characteristic time intrinsic to the asperity deformation behavior.

The single asperity model is then further developed to elastic-creep Gaussian surfaces in contact with a rigid flat. Following a similar methodology, a design of experiment is used to guide micro-contact simulations. The derived predictive contact model follows a general exponential function that eventually saturates at high fractional contact areas. The expression provides a powerful universal solution that is applicable to both Gaussian surfaces and single asperities under power law creep conditions. A new characteristic time is introduced for rough surfaces, which is derived analytically based on first engineering principles. The characteristic time provides a self-similar behavior for any given pressure and power law creep multiplier coefficient. Finally, it is shown that the friction model adequately captures the general deformation behavior for SPF processes and a semi-empirical equation of the real contact area and friction is established.