Crazing is a yielding mechanism in polymers characterized by the formation of a fine network of microvoids and fibrils. These structures (known as crazes) typically appear as linear features and frequently precede brittle fracture. The fundamental difference between crazes and cracks is that crazes contain polymer fibrils (5-30 nm in diameterKramer, E. J., & Berger, L. L. (1990). Effect of Molecular Variables on Crazing and Fatigue of Polymers. In H. H. Kausch (Ed.), *Crazing in Polymers, Volume 2: Advances in Polymer Science* (pp. 1-67). Springer-Verlag.), constituting about 50% of their volume, whereas cracks do not. Unlike cracks, crazes can transmit load between their two faces through these fibrils.
Crazes typically initiate when applied tensile stress causes microvoids to nucleate at points of high stress concentration within the polymer, such as those created by scratches, flaws, cracks, dust particles, and molecular heterogeneities. Crazes grow normal to the principal (tensile) stress, they may extend up to centimeters in length and fractions of a millimeter in thickness if conditions prevent early failure and crack propagation. The refractive index of crazes is lower than that of the surrounding material, causing them to scatter light. Consequently, a stressed material with a high density of crazes may appear 'stress-whitened,' as the scattering makes a normally clear material become opaque.
Crazing is a phenomenon typical of glassy amorphous polymers,Sauer, J. A., & Chen, C. C. (1983). Crazing and Fatigue Behavior in One- and Two-Phase Glassy Polymers. In H. H. Kausch (Ed.), *Crazing in Polymers, Volume 1: Advances in Polymer Science* (Vol. 52/53, pp. 169-223). Springer-Verlag Berlin Heidelberg. but can also be observed in semicrystalline polymers.Friedrich, K. (1983). Crazes and Shear Bands in Semi-Crystalline Thermoplastics. In H. H. Kausch (Ed.), *Crazing in Polymers, Volume 1: Advances in Polymer Science* (Vol. 52/53, pp. 226-271). Springer-Verlag Berlin Heidelberg.Narisawa, I., & Ishikawa, M. (1990). Crazing in semicrystalline thermoplastics. In H. H. Kausch (Ed.), *Crazing in Polymers Volume 2 Advances in Polymer Science* (pp. 355-389). Springer-Verlag. In thermosetting polymers crazing is less frequently observed because of the inability of the crosslinked molecules to undergo significant molecular stretching and disentanglement,Kinloch, A. J. (1985). Mechanics and Mechanisms of Fracture of Thermosetting Epoxy Polymers. In R. J. Morgan (Ed.), Epoxy Resins and Composites I (pp. 45-67). Springer-Verlag. if crazing does occur, it is often due to the interaction with second-phase particles incorporated as a toughening mechanism.
Historical background Crazing, derived from the Middle English term "crasen" meaning "to break", has historically been used to describe a network of fine cracks on the surfaces of glasses and ceramics. This term was naturally extended to describe similar phenomena observed in transparent glassy polymers. Under tensile stress, these polymers develop what appear to be cracks on their surfaces, often very gradually or after prolonged periods. These fine cracks, or crazes, were noted for their ability to propagate across specimens without causing immediate failure.
Crazing in polymers was first identified as a distinct deformation mechanism in the mid-20th century. Unlike inorganic glasses, most glassy polymers were found to be able to undergo significant plastic deformation before fracture occurs. Early observations noted the presence of crazes that propagated across specimens without causing immediate failure, indicating their load-bearing capacity and providing further insights into the nature of crazes, describing their appearance and behaviour under stress.
Significant advancements in the understanding of crazing were made in the 1960s and 1970s, illustrating the formation and structure of crazes in various polymers and on the stress conditions necessary for craze formation in polymers.Sternstein, S. S. and Ongchin, L. (1969) "Yield criteria for plastic deformation of glassy high polymers in general stress fields," Polymer Preprints, 10(2), 1117–1124.Sternstein, S. S. and Myers, F. A. (1973) "Yielding of glassy polymers in the second quadrant of principal stress space," J. Macromol. Sci. Phys., B8, 539–571. Researchers demonstrated that crazes grow perpendicular to the principal stress and highlighted the critical stress levels required for their initiation.Rabinowitz, S. and Beardmore, P. (1972) "Craze formation and fracture in glassy polymers," CRC Crit. Rev. Macromol. Sci., 1, 1–45.
Mechanisms of crazing
Craze nucleation and growth There is typically a delay between the application of stress and the visible appearance of crazes, indicating a barrier to craze nucleation. The time delay between the application of stress and the nucleation of crazes can be attributed to the viscoelastic nature of the process. Like other viscoelastic phenomena, this delay results from the thermally activated movements of polymer segments under mechanical stress. Crazing involves a localized or inhomogeneous plastic strain of the material. However, while plastic deformation essentially occurs at constant volume, crazing is a cavitation process that takes place with an increase in volume. The initiation of crazing typically requires a dilative component in the stress tensor and can be inhibited by applying hydrostatic pressure. From a solid mechanics perspective this means that a necessary condition for craze nucleation is having a positive value of , the first stress invariant that represent the dilatational component:
This condition is favored by the presence of triaxial tensile stresses, a condition that exist in defects of bulky samples subjected to plane strain. The cavitation involved in crazing allows the material to achieve plastic strain faster. The presence of cracks or defects in bulky samples will favor the initiation of crazing, as these defects are points of high concentration of stresses and can cause the formation of initial microvoids.
Crazes grow on the plane of maximum principal stress. Craze fibrils can endure substantial tensile forces across the craze but cannot withstand shear forces. Consequently, the highest plastic resistance is achieved by maximizing the normal stress on the plane of the craze. The concept of Taylor's meniscus instability provides a fundamental explanation for the growth of crazes.
This phenomenon is commonly observed when two flat plates with a layer of liquid between them are forced apart or when adhesive tape is peeled off from a substrate. The hypothesis concerning craze formation states that a wedge-shaped zone of plastically deformed and strain-softened polymer forms ahead of the craze tip. This deformed polymer constitutes the "fluid" layer into which the craze tip "meniscus" propagates, while the undeformed polymer outside the zone acts as the rigid "plates" constraining the fluid. As the finger-like structure of the craze tip advances, fibrils form by the deformation of the polymer webs between the fingers, and the interconnected void network emerges naturally right at the craze tip. Stereo-transmission electron microscopy has demonstrated that meniscus instability is the operative craze tip advancement mechanism in various glassy polymers.Donald, A.M. and Kramer, E.J. (1981) The Mechanism for Craze-Tip Advance in Glassy Polymers. Philosophical Magazine A, 43, 857-870.
The meniscus formation is a result of the imbalance of surface tension forces, surface tension acts to minimize the surface area, and any disturbance can create a meniscus, a curved surface at the interface between two phases. This causes the polymer chains to pull apart and form a cavity filled with a fibrillar network. This type of instability is well documented in various classes of materials and the concepts were developed from experiments involving the interpenetration of two fluids with different densities. In this scenario, the voided structure of the craze acts like a low-density fluid spreading into the denser, undeformed polymer. The physical principle behind this instability is the difference in hydrostatic pressure across a curved surface. Any disturbance that introduces curvature can propagate if the pressure difference due to the curvature is significant enough to overcome the surface tension. This condition can be written as:
where is the surface energy and is the radius of curvature. In theory, any disturbance meeting the criteria of the previous equation can grow, but in reality, a predominant wavelength emerges, which grows the quickest.
Craze breakdown and fracture
Crazes in polymers are typically load-bearing and expand in width and area until a region within the craze breaks down, forming a large void. With further stress or over time, this void can develop into a subcritical crack, growing slowly until it reaches a critical length, causing the sample to fracture. For polymers of practical molecular weight, craze growth is necessary but not sufficient for fracture. The critical step in the fracture of most glassy polymer crazes is the initiation of the first large void, defined as several fibril spacing in diameter. This process, known as craze fibril breakdown, is closely linked to the active zone and craze growth at the craze interface.Kramer, E. J., & Berger, L. L. (1990). Fundamental Processes of Craze Growth and Fracture. In H. H. Kausch (Ed.), *Crazing in Polymers: Volume 2 Advances in Polymer Science* (Vol. 91/92, pp. 1-68). Springer-Verlag. The breakdown of the craze starts gradually as voids coalesce to produce a cavity equal in thickness to the craze itself. Craze breakdown, which leads to crack extension, is crucial to the failure process. However, the detailed mechanisms involved remain a subject of debate among experts, despite the many models that have been suggested.Brown, H. R. "A molecular interpretation of the toughness of glassy polymers." Macromolecules 24.10 (1991): 2752-2756.Hui, C. Y., et al. "Micromechanics of crack growth into a craze in a polymer glass." Macromolecules 25.15 (1992): 3948-3955.
In the framework of fracture mechanics, once a crack of size is initiated due to an applied stress , its propagation can be analyzed using the stress intensity factor :
which describes the stress state near the tip of a crack. According to linear elastic fracture mechanics (LEFM), the crack will propagate when the stress intensity factor reaches a critical value , known as the fracture toughness of the material. This approach allows for the prediction of crack growth and the evaluation of the material's resistance to fracture under various loading conditions. It has been observed that for a crack growing relatively slowly in a stable manner and preceded by a craze, then the relationship between and crack propagation speed can be described by an equation of the form:
Where is related to the viscoelastic processes at the crack tip that stabilize crack growth.
Craze yielding and shear yielding
The yield point of a material represents the maximum stress it can endure without resulting in a permanent strain after the load is removed, it refers to the stress level required to initiate plastic deformation. When analyzing the yielding behavior of polymers, it is crucial to differentiate between shear yielding and craze yielding due to their distinct microstructural characteristics. Shear yielding involves the material undergoing shear flow with minimal or no change in density. In contrast, craze yielding, is highly localized and the macroscopic behaviors of shear and craze yielding differ significantly.Brown, N. (1986). Yield Behavior of Polymers. In W. Brostow & R. D. Corneliussen (Eds.), Failure of Plastics (pp. 98-105). Hanser Publishers