1 Fracture mechanical behavior of polymers: 1. Amorphous glassy state Travis Smith, Chaitanya Gupta, Caleb Carr, Shi-Qing Wang * School of Polymer Science and Polymer Engineering, University of Akron, OH 44325, USA Abstract Theoretical analyses and experiments have been carried out to investigate fracture and failure behavior of glassy polymers, aiming to obtain new insights into the extreme mechanics of plastics. Our birefringence measurements quantify the local stress buildup at cut tip during different stages of drawing of a precut specimen. Based on brittle polymethyl methacrylate (PMMA), ductile bisphenol A polycarbonate (PC) and polyethylene terephthalate (PET), we find several key results beyond the existing knowledge base. (1) The inherent fracture and yield strengths F(inh) and Y(inh) differ little in magnitude from the breaking and yield stress (b and y) respectively measured from uncut specimens. (2) Stress intensification (SI) near a pre-through-cut build up ceases because of finite tip sharpness. (3) The stress tip at cut tip shows a trend of approximate linear increase with the stress intensity factor KI = 0(a) 1/2 or far-field load 0 for all three polymers and different cut size a. (4) A characteristic length scale P emerges from the linear relation between tip and KI. For these glassy polymers, P is on the order of 0.1 mm, apparently determined by the tip bluntness that occurs during the precut making. (5) Fracture toughness of brittle polymers is characterized by critical stress intensity factor KIc = F(inh)(2P) 1/2 , revealing relevance of the two crucial quantities. (6) The critical energy release rate GIc for brittle glass polymers such as PMMA is determined by the product of its work of fracture wF (of uncut specimen) and P. (7) The elusive fractocohesive length Lfc defined in the literature as GIc/ wF naturally arises from the new expression for GIc as stated in (6), i.e., it is essentially proportional to P. These results suggest that a great deal of future work is required to acquire additional understanding with regards to fracture and failure behaviors of plastics. 1. Introduction Fracture mechanics is a successful paradigm to understand fracture behavior by rationalizing the phenomenology of material failure in presence of intentional flaws or inherent defects at continuum level. It has provided a most effective description of extremely brittle solids such as silica glasses and ceramics. Besides brittle steels, linear elastic fracture mechanics (LEFM) has also been applied 1-3 to characterize fracture behavior of brittle glassy polymers. 4-6 On one hand, these textbooks 4, 5 assume that observed brittle fracture 7, 8 in uncut polymers takes place prematurely at breaking stress b, caused by stress intensification arising from inherent flaws, in absence of which brittle polymers would have shown significantly higher inherent fracture strength F(inh) (>> b). On the other hand, fracture mechanics has inspired molecular design to achieve rubber toughening 9 of polystyrene (PS) and polymethyl methacrylate (PMMA). Before a literature survey on fracture behavior of PS and PMMA, we first indicate effects that are beyond fracture mechanics description. For example, we have to leave it to polymer physics to answer why physical aging turns a ductile glassy polymer brittle, 10, 11 why hydrostatic pressure does the opposite, 12 why brittle polymers no longer undergo brittle fracture after melt stretching 13, 14 or why pre-melt-stretched ductile polymer appears brittle when drawn perpendicular to the melt-stretching direction, 11 why mechanical rejuvenation makes a brittle polymer ductile. 15 There are other deep questions such as why crazing 16, 17 arises, 18 why glassy polymers can yield in presence of crazing as well as when, how and why they undergo brittle-ductile transition (BDT) over a * Corresponding author at [email protected] narrow temperature window. Until recently, 14,18 the Ludwig- Davidenkov-Orowan (LDO) hypothesis 4, 6 has been regarded as a standard way to rationalize BDT; on the other hand, lack of ductility and appearance of crazing has been said to arise from insufficient entanglement. 16, 19 The statement 6 that "polymers are intrinsically brittle solids and fracture in a brittle manner at low temperatures and/or high strain rates" is actually a paraphrase of the LDO hypothesis. According to the recent theoretical considerations based on a coherent analysis of available phenomenology, 14 chain networking due to interchain uncrossability is the driver for molecular activation and ductility while no predictive description exists 18 of short-ranged intersegmental interactions. Bisphenol A polycarbonate (PC) is ductile, whereas polystyrene (PS) is brittle at room temperature not because PC is more "entangled" than PS, but because PC apparently can more readily undergo activation in its glassy state. At their BDT, all glassy polymers made of linear flexible chains, such as PS and PC, presumably have the same capacity to bring about activation. 18 According to this phenomenological model, 14 inherent fracture strength F(inh) at BDT scales linearly with the areal density LBS of load-bearing strands (LBS) that characterizes the structure of chain networking. Consequently the classic Vincent plot 7 acquired a new interpretation: F(inh) = LBSfcp at BDT due to chain pullout at critical force fcp rather than chain scission. 20 In this plot, thirteen different polymers show the breaking stress b (fracture strength) to scale linearly with the areal density of backbone bonds, i.e. b ~ . Because can be shown 14 to be proportional to LBS, the Vincent plot hints that b ~ F(inh) if fcp is the same for the different
Fracture mechanical behavior of polymers: 1. Amorphous glassy state
May 21, 2023
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