Nonlinear rheological behavior and flow-induced crystallization of low-entangled UHMWPE/HDPE melt blends: Insights from transient shear and extensional flows Open Access

Studying the rheological behavior of polymeric materials within the linear viscoelastic regime (LVE) offers important insights into their molecular structure and dynamics [1]. However, accurately predicting polymer behavior during industrial processing techniques like extrusion and injection molding necessitates a robust understanding of flow behavior beyond the LVE regime [2]. In these industrial melt-processing scenarios, polymers experience significant nonlinear deformations in both shear and extensional flows. Therefore, comprehending the nonlinear viscoelastic (NLVE) response of polymeric materials in both flow fields is essential for their practical applications. Additionally, although considerable progress has been achieved in understanding the linear and nonlinear rheology of monodisperse entangled linear polymers, advancements in constitutive modeling and the availability of experimental data for polydisperse polymeric materials still do not meet industry requirements [3,4]. Industrially sourced polymers are typically polydisperse, exhibiting a broad distribution of molecular weights. While this polydispersity improves their processing characteristics, it also complicates predictions of their rheological behavior. Furthermore, the inclusion of an ultrahigh molecular weight (UHMW) tail, which enhances the mechanical properties of industrial materials—especially in high-strength applications—can complicate modeling efforts by making it challenging to capture the complete viscoelastic spectrum [5,6].

The nonlinear flow conditions imposed on the semicrystalline polymer during melt-processing plays a significant role in the crystalline morphology and mechanical properties of the end product [7]. Unlike isotropic structures (spherulites), the formation of oriented crystal structures—known as shish-kebabs—due to flow-induced crystallization (FIC) greatly enhances the directional mechanical strength of the end product [8]. The development of FIC requires chain stretching, which can occur in both types of flow fields, shear and extension [9,10]. However, chain stretching is rather difficult to achieve in shear deformation (often termed weak flow), while extensional deformation generates a stronger flow that leads to highly oriented and stretched molecules in the direction of the extension, effectively promoting FIC (termed strong flow) [11,12]. Additionally, the presence of high molecular weight chain fraction in the polymer melt governs FIC and the formation of the shish-kebab structure [9]. Hence, melt-blending commercial low-molecular weight polymers with a fraction of disentangled ultrahigh molecular weight polymers (dis-UH) is a promising method to facilitate FIC and, consequently, improve the mechanical properties of the commercial grade, as proven in our previous work on linear high-density PE (HDPE)/dis-UH blends [13]. While the concept of melt-blending a fraction of dis-UHMW polyethylene can be applied to other dis-UHMW polyolefins, such as isotactic-polypropylene [14] and trans-1,4 polybutadiene [15], this study will focus specifically on the nonlinear shear and extensional rheology and their implications for flow-induced crystallization (FIC) of blended linear UHMWPE with commodity linear PE.

Research on the effects of melt blending linear UHMWPE with commodity linear PE matrix on nonlinear shear and extensional flow fields, as well as flow-induced crystallization (FIC), is quite limited. For instance, Keum et al. investigated the formation of shish-kebab crystalline structures resulting from shear-induced crystallization in solution-blended UHMWPE (at 2 and 5 wt. %) with HDPE [16]. Using in situ rheo-SAXS and -WAXD techniques, they demonstrated that the shear-induced extended chain crystalline structures (shish) primarily stemmed from the presence of ultralong chains of UHMWPE. However, their study lacked a systematic investigation of nonlinear rheological behavior. Similarly, Wingstrand et al. explored the influence of UHMWPE tails in the HDPE matrix on extensional behavior and the development of oriented crystalline structures [17]. Through solution blending, they incorporated 1 wt. % of UHMWPE into HDPE and observed a notable increase in extensional stress in the samples containing UHMWPE. Nonetheless, the impact of UHMWPE tails on transient nonlinear shear behavior was not addressed.

On another note, Hofmann et al. employed in situ reaction blending to create self-reinforced polyethylene composites with an ultrabroad molecular weight distribution [18]. This composite included UHMWPE, HDPE, and HDPE wax, with UHMWPE content reaching up to 12 wt. %. They demonstrated that the resulting PE composites developed extended-chain fiber structures that enhanced toughness, stiffness, and strength. However, their study lacked any rheological investigation. The extensional rheological behavior of such PE blends was examined by Szántó et al., who focused on the strain-hardening behavior in the nonlinear extensional flow of in situ multimodal PE blends containing UHMWPE [19]. Their analysis at low extensional rates indicated that the strain hardening observed after necking might result from both chain stretching and FIC. Nonetheless, their work concentrated exclusively on the extensional rheology of FIC, lacking the use of techniques such as small-angle X-ray scattering (SAXS), wide-angle x-ray diffraction (WAXD), scanning electron microscopy (SEM), or transient nonlinear shear analysis.

In our recent work, we demonstrated that linear disentangled UHMWPE can effectively reinforce linear PE grades through a solvent-free melt-blending process, as shown by our investigations into linear viscoelastic (LVE) behavior and solid-state tensile tests [13]. In contrast to the commercially available fully entangled UHMWPE (eUH), the low-entangled initial state of dis-UH promotes enhanced dispersion kinetics within the HDPE matrix, resulting in a homogeneous blend containing up to 20 wt. % of dis-UH with improved mechanical properties. The success of this homogeneous blending can be explained as follows: dis-UH has a low density of long-long entanglements, while HDPE possesses a high density of short-short entanglements. This difference facilitates the formation of long-short entanglements between dis-UH and HDPE. In contrast, establishing long-short entanglements in eUH/HDPE blends requires the unwinding of long-long entanglements, which presents a higher kinetic barrier than in dis-UH/HDPE blends, ultimately leading to unsuccessful homogenization.

In this study, we provide a systematic analysis of the novel solvent-free melt-blended samples of dis-UH with commercial polydisperse HDPE, having dis-UH content of up to 20 wt. %. We begin with the first comprehensive analysis of transient nonlinear shear flow during start-up and relaxation for HDPE/dis-UH blends, which is particularly challenging for highly elastic polymers, such as those with a high fraction of dis-UH. By varying shear rates (from 0.001 to 10 s⁻¹) and dis-UH content (0–10 wt. %), we investigate the start-up overshoot in viscosity, focusing on parameters such as the strain at which the maximum occurs $( γ max)$⁠, the normalized maximum stress relative to the steady-state stress $( σ max/ σ steady)$⁠, the steady-state stress $( σ steady)$⁠, and viscosity $( η steady)$⁠. Following this, we analyze the relaxation behavior by extracting the relaxation rates at both short times and long times after each start-up shear rate for HDPE/dis-UH blends. Next, we explore the uniaxial extensional flow of the blends, examining the strain-hardening (SH) phenomenon at two different temperatures (135 and 140 °C) and four dis-UH weight fractions (0, 5, 10, and 20 wt. %) by analyzing the induction time and strain at the onset of SH, the critical elongational rate $( ε ˙ critical)$⁠, and the relaxation behavior before and after SH. Finally, we examine the crystalline structure resulting from flow-induced crystallization using 2D SAXS, WAXD, and SEM. This analysis involves fixing the dis-UH fraction at 20 wt. % while varying the strain (0.5, 2.5, and 3.3) and fixing the strain at 3.3 while varying the dis-UH fraction (5, 10, and 20 wt. %).

Our fundamental study provides several significant advances in molecular blending of the intractable polymer with the commercially available polyethylene grades. The study conclusively demonstrates the influence of entanglement state, tailored during synthesis, on industrially viable solvent-free melt blending between commercial HDPE and the low-entangled UHMWPE, where the latter is synthesized using a single-site catalytic system. To recall, Boscoletto et al. demonstrated that only 3 wt. % of the commercially available UHMWPE (synthesized using a Ziegler–Natta catalytic system) could be successfully melt-blended into an HDPE matrix without phase separation [20]. In contrast, our work shows unprecedented melt blending of UHMWPE up to 20 wt. %, with proven homogeneity through linear viscoelastic investigations [13]. This paper systematically investigates nonlinear viscoelastic response of the melt-blended 5%, 10%, and 20 wt. % of UHMWPE in a commercial HDPE. To the best of our knowledge, this study is one of the few, if not the only one, to explore the transient behavior of nonlinear steady shear in highly elastic materials, specifically UHMWPE-based blends. Finally, our work represents the first comprehensive experimental investigation of industrial polydisperse UHMWPE/HDPE blends that combine transient nonlinear shear flow, uniaxial extensional flow, SAXS, WAXS, and SEM analyses. These contributions, while linking the strong influence of polymerization conditions on the entanglement state and its influence on molecular blending, show advancement in the understanding and application of UHMWPE/HDPE systems in industrial contexts, providing further opportunities on molecular modeling of industrial polydisperse polymers.

The details regarding the materials utilized in this study, including their preparation, blending methods, and molecular characteristics, can be found in our earlier publication [13]. High-density polyethylene (HDPE P6006N, pipe grade) is sourced from SABIC as a nascent powder, free of additives, with a melt flow rate of 0.23 g/10 min, an apparent molecular weight (M_w) of 0.37 × 10⁶ g/mol, and a dispersity index (Ð) of 2.9, serving as the matrix for our blends. The disentangled ultrahigh molecular weight polyethylene (dis-UH) is synthesized in-house using a single-site catalyst system, yielding an apparent M_w of 3.3 × 10⁶ g/mol and a Ð of 11, with the synthesis method detailed elsewhere [21]. The dis-UH is incorporated into the HDPE matrix at varying weight percentages: 5%, 10%, and 20%. The powder mixture of HDPE/dis-UH is then fed into the corotating twin-screw microcompounder (Thermo Scientific HAAKE MiniLab 3 Micro Compounder). The compounding condition is 190 °C, 150 RPM, and 5 min of residence time. The resulting blends are labeled as “dBx,” where x denotes the dis-UH content in wt. %. For instance, a blend containing 5% dis-UH in HDPE is designated as dB05. Table I presents the parameters and compositions of all blends used in this study, including the average cross-over relaxation times (τ_co), which is measured as an average of multiple small-amplitude oscillatory shear (SAOS) runs (see Sec. II B 1), and melting temperature (T_m). These parameters are obtained through melt rheology in an equilibrium state, while T_m is determined using differential scanning calorimetry (DSC), as explained in our previous work [13].

For the nonlinear shear experiments, the samples are molded into disks with an 8 mm (for dB05 and dB10) and 10 mm (for HDPE) diameter at 160 °C and 1 bar using a Collin (P300S) hot compression system. Additionally, for the uniaxial extensional experiments, the samples are shaped into rectangular strips measuring 10 mm in width, 60 mm in length, and 0.2 mm in thickness. These strips are then cut into smaller rectangular samples with dimensions of 5 ± 0.5 mm in width, 15 ± 1 mm in length, and 0.2 ± 0.05 mm in thickness.

The details of all LVE experiments and analysis are discussed in depth in our previous work [13], where prior to linear viscoelastic rheological experiments, all blends are maintained at 160 °C in the rheometer for at least 3 h. Multiple SAOS experiments are then monitored at 160 °C over an ∼2-day period to ensure data consistency and thermal stabilization of the samples studied.

In the current work, SAOS measurements are done at 160 °C between each transient shear flow and relaxation to ensure the stability of the samples in the nonlinear flow. The SAOS data, shown in Fig. S1 in the supplementary material, exhibit runs from previous study [13], and SAOS runs performed between each nonlinear transient shear flow experiments. Additionally, for comparison, the average LVE data include SAOS runs performed on two different instruments: strain-controlled ARES-G2 rheometer (TA Instruments) and Discovery Hybrid Rheometer (DHR-20, TA Instrument, USA). Fig. S1 in the supplementary material shows that the resulting curves align closely, confirming the absence of polymer degradation during the measured timescale and equilibration process of the nonequilibrium polymer melt. For all samples, the average τ_co and their standard deviation are recorded in Table I. The complex viscosity $( η ∗)$ LVE envelope for both, steady shear and uniaxial extensional transient, flows is taken from the average SAOS analysis. In addition, the LVE envelope extracted from SAOS data accessible to low frequencies via creep is recalled for comparison.

The nonlinear rheological measurements are performed using a strain-controlled ARES-G2 rheometer (TA Instruments) in a controlled environment under nitrogen, with a temperature control of ±0.1 °C. All nonlinear shear measurements are done at a fixed temperature of 160 °C using cone-and-plate (CP) geometry, with the top plate having a diameter of 8 mm (for dB05 and dB10) and 10 mm (for HDPE), while the bottom cone having a diameter of 25 mm, a cone angle of 0.04 rad, and a truncation of 53 μm. In each nonlinear shear run with a specific shear rate, the time is controlled such that a total of 20 strain units is achieved. The polymer is allowed to relax for 10 h after each nonlinear shear experiment, followed by SAOS run to ensure the response of the material remains unchanged prior to initiating the next experiment with a different shear rate. However, in some of the measured data, the signal becomes weak and lost before reaching the 10 h duration. Nevertheless, the consistency of the SAOS data and their excellent superimposition indicate that the measured samples have fully relaxed, and no polymer degradation occurred during the experimental timeframe. The multiple SAOS runs following each nonlinear shear experiment, and the raw relaxation data are presented in Figs. S2 and S3(g)–S3(i) in the supplementary material, respectively. Due to the high elasticity of dB20, the loading gap is not reached (53 μm). Accordingly, our nonlinear shear experiments are limited to HDPE, dB05, and dB10.

For the uniaxial extensional experiments, the extensional viscosity fixture (EVF) mounted on the ARES-G2 rheometer is used at temperatures of 135 and 140 °C, with elongational strain rates of 0.01, 0.1, 0.5, 1, 3, and 5 s⁻¹. Sample dimensions are maintained at 5 ± 0.5 mm in width, 15 ± 1 mm in length, and 0.2 ± 0.05 mm in thickness. Each sample is placed in the EVF and allowed to rest for 20 min to ensure thermal stability. The 20-min waiting time is sufficient to erase any crystalline memory, as evidenced by the superimposition of the linear envelope obtained from the average SAOS data measured at 160 °C, which is well above the melting point, with the extensional data at 135 and 140 °C. This is further supported by the steady-state viscosity obtained from the nonlinear transient steady flow measurements at 160 °C and plotted with average $η ∗$ data in Fig. 2. The linear envelopes obtained from SAOS data, shown in Figs. 8 and 9, are shifted to the pertinent temperatures (135 and 140 °C) by means of the horizontal shift factors extracted from the time-temperature superposition (TTS) and multiplied by 3 (Trouton ratio). The Arrhenius plot of the horizontal shift factor as a function 1/T, at a reference temperature of 160 °C, is shown in Figure S4 in the supplementary material. In the isothermal stress-relaxation measurements, the main curve is interrupted (set $ε ˙=0$⁠) at different strain levels, where the experiment stops upon reaching 0.5, 0.8, 2.5, and 2.7 strain units at 1 s⁻¹ strain rate.

X-ray diffraction is employed to examine the crystalline structure formed during uniaxial extensional flow. To preserve the crystalline structure, the extensional flow is stopped as soon as the target strain is achieved, and the sample is rapidly quenched from 140 °C to room temperature using nitrogen gas. However, it is important to note that the quenched samples may undergo partial relaxation during the quenching process, experiencing stress decay before the structure is fully locked in. To estimate the decay time, we conducted independent quenching experiments using the ARES-G2 rheometer’s maximum cooling rate (Fig. S18 in the supplementary material). The results show that stress decays for approximately 10 s during cooling, from 140 °C until an upturn in stress occurs, signaling the onset of crystallization. Accordingly, the stress variation at quench is estimated to be within 50% drop, which is evaluated by considering the mean value of the stress monitored during cooling of the three different measurements. It is worth mentioning that our actual quenching protocol involves nitrogen gas, which provides a much faster cooling rate than the ARES-G2 maximum cooling rate. Therefore, the 10 s decay and 50% drop in stress at quench represents overestimation of the actual stress decay. The quenched samples are then investigated via SAXS, WAXD, and SEM.

Teneo scanning electron microscopy (Thermo Fisher Scientific, USA) is used to capture images of etched uniaxially stretched samples after quenching (see Sec. II B 2 for quenching and sample preparation method). To examine the impact of strain on the crystalline structure, the first set of images is obtained by varying strains (0.8, 2.5, and 3.3) while maintaining a constant dis-UH content of 20 wt. % (dB20). The subsequent set of images investigates the effect of dis-UH fraction, capturing samples with different weight percentages (dB05, dB10, and dB20) at a fixed elongational strain (ɛ) of 3.3. The uniaxially stretched samples are coated with iridium to prevent electrostatic charging and improve both image resolution and conductivity of the insulating polymer. An acceleration voltage of 5 kV is used during the SEM measurements, with a working distance of 2 mm between the sample and the Everhart–Thornley detector.

The etching process is performed for 30 minutes in a mixture containing sulfuric acid (H₂SO₄) and phosphoric acid (H₃PO₄) at 1 vol.% each, along with potassium permanganate (KMnO₄) at 1 wt.% of the total weight. During etching, the mixture is periodically placed in an ultrasonic bath for short intervals. After etching is completed, the specimens are washed in a sequence of four washing baths: (1) Cold dilute H₂SO₄ (2 volumes of H₂SO₄ to 7 volumes of distilled water), (2) concentrated H₂O₂ (30%) from the fridge, (3) distilled water, and (4) acetone. Each washing bath is also placed in an ultrasonic bath for brief periods, with each wash lasting at least 2 min. The etching recipe follows established procedures in the literature [23].

In this section, the NLVE start-up shear flow is investigated by means of stress growth coefficient $( η +)$ for HDPE, dB05, and dB10 at 160 °C with varying shear rate, ranging from 0.001 up to 10 s⁻¹. The resultant $η +$ for all the samples are shown in Figs. 1(a)–1(c). To validate the NLVE data, the linear envelope is calculated and plotted through a direct transformation of the average SAOS data at 160 °C (black open star), as well as SAOS data extended by creep experiment data from previous study (dashed blue line) [13], by applying the Cox–Merz rule $η( γ ˙)= η ∗(ω) | ω = γ ˙$ in conjunction with the Gleissle rule $η +(t)=η( γ ˙) | γ ˙ = 1 / t$ [24,25]. The linear envelopes of HDPE, dB05, and dB10 are very well mapping the start-up of $η +$⁠, indicating the consistency of the LVE and NLVE experiments of our blends.

At short times on each $η +( t)$ curve for a given shear rate, the data initially follow the LVE envelope but deviate noticeably at longer times. This deviation manifests as a viscosity overshoot, where $η +( t)$ reaches a maximum value before eventually decreasing to a metastable steady state. As the rate of deformation increases, the deviation from the linear envelope occurs more rapidly, the magnitude of the overshoot increases, and the steady-state value decreases. This behavior aligns with observations reported in previous studies on various soft materials [26–33]. This universal transient behavior has been robustly rationalized and understood through the tube model and its advanced generations [34,35]. The occurrence of the viscosity overshoot is observed only when the shear rate is faster than the inverse of the cross-over relaxation time $( τ c o − 1)$⁠. At shear rates faster than $τ c o − 1$ but slower than the inverse of the Rouse time $τ R − 1$⁠, the strain at the peak viscosity $γ Max$ occurs at a constant value of about 2.3. In this regime, the occurrence of the overshoot is driven by the chain orientation mainly. However, at shear rates faster than $τ R − 1$⁠, the combined action of stretch and orientation is found to control the overshoot appearance. Consequently, a power law trend of $γ max$ and an increase in the overshoot amplitude as a function of the shear rate are measured. In entangled polymers, the overshoot amplitude is attributed to the number of lost entanglements. Therefore, the steady-state viscosity reflects the equilibrium between entanglements and disentanglements under a steady shear flow. Another key observation is that at a given shear rate, with the increasing amount of dis-UH in the blend, the peak viscosity shifts to higher strains, Fig. 1(d). For an example, at a shear rate of $γ ˙=1 s − 1$⁠, $η max$ occurs at $γ max=2.2$⁠, 2.6, and 3.3 for HDPE, dB05, and dB10, respectively. This will be elaborated in more detail in the discussion related to Fig. 3.

It is important to note that a fully developed steady state is not achieved in our experiments. Each sample is subjected to 10 consecutive runs, where in each run the sample experiences shear start-up having a total of 20 strain units (time × shear rate), followed by 10 h of relaxation time, and SAOS measurements (frequency sweep). This protocol for the total runs required 108 h (4.5 days) per sample in the rheometer at elevated temperature (160 °C). Increasing the strain unit for a fully developed steady state would significantly extend the experimental time and raise the risk of thermal degradation. To ensure consistency and minimize this risk, we proceed with the chosen strain unit. Despite these limitations, the steady-state data align well with the LVE envelope from various experiments, as shown in Fig. 1, and later in Fig. 2. Additionally, it is worth noting that the high shear rate data, i.e., $7$ and $10 s − 1$⁠, are clearly affected by edge fracture instability due to the high elasticity of the measured samples [36–38]. The impacted data do not alter significantly the main findings and conclusions of the present study, as it will be further discussed in the following sections. For a more detailed analysis, we present in Figs. 2–5 several nonlinear quantities as functions of Weissenberg number $( W i 0)$ or shear rate $( γ ˙)$⁠.

Figure 2 presents the steady-state viscosity $( η steady)$ as a function of shear rate $( γ ˙)$ (filled symbols), alongside the average complex viscosity $( η ∗)$ as a function of frequency $(ω)$ (open symbols). Additionally, the linear $η ∗$ data from our previous work [13], which includes data obtained from SAOS and extended toward lower frequency range via creep experiments, are also plotted (blue dashed line). All NLVE steady-state viscosities align closely with the complex viscosity, confirming the applicability of the Cox–Merz rule. This validation indicates that the samples did not experience any irreversible instabilities, highlighting the effectiveness of our careful protocol, which includes a long relaxation time (10 h) after each experiment. This approach ensures that the LVE data reach the same equilibrated state before starting a new NLVE experiment (see Fig. S2 in the supplementary material). Additionally, it is worth noting a slight deviation of $η steady$ from $η ∗$ at the higher shear rates (7 and 10 s⁻¹), which is consistent across all samples. This deviation is attributed to edge fracture, which is known to become more pronounced at high shear rates [38]. To validate this, a recent study introduced a new criterion to classify edge fracture using the Cox–Merz rule [39]. According to their proposal [39], a 20% deviation of the steady-state viscosity below the linear envelope is considered indicative of edge fracture. Thus, we have created a curve that represents the 20% cutoff line (solid red line) lower than the average linear envelope, in which steady-state values falling below this line indicate that they suffer from edge fracture. Thus, the deviation observed at the highest two shear rates, 7 and 10 s⁻¹, confirms the occurrence of edge fracture, as evidenced by the drop that exceeds 20% from the LVE line.

Figure 3 displays a double logarithmic plot of the strain at which the maximum occurs $( γ max= γ ˙× t peak)$ against the characteristic Weissenberg number $( W i 0)$⁠, calculated based on the cross-over relaxation time $( τ c o)$⁠: $W i 0= γ ˙× τ c o$⁠. The horizontal error bars on $W i 0$ are calculated from the propagation of the standard deviation of $τ c o$⁠, and the vertical error bars on $γ max$ are obtained by multiplying the shear rate with the maximum time resolution of the ARES-G2 data acquisition (0.01 s). Unlike monodisperse polymers, the cross-over relaxation time (τ_co), defined as the inverse of the cross-over frequency, is an apparent parameter for polydisperse polymers. We have chosen to use this time as a reference clock to rescale all the data, enabling us to compare our findings at the same relative distance from a consistent reference point. This approach aligns with current and widely accepted practices within the framework of transient nonlinear shear studies [40–42]. Within the measured range of $W i 0$⁠, the $γ max$ data appear scattered around a constant average value, independent of $W i 0$⁠. However, the average value of $γ max$ increases with a higher wt. % content of dis-UH in the blend. In HDPE, which contains no dis-UH, $γ max , a v g$ is found to be 2.33 ± 0.21. This specific strain value aligns with predictions from Doi–Edwards theory, which suggests that chains experience orientation without stretching [29,43]. In contrast, $γ max , a v g$ increases to 2.51 ± 0.13 and 3.26 ± 0.28 for dB05 and dB10, respectively. The increase in strain beyond 2.3 indicates that the chains are experiencing both orientation and stretching. This enhancement in stretch for dB05 and dB10 is attributed to the increased polydispersity resulting from the inclusion of the UHMW fraction. This leads to a more constrained polymeric network and a slowdown in relaxation dynamics, as demonstrated in our earlier study [13]. The presence of long UHMW chains increases the flow resistance under applied shear rates, as the entanglements imposed by these long chains on the shorter HDPE chains act as permanent obstacles over the relaxation timescale of the short HDPE chains. This interaction results in a slight, yet noticeable, increase in chain stretch.

Figure 4 illustrates the normalized maximum stress relative to the steady-state stress $( σ peak/ σ steady)$ as a function of $W i 0$⁠. The error bars on $σ peak/ σ steady$ values are obtained by considering the standard deviation measured on $σ steady$ at the lowest shear rate for each sample (i.e., 0.001 s⁻¹), where the data scattering is greatest, and then propagating the relative error to $σ steady$ and $σ peak/ σ steady$ data measured at higher shear rates. At $W i 0<1$⁠, the $σ peak/ σ steady$ data for both HDPE and its blends appear to cluster around a constant value within experimental errors, i.e., $σ peak/ σ steady=1.06±0.04$⁠. At $W i 0>1$ of 1, the data points begin to rise, exhibiting a slope of approximately 0.1. Notably, this slope is lower than the value of 0.25 typically measured for linear monodisperse entangled polymers [36]. This slope quantifies the rate at which entanglements are lost and reformed under the action of convective constraint release (CCR) to reach the metastable steady state [29,45]. Another relatively new model used to explain the mechanism effective deformation of our UHMWPE-based blends and their HDPE matrix is reduced, indicating that the rate of partial entanglement loss and reformation is more constrained in our samples than is commonly observed in linear monodisperse entangled polymer melts. Indeed, the HDPE matrix is polydisperse, and the inclusion of UHMWPE further increases the polydispersity of the obtained blends, potentially affecting the slope of the $σ peak/ σ steady$ ratio.

To highlight the impact of polydispersity on this slope, we graphically analyzed the slope for linear entangled monodisperse polystyrene (m-PS) samples of various molecular weights, along with their blends to create polydisperse PS (p-PS) samples, based on the raw data from Parisi et al. [44]. The results are presented in Fig. 4(b) along with the data from this study. Notably, all mPS samples show a consistent slope of approximately 0.25, regardless of molecular weight, which ranges from 84 × 10³ to 200 × 10³ g/mol. However, when blended, most of the p-PS samples display a reduced slope of 0.18. However, introducing a small amount (6 wt. %) of low molecular weight sample into a higher molecular weight matrix (L185/L84 94/06, black open-rhombus) results in almost no change in the slope. In contrast, incorporating 2 wt. % of a high molecular weight sample into a lower molecular weight matrix (L200/L90 02/98, black open-circle) leads to a noticeable deviation from the 0.25 slope, even though the added fraction is only 2 wt. %. This interesting observation suggests that the low deformability is related to the slowing down of dynamics resulting from the added higher molecular weight components to the matrix, rather than when lower molecular weight components are used.

The proposed cause of low deformability, arising from the presence of high molecular weight fraction, is consistent with our finding, as presented in Fig. 4(b). In the context of our UHMWPE-based blends and their HDPE matrix, the skinny tube model (the opposite extreme of the fat tube) can be used to rationalize the reduced slope as compared to monodisperse polymers [13,46]. The extremely long relaxation times of the long chains of UHMWPE act as permanent obstacles, which will constrain the dynamics considerably [46–48]. Here, it is important to note that even the HDPE matrix has a UHMW tail, as shown by the GPC data presented in Fig. S12 in the supplementary material. Under nonlinear flow, these obstacles restrict the CCR action, resulting in weaker deformability of the dis-UH/HDPE blends and their HDPE matrix compared to linear monodisperse polymers.

Another relatively new model used to explain the mechanism behind the stress overshoot under nonlinear shear flow is the “grip force” model [49–51]. This model suggests that the action of CCR, which typically reduces entanglements and causes the overshoot, is influenced by an inter-chain “grip force.” This force prevents chain retraction until the strands reach a critical tension. By delaying retraction, the grip force postpones the CCR mechanism, reducing the number of constraints (entanglements) that are released. The grip force, as a competing effect to CCR, is expected to be more prominent in chains with a high number of entanglement strands $( Z)$⁠, such as ultrahigh molecular weight chains. Consequently, this leads to a lower stress ratio in the presence of UHMW content, as illustrated in Fig. 4. While this model presents an interesting dynamic, drawing valid conclusions would require sophisticated modeling capabilities, which are beyond the scope of this experimental work.

Furthermore, a similar slope for $σ peak/ σ steady$⁠, i.e., 0.1, has been noted in ring-linear polymer blends, where the weak deformability associated with a lower slope was attributed to the limited ability of ring polymers to change their conformation under shear flow [41,42]. In fact, we recently proposed a molecular model to rationalize the equilibrium behavior of dis-UH, suggesting that cores of nonwoven entangled chains, akin to ring polymers, are surrounded by shells of woven entangled chains. These cores remain trapped in this conformation, even when the melt plateau modulus seems to have reached an equilibrium state. As a result, the entire core–shell system exhibits self-similar dynamics, resembling the behavior of critical gels [52]. In analogy with the direct findings on ring-based blends, the complex conformation, i.e., core–shell, that long ultrahigh-molecular-weight chains are expected to adopt, in either the HDPE matrix or the corresponding blends, may explain the weak deformability observed in this study.

Figure 5 illustrates the steady stress $( σ s t e a d y= η steady× γ ˙)$ as a function of $γ ˙$ for the samples studied. The inset of Fig. 5 presents the power law exponent measured at low $γ ˙$ as a function dis-UH wt. % fraction. The $σ s t e a d y$ increases with $γ ˙$⁠, showing a clear distinction between the samples. At $γ ˙≤1 s − 1$⁠, dB10 consistently exhibits the highest $σ s t e a d y$⁠, followed by dB05 and then HDPE. The increase in $σ s t e a d y$ with higher content of dis-UH confirms the increased resistance to deformation of the blends compared to their matrix. However, the drop in $σ s t e a d y$ at the last two points, at $γ ˙$ of 7 and 10 s⁻¹, is attributed to edge fracture, whose effect becomes more pronounced at higher $γ ˙$ [36–38], as explained in the discussion related to Fig. 2. Additionally, at $γ ˙≤1 s − 1$⁠, $σ s t e a d y$ follows a power law increase with $γ ˙$ (slope of the data), with the power exponent decreasing as the UHMW fraction increases. The data presented in Fig. 5 show power law exponents of 0.71 for HDPE, 0.64 for dB05, and 0.61 for dB10. Notably, all measured exponents are below 1, indicating shear thinning behavior. It is important to highlight that an exponent of 1 corresponds to Newtonian behavior, which is expected to occur at lower $γ ˙$ than the shear rates explored in this study. The delayed Newtonian behavior is likely attributed to the increase in polydispersity and average molecular weight of the blended polymers with higher dis-UH content. This extends the terminal relaxation time, shifting the shear rate required to reach the zero-shear viscosity region (or a slope of 1 in the $σ s t e a d y$ vs $γ ˙$ plot) to lower values.

Finally, we would like to stress that data affected by edge fracture concern mainly the two highest shear rates (7 and 10 s⁻¹) and do not significantly affect our conclusions within the scope of the present experimental work. It must be recognized that assessing the nonlinear shear response of highly elastic materials is inherently challenging [36]. To address these difficulties, future work will utilize the mg-Rheology setup to study UHMWPE-based polymers [53], a cutting-edge technique designed to overcome the complexities of nonlinear behavior in such materials under high shear rates [38].

After achieving an apparent steady-state flow during the transient start-up shear, we monitor the subsequent stress relaxation following shear cessation for each $γ ˙$ over a duration of 10 h. This timeframe is sufficiently long to allow the stress to fully relax before commencing the next experiment. Figure 6(a) displays representative data for the stress relaxation decay, normalized by the steady-state stress value $( σ −/ σ steady)$⁠, as a function of time normalized by the cross-over relaxation time $( t/ τ c o)$ for the HDPE sample. The data for dB05 and dB10 are shown in Figs. S3(b) and S3(c) in the supplementary material. It is important to note that the data for $γ ˙= 10 − 3 s − 1$ is excluded from the analysis due to a weak signal, resulting in a significant error margin.

The following observations are made. First, the relaxation rate of each dataset (the slope of the curve) decreases over time, characterized by two principal relaxation rates. A fast relaxation rate is observed at short times, while a slow relaxation rate is noted at longer times. Second, the fast relaxation rates are significantly influenced by $γ ˙$ during shear flow: Higher $γ ˙$ leads to faster initial relaxation rates at short times. A quantitative analysis of these fast relaxation rates will be presented in Fig. 7(a). Conversely, the slow relaxation rates at long times are nearly independent of $γ ˙$⁠, which aligns with findings from previous studies on linear entangled polymer melts and solutions [36,54,55].

To gain further insights into the behavior of the slow relaxation rate, we plot $σ −/ σ steady$ as a function of $(α. γ ˙t)$⁠. In this context, the time $t$ for each relaxation dataset is multiplied by the corresponding shear rate $γ ˙$⁠, and $α$ is the shift factor used to align all data with that of $γ ˙$ = 10 s⁻¹. The $α$ values are shown in Fig. S3(f) in the supplementary material. Representative data for the HDPE sample are presented in Fig. 6(b), while the data for dB05 and dB10 can be found in Figs. S3(d)–S3(e) in the supplementary material. The clear collapse of the data at long times, achieved through shifting, confirms that the slow relaxation rate has a common origin and is not influenced by the shear rate. We define the long-time regime for evaluating the slow relaxation rates starting when the relaxation data exhibit a constant slope across all shear rates, as indicated by the dashed lines for each sample in the data presented in Figs. S3(a)–S3(c) in the supplementary material. It is important to note that the scattered data observed at the end of the relaxation experiments in Fig. 6(b) is attributed to the weak signal resulting from the extended relaxation time allocated to the samples’ relaxation (10 h).

Figure 7(a) illustrates the initial relaxation rates (1/τ_i) as a function of $W i 0$ in a linear-log scale for all shear rates $( γ ˙)$ of HDPE, dB05, and dB10. These rates are calculated from the slope $Δ ( σ − σ steady )/ Δ ( t τ c o )$ at short times, specifically within the range of $0.02< t τ c o<0.03$⁠. Overall, the initial relaxation rates increase monotonically with increasing $W i 0$⁠. At $W i 0<1$⁠, the increase is relatively slow, followed by a noticeable increase starting around $W i 0≥1$⁠. This increase at high $W i 0$ is classically attributed to the CCR [29,41]. When a polymer chain is confined within a virtual tube created by topological obstacles, i.e., entanglements, from neighboring chains, high deformation causes the chains to stretch and retract, thereby sweeping away the tube constraints [56,57]. Consequently, the CCR relaxation mechanism becomes more pronounced as $γ ˙$ approaches $τ c o − 1$⁠, resulting in accelerated relaxation rates above $W i 0=1$⁠, as depicted in Fig. 7(a). While it is well-established that CCR occurs during high $γ ˙$ of steady shear flow [56,57], the initial relaxation rate increases with $W i 0$ even after flow cessation. This observation has been reported in comb [40] and star polymers [29], where it is suggested that the increase in the initial relaxation rates after immediately stopping shear flow is due to CCR. At shear rates corresponding to $W i 0≥1$⁠, the polymer’s initial state in the relaxation experiment has fewer entanglements compared to its original state before the shear start-up, likely as a result of CCR during steady flow. Furthermore, the acceleration in dynamics evidenced by the fast relaxation rates is coherent with findings across various polymeric based systems with different architectures [29,40,58]. This suggests a universal feature of the fast stress relaxation rate due to the localized nature of the relaxation mechanisms occurring immediately after flow cessation.

To highlight the differences among the samples studied, we quantify the slopes extracted from the plot of $σ −/ σ steady$ as a function of $(α γ ˙t)$ shown in Fig. 6(b). These slopes are depicted in Fig. 7(b) as a function of the dis-UH wt. % content. The data reveal that the slope increases with the dis-UH fraction, amounting to −0.78, −0.57, and −0.49 for HDPE, dB05, and dB10, respectively. The slowing down of relaxation rate observed in our samples with increasing dis-UH wt. % content is attributed to the overall increase in molecular weight, confirming the successful molecular blending of our samples. In theory, slow relaxation rates should correspond to the longest relaxation time from the linear viscoelastic spectrum. However, the measured samples lack a well-defined longest relaxation time due to their high polydispersity. As a result, comparing the slow relaxation rate after the cessation of nonlinear start-up with the dynamic sweep does not yield a definitive conclusion.

To summarize, by analyzing the transient nonlinear shear data and the subsequent stress relaxation after flow cessation, we have evidenced the effect of incorporating, at the molecular level, a higher wt. % of ultrahigh molecular weight PE into the HDPE matrix. The molecular blending is facilitated by using dis-UH instead of the classically used entangled-UH chains. We found that the stress ratio $σ peak/ σ steady$ (Fig. 4) for HDPE and the blends share the same reduced slope at $W i 0>1$⁠, thus attesting for their lower deformability as compared to linear monodisperse polymers under the action of CCR. This low slope is attributed to the polydisperse nature, arising from the presence of UHMW tail in neat and blended polymers (commercial HDPE and blends), as shown by comparison with a series of linear m-PS-based blends in Fig. 4(b). Note that we have shown that even the chosen commercial pipe grade of HDPE has a considerable fraction of UHMW chains. Nevertheless, we attempted to give a better understanding of the molecular origin of this low deformability, by evoking a constraint action of CCR due to the permanent obstacles imposed by the molecular mixing of UHMW chains (skinny tube picture), or alternatively, by the opposite action of grip force that delays chain retraction until critical tension is reached. Moreover, we have noted the analogy with ring polymers, where the measured low slope of $σ peak/ σ steady$ is related to the low deformability due to restricted degree of freedom that the conformation of ring polymers may adopt under nonlinear flow. By analogy, we have evoked the core–shell conformation, proposed by McLeish (2007) [59] in conjunction with our recently proposed molecular picture [52] that UHMW chains are expected to adopt upon melting, which may result in the lower deformability we measured for our blends and their HDPE matrix.

While this low deformability is reflecting a high resistance to deformation for the UHMWPE blends and the neat HDPE, we measure a higher stretch with increasing concentration of dis-UH wt. %, through the quantification of the strain at which the peak stress occurs, $γ max$ (Fig. 3). This finding is consistent with the Doi–Edwards theory and confirms the synergistic effect of the molecular blending of an increasing fraction of UHMW chains. The increase in stretch, experienced by the polymer network, indicates that the dynamics is slowed down by UHMW chains, delaying network relaxation and leading to greater stretch [60]. Additionally, a phenomenological analysis inspired by the time-dependent behavior and metastable characteristics of soft materials, namely, the Soft Glassy Rheology (SGR) model, is employed. Based on this approach, observations derived from the data in Figs. 5 and 7(b) are discussed in the supplementary material.

Even under these weak flow conditions, i.e., shear [9], blends with high fractions of dis-UH exhibit slowdown of the chain-dynamics, resulting in increased chain stretchability. Therefore, testing our blends under a stronger flow field, such as a uniaxial extensional flow, is expected to provide further insights. In a fact, the importance of chain stretching during flow lies in its role as a prerequisite for the formation of the “shish-kebab” crystalline structure through flow-induced crystallization [10], which is an important physical property that enhances the polymer’s mechanical performance. Yet, more effort is required to fully understand its origin and finely control its occurrence [10,61]. What follows concerns the investigation of the impact of dis-UH weight percent on chain stretchability and the resulting flow-induced crystallization (FIC) envisaged by analyzing the induced SH during uniaxial extensional flow, which leads to the formation of the “shish-kebab” crystalline structures.

In this section, we examine the uniaxial extensional behavior and strain-hardening of HDPE and its blends. Figures 8 and 9 display the uniaxial stress growth coefficient, $η E +$⁠, at temperatures of 135 and 140 °C, respectively, across six elongational strain rates (⁠ $ε ˙$ = 0.01, 0.1, 0.5, 1, 3, and 5 s⁻¹) for HDPE, dB05, dB10, and dB20. All data are presented on a double logarithmic scale, with consistent vertical and horizontal axes across the graphs for easier comparison. Additionally, we plot the linear envelope that is calculated by transforming the complex viscosity from the average SAOS data (open stars), in addition to the SAOS data obtained from our previous work (dashed blue line) [13], using Trouton’s ratio $( η E +=3 η S +)$ [62]. To account for the temperature differences between the shear LVE data (conducted at 160 °C) and the uniaxial extension data (conducted at 135 and 140 °C), we apply the shift factor from TTS experiments (see Fig. S4 in the supplementary material). The uniaxial extensional data for all samples closely align with the linear envelopes. The excellent superimposition of the SAOS shifted from the molten state at 160 °C, along with the extensional data at 135 and 140 °C, indicates that no crystalline memory remains before the initiation of the extensional experiment.

Figure 8 illustrates the uniaxial extensional viscosity growth of HDPE and its blends at 135 °C, which is approximately 2 °C above the samples’ melting points (see T_m values in Table I). The stress growth coefficient, $η E +$⁠, increases over time, closely following the linear envelope until a deviation occurs. This deviation may result from either the breaking or rupturing of the sample, causing $η E +$ to fall below the linear envelope, or from SH, where $η E +$ increases sharply above the linear envelope. Notably, there is a slight dip in $η E +$ at the transition from the LVE envelope to strain hardening in many samples. This is attributed to necking, which occurs due to an instability arising from phase separation between the crystalline and amorphous phases as flow-induced crystallization (FIC) begins [12,19,63]. The occurrence of necking suggests that the subsequent SH behavior is linked to FIC in semicrystalline polymers [12,63]. However, further analysis of SH is required to confirm the occurrence of FIC, which will be discussed in the following sections. Among the strain rates examined, the minimum $ε ˙$ required to induce SH (referred to as the critical elongational strain rate, $ε ˙ critical$⁠) is determined to be 0.5 s⁻¹ for HDPE and dB05, 0.1 s⁻¹ for dB10, and 0.01 s⁻¹ for dB20. The SH behavior, potentially arising from FIC, of the samples at temperatures well above the melting point presents a greater challenge and is anticipated to provide deeper and more interesting insights from the industrial processing perspective. Thus, the uniaxial extensional viscosity, $η E +$⁠, at 140 °C is presented in Fig. 9 and analyzed in the following paragraph.

Figure 9 illustrates the uniaxial extensional viscosity growth of HDPE and its blends at 140 °C, which is approximately 7 °C above the melting point. Among the strain rates examined, $ε ˙ c r i t i c a l$ are found to be 0.5 s⁻¹ for dB05 and dB10 and 0.1 s⁻¹ for dB20. In contrast, HDPE showed no evidence of SH at the examined $ε ˙$ at 140 °C. The absence of SH at temperatures well above the melting point is due to the fast relaxation time of HDPE at this temperature, which also may cause the sample sagging under EVF fixture (see Sec. II B 1).

In Section III C 1, we analyze the characteristics of SH in the examined polymers at 135 and 140 °C. This includes evaluating the induction time, the critical strain rate $( ε ˙ critical)$⁠, the strain at the onset of hardening $( ε S H _ onset)$⁠, and the work done per unit volume (W/V). The stress relaxation behavior before and after SH (pre-SH and post-SH) is examined in Sec. III C 2, providing potential evidence of FIC.

A key aspect of the strain-hardening phenomenon in polymers is the induction time for the onset of SH, which is the duration required for the stress growth coefficient to exceed the linear envelope [12]. Figure 10(a) illustrates how elongational strain rate, dis-UH weight percentage, and temperature affect the induction time of HDPE and its blends. For all samples across various temperatures, an increase in leads to a significant decrease in induction time. The slope of the data is −1, consistent with previously reported data for various linear polyethylene types, such as HDPE and HDPE/UHMWPE blends at different temperatures (open-cross symbol). These data are derived by extracting the induction time from the reported extensional viscosity curves [12,17,19]. This suggests a universal trend for linear polyethylene, where the induction time for the onset of strain-hardening and elongational strain rate follows a power law with an exponent of −1: $τ induction∝ ε ˙ − 1$⁠. Furthermore, both the increase in dis-UH wt. % and temperature (from 135 to 140 °C) does not result in any noticeable changes in the induction time at various strain rates.

Figure 10(b) shows the average strain at the onset of SH, denoted $ε S H _ onset$⁠, as a function of dis-UH wt. %, at 135 and 140 °C. For each sample, the average value is calculated by averaging $ε S H _ onset$ at six elongational strain rates: 0.01, 0.1, 0.5, 1, 3, and 5 s⁻¹. The results indicate that neither the dis-UH content nor the temperature has a significant effect on $ε S H _ onset$⁠. Interestingly, we find the experimentally measured values of $ε S H _ onset$ to be scattered around the calculated value based on theoretical parameters for entangled polymer networks, i.e., $ε S H _ onset calculated=2.63$⁠. To calculate this value, we evaluate the ratio $L e x ⟨ R 2 ⟩ 1 / 2$ between the extended chain length $L e x$ and the chain’s equilibrium root-mean-square end-to-end distance $⟨ R 2 ⟩ 0 1 / 2$ of the chain segment between two entanglement junctions [64]. By considering the PE molecular characteristics reported by Fetters et al. [64,65], we find $L e x ⟨ R 2 ⟩ 0 1 / 2=2.63$⁠, as highlighted by the horizontal line in Fig. 10(b). Theoretically, in entangled polymers, the finite extensibility of network strands is expected to enhance chain stretching up to a finite strain, potentially contributing to the onset of extreme strain-hardening [66,67]. The chain entanglements are expected to lock the dynamics of the entanglement segments, thus causing chain stretching [68–70]. This finding further supports the successful molecular blending of dis-UH in an HDPE matrix, which is made possible by the low-entangled nascent state of the dis-UH chains.

Furthermore, increasing the weight percentage of dis-UH notably alters the minimum strain rate required to induce strain hardening $( ε ˙ critical)$⁠, as it is clear from Fig. S14 in the supplementary material, where $ε ˙ critical$ as a function of the weight percentage of dis-UH at 135 and 140 °C is presented. At 135 °C, $ε ˙ critical$ values are 0.5 s⁻¹ for both HDPE and dB05, 0.1 s⁻¹ for dB10, and 0.01 s⁻¹ for dB20. At 140 °C, the overall $ε ˙ critical$ values increase: For dB10, it rises to 0.5 s⁻¹ (five times higher than at 135 °C), and for dB20, it reaches 0.1 s⁻¹ (ten times higher than at 135 °C). Notably, HDPE shows no evidence of strain hardening within the tested strain rates at 140 °C, and $ε ˙ critical$ for dB05 remains unchanged, likely due to the limited range of tested $ε ˙$⁠. On the one hand, the decrease in $ε ˙ critical$ as a function of dis-UH wt. % content is attributed to the slowing down of the dynamics by introducing a higher fraction of long chains. The slow relaxation rate of the long chains in the blends induces chain stretch at lower strain rates, promoting SH, and potentially FIC, at weaker flow conditions compared to HDPE. On the other hand, the overall increase in $ε ˙ critical$ with rising temperature is attributed to the accelerated dynamics at higher temperatures, requiring the chains to experience stretching at higher rates.

In this section, we discuss stress relaxation associated with SH behavior in $η E +$ observed during uniaxial extension experiments. We monitor the stress relaxation at 140 °C and 1 s⁻¹ for dB20. To do this, we stop the uniaxial stretching deformation at predetermined times before (pre-SH) and after (post-SH) the onset of SH (0.5, 0.8, 2.5, and 2.7 s), followed by isothermal stress relaxation $( σ −)$⁠. The resulting stress growth and relaxation data are presented in Fig. 11. The raw data for each experiment are shown in Fig. S15 in the supplementary material.

Interestingly, at cessation times pre-SH (specifically at 0.5 and 0.8 s), the isothermal stress relaxation rates are measured at 0.63 ± 0.01 and 0.64 ± 0.01 MPa/s, respectively, which reduce the stress to nearly zero within approximately 10 min, as shown in Fig. 11(b). In contrast, in post-SH (at 2.5 and 2.7 s), the relaxation rates decrease to approximately 0.26 MPa/s, making them about three times slower. Additionally, the stress values at 10 min mark in post-SH increase by 1–2 orders of magnitude compared to that pre-SH, reaching 0.64 and 0.97 MPa, respectively, as illustrated in Fig. 11(b). The lower stress relaxation rates and higher stress values in post-SH are characteristic of rubber-like materials and indicate a liquid-to-solid transition [12]. This observation suggests that strain-hardening results from flow-induced crystallization occurring at temperatures significantly above the melting point of the blends (140 °C). This phenomenon is facilitated by the presence of ultralong chains of dis-UH in HDPE.

In this section, we have demonstrated that the incorporation of dis-UH into HDPE promotes SH even at temperatures significantly above the melting point. Quantitative analysis indicates that SH arises from the finite extensibility of entanglement strands within the polymeric network, further supporting the success of molecular blending due to the low-entanglement state of the nascent UHMWPE. Examination of isothermal stress relaxation before and after SH shows that the strain-hardening is driven by flow-induced crystallization (FIC). Section III D explores the impact of elongational strain and dis-UH wt. % content on the flow-induced crystalline structure formed during elongational flow, using SEM, 2D-SAXS, and -WAXS.

The formation of extended-chain crystals (ECC or “shish”) and folded-chain crystals (FCC or “kebab”) during flow-induced crystallization relies on chain stretching [9,10]. Stretched polymer chains crystallize to form the central fibrillar shish structure, while coiled chains initially create single-chain lamellae. These lamellae subsequently adsorb onto the shish structure, contributing to the development of kebab crystalline structures that grow around the fibril [10]. The impact of elongational deformation $( ε)$ and dis-UH wt. % content in the HDPE matrix on crystalline structure formation induced by elongational flow (FIC) at 140 °C is investigated. This analysis is conducted using SEM, SAXS, and WAXD.

Figure 12(a) displays the time cessation of stress growth $( σ +)$ for dB20 at 140 °C and a stretching rate of 1 s⁻¹. The stretching deformation is stopped immediately upon reaching three different strains (0.5, 2.5, and 3.3), followed by a temperature quenching from 140 °C to room temperature using nitrogen gas. This temperature quenching is essential for preserving the crystalline structure formed during flow-induced crystallization (FIC) [17]. However, it is important to note that the quenched samples may be partially relaxed, undergoing stress decay for a few seconds during the quenching process, as they cool from 140 °C before crystallization sets in (see experimental part, Sec. II B 2). The raw data for each experiment are shown in Fig. S16 in the supplementary material. The resulting samples are then analyzed ex-situ using SEM, SAXS, and WAXD to assess the crystalline morphology and the orientation degree. The SEM, SAXS, and WAXD experiments are performed on the same physical sample, ensuring a consistent basis for structural characterization across all techniques.

Figures 12(b)–12(d) present SEM images of dB20 at three different ɛ: 0.5, 2.5, and 3.3. At a small deformation of ɛ = 0.5, before strain hardening begins, the crystalline morphology appears as an unoriented leaf-like structure. In contrast, as the strain increases to 2.5 and 3.3, following the initiation of FIC, an oriented shish-kebab crystalline morphology emerges. This structure consists of extended-chain crystals along the stretch direction (ECC or the shish) and folded-chain crystals (FCC or the kebab), as shown in Fig. 12(k). Notably, as ɛ increases from 2.5 to 3.3, the packing of shish crystals becomes more compact, which increases the density of shish crystals while reducing the density of the kebab crystals. This is evident from SEM images, where the structure observed at ɛ = 2.5 has larger voids in between the shish-shish and kebab-kebab structures compared to the one observed at ɛ = 3.3. The increase in packing density observed in SEM images is further confirmed by the calculated long period (L_kebab), decreasing from 27.3 (ɛ = 2.5) to 23.2 nm (ɛ = 3.3), as summarized in Table S1 in the supplementary material.

Figures 12(e)–12(j) display 2D WAXS and SAXS patterns at different strains $(ε)$⁠. The 2D-WAXD patterns indicate that an almost isotropic diffraction ring appears at ɛ = 0.5, which gradually transitions to an oriented diffraction arc at ɛ = 2.5, and finally becomes a highly oriented diffraction point at ɛ = 3.3. Correspondingly, the orientation degree S₍₁₁₀₎, which is calculated based on the azimuthal intensity distribution of the (110) crystal plane in 2D WAXD (Fig. S6 in the supplementary material), continuously decreases with increasing strain ɛ: −0.13 $(ε=0.5)$⁠, −0.28 $(ε=2.5)$⁠, and −0.41 $(ε=3.3)$⁠, as presented in Table S1 and Fig. S9 in the supplementary material.

At ɛ = 0.5, the 2D SAXS pattern [Fig. 12(h)] shows almost no equatorial streak around the beam. The broad distribution of the lobe structure along the meridional direction (Fig. S7 in the supplementary material), with a long period of 26.7 nm, suggests that the structure is primarily due to the lamellar structure, indicating that shish-kebab crystals have not yet formed. The weak equatorial streak in the 2D SAXS pattern at ɛ = 2.5, as well as the low integrated intensity along the equatorial direction shown in Fig. S5(a) in the supplementary material, provides evidence of shish formation, which serves as nucleation sites for the epitaxial crystallization of the kebab structure on the shish [16,75]. To further clarify, Fig. S5(a) in the supplementary material demonstrates the shift in the average periodic structure from $d ∼ 25 nm ( = 2 π 0.025 A ° )$ to $d ∼ 21 nm ( = 2 π 0.030 A ° )$ and further to $d ∼ 16 nm ( = 2 π 0.040 A ° )$⁠, with increasing strain from 0.5 to 2.5 and 3.3, respectively. Considering that the intensity is recorded along the equator, perpendicular to the flow-direction, the electron density fluctuation contributing to the peak position and scattering intensity is attributed to shish (near-extended chains having higher crystallinity and electron density) and kebab (folded chains having lower crystallinity and electron density) structures. The broadness of the SAXS peak would be influenced by the correlation length between shish and kebab structures, and the average position of the peak will be determined by the periodicity between shish and kebab. The SAXS intensity will be dependent on the electron density fluctuation (also on the amount of shish and kebabs in the specific volume) and its spread over the q-range (correlation length). The chain orientation, with increasing strain, is further supported by WAXD, where orientation perpendicular to the flow direction increases, Figs. 12(e)–12(g).

Moreover, the calculated orientation degree of the kebab structure S_kebab increased with strain ɛ: 0.14 $(ε=0.5)$⁠, 0.45 $(ε=2.5)$⁠, and 0.51 $(ε=3.3)$⁠, as presented in Table S1 and Fig. S9 in the supplementary material. The intensity distribution of the kebab structure decreases at ɛ = 2.5, and the long period slightly increases to 27.3 nm, suggesting elongation of the amorphous region during the formation of the shish-kebab structure. Thus, the highly oriented structure at ɛ = 3.3 results in a more compact packing and a decreased long period to 23.2 nm.

In a similar manner, the influence of dis-UH content on the formation of the shish-kebab crystalline structure is investigated in this section by fixing the strain at ɛ = 3.3 and varying dis-UH wt. % content. Figure 13(a) shows time cessation of stress growth $( σ +)$ of dB05, dB10, and dB20 at 140 °C, in which the stretching deformation is stopped immediately upon reaching ɛ = 3.3, followed by a temperature quenching from 140 °C to room temperature. After deformation and quenching processes, the samples are analyzed ex situ using SEM, 2D-SAXS and -WAXD.

Figures 13(b)–13(d) display SEM images of dB05, dB10, and dB20, all deformed at a constant strain (ɛ = 3.3) at 140 °C and a stretching rate of 1 s⁻¹. Clearly, the shish and kebab crystal structures appear in all samples. However, as the content of dis-UH in HDPE increases from 5 to 20 wt. %, a higher degree of alignment is observed, attributed to the greater amount of shish elongated along the direction of stretching. According to the 2D-WAXD patterns [Figs. 13(e)–13(g)] and the calculated orientation degree S₍₁₁₀₎ (Table S1 and Fig. S9 in the supplementary material), the orientation improves with increasing dis-UH content at the fixed strain of ɛ = 3.3: −0.17 (dB05), −0.24 (dB10), and −0.41 (dB20).

The broader distribution of the structure along the meridional direction in 2D SAXS data of dB05 indicates a partial formation of the shish-kebab structure and the unoriented lamellar residue, consistent with the SEM images. In contrast, both dB10 and dB20 show a sharper azimuthal intensity distribution of the kebab structure compared to dB05 (Fig. S7 in the supplementary material), accompanied by a thicker long period of 23.2 nm. The 1D integrated SAXS intensity along the equatorial direction decreased with increasing content of dis-UH as shown in Fig. S5(b) in the supplementary material, indicating that the shish-kebab structure is fully generated. The effect of shish volume on SAXS intensity and peak position, as discussed in this section in relation to Fig. S5(a) in the supplementary material, is further reinforced by Fig. S5(b) in the supplementary material. In Figure S5(b) in the supplementary material, the shish concentration is adjusted by varying the wt. % of dis-UH from 5 to 20 wt. %, while maintaining the same strain across all three samples. The figure shows relatively well-defined strong intensity, confined to a peak, in the sample having least amount of dis-UH (dB05) at higher d values (lower q). The broad, weak peak at the lower d values (higher q) is found in the samples having 10 and 20 wt. % of dis-UH. The higher concentration of dis-UH facilitates larger volume of shish in the specific volume, thus the associated shift in the peak position and drop in intensity.

In addition, the kebab structure’s orientation (S_kebab) globally increases with dis-UH content at fixed strain of ɛ = 3.3: 0.20 (dB05), 0.55 (dB10), and 0.51 (dB20), as presented in Table S1 and Fig. S9 in the supplementary material. This suggests that even a small amount of dis-UH in HDPE enhances its FIC behavior, ultimately leading to the development of a “shish-kebab” crystalline morphology at temperatures significantly above the melting point.

In this section, we have demonstrated that the orientation of the flow-induced shish-kebab structure is enhanced by increasing both the extensional strain and the dis-UH fraction. This enhancement is particularly evident from the quantification of the long period (L_kebab), the S₍₁₁₀₎ orientation, and the kebab structure’s orientation (S_kebab). Since a key objective of this study is to validate the successful molecular melt-blending of UHMWPE under nonlinear flows, we use S_kebab to compare our findings with previous studies on various PE grades and blends [17,76]. These studies employed the same quenching protocol and subsequent ex situ characterization. Figure 14 presents S_kebab as a function of stress at quench for our blends, alongside with previously measured data at 140 °C for a HDPE with $M w=156$ $× 10 3 g / mol$ and its solution blend containing 1 wt. % UHMWPE having M_w = 4 × 10⁶ g/mol. Additionally, it includes data for a HDPE with M_w = 460 × 10³ g/mol measured at three different temperatures (140, 144, and 150 °C). As shown in Fig. 14(a), the S_kebab range achieved by our blends closely aligns, within experimental error, with previously reported values. Note that the standard deviation in stress at quench is estimated as explained in Experimental Sec. II B 2. However, the stress at quench exhibited by our blends is approximately an order of magnitude higher than that observed in earlier studies. This significantly higher stress level provides further evidence of the greater fraction of UHMWPE successfully incorporated into the HDPE matrix, 5, 10, and 20 wt. %, through melt blending, facilitated by the initially low-entangled nature of our dis-UHMWPE.

To account for the stress difference, we normalize the stress values by the number of entanglements $( Z = M w M e )$⁠, as presented Fig. 14(b). Here, we choose to use the nominal M_e = 1000 g/mol for all the data [64]. In this way, S_kebab is compared to the stress experienced by the entanglement segment. Interestingly, within the experimental errors, a master curve is obtained for all the tested data, having a slope of 0.4, which is a characteristic of semicrystalline polymers [17,76]. The successful construction of the master curve for the normalized stress by $Z$ supports the hypothesis that the alignment and stretching of chain segments between entanglement junctions serve as the precursor for FIC. This finding aligns with the discussion presented in Fig. 10(b). Moreover, it also validates the molecular blending of a high fraction of UHMWPE through melt blending, facilitated by the initially low-entangled nature of our dis-UHMWPE.

This study systematically investigates the effects of incorporating dis-UH into a polydisperse HDPE matrix through a solvent-free melt-blending extrusion process, with dis-UH concentrations reaching up to 20 wt. %, focusing on the resulting nonlinear shear and extensional behavior. The findings demonstrate that adding dis-UH significantly enhances the rheological properties of the blends. In the nonlinear shear flow, the blends exhibit low deformability, as indicated by the stress ratio $( σ peak/ σ steady)$ and in comparison to both monodisperse and polydisperse solution-blended PS. However, the incorporation of a higher fraction of dis-UH leads to a greater stretch of the polymer network as evidenced by a notable increase in maximum strain $( γ max)$ from 2.3 to 3.3. Furthermore, the slowdown of polymer dynamics is evidenced by the long-time stress relaxation rate after shear cessation with the UH fraction.

Additionally, increasing the dis-UH fraction up to 20 wt. % promotes SH even at elevated temperatures under elongational flow, confirmed to occur as a direct consequence of flow-induced crystallization (FIC), a key mechanism for improving the mechanical properties of the polymer blends. By considering finite extensibility, we found that the onset of strain hardening occurs at a constant strain, resulting from the stretching experienced by the entanglement strands.

Structural analysis of FIC using SEM, WAXD, and SAXS provides strong evidence in the formation of shish-kebab crystalline structures, with their orientation enhanced by increasing both elongational strain and dis-UH content. This is quantitatively supported by the analysis of the long period (L_kebab), the S₍₁₁₀₎ orientation, and the kebab structure’s orientation (S_kebab). By comparing the kebab orientation of our samples to previous studies as a function of stress at quench normalized by the entanglement number $( Z)$⁠, we establish the consistency of our results with prior findings, validating the molecular blending of a high fraction of UHMWPE via melt blending, facilitated by the initially low-entangled nature of our dis-UHMWPE.

The practical significance of this work lies in demonstrating that dis-UH can be successfully incorporated into HDPE under industrially relevant conditions, specifically at extrusion temperatures of 190 °C and elongational rates of approximately 40 s⁻¹. Despite the typically harsher temperatures used in extrusion, the dis-UH/HDPE extrudate retains the ability to undergo flow-induced crystallization (FIC), leading to the formation of the shish-kebab crystalline structure, as illustrated in Fig. S19 in the supplementary material and the corresponding discussion.

See the supplementary material for further rheological and structural evolution data on the investigated samples. The data in the section further support the information given in the manuscript and are stated wherever needed.

The authors would like to extend their thanks to Shahaji Gaikwad (KAUST) for electron microscopy samples’ preparation and to acknowledge SABIC R&D Center at KAUST for providing the industrial grade sample. KAUST core lab imaging and analytical facilities, together with the financial support from KAUST BAS/1/1407-01, are acknowledged.

The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article and its supplementary material.