All spacecraft continue to face a growing risk of hypervelocity impact (HVI) by micrometeoroids and orbital debris (MMOD). Concurrently, emerging hypersonic weapons pose acute ballistic threats to military and civilian assets. In both cases, the diminishing e ↵ectiveness of legacy armor demands the development of specialized, layered HVI protective structures. Ultra-high molecular weight polyethylene (UHMWPE) and high-density polyethylene (HDPE) stand out as promising intermediate layers due to their high mass-speciﬁc energy absorption and tailorability. Yet, their behaviors at HVI-induced strain rates ( >106s1) remain understudied and poorly understood, particularly near their glass transition ( 116C) and melt (130C) temperatures. A recent HVI study revealed that, when impacted at room temperature, UHMWPE targets exhibited bulk fragmentation while similar HDPE samples showed extensive melting and visco-plastic ﬂow, di↵erences attributed to molecular mobility. This follow-on study probes the interplay of initial target temperature ( T0), impact velocity ( v0), and average entanglements per chain ( Ne) on polyethylene’s (PE’s) HVI response. 12.7 mm thick UHMWPE and HDPE plates at T0⇡120C, 20C, and 140Cw e r es u b j e c t e d to 2.5 km/s and 6.0 km/s HVIs by 6.35 mm diameter aluminum spheres. PE’s HVI response was found to be largely governed by a competition between rates of strain and polymer chain relaxation. Lowering T0for a ﬁxed Neconstrained chain motion analogously to increasing Neat a ﬁxed T0. This caused HDPE’s HVI response to increasingly align with UHMWPE’s at similar v0. The opposite was also observed. Increasing v0 alone made both materials more prone to widespread fracture by raising strain rates beyond rates of chain disentanglement and reorientation. The material exhibiting the most visco-plastic ﬂow without subsequent bulk fragmentation lost less mass, had smaller perforations, and better absorbed energy, suggesting that, ⇤Corresponding author. J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, Texas, 77843, United States. Email Address :jacob rogers@tamu.edu ⇤⇤Corresponding author. J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, Texas, 77843, United States. Email Address :telacyjr@tamu.edu Preprint submitted to Macromolecules April 15, 2024 for a given T0andv0, there is an optimal Nevalue that maximizes PE energy absorption. Increasing v0or decreasing T0necessitates a reduction in Neto sustain the degree of molecular mobility that gives maximum energy absorption. These ﬁndings motivate the development of a protective structure composed of PE layers, each optimized for an anticipated average strain rate. Keywords: hypervelocity impact (HVI), two-stage light gas gun (2SLGG), polyethylene (PE), UHMWPE, HDPE, impact energy absorption, thermoplastic, semi-crystalline, entanglement density 1. Introduction and Motivation All spacecraft, manned or unmanned, face a signiﬁcant threat of hypervelocity impacts (HVIs) from micrometeoroids and orbital debris (MMOD), with the danger from micrometeoroids escalating during long interplanetary voyages [1, 2]. Similarly, emerging commercial and military hypersonic vehicles continue to present formidable challenges to legacy thermal and ballistic protection measures [3–5]. With impact veloci- ties exceeding 3 km/s ( ⇠Mach 9), HVIs can severely deform, erode, fracture, fragment, heat, melt, vaporize, and even sublimate materials, often leading to catastrophic system and mission failure, or, more critically, loss of life [6–8]. Numerically modeling the HVI response of materials generally involves a combination of constitutive and failure models and equations of state that are empirical in nature [9]. For this reason, protective structure development and optimization usually involves costly HVI experiments at room temper- ature using sophisticated launch apparatuses, such as two-stage light gas gun (2SLGG) aeroballistic ranges [10]. In many practical applications, materials not only see ultra-high impact velocities but also extreme temperatures. Spacecraft in orbit, for example, can experience temperatures ranging 160C to 120C [11], while ambient temperatures on Earth can vary from 80C to 110C [12]. Materials on the leading edges of hypersonic vehicles are subjected to temperatures exceeding ⇠2,000C [13]. Hence, characterizing the HVI response of materials at extreme temperatures through methodical laboratory tests is essential for the development and application of next-generation protective structures. Many spacecraft utilize polymers as window materials or as intermediate layers in MMOD (Whipple) shields [14, 15], while ballistic “bulletproof” vests often incorporate polymer composites for enhanced energy absorption [16]. The e↵ectiveness of polymers and polymer composites in these applications, combined with their customizable properties, has positioned them as top choice materials for innovative space and military protective structures. This interest has spurred numerous investigations into the room temperature HVI re- sponse of polycarbonate (PC), polymethyl methacrylate (PMMA), polyethylene (PE) and their composites, and more [17–22]. In these previous studies, targets were typically subjected to normal HVIs by projectiles representing anticipated threats (spacecraft debris, dust, ice, etc.). High-rate diagnostics and post-impact target characterization methods were used to unravel HVI-induced target deformation and failure, as well 2 as identify predominant energy absorbing mechanisms. Ultra-high molecular weight PE (UHMWPE) and high-density PE (HDPE), in particular, have been identiﬁed as promising intermediate layers in protective structures due to their high tailorability, low density and cost, and relatively high energy dissipation capabil- ities [23, 24]. Despite their current and anticipated use in extreme environments, these thermoplastics have not been systematically studied under conditions of both extreme temperature and strain rate. In fact, there have been very few HVI experiments at cryogenic temperatures involving anytype of material [25–27], and even fewer investigations have been conducted with targets pre-heated well above room temperature [28]. UHMWPE and HDPE are commercially available semi-crystalline polymers of (–C 2H4–)nthat share similar densities ( ⇢0⇠0.95 g/cc) and physical appearances. They primarily di↵er in average molecular chain length ( i.e., degree of polymerization, n) or, equivalently, average molecular weight [29, 30]. The average molecular weight is much higher for UHMWPE ( Mw>3,000 kg/mol) than for HDPE ( Mw⇠100– 500 kg/mol) [31]. The longer chains in UHMWPE lead to fewer chain ends per unit weight and more entanglements per chain ( Ne⇠3,000–8,000) compared to HDPE ( Ne⇠120–250). UHMWPE can be over 60 times (6,000%) more entangled than HDPE! Entanglements generally boost material toughness and defor- mation resistance by creating an energy-absorbing network that inhibits chain mobility, uniformly distributes stress, increases elasticity, and reduces crack propagation [32–36]. Yet, UHMWPE’s entanglements raise its melt viscosity to around 1010Pa·s, roughly 107times more than HDPE’s ( <103Pa·s), hindering standard high shear processing [37]. The variations in Neand molecular weight inﬂuence molecular packing,1resulting in di↵erent crystallinity degrees (40–75% in UHMWPE and 70–80% in HDPE) and crystalline structure sizes [30, 35]. Chain branching also a↵ects PE’s mechanical behavior. Less branching generally promotes crys- tallinity and density, making processing challenging [38, 39]. Thus, commercial PEs often have been designed to have some degree of short chain branches to facilitate manufacturing ( e.g.,C H 3groups adjust molecular conformation to reduce melt viscosity). Although detailed information on chain branching and comonomer content is limited, most commercial PEs are remarkably linear ( <3% branching) and pure (additives levels <5% by weight) to avoid impeding powder fusion during molding and to preserve mechanical properties [31]. UHMWPE typically has greater tensile strength, abrasion and crack resistance, and ballistic impact strength due to these morphological variations. HDPE, with its higher crystallinity, o↵ers a higher tensile modulus but lower strength and wear resistance [40]. UHMWPE is used in high-wear applications such as medical devices ( e.g., knee joint replacements) and bulletproof vests in the form of Spectra®or Dyneema® gel spun ﬁbers [41]. HDPE is commonly found in containers and corrosion-resistant piping. Both exhibit excellent chemical resistance. However, their mechanical and dynamic mechanical property di↵erences at 1Neinhibits the growth of parallel chain folding crystals. 3 extreme temperatures andvery high strain rates are less well investigated and understood. Like many polymers, PE’s mechanical properties and dynamic behavior are highly sensitive to strain, strain rate, temperature, and pressure. At room temperature, UHMWPE shows signiﬁcant strain hardening in tension and compression at strain rates up to ˙ "⇠103s1for strains under 300% [40, 42]. HDPE, however, demonstrates nearly perfect plastic behavior across similar strains and strain rates [40, 43]. HDPE undergoes signiﬁcant adiabatic heating and thermal softening at rates above ˙ "⇠102s1[44]. The e↵ective thermal plastic work conversion factor (0 << 1) quantiﬁes the portion of plastic work converted into heat. HDPE tends to covert nearly all plastic work to heat ( ⇡1), while UHMWPE converts less than half ( <0.5) [30, 44]. The ballistic impact resistance and deformation behavior of these PEs are well-documented for impact velocities ⇠102m/s and ˙ "<105s1[30, 36, 45–47]. Generally, higher molecular weight enhances impact strength and resistance to thermal softening/melting and crack propagation promoting tearing brittle fractures [48, 49]. Increased crystallinity does improve yield strength but at the cost of impact performance [30, 50, 51]. At and above room temperature, UHMWPE has slightly better ballistic performance than HDPE [30, 52]. However, these ﬁndings cannot be directly extrapolated to HVI-induced strain rates ( ˙ "⇠106– 108s1). For PE, the time-temperature superposition principle may be used to relate low-rate material data to that for higher rates. In essence, a one decade increase in ˙ "corresponds to a 10C drop in temperature for both PEs. Employing this superposition to match temperatures corresponding to HVI-induced strain rates, HDPE still showed signiﬁcant thermal softening. In contrast, UHMWPE demonstrated only mild softening and continued to exhibit strain hardening [44]. This implies that the variation in thermal softening (adiabatic heating) between the two materials could stem from microstructural factors. These ﬁndings are consistent with molecular dynamics (MD) simulations of PE subjected to strain rates over 106s1,w h i c h predicted strain hardening, thermal softening, and a linear relationship between yield stress and logarithm of strain rate [53–55]. Some e↵orts have been made to understand PE’s behavior under HVI conditions. For example, Cha et al. [24] conducted HVI tests at approximately 4 km/s using 5.56 mm diameter aluminum projectiles, observing that UHMWPE targets showed superior HVI performance compared to Kevlar used in stu↵ed Whipple shields ( i.e., Whipple shields enhanced with lightweight, energy-absorbing layers ﬁlling the space between their often metallic plates). Bowering [56] conducted experiments with 4 mm aluminum spheres impacting UHMWPE, HDPE, and PMMA plates at 2.0–6.5 km/s. UHMWPE appeared to absorb more impact energy. However, these studies were more qualitative in nature and raised further questions about PE’s fundamental behavior when subjected to HVIs. More recently, Rogers et al. [23] carried out a study comparing 6.35 mm thick UHMWPE ( Mw=4.7⇥106g/mol) and HDPE ( Mw=1.7⇥105g/mol) plates, focusing on their distinct bulk responses to 2.0–6.5 km/s HVIs by 10 mm diameter aluminum spheres. For impacts near 4 2.0 km/s, the impactor was signiﬁcantly deformed and eroded but largely remained intact. As velocity increased, the projectile progressively fractured and became more pulverized. Regardless of impact velocity, UHMWPE showed a more quasi-brittle response (extensive fragmentation in the ejecta and debris cloud), likely driven by its highly entangled (constrained) chains. Contrarily, HDPE exhibited substantial bulk- melting and large-scale visco-plastic deformation, due to intense adiabatic heating (Fig. 1). Despite having similar debris cloud geometries and leading-edge velocities, UHMWPE targets lost about 40% more mass than HDPE targets (on average) at the same impact velocities, indicating potentially greater momentum and kinetic energy in the UHMWPE debris clouds. HDPE targets had perforation radii around 20% larger than those in UHMWPE. Initial SEM analysis also revealed that while UHMWPE fracture surfaces were ﬂat and resembled brittle fractures, HDPE surfaces exhibited drawn oriented ﬁbrils, thermal melting/softening, and ﬂow. This reported bulk behavior and performance of PE at ultra-high strain rates is expected to be highly temperature-dependent. For semi-crystalline polymers, higher temperatures generally lead to increased free volume and chain mobility, faster disentanglement rates, shorter relaxation times, reduced viscosity in noncrystalline regions, and ultimately earlier and more complete melting [35]. Conversely, lowering the temperature has the opposite e↵ect. Such temperature-related phenomena are often characterized with reference to a polymer’s glass transition temperature ( Tg) and melt temperature ( Tm). For UHMWPE and Figure 1: Comparing fully-developed ejecta and debris clouds at di↵erent nominal impact velocities in the tested range: (a–c) UHMWPE and (d–f) HDPE. With increasing nominal impact velocity (from left to right), UHMWPE debris fragments become smaller on average, and bulk melting in HDPE becomes more pronounced. Reprinted from Ref. [23]. 5 HDPE, Tg⇡120C and Tm⇡130C. Below Tg, the free volume is minimal, and polymer chain segment motion is highly constrained. Above Tg, a signiﬁcant increase in free volume enhances chain mobility, transitioning the polymer from a glassy to a rubbery state. However, this transition primarily a↵ects the noncrystalline regions; crystalline regions remain largely intact, interconnected by tie molecules and inter- crystalline links that span the amorphous regions. Chain entanglements also contribute to sti↵ness above Tg. Near and above Tm, thermal energy overcomes intermolecular forces holding the crystals together, causing them to melt. UHMWPE and HDPE then become viscous liquids, with UHMWPE showing particularly high viscosity due to its dense entanglements. At temperatures much higher than Tm, the PEs start to decompose viapyrolysis and combustion. This temperature dependent behavior in PE is well characterized for relatively low loading rates ( ˙ ".102s1) [44, 57–59]. However, there have been no comprehensive studies on semi-crystalline PE’s HVI ( ˙ "&106s1) response at temperatures near its glass transition ( Tg) and melt (Tm) temperatures. Therefore, a systematic study probing the interplay of initial target temperature ( T0) and impact velocity ( v0) on the HVI response of PE could help address fundamental questions about PE’s dynamic behavior, as well as shed light on its engineering applications. The distinct phenomenological responses of UHMWPE and HDPE to HVI, despite their similar density, crystallinity, and chemistry, can likely be attributed to their signiﬁcant di↵erences in Ne. During a HVI, adiabatic shock heating and rapid plastic deformation quickly induce strong gradients in temperature, as well as strain, strain rate, and state of stress, in the target’s impacted region that evolve spatially and temporally. PE’s poor thermal conductivity intensiﬁes the localized heating. In the HVI tests conducted by Rogers et al.[23], HDPE plates exhibited perforation volumes ⇠1.4 times larger than those of UHMWPE plates with identical thickness. The average size (pervaded volume) of the UHMWPE chains was roughly 150 times larger than that of the HDPE chains, as estimated by their unperturbed RMS end-to-end distances and molecular weights [60]. These estimates suggest that perhaps 200 times more HDPE chains were involved in deformation, heating, etc.compared to UHMWPE chains. For the molecules undergoing rapid deformation, the temperature increase quickly enhances free volume and chain mobility, facilitating chain disentanglement and shortening relaxation times. HVI-induced temperatures can readily exceed the melt temperatures of UHMWPE and HDPE, encouraging bulk melting and ﬂow. However, PE’s average molecular weight (chain length) is proportional to the average number of entanglements per chain and inversely proportional to the nominal disentanglement rate. When this disentanglement rate is surpassed by the HVI-induced loading rate, the entangled molecular network becomes virtually frozen, causing internal stresses to rise until chain scission occurs. This phenomenon can be observed macroscopically as brittle failure and bulk fragmentation. One way to probe this hypothesis is to subject UHMWPE and HDPE to extreme strain rates at temperatures from T0<T gtoT0>T m. 6 In this study, commercially available 12.7 mm thick UHMWPE ( Mw=4.7⇥106g/mol, Ne⇠3,800, PDI ⇠10) and HDPE ( Mw=1.7⇥105g/mol, Ne⇠140, PDI =9.6) plates were subjected to 2.5 km/s and 6.0 km/s HVIs by 6.35 mm diameter 2017-T4 aluminum spheres. The target plates were brought to temperatures below Tg⇡120C and above Tm⇡130C using passive cooling and heating methods, respectively. For direct comparison, similar HVI experiments were conducted at room temperature. The PE materials used matched those of Ref. [23], ensuring consistency with previous work. The projectiles were launched using a 2SLGG, and the deformation and failures of the PE were analyzed using high-speed cameras and pre/post-impact characterization. Notably, the HVI response of HDPE shifted from bulk melting to quasi-brittle fragmentation at v0=2.5 km/s and T0<T g. Conversely, the behavior of UHMWPE started to align with that of HDPE at T0>T m. The variations in HVI-induced deformation and failure, as well as HVI performance, were signiﬁcantly dependent on T0, strongly suggesting that microstructural characteristics, particularly the degree of chain mobility, are responsible for the distinct HVI behaviors of UHMWPE and HDPE observed at room temperature. Numerical simulations of HVIs to PE were used to infer impact conditions. 2. Methods This section provides an overview of the UHMWPE and HDPE materials utilized in this study, as well as target sample preparation and ﬁxturing for HVI experiments. The experimental methodology, with an emphasis on the passive target cooling and heating techniques, is also outlined. A simple conservative metric for comparing debris cloud lethality ( i.e., the threat level posed by debris cloud to subsequent struc- tures/assets/personnel) is presented. An overview of the numerical simulation approach is brieﬂy detailed. 2.1. Materials and Sample Preparation Monolithic plates of UHMWPE and HDPE with dimensions 600 x 600 x 12.7 mm3were sourced from Mitsubishi Chemical Advanced Materials (TIVAR®1000) [61] and King Plastic Corporation (King KPC® HDPE) [62], respectively. TIVAR®1000 (compression molded GUR 4120 powder) has over 97% purity (.3% processing/lubrication additives) and an average molecular weight of Mw=4.7⇥106g/mol, as calculated from its melt viscosity using the Margolies equation [63, 64]. The King KPC®HDPE plates were also prepared viacompression molding, without the use of any additives [65]. The as-received PE plates were cut into smaller 102 x 102 x 12.7 mm3HVI targets using a band saw. For the remainder of this paper, “UHMWPE” exclusively denotes TIVAR®1000 and “HDPE” refers solely to King KPC®HDPE. Zhang et al. [65] characterized the molecular weight distribution of this HDPE using gel permeation chromatography, reporting number average, weight average, and Z-average molecular weights of Mn=1.8⇥104g/mol, Mw= 7 Table 1: Material characterization data for UHMWPE (TIVAR®1000) and HDPE (King KPC®HDPE). Molecular weights for UHMWPE and HDPE were sourced from Refs. [63, 64] and [65], respectively. Additional data, including TGA, DSC, and DMA results previously reported in [23] are also included. Key mechanical properties were sourced from Refs. [61, 62]. Property UHMWPE HDPE % Di↵erence Standard(s) Number average molecular weight, Mn[g/mol] ··· 1.8⇥104··· ··· Weight average molecular weight, Mw[g/mol] 4 .7⇥106†1.7⇥105190% ··· Z-average molecular weight, Mz[g/mol] ··· 1.0⇥106··· ··· Polydispersity index, PDI =Mw/Mn ··· 9.6 ··· ··· Entanglement molecular weight, Me[g/mol] ⇠1,250‡⇠1,250‡0% ··· Average entanglements per chain, Ne⇠Mw/Me ⇠3,800 ⇠140 190% ··· Glass transition temperature, Tg[C] 116.1 116.2 0.1% ASTM E1640-18 Melting temperature, Tm[C] 134.1 131.1 2.3% ASTM F2625, D3418 Crystallinity, [%] 52.5 70.2 28% ASTM F2625, D3418 Initial decomposition temperature, IDT [C] 439.1 423.2 3.7% ASTM E2550 Density, ⇢[g/cc] 0.927 0.954 2.9% ASTM D792 Yield strength, y[MPa] 40 31 25% ASTM D638 Elastic modulus, E[GPa] 0.55 1.8 110% ASTM D638 Thermal conductivity, [W/(K ·m)] 0.4 0.5 22% ··· Izod Impact Resistance no break 1.1 ··· ASTM D256 Shore D Hardness 66 68 3% ASTM D2240 Speciﬁc heat capacity, cv[kJ/(kg ·K)] 1.8 2.3 24% ··· †This Mwvalue was determined using the Margolies equation [64]. Hence, Mn,Mz,a n d PDI values are not reported for UHMWPE.‡This Mevalue is generally accepted for linear PE in the melt state [67, 68] 1.7⇥105g/mol, and Mz=1.0⇥106g/mol, respectively. The polydispersity index was PDI =Mw/Mn=9.6. Acquiring comparable chromatographs for UHMWPE is generally challenging due to its high viscosity and limited solubility [31, 66]. Consequently, there is no available data on UHMWPE’s PDI, but it is presumed to be akin to other commercial UHMWPEs ( PDI ⇠10) [66]. Rogers et al. [23] previously reported measured Tg,Tm,d e n s i t y( ⇢0), crystallinity ( ), and initial decomposition temperature ( IDT) values for each PE, which aligned well with supplier and literature values. Tg⇡116C for both PEs, while Tm= 134C and 131C for UHMWPE and HDPE, respectively. The density and crystallinity were lower in UHMWPE (⇢0=0.93 g/cm3and= 52%) compared to that of HDPE ( ⇢0=0.95 g/cm3and= 70%). UHMWPE experienced an onset of thermal degradation at a slightly higher temperature (439C) compared to HDPE (423C). This material characterization data is summarized in Table 1. The semi-crystalline structure of UHMWPE and HDPE complicates precise determination of their en- tanglement densities and Nevalues. A simple approach to estimate Nein the melt involves dividing the weight average molecular weight by the entanglement molecular weight ( i.e.,Ne⇠Mw/Me). An accepted Mevalue for linear PE in the melt state is Me⇡1,250 g/mol [67, 68]. Using this Mevalue, Ne⇠3,800 and Ne⇠140 monomer for UHMWPE and HDPE, respectively. Hence, UHMWPE’s chains are about 30 times more entangled than HDPE’s ( cf. Table 1).2These calculations, while not accounting for the full e↵ect of 2As crystals form, they drive entanglements to their surfaces, leaving few or no entangled chains within the crystal itself. 8 Figure 2: An overview of the HVI testing method. For each PE, 600 x 600 mm2square plates of thickness ht=1 2 .7m m were subjected to v0=2.5a n d6 . 0k m / si m p a c t sa t T0⇡(a)120C, (b) 20C, and (c) 140C, resulting in twelve total HVI experiments. molecular weight distribution or crystalline regions, do highlight that the primary distinction between the PEs lies in their Nevalues (and molecular weight). 2.2. The Impact Experiments The HVI experiments were conducted using a 12.7 mm bore 2SLGG, capable of accelerating single projectiles of diameter dp=2.0–12.7 mm to impact velocities ranging v0=0.5–8.0 km/s. Each projectile, encased in a polymer sabot, was launched into an enclosed aeroballistic range (composed of a blast and target tank) under a vacuum pressure of P⇡13 kPa.3The sabot separated aerodynamically, enabling the projectile to enter the target tank independently and impact the PE target at normal incidence. The impact velocity of the projectile was measured using laser velocimetry. Further details on the 2SLGG aeroballistic range and testing methodology can be found in Refs. [10, 23, 69]. Experiments were conducted at three distinct initial target temperatures: T0⇡120C<T g,T0⇡20C, and T0⇡140C>T m. For each T0value, the PE plates of thickness ht= 12 .7m mw e r es u b j e c t e dt o v0=2.5 and 6.0 km/s HVIs by dp=6.35 mm 2017-T4 aluminum spheres. This procedure led to six HVI experiments per PE type (twelve total), all conducted with a ﬁxed target thickness to projectile diameter ratio of ht/dp= 2. Hence, for a given PE, the sole variables were v0andT0, e↵ectively isolating the PE HVI response to particular temperature and impact velocity (strain rate) conditions (Fig. 2). Notably, the chosen ht/dpratio is roughly three times greater than that used in Ref. [23], largely due to a deliberate increase in htto enhance the e↵ective thermal mass of the target so as to maintain its T0before impact. This process elevates the number of entanglements per volume (entanglement density) in the noncrystalline regions by a factor of 1/(1). Consequently, HDPE concentrates entanglements into its noncrystalline regions by a factor of ⇠1.6 times greater compared to UHMWPE. 3The tankage assembly was initially evacuated to P⇡0.13 kPa, then backﬁlled with nitrogen gas until the pressure reached P⇡13 kPa. This procedure aimed to minimize the mixing of O 2with the hot jet of H 2exiting the 2SLGG launch tube [10]. 9 2.3. Cooling and Heating the Polyethylene Plates All four PE targets impacted at T0⇡120C were ﬁrst cooled to about 180Cbefore being placed in the target tank ( i.e., passive cooling). After sealing the tank, a ten-minute waiting period was necessary to achieve the required vacuum pressure (13 kPa). Benchtop experiments were conducted to characterize the time for the mid-plane of the plate to warm to PE’s glass transition temperature ( T0=Tg⇡116C). A representative HDPE plate was ﬁrst cooled in a liquid nitrogen (LN2) bath for about two hours, then exposed to lab air at 20C. The plate’s through-thickness centerline temperature was monitored with thermocouples, revealing a warming time of about eight minutes (Fig 3a). Simple two-dimensional heat transfer calculations indicate that the surface temperature of a representative PE plate, in room temperature air, lags the mid- plane temperature by approximately 5–7C during the warming period (see Sect. SI.2). When the PE plate was cooled between two 12.7 mm thick steel plates, the warming time exceeded the vacuum time by roughly four minutes. For this reason, a specialized cryogenic ﬁxture was developed to delay the warming time beyond the vacuum period. This ﬁxture enclosed the PE plates on all sides with at least 12.7 mm thick steel, except for 76 mm diameter circular apertures (windows) to be aligned with the projectile impact axis (Figs. 3b and 3c).4For all experiments, the projectile perforated the target roughly twice as fast as the time required for shock waves to reﬂect o↵ the boundaries and return to the impact site (see Section SI.1). Thus, the ﬁxture boundaries had no inﬂuence on the perforation event.5In lab air tests, the cryogenic ﬁxture extended the target warming times to over ﬁfteen minutes, beyond the required duration for e↵ective HVI testing. Hence, for the cooling experiments, the as-received PE plates cut to 102 x 102 x 12.7 mm3 (Fig. 4a) were placed in the cryogenic target ﬁxture (Fig. 4b), submerged in a LN2 bath for two hours (Fig. 4c), and rapidly transferred to the target tank (Fig. 4e). The tank was immediately sealed and the vacuum pump initiated. A thermocouple, positioned about 30 mm from the target’s center, recorded target plate centerline temperatures in the exposed window region (Fig. 3c).6When the centerline temperature within the window region reached T0⇡125C, the 2SLGG was ﬁred, accelerating the aluminum spheres to either 2.5 or 6.0 km/s. The impactors reached their targets some ⇠300–500 µs later, depending on v0. For the high-temperature HVI experiments, the same target ﬁxture (Fig. 3b), providing additional thermal mass, was employed. Each of the four 102 x 102 x 12.7 mm3PE targets intended for impact atT0⇡140C was initially heated to ⇠170C inside this ﬁxture using an induction burner (Fig. 4d). 4An optional feature to cover these windows was available to aid in cooling/heating but was found unnecessary in these HVI experiments. 5The boundary conditions set by the steel ﬁxture might have inﬂuenced the targets’ post-perforation responses to a certain extent. Even so, since all targets shared identical geometries and similar asymmetric boundary conditions during the HVIs, direct comparison is viable/reasonable. 6In the benchtop tests, thermocouples measured temperatures at the target centerline both between the steel plates and in the exposed window region. The former showed a lag of ⇠10C. 10 Figure 3: Fixture development for cold-temperature HVI experiments: (a) measurements of through-thickness centerline tem- peratures of an HDPE plate alone and between steel plates, highlighting extended warming times. Figure (b) displays the cryogenic target ﬁxture in an isometric perspective, with (c) highlighting the thermocouple placement location and target cen- terline. Above T0⇠130C, the HDPE targets began to ﬂow/deform. For this reason, each molten plate was placed between two 100 x 100 x 0.050 mm3square Mylar (polyethylene terephthalate) sheets to retain target thickness and planarity.7For both PEs, the assembly remained on the burner until the temperature of both the ﬁxture and the PE plate stabilized. Due to PE’s poor thermal conductivity, the entire heating process (from T0⇡20Ct o T0⇡170C) took approximately thirty minutes, veriﬁed by thermocouples and infrared thermometry. After reaching equilibrium, the target assembly was quickly moved to the target tank, which was then sealed, and the vacuum pump activated (Fig. 4e). Similar to the cooling experiments, the centerline temperature of the PE target was continuously monitored in the window region and between the steel plates using thermocouples. The HVI experiment commenced once the target centerline temperature reached T0⇡145C. Following the HVI tests, these targets were quenched in chilled water to arrest post- impact viscous ﬂow. For the four room temperature experiments, no extra thermal mass was needed, so the ﬁxture depicted in Fig. 3b was not employed. Instead, the targets were sandwiched between two 4.8 mm thick steel plates each with a 100 mm diameter circular aperture, similar to the method used in Ref. [23].8 7Mylar maintains its mechanical strength up to about 150Ca n di ss u i t a b l ef o ru s eu pt o2 0 0Cu n d e rm o d e r a t el o a d s . Hence, the Mylar sheets o↵ered essential support to the molten HDPE target without signiﬁcantly a↵ecting experimental outcomes, as the projectile interacted with 130 times more HDPE than Mylar (by volume). 8This distinct ﬁxture enabled the preparation of low/high temperature experiments concurrently with ongoing room tem- perature tests. 11 Figure 4: The cooling and heating methodology for the HVI experiments. The (a) as-received PE plates cut to 102 x 102 x1 2 . 7m m3were (b) placed in the target ﬁxture, either (c) submerged in a LN2 bath for three hours or (d) placed on an induction burner for sixty minutes, and (e) rapidly transferred to the target tank. Target through-thickness centerline and surface temperatures were monitored using thermocouples. The room temperature PE target assembly was then placed in the target tank, and once the appropriate vacuum pressure was attained, the HVI experiment was conducted. In all experiments, irrespective of the T0value, the center of the target ﬁxture aperture coincided with the projectile impact axis, deﬁned by the projectile’s velocity vector. In each experiment, a Shimadzu HPV-X2 high-speed camera, operating at 1 MHz, captured the HVI event in-situ , including the projectile’s approach, impact, and perforation, as well as the ensuing expansion of the projectile/target ejecta and debris clouds (128 total images per experiment). The camera was oriented orthogonally to the impact axis and conﬁgured for shadowgraphic imaging, yielding high-contrast, stop- motion images, consistent with previous HVI experiments involving PE ( cf. Fig 1) [23]. These images were vital in evaluating how T0a↵ected target failure and bulk HVI response. Additionally, these images were used in conjunction with motion tracking software to measure the horizontal velocity of the debris cloud’s leading edge or tip ( i.e., “debris cloud tip velocity”) [23]. The PE plates were analyzed pre- and post-HVI to determine target mass loss ( mt). For a number of impacted targets, the perforations were mostly circular in the plane but had irregular/jagged edges. The opening diameter somewhat increased from the front to the back of the target in the through-thickness direction, resulting in a conical perforation surface. For these reasons, the ImageJ software was used to trace the inner-most perimeter of each perforation to measure an e↵ective perforation area ( Ae). This area was then used to calculate an e↵ective perforation diameter (de=p 4Ae/⇡), representing the diameter of a circle with equivalent area. 12 2.4. Numerical Simulations of HVIs to PE The HVI experiments were supplemented with simulations using the Elastic Plastic Impact Computation (EPIC) code, which integrates ﬁnite element analysis and smooth particle hydrodynamics for modeling large- scale deformations, fractures, and fragmentation [70]. The simulations calculated impact-induced equivalent plastic strain, strain rate, and temperature distributions for each T0andv0combination. The idealized 3D quarter-symmetry PE targets were meshed with tetrahedral ﬁnite elements, with element size increasing radially from the impact axis. The projectile mesh size matched that of the target in their contact area. Both projectile and target meshes, totaling ⇠3⇥106elements, were used in all simulations, and a mesh sensitivity analysis conﬁrmed solution convergence. The EPIC code’s element-to-particle conversion feature was employed, setting the equivalent plastic strain required for conversion in the target at 30%, a standard value for ductile materials [71]. Projectile and target material behaviors were captured using Mie-Gruneisen equation of state [72], JC constitutive model [73], and JC fracture model [74], with parameters sourced from Ref. [75] and the EPIC materials library. This library notably does not include speciﬁc material models for UHMWPE. Consequently, a total of six HVIs into HDPE were simulated to infer HVI-induced conditions in the PE targets during the early stages of target perforation. It is expected that incorporating dedicated UHMWPE models would not substantially change the simulated target response, especially at these early event times. Unfortunately, EPIC’s continuum basis signiﬁcantly limits its ability to represent the microstructural features responsible for the di↵ering HVI responses observed between the two PEs. 2.5. A Comparative Metric for Target HVI Performance This section brieﬂy introduces a simple debris cloud kinetic energy based metric for comparing the HVI performance of targets subjected to similar impact conditions. A more complete presentation is available in the Supplementary Information, Section SI.3. During a HVI, the projectile’s kinetic energy is absorbed through intense deformation, erosion, fracture, fragmentation, heating, melting, vaporization, and sometimes sublimation of both projectile and target. An ejecta cloud usually forms at the impact (front) face of the tar- get, moving “uprange” ( cf. Figs. 1 and 2) in the opposite direction to the projectile [8, 76]. When perforation occurs, a debris cloud composed largely of molten or solid target material fragments, plus the projectile or its fragments,9emerges and expands “downrange” from the target’s back side. In non-perforating cratering events, only an ejecta cloud forms. Determining the projectile momentum and kinetic energy absorbed by the target requires resolving the three-dimensional (3D) momenta and kinetic energies of all fragments in the ejecta and debris clouds. This is a challenging task, as di↵erentiating between projectile and target 9Vaporized material from the pro jectile or target may be present in the debris cloud but likely has negligible contribution to the debris cloud’s kinetic energy due to its low mass. 13 fragments in these clouds is nontrivial, even with advanced diagnostics. Additionally, even if a fragment’s origin is identiﬁed, assumptions about its mass, material state, and 3D geometry would still be required. For ballistic performance studies, the projectile often stays intact and, if perforation occurs, exits the target with residual velocity vr. In such cases, target performance evaluation often focuses on ratios like vr/v0⇠vdc/v0 or a normalized variation of Ep=1 2mp(v2 0v2 r), (1) where Epis typically considered the energy absorbed by the target (see, e.g., [77]). Such an approach is valid since often  mt⌧mpand the projectile remains largely intact and undeformed. However, when comparing theHVI performance of di↵erent target materials, using vdc/v0orEpalone is inadequate because ( i)t h e projectile rarely stays intact for v0>2.0 km/s and ( ii) a large portion of the target mass is often launched uprange/downrange with signiﬁcant momentum and kinetic energy. Hence, incorporating target mass loss (mt) into a comparative metric is advantageous. When comparing the HVI performance of targets with similar densities and identical geometries impacted by the same projectile, the following assumptions can be made: ( i) the projectile or its fragments concentrate at the debris cloud tip, ( ii) the ratio of target material in the ejecta cloud to that in the debris cloud remains similar for all considered impact conditions, and ( iii) the ratio vdc/v0between the two materials is assumed to be similar and does not signiﬁcantly vary with v0(vdc/v0=0.45±0.04 in this study). Under these assumptions, a simple metric, such as the normalized critical debris cloud kinetic energy10can be deﬁned, which accounts for both  mtandvdc: ˜Ej dc Ej 0= ˜mj t mp+1! (vj dc)2 (vj 0)2, (2) where jindexes the experimental observations in set M, and  mj tis the mass loss and vj dc/vj 0is the normalized debris cloud tip velocity for the j-th target, respectively. Notably, 0 ˜Ej dc/Ej 01. Here, mpis assumed to be ﬁxed, and 0˜=m i n 1jM" (vj 0)2 (vj dc)21! mp mj t# 1 (3) is e↵ectively the fraction of  mtin the debris cloud corresponding to the worst-case scenario among MHVI experiments: the target experiencing maximum mass loss where all projectile kinetic energy is transferred to the debris cloud ( ˜Edc/E0= 1). In this study, the highest HVI-induced normalized target mass loss was mt/mp⇡90, yielding ˜ ⇡0.04 for the materials and HVI conditions considered ( v0=2.5,6.0 km/s, 10The term “critical” is used here to emphasize that all fragments (projectile and target) are assumed to be traveling directly downrange at vdc. 14 ht/dp= 2). This indicates that for the target experiencing the maximum mass loss, if all E0were transformed into Edc, only 0.04 mtwould contribute to the debris cloud’s kinetic energy. As an aside, this procedure was used on previous UHMWPE and HDPE HVI data (see Table S2 and Fig. S4) [23], indicating that HDPE marginally outperformed UHMWPE at various impact velocities for ﬁxed target temperature and projectile/target geometry. 3. Hypervelocity Impact Experimental Results and Discussion This section details results for the 2.5 km/s and 6.0 km/s HVIs on the 12.7 mm thick UHMWPE and HDPE plates, whose initial temperatures were set at T0⇡120C, 20C, and 140C.In-situ high-speed images of the HVIs events, perforation photographs, and performance metric plots are featured. Table 2 summarizes the key experimental results for each combination of PE type, impact velocity ( v0), and initial target temperature ( T0), including normalized target mass loss ( mt/mp), target e↵ective perforation di- ameter ( de/dp), debris cloud tip velocity ( vdc/v0), and critical debris cloud kinetic energy ( ˜Edc/E0). Table rows corresponding to T0⇡120C, 20C, and 140C are highlighted in blue (cold), white (room tem- perature), and red (hot), respectively. Impact velocities varied across the experiments, with measurements atv0=2.49±0.25 km/s and v0=6.17±0.10 km/s for each desired v0value. These ﬂuctuations at a targeted v0value had little e↵ect on impact loading conditions ( i.e., temperature, stress, strain, and strain rate distributions) compared to that resulting from the ⇠150% increase from v0⇡2.5 km/s to v0⇡6.0 km/s (cf. Fig. S7). T0measurements varied within a range of ±2C and corresponded to PE plate centerline temperatures in the aperture/window region of the ﬁxture ( cf.Fig. 3c). In HVI shielding applications, the debris cloud generally poses a more signiﬁcant threat to subsequent Table 2: A summary of the temperature-controlled HVI experiments performed in this study (twelve total), including measure- ments of impact velocity, mass loss, and e↵ective perforation diameter. No. Material v0(km/s) T0(C)  mt/mpde/dpvdc/v0˜Edc/E0 1 UHMWPE 2.64 -120 1.10 1.33 0.40 0.17 2 UHMWPE 6.10 -120 68.01 7.77 0.42 0.68 3 UHMWPE 2.20 20 2.39 1.14 0.47 0.24 4 UHMWPE 6.30 20 13.60 3.25 0.46 0.33 5 UHMWPE 2.69 140 33.60 4.17 0.48 0.55 6 UHMWPE 6.00 140 90.32 8.87 0.46 1.00 7 HDPE 2.40 -120 6.42 1.60 0.40 0.20 8 HDPE 6.20 -120 86.83 7.83 0.41 0.75 9H D P E 2 . 2 0 2 0 0 . 7 31 . 4 2 0 . 4 4 0 . 2 0 10 HDPE 6.20 20 7.98 4.65 0.45 0.27 11 HDPE 2.78 140 9.86 1.50 0.37 0.19 12 HDPE 6.20 140 36.10 6.33 0.35 0.30 v0,p r o j e c t i l ei m p a c tv e l o c i t y ; mp=0.372 g, projectile mass; dp=6.35 mm, projectile diameter; T0,i n i t i a lt a r g e tt e m p e r a t u r e ; mt/mp,n o r m a l i z e dm a s sl o s s ; de/dp,n o r m a l i z e de ↵ e c t i v ep e r f o r a t i o nd i a m e t e r ; vdc/v0,n o r m a l i z e dd e b r i sc l o u dv e l o c i t y ; ˜Edc/E0,n o r m a l i z e dc r i t i c a ld e b r i sc l o u dk i n e t i ce n e r g y[ E q .( S 1 4 ) ] . 15 assets, personnel, or infrastructure than the corresponding ejecta cloud. In addition, the debris cloud con- tains most of the failed projectile/target material. For these reasons, the following discussion prioritizes its formation, expansion, and characteristics. Nevertheless, many conclusions drawn about the debris cloud are also applicable to the ejecta cloud. For each of the twelve HVI experiments, the high-speed camera captured shadowgraphs of the projectile’s approach to and impact on the target, as well as the ensuing ejecta and debris clouds. In general, the debris cloud started forming immediately after target perforation. However, the concentration of emerging PE material initially obstructed shadowgraphic light transmission, delaying full visibility of the debris cloud’s features until it reached a “fully developed” state. For both PEs, this state was typically achieved at t⇡100µs regardless of v0,w h e r e tdenotes the event time relative to projectile impact. High-speed images showing debris cloud development are available in the Supplementary Informa- tion, Figs. S5 and S6. Figure 5 displays high-speed images of fully developed debris clouds resulting from v0⇡2.5 km/s HVIs into the UHMWPE (left) and HDPE (right) plates, with initial target temperature increasing sequentially from top to bottom: T0⇡120C (Fig. 5a and 5b), T0⇡20C (Fig. 5c and 5d), and T0⇡140C (Fig. 5e and 5f). The UHMWPE and HDPE target locations are highlighted in blue and green, respectively, due to the target assemblies (target inside ﬁxture) being two to four times thicker than the targets themselves. These assemblies were positioned slightly uprange within the camera’s ﬁeld of view (FOV) to better showcase the debris cloud’s deﬁning features. Each image displays a scaled projectile icon on the target’s uprange side to indicate the direction of impactor motion. In some experiments, the thermocouple wire was visible in the camera’s FOV but was far enough from the impact axis to not a↵ect the experiments. For the v0⇡2.5 km/s impacts, both PEs underwent comparable adiabatic shock heating at each T0due to their similar densities and heat capacities, and each target’s local internal energy surpassed the threshold to fully melt the material (see Sect. SI.8). Regardless of T0, the projectile immediately after perforation ap- peared to be deformed/eroded but largely intact, leading its debris cloud. For the UHMWPE plate, lowering its temperature below Tgresulted in signiﬁcant target brittleness under the dynamic loading, with a large presence of small particles in the debris cloud (Fig. 5a). This low ( T0⇡120C) target temperature further restricted the UHMWPE chains’ freedom to move relative to one another while undergoing rapid deformation beyond the constraint already imposed by its extremely entangled molecular network ( Ne⇠3,800). Con- sequently, the increased molecular relaxation times caused stresses to spike, resulting in pronounced brittle fragmentation behavior, even as impact-induced temperatures exceeded Tm(cf. Fig. S7). For the same T0, HDPE notably displayed a similar quasi-brittle fragmentation response, with the exception of a minor presence of melted material around and trailing the deformed projectile (Fig. 5b). This molten material, being closest to the projectile during perforation, likely experienced a temperature rise sucient to overcome 16 Figure 5: Fully developed HVI debris clouds for UHMWPE and HDPE impacted at v0⇡2.5k m / sf o rt e m p e r a t u r e s( a ,b ) T0⇡120C, (c, d) T0⇡20C, and (e, f) T0⇡140C. At T0<T g, HDPE shows bulk fragmentation (b) similar to UHMWPE at room temperature (c). At T0>T m, UHMWPE’s melt response increases (e), aligning its debris cloud geometry closer to that of HDPE (f). Times tare given relative to impact. More debris cloud development is shown in Fig. S5. the e↵ective chain immobilization caused by its entanglements and depressed T0value. The low-temperature PEs’ fully developed debris cloud envelopes were each traced and then superimposed to underscore their similarities at this T0value (Fig. 6a). These key observations strongly support the conclusion by Rogers et al.[23] that the major di↵erences in the PEs’ HVI responses at room temperature stemmed from an interplay between the rate of loading and the average rate of molecular disentanglement and reorientation. In essence, lowering T0for ﬁxed Neinhibited high-rate chain motion analogously to increasing Neat ﬁxed T0, making HDPE behave more like UHMWPE when subjected to similar HVIs (more later). At room temperature, UHMWPE and HDPE showed the “bulk fragmentation” and “bulk melting” behavior (Fig. 5c and 5d), respectively, reported in Ref. [23] ( cf. Fig. 1). This consistency underscores the repeatability of the PEs’ HVI responses, even with a nearly threefold increase in ht/dp.11The PEs’ dynamic failure behavior di↵ered 11As an aside, changing the material manufacturer also does not appear to a↵ect the ultra-high-rate response of each PE at room temperature ( cf.[ 5 6 ] ) . 17 Figure 6: Superimposed HVI debris cloud envelopes for UHMWPE and HDPE at speciﬁc temperatures (rows) and impact velocities (columns), with times tgiven relative to impact. At T0⇡20Ca n d v0⇡2.5k m / s( c ) ,d e b r i sc l o u ds h a p e sd i ↵ e r signiﬁcantly, but at T0⇡120Ca n d T0⇡140C, they are similar, indicating comparable failure modes and expansion rates at these transition temperatures. At v0⇡6.0k m / s ,d e b r i sc l o u dg e o m e t r i e sa n de x p a n s i o nr a t e sa r ea l i k ea c r o s sa l l T0,s h o w i n g that temperature sensitivity diminishes as strain rate increases. the most at this 20CT0value, leading to pronounced di↵erences in fully developed debris cloud expansion behavior (Fig. 6c). ForT0>T mandv0⇡2.5 km/s, the UHMWPE target’s debris cloud was more elongated along the impact axis and denser in appearance due to an increased presence of apparent interconnected material (Fig. 5e). This shift in bulk HVI response at this higher ( ⇠140C) target temperature is also attributable to the enhanced available molecular motion, which decreases as temperature drops. Increasing T0above 18 Tmsubstantially enhanced free volume, increased rates of disentanglement and reorientation, and shortened relaxation times for the long PE chains. The impact-induced shocks and rapid visco-plastic deformation elevated local temperatures well beyond Tm, further amplifying molecular motion ( cf. Fig. S7). As a result, the molten UHMWPE in the nascent debris cloud ﬂowed readily during early expansion. However, the amorphous polymer network remained extremely entangled and constrained. As the hot expanding material stretched and thinned, it experienced some disentanglement and cooled. The extremely long PE molecules undergoing rapid deformation became increasingly immobile. Instantaneous rates of disentanglement and reorientation dropped and relaxation times spiked. At some critical level of material expansion, the polymer chains could no longer disentangle and/or reorient to relax the rapidly rising stresses. Stress accumulation then gave way to chain scission. Macroscopically, the highly viscous liquid ceased to ﬂow and fractured rather uniformly, producing a dense cloud of UHMWPE fragments. The quasi-brittle HVI responses of room temperature UHMWPE and T0<T gHDPE were also attributed in part to this failure process; however, material fracture occurred prior to such extensive ﬂow, creating noticeably less dense, interconnected, and elongated debris clouds. A more extreme case of UHMWPE’s dynamic failure process explains the characteristic web-like struc- ture seen in the room temperature HDPE target debris cloud ( cf. Fig. 5d). Initially, this debris cloud resembled a thick, rapidly expanding membrane or “bubble” of continuous molten material. The thickness of this membrane, however, was nonuniform. As expansion continued, its thinner regions experienced dispro- portionately more biaxial strain, forcing the deforming HDPE chains to disentangle, reorient, and relax in the ﬂow directions faster than those in the thicker regions. Some molecules perhaps even became suciently aligned in the strain directions to form strain-induced crystalline domains [78]. Relative chain motion in the more quickly rearranging chains decreased until the thinning bulk material could no longer sustain ﬂow and elongation. Stresses within the local polymer network increased until chain scission occurred. Macroscop- ically, the membrane material in the thinner regions ruptured and subsequently retracted into the thicker regions as in-plane stresses relaxed. Elongated PE chains returned to more entropically favored conforma- tions, and the average distance between chain ends dropped. Following this rupture process, the thicker regions elongated and formed an expanding network of interconnected molten HDPE ﬁbrils. Given that both PEs were subjected to similar loading conditions ( v0⇡2.5 km/s), the di↵erence in their fragmentation/rupture thresholds at a given T0value is largely due to the drastic di↵erence in their average number of entanglements ( i.e., UHMWPE is ⇠2,600% more entangled that HDPE).12Experimental 12For the PE plates heated to T0>T m,m o s to ft h ec r y s t a l l i n er e g i o n si nt h es e m i - c r y s t a l l i n eP E sw e r em e l t e da n dc o n v e r t e d to amorphous arrangements. This suggests that both PEs in the following discussion were both amorphous networks of entangled PE molecules, primarily di↵ering in MwandNe. 19 observations support this interpretation. For HDPE heated above its Tm, the increased free volume enabled its shorter, less entangled chains to become highly mobile. Adiabatic heating from shocks and rapid visco- plastic deformation further enhanced this molecular mobility to levels sucient for bulk material ﬂow at extremely high impact loading rates ( ˙ "⇠106s1). This shift in microstructural response time facilitated the formation of a membrane-like debris cloud that could sustain remarkable levels of expansion without rupturing (Fig. 5f). Hence, HDPE’s debris cloud expansion threshold was signiﬁcantly extended by a T0-induced increase in chain mobility. In addition, the HVI-induced debris clouds for the UHMWPE and HDPE targets at T0>T mwere similar (Fig. 6e). These ﬁndings strongly suggest that rising T0increasingly aligns UHMWPE’s HVI behavior with HDPE’s. Furthermore, decreasing T0brings HDPE’s response closer to UHMWPE’s, provided that v0is ﬁxed. For both PEs, the degree of debris cloud expansion at which material breakup begins primarily determined the size and shape of debris cloud fragments/ﬁbrils and the level of apparent material connectivity. This threshold is governed by the average rate at which neighboring chains can disentangle and reorient, which depends largely on T0,v0, and Ne. Increasing the impact velocity to v0⇡6.0 km/s shortened the perforation event duration by roughly 60%, which in turn raised both the heating and loading rates experienced by the deforming PE material. As a result, local target temperatures well exceeded Tmfor both PEs regardless of T0, and strain rates reached 107s1(cf. Fig. S7). These changes to the temporal and spatial distributions of temperature and strain rate undoubtedly altered the predominant energy absorption mechanisms and dynamic failure behaviors for both PEs. High-speed images of debris clouds resulting from v0⇡6.0 km/s HVIs on the roughly 120C, 20C, and 140C PE plates are shown in Fig. 7, which is arranged similarly to Fig. 5. AtT0⇡120C, UHMWPE’s debris cloud consisted of discrete, irregularly shaped fragments of varying size (Fig. 7a), consistent with ﬁndings at v0⇡2.5 km/s ( cf. Fig. 5a). The signiﬁcant fragmentation seen for HDPE at v0⇡2.5 km/s and T0<T gwas partially reversed at the higher velocity, as the more severe impact-induced heating facilitated more instantaneous chain mobility. Instead, HDPE’s debris cloud featured disconnected, elongated fragments (Fig. 7b), shaped by the process that formed its ruptured and unruptured membrane structures at T0⇡20C and T0⇡140C, respectively ( cf. Figs. 5d and 5f). Yet, when T0⇡120C, impact-induced heating could not raise the target temperature enough to facilitate the same degree of chain elongation, separation, or disentanglement on the time scale of the strain. Hence, the HDPE molecules became e↵ectively frozen within the rapidly stretching ﬁbrils, causing them to fracture prematurely at necking regions during elongation. At room temperature, the debris clouds for the UHMWPE and HDPE plates impacted at v0⇡6.0 km/s exhibited bulk fragmentation (Figs. 7c) and bulk melting (Fig. 7d) responses, respectively, that were virtually indistinguishable from those reported in Ref. [23] ( cf. Fig. 1). At T0⇡140C, the UHMWPE 20 Figure 7: Fully developed HVI debris clouds for UHMWPE and HDPE impacted at v0⇡6.0k m / sf o rt e m p e r a t u r e s( a ,b ) T0⇡120C, (c, d) T0⇡20C, and (e, f) T0⇡140C. The fraction of melted material in the UHMWPE debris cloud increases with rising T0(a, c, e), despite concurrent bulk fragmentation at a given degree of debris cloud expansion (e). Conversely, melting in HDPE decreases below T0<T g,a l t h o u g hi tr e m a i n sp r e s e n t( b ) .T h e s eﬁ n d i n g si n d i c a t et h a tt h eb u l kb e h a v i o ro f the PEs is inﬂuenced by a competition between temperature, strain rate, and disentanglement rate (chain mobility). Times t are given relative to impact. More debris cloud development is shown in Fig. S6. debris cloud contained more molten material, as indicated by the presence of a dense web-like structure in its uprange portion, where expansion rates were lowest (Fig. 7e). The HDPE plate impacted under similar conditions displayed a continuous membrane-like debris cloud of molten material that withstood much greater levels of expansion without rupturing (Fig. 7f), similar to observations at v0⇡2.5 km/s for the same T0(cf. Fig. 5e). Both PEs’ debris clouds densiﬁed with rising temperatures, featuring fewer distinct fragments/ﬁbrils and more continuous material. This ﬁnding further emphasizes that, at a constant v0, a higher T0increased the expansion threshold at which debris cloud fragmentation/rupture began due to added chain mobility ( i.e., higher rates of disentanglement/reorientation and thus shorter relaxation times). Atv0⇡6.0 km/s for all T0values, both PEs showed similar debris cloud geometries and expansion rates, indicating reduced temperature sensitivity at higher loading rates. The considerable alterations in PE molecular mobility, caused by cooling and heating the targets pre- impact, likewise resulted in signiﬁcant variations in their deformation and failure features observed post- 21 impact. For the 120C UHMWPE plate impacted at v0⇡2.5 km/s, the perforation diameter was only marginally larger than that of the impactor (Fig. 8a). Residual out-of-plane deformation was present on both target faces but most prominent on the back side (Fig. 8b). Radial, circumferential, and in-plane target cracks nucleated but were quickly arrested, resulting in a jagged and rough failure surface akin to those seen in similar room temperature samples in Ref. [23]. UHMWPE’s quasi-brittle failure was thus mainly localized to the material in contact with and immediately surrounding the projectile during target perforation. The resulting fragments ultimately populated its debris cloud ( cf. Fig. 5a). The absence of extensive radial or circumferential cracking underscores UHMWPE’s strong resistance to crack propagation even when subjected to HVI near its Tg. Impact-induced stress waves, however, interacted to focus extreme tensile stresses on an inclined conical plane encircling the impact site. These stresses readily surpassed the material’s dynamic strength, causing voids to nucleate. These voids coalesced into a large cone-shaped fracture surface ( i.e., “cone crack”), akin to that observed in impacted brittle materials [79]. The spalled material, lacking enough residual momentum and energy for complete ejection, formed a raised circular region on the target’s back side (Fig. 8b). The T0⇡120C HDPE target, impacted at the same v0⇡2.5 km/s, showed widespread radial, circumferential, and in-plane cracks (Fig. 8c and 8d). With T0<T g, the crystalline regions in the highly crystalline HDPE target could not melt in the impact event’s time frame. As HDPE lacked UHMWPE’s densely entangled molecular network to facilitate load transfer, stresses concentrated in these regions until they e↵ectively shattered, leading to pronounced brittle failure of the bulk material. The perforation diameter for the HDPE target was almost double that of the projectile. The extreme adiabatic heating during impact softened/melted the material directly around the projectile, resulting in ﬂow patterns on the perforation surface. These features were localized to the inner walls of the opening, as HDPE’s poor thermal conductivity inhibited the lateral heating needed to enable any additional material ductility and/or ﬂow. This observation explains the relatively small amount of melted HDPE trailing the deformed projectile in the high-speed images ( cf.Fig. 5b). There was minimal out-of-plane deformation on either side of the target. Spalled and ejected material from the target’s back side, however, left behind a conical indentation concentric with the perforation (Fig. 8d). The perforation characteristics for the room temperature PE plates impacted at v0⇡2.5 were consistent with those observed in Ref. [23]. The e↵ective perforation diameter for the UHMWPE target was slightly smaller than that for the HDPE target (Fig. 8e–8h). The opening in each target was smaller in size than its respective counterpart at the lower T0value ( cf.Fig. 8a–8d). For both 20C PE plates, the impact-induced deformation morphology and failure features were more localized around the perforation. For example, the cone crack and raised circular region were now missing from the UHMWPE target’s back side. Yet, its failure 22 Figure 8: Front and back side images of UHMWPE (left) and HDPE (right) target perforations resulting from HVIs at v0⇡2.5k m / sa c r o s st a r g e tt e m p e r a t u r e s : ( a – d ) T0⇡120C, (e–h) T0⇡20C, and (i–l) T0⇡140C. For both PEs, perforation diameters ( de)w e r es m a l l e s ta tr o o mt e m p e r a t u r e( e – h )a n dn o t a b l yi n c r e a s e da t T0>T m(c, d, k, l). Residual out-of-plane deformation was also most pronounced for both materials at this T0. UHMWPE resisted crack propagation and ﬂow at each T0,w h i l eH D P Ee x h i b i t e de x t e n s i v eb r i t t l ef r a c t u r e( r a d i a l ,c i r c u m f e r e n t i a l ,a n di n - p l a n ec r a c k i n g )a t T0<T g(c, d) and ﬂow at T0>T m(k, l). A projectile is superimposed on each image for scale. surfaces remained jagged and rough. The comparable HDPE plate showed signiﬁcant residual out-of-plane deformation on the rear side (Fig. 8h), suggesting extensive impact-induced material softening/melt and ﬂow. Notably, ﬁnger-like protrusions on the circumferential rim surrounding the perforation indicated former attachment points of molten drawn HDPE ﬁbrils seen in the high-speed images ( cf.Fig. 5d). Heating the targets to T0⇡140C drastically changed the perforations for the same v0⇡2.5 km/s. The molten UHMWPE target showed a more jagged, asymmetrical perforation (Fig. 8i and 8j), with its e↵ective diameter increasing by nearly 280% compared to that at room temperature (Fig. 8e and 8f). Virtually no cracks or out-of-plane deformation surrounded the perforation on either target side, and failure surfaces showed minimal signs of melting and ﬂow. Extreme adiabatic heating from impact-induced shocks and rapid plastic deformation raised the target temperature to levels were some material ﬂow was possible, as observed in the early stages of debris cloud expansion ( cf. Fig. S5i). However, PE’s poor thermal conductivity limited 23 this ﬂow to heated material near and along the impact axis. Target material further (radially) from the impact axis did not experience this temperature rise but still experienced considerable strains, strain rates, and stresses. In these peripheral regions, UHMWPE’s molten, but still highly entangled, molecular network lacked the mobility necessary to ﬂow on the time scale of the strain. As the opening expanded radially due to residual momentum and energy in the target material, the highly viscous liquid PE resisted ﬂow, experienced intense stress, and succumbed to melt fracture [80]. Warming the HDPE target dramatically suppressed its viscosity, leading to an increased susceptibility for bulk softening and ﬂow. Consequently, its deformation morphology and failure surfaces di↵ered markedly from those observed at the lower T0 values. For example, the material around the perforation appeared to have been signiﬁcantly stretched before elastically recovering/retracting post-impact (Fig. 8k). This process produced a target opening with an e↵ective diameter virtually no larger than that seen for the room temperature sample. Signiﬁcant charring/discoloration present on the failure surface (Fig. 8l) indicated that the impact elevated local target temperatures enough to activate HDPE’s thermal degradation, consistent with numerical predictions ( cf. Fig. S7). Some visco-plastic deformation from stress waves traveling through the target rippled its once ﬂat surfaces. Even so, the elastic recovery of the material in the perforation region minimized residual out-of-plane deformation. The PE targets experienced signiﬁcantly more catastrophic failure when impacted at v0⇡6.0 km/s, inde- pendent of T0. Yet, altering T0at this velocity did lead to notable variations in the primary deformation and failure mechanisms exhibited by each PE. For instance, the 120C UHMWPE plate showed a perforation roughly eight times larger in diameter than the impactor (Fig. 9a) and ﬁve times larger in diameter than that seen for the comparable target impacted at v0⇡2.5 km/s ( cf. Fig. 8a). The morphology of the irreg- ular perforation surface clearly suggested UHMWPE brittle fracture, and residual out-of-plane deformation was virtually nonexistent. A cone-shaped fracture surface, showing signs of extensive charring/discoloration indicative of PE thermal degradation, formed around the perimeter of the opening (Fig. 9b). A large ring- shaped spall fragment, akin to the one not fully detached from the cold target impacted at v0⇡2.5 km/s, was ejected following the primary HVI event ( cf. Fig. S8). At the ampliﬁed impact-induced strain rates, UHMWPE’s highly entangled microstructure struggled to evenly distributed sharply rising stresses, and the target succumbed to some radial and in-plane cracking. For the same T0, the HDPE plate exhibited an e↵ective perforation diameter similar to that for the 120C UHMWPE target. However, the HDPE plate’s target opening had a notably more jagged and non-circular perimeter (Fig. 9c and 9d). The fracture surfaces deﬁning the perforation wall also showed evidence of PE thermal degradation. Extensive radial, circumferential, and in-plane cracking e↵ectively shattered the embrittled HDPE plate during and immedi- ately after impact. Consequently, the plate was kept in the ﬁxture for post-impact perforation imaging, and 24 Figure 9: Front and back side images of UHMWPE and HDPE target perforations resulting from HVIs at v0⇡6.0k m / sa c r o s s target temperatures: (a–d) T0⇡120C, (e–h) T0⇡20C, and (i–l) T0⇡140C. At T0⇡120C, UHMWPE still resisted crack propagation, while HDPE exhibited bulk brittle fracture. For the sample in (a, b), a cone fracture surface formed on the exit side, and a large annular fragment was later ejected (Fig. S8). The HDPE sample in (c, d) completely shattered and was thus photographed before removal from the ﬁxture to prevent it from disassembling (Fig. S9). Extensive material ﬂow, as well as charring (thermal degradation), were evident for the HDPE target at T0⇡140C( k ,l ) .O u t - o f - p l a n ed e f o r m a t i o nw a sm o s t pronounced for both PEs at room temperature. A projectile is superimposed on each image for scale. the fragments were collected and imaged once removed from the ﬁxture ( cf. Fig. S9). The predominant deformation and failure features observed for each room temperature PE target im- pacted at v0⇡2.5 km/s did not appear to change when v0was increased to 6.0 km/s. In addition, they continued to align with those from similar HVI experiments presented in [23]. However, the faster perforation event at T0⇡20C resulted in much more severe out-of-plane deformation for both PE targets, especially on their front faces (Figs. 9e–9h). The ⇠150% increase in v0resulted in a 200% and 236% increase in e↵ective perforation diameter for the T0⇡20C UHMWPE and HDPE targets, respectively. The fracture surfaces originally seen in the UHMWPE sample impacted at v0⇡2.5 km/s were even more apparent at the higher velocity. The opening’s in-plane perimeter was highly irregular due to short radial cracks, and stunted in-plane cracks caused the surrounding material to fan out perpendicularly. Together, these cracks 25 formed a perforation wall with a distinctive peak-and-valley morphology (Fig. 9e and 9f). Conversely, the HDPE target impacted at v0⇡6.0 km/s displayed smooth perforation surfaces with clear signs of material softening, melting, and ﬂow at 20C (Fig. 9g and 9h). The ﬁnger-like protrusions that were noticeable on the back surface of the room temperature target impacted at v0⇡2.5 km/s became more deﬁned and were also present on the impact side. Material thermal degradation was evident along the inner surface(s) of the opening for both PEs. On its front side, the HDPE target also showed signs of thermal degradation along the rim of out-of-plane deformation that surrounded the perforation (Fig. 9g). Elevating the PE targets’ temperature to T0⇡140C again signiﬁcantly altered their perforation mor- phologies when impacted at v0⇡6.0 km/s. Despite T0exceeding Tm, the UHWMPE plate still exhibited jagged, brittle-like fracture surfaces that lined the perimeter of the perforation (Fig. 9i and 9j), which was 170% larger in e↵ective diameter than that of the 20C target impacted at the same v0(Fig. 9e and 9f). Any signs of the molten, ﬂowing material visible in the high-speed images ( cf.Fig. S6i) were erased/removed as the perforation expanded due to residual momentum and energy in the surrounding target material (residual hole enlargment). At some degree of UHMWPE hole enlargement, the cooler, yet molten, encircling mate- rial ceased ﬂowing and started to experience melt fracture, mirroring the behavior seen in the 140C target impacted at 2.5 km/s ( cf. Fig. 8i and 8j). This was not the case for the 140C HDPE target impacted at 6.0 km/s. Instead, its perforation was encircled by material that had undergone extensive ﬂow, elon- gation/stretching, fracture/puncture, and elastic recovery (Fig. 9k and 9l). This HDPE deformation and failure resulted in an asymmetrical perforation roughly 30% smaller than that seen in the 140C UHMWPE plate impacted at the same v0(cf.Fig. 9i). The HDPE perforation was encircled by ﬁnger-like protrusions, which were fewer in number but larger in diameter than those seen on comparable targets impacted at lower T0. Failed target surfaces for both PEs appeared signiﬁcantly charred, indicating some material pyrolysis and combustion had occurred. The perforated plates were also inspected quantitatively to better characterize and understand the dif- ferences in their HVI-induced responses. The mass of each PE target was measured before and after impact to determine its normalized mass loss ( mt/mp). For both PEs across all T0, these values increased with impact velocity ( mt/mp/v0). At v0⇡2.5 km/s, the  mt/mpvalues for UHMWPE showed a monotonic increase with T0, rising nearly thirtyfold from 120C to 140C (Fig. 10a). This trend, however, did not hold for v0⇡6.0 km/s. Instead, the 20C UHMWPE target lost ⇠80–85% less mass than the 120C and 140C plates. This transition underscores the intricate interplay of T0,v0, and molecular mobility on dynamic material behavior/failure. In essence, lowering T0does make PE more brittle but simultaneously decreases the fraction of material undergoing visco-plastic ﬂow during perforation. UHMWPE’s ﬂow, elonga- tion, cooling, and ultimate fracture iswhat primarily drives its fragmentation. At v0⇡2.5 km/s, decreasing 26 T0suppressed UHMWPE ﬂow without inducing additional fracture/fragmentation, enabling a consistent reduction in  mt/mp. Conversely, the 6 .0 km/s impact into the 120C UHMWPE target didcause more material to fracture, and the resulting fragments (including the spall fragment) together had sixty times more mass than that ejected from the 120C target impacted at the lower velocity ( cf. Figs. 9a and 9b). AtT0⇡140C, the UHMWPE target’s mass loss was maximized for both v0, as increased bulk material ﬂow gave way to extensive melt fracture ( cf. Figs. 9i and 9j). These results show that the degree to which a PE target will fracture/fragment ( i.e., lose mass) as T0and/or v0vary is largely governed by the proportion of its material that can simultaneously resist ﬂow and retain toughness. Hence, at a given combination of v0andT0, the PE plate exhibiting the highest level of combined bulk ﬂow and quasi-brittle fragmentation loses the greatest mass ( e.g., the UHMWPE plates at T0⇡140C). This ﬁnding also aligns with the HVI response of the HDPE targets. At T0⇡120C, both HDPE targets experienced widespread brittle fracture (cracking), leading to 80–100% more mass loss than its room temperature samples ( cf. Figs. 8c, 8d, 9c, 9d). The 140C HDPE targets likewise experienced more mass loss but due to extensive visco-plastic ﬂow, elongation, and moderate fracture ( cf. Figs. 8k, 8l, 9k, 9l). These T0-induced transitions in HDPE’s HVI response resulted in trough-shaped  mt/mpvs.T0trends for both v0(Fig. 10a). All 20C and 140C HDPE targets, experiencing primarily thermal softening/melting and ﬂow, consistently lost less mass than the comparable UHMWPE targets, consistent with ﬁndings from Ref. [23]. However, this relationship was reversed at T0⇡120C due to HDPE embrittling more than UHMWPE. Interestingly, the highest target mass loss value for each PE was achieved at opposite extremes of the T0range, with both losing around ninety times the projectile’s mass. Comparable data from Ref. [23] (ht/dp=0.64,mp=1.41 g) is also displayed on the plot for comparison. Perforations were also compared across experiments using their normalized e↵ective diameter ratios (de/dp). In general, de/dpincreased with impact velocity. For each v0, the perforations in the 120C and 20C HDPE targets were larger than those in the similar UHMWPE targets (Fig. 10b), a trend consistent with ﬁndings reported in Ref. [23]. However, at T0⇡140C, the UHMWPE targets had larger de/dp values, as they underwent substantial post-impact residual hole enlargement viamelt fracture ( cf. Figs. 8i and 9i). Such hole enlargement was suppressed in the hot HDPE melted plates due to the material elastic recovery/retraction that occurred post-perforation ( cf. Figs. 8k and 9k). The HDPE targets impacted at 2.5 km/s showed no signiﬁcant change in de/dpwith varying T0, though there were some variations atv0⇡6.0 km/s. At room temperature, the HDPE targets showed larger de/dpvalues but less mass loss compared to the UHMWPE targets because of HDPE’s capacity for large-scale plastic deformation, as opposed to UHMWPE’s tendency to fragment ( cf. Fig. 10a). At T0⇡120C and 140C, larger perforation diameters were associated with greater mass loss values for both PEs regardless of v0, a change attributed 27 Figure 10: Response of UHMWPE and HDPE plates to HVIs at v0⇡2.5k m / sa n d6 .0k m / sa n d T0⇡120C, 20C, and 140C: normalized (a) mass loss,  mt/mp;( b )e ↵ e c t i v ep e r f o r a t i o nd i a m e t e r , de/dp;( c )d e b r i sc l o u dt i pv e l o c i t y , vdc/v0; and (d) critical debris cloud KE, ˜Edc/E0;a l l vs.T0.F o r a g i v e n P E ,  mt/mpwas greater at the transition temperatures, expect for UHMWPE at v0⇡2.5k m / sa n d T0⇡120C( a ) . de/dp(b) also increased at T0⇡120Ca n d1 4 0C.vdc/v0 nominally increased with T0,e x p e c tf o rt h ec a s eo fH D P Ea t T0⇡140C. Considering  mtindicates signiﬁcant variation in KE absorption with T0for both PEs (d). Data reported in Ref. [23] for ht/dp=0.64 is included for reference. to HDPE’s distinct deformation behaviors and failure mechanisms at the extreme temperatures. Analyzing the high-speed in-situ images of each HVI event o↵ered insight into the PE targets’ relative degrees of energy absorption. For each experiment, the debris cloud’s downrange-most tip was tracked over 28 time (along the impact axis) to calculate its average velocity ( vdc).13This velocity was then normalized by the corresponding v0for comparison with the other experiments. The vdc/v0values for the UHMWPE targets impacted at 2.5 km/s increased by 15–20% from T0⇡120Ct o T0⇡140C(vdc/v0/T0; Fig. 10c). A similar increase was seen between the 120C and 140C UHMWPE targets impact at 6.0 km/s; however, there was virtually no change in vdc/v0from T0⇡20Ct o T0⇡140C. The normalized tip velocities similarly increased for the 120C and 20C HDPE targets. These vdc/v0/T0trends align with expectations, as increases in temperature typically reduce material viscosity, hardness, and strength due to enhanced chain mobility. Notably, UHMWPE’s densely entangled microstructure fought activation of any new/additional predominant energy dissipation mechanisms as T0andv0varied. For all T0,t h e vdc/v0values for the UHMWPE plates were the same as or higher than those for the HDPE targets, a ﬁnding that suggests HDPE absorbed more projectile energy [ Ep/1(vdc/v0)2,e x c l u d i n g mtcontribution; cf. Eq. 1]. The normalized tip velocities for the 140C HDPE plates were notably the lowest among all targets, regardless ofv0orT0. In particular, they were about 25% lower than those for the UHMWPE targets heated to the same temperature (Fig. 10c). This reversal in HDPE’s trend ( i.e.,vdc/v0/T0!vdc/v0/1/T0) suggests that ( i) there is a shift in its predominant energy dissipation/failure mechanisms, ( ii) these mechanisms are being engaged for a longer duration of time, or ( iii) more mechanisms are being activated simultaneously (more later). Comparable debris cloud tip velocity data for the HVI samples in Ref. [23] are plotted in Fig. 10c for comparison. Using the normalized critical debris cloud kinetic energy ratio [ ˜Edc/E0,cf. Eq. (2)] to account for the combined e↵ect of target mass loss and debris cloud tip velocity may provide better insight into each PE target’s relative energy absorption ( Ep/1˜Edc/E0) and thus HVI performance. Since vdc/v0saw only moderate variation with v0andT0for both PEs, the  mt/mpvalue for a given target somewhat dominated the magnitude of its ˜Edc/E0ratio. Hence, the PEs’ trends in ˜Edc/E0with T0andv0tended to align with those seen in Fig. 10a. One exception is the HDPE targets impacted at 2.5 km/s, which showed no change in ˜Edc/E0with initial target temperature. In fact, except at T0⇡120C, the HDPE targets showed less sen- sitivity to changes in impact velocity (average strain rate) and temperature (molecular mobility) compared to UHMWPE targets. This distinction is attributable to their vastly di↵erent entanglement densities. For each v0,t h e ⇠20C and ⇠140C HDPE targets, which did not experience brittle fracture/fragmentation, ap- peared to better absorb projectile kinetic energy compared to the similar UHMWPE targets. Put di↵erently, the UHMWPE debris clouds possessed higher total kinetic energy, a ﬁnding consistent with previous work [23]. At T0⇡120C, the tougher UHMWPE targets better resisted crack propagation, fragmentation, and 13The variations in the vdcmeasurements, caused by the camera’s pixel resolution, were approximately ±0.05 km/s. 29 mass loss, leading to marginally lower ˜Edc/E0values compared to those for the comparable HDPE plates. Atv0⇡6.0 km/s, raising T0from about 120C to room temperature enhanced the performance of both PEs, primarily because increased molecular mobility facilitated strain delocalization and more visco-plastic deformation/ﬂow. Increasing T0further to roughly 140C resulted in virtually no change to HDPE’s per- formance at a given v0due to additional thermal softening/melting supporting progressively more material ﬂow. Conversely, the ⇠140C UHMWPE target experienced a sharp drop in performance for both v0.These results strongly suggest that, for a PE target impacted at a given v0,there exists an optimal T0value or, alternatively, degree of molecular mobility, that maximizes its energy absorption (Ep). The debris cloud tip velocity measurements independently support this conclusion [ i.e.,Ep/1(vdc/v0)2;cf. Fig. 10c]. The pre-impact, in-situ , and post-impact ﬁndings together arm that di↵erences in deformation be- havior, failure modes, and relative energy absorption between UHMWPE and HDPE can essentially be attributed to molecular mobility. At a constant Nevalue, raising the temperature of a given PE target increases its free volume, promotes chain disentanglement and reorientation, and reduces relaxation times. Conversely, increasing Neat constant T0has the opposite e↵ect. When subjected to HVI, a PE target with less constrained chains will experience increased large-scale thermal softening/melting and ﬂow. Under iden- tical impact conditions, imposed constraints on the target’s microstructure, either by reduced T0or elevated Ne, will induce more pronounced quasi-brittle fragmentation. Increasing v0alone can e↵ectively embrittle a target by raising the average strain rate [ ˙˜"=f(v0,ht,dp,...)] beyond the rates of disentanglement and reorientation. The target that exhibits the most visco-plastic ﬂow without bulk fragmentation will generally lose less mass, have smaller perforations, and better absorb energy. These observations suggest there is a critical average number of entanglements, N⇤ e=f(T0,v0,ht,dp,...)=f(T0,˙˜"...), (4) that, for ﬁxed v0,T0, and projectile-target combination, characterizes a PE target’s transition in HVI response from extensive quasi-brittle fragmentation to bulk thermal softening/melting and ﬂow. Hence, the proximity of a target’s Nevalue to N⇤ eis a strong indicator of its ability to absorb energy. In general, the energy absorbed by a target subjected to HVI can be expressed as Ep=Z⌧ 0˙Ep(t)dt, (5) where ⌧represents the time (relative to impact) at which the projectile (or its fragments) and the target cease to interact, tis the event time, and ˙Ep(t) is the target’s instantaneous energy dissipation rate. The 30 Figure 11: The e↵ect of a PE’s average number of entanglements per chain ( Ne)o ni t sp r i m a r yf a i l u r em o d e sw h e ns u b j e c t e d to HVI: (a) at NeN⇤ e,r e s t r i c t e dm o l e c u l a rm o b i l i t yl e a d st od e b r i sc l o u df r a g m e n t a t i o n ;( b )a t Ne⇡N⇤ e,an o n u n i f o r m membrane-like debris cloud forms, thins, and ruptures, resulting in an interconnected web-like network of PE ﬁbrils; (c) at Ne⌧N⇤ e,t h ed e c r e a s e dr e s t r i c t i o no nm o l e c u l a rm o b i l i t yf a c i l i t a t e st h ef o r m a t i o no fam e m b r a n e - l i k es t r u c t u r et h a tc a n extensively expand without rupturing. The critical average number of entanglements per chain, N⇤ e=f(v0,T0,ht,dp,...), marks the threshold at which the material shifts from predominantly bulk fragmentation to bulk ﬂow. PEs with intermediate Nevalues display a mixture of these behaviors. Each bulk material failure mechanism initiates at a di↵erent event time, t, leading to variations in target energy absorption, Ep=R˙Epdt,(i.e.,f a i l e dm a t e r i a l sc e a s et od i s s i p a t ee n e r g y ) . longer the material remains intact during perforation, the more time energy dissipation mechanisms can operate ( i.e., increased ⌧). Similarly, the more material that stays intact during perforation, the greater the proportion of deforming material that can dissipate energy ( i.e., enhanced ˙Ep). For ﬁxed T0and ˙˜", an impacted PE target will initially dissipate some energy through adiabatic shock heating, light emission, vaporization, and more, regardless of Ne.I f NeN⇤ e, the target continues to dissipate energy viarapid plastic work, thermal degradation, chain scission, and some local fracture before sudden widespread fragmentation of the deforming/ﬂowing material causes a premature drop in ˙Ep(Fig. 11a, E(a) p). For Ne⇡N⇤ e, fragmentation does not occur; instead, the target absorbs more energy due 31 to increased thermal softening/melting and prolonged visco-plastic ﬂow. The expanding material behaves like a membrane, prolonging interaction with the projectile and extending the impact time, ⌧. As the material expands, it begins to experience rupture and ﬁbrillation, leading to a gradual decrease in the target’s instantaneous energy dissipation rate, ˙Ep, as more material fractures (Fig. 11b, E(b) p). When Ne⌧N⇤ e, rupture is avoided, and ˙Epremains nonzero while the projectile interacts with the expanding, cooling, and sti↵ening PE material. Eventually, at a certain ⌧, the projectile punctures the membrane, ceasing its interaction with the target (Fig. 11c, E(c) p). AsNe!0 for the same impact conditions, the accompanying reduction in PE viscosity, strength, toughness, etc. begins to negate the improvements in Ep. Thus, there is an optimal Nevalue, ˆNe<N⇤ e, that maximizes Ep. For ﬁxed T0, a target impacted at v(1) 0will experience an average strain rate of ˙˜"(1).T h e target’s energy absorption is maximum (max E(1) p)w h e n Ne=ˆN(1) e<N⇤ e(1). Another target of identical geometry impacted by the same projectile at v(2) 0will experience average strain rate ˙˜"(2). Its maximum energy absorption value (max E(2) p) will be achieved at Ne=ˆN(2) e<N⇤ e(2).I fv(1) 0>v(2) 0,t h e n ˙˜"(1)>˙˜"(2) and ˆN(1) e<ˆN(2) e(Fig. 12a and 12b). This ˆNe/1/˙˜"relationship is analogous to the time-temperature superposition principle exhibited by PE. In essence, increasing average strain rate requires a reduction in Neto sustain the degree of molecular mobility that leads to maximum Ep(Fig. 12c).14This ﬁnding demonstrates the feasibility of a layered protective structure composed of Nmonolithic PE plates that is optimized for a speciﬁc impact threat envelope ( i.e., ranges of v0,dp,mp,etc.). Given an envelope, Neof thei-th plate ( i=1,2,3,..., N) would be tuned to the optimal value ( ˆN(i) e) speciﬁc to the local anticipated average strain rate ( ˙˜"(i)). Assuming the projectile impacts the i= 1 plate, ˙˜"(i)will decrease and ˆN(i) ewill increase as iincreases (Fig. 12d). In this way, each PE layer is designed for optimal energy absorption. 4. Conclusions The declining ecacy of traditional spacecraft MMOD shields and military ballistic armor necessitates the development of layered, threat-optimized protective structures for HVI mitigation. UHMWPE and HDPE show promise as intermediate layers, owing to their high mass-speciﬁc energy absorption, tailorability, and low density and cost. While the relatively low-rate ( ˙ "< 103s1) behaviors of these PEs are well- documented, their responses to HVI-induced strain rates ( ˙ ">106s1) are virtually unexplored and not well understood, especially near their TgandTmvalues. This study investigated the interplay of T0,v0, and Neon PE’s HVI response to help address fundamental questions about its dynamic behavior and highlight its engineering applications. 12.7 mm thick UHMWPE ( Mw=4.7⇥106g/mol, Ne⇠3,800) and HDPE 14Since T0increases molecular mobility, ˆNe/T0. 32 Figure 12: PE target energy absorption optimization: (a, b) the number of entanglements resulting in maximum Ep(ˆNe) decreases with increasing v0and thus average strain rate ( ˙˜").ˆNeis less than N⇤ e=f(T0,˙˜", . . . ), the Nevalue deﬁning PE’s transition from bulk quasi-brittle fragmentation to large-scale plastic deformation/ﬂow at a given v0,T0,a n dp r o j e c t i l e - t a r g e t combination. (c) For ﬁxed T0,ˆNedecreases with increasing average strain rate. (d) A layered PE plate protective structure where, give a threat envelope ( v0,dp,...), each i-th layer ( i=1,2,3,..., N)i st u n e dt od i s s i p a t et h em a x i m u me n e r g yf o ri t s local anticipated average strain rate. The plates are chosen to be more entangled as strain rate decreases. (Mw=1.7⇥105g/mol, Ne⇠140) plates were subjected to 2.5 km/s and 6.0 km/s HVIs by 6.35 mm diameter 2017-T4 aluminum spheres. Targets were impacted at T0⇡120C, 20C, and 140C. Pre-impact, in-situ , and post-impact results together arm that di↵erences in deformation behavior, failure modes, and relative energy absorption between the two PEs can be attributed to a competition between average rates of loading and chain relaxation. At T0⇡120C, both HDPE targets showed exten- sive cracking and fragmented completely. Conversely, the UHMWPE samples resisted widespread cracking but developed cone cracks around their perforations that generated large annular spall fragments. Debris clouds for both 120C PE plates were populated with distinct target fragments. At room temperature, 33 the UHMWPE targets fragmented extensively, whereas HDPE samples underwent signiﬁcant thermal soft- ening/melting and visco-plastic ﬂow. UHMWPE debris clouds consisted of distinct fragments, while HDPE debris clouds were akin to expanding, web-like networks of interconnected molten ﬁbrils, observations consis- tent with previous work. Heating the UHMWPE targets to 140C increased the amount of ﬂowing/molten material in the debris clouds. Yet, this enhanced ﬂow ultimately gave way to widespread melt fracture, resulting in bulk UHMWPE fragmentation even when impacted above its Tm. The 140C HDPE sam- ples instead exhibited increased high-rate softening, melting, and ﬂow without fracturing, leading to the formation of membrane-like debris clouds that underwent extreme expansion without rupture. All targets exhibited charring and discoloration indicative of thermal degradation from impact-induced heating, in line with predictions. In general, lowering T0for ﬁxed Neinhibited high-rate chain motion analogously to in- creasing Neat ﬁxed T0, making HDPE behave more like UHMWPE when subjected to similar HVIs. The opposite was also observed. Increasing v0heightened fracture/fragmentation susceptibility in both PEs by elevating strain rates beyond their rates of chain disentanglement and reorientation. The PE that lost less mass, had smaller perforations, and better absorbed energy generally exhibited the most visco-plastic ﬂow without subsequent bulk fragmentation. These observations suggest a critical Nevalue exists, which, given constant v0,T0, and projectile-target combination, marks a PE target’s HVI response shift from widespread fragmentation to bulk thermal soft- ening/melting and ﬂow. Consequently, for the same impact conditions, there is an optimal Nevalue that maximizes PE target energy absorption. Raising v0or lowering T0necessitates a decrease in Neto main- tain the molecular mobility essential for optimal energy absorption. Hence, a layered, strain-rate-tuned PE protective structure is viable. Acknowledgments This research is based upon work partially supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1746932. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the ocial policies, either expressed or implied, of the Army Research Oce or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.