On the origin of strain hardening in glassy polymers

Abstract

The influence of network density on the strain hardening behaviour of amorphous polymers is studied. The network density of polystyrene is altered by blending with poly(2,6-dimethyl-1,4-phenylene-oxide) and by cross-linking during polymerisation. The network density is derived from the rubber-plateau modulus determined by dynamic mechanical thermal analysis. Subsequently uniaxial compression tests are performed to obtain the intrinsic deformation behaviour and, in particular, the strain hardening modulus. At room temperature, the strain hardening modulus proves to be proportional to the network density, irrespective of the nature of the network, i.e. physical entanglements or chemical cross-links. With increasing temperature, the strain hardening modulus is observed to decrease. This decrease appears to be related to the influence of thermal mobility of the chains, determined by the distance to the glass-transition temperature ðT 2 T g Þ: q

Deforming glassy polystyrene: Influence of pressure, thermal history, and deformation mode on yielding and hardening

“…This is below the entanglement length N e of PS ͑simulations 45 at T = 450 K: N e = 83 monomers; experiments 46 at T = 413 K: N e = 128 monomers and 47 at T = 490 K: N e = 139 monomers, determined by measuring the rubberlike plateau modulus G N of an entangled PS melt above the glass transition and using this value to calculate the molecular weight between entanglements M e by means of 48 M e = 4 5 RT / G N , with R as the universal gas constant͒. Usually deformation would be affine for large length scales; for very long chains the ends do not feel immediately the connectivity constraint of each other as they are separated by many segments.…”

“…Rubber-elasticity theory, based on the entropic picture of a polymer chain, predicts a strainhardening modulus two orders of magnitude lower than what is measured experimentally. 4,5 A better understanding of these two phenomena can be reached by studying microscopic properties. Despite the vast literature of experimental results on the mechanical properties of PS, studies at the molecular level are rather scarce, as it is experimentally very hard to measure changes at this level.…”

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

“…This highly cross-linked thermoset possesses a high density of reticulation points which affect the physical properties, as discussed by Nielsen (1969);van Melick et al (2003). Consequently, the thermo-mechanical properties of the tested epoxy resin differ from moderately cross-linked thermosets and from thermoplastics but the physical origins of the plastic flow, softening, and re-hardening can be similar (Yamini and Young, 1980).…”

Correlation between rheological and mechanical properties of black PE100 compounds – Effect of carbon black masterbatch

“…Sun et al [11] and Wu et al [4] showed that the number of thicker lamellas can be increased by increasing lower molecular weight fraction in bimodal PE materials while total crystallinity remains the same, which explains higher average lamellar thickness in PE100-MK. On the other hand, this facilitated chain folding of high molecular weight molecules in thick lamellas can lead to lower number of long chains tie-molecules in amorphous region and subsequently decreased chain entanglements in interlamellar areas, effectively obstructing demonstration of strain hardening as it is believed that strain hardening is directly correlated with density of chain entanglements [37]. As can be seen in Table 5 and Figure 6c, PE100-MK exhibits highest tensile modulus while NPE100 has the lowest, but as Cheng et al [9] demonstrated, resistance to slow crack growth is not proved to be correlated with yield strength of the material.…”