Plastic Craze and Shear Yield
Crazing and Shear Yielding in Plastics: A Comprehensive Analysis
Enhanced with Thermodynamic Energy Perspectives
J.P. McFadden Sr. & Claude
November 2025 - Enhanced Edition
Introduction
When polymeric materials fail, they rarely do so through a single, simple mechanism. Instead, they exhibit complex deformation and fracture behaviors that reflect the unique molecular architecture of long-chain molecules. Two fundamental competing mechanisms dominate plastic deformation in glassy polymers: crazing and shear yielding. Understanding these mechanisms—their initiation, growth, competition, and ultimate role in fracture—is essential for designing durable plastic components and diagnosing failures.
This essay explores the physics, mechanics, and practical implications of crazing and shear yielding, examining how molecular structure, stress state, temperature, and strain rate determine which mechanism dominates. Critically, we now recognize that these mechanisms represent competing thermodynamic pathways, where surface energy plays the pivotal role in determining whether a polymer accommodates stress through ordered structural response (shear yielding) or entropy-driven disruption (crazing).
We'll see that these aren't merely academic curiosities but critical factors determining whether a plastic component performs reliably or fails catastrophically in service. The integration of Griffith's energy balance framework reveals that material behavior reflects an ongoing competition between molecular order (representing material "intelligence") and entropic disorder—a competition profoundly influenced by environmental factors.
The Nature of Glassy Polymers
Before diving into deformation mechanisms, we must understand what makes polymers unique. Unlike metals with their regular crystalline lattices and mobile dislocations, glassy polymers consist of long, entangled molecular chains frozen in random configurations below their glass transition temperature (Tg). At temperatures below Tg, these chains lack the thermal energy for large-scale rearrangement, creating a material that's rigid but also complex in its response to stress.
The molecular weight, chain entanglement density, crosslinking, and presence of secondary molecular motions all influence how these materials deform. When we apply stress to a glassy polymer, we're essentially asking these frozen, entangled chains to accommodate deformation—and they can respond in fundamentally different ways depending on the stress state and material characteristics.
From a thermodynamic perspective, the polymer's molecular architecture represents a state of organized complexity—a system where entropy has been temporarily suppressed during processing. The entangled chains, frozen below Tg, embody material "intelligence" in their ability to maintain structural order and resist random molecular motion. Deformation mechanisms represent different pathways by which this order can be disrupted or maintained under stress.
Crazing: Cavitation Under Constraint
What is a Craze?
A craze represents one of the most distinctive features of polymer deformation—a damage zone that appears crack-like at first glance but possesses unique properties that distinguish it from true cracks. Crazes are thin, planar zones of highly localized deformation oriented perpendicular to the maximum principal tensile stress. Under an optical microscope, they appear as bright, silvery bands due to their ability to scatter light.
The remarkable feature of crazes is their internal structure. Rather than being void spaces like cracks, crazes contain a network of highly oriented polymer fibrils bridging across the craze, spanning from one craze interface to the other. These fibrils, typically 5-30 nanometers in diameter, are separated by voids, creating a structure that's approximately 50% void and 50% highly drawn polymer. The fibrils themselves may be stretched to several times their original length, with polymer chains highly oriented along the stress direction.
This fibrillar structure gives crazes their unique mechanical properties: they can bear stress (unlike cracks), but they also represent zones of significant damage and reduced load-bearing capacity compared to the bulk material.
Thermodynamically, crazes represent a partial victory for entropy. The void formation dramatically increases the system's disorder, creating new surfaces that require energy to maintain. However, the bridging fibrils represent the material's residual order—the entangled network's last stand against complete disintegration. The energy required to create these new surfaces is the critical factor governing craze stability.
The Energy Balance: Griffith's Framework Applied to Crazing
The formation and growth of crazes can be understood through A.A. Griffith's 1921 energy balance framework, which revolutionized fracture mechanics by recognizing that crack propagation is fundamentally an energy problem, not merely a stress problem.
For a crack (or craze) of length 2a under tensile stress σ in a material with Young's modulus E, the critical stress for propagation is:
σc = √(2Eγ / πa)
where γ is the surface energy required to create new crack surfaces (typically 30-50 mJ/m² for polymers in air).
This equation reveals several critical insights:
Larger flaws reduce strength: As flaw size (a) increases, the critical stress decreases—explaining why surface scratches and internal defects are so damaging.
Surface energy is protective: Higher γ increases fracture resistance. This is why anything that reduces surface energy makes cracking easier.
Polymer crazes complicate the picture: In polymers, the effective surface energy is augmented by the plastic work required to draw fibrils. A craze isn't just creating void surfaces—it's also stretching highly oriented polymer chains across those voids.
This framework explains why environmental stress cracking (ESC) is so insidious: aggressive fluids reduce γ at craze interfaces, dramatically lowering σc. A craze that would remain stable in air becomes unstable in the presence of certain chemicals, not because the chemical dissolves the polymer, but because it reduces the energy cost of creating new surface area.
The energy balance for craze growth becomes:
Energy Input (from applied stress) ≥ Energy Cost (surface creation + fibril stretching + chain disentanglement)
When fluids reduce the surface energy term, the balance tips toward uncontrolled craze growth, converting what should be stable damage into catastrophic failure.
Craze Initiation
Crazing initiates when the local stress state satisfies specific criteria. The most widely accepted criterion for craze initiation comes from Sternstein and Ongchin, who proposed that crazing occurs when:
σ₁ - σ₂ ≥ A + Bσₘ
where σ₁ and σ₂ are the maximum and minimum principal stresses, σₘ is the mean stress (hydrostatic component), and A and B are material constants.
This criterion reveals that crazing requires both:
A deviatoric stress component (σ₁ - σ₂) to drive deformation and molecular chain orientation
A tensile hydrostatic stress component to promote void formation
The physical interpretation is illuminating: the deviatoric stress causes the initial plastic deformation and molecular chain orientation, while the tensile hydrostatic stress pulls the deforming material apart, creating voids between the orienting polymer chains. Without sufficient tensile hydrostatic stress, the material would deform by shear yielding instead.
From an energy perspective, the hydrostatic tension directly opposes the surface energy that resists void formation. The mean stress effectively "subsidizes" the energy cost of creating new surfaces, making crazing thermodynamically favorable when it would otherwise be prohibitive.
Craze initiation often occurs at stress concentrations—surface scratches, internal particles, molecular-level heterogeneities, or regions of residual stress. These defects create local stress states that exceed the craze initiation criterion even when the nominal applied stress is relatively low. This sensitivity to defects explains why surface finish, processing conditions, and contamination critically affect the strength of plastic components.
Craze Growth
Once initiated, a craze can grow in two directions: thickening (perpendicular to the craze plane) and widening (parallel to the craze plane, in the direction of applied stress). The mechanisms differ fundamentally:
Craze Thickening
The craze advances into the surrounding polymer by a process called "active zone" advancement. At the craze tip, polymer chains are drawn from the bulk material into the craze, undergoing enormous extension as they transform into the fibrillar structure. This process requires breaking or rearranging molecular entanglements, essentially "dissolving" the entanglement network at the craze tip and reconstituting it as oriented fibrils.
The rate of craze thickening depends on temperature, molecular weight, and applied stress:
Higher temperatures increase molecular mobility, facilitating chain disentanglement
Higher molecular weights increase entanglement density, requiring more stress or time to accomplish the transformation
Applied stress provides the driving force for chain extension and fibril formation
Energetically, craze thickening represents a continuous transformation process where:
Ordered entanglement network → Highly oriented fibrils + voids
Low entropy state → Higher entropy state (due to voids) + localized order (in fibrils)
The rate is controlled by the energy barrier to disentanglement and the driving force from applied stress.
Craze Widening
Crazes widen by advancing along their length, typically at stress concentrations at the craze tips. This lateral growth often follows planes of weakness or high stress. In some polymers, crazes can extend completely across a component, creating an array of bridging fibrils that still carry load but represent significant damage accumulation.
The Critical Role of Craze Fibrils
The fibrils bridging across a craze perform a crucial function: they transmit stress across what would otherwise be a void, preventing the craze from immediately becoming a propagating crack. The fibril structure imparts a kind of "toughness" to crazed material—energy must be expended to break the fibrils before crack propagation can occur.
However, fibrils are not permanent. They can fail by several mechanisms:
Fibril breakdown: Individual fibrils can rupture under sustained stress, especially in the presence of environmental agents
Meniscus instability: The fibril-void interface can become unstable, causing fibril collapse
Chain scission: Molecular bonds within highly stressed fibrils can break, particularly under fatigue loading or chemical attack
When sufficient fibrils have failed, the craze transforms into a crack, and rapid fracture can follow. This transition from craze to crack represents the critical moment when damage becomes catastrophic failure.
From an energy perspective, fibrils represent the material's last defense against entropy. They maintain partial structural integrity across the craze, requiring additional energy input to break. The fibril strength depends critically on:
Molecular weight (higher MW = more entanglements per fibril = higher strength)
Chain orientation (highly aligned chains can bear enormous stress)
Environmental factors (fluids that reduce surface energy also weaken fibrils)
The effective surface energy of a crazed region includes not just the void surfaces but also the work required to break fibrils:
γeffective = γsurface + γfibril-drawing + γfibril-rupture
This is why high molecular weight grades resist environmental stress cracking better—they increase γfibril-rupture, maintaining a higher energy barrier against catastrophic failure.
Environmental Stress Cracking: When Surface Energy Betrays the Material
Environmental stress cracking (ESC) represents the most important practical manifestation of the surface energy principle in crazing. ESC occurs when a polymer under stress fails prematurely in the presence of specific chemicals, even though neither the stress alone nor the chemical alone would cause failure.
The classic example is polyethylene bottles failing in contact with detergents, oils, or other organic liquids. This phenomenon costs industries billions of dollars annually in product failures and warranty claims.
Mechanisms of ESC
ESC works by dramatically accelerating crazing through reduction of surface energy:
1. Adsorption and the Dupré Effect
Fluid molecules adsorb onto polymer surfaces, replacing high-energy polymer-air interfaces (γPA) with lower-energy polymer-fluid (γPF) and fluid-air (γFA) interfaces. The Dupré equation quantifies this:
Δγ = γPA - (γPF + γFA)
For an aggressive ESC agent, Δγ is large and positive—meaning the fluid substantially reduces the effective surface energy. Surfactants in detergents are particularly effective because they align their hydrophobic tails toward the polymer surface, creating extremely low interfacial energy.
For example:
Polycarbonate in air: γ ≈ 45 mJ/m²
Polycarbonate in acetone: γ drops toward zero due to excellent molecular compatibility
2. Wetting and Capillary Penetration
Low contact angles enable fluid to spread into craze voids via capillary action. The penetration depth follows Washburn kinetics:
Penetration depth ∝ √t
Crazes, with their nanoporous fibrillar networks, act as highways for fluid transport. Aggressive fluids can reach craze tips in seconds, continuously reducing surface energy at the advancing crack front.
3. Plasticization
Compatible fluids slightly swell polymer chains, lowering the local glass transition temperature (Tg) and increasing molecular mobility. This:
Facilitates fibril drawing (reducing γfibril-drawing)
Eases chain disentanglement (lowering the energy barrier to craze growth)
Increases configurational entropy, further reducing energy barriers
Fluid Specificity: Solubility Parameters and Surface Energy
The specificity of ESC—why certain fluids attack certain polymers—arises from solubility parameter matching. Hildebrand's total solubility parameter (δ) provides a first approximation: "like dissolves like," but for ESC, "like attacks like."
Hansen solubility parameters refine this understanding by decomposing interactions into three components:
δtotal = √(δd² + δp² + δh²)
where:
δd = dispersion interactions (London forces)
δp = polar interactions (dipole-dipole)
δh = hydrogen bonding
For ESC susceptibility, close matching between fluid and polymer parameters correlates with:
High work of adhesion (WA)
Low interfacial energy (γPF)
Significant surface energy reduction per Dupré's equation
Examples:
Polyethylene (δ ≈ 16 MPa^1/2): Attacked by hydrocarbons, surfactants (δ ≈ 16-18)
Polycarbonate (δ ≈ 20 MPa^1/2): Attacked by alcohols, acetone (δ ≈ 19-21)
Polyethylene in water (δ ≈ 48 MPa^1/2): No ESC—huge parameter mismatch means minimal surface energy reduction
Kinetics and Field Observations
While thermodynamics determines whether ESC is possible, kinetics determines how fast it occurs. Field observations reveal counterintuitive behaviors:
Cyclic vs. Continuous Exposure
Intermittent application of aggressive fluids (e.g., repeated alcohol wiping of polycarbonate) is often more damaging than continuous immersion. Why?
Fresh fluid applications prevent stress relaxation
Each cycle accumulates irreversible damage
The material never gets time to redistribute stress through creep
From an entropy perspective: repeated cycles prevent any recovery of order
The Wet Storage Paradox
Parts stored wet at elevated temperature often resist ESC better than dry-stored parts subsequently exposed. The reason:
Elevated temperature accelerates stress relaxation (creep)
Residual stresses relax before fluid can fully reduce surface energy
Lower driving stress when γ finally drops
The material "learns" to accommodate the fluid environment
Localized Application
Swabs or sprays concentrate fluid at high-stress zones, outpacing global stress relaxation that would occur in immersion. This explains why cleaning procedures can be more damaging than service exposure.
Predicting and Preventing ESC
Understanding the surface energy mechanism enables rational prevention strategies:
Material Selection:
Choose polymers with higher surface energy (harder to reduce)
Select high molecular weight grades (stronger fibrils, higher γfibril-rupture)
Consider crystalline regions (resist fluid penetration, maintain structure)
Design Strategies:
Minimize sustained tensile stress
Avoid sharp corners and stress concentrations (reduce local stress intensification)
Design for compressive loading where possible (suppresses crazing entirely)
Processing Control:
Minimize residual stresses from molding, especially near surfaces
Optimize cooling rates to reduce internal stress
Consider annealing to relieve process-induced stress (lowers driving force for crazing)
Chemical Compatibility:
Test materials against intended environments using Hansen parameter mapping
Use barrier layers or coatings to prevent fluid contact
Consider chemical modification to increase surface energy in specific environments
Shear Yielding: Plastic Flow Without Cavitation
The Nature of Shear Yielding
Shear yielding represents the other fundamental deformation mechanism in glassy polymers—plastic flow driven by shear stress without the cavitation characteristic of crazing. When a polymer shear yields, molecular chains slide past one another, producing permanent deformation without creating voids or reducing density. The material necks down, thins, and elongates, similar to the yielding behavior of ductile metals, though the underlying molecular mechanisms differ profoundly.
During shear yielding, polymer chains undergo cooperative rearrangements. Molecular segments rotate, translate, and disentangle partially, allowing the material to flow plastically. Unlike crazing, which produces highly oriented fibrils bridging voids, shear yielding produces more uniform molecular orientation throughout the deformed region, with density remaining essentially constant.
From a thermodynamic and structural perspective, shear yielding represents material "intelligence" in action:
The polymer accommodates stress through organized molecular rearrangement
Entanglement network integrity is maintained, though locally disrupted
No catastrophic increase in surface area (no voids)
The material trades one form of order (random chain configurations) for another (oriented chains)
Entropy increases, but not as dramatically as in crazing
Shear yielding can be viewed as the material's "smart" response to stress—it deforms to relieve stress while preserving structural continuity.
Shear Yielding Mechanisms
The molecular mechanisms enabling shear yielding in glassy polymers remain subjects of active research, but several key processes are recognized:
Chain Segment Rotation
Below Tg, most polymer chains are frozen in place, but local molecular motions can still occur. Under applied shear stress, molecular segments can rotate around backbone bonds, allowing limited rearrangement without requiring full-chain diffusion. These local conformational changes accumulate to produce macroscopic plastic flow.
Energy perspective: Shear stress lowers the activation energy for local conformational changes, effectively "activating" molecular motions that would normally require higher temperatures.
Partial Disentanglement
While complete chain disentanglement would require temperatures above Tg, applied stress can promote partial, localized disentanglement. Molecular chains slide past one another at entanglement points, effectively reducing the local entanglement density and allowing plastic flow. The stress state "activates" molecular motions that would normally require higher temperatures.
Critically, this process maintains network connectivity—chains slide but don't separate completely, preserving structural integrity.
Free Volume Redistribution
Glassy polymers contain "free volume"—nanoscale voids between and within molecular chains. Under shear stress, this free volume can redistribute, migrating toward regions of high stress and facilitating molecular rearrangement. This free volume concept, developed by researchers like Eyring and Robertson, provides a framework for understanding how stress assists molecular mobility below Tg.
Thermodynamically: Free volume represents configurational entropy. Stress-driven redistribution increases local entropy in deforming regions while maintaining overall structural order.
Shear Band Formation
In many polymers, shear yielding doesn't occur uniformly but localizes into narrow "shear bands"—thin zones of intense plastic deformation oriented approximately 45° to the tensile axis (the plane of maximum shear stress). Within these bands, strain can reach several hundred percent while surrounding material remains elastic or only lightly deformed.
Multiple shear bands may form and propagate, distributing deformation and contributing to ductility.
Energetically, shear bands represent:
Localized entropy maxima (high molecular mobility, disorder)
But surrounded by ordered matrix
A compromise between global disorder (catastrophic) and rigid order (brittle)
Yield Criteria
The onset of shear yielding is typically described by yield criteria similar to those used for metals. The von Mises criterion states that yielding occurs when:
(σ₁ - σ₂)² + (σ₂ - σ₃)² + (σ₃ - σ₁)² ≥ 2σy²
where σ₁, σ₂, σ₃ are principal stresses and σy is the yield strength. This criterion depends only on the deviatoric stress components (shape change), not the hydrostatic component (volume change).
However, polymers often deviate from von Mises behavior. Many glassy polymers exhibit pressure-dependent yielding, where compressive hydrostatic stress increases the yield strength. This pressure sensitivity distinguishes polymers from most metals and reflects the influence of free volume and molecular packing on yield behavior.
The Mohr-Coulomb criterion captures this pressure dependence:
τ = c + μσn
where τ is shear stress, σn is normal stress, c is cohesion, and μ is an internal friction coefficient. This criterion, borrowed from soil mechanics, describes polymers where compressive normal stress increases shear strength—behavior commonly observed in many glassy polymers.
Physical interpretation: Compressive stress:
Reduces free volume (less room for chain rearrangement)
Increases entanglement density
Raises the energy barrier to molecular motion
Makes plastic flow harder
The Competition: Crazing vs. Shear Yielding
What Determines the Dominant Mechanism?
The most critical question for understanding polymer behavior is: under what conditions does crazing dominate versus shear yielding? The answer determines whether a component fails in a brittle, catastrophic manner (crazing leading to crack propagation) or deforms ductilely with warning (shear yielding with necking).
From our enhanced thermodynamic perspective, this competition represents a choice between two energetic pathways:
Crazing path: Create voids (high surface energy cost) + draw fibrils (plastic work) → Entropy increases dramatically
Shear yielding path: Molecular rearrangement (lower activation energy) → Moderate entropy increase, order maintained
The pathway taken depends on which has the lower total energy barrier under the prevailing conditions.
Several factors govern this competition:
Stress State
Hydrostatic Tension Promotes Crazing
The most important factor is the hydrostatic stress component. Tensile hydrostatic stress (positive mean stress) strongly promotes crazing by facilitating void formation. The Sternstein-Ongchin criterion explicitly includes mean stress, showing that increasing hydrostatic tension lowers the stress required for crazing.
Thermodynamically: Hydrostatic tension directly opposes the surface energy (γ) that resists void formation. It effectively "pays" part of the energy cost, making the crazing pathway thermodynamically favorable.
Conversely, compressive hydrostatic stress suppresses crazing by opposing void formation. Under sufficient compression, crazing becomes thermodynamically impossible (you can't create voids when pressure is pushing the material together), and the material must deform by shear yielding if it deforms at all.
Geometry and Loading Create Stress States
Component geometry and loading conditions determine the local stress state. Consider these examples:
Uniaxial tension: Creates positive hydrostatic stress (σm = σ/3), promoting crazing. Most polymers will craze under uniaxial tension before shear yielding occurs, especially in the presence of stress concentrations.
Pure shear: Creates zero mean stress (σm = 0), favoring shear yielding over crazing. Thin-walled tubes under torsion approximate pure shear and typically show shear yielding.
Confined compression: Creates negative hydrostatic stress, suppressing crazing completely. Polymers under high confinement deform by shear yielding even if they would normally be craze-prone.
Triaxial tension: Creates high positive hydrostatic stress, strongly promoting crazing. Notched specimens under tension create triaxial stress states near the notch root, explaining why notches are particularly damaging to polymers—they shift the stress state toward the crazing pathway.
This stress state dependence explains why the same material can be brittle or ductile depending on component geometry—it's not a material property change, but a shift in which deformation pathway is thermodynamically favored.
Temperature
Temperature profoundly affects the crazing vs. shear yielding competition, but in a complex manner. As temperature increases toward Tg:
Molecular Mobility Increases
Higher temperature increases chain segment mobility, facilitating both craze fibril formation and shear yielding. However, the temperature sensitivity of these two mechanisms differs.
Brittle-to-Ductile Transition Temperature (BDTT)
Many polymers exhibit a "brittle-to-ductile transition temperature" where the dominant deformation mechanism shifts from crazing to shear yielding:
Below BDTT: Crazing dominates and fracture occurs at low strains with limited energy absorption (brittle failure)
Above BDTT: Shear yielding dominates, producing ductile behavior with necking and high energy absorption before failure
The BDTT doesn't represent a material property change at that temperature—both mechanisms remain possible across the temperature range. Rather, it reflects the shifting competition between mechanisms as temperature alters their relative kinetics.
Thermodynamic interpretation: As temperature rises:
Activation energy for shear yielding decreases faster than for crazing
Molecular mobility allows stress relaxation, reducing driving force
Above BDTT, shear yielding occurs fast enough to outpace craze initiation
The material effectively "chooses" the lower-energy pathway (shear yielding) when given sufficient thermal activation
Near-Tg Behavior
As temperature approaches Tg, molecular mobility increases dramatically:
Shear yielding becomes progressively easier
Materials that are brittle and craze-prone at room temperature may become highly ductile
Materials that shear yield at room temperature may show extensive necking and drawing
This temperature dependence reveals that deformation mechanism is not an intrinsic material property but a competition between pathways influenced by environmental conditions.
Strain Rate
Strain rate—the speed at which load is applied—influences the crazing-shear yielding competition through its effect on molecular relaxation:
High Strain Rates Promote Crazing
Rapid loading doesn't allow time for the molecular rearrangements necessary for shear yielding. The material behaves more "glassy," and stress concentrations build rapidly, promoting crazing.
Thermodynamically: Fast loading means:
Insufficient time for stress-activated molecular motions
Shear yielding pathway becomes kinetically inaccessible
Crazing pathway (which can occur faster) dominates
The material is "forced" into the higher-entropy pathway because the lower-entropy pathway is too slow
This explains why the same polymer can exhibit ductile behavior in a slow tensile test but fail in a brittle, crazed manner under impact. The Charpy or Izod impact tests exploit this effect, using high strain rates to reveal a material's impact brittleness.
Low Strain Rates Favor Shear Yielding
Slow loading allows molecular relaxation processes to occur, facilitating shear yielding. Stress concentrations relax through local plastic flow rather than accumulating to craze initiation levels.
This time-dependent behavior means that creep loading (constant low stress over long times) often produces shear yielding even in materials that would craze under rapid loading.
The material "has time" to explore lower-energy conformational states, choosing shear yielding over crazing when kinetically possible.
Rate-Temperature Equivalence
The effects of strain rate and temperature are related through time-temperature superposition. Increasing temperature has a similar effect to decreasing strain rate—both allow more molecular relaxation.
A material tested at:
High temperature + high strain rate ≈ Low temperature + low strain rate
This equivalence principle allows prediction of behavior across conditions and explains many apparently contradictory field observations.
Molecular Weight and Architecture
Molecular Weight Effects
Molecular weight strongly influences deformation mechanisms through its effect on entanglement density:
Low molecular weight polymers (below the critical entanglement molecular weight, Mc):
Chains aren't entangled
Low strength and limited capacity for either crazing or shear yielding
Often fail by chain pullout (no ordered response possible)
Minimal material "intelligence"
Moderate molecular weight (above Mc but not extremely high):
Entanglements provide strength but can be overcome by stress
Often show crazing because entanglement rearrangement is difficult
Void formation provides an alternative deformation path
Lower γfibril-rupture makes crazes more vulnerable
High molecular weight:
Very high entanglement density
Increased strength but also makes shear yielding more difficult
Paradoxical effect on crazing: More entanglements make craze fibril formation harder, BUT once formed, high MW fibrils are much stronger (higher γfibril-rupture)
Generally better ESC resistance due to stronger fibrils
From an energy perspective: Higher MW increases the "material intelligence quotient"—more entanglements mean more organized structure to maintain, higher energy barriers to disruption, and better resistance to entropy-driven failure.
Chain Architecture
The molecular architecture beyond simple molecular weight also matters:
Linear chains: More mobile, facilitate shear yielding (can rearrange more easily)
Branched chains: Branch points act as physical crosslinks, hindering both crazing and shear yielding but affecting them differently. Branches increase the energy cost of chain rearrangement.
Crosslinked polymers: Chemical crosslinks prevent chain slippage, suppressing shear yielding. Such materials often must craze or fracture brittlely since plastic flow by chain slippage is thermodynamically prohibited. The material "loses" its ability to respond intelligently through shear yielding.
Rubber Toughening: Engineering the Competition
One of the most successful strategies for improving polymer toughness exploits the crazing-shear yielding competition through deliberate microstructural design. Rubber-toughened polymers contain dispersed rubber particles (typically 0.1-10 μm diameter) distributed throughout a glassy polymer matrix.
These rubber particles don't significantly strengthen the material—in fact, they slightly reduce yield strength—but they dramatically increase toughness by altering the energetic landscape of deformation mechanisms.
How Rubber Particles Work: An Energy-Based Mechanism
The mechanism is elegant and reveals deep insights into the thermodynamic competition:
1. Stress Concentration
The modulus mismatch between soft rubber particles (E ≈ 1-10 MPa) and stiff matrix (E ≈ 2-3 GPa) creates stress concentrations around particles under applied load.
2. Controlled Cavitation
These stress concentrations cause cavitation within or around rubber particles, creating small voids at relatively low applied stress—much lower than the craze initiation stress of the matrix.
3. Hydrostatic Stress Relief (The Key Step)
The formation of these small, controlled voids relieves hydrostatic tension locally. This is the critical thermodynamic shift:
Before cavitation: High σm → Crazing pathway favored
After cavitation: Low σm → Shear yielding pathway favored
The rubber particles essentially "pay" the surface energy cost of void formation at low stress, changing the local stress state from one that promotes catastrophic crazing to one that promotes controlled shear yielding.
4. Multiple Shear Yielding
With crazing suppressed (low hydrostatic tension) and stress concentrations present (high shear stress), multiple shear bands initiate throughout the material. Plastic deformation distributes over a large volume rather than concentrating in a single craze that could evolve into a crack.
Energetically: Rubber toughening works by:
Reducing the "subsidy" that hydrostatic tension provides to surface energy
Making the crazing pathway thermodynamically less favorable
Simultaneously making shear yielding more accessible (high shear stress)
Distributing energy dissipation across many shear bands instead of one craze
Examples and Effectiveness
This mechanism explains why:
High-Impact Polystyrene (HIPS) and ABS are so much tougher than pure polystyrene, despite similar yield strengths
The rubber particles convert what would be brittle, crazed fracture into ductile failure with extensive shear yielding
Toughening effectiveness depends on particle size, distribution, and volume fraction—all of which influence the stress field and local energy balance
The material is "taught" to respond intelligently (shear yielding) rather than catastrophically (crazing) through clever microstructural engineering that manipulates local thermodynamics.
Practical Implications for Design and Failure Analysis
Design Considerations
Understanding crazing, shear yielding, and their energetic foundations enables intelligent design decisions:
When Ductility is Critical
For applications requiring impact resistance or overload protection, design to promote shear yielding:
Avoid sharp notches and stress concentrations that create triaxial tension (high σm)
Consider rubber-toughened grades (manipulate local stress state)
Operate at temperatures above the BDTT (make shear yielding kinetically favorable)
Design for lower strain rates where feasible (allow time for molecular relaxation)
Avoid thin sections that constrain deformation (plane strain conditions increase σm)
When Dimensional Stability is Critical
For applications requiring tight tolerances under sustained load:
Both crazing and shear yielding represent unwanted permanent deformation
Design for low stress levels below both craze initiation and yield stress
Consider crystalline polymers (higher creep resistance, better structural order)
Use reinforced grades (fibers constrain deformation)
Operate at lower temperatures (reduces molecular mobility, maintains order)
When Environmental Exposure is Expected
For applications involving chemical contact (the ESC case):
Test for ESC with actual service chemicals using Hansen parameter screening
Design for compressive rather than tensile stress (suppresses crazing thermodynamically)
Minimize surface stress concentrations where chemical contact occurs (reduce local stress intensification)
Consider barrier coatings or multi-layer structures (prevent surface energy reduction)
Use crystalline polymers (better chemical resistance, crystalline regions maintain order)
Select high molecular weight grades (stronger fibrils, higher γfibril-rupture)
Failure Analysis: Reading the Evidence
When a plastic component fails, the fracture surface tells stories about the mechanisms involved—and the thermodynamic pathways taken—if we're willing to listen:
Crazed Failures
Crazed regions appear whitened or silvery due to light scattering from voids (refractive index contrast). Under magnification:
Crazes appear as parallel lines perpendicular to the tensile stress
Multiple crazes may be present, often initiating from stress concentrations
Crack initiation sites often show dense craze networks
The crack path may follow craze planes
A predominantly crazed fracture suggests:
High hydrostatic tension (notched geometry, triaxial stress state)
Temperature below BDTT (shear yielding kinetically suppressed)
Rapid loading/impact (insufficient time for relaxation)
Possible ESC if chemical exposure occurred (surface energy reduction)
Material with high craze susceptibility (low MW, no rubber toughening, low γfibril-rupture)
Thermodynamic interpretation: The crazing pathway was energetically favored—either through high σm reducing the energy barrier or through environmental surface energy reduction (ESC).
Shear Yielded Failures
Shear yielding produces:
Necking or drawing visible at the macroscopic scale
Whitening from light scattering due to void formation or molecular orientation (different mechanism than craze whitening)
Shear bands visible under magnification (typically ~45° to tensile axis)
Ductile, fibrous fracture surfaces
A predominantly shear yielded fracture suggests:
Lower hydrostatic tension (less constraint, lower σm)
Temperature above BDTT (shear yielding kinetically accessible)
Slower loading rates (time for molecular relaxation)
Material with good ductility (higher MW, rubber toughening, good "material intelligence")
Thermodynamic interpretation: The shear yielding pathway was energetically favored—low σm maintained high surface energy cost for crazing, temperature/strain rate allowed molecular rearrangement.
Mixed Mode Failures
Many real failures show both crazing and shear yielding:
Crazes may initiate first, creating stress concentrations that trigger shear yielding
Shear bands may form between crazes
The crack may alternate between following craze planes and cutting through shear-yielded regions
Mixed-mode fractures often indicate:
Operation near the brittle-ductile transition (marginal thermodynamic competition)
Variable local stress states within the component
Changes in loading rate during the failure process
Partial effectiveness of toughening mechanisms (some regions toughened, others not)
Thermodynamic interpretation: The material was "on the fence" energetically—some regions favored crazing, others shear yielding, revealing the competitive nature of these pathways.
Case Examples with Energy Analysis
Case 1: Snap-Fit Failure
Scenario: A polycarbonate electrical connector fails at snap-fit hooks after months in service.
Examination reveals:
Dense craze networks at hook roots
Environmental exposure to cleaning solvents (isopropanol)
High local stress at sharp corners (stress concentration)
Analysis:
Mechanical: Sharp corners create triaxial tension at hook roots (high σm)
Environmental: Isopropanol (δ ≈ 23 MPa^1/2) matches PC (δ ≈ 20 MPa^1/2)
Thermodynamic: Solvent reduces γ at craze interfaces dramatically (Dupré effect)
Result: σc drops far below design stress; stable crazes become unstable
Solutions:
Increase fillet radii (reduce σm, lower stress concentration)
Switch to solvent-resistant grade (increase γ, wider δ mismatch)
Eliminate cleaning chemical contact (barrier coating)
Use mechanical snap design that favors compression (suppress crazing thermodynamically)
Case 2: Impact Failure
Scenario: An ABS automotive component fails under impact that similar components previously survived.
Investigation shows:
Brittle fracture with limited crazing
Testing reveals low temperature at failure time (-10°C)
Material operated below BDTT (~0°C for this grade)
Analysis:
Temperature: Below BDTT, shear yielding kinetically suppressed
Strain rate: Impact loading (no time for relaxation)
Thermodynamic: Only crazing pathway accessible; rubber toughening ineffective at low temperature
Rubber particles: Cannot cavitate effectively when rubber phase is glassy
Solution:
Redesign for lower operating temperature (specify BDTT < -20°C)
Switch to lower-BDTT material (different polymer or rubber phase)
Reduce stress concentrations to lower σm even at low temperature
Consider using material with better low-temperature toughening
Case 3: Creep Failure
Scenario: A polypropylene pressure vessel slowly deforms and eventually fails under constant pressure.
Examination reveals:
Extensive shear yielding and necking
Whitening throughout stressed regions (shear yielding type)
No evidence of crazing
Failure after months of service under constant 60% of rated pressure
Analysis:
Stress state: Biaxial tension (moderate σm, not triaxial)
Strain rate: Very slow (creep conditions)
Thermodynamic: Slow loading allowed continuous stress relaxation; shear yielding pathway accessible and lower-energy than crazing
Progressive: Deformation gradually reduced wall thickness, increasing stress, accelerating further deformation (positive feedback)
Solution:
Reduce design stress to account for creep (50% of yield → 30% of yield)
Increase wall thickness (margin for creep deformation)
Select higher-creep-resistance material (more crystalline PP, fiber reinforcement)
Consider time-temperature superposition in design calculations
Advanced Topics: Connecting Scales and Perspectives
Craze Fracture Mechanics
Researchers have developed fracture mechanics approaches specifically for crazed materials. Unlike linear elastic fracture mechanics (LEFM), which assumes crack tips are singular stress concentrations, craze fracture mechanics recognizes that crazes have finite tip dimensions and bear stress through their fibrillar structure.
The "craze toughness" Gc represents the energy required to extend a craze and break its fibrils. For many polymers, this craze toughness dominates the overall fracture toughness.
The fracture process involves:
Craze initiation at a flaw or stress concentration (overcome γ barrier)
Craze growth—thickening and widening (continuous energy input)
Fibril formation within the growing craze (plastic work, chain disentanglement)
Fibril breakdown (overcome γfibril-rupture), converting craze to crack
Crack propagation through bulk material or along craze-bulk interfaces
Energy balance perspective:
Gc,total = γsurface + γfibril-drawing + γfibril-rupture + γplastic
Each term represents an energy dissipation mechanism. High molecular weight increases γfibril-rupture; rubber toughening adds γplastic through multiple shear bands.
Understanding this sequence enables modeling crack growth rates in polymers under:
Fatigue loading (cyclic fibril stress)
Creep (time-dependent fibril degradation)
ESC conditions (fluid reduces multiple γ terms)
Computational Modeling
Modern finite element analysis (FEA) increasingly incorporates sophisticated constitutive models capturing both crazing and shear yielding. These models must account for:
Pressure-Dependent Plasticity
Unlike metals, polymers show yield strength dependence on hydrostatic pressure (σm). Modified Drucker-Prager or Mohr-Coulomb criteria capture this effect, enabling prediction of where shear yielding will initiate based on local stress state.
Craze Initiation and Growth
Some advanced models include craze initiation criteria based on local stress state (Sternstein-Ongchin) and accumulated plastic strain. Craze growth can be modeled by introducing material softening in regions meeting craze criteria, with special elements representing the craze fibrillar structure (reduced modulus but non-zero stress-bearing capacity).
Damage Accumulation
Both crazing and shear yielding represent damage—permanent changes that reduce material load-bearing capacity. Progressive damage models track this degradation:
Crazing: Reduces effective load-bearing area, creates stress concentrations
Shear yielding: Reduces local stiffness, changes geometry (necking)
Models predict eventual failure as damage accumulates to critical levels.
Rate and Temperature Dependence
Sophisticated constitutive models incorporate viscoelastic-viscoplastic behavior, capturing how:
Yield strength varies with strain rate and temperature
Craze initiation stress changes with conditions
BDTT shifts with strain rate
ESC susceptibility depends on exposure kinetics
These computational approaches enable virtual testing of designs, predicting failure modes and locations before physical prototypes exist. Increasingly, they incorporate energy-based failure criteria that directly calculate:
Local surface energy based on stress state
Energy available for crack propagation (G)
Critical energy release rate (Gc)
Pathway competition (crazing vs. shear yielding) based on relative energy barriers
Nano-Scale Perspectives
Recent research using atomic force microscopy (AFM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) has revealed nano-scale details of crazing and shear yielding:
Craze Structure
High-resolution imaging shows that craze fibrils aren't uniform cylinders but have complex internal structure:
Individual fibrils may contain multiple molecular bundles
Void spaces exist between bundles within fibrils
Fibrils show periodic variations in thickness (possibly related to MW distribution)
Chain orientation varies across fibril diameter
Energy implications: The nano-structure affects:
Effective surface area (more complex than assumed)
Fibril strength (non-uniform stress distribution)
Failure modes (where does rupture initiate within fibrils?)
Shear Band Structure
Nano-scale examination of shear bands reveals:
Highly localized deformation zones (sometimes only 100-200 nm thick)
Enormous local strains (>200%)
Within shear bands: free volume increases, molecular orientation develops
Regions of fundamentally altered structure (locally approaching rubbery state)
Energy perspective: Shear bands are entropy maxima—regions where the Second Law has locally "won" but remain contained within an ordered matrix.
Craze-Shear Interaction
At the nano-scale, the boundary between crazing and shear yielding blurs:
Some materials show "hybrid" structures with characteristics of both mechanisms
Craze tips can trigger shear band nucleation
Shear bands can initiate crazes through stress concentration
The competitive/cooperative nature is more complex than macroscopic models assume
Understanding these nano-scale phenomena may enable development of polymers with enhanced toughness through controlled deformation mechanisms—materials that intelligently select the optimal response at each scale.
Conclusion: Materials Tell Us How They Want to Deform
The competition between crazing and shear yielding represents a fundamental aspect of polymer behavior—two distinct molecular responses to applied stress, each representing a different thermodynamic pathway with its own energetics, advantages, and failure modes.
From our enhanced energy perspective, we understand that:
Crazing represents an entropy-driven pathway where void formation dramatically increases disorder, enabled when surface energy (γ) is low or when hydrostatic tension (σm) subsidizes the energy cost. Environmental fluids accelerate this pathway by reducing γ.
Shear yielding represents the material's "intelligent" response—organized molecular rearrangement that maintains structural integrity while accommodating stress. This pathway is favored when crazing is thermodynamically expensive (high γ, low σm) or when temperature/strain rate make it kinetically accessible.
The competition between these mechanisms isn't random—it's determined by which pathway has the lower total energy barrier under prevailing conditions. We can manipulate this competition through:
Material selection (molecular weight, architecture affecting γfibril-rupture)
Design (geometry determining σm)
Processing (residual stress, molecular orientation)
Environment (temperature, chemical exposure affecting γ)
Microstructure (rubber toughening manipulating local stress state)
Understanding this competition enables:
Intelligent Material Selection: Choose polymers whose deformation mechanisms match application requirements through understanding of their energetic landscape
Thoughtful Design: Create geometries and loading conditions that promote beneficial deformation mechanisms (shear yielding for toughness) while thermodynamically suppressing harmful ones (crazing for brittle failure)
Effective Failure Analysis: Read the evidence on fracture surfaces to understand the energetic pathway taken. Was crazing triggered by ESC (γ reduction), stress concentrations (high σm), or operating below BDTT? Did shear yielding lead to excessive creep? Let the material tell you its thermodynamic story.
Innovative Materials Development: Understanding fundamental mechanisms enables rational toughening strategies. Rubber-toughened polymers succeed by manipulating the crazing-shear yielding competition at the microstructural level through stress state engineering. Future developments may offer even more sophisticated control over deformation mechanisms through hierarchical structures, self-healing systems, or responsive materials.
Perhaps most importantly, the study of crazing and shear yielding, enhanced by thermodynamic and energy perspectives, illustrates a central truth of materials science: materials aren't passive objects that simply "have" properties. They're complex systems with internal structure, molecular architecture, and multiple possible responses to stress—each representing a different point on an energy landscape.
The material's "choice" of deformation mechanism reflects thermodynamic principles: it follows the path of least resistance, the pathway requiring the minimum energy input under prevailing conditions. Our job as engineers and scientists isn't to force materials to behave as we wish—it's to:
Understand the energy landscape they navigate
Shape that landscape through material selection, design, and processing
Work with their natural tendencies to create successful designs
Learn from failures by reading the thermodynamic story written in crack patterns
When we see crazes forming under a microscope or observe necking in a tensile test, we're witnessing molecular-scale thermodynamics playing out at the macroscopic scale—billions of molecular chains responding to stress according to Griffith's energy balance, their architecture, their environment, and the fundamental physics governing their behavior.
The integration of surface energy considerations transforms our understanding: ESC isn't mysterious chemical attack—it's thermodynamics in action, where fluids reduce γ and tip the energy balance toward entropy's victory. Rubber toughening isn't just empirical magic—it's clever manipulation of local stress states to shift the thermodynamic competition toward shear yielding.
This molecular-to-macro, thermodynamic-to-practical perspective transforms failure analysis from post-mortem examination into dialogue with materials, where failures become teachers if we're willing to listen to what they're telling us about the energetic pathways they explored.
By understanding that materials embody a competition between order and entropy, between structural intelligence and thermodynamic inevitability, we can engineer resilience into plastic components. We design with thermodynamics, not against it, creating structures that channel stress along energetically favorable pathways that lead to safe, predictable outcomes rather than catastrophic failures.
The lesson is profound: Listen to the material. Understand its energetic preferences. Shape the landscape it navigates. And it will reward you by performing reliably in service, telling you when it's stressed, and failing gracefully when it must fail at all.
Further Reading and Key References
Foundational Works on Crazing
Kambour, R.P. (1973). "A Review of Crazing and Fracture in Thermoplastics." Journal of Polymer Science: Macromolecular Reviews, 7, 1-154. [Comprehensive review of early crazing research]
Kramer, E.J. (1983). "Microscopic and Molecular Fundamentals of Crazing." Advances in Polymer Science, 52/53, 1-56. [Detailed mechanism of craze formation and growth]
Sternstein, S.S., & Ongchin, L. (1969). "Yield Criteria for Plastic Deformation of Glassy High Polymers in General Stress Fields." Polymer Preprints, 10(2), 1117-1124. [Original craze initiation criterion]
Shear Yielding Mechanisms
Bowden, P.B., & Raha, S. (1974). "A Molecular Model for Yield and Flow in Amorphous Glassy Polymers Making Use of a Dislocation Analogue." Philosophical Magazine, 29(1), 149-166.
Argon, A.S. (1973). "A Theory for the Low-Temperature Plastic Deformation of Glassy Polymers." Philosophical Magazine, 28(4), 839-865.
Rubber Toughening
Bucknall, C.B. (1977). Toughened Plastics. Applied Science Publishers. [Definitive text on rubber toughening mechanisms]
Yee, A.F., & Pearson, R.A. (1986). "Toughening Mechanisms in Elastomer-Modified Epoxies." Journal of Materials Science, 21, 2462-2474.
Environmental Stress Cracking and Surface Energy
Arnold, J.C. (1995). "Environmental Stress Crack Initiation in Glassy Polymers." Trends in Polymer Science, 3(1), 14-20.
Hansen, C.M. (2007). Hansen Solubility Parameters: A User's Handbook. CRC Press. [Predicting polymer-solvent interactions relevant to ESC]
Wright, D.C. (2001). Environmental Stress Cracking of Plastics. RAPRA Technology. [Comprehensive practical guide to ESC testing and prediction]
Fracture Mechanics and Energy Approaches
Griffith, A.A. (1921). "The Phenomena of Rupture and Flow in Solids." Philosophical Transactions of the Royal Society of London, A221, 163-198. [Original energy balance framework]
Williams, J.G. (1984). Fracture Mechanics of Polymers. Ellis Horwood. [Application of fracture mechanics to polymers]
Modern Perspectives
Meijer, H.E.H., & Govaert, L.E. (2005). "Mechanical Performance of Polymer Systems: The Relation Between Structure and Properties." Progress in Polymer Science, 30, 915-938.
Haward, R.N., & Young, R.J. (1997). The Physics of Glassy Polymers, 2nd Edition. Chapman & Hall. [Comprehensive modern treatment]
J.P. McFadden Sr.
November 2025 - Enhanced Edition
Integrating Surface Energy and Thermodynamic Perspectives on Polymer Deformation
