Equation of State and Damage in Polyethylene
The dynamic response of polymers differs significantly from those of metals, upon which many of the National Laboratories' deformation, damage, and failure models are based. Their moduli, yield strength, and damage characteristics are highly strain rate-, temperature-, and phase-dependent, requiring models that encompass a wide range of phenomena including some not in equilibrium. Recently, Los Alamos developed the Glassy Amorphous Polymer (GAP) 1 model [1] to address limitations in existing models of polymer deformation. GAP captures both volumetric (equation of state) and deviatoric (shear) response, including a non-equilibrium component to the former (a feature determined to be crucial in capturing the low-pressure, viscoelastic response to impact loading). GAP has already been applied to polymers such as PMMA, PTFE, epoxy, and Kel-F 800, but with an emphasis on impact response as opposed to damage or failure. The current effort was launched to address this gap in predictive capability. For reasons that will be made clear, semi-crystalline polyethylene (PE) was chosen to serve as a model system for parameterization and validation. PE (-C 2 H 4- )n is one of the most widely used polymers in industrial and engineering contexts, chiey due to the versatility of its mechanical response. This response can be tuned through network and chain structure, degree of crystallinity, and molecular weight. PE is found in several forms including low density (LDPE), high density (HDPE), and ultra-high molecular weight (UHMWPE). The focus here was on HDPE and UHMWPE, of pedigree described in the following section. Materials were well-characterized prior to study and are representative of semi-crystalline polymers of interest to DOE and DoD. Semi-crystalline PE undergoes a glass transition at low temperature (-35°C) and melts across a range of moderate temperatures (~80-180°C), depending on its structure. It is typically inert chemically, has low strength and high ductility, and the high strength and anisotropy of UHMWPE ber, in particular, have driven its use in engineering, impact, and armor applications. Surprisingly little is known, however, about the influence of PE's crystalline structure and associated phase transitions (including melt) on its response to dynamic compression. A broad suite of experiments was used to calibrate the GAP model for HDPE and UHMWPE. Section IV examines the effects of tensile strain on the structure and integrity of PE crystalline domains. These data were used to inform the preliminary damage model described in Section XII, whose roots lie in statistical physics and network theory. The viscoelastic and plastic components of GAP rely heavily on the stress-strain data of Section VI, which also include dynamic extrusion and Taylor anvil experiments used to validate the damage model. The thermal data of Section X provide crucial inputs to the equilibrium EOS in GAP, as well as the much broader range SESAME EOS whose construction is outlined in Section XI. Section VII details plate impact experiments characterizing the low-pressure shock locus and failure (spall) using in situ electromagnetic gauges. A previously reported \cusp" in the principal Hugoniot near 0.5 kbar was confirmed, and a multi-wave structure was observed over a limited input stress range above the cusp. This cusp is believed due to solid-solid phase transitions associated with the crystalline domains of the polymer.