A diffusion-coupled thermomechanical constitutive model for polymers in a hydrogen environment

Hydrogen infrastructure such as storage vessels and pipelines for fuel-based applications in the automotive sector has necessitated research into the effects of hydrogen exposure on polymers that are used in O-rings for high-pressure seals, as liners in Type IV storage tanks and in composite shells of Type V tanks. Particularly, the concerns are the variation in material properties due to hydrogen sorption in polymers and effects of sustained pressure and decompression cycles during fueling-refueling stages. Sorption of hydrogen is known to have a pronounced plasticising effect on rubbery polymers denoted by a higher segmental chain mobility and a consequent shift in glass transition temperatures. Rapid decompression stages are associated with significant temperature drops and high gas release rates exceeding that of desorption, leading to swelling in elastomeric O-rings and detachment of semi-crystalline polymer liners from the vessel shell [1, 2]. To study these unique failure modes, a rigorous analysis of the effects of hydrogen sorption on polymer relaxation is essential. To this end, this study proposes a hydrogen diffusion-coupled deformation constitutive law to account for hydrogen-influenced viscoelasticity, viscoplasticity and a Mullins-like effect to model high-pressure loading-unloading scenarios. In addition to the momentum and heat equations, the additional coupling implies a fluid continuity equation which for gaseous diffusion in polymers is found to be a Non-Fickian diffusion equation due to the comparable time scales of diffusion and polymer relaxation [3]. Existing thermomechanical models use Generalised Maxwell-based viscoelasticity with shifted time integration to account for variability in relaxation modulus with temperature [4]. Hyperelastic strain dependent functions are used to model large non-linearities and viscoelastic tension-compression asymmetry [5]. In this work, this formulation is extended to
hydrogen content dependency by using a combined shift factor – a temperature based
Williams-Landel-Ferry shift factor multiplied by a concentration based Dolittle expression [6] to account for a shift in dynamic modulus master curve (and consequently, glass transition
temperature) due to hydrogen. A common approach is to add phenomenological
viscoplasticity with a Perzyna type flow rule and a mixed hardening formulation to displace the yield surface [7]. Ad hoc functions are used to model temperature dependencies of viscosity and hardening moduli [5]. Similar functions are proposed in this study to account for the variability in viscoplastic properties due to varying hydrogen concentration. Combined with the Mullins-like effect, this constitutive law is hypothesised to produce stress-strain behaviour. Furthermore, unlike the entropic Williams-Landel-Ferry shift factor, the Dolittle expression requires an enthalpic contribution that corresponds to mixing terms in the free energy and the fluid flow related chemical potential. Typical assumptions include a modified Flory-Huggins theory to model the mixing of gas in polymer [6,8]. This complex diffusion process is adopted to model deformation-dependent diffusion and to produce linear concentration versus time profiles as induced by a plasticising diffusion front in the polymer during hydrogen permeation [7].