A possible mechanism for cross-tie fibril generation in crazing of amorphous polymers

Tijssens, M.G.A.

doi:10.1016/s0032-3861(01)00642-5

Cited by 16 publications

(17 citation statements)

References 12 publications

(14 reference statements)

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“…The growth mechanism is very similar to the picture outlined by Tijssens and van der Giessen (2002). An additional feature observed here is the development of local regions of high entanglement density that can pin a growing craze.…”

supporting

confidence: 77%

“…Similar conclusions were obtained through Finite Element (FE) simulations conducted by Tijssens and van der Giessen (2002). Further, Tijssens and van der Giessen (2002), using a unit-cell model of a craze (similar to that proposed by Leonov and Brown, 1991) and a realistic constitutive model for the polymer, showed that crazes with a cellular structure can, in principle, be generated by a process of repeated triggering of a cavitation instability above the craze dome and subsequent expansion of the void. Crazes with a fibrillar structure, on the other hand, can be generated by a model proposed by Basu et al (2005).…”

Section: Introductionsupporting

confidence: 68%

“…We show in this work that the model due to Tijssens and van der Giessen (2002) is probably one that best mimics the mechanics of craze growth. Whether a growing craze will evolve into a cellular structure or a fibrillar one is decided by the strength of the entanglements it has.…”

Section: Introductionmentioning

confidence: 71%

“…Crazes with a fibrillar structure, on the other hand, can be generated by a model proposed by Basu et al (2005). In this work, the possibility of stress induced disentanglement was added to the constitutive model used by Tijssens and van der Giessen (2002). Large scale disentanglement creates a soft region sandwiched between the stiff midriff and the bulk.…”

Section: Introductionmentioning

confidence: 99%

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Investigations into crazing in glassy amorphous polymers through molecular dynamics simulations

Venkatesan

Basu

2015

Journal of the Mechanics and Physics of Solids

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supporting

confidence: 77%

Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

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Investigations into crazing in glassy amorphous polymers through molecular dynamics simulations

Venkatesan

Basu

2015

Journal of the Mechanics and Physics of Solids

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“…A number of micromechanical and computational models, ranging from atomistic to continuum, have been put forth (cf., e. g., Leonov and Brown (1991); Krupenkin and Fredrickson (1999a,b); Tijssens et al (2000a,b); Estevez et al (2000a,b); Baljon and Robbins (2001); Socrate et al (2001); Drozdov (2001); Tijssens and van der Giessen (2002); Robbins (2003, 2004); Basu et al (2005); Saad-Gouider et al (2006); Zairi et al (2008); Seelig and Van der Giessen (2009) ;Reina et al (2013)), including consideration of nucleation and growth Figure 2: Crazing process in a steel/polyurea/steel sandwich specimen under opening mode fracture (Yong et al, 2009). of voids, craze nucleation, network hardening and disentanglement, chain strength, surface energy and other, that account, to varying degrees, for the observational evidence and relate macroscopic properties to material structure and behavior at the microscale. In parallel a large mathematical literature has evolved, discussing the possibility of cavitation in local models and possible nonlocal extensions which may ensure existence of minimizers, see for example Ball (1982); James and Spector (1991); Müller and Spector (1995); Conti and DeLellis (2003); Henao and Mora-Corral (2010).…”

Section: Introductionmentioning

confidence: 99%

A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity

Kröger

Weinberg

et al. 2015

Journal of the Mechanics and Physics of Solids

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We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.

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Yield and Crazing in Polymers

O’Connell

McKenna

2004

Encyclopedia of Polymer Science and Technology

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The present article discusses yield and crazing in polymeric materials. After introducing the definitions of stress and strain states, we present a brief summary of the general stress–strain responses for polymers under uniaxial tensile and compressive loading. We introduce the various regimes of behavior, from almost linear elastic through the nonlinear response to rubber‐like behavior. We also include the concepts of necking and cold drawing and the Considère construction for determining whether a material will undergo either of these processes. The history of the development of yield criteria and models is then examined in some details. Yield criteria, which may be considered as macroscopic criteria relating the applied stress state to a critical value for yielding, are first discussed and the modifications for pressure dependence introduced. These criteria, while useful from an engineering point of view in that they offer a method to estimate the likelihood of failure for a given loading situation, provide no insight into the microscopic or molecular mechanisms that give rise to yield. Early theories of yield (eg adiabatic heating and strain induced dilatation), though now considered incorrect, are mentioned in their historical context. A number of models are then presented which consider yield as an activated process. In these models, resistance to yielding is considered as being due to inter‐ and/or intramolecular forces. Application of stress (or the associated strain) affects the energy landscape of the material such that the energy barrier for this resistance is reduced and yield can occur. More complex models are then presented which address not only the yield of the material but the subsequent strain‐softening and strain‐hardening events that are observed. We conclude the section on yield by some brief, general observations on dislocation plasticity, the ultimate shear strength, dilatometry and calorimetry, computer modeling, and finally some discussion of yield in semi‐crystalline materials. The second section of the current chapter discusses the phenomenon of crazing. Crazing is a microscopically localized phenomenon, which involves a large degree of localized plastic deformation. Yet, crazing is generally the precursor to macroscopically brittle failure at low craze densities. An overview of craze morphology is first given to familiarize the reader with the main structural features of crazes. The development of a craze can be conveniently subdivided into three stages—initiation, growth, and failure—and each stage is examined separately. As with the yield section, craze initiation is examined in an historical context and the development of theories considering, variously, a critical cavitation stress, a critical strain, or the presence of inherent microvoids which can grow under the applied local stress or strain are discussed. There is general consensus on the mechanisms for craze growth. Craze tip advance is thought to occur by the Taylor meniscus instability mechanism, while craze thickening is due to the drawing in of material from the bulk–fibril interface. Both these mechanisms are presented and the dependence on, for example, molecular weight and cross‐link density discussed. Craze failure is examined in terms of either fibril failure or failure at the bulk–fibril interface. The section is completed by considering other factors for craze formation and failure (effect of cross‐tie fibrils, environmental‐stress cracking, and fatigue failure).

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A possible mechanism for cross-tie fibril generation in crazing of amorphous polymers

Cited by 16 publications

References 12 publications

Investigations into crazing in glassy amorphous polymers through molecular dynamics simulations

Investigations into crazing in glassy amorphous polymers through molecular dynamics simulations

A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity

Yield and Crazing in Polymers

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