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Crazing

Crazing is a materials phenomenon characterized by the development of a fine network of surface cracks, often appearing as interconnected fissures or whitish streaks, that occurs in polymers and ceramics under specific stress conditions. In polymers, it represents a localized yielding mechanism involving the formation of microvoids bridged by fibrils, while in ceramics, it stems from thermal expansion mismatches between the glaze and body during cooling.^[1]^[2] In glassy polymers, such as polystyrene and polymethyl methacrylate (PMMA), crazing initiates under tensile loading in amorphous regions, where stress concentrations—often from scratches or impurities—nucleate small voids that elongate into fibrillar structures perpendicular to the applied stress. These crazes, which can contain up to 50% void volume, scatter light to produce a characteristic opaque appearance and serve as precursors to brittle fracture if the load persists or environmental agents like solvents are present.^[3]^[1] Unlike shear banding, which occurs under compression and involves localized plastic flow at 45-degree angles, crazing is tension-driven and constrained by surrounding material, making it prevalent in brittle thermoplastics.^[3] In ceramics, crazing manifests as a web of microcracks in the fired glaze, typically due to the glaze having a higher coefficient of thermal expansion than the body, leading to tensile stresses as the piece cools from the kiln. This mismatch causes the glaze to contract more rapidly, fracturing when the stress exceeds its tensile strength, and can be exacerbated by underfiring the body, thick glaze layers, or post-firing moisture expansion in porous ceramics.^[2]^[4] The defect significantly reduces the mechanical strength of the ware (making it 3–4 times weaker), increases leaching of glaze components, and poses hygiene risks by trapping bacteria and dirt in the cracks, particularly in functional pottery.^[2]^[5] Prevention involves formulating glazes and bodies with compatible expansion coefficients, often by adjusting silica, alumina, or flux content in the glaze.^[2]

Fundamentals

Definition and Characteristics

Crazing is a localized yielding mechanism in polymers under tensile stress, characterized by the formation of microvoids approximately 5-30 nm in diameter that are bridged and stabilized by oriented polymer fibrils. These fibrils, which constitute roughly half the volume of the craze, create an interpenetrating network of voids and drawn polymer material, allowing the structure to bear load unlike a simple void or separation.^[6] Crazes typically grow perpendicular to the direction of the principal tensile stress, extending as thin, wedge-shaped regions that can reach lengths of centimeters and thicknesses on the order of micrometers.^[6] This growth produces stress-whitening in the material due to light scattering from the fibril-void network, a visible indicator of deformation.^[7] If the fibrils within the craze break down under continued loading, the structure can propagate as a crack, contributing to brittle fracture.^[6] Unlike macroscopic cracking, which involves clean separation of material faces with no load transmission, crazes maintain connectivity through the fibrillar bridges, forming a load-bearing network of oriented polymer interspersed with voids rather than a discrete gap.^[6] This distinction underscores crazing as a form of plastic deformation rather than immediate failure. Common examples of polymers prone to crazing include glassy amorphous materials such as polystyrene and poly(methyl methacrylate (PMMA), which exhibit this mechanism across a wide range of temperatures below their glass transition points.^[8]

Observation Methods

Optical microscopy serves as a primary technique for the initial detection and observation of crazes in polymers, particularly through the visualization of stress-whitening, which appears as opaque regions due to light scattering from craze voids.^[9] This method enables real-time monitoring of craze initiation and propagation in transparent glassy polymers like polystyrene, where crazes manifest as fine, reflective cracks under transmitted or reflected light.^[10] For instance, low-power optical microscopy has been employed in creep experiments to measure craze length and assess initiation in small polymer specimens under three-point bending.^[11] Its non-destructive nature and accessibility make it suitable for preliminary assessments, though resolution is limited to micrometer scales, often requiring complementary techniques for finer details.^[12] Transmission electron microscopy (TEM) provides high-resolution imaging of the internal fibril-void structure within crazes, revealing the nanoscale organization of drawn polymer fibrils separated by voids.^[13] Seminal studies using TEM on thin films of polystyrene demonstrated that crazes consist of interconnected fibrils approximately 10-20 nm in diameter, with void widths around 5-10 nm, confirming the fibrillar model of craze morphology.^[13] This technique involves preparing ultrathin sections or replicas of craze regions, allowing direct visualization of craze tips and maturation zones, which has been crucial for understanding craze stability and breakdown.^[14] TEM's atomic-level resolution surpasses optical methods, enabling precise measurement of fibril spacing and orientation, though sample preparation can introduce artifacts in bulk polymers.^[15] Scanning electron microscopy (SEM) is widely used to examine surface craze morphology, capturing the topography of craze openings, tips, and fracture surfaces in polymers.^[16] In situ SEM observations during deformation have shown craze initiation and growth rates in materials like PLA-based composites, highlighting how environmental factors influence surface features such as fibril bridging.^[16] This method excels in three-dimensional visualization of craze networks on fracture surfaces, with resolutions down to tens of nanometers after conductive coating, providing insights into craze density and distribution without sectioning the sample.^[17] SEM complements TEM by focusing on external features, though it requires vacuum conditions that limit in-situ dynamic studies compared to optical approaches.^[18] Small-angle X-ray scattering (SAXS) offers a non-destructive analytical method for probing the internal nanostructure of crazes, particularly the average fibril and void dimensions in bulk polymers.^[19] Early SAXS studies on polystyrene crazes measured interfibrillar spacings of about 6 nm, aligning closely with TEM observations and validating the void-fibril model across thicker samples.^[19] Real-time SAXS during fatigue loading has captured dynamic changes in craze orientation and density, with scattering patterns indicating fibril alignment perpendicular to the craze plane.^[20] This technique's ability to analyze larger volumes without preparation artifacts makes it ideal for quantifying craze microstructure in rubber-toughened polymers, where particle deformation influences scattering profiles.^[21] Interference microscopy and birefringence measurements are employed to quantify craze thickness and molecular orientation, leveraging optical path differences in polarized light.^[9] Using Pluta polarizing interference microscopy, researchers have determined craze thicknesses in deformed fibers by analyzing fringe shifts, revealing variations from 0.1 to several micrometers depending on strain.^[22] Birefringence assessments via polarized light microscopy detect orientation-induced refractive index changes in craze fibrils, with values up to 0.1 in polystyrene indicating high chain alignment.^[9] These methods provide quantitative data on craze geometry and stress distribution, with interference techniques offering sub-micrometer precision for thickness profiling along craze lengths.^[23] Modern techniques like atomic force microscopy (AFM) enable nanoscale topography mapping of craze surfaces, surpassing the resolution of earlier methods for direct height and roughness measurements.^[24] AFM studies on high-density polyethylene crazes have visualized fibril networks and void depths with sub-10 nm accuracy, facilitating high-throughput analysis in gradient thin films.^[25] Its advantages include non-vacuum operation and the ability to combine topography with mechanical property mapping via force spectroscopy, allowing observation of craze evolution under ambient conditions without destructive sectioning.^[24] AFM thus bridges the gap between surface SEM imaging and internal TEM/SAXS insights, particularly for studying craze tips in confined geometries.^[25]

Historical Background

Early Observations

The term "crazing" derives from the Middle English verb "crasen," meaning to break or crush, with roots in Old Norse and Scandinavian languages denoting shattering or cracking.^[26] In materials science, the term was initially applied to non-polymer contexts, such as glass and ceramics, where it described networks of fine surface cracks resulting from thermal expansion mismatches between the glaze and body during cooling. In polymers, crazing was first systematically studied in the mid-20th century, particularly in polystyrene under tensile loading, following anecdotal observations in early synthetic plastics like celluloid during the late 19th century. Key early experiments in the 1950s focused on the whitening observed in stretched polystyrene films, which was linked to localized stress concentrations and interpreted as a precursor to fracture.^[27] For instance, researchers examined polystyrene specimens using light microscopy and X-ray diffraction, revealing that crazing involved oriented molecular structures perpendicular to the applied stress.^[27] Initially, crazing was misconceived as mere surface cracking or simple brittle failure, with limited understanding of its internal morphology. This view persisted until the 1960s, when transmission electron microscopy first revealed the fibrillar, voided structure within crazes, distinguishing them as a distinct deformation mode involving localized plastic drawing rather than pure fracture.^[28]

Key Theoretical Developments

In the 1960s, significant progress in understanding crazing was driven by advancements in electron microscopy, which allowed researchers like Robert P. Kambour to visualize the internal structure of crazes in glassy polymers such as polycarbonate. Kambour's work demonstrated that crazes consist of a network of fine fibrils interspersed with voids, with the fibrils exhibiting draw ratios of approximately 2-4 and void contents around 50-70% by volume, challenging earlier views of crazes as mere microcracks. Concurrently, Sternstein and Ongchin proposed a seminal criterion in the late 1960s linking craze initiation to hydrostatic tension, suggesting that a critical dilatational strain, influenced by the polymer's bulk modulus, triggers the process under tensile stress states. This model emphasized the role of volumetric stress in distinguishing crazing from shear-dominated yielding, providing a foundational theoretical framework for subsequent studies. The 1970s saw further theoretical integration of crazing with fracture mechanics, particularly through the efforts of Edward J. Kramer, who analyzed stresses at craze tips using concepts from linear elastic fracture mechanics adapted for viscoelastic materials. Kramer's models highlighted how fibril bridging and craze tip opening displacements control growth rates, with stresses concentrated at the tip reaching levels sufficient to initiate new fibril formation.^[13] Early pressure-dependent yielding models emerged during this period, incorporating hydrostatic pressure effects on yield stress to predict transitions between crazing and shear yielding; for instance, experiments showed yield stress increasing linearly with pressure at rates of 0.1-0.2 times the shear modulus. Additionally, A. S. Argon developed models in the 1970s to explain fibril formation, positing that initial voids or shear transformation zones at the craze tip undergo instability-driven fingering, leading to the elongation and alignment of polymer chains into fibrils. By the 1990s, theoretical developments transitioned toward computational approaches, with early finite element simulations enabling predictions of craze initiation sites under complex stress fields.^[29] These models, such as those analyzing three-dimensional craze geometries in glassy polymers, revealed stress concentrations at surface flaws or inclusions as primary nucleation points, validating experimental observations of preferential crazing at heterogeneous sites.^[29] The meniscus instability theory, formalized by Argon and Salama in 1977, was increasingly incorporated into these simulations to describe craze tip advance, where surface tension-driven perturbations lead to periodic fibril spacing on the order of 10-20 nm. This progression marked a shift from empirical microscopy to predictive modeling, laying groundwork for quantitative assessments of craze stability.

Mechanisms of Crazing

Nucleation and Growth

Crazes in polymers nucleate at localized stress concentrations, such as microscopic flaws, inclusions, or defects, where the applied stress creates regions of high triaxiality. This initiation process requires a stress state characterized by a positive first stress invariant, I_1 = \sigma_{11} + \sigma_{22} + \sigma_{33} > 0, which corresponds to hydrostatic tension and facilitates the formation of initial microvoids through dilatational yielding.^[30] The first invariant I_1 represents the trace of the stress tensor and quantifies the volumetric stress component, distinguishing crazing—favored under tensile hydrostatic conditions—from shear-dominated deformation modes.^[31] In viscoelastic polymers, nucleation is further delayed by time-dependent relaxation processes, which dissipate energy and hinder the rapid buildup of sufficient local stress for void formation.^[30] Once nucleated, craze growth proceeds via meniscus instability at the advancing tip, where the curved polymer-air interface destabilizes under tensile stress, generating finger-like protrusions that evolve into voids separated by drawn fibrils. This instability, akin to the Taylor instability in fluid dynamics but adapted to solid polymer drawing, drives the transformation of bulk polymer into a fibrillar network, with the craze propagating perpendicular to the principal tensile stress direction.^[32] The growth velocity typically ranges from $10^{-6} to $10^{-3} m/s in glassy polymers, reflecting the balance between applied stress and material resistance.^[33] During growth, fibrils form by cold-drawing of polymer chains, extending up to 5-10 times their original length while bridging the voids and bearing the load; failure occurs when this extension limit is exceeded. Molecular entanglements play a critical role in stabilizing these fibrils, acting as topological constraints that resist chain pull-out and maintain structural integrity under tension. This entanglement network, present in polymers above the critical molecular weight, enables the high drawability observed in crazes and contrasts with unentangled systems that fail prematurely.^[15]

Breakdown and Fracture

As mature crazes develop under sustained tensile loads, breakdown initiates through the necking and subsequent rupture of individual fibrils, which are highly oriented polymer chains bridging the craze voids. This process occurs when the applied stress exceeds the fibrils' maximum load-bearing capacity, leading to localized deformation and thinning until scission or disentanglement propagates. The rupture of these fibrils causes adjacent voids to coalesce, forming interconnected crack-like openings that destabilize the craze structure and propagate failure.^[34]^[35] Fracture progression in crazes follows a characteristic thickening phase, where the craze width expands to approximately 1-10 μm prior to reaching critical instability. At this stage, the accumulated damage transitions the deformation from a localized, fibril-mediated process to rapid crack advancement. This instability is analyzed through linear elastic fracture mechanics (LEFM), adapting the Griffith criterion to model crazes as bridged cracks. The stress intensity factor K at the craze tip is given by

K = \sigma_{\infty} \sqrt{\pi a},

where \sigma_{\infty} is the remote applied stress and a is the half-length of the craze or crack. This equation derives from the original Griffith energy balance for brittle fracture, modified to account for the fibril-bridged nature of crazes, which provides partial closure and influences the effective toughness.^[34]^[35] The overall consequence of craze breakdown is a shift from ductile-like deformation, characterized by energy absorption in fibril extension, to brittle fracture dominated by rapid crack growth. Significant energy dissipation occurs through fibril pull-out, where disentangled chains slide out of the matrix, contributing to elevated fracture toughness values (e.g., up to thousands of J/m² in glassy polymers). This mechanism highlights the role of molecular entanglements in delaying catastrophic failure, though eventual void coalescence ensures progression to cleavage-like rupture.^[34]^[35]

Yielding Behaviors in Polymers

Shear Yielding

Shear yielding represents a primary mode of ductile deformation in polymers, characterized by uniform plastic flow through the propagation of shear bands or the development of necking regions. This process involves the slippage of molecular chains relative to one another, enabling significant shape change without the initiation of voids or cracks. This yielding mechanism predominates under conditions of elevated deviatoric stress, which drives the shear component of deformation, coupled with low or absent hydrostatic tension that might otherwise promote alternative failure paths. In ductile polymers such as polyethylene, shear yielding facilitates substantial elongations, often exceeding 500% and reaching up to 1000% in highly oriented samples, reflecting the material's capacity for extensive molecular reorientation before failure.^[36] At the microscopic level, shear yielding manifests as dislocation-like slip processes within the amorphous regions of the polymer structure, where localized shear transformations allow chains to disentangle and realign. Energy dissipation during this flow occurs primarily through frictional heating and conformational reorganization of the molecular segments, contributing to the observed post-yield softening followed by strain hardening.^[37]^[38]/Chapter_15:_Yielding) Shear yielding is particularly dominant in semi-crystalline polymers, such as polyethylene and polypropylene, when subjected to compressive or pure shear loading, where the crystalline lamellae facilitate chain slip in interlamellar amorphous domains without transitioning to brittle modes.^[39]^[7] In contrast to the localized deformation seen in craze yielding, this mechanism distributes strain more diffusely across the material.

Craze Yielding

Craze yielding represents a distinct mode of localized deformation in polymers, characterized by the formation of crazes—thin, planar voids bridged by fibrillar material—that mimic brittle behavior while providing limited apparent ductility through fibril extension. Unlike uniform yielding, this process initiates under tensile stresses, leading to the development of microvoids that coalesce into craze bands oriented perpendicular to the principal stress direction. In glassy polymers such as polystyrene (PS), craze yielding predominates due to the material's rigidity and low entanglement density, resulting in a brittle-like response with a high risk of sudden failure if crazes propagate unchecked.^[40] The characteristics of craze yielding include its confinement to narrow bands on the micrometer scale, typically 0.1–10 μm thick, where deformation is highly localized and strain is restricted to 1–5% before potential breakdown into cracks. This contrasts with more distributed plastic flow, as the fibrillar structure within the craze zone undergoes significant drawing, achieving local extensions up to 10–100 times the initial separation, yet the overall macroscopic strain remains modest. Crazing is particularly prevalent in amorphous glassy polymers like PS under uniaxial tension, where the process absorbs energy primarily through void formation and fibril elongation rather than shear flow.^[41]^[40] In comparison to shear yielding, craze yielding is favored by states of hydrostatic tension, which promote volumetric dilation and cavitation, whereas shear yielding is driven by deviatoric stresses that induce slip and flow without significant volume change. Energy absorption in craze yielding is generally lower than in shear yielding, as the fibril-mediated deformation dissipates less energy per unit volume and is prone to instability, limiting its contribution to overall toughness. This distinction underscores why crazing often occurs in thin films or constrained geometries where triaxial stress states prevail.^[41]^[7] Behaviorally, craze yielding can temporarily enhance a polymer's toughness by distributing deformation and delaying catastrophic failure, as seen in service conditions where multiple crazes form and extend before coalescing. However, it frequently precedes fracture, especially in environments promoting craze growth, such as elevated temperatures or chemical exposure, where fibril breakdown leads to crack initiation and brittle rupture. This mode thus balances limited ductility against the inherent vulnerability to sudden failure in applications like structural components.^[41]

Yielding Criteria

General Criteria for Polymers

Classical yielding criteria, such as the von Mises and Tresca criteria, were originally developed for metals and assume that yielding is independent of hydrostatic stress.^[42] The von Mises criterion posits that yielding occurs when the effective stress reaches a critical value, defined as:

\sigma_e = \frac{1}{\sqrt{2}} \sqrt{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}

where \sigma_1, \sigma_2, and \sigma_3 are the principal stresses, and yielding happens when \sigma_e = \sigma_y, the uniaxial yield stress.^[43] Similarly, the Tresca criterion states that yielding initiates when the maximum shear stress, \frac{1}{2} \max(|\sigma_i - \sigma_j|), equals half the uniaxial yield stress.^[44] These criteria perform adequately for metals but are limited for polymers, which exhibit significant pressure sensitivity in their yielding behavior.^[42] For polymers, yielding criteria must account for the influence of hydrostatic pressure \sigma_m, which arises from the mean normal stress and affects the yield stress.^[44] In polymers, the yield stress \sigma_y increases under hydrostatic tension (positive \sigma_m) and decreases under hydrostatic compression (negative \sigma_m), reflecting the material's sensitivity to the stress state.^[43] This pressure dependence stems from the molecular structure of polymers, where dilatational effects play a key role in deformation mechanisms.^[42] To incorporate these effects, polymer yielding criteria often employ stress invariants: the first invariant I_1 = \sigma_1 + \sigma_2 + \sigma_3, which represents the hydrostatic component (\sigma_m = I_1 / 3), and the octahedral shear stress \tau_{oct} = \frac{1}{3} \sqrt{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}, which captures the deviatoric shear component.^[43] Yielding is then described by a relationship between these invariants, modifying classical criteria to include terms dependent on I_1.^[44] Additionally, the yield stress \sigma_y in polymers is highly dependent on temperature and strain rate.^[45] As temperature increases, \sigma_y decreases due to enhanced molecular mobility, while higher strain rates increase \sigma_y by limiting time for relaxation processes.^[46] These dependencies are critical for understanding yielding in both shear and craze modes under varying conditions.^[45]

Modified von Mises Criterion for Shear Yielding

Unlike metals, where yielding is largely independent of hydrostatic pressure (μ = 0), polymers exhibit significant pressure sensitivity in their shear yielding behavior, with the pressure coefficient μ typically ranging from 0.1 to 0.2. This sensitivity arises from the molecular structure of polymers, where hydrostatic tension promotes chain disentanglement and reduces the shear stress required for yielding, while compression enhances intermolecular forces and increases resistance to shear. The modified von Mises criterion accounts for this by incorporating the mean stress into the octahedral shear stress formulation, providing a more accurate prediction for polymer deformation under multiaxial loading.^[47] The criterion is expressed as

\tau_{\oct} = \tau_0 - \mu \sigma_m

where \tau_{\oct} is the octahedral shear stress, \tau_0 is the shear yield stress at zero mean stress, \sigma_m is the mean (hydrostatic) stress, and \mu is the pressure sensitivity coefficient. This equation represents the yield condition, such that yielding occurs when the applied \tau_{\oct} equals the right-hand side. The derivation stems from experimental yield data collected from multiaxial tests on amorphous glassy polymers, such as polymethyl methacrylate (PMMA) and polystyrene (PS), under uniaxial tension/compression, plane strain compression, and biaxial states. Researchers plotted yield loci in principal stress space and fitted a linear relationship between the critical octahedral shear stress and \sigma_m, confirming the form's validity across the compressive and low-tensile quadrants with μ values around 0.15 for typical glassy polymers. This modification extends the classical von Mises criterion, which ignores \sigma_m, by linearly adjusting the yield surface based on empirical pressure dependence observed in these tests.^[47] In applications, the criterion effectively predicts shear band formation in polymers under biaxial compression, where negative \sigma_m elevates the critical \tau_{\oct}, delaying localized shear until higher deviatoric stresses are reached. For instance, in simulations and experiments on polystyrene, it delineates the transition from uniform deformation to shear banding by quantifying the pressure-enhanced yield threshold. Validation with polyethylene demonstrates strong agreement; biaxial shear-compression tests on high-density polyethylene (HDPE) using butterfly specimens yielded data points that closely match the criterion's predictions, with μ ≈ 0.12 fitting the observed increase in compressive yield strength over tensile by a factor of about 1.2–1.5. These results highlight its utility in modeling necking and post-yield behavior in semi-crystalline polymers like HDPE under complex loading. However, the criterion has limitations under high tensile stresses, where the linear pressure dependence underpredicts yielding because crazing—a dilatational failure mode—supersedes shear yielding, altering the dominant deformation mechanism and deviating from the shear-focused yield surface. In such regimes, particularly for glassy polymers like PMMA, alternative criteria incorporating dilatancy are needed for accuracy.^[47]

Criteria Specific to Crazing

The Sternstein criterion predicts the onset of crazing in glassy polymers under biaxial tensile stress states through the condition that the normal stress bias \sigma_b = \sigma_1 - \sigma_2 surpasses a material-specific threshold: \sigma_b > A(t,T) + \frac{B(t,T)}{I_1}, where I_1 = \sigma_1 + \sigma_2 (assuming plane stress with \sigma_3 = 0) is the first stress invariant, and A(t,T) and B(t,T) are functions capturing time t and temperature T dependencies of the polymer's resistance to dilatational yielding. This model emerged from biaxial tension experiments on polystyrene specimens, where crazing was observed only when I_1 reached a critical level, underscoring the dominant role of hydrostatic tension in nucleating microvoids and initiating fibrillar structures perpendicular to the maximum principal stress direction.^[48] The Argon model complements this by focusing on the micromechanical process of crazing initiation, involving the thermally activated expansion of pores that lead to fibril formation. Derived from continuum analyses of void growth under triaxial tension, the model highlights how hydrostatic tension facilitates dilatational deformation necessary for craze development in glassy polymers. Experimentally, biaxial and triaxial tests on glassy polymers like polystyrene and poly(methyl methacrylate confirm a threshold I_1 \approx 50--$100 MPa for craze nucleation at ambient conditions, equivalent to the dilatational strain energy needed to overcome intermolecular cohesion and form initial voids of nanoscale dimensions. This critical invariant reflects the energy contribution from hydrostatic components, as pure shear states below this threshold fail to induce the volume expansion essential for craze development. In contrast to shear yielding mechanisms, which depend primarily on deviatoric stress components for localized slip, crazing demands I_1 exceeding the critical threshold regardless of accompanying shear levels, ensuring that only tensile-dominated fields promote the void-fibril morphology characteristic of this failure mode.^[49]

Unified General Yielding Criterion

Approaches to unify yielding criteria for polymers integrate shear yielding and craze yielding mechanisms to predict the dominant deformation mode under multiaxial stress states. These frameworks evaluate thresholds for octahedral shear stress \tau_\mathrm{oct} relative to shear yielding and the first stress invariant I_1 relative to crazing initiation, with the mode determined by which limit is reached first.^[50]^[41] The Bowden and Raha model forms the basis of molecular-level descriptions in such integrations by portraying yielding as the thermally activated nucleation of disc-shaped sheared domains, analogous to dislocation loops, with an effective stress that incorporates a hydrostatic pressure term to account for dilatational effects. The activation energy for loop formation is expressed as U = \frac{2\pi R G b^2}{4\pi} \ln\left(\frac{2R}{r_0}\right) - \pi R^2 \tau b, where R is the loop radius, G the shear modulus, b the Burgers vector (on the order of molecular chain spacing), \tau the resolved shear stress modified by pressure, and r_0 the core radius; this pressure sensitivity predicts mode transitions by elevating the shear yield stress under positive hydrostatic pressure, thereby favoring crazing over shear in tensile-dominant states.^[50] This type of criterion enables the development of phase diagrams in principal stress space, delineating regions where uniaxial tension promotes crazing due to elevated I_1, while pure shear or compression drives shear yielding through dominant \tau_\mathrm{oct}; for instance, in polystyrene under plane strain conditions, the transition boundary shifts with increasing hydrostatic tension to favor craze nucleation. Temperature and strain rate further modulate these boundaries, as higher temperatures reduce I_1^\mathrm{crit} via enhanced chain mobility, while elevated rates increase both thresholds, often stabilizing shear yielding.^[41]^[50] A key advantage of such unified models is their capacity to forecast mixed modes in complex loadings, such as biaxial tension where initial crazing may transition to shear bands upon stress redistribution, providing insights into toughening strategies. Experimental validation from 1970s–1980s studies, including compression and tension tests on glassy polymers like polymethyl methacrylate, confirmed the predicted transitions and boundary shifts with pressure and temperature.^[41]

Influencing Factors

Material and Structural Influences

Glassy amorphous polymers, particularly those with high glass transition temperatures (T_g > 100°C) such as polystyrene (PS), exhibit a strong propensity for crazing as a primary yielding mechanism under tensile loading. This behavior arises from their molecular rigidity, which promotes the formation of microvoids and fibrils rather than homogeneous shear yielding, leading to localized deformation and potential fracture initiation. In contrast, rubber-toughened polymer blends, such as high-impact polystyrene (HIPS), mitigate crazing's detrimental effects by incorporating dispersed rubber particles that induce multiple, distributed crazes; these particles cavitate under stress, facilitating energy absorption through matrix shear yielding and fibrillation, thereby enhancing overall toughness by up to an order of magnitude compared to unmodified glassy polymers.^[51] At the molecular level, entanglement density plays a critical role in craze formation and fibril stability, with densities exceeding 10^{25} m^{-3}—as observed in PS—enabling effective load-bearing in stretched fibrils and preventing premature breakdown during craze growth. Higher entanglement densities increase the maximum stretch ratio of molecular strands, enhancing network hardening and reducing the overall proneness to crazing by limiting fibril elongation and void coalescence. Conversely, lower molecular weight (MW) polymers, such as polycarbonates with viscosimetric MW (M_v) below 20,000, lower the stress required for craze nucleation by reducing chain entanglement and slippage resistance, thereby increasing the density of nucleation sites and accelerating craze initiation under applied stress.^[52]^[53] Structural modifications, including the incorporation of fillers and nanoparticles, significantly influence craze development by altering stress distribution within the polymer matrix. For instance, silica nanoparticles in polymer nanocomposites can inhibit void nucleation at particle interfaces through attractive interactions with grafted chains, raising the yield stress to levels comparable to neat polymers and suppressing craze propagation by redistributing triaxial stresses, which significantly reduces craze-related failure depending on filler content and dispersion. Processing-induced molecular orientation, such as uniaxial stretching in polymethyl methacrylate (PMMA), further elevates crazing thresholds by aligning polymer chains and minimizing stress gradients; oriented PMMA demonstrates approximately 20 MPa higher resistance to crazing stress than isotropic counterparts, shifting the onset of deformation to higher first stress invariant (I_1) values.^[54]^[55] In modern applications involving biopolymers and recycled plastics, additives play a pivotal role in modulating crazing behavior and yielding modes. Polyhydroxyalkanoates (PHAs), such as poly(3-hydroxybutyrate) (PHB), naturally exhibit brittle crazing with limited ductility, but blending with biodegradable polyesters like poly(butylene adipate-co-terephthalate) (PBAT) at 30-45 wt.% promotes homogeneous crazing and extensive plastic flow, altering the deformation from single craze-cracking to networked fibril structures that increase strain capacity by up to 800%. Similarly, in recycled polylactic acid (PLA) formulations, compatibilizing additives enhance interfacial adhesion, suppressing localized crazing while favoring shear-dominated yielding, though older literature underrepresents these effects in sustainable materials.^[16]

Environmental and Loading Effects

Crazing in polymers is significantly influenced by temperature, with the process being suppressed above the glass transition temperature (T_g) due to enhanced chain mobility that promotes homogeneous deformation rather than localized void formation. For instance, in oriented polystyrene, crazing does not occur at temperatures around or above 110°C, where the material undergoes uniform plastic flow instead. Conversely, at sub-zero temperatures, crazing propensity increases as the polymer becomes more brittle, favoring chain scission mechanisms that lead to rapid craze initiation and brittle failure under tensile stress.^[56]^[57] Strain rate plays a critical role in determining whether crazing or shear yielding dominates, with high rates exceeding 10^{-2} s^{-1} promoting crazing by limiting time for molecular relaxation and chain disentanglement. At such rates, the yield stress for shear deformation rises sharply relative to the craze stress, shifting the failure mode toward brittle crazing, particularly at low temperatures. In contrast, low strain rates allow sufficient relaxation, enabling shear yielding to prevail as chains can rearrange without forming voids.^[57] Environmental factors, such as exposure to solvents or plasticizers, accelerate crazing by reducing the yield stress and facilitating nucleation at lower applied loads. For example, methanol immersion in poly(methyl methacrylate (PMMA) induces significant strain increases during creep tests through enhanced craze formation, effectively lowering the stress threshold for initiation by promoting surface flaw growth and fibril development. Similar effects occur with other active agents, where yield stress reductions of 20-50% are observed, hastening void coalescence and craze propagation.^[58] Loading history further modulates crazing behavior, with cyclic loading inducing fatigue crazing at stresses below the monotonic yield point through progressive microcrack initiation and propagation. In glassy polymers, repeated tension-compression cycles lead to fibril creep and eventual craze thickening, exacerbated by localized heating at crack tips that blunts propagation but ultimately reduces fatigue life. Multiaxial stress states can shift deformation modes according to unified yielding criteria, where hydrostatic components favor crazing over shear in tensile-dominant regimes.^[59] Recent research addresses gaps in predicting environmental and loading effects on crazing, particularly in nanocomposites, through advanced simulations like molecular dynamics (MD) and finite element modeling (FEM). MD studies using tools such as LAMMPS have modeled fibril drawing and disentanglement under varying temperatures and chain lengths, revealing how adhesive interactions influence craze widening in entangled networks. In 2020s investigations, these approaches simulate cyclic loading in glassy polymers, showing hysteresis-dominated responses and reduced stiffness in craze zones, aiding design of solvent-resistant nanocomposites.^[60]^[61]

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... polymers. Type I polymers such as polystyrene (PST) and polymethyl methacrylate (PMMA) craze at all temperatures below the glass transition temperature (~).Missing: prone | Show results with:prone
[9]
Optical Properties and Structure of Crazes in Transparent Glassy ...
IT has been known for about a year that a large fraction of what appear to be planar reflective cracks in transparent polymers such as polystyrene, ...
[10]
[PDF] Optical Studies of Crazed Plastic Surfaces 1
Whereas crazing in polymethyl methacrylate manifests itself primarily on the surface, in cast polystyrene and cast polymethyl alpha-chloroacry- late sheets it ...Missing: prone | Show results with:prone
[11]
Determination of craze initiation stress in very small polymer ...
The method consists of three-point bending creep experiments followed by low-power optical microscopy to determine the length of the crazed region, and hence ...Missing: observing | Show results with:observing
[12]
Journal of Applied Polymer Science | Wiley Online Library
Sep 28, 2012 · When a crazed filament sample is observed with transmitted light in an optical microscope, the transmitted light from the craze layer is ...
[13]
Microscopic mechanisms and mechanics of craze growth and fracture
Isolated air crazes have been produced in thin films of polystyrene (PS) bonded to copper grids by straining these in tension. The craze thickness profile, r(x) ...
[14]
[PDF] Relationships Between Mechanical Behavior and Craze ... - DTIC
A new technique has been developed to study the relationship between mechanical properties and craze microstructure in thin films (l—lO~m) of polystyrene. These ...
[15]
The role of crazing, shear yielding and the entanglement network
Jun 22, 2011 · Crazing as observed by Transmission Electron Microscopy in a thin film of polystyrene. The white arrow (in 1A) shows the craze opening and ...
[16]
Approaches to Control Crazing Deformation of PHA-Based ... - NIH
Oct 26, 2023 · Microvoids generated next to fibers within the tensile crazes merge with the other microvoids of the neighboring crazes.Missing: definition | Show results with:definition
[17]
Crazing Effect on the Bio-Based Conducting Polymer Film
Oct 15, 2025 · The presence of crazes in PLA/PAni film was evaluated using an optical microscope and scanning electron microscopy (SEM). The optical microscope ...
[18]
Regulating the formation and extent of crazing through the ...
Polymer crazing is a phenomenon observable as fine cracks on the surface of a material. For polymers crazing is often a precursor to mechanical failure with ...
[19]
Craze microstructure from small-angle x-ray scattering (SAXS)
Filling polystyrene crazes with methanol produces a 40 fold decrease in intensity I at a scattering angle 20 of 3 mrad and an increase in slope of the I vs. 2Θ ...
[20]
Real time small-angle X-ray scattering from polystyrene crazes ...
Real time small-angle X-ray scattering (SAXS) from polystyrene (PS) crazed in cyclic three-point bending is investigated using intense X-ray radiation from.
[21]
Small angle X-ray scattering analysis of crazing in rubber toughened ...
In this paper we explore how deformation of a three layer core-shell rubber particle affects such analysis. It is shown that, for a submicron rubber particle ...
[22]
Optical birefringence and molecular orientation of crazed fibres ...
Sep 1, 2017 · This article aims to report the role of crazes in the fracture process using the non-duplicated position of the Pluta polarizing interference ...
[23]
The effect of plasticization on craze microstructure - Brown - 1986
The structure of crazes in plasticized polystyrene has been studied by means of small-angle x-ray scattering and optical interference microscopy.
[24]
[PDF] High-Throughput Craze Studies in Gradient Thin Films Using Ductile ...
Craze microstructure was characterized by atomic force microscopy, which allows precise measurements of the craze dimensions, even very close to the tip. AFM ...
[25]
The structural evolution of high-density polyethylene during crazing ...
As has been shown [48], atomic force microscopy (AFM) is very suitable for investigation of polymer deformed by the crazing mechanism, although this method ...
[26]
Craze - Etymology, Origin & Meaning
Entries linking to craze ... crazy(adj.) 1570s, "diseased, sickly" (a sense now obsolete); 1580s, "broken, impaired, full of cracks or flaws," from craze + -y (2) ...
[27]
Crazing - Wikipedia
Crazing is a yielding mechanism in polymers characterized by the formation of a fine network of microvoids and fibrils. These structures (known as crazes) ...Mechanisms of crazing · Craze yielding and shear... · Yielding criteria for polymers
[28]
On Crazing of Linear High Polymers - AIP Publishing
The basic nature of crazing is investigated in some detail for polystyrene specimens by means of the light microscope, the electron microscope and the x‐ray ...<|control11|><|separator|>
[29]
Electron microscopy of crazes in glassy polymers: Use of reinforcing ...
The resultant, largely undamaged craze structure is seen by transmission electron microscopy to resemble an open-cell foam, the holes and polymer elements of ...
[30]
Stress analysis around a three‐dimensional craze in glassy polymers
The craze is assumed to consist of primary fibrils and cross-tie fibrils, such that a penny-shaped crack may form at the central regime of the craze. The craze ...
[31]
[PDF] 332: Mechanical Behavior of Materials
tity referred to as the 'first stress invariant', I1: I1 = 711 + 722 + 733 ... Crazing occurs first for PMMA in uniaxial extension (σ2 = 0). 5. GIc is ...
[32]
A general critical-strain criterion for crazing in amorphous glassy ...
Aug 20, 2006 · The results are consistent with the suggestion of Sternstein ... crazes to form the hydrostatic component of the stress tensor must be tensile.Missing: tension | Show results with:tension
[33]
The mechanism for craze-tip advance in glassy polymers
Stereo electron microscopy of the craze tip in glassy polymers shows unequivocally that the tip breaks up into a series of fingers, as predicted by the meniscus ...
[34]
Micromechanics of toughening in ductile/brittle polymeric ...
Since the 1960s, numerous studies on crazing have shed light on the craze ... Sternstein-Ongchin craze locus (Sharma, 2006). The parameters B/KΘ, Y ^ and ...
[35]
[PDF] entanglements in large deformation and mechanical failure of glassy ...
1.3 Crazing in polymer glasses. Crazing is a fracture mechanism unique to polymeric materials. It occurs prior to the ultimate propagation of the crack tip ...
[36]
Microscopic and molecular fundamentals of crazing
Craze nucleation has been accomplished and craze growth has begun. Page 9. Microscopic and Molecular Fundamentals of Crazing. 9. It is not so easy to ...
[37]
Tensile Behavior of High-Density Polyethylene Including the Effects ...
Aug 19, 2020 · During injection molding, the induced shear to the melted polymer might cause aligning of the molecular chains. This mechanical deformation ...
[38]
https://www.sciencedirect.com/science/article/abs/pii/S0020740314004251
[39]
Molecular chain plasticity model similar to crystal plasticity theory ...
In this paper, the new concept of a “molecular chain slip system” is analogically proposed on the basis of crystal plasticity theory for metals, ...
[40]
Plastic yielding of semicrystalline polymers affected by amorphous ...
If the crystals in a polymer are thick and more perfect then the barrier for their deformation, represented by shear yielding stress, is increased and the ...
[41]
https://doi.org/10.1016/S0022-5096(00)00016-8
[42]
https://www.researchgate.net/publication/275417522_Pressure_Dependent_Yield_Criteria_Applied_for_Improving_Design_Practices_and_Integrity_Assessments_against_Yielding_of_Engineering_Polymers
[43]
(PDF) Pressure Dependent Yield Criteria Applied for Improving ...
Aug 6, 2025 · Conventional yield criteria for ductile materials, such as Tresca and von Mises, predict that yielding is independent on the hydrostatic ...
[44]
[PDF] Physical Basis for a Pressure-Dependent Yield Criterion for Polymers
Von Mises (1913) assumed that a critical value of the mean difference in the principle stresses caused yielding and proposed that (J2,), = k. Although derived ...
[45]
Pressure dependent yield criteria for polymers - ScienceDirect.com
This paper considers two forms of a pressure modified von Mises criterion and shows a comparison with available experimental information.
[46]
High Strain Rate Mechanics of Polymers: A Review
Jan 25, 2016 · Most polymers exhibit time dependent mechanical behavior, as evidenced by rate dependent elastic moduli, yield strength, and post-yield behavior ...
[47]
Influence of temperature and strain rate on the mechanical behavior ...
Temperature and strain rate significantly affect polymer mechanical behavior. Increased temperature decreases yield stress, while increased strain rate ...
[48]
Yield criteria for amorphous glassy polymers | Journal of Materials ...
Mar 1, 1997 · QUINSON, R., PEREZ, J., RINK, M. et al. Yield criteria for amorphous glassy polymers. Journal of Materials Science 32, 1371–1379 (1997).
[49]
Yield criteria for plastic deformation on glassy high polymers in ...
Crazing is described with a viscoplastic cohesive zone which accounts for its initiation for a critical stress state, the thickening of the craze surfaces ...
[50]
Crazing and toughness of block copolymers and blends - SpringerLink
In unmodified homopolymers such crazing is initiated almost exclusively from surface imperfections which require a relatively high stress to initiate crazes.
[51]
[PDF] Modeling of the competition between shear yielding and crazing in ...
Before powerful experimental techniques were available for craze microstructure observation, such as TEM (Lauterwasser and Kramer, 1979) or SAXS (Brown and ...
[52]
None
Below is a merged summary of the yielding criteria and related topics from Chapter 12 of *Mechanical Properties of Solid Polymers* (3rd Edition by I. M. Ward and J. Sweeney), incorporating all information from the provided segments. To retain maximum detail in a dense and organized format, I will use tables where appropriate, followed by a narrative summary for additional context. The focus is on Chapter 12, with relevant information from other chapters (e.g., Chapter 13) included where explicitly referenced or highly relevant.
[53]
Advances in toughened polymer materials by structured rubber particles
Summary of each segment:
[54]
Micromechanics of the growth of a craze fibril in glassy polymers
The primary objective of this work is to model the growth and eventual failure of a craze fibril in a glassy polymer, starting from a primitive fibril.
[55]
Molecular weight dependence of the physical aging of polycarbonate
Sep 12, 2019 · The results show that the stress for craze nucleation increased as the molecular weight increased but was not affected by annealing.
[56]
Crazing of nanocomposites with polymer-tethered nanoparticles
It is well known that the addition of nanoscale fillers to polymer materials can lead to markedly enhanced mechanical properties. Polymer nanocomposites ...
[57]
Crazing Initiation and Growth in Polymethyl Methacrylate under ...
Mar 9, 2023 · Polymer crazing is typically a precursor to damage and considerably reduces the mechanical performance of polymer materials.
[58]
https://doi.org/10.1016/0032-3861(75)90214-1
[59]
https://www.researchgate.net/publication/225721883_Effect_of_molecular_variables_on_crazing_and_fatigue_of_polymers
[60]
https://doi.org/10.1103/PhysRevE.68.011801
[61]
Effect of molecular variables on crazing and fatigue of polymers
Aug 5, 2025 · In cyclic loading, crazing behaviour differs markedly from that observed in continuous loading. The defects grow linearly with the number of ...
[62]
https://doi.org/10.1103/PhysRevE.68.011801
[63]
https://doi.org/10.1021/acs.macromol.4c01445