Crazing

Crazing is a yielding mechanism in polymers characterized by the formation of a fine network of microvoids and fibrils.

[1][2] These structures (known as crazes) typically appear as linear features and frequently precede brittle fracture.

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.

[5] The refractive index of crazes is lower than that of the surrounding material, causing them to scatter light.

[12][13] Crazing, derived from the Middle English term "crasen"[14] meaning "to break", has historically been used to describe a network of fine cracks in 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.

Unlike inorganic glasses, most glassy polymers were found to be able to undergo significant plastic deformation before fracture occurs.

[24][25] 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.

The initiation of crazing normally requires the presence of a dilative component of the stress tensor and can be inhibited by applying hydrostatic pressure.

Consequently, the highest plastic resistance is achieved by maximizing the normal stress on the plane of the craze.

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.

Stereo-transmission electron microscopy has demonstrated that meniscus instability is the operative craze tip advancement mechanism in various glassy polymers.

This type of instability is well documented in various classes of materials[32][33][34] and the concepts were developed from experiments involving the interpenetration of two fluids with different densities.

[28] In this scenario, the voided structure of the craze acts like the low-density fluid, spreading into the denser, undeformed polymer.

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.

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.

However, the detailed mechanisms involved remain a subject of debate among experts, despite the many models that have been suggested.

[40] According to linear elastic fracture mechanics (LEFM), the crack will propagate when the stress intensity factor reaches a critical value

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[41] that for a crack growing relatively slowly in a stable manner and preceded by a craze, then the relationship between

Those two phenomenon are competitive mechanisms (although they are not mutually exclusive and can coexist[8]), with shear yielding being the more ductile failure mode because it involves the deformation of significant volume of the material while crazing is a more localized phenomenon ad it is more often associated with brittle failure.

With continued deformation, the material undergoes hardening due to molecular orientation, resulting in the multiplication and propagation of shear bands.

The criterion assumes that for yield to not occur the stress coordinate must be contained within the cylindrical surface described by the following equation:

[50][51][52][53] The von Mises criterion can be modified to incorporate the effect of pressure on the state of the material by substituting in its original formulation:

In plane stress the modified von Mises criterion is an ellipse on the principal axis space, but differently from the standard criterion it is shifted with respect to the origin, due to the different behavior of the polymeric materials depending on the hydrostatic component of the stress tensor.

Below this line crazing does not occur because the pressure component of the stress matrix tends to reduce the volume, instead of increasing it.

Oxborough and Bowden[56] attempted to create a more comprehensive relationship valid for a general triaxial state of stress.

Crazes in polystyrene (PS)
Crazing and fracture during a tensile test on a transparent polymer (x0.25 speed)
Diagram illustrating the mechanism of craze tip advancement through meniscus instability. a) wedge of deformed polymer situated ahead of the void fingers and trailing fibrils. b) to d) sections through the craze, showing the sequence of events as the craze tip progresses by one fibril spacing.
The image shows craze formation, growth and breakdown in a polymer under tensile stress. The left section depicts a polymer sample under stress, while the right section provides a detailed view of craze development at the crack tip.
A constant strain rate stress-strain curve for a polymer, displaying 1) ductile failure (shear yielding) 2) brittle failure (craze yielding).
The left draw shows the mechanism of shear yielding. The right section cut from a PS sample reveals the dense network of shear bands. [ 42 ]
The von Mises yield surfaces in principal stress coordinates circumscribes a cylinder with radius around the hydrostatic axis. Also shown is Tresca 's hexagonal yield surface.
Modified von Mises criterion in principal stress coordinates.
Modified von Mises criterion in principal stress coordinates (plane stress conditions).
Sternstein crazing criterion at different temperatures for biaxial stress state. For a given temperature, crazing does not occur for any stress state below the curves.
Argon crazing criterion (blue) vs Sternstein (red dashed), plane stress conditions.
Example of a yield-safe region in plane stress condition, considering both shear yielding and craze yielding.