Effects of temperature and strain rate on the deformation of amorphous polyethylene: a comparison between molecular dynamics simulations and experimental results
Open accessAbstract
Molecular dynamics simulations are used to investigate the effects of temperature and strain rate on the deformation of amorphous polyethylene. The simulations predict the effects of temperature and strain rate on the stress–strain responses, Young's modulus and Poisson's ratio similar to those observed in laboratory experiments performed by other researchers. The time–temperature superposition principle is applied to the Young's modulus and Poisson's ratio to form a master curve to address the discrepancies in strain rates between the simulations and the experiments. Differences in the numbers of monomers and chains, the degree of crystallinity and molecular orientation lead to discrepancies in the Young's modulus and Poisson's ratio between simulations and experiments.
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8 of 51 cited sources checked · 7 supported · 0 flagged · accuracy not yet measured
- Interpretationcitation
The values of the constants C1 and C2 for the previous WLF equation could not be used because the samples studied by Bucknall have degrees of crystallinity between 94% and 97%.
“The values of the constants C1 and C2 for the previous WLF equation could not be used because the samples studied by Bucknall [29] have degrees of crystallinity between 94% and 97%.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [29] source
The Materials and Moulding section identifies the polymers studied, including high-density polyethylene, but gives no crystallinity percentages. Searches for 94–97% crystallinity and WLF constants C1 and C2 found no passage addressing either the stated range or the reason the constants could not be used; page numbers were unavailable in our copy. (LLM, conf=0.76)
Experimental — accuracy not yet measured
- Findingcitation
The simulated yield stress is the same order of magnitude as found in other simulations.
“This is the same order of magnitude as found in other simulations, for instance [2][3][4].”
Quote in the paperNot a substantial claim1 of 3 sources checked - Premisecitation
Equation (2) has been validated with higher strain rates than typical experimental test rates.
“Equation ( 2) has been validated with higher strain rates than typical experimental test rates [24,25].”
Quote in the paperSubstantial claim1 of 2 sources checked - Premisecitation
The sigmoidal increase of Poisson's ratio with temperature is similar to experimental results reported for other polymers (PC, PS, PMMA, PVT, ST/MMA, PVC, POMS, PBT and epoxy resins).
“This trend is similar to the experimental results of other polymers reported by Seitz [36] for PC, PS, PMMA, PVT, ST/MMA, PVC and POMS; by Mott et al [37] for PS and PMMA; by Pandini and Pegoretti [38] for PBT and by Pandini and Pegoretti [39] for epoxy resins.”
Quote in the paperNot a substantial claim1 of 3 sources checked - Findingreasoning
At a higher strain, above approximately 0.2% or 20%, the stress-strain responses of the sample differ depending on the direction of elongation.
“At a higher strain, above approximately 0.2% or 20%, the curves demonstrate that the stress-strain responses of the sample differ depending on the direction of elongation.”
Quote in the paperSubstantial claim
- Findingown data
The three stress-strain curves are close to each other at a low strain.
“The three curves are close to each other at a low strain.”
Quote in the paperSubstantial claim - Findingnone given
The sample of this study, after being equilibrated at a temperature of 500 K, has a characteristic ratio C of 3.4.
“The sample of this study, after being equilibrated at a temperature of 500 K (= 227 •C) has a characteristic ratio, C, of 3.4.”
Quote in the paperSubstantial claim - Findingnone given
The simulations predict the effects of temperature and strain rate on the stress-strain responses, Young's modulus and Poisson's ratio similar to those observed in laboratory experiments performed by other researchers.
“The simulations predict the effects of temperature and strain rate on the stress-strain responses, Young's modulus and Poisson's ratio similar to those observed in laboratory experiments performed by other researchers.”
Quote in the paperSubstantial claim - Findingown data
The heterogeneity and small size of the sample produced noisy stress-strain curves.
“The heterogeneity and small size of the sample produced noisy stress-strain curves and therefore polynomial smoothing was used to reduce the fluctuation of the stress.”
Quote in the paperNot a substantial claim - Findingown data
The Young's modulus decreases with increasing temperature in all simulations.
“Figure 5 indicates that the Young's modulus decreases with increasing temperature in all simulations.”
Quote in the paperSubstantial claim - Findingown data
There is a significant difference in yield stress between experiments and simulations.
“However, there is a significant difference in yield stress between experiments and simulations.”
Quote in the paperSubstantial claim - Findingown data
The simulations show Hookean elasticity responses to the applied uniaxial load at low strains.
“The simulations show Hookean elasticity responses to the applied uniaxial load at low strains.”
Quote in the paperSubstantial claim - Findingown data
In the master curve at Tg (155 K), the original log strain rate between 8 and 10 has been shifted to between about -4 and 5.
“This figure shows that the original log strain rate between 8 and 10 has been shifted to between about -4 and 5.”
Quote in the paperSubstantial claim - Findingown data
Increasing the temperature affects the Young's modulus in a similar way as decreasing the strain rate.
“As indicated in figure 5, increasing the temperature affects the Young's modulus in a similar way as decreasing the strain rate.”
Quote in the paperSubstantial claim - Findingown data
In the simulations, a higher strain rate produces a higher Young's modulus compared with a slower strain rate.
“also show that the simulation using a higher strain rate produces a higher Young's modulus compared with the simulation using a slower rate.”
Quote in the paperSubstantial claim - Findingcitation
The curve for X-direction elongation has the same typical shape as those obtained from laboratory experiments on PE, for instance experiments using strain rates between 10^-4 and 10^-2 s^-1 performed by Hiss et al and Addiego et al.
“The curve for X-direction elongation in figure 2 has the same typical shape as those obtained from laboratory experiments on PE, for instance the experiments using strain rates between 10-4 and 10-2 s-1 performed by Hiss et al [17] and Addiego et al [18].”
Quote in the paperSubstantial claim0 of 2 sources checked - Findingown data
The trends of the effects of strain rate and temperature on Poisson's ratio in the simulations are similar to those in the experiments.
“Figure 11 shows that the trends of the effects of strain rate and temperature on Poisson's ratio in the simulations are similar to those in the experiments.”
Quote in the paperSubstantial claim - Findingown data
Poisson's ratio depends on the strain rate and temperature.
“Poisson's ratio depends on the strain rate and temperature, as indicated in figure 9.”
Quote in the paperSubstantial claim - Findingnone given
The stress-strain curves at a low strain obtained from the simulations have the same typical shapes as those obtained from laboratory experiments.
“The stress-strain curves at a low strain obtained from the simulations have the same typical shapes as those obtained from laboratory experiments.”
Quote in the paperSubstantial claim - Findingown data
In the simulations using strain rates of 10^8, 10^9 and 10^10 s^-1, Poisson's ratio increases with temperature following a sigmoidal trend.
“Figure 9 indicates that in the simulations using strain rates of 108, 109 and 1010 s-1, Poisson's ratio increases with temperature following a sigmoidal trend.”
Quote in the paperSubstantial claim - Premisereasoning
There is a huge discrepancy between the simulated and laboratory strain rates.
“However, there is a huge discrepancy between the simulated and laboratory strain rates.”
Quote in the paperSubstantial claim - Interpretationnone given
This model is not an adequate model to predict properties beyond the elastic limit, such as the yield stress, softening and hardening.
“However, this model is not an adequate model to predict properties beyond the elastic limit, such as the yield stress, softening and hardening, which is typically also beyond the practical application of polymers.”
Quote in the paperSubstantial claim - Interpretationreasoning
The model is considered adequate for studying elastic properties at low strains.
“For this reason, the model is considered adequate for studying elastic properties at low strains.”
Quote in the paperSubstantial claim - Premisecitation
The accuracy of the stress-strain response of glassy polymers with MD simulations depends on the characteristic ratio C.
“The accuracy of the stress-strain response of glassy polymers with MD simulations depends on the characteristic ratio, C [6].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [6] source
- Interpretationown data
The simulation sample is composed of more tightly coiled chains compared with real PE.
“This indicates that the simulation sample is composed of more tightly coiled chains compared with the real PE.”
Quote in the paperSubstantial claim - Interpretationnone given
Differences in the numbers of monomers and chains, the degree of crystallinity and molecular orientation lead to discrepancies in the Young's modulus and Poisson's ratio between simulations and experiments.
“Differences in the numbers of monomers and chains, the degree of crystallinity and molecular orientation lead to discrepancies in the Young's modulus and Poisson's ratio between simulations and experiments.”
Quote in the paperNot a substantial claim - Premisereasoning
MD simulations typically use strain rates about six to ten orders of magnitude larger than the highest strain rates commonly used in laboratory experiments.
“Because of the computational cost and time required, MD simulations typically use strain rates about six to ten orders of magnitude larger than the highest strain rates commonly used in laboratory experiments.”
Quote in the paperSubstantial claim - Premisenone given
The initial low strain is not influenced significantly by the value of C.
“The initial low strain is not influenced significantly by the value of C.”
Quote in the paperSubstantial claim - Premisecitation
The elastic modulus increases approximately in proportion to the degree of crystallinity in a certain range.
“The elastic modulus increases approximately in proportion to the degree of crystallinity in a certain range [30][31][32].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [30][31][32]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
Similar initial deformation responses of the simulations in three different directions could be used to calculate the elastic properties because the focus is on low strain.
“As the focus of this study is on the Young's modulus and Poisson's ratio calculated at a low strain (0.02 or 2%), similar initial deformation responses of the simulations in three different directions could be used to calculate the elastic properties.”
Quote in the paperSubstantial claim - Interpretationreasoning
As the yield stress increases with the strain rate, the simulations are expected to produce a higher yield stress than the experiments.
“As the yield stress increases with the strain rate, the simulations are expected to produce a higher yield stress than the experiments.”
Quote in the paperSubstantial claim - Interpretationown data
The simulations predict Young's modulus behaviour in accordance with the time-temperature superposition principle.
“This indicates that the simulations predict Young's modulus behaviour in accordance with the time-temperature superposition principle.”
Quote in the paperSubstantial claim - Premisecitation
Over a range of temperatures between Tg and Tg + 100, the values C1 = 8.86 and C2 = 101.6 are valid for a wide variety of polymers, polymer solutions, organic glass-forming liquids and inorganic glasses.
“Over a range of temperatures between Tg and Tg + 100, these values are valid for a wide variety of polymers, polymer solutions, organic glass-forming liquids and inorganic glasses [22].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [22] source
- Interpretationreasoning
The changes of the atomic positions could be sufficiently large compared with the atomic oscillations, resulting in a discontinuous jump in the molecular bond distance without any physical meaning.
“The changes of the atomic positions could be sufficiently large compared with the atomic oscillations, resulting in a discontinuous jump in the molecular bond distance without any physical meaning.”
Quote in the paperSubstantial claim - Premisecitation
Hiss et al and Addiego et al also found that increasing strain rate increases the yield stress.
“Hiss et al [17] and Addiego et al [18] also found that increasing strain rate increases the yield stress.”
Quote in the paperNot a substantial claim0 of 2 sources checked - Premisecitation
The WLF constants C1 and C2 used for these simulations were calculated using experimental results of an HDPE sample.
“They were calculated using experimental results of an HDPE sample.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [26] source
- Interpretationreasoning
The direction-dependent stress-strain responses at higher strain are due to the anisotropy of the structure of the polymer chain in the small sample modelled.
“This is due to the anisotropy of the structure of the polymer chain in the small sample modelled here.”
Quote in the paperSubstantial claim - Premisecitation
The 10^11 s^-1 strain rate is close to the vibrational frequency of PE, which is between 1.53 x 10^12 and 8.76 x 10^13 s^-1.
“This strain rate is close to the vibrational frequency of PE, which is between 1.53 × 1012 and 8.76 × 1013 s-1 according to [21].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [21] source
- Interpretationreasoning
The master curves can be used to bridge the difference between the high strain rates of the simulations and the much lower rates of the laboratory experiments.
“These master curves can be used to bridge the difference between the high strain rates of the simulations and the much lower rates of the laboratory experiments.”
Quote in the paperSubstantial claim - Interpretationreasoning
The differences in the numbers of monomers and chains, the degree of crystallinity and the molecular orientation lead to discrepancies between the Young's modulus and Poisson's ratio values calculated from the simulations and those measured in laboratory experiments.
“The differences in terms of the numbers of monomers and chains, the degree of crystallinity and the molecular orientation lead to discrepancies between the Young's modulus and Poisson's ratio values calculated from the simulations and those measured in laboratory experiments.”
Quote in the paperSubstantial claim - Interpretationreasoning
The difference between Poisson's ratios measured experimentally and calculated in the simulations results from the same factors that influence the Young's modulus.
“The difference between Poisson's ratios measured experimentally and calculated in the simulations results from the same factors that influence the Young's modulus as discussed in the previous section.”
Quote in the paperNot a substantial claim - Premisecitation
Bilgin et al found that Poisson's ratio of the MDPE pipe at a strain rate close to 1000 microstrain min-1 increased from 0.42 at -6.7 degrees C to 0.48 at 49 degrees C.
“Bilgin et al [40] found that Poisson's ratio of the MDPE pipe at a strain rate close to 1000 µε min-1 (approximately 1.6 × 10-5 s-1) increased from 0.42 at -6.7 •C to 0.48 at 49 •C.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [40] source
- Interpretationreasoning
The degree of crystallinity leads to a difference in the Young's modulus between experimental measurements and the simulated results.
“Therefore, the degree of crystallinity leads to a difference in the Young's modulus between experimental measurements and the simulated results.”
Quote in the paperSubstantial claim - Interpretationown data
These simulations are able to produce the trend in Poisson's ratio following the time (or strain rate)-temperature superposition principle.
“These simulations are 12 Figure 11.Comparison of Poisson's ratio from data measured by Bilgin et al [40], Waterman [41] and the simulation model.able to produce the trend in Poisson's ratio following the time (or strain rate)-temperature superposition principle.”
Quote in the paperSubstantial claim - Premisecitation
HDPE elongated in the solid state exhibits a strong dependence of the Young's modulus on molecular orientation.
“HDPE elongated in the solid state exhibits a strong dependence of the Young's modulus on molecular orientation, for instance as reported by Capaccio and Ward [34] and Capaccio et al [35].”
Quote in the paperSubstantial claim0 of 2 sources checked - Premisecitation
The real part of the complex Poisson's ratio is close to the time-dependent Poisson's ratio.
“we used the real part of the complex Poisson's ratios of these measurements because the value of the real part is close to the time-dependent Poisson's ratio [42].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [42] source
- Premisecitation
For degrees of crystallinity less than 25%, the moduli remain constant at approximately 20 MPa.
“According to Popli and Mandelkern [32], for degrees of crystallinity less than 25%, the moduli remain constant at approximately 20 MPa.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [32] source
- Classified as probably not a substantial claim. 28
- May combine two claims. 24
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe united-atom approach simplifies each CH2 monomer as a single monomer particle and has been used by several researchers.
“This approach simplifies each CH2 monomer as a single monomer particle and has been used by several researchers [2][3][4].”
Quote in the paperNot a substantial claim1 of 3 sources checkedMay combine two claims.
InterpretationcitationMD is a useful tool to qualitatively investigate the relationship between micro-scale phenomena and macro-scale mechanical properties and, to some extent, to quantitatively determine these terms.
“These previous results indicate that MD is a useful tool to qualitatively investigate the relationship between micro-scale phenomena and macro-scale mechanical properties and, to some extent, to quantitatively determine these terms.”
Quote in the paperSubstantial claim1 of 3 sources checkedClassified as probably not a substantial claim.
PremisecitationIn Bucknall's report, the Young's modulus was measured from HDPE samples using tensile tests over a range of strain rates and at different temperatures.
“In his report, the Young's modulus was measured from HDPE samples using tensile tests over a range of strain rates and at different temperatures.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [29] source
Probably not a substantial claim: may not pass S3 (load-bearing).
InterpretationreasoningThe experimental samples studied by Bucknall were prepared by an injection moulding process and could have had higher degree of molecular orientation compared with the simulated samples.
“The experimental samples studied by Bucknall [29] were prepared by an injection moulding process and could have had higher degree of molecular orientation compared with the simulated samples.”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [29] source
May combine two claims.
Findingown dataThe stiffness and yield stress increase with increasing strain rate.
“Figure 3 indicates that the stiffness and yield stress increase with increasing strain rate.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAfter final equilibration at 200 K, the mean bond length is 1.529 Å with a standard deviation of 0.023 Å, and the mean bond angle is 109.29° with a standard deviation of 3.393°.
“The mean value of bond length is 1.529 Å with a standard deviation of 0.023 Å, while the mean value of bond angle is 109.29• with a standard deviation of 3.393•.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataThe dihedral angles are distributed around trans and gauche states, centred around 66° and 180°.
“The dihedral angles are distributed around trans and gauche states, centred around 66• and 180•.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe experimentally obtained yield stresses are between 20 and 30 MPa while in this simulation they are about 120 MPa.
“The experimentally obtained yield stresses are between 20 and 30 MPa while in this simulation they are about 120 MPa.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataDecreasing temperature increases the stiffness and the yield stress.
“Decreasing temperature increases the stiffness and the yield stress.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
FindingcitationThe distributions of bond length, bond angle and dihedral angle are similar to those in other MD simulations of PE.
“The distributions are similar to those in other MD simulations of PE [6,10].”
Quote in the paperNot a substantial claim0 of 2 sources checkedMay combine two claims.
Findingown dataThe Young's moduli of these simulations are lower than those of the experiments, but the master curves have similar shapes.
“The Young's moduli of these simulations are lower than those of the experiments, but the master curves have similar shapes.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataIn the simulations, Poisson's ratio was 0.39 at -80 degrees C and 0.48 at 50 degrees C.
“In the simulations, Poisson's ratio was 0.39 at -80 •C (approximately 193 K) and 0.48 at 50 •C (approximately 323 K).”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe Young's modulus and Poisson's ratio values calculated from the simulations show the strain rate and temperature dependences and were in reasonable agreement with the experimental measurements.
“The Young's modulus and Poisson's ratio values were calculated from the simulations showing the strain rate and temperature dependences and were in reasonable agreement with the experimental measurements.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe curve fit to the simulation at a strain rate of 10^9 s^-1 showed that Poisson's ratio was 0.464 at -6.7 degrees C and 0.481 at 49 degrees C.
“The equation of the curve fit to the simulation at a strain rate of 109 s-1 in figure 10 showed that Poisson's ratio was 0.464 at a temperature of -6.7 •C (approximately 266 K), and 0.481 at 49 •C (approximately 322 K).”
Quote in the paperNot a substantial claimMay combine two claims.
FindingcitationIn this simulation, the PE system is purely amorphous, while the HDPE in Bucknall's report has a degree of crystallinity between 94% and 97%.
“In this simulation, the PE system is purely amorphous, while the HDPE in Bucknall's report has a degree of crystallinity between 94% and 97% as measured by Pranadi and Manuel [33].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [33] source
Probably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductreasoningThe use of three simulations with elongation in X, Y or Z directions is similar to the practice of using several samples in laboratory experiments to ensure that the results are statistically representative of the material properties.
“This is similar to the practice of using several samples in laboratory experiments to ensure that the results are statistically representative of the material properties, which could vary.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationThe accuracy of C is especially important for the stress-strain response after the yield stress and for the slope of the rehardening part.
“However, the accuracy of C is especially important for the stress-strain response after the yield stress and for the slope of the rehardening part.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [6] source
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationHDPE has a simple molecular structure, even though it has amorphous and crystalline phases, and is employed in a wide range of demanding industrial applications, for example in gas distribution pipes.
“HDPE has a simple molecular structure, even though it has amorphous and crystalline phases, and this polymer is employed in a wide range of demanding industrial applications, for example in gas distribution pipes [1].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [1] ISO/TS 10839 : 2000
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim. May combine two claims.
Study design and conductreasoningFor each combination of temperature and strain rate, three simulations were performed to calculate the Young's modulus and Poisson's ratio, and the obtained values were averaged.
“For each combination of temperature and strain rate, three simulations were performed to calculate the Young's modulus and Poisson's ratio. In each of the three simulations, the system was either elongated in the X, Y or Z direction and the obtained Young's modulus and Poisson's ratio were averaged.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
PremisereasoningHDPE has the chemical structure closest to pure PE because it consists primarily of unbranched PE molecules compared with other types of PE such as low-density polyethylene (LDPE).
“HDPE has the chemical structure closest to pure PE because it consists primarily of unbranched PE molecules compared with other types of PE such as low-density polyethylene (LDPE).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThis dependence of stiffness on temperature has also been observed for other polymers, for instance by Mahieux and Reifsnider and Richeton et al.
“This dependence of stiffness on temperature has also been observed for other polymers, for instance by Mahieux and Reifsnider [19] and Richeton et al [20].”
Quote in the paperNot a substantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe theoretical basis to the WLF equation is Doolittle's free volume, which is based on experimental data.
“The theoretical basis to this equation is Doolittle's free volume [23] that is based on experimental data.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [23] source
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe shift factor used to construct a master curve was experimentally determined for a large number of amorphous polymers by Williams, Landel and Ferry, who expressed the WLF equation.
“The shift factor used to construct a master curve was experimentally determined for a large number of amorphous polymers by Williams, Landel and Ferry [22], who expressed the WLF equation”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [22] source
Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Premisenone givenThe linear form of the Eyring equation is similar to the Arrhenius activation energy equation.
“The linear form of the Eyring equation is similar to the Arrhenius activation energy equation.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisenone givenThe time-temperature superposition is widely used to form a master curve using a shift factor to superimpose mechanical properties measured at different temperatures.
“The timetemperature superposition based on this phenomenon is widely used to form a 'master curve' using a shift factor to superimpose mechanical properties measured at different temperatures.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataThe standard deviations of the average Young's modulus and Poisson's ratio values for different strain rates and temperatures are reasonably low.
“The standard deviations are reasonably low.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationIn the freely jointed PE chain, C = 1, in the freely rotating chain, C = 2, and in the hindered rotation chain, C = 3.4.
“In the freely jointed PE chain, C = 1, in the freely rotating chain, C = 2, and in the hindered rotation chain, C = 3.4 [14].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [14] Gedde U W, 1995, Polymer Physics
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim.
PremisecitationThe yield stress of glassy polymers below Tg can be described by the Eyring theory of non-Newtonian flow.
“Bauwens et al [27] reported that the yield stress of glassy polymers below Tg can be described by the Eyring theory of non-Newtonian flow.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [27] source
May combine two claims.
Interpretationnone givenUsing the WLF equation at much higher strain rates than used in laboratory experiments is an unproven approach, but it can explain results from MD fairly well.
“Using the WLF equation at much higher strain rates than used in laboratory experiments is an unproven approach, but as discussed later it can explain results from MD fairly well.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationEquation (2) is an empirical equation found as an approximately identical shift factor-temperature relation for a wide variety of polymers, polymer solutions, organic glass-forming liquids and inorganic glasses.
“Equation ( 2) is an empirical equation found as an approximately identical shift factor-temperature relation for a wide variety of polymers, polymer solutions, organic glass-forming liquids and inorganic glasses.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
PremisecitationThe free volume is constant up to Tg and then increases linearly with increasing temperature.
“The free volume is constant up to Tg and then increases linearly with increasing temperature.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [23] source
Classified as probably not a substantial claim.
PremisecitationThe temperature dependence of viscosity arises largely from its dependence on free volume.
“The temperature dependence of viscosity arises largely from its dependence on free volume.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [23] source
May combine two claims.
InterpretationreasoningStrain rates close to the vibrational frequencies may lead to errors in the molecular trajectories, with the result that the system may no longer have a normal structure.
“Strain rates close to the vibrational frequencies may lead to errors in the molecular trajectories, with the result that the system may no longer have a normal structure.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
PremisecitationThe activation energy of linear PE is 27 kJ mol-1.
“The activation energy of linear PE is taken from [28] as 27 kJ mol-1.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [28] source
Classified as probably not a substantial claim.
PremisecitationIn more recent light scattering measurements on linear PE in diphenyl at 400 K, characteristic ratios from 8.7 to 10.5 were found.
“In more recent light scattering measurements on linear PE in diphenyl at 400 K (= 127 •C), characteristic ratios from 8.7 to 10.5 were found [16].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [16] source
Classified as probably not a substantial claim.
Study design and conductreasoningThe 10^11 s^-1 simulation results are excluded from the subsequent analysis and discussion.
“Therefore, the 1011 s-1 simulation results will not be used in the subsequent analysis and discussion.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisenone givenThe mechanical properties of polymers vary with both time and temperature.
“It is well known that the mechanical properties of polymers vary with both time and temperature.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationEquation (2) is valid above the glass transition temperature (Tg) because below this temperature, log aT increases less rapidly with decreasing temperature.
“Equation (2) is valid above the glass transition temperature (Tg) because below this temperature, log aT increases less rapidly with decreasing temperature [22].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [22] source
Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.
Premisenone givenHDPE has a high degree of crystallinity and a varying amount of amorphous structure.
“HDPE has a high degree of crystallinity and a varying amount of amorphous structure.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationcitationAnother possible reason for the discrepancy between the simulations and experimental measurements is the effect of molecular orientation.
“Another possible reason for the discrepancy between the simulations and experimental measurements is the effect of molecular orientation.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Premisenone givenSemicrystalline PE has not only a crystalline region surrounded by a disordered (amorphous) region, but also an interfacial region that connects the two.
“Semicrystalline PE has not only a crystalline region surrounded by a disordered (amorphous) region, but also an interfacial region that connects the two.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationIn Waterman's measurements, the experimental value of Poisson's ratio was 0.35 at -80 degrees C and 0.47 at 50 degrees C.
“At -80 •C, the experimental value of Poisson's ratio was 0.35, and at 50 •C it was 0.47.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [41] source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationWaterman calculated the complex Poisson's ratio of six different samples of PE by measuring the velocity and attenuation of ultrasonic longitudinal and transverse pulses at a frequency of 5 MHz and a strain rate of approximately 10^2 s^-1.
“Waterman [41] calculated the complex Poisson's ratio of six different samples of PE by measuring the velocity and attenuation of ultrasonic longitudinal and transverse pulses at a frequency of 5 MHz and a strain rate of approximately 102 s-1.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [41] source
May combine two claims.
InterpretationreasoningThe elastic modulus will be affected both by the degree of crystallinity and by how the interfacial region connects the crystalline and amorphous regions.
“Therefore, the elastic modulus will be affected both by the degree of crystallinity and by how the interfacial region connects the crystalline and amorphous regions.”
Quote in the paperSubstantial claim
The paper relies on this without support.
MD can predict material properties based on first principles, mainly using the atomistic forces between molecules.
“Molecular dynamics (MD) can predict material properties based on first principles, mainly using the atomistic forces between molecules.”
The paper relies on this without support.
Current computational power is not sufficient to model the many macromolecules in polymeric materials and describe all the interactions within a reasonable time frame.
“Current computational power is not sufficient to model the many macromolecules in polymeric materials and describe all the interactions within a reasonable time frame.”
The paper relies on this without support.
The time-temperature superposition principle is applicable to the Young's modulus and Poisson's ratio of amorphous PE to form a master curve.
“The time-temperature superposition principle is applied to the Young's modulus and Poisson's ratio to form a master curve to address the discrepancies in strain rates between the simulations and the experiments.”
The paper relies on this without support.
Polynomial smoothing does not alter the stress-strain response in the low-strain region used to calculate the Young's modulus and Poisson's ratio.
“The heterogeneity and small size of the sample produced noisy stress-strain curves and therefore polynomial smoothing was used to reduce the fluctuation of the stress.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
The higher-strain threshold differs by a factor of 100
MinorThe two percentages presented as alternatives are not equivalent: 0.2% is one-hundredth of 20%. This makes the threshold for the reported directional differences unclear.
“above approximately 0.2% or 20%”
“0.2% or 20%”
The low-strain limit is given as two different percentages
MinorA strain of 0.02% is one-hundredth of 2%. Elsewhere, the paper writes the equivalent pair as 0.02 and 2%, leaving the stated strain limit ambiguous.
“at a low strain (0.02% or 2%)”
“at a low strain (0.02 or 2%)”
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- Authors
- Sahputra, I. H., & Echtermeyer, A. T.
- Affiliations
- Norwegian University of Science and Technology (NO)
- Corresponding author
- Sahputra, I H
- Venue
- Modelling and Simulation in Materials Science and Engineering
- Publisher
- IOP Publishing
- Published
- 2013-08-08
- Volume
- 21
- Issue
- 6
- Pages
- 065016
- ISSN
- 0965-0393 (ISSN-L)
- 1361-651X
- OpenAlex
- W2077237797
- Cited by
- 76
- References
- 41
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 8 · 2023: 6 · 2022: 9 · 2021: 12 · 2020: 12 · 2019: 5 · 2018: 4 · 2017: 1 · 2016: 3 · 2015: 1 · 2014: 4 · 2013: 1
- FWCI
- 1.96
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Modelling and Simulation in Materials Science and Engineering (publishedVersion)
- UTPedia (Universiti Teknologi Petronas) (acceptedVersion)
- Scientific Repository (Petra Christian University) (submittedVersion)
- Topics
- Physical Sciences › Materials Science › Polymers and Plastics › Polymer crystallization and properties
- Physical Sciences › Materials Science › Polymers and Plastics › Polymer Nanocomposites and Properties
- Physical Sciences › Materials Science › Materials Chemistry › Material Dynamics and Properties
- Keywords
- amorphous polyethylene, temperature dependence, strain rate sensitivity, deformation, stress-strain behavior, Young's modulus, Poisson's ratio, time-temperature superposition
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