Inverse analysis of viscoelastic stress relaxation in small AA7175 rings

Sub-yield viscous behaviour in metallic alloys at high homologous temperatures is often overlooked as loading below initial macroscopic yield is considered to be thermodynamically reversible and thus non-damaging. Understanding this behaviour, usually called viscoelasticity, is however critical for reliable lifetime assessment of components used at high temperatures. This paper proposes a novel inverse analysis methodology for investigating and modelling this sub-yield behaviour using cost-effective, high-throughput small ring specimens with a high equivalent gauge length. A thermodynamically-based viscoelastic constitutive model is employed to capture the behaviour and implemented in Abaqus via a custom UMAT Fortran subroutine. The model is formulated with three Kelvin-Voigt elements to represent short, medium, and long-term viscosity. To observe viscous behaviour in aluminium alloy AA7175 at 200°C at stresses around initial macroscopic yield, a series of relaxation tests are conducted at three pin displacement levels, capturing responses ranging from purely sub-yield to localised plastic deformation. The results demonstrate that significant load relaxation (over 45% in 2 h) occurs even in specimens loaded entirely below the macroscopic yield stress. An optimisation loop, coupling the finite element model with a trust-region reflective algorithm, is then used to inversely determine the parameters of the Kelvin-Voigt elements by fitting simulation data to the experimental load-relaxation curves. The inverse analysis method provides an excellent and repeatable fit to the experimental data, with median absolute errors of under 1 N for initial relaxation loads of over 200 N. This novel experimental-numerical technique is offered as a practical and efficient method for investigating and modelling sub-yield viscous behaviour in metals.