A distributed dislocation stress analysis for crazes and plastic zones at crack tips

The topography of crazes in polystyrene films was studied by scanning force microscopy (SFM), and evidence of micronecking operative during crazing was observed. It was found that crazing not only generates fibrillar structures but also creates an unexpectedly large surface depression in the crazed regions. The depression was found to initially increase linearly with the craze width but leveled off to approximately 35% of the original film thickness when the craze width became larger than a critical width wc. This behavior is independent of strain rate, aging time and the total applied deformation. The micronecking process during crazing indicates that the newly drawn fibrils were continuously deformed even after the fibrillation. Due to the large depression, the surface-to-surface distance between the craze fibrils is much smaller than that previously realized. This discovery may help to explain the fast fibril coalescence at room temperature and to examine the process of solvent-induced crazing. The mechanics of craze initiation and breakdown were then studied on the basis of necking theories of Considere construction and Bridgman's plasticity theory.The results from the stress analysis are in excellent agreement with the fibril breakdown behavior observed experimentally.

Section: Resultsmentioning

confidence: 99%

Micronecking operative during crazing in polymer glasses

Yang¹,

Kunz²,

Logan³

1993

“…For simplicity, the polymer outside the craze is assumed to be under linear elastic deformation, and the dislocation method of stress analysis is used to determine craze stress fields. 27 The stress S(x) can be expressed as 11,13,14,27 where E* ) E/(1ν 2 ) in which ν is the Poisson ratio, b is the Burger vector of the array of continuously distributed dislocations which are used to model the behavior of craze, c and a are the half lengths of the crack and the total defect (crack and craze combined), respectively, R(x) is the dislocation density, and x is the distance away from crack. In this way, the stress distribution along the longitudinal direction of the craze can be obtained and analyzed in detail.…”

Section: Introductionmentioning

confidence: 99%

Crazing Micromechanism in Glassy Atactic Polystyrene and Its Blends with Poly(2,6-dimethyl-1,4-diphenyl oxides) by AFM

Lin

Yang

2001

Crazing in glassy polymer thin films was found to follow a micronecking process similar to that of local shear deformation in ductile polymers. The void fraction in the fully necked craze region was determined, and a close-packed fibril structure was concluded. The local stress and strain within the craze were obtained from AFM topographic data by the Bridgman's plasticity analysis. The stress/ strain curve of craze fibrillation was subsequently determined where an apparent strain softening was found in the initiation of fibrillation, which was then followed by strain hardening as fibrils were drawn into the neck region. Strain rate was found to peak at the craze boundaries, consistent with the surface drawing mechanism from TEM results. During craze fibrillation, the local strain rate of the drawn polymer increased with drawing strain until a critical strain h was reached; beyond that, the strain rate decreased with the strain. The critical strain h, identified as the onset of strain hardening, was found to decrease with entanglement density νe in the low-νe, craze-forming regime but become a constant in the high-νe regime where crazing was replaced by shear yielding. The transition between crazing and shearing is controlled by the tendency of strain localization in the entanglement network.

“…Crazes greatly reduce the energy necessary for crack propagation in polymers and thus prevent them from exhibiting their ultimate toughness. The phenomenon of crazing was a subject of numerous studies over the last two decades, and a wealth of information, especially of experimental nature, can be found in the literature. − A number of excellent review papers − are also available.…”

Section: Introductionmentioning

confidence: 99%

Crazing in Two and Three Dimensions. 1. Two-Dimensional Crazing

Krupenkin¹,

Fredrickson

1999

A simple model is proposed to describe crazing in a very thin polymer film. It is argued that if the thickness of the film is below a certain critical value, the craze microstructure becomes similar to the deformation zone (two-dimensional neck) with the superimposed fibril structure. Deformation zone profile, characteristic fibril size, draw ratio, and critical film thickness are calculated as functions of material parameters and imposed strain rate. The results obtained are in good agreement with experimental values. The predictions of the model can also be used to verify the model of crazing in thick films and bulk polymers, which is described in Part 2 of the present series.