Optical Strain Mapping for Fiber Network Rupture Mechanics in Multi Ply Recycled Liners

Gauge

A digital image correlation bench recording tensile deformation on multi-ply testliner resolves displacement gradients that standard crosshead extensometers average into fiction. Placed under uniaxial tension at 23 degrees Celsius and 50 percent relative humidity in conformance with ISO 1924-3, an unbleached recycled containerboard linerboard displays non-uniform displacement long before the global load curve departs from linearity. The field cameras map surface strain through stochastic speckle tracking, capturing the transition from elastic network distribution to concentrated micro-shear bands.

Standard testing records load and clamp displacement at a constant elongation rate of 100 millimetres per minute. That bulk measurement assumes uniform strain distribution across the 180 millimetre gauge span. Optical full-field measurement reveals that strain localizes into distinct bands measuring 0.8 to 2.4 millimetres in width within the early elastic-plastic transition, often at 30 to 45 percent of peak tensile failure load.

Optical full-field correlation captures localized micro-strain bands at 35 percent of ultimate tensile load on multi-ply containerboard conditioned under ISO 187 parameters.

These local strain concentrations correlate with variations in local basis weight, forming anomalies across individual plies, and variations in fiber-to-fiber bond density. In recycled furnishes composed of mixed old corrugated containers, local fiber hornification restricts micro-conformability. The optical system tracks these structural weaknesses as steep displacement gradients across the specimen surface.

Full-Field Optical Metrology across Heterogeneous Plies

A dual-camera stereoscopic setup eliminates out-of-plane displacement errors that routinely distort planar measurements on uneven paperboard surfaces. Multi-ply testliners develop localized out-of-plane buckling, termed cockling, when tensile fields activate transverse Poisson contractions across constrained network boundaries. A single-camera two-dimensional configuration records these out-of-plane movements as false in-plane tensile strains.

Stereoscopic calibration using high-precision ceramic targets defines three-dimensional surface coordinates with sub-pixel spatial resolution below 0.02 pixels.

The speckle pattern applied to the linerboard surface governs measurement fidelity. Solvent-based aerosols distort recycled fiber bonds by dissolving residual starch and sizing agents. High-pressure airbrushing with water-insoluble, matte carbon black suspended in fast-evaporating carrier agents produces a random pattern with a mean speckle size of 3 to 5 pixels per feature.

This pattern preserves the underlying fiber network while offering adequate grayscale gradients across charge-coupled device sensors.

Specimen geometry must balance optical field requirements with papermaking reality. Standard 15-millimetre-wide tensile strips under ISO 1924-2 constrain edge boundaries and generate lateral shear anomalies near the grip faces. Modifying the geometry to a dog-bone profile with a central gauge width of 25 millimetres or maintaining a wider rectangular geometry of 50 millimetres allows the optical system to map unconstrained strain fields.

A wider field of view exposes the interaction between the individual plies through the sheet thickness.

Tensile stress fields applied in the cross direction reveal severe localization. Machine direction orientation aligns fibers, providing contiguous axial load paths that delay rupture. Cross-direction loading relies on interfiber hydrogen bonding and contact friction among misaligned short fibers.

Optical strain mapping quantifies this cross-direction vulnerability through high localized transverse strain values that appear shortly after load application.

When converters bypass optical verification and rely entirely on vendor mill certificates for tensile index, catastrophic web breaks multiply on high-speed corrugators.

Network

The fibrous framework of a multi-ply recycled linerboard functions as a layered continuum of hornified secondary fibers, fines, and residual mineral fillers. Industrial testliner grades, manufactured according to DIN 6720 or FEFCO standards, rely on stratified web forming where each layer performs a distinct structural function. The top ply, engineered for printability and scuff resistance, features cleaner, refined pulp with higher starch uptake.

The middle and bottom plies, formed from lower-grade secondary fibers, carry high levels of residual ash, ash-based micro-particles, and fragmented short fibers.

Recycled pulp undergoes irreversible structural changes during initial drying and re-slushing cycles. Fiber cell walls lose swelling ability and collapse into rigid, low-flexibility ribbons. This hornification reduces the relative bonded area within the fiber network, lowering individual fiber-to-fiber bond shear strength from 14 megapascals in virgin unbleached kraft down to 6 to 8 megapascals in multi-recycled furnishes.

The loss of internal fibrillar swelling prevents network conformability during wet pressing, leaving micro-voids across ply consolidation zones.

Rupture mechanics within these recycled networks follow distinct pathways governed by localized network cohesion. Optical strain maps capture these structural anomalies through characteristic displacement jumps across fiber crossings. The following failure sequence describes this progression under monotonic tensile load:

1. Elastic distribution transfers global boundary displacement through the oriented primary network without detectable localized shear bands.
2. Bond rupture initiation activates at low-density flocs where local grammage drops below 85 percent of the sheet mean nominal value.
3. Micro-void coalescence aligns micro-cracks along cross-direction fiber orientations, creating steep local strain gradients exceeding 4 percent.
4. Macro-crack propagation shears remaining fiber contacts across adjacent sheet plies, precipitating rapid catastrophic transverse separation.

Optical measurement isolates the onset of bond rupture from catastrophic crack propagation. Conventional tensile load-displacement curves show smooth, progressive deviation from linear elasticity, masking the micro-failures occurring within internal plies. Digital image correlation identifies discrete zones where strain increases sharply while applied load rises marginally.

These zones define micro-damage clusters where hydrogen bonds detach, shedding load onto surrounding fiber chains.

Displacement Gradients across Stratified Plies

Multi-ply sheet formation creates structural boundary zones that govern global rupture mechanics. Inter-ply bonding, evaluated through Scott Bond energy measurements under TAPPI T 569, ranges between 150 and 280 joules per square meter for high-grade testliner, falling below 120 joules per square meter in low-cost recycled stocks with excessive mineral filler. When tensile loads pass through the stratified sheet, individual plies deform heterogeneously due to differing elastic moduli and fiber orientation ratios.

The top ply, carrying an orientation ratio often exceeding 2.5:1 machine direction to cross direction, exhibits a higher initial tensile modulus. The lower plies, formed on fourdrinier tables or cylinder vats with different drainage dynamics, exhibit lower orientation ratios and lower elastic moduli. The mismatch in Poisson ratios between plies induces out-of-plane shear stresses across the ply interfaces.

The data demonstrates the severe mechanical divergence between composite layers. The middle core exhibits low relative bonded area alongside high ash content, creating a mechanically compliant, weak core bounded by stiffer surface plies. Digital image correlation shows that when the composite sheet undergoes uniform in-plane elongation, localized plastic strain concentrates in this middle layer, prompting internal shear de-bonding prior to visible surface failure.

Starch distribution influences these displacement fields. Surface-applied oxidized or cationic starch penetrates only 15 to 35 percent of the outer ply thickness, leaving the central core dependent on wet-end native starch retention. Weak internal sizing produces pockets of loose, unbonded short fibers that act as crack-initiation defects under mechanical stress.

A supplier will state that minor variations in middle-ply furnish have no measurable impact on global burst strength, citing average Mullen burst values that obscure the localized micro-rupture behaviors driving score-line failure.

Rupture

Fracture mechanics in recycled cellulose networks departs from classical linear elastic assumptions. Multi-ply testliners develop an extensive fracture process zone ahead of propagating cracks. This zone, rich in fiber pull-out, fiber bridging, and progressive inter-ply micro-delamination, absorbs energy through distributed micro-damage rather than sharp cleavage.

The effective crack length and the resistance curve, termed the R-curve, characterize this fracture behavior. Under ASTM E1820 modifications adapted for planar fibrous structures, the energy required to extend a crack rises as the fracture process zone expands. Fibers bridging the crack flanks apply closing stresses, transferring load away from the singular crack tip.

In virgin softwood kraft liners, these crack-bridging fibers sustain structural integrity across spans reaching 3 millimetres. In recycled multi-ply testliner, shortened secondary fibers and hornified cell walls reduce the bridging zone to less than 0.8 millimetres, producing steep, unstable crack growth.

A shortened bridging zone under 1 millimetre produces catastrophic crack propagation once localized strain exceeds 2.8 percent in cross-direction recycled testliner.

Full-field optical strain mapping measures this process zone in real time. By tracking horizontal and vertical displacement vectors around a machined notch or a naturally forming defect, digital image correlation calculates the critical J-integral value across arbitrary integration contours. Optical measurements capture the energy dissipation profile by integrating the strain energy density across the full deformation field.

Crack Tip Opening Displacement in Recycled Webs

Crack tip opening displacement, measured via sub-pixel optical tracking at the root of a propagating notch, correlates directly with internal bond durability. In multi-ply boards, the crack tip does not advance as a flat, two-dimensional front. The internal, low-strength core ply fractures ahead of the outer plies, creating an internal tunneling effect.

The optical system detects this internal rupture prior to surface breach through subtle out-of-plane surface depressions and localized transverse contraction anomalies.

Local strain fields around the advancing tip reveal steep gradients. While global strain across the tensile specimen remains below 1.5 percent, optical correlation records strains exceeding 8 to 12 percent within a 500-micrometer radius of the crack tip. These values exceed the ultimate elongation limit of single recycled cellulose fibers, indicating that this localized field reflects fiber rotation, bond shear, and inter-ply matrix voiding rather than pure axial fiber stretching.

As the crack advances, the failure mode alternates between fiber fracture and fiber pull-out. Lower refining degrees in secondary furnishes favor fiber pull-out due to weak individual bond shear strength. Fiber pull-out expends friction energy, moderating fracture velocity.

Excessive wet-end starch addition increases bond strength relative to fiber wall strength, prompting brittle trans-fiber fracture that accelerates rupture across the sheet.

Multi-ply architecture governs the overall fracture path. A crack initiating in the brittle top ply often deflects along the inter-ply interface upon contacting the compliant middle core. This interface delamination expends mechanical energy, acting as a natural crack arrester.

If inter-ply bond strength is deficient, delamination runs unchecked across the converting crease, destroying panel compressive rigidity.

A standard tensile test measures the average energy absorbed across an unnotched strip. Optical strain mapping quantifies fracture toughness by isolating local energy dissipation within the fracture process zone from global plastic frame deformation. This differentiation establishes the real converting boundary for corrugated board production.

Uncontrolled fiber pull-out without sufficient bridging mechanics leads directly to web delamination inside the double-backer section of high-speed corrugating lines.

Corrugation

Converting multi-ply recycled liners into corrugated board introduces complex multiaxial strain fields. When the linerboard contacts the flute tips of the corrugated medium at the single-facer and double-backer, it encounters combined thermal, compressive, and tensile stresses. The liner must withstand localized transverse compression from the corrugating rolls while resisting tensile pull along the machine direction at web speeds often exceeding 300 meters per minute.

The fluting nip applies concentrated lines of mechanical force spaced at flute pitches of 8.5 millimetres for A-flute, 4.8 millimetres for C-flute, or 3.2 millimetres for B-flute configurations. Between these glue lines, the liner spans unsupported gaps. During drying and adhesive gelatinization, moisture transfers from the starch adhesive into the bottom ply of the liner, generating localized moisture gradients that degrade the local elastic modulus by up to 50 percent within seconds.

Digital image correlation adapted to converting simulators maps the strain fields generated during this combined thermo-mechanical cycle. Thermal cameras paired with high-speed stereoscopic optical sensors record strain localization across the glue line bonds. Optical strain maps show that severe shear strains concentrate at the margins of the adhesive bead, where wet, swollen fibers transition abruptly into dry, rigid base paper.

Scoring Profiles across Variable Fluting Geometries?

Rotary scoring wheels exert intense triaxial stress states that challenge multi-ply integrity. Scoring compresses the corrugated sandwich to form a well-defined hinge for box blank erection. The upper plies undergo tensile stretching across the male profile, while the internal plies suffer intense shear deformation, and the reverse liner encounters three-point bending across the female score anvil.

Optical strain mapping of scoring profiles demonstrates that score failure initiates as shear cracks along the internal ply interfaces. If the female anvil clearance is narrow, local tensile strain across the exterior top ply surpasses 4.5 percent, driving score-line rupture. Optical measurements quantify the influence of different score profiles, comparing point-to-point, point-to-flat, and three-point configurations across diverse fluting structures.

The tabulated optical data proves that score cracking is controlled by strain redistribution rather than applied vertical force alone. The point-to-flat profile concentrates tensile strain directly beneath the score point, exceeding the failure limit of short recycled fibers. The three-point profile distributes strain across two secondary bending shoulders, keeping maximum surface strain well within the safe operational envelope below 2.5 percent.

High mineral filler content in the recycled furnish exacerbates score vulnerability. When ash content exceeds 12 percent, internal shear resistance degrades, causing the linerboard plies to slip uncontrollably under the scoring wheel. This uncontrolled slippage weakens box edge crush resistance under ISO 3037, lowering finished box top-to-bottom compression performance.

A rigorous converting audit verifies the alignment of the scoring profile with the specific fiber orientation of the liner. Misaligned corrugator tooling induces asymmetric cross-direction shear that splits the outer ply along network fiber bundles.

Substrates running near the edge of their strain limits fracture without warning when ambient relative humidity drops below 40 percent on high-speed folder-gluers.

Yield

Procuring multi-ply testliner requires aligning sheet mechanics with net commercial tonnage yield. Board mills market containerboard on basis weight, billed per metric tonne under standard trade custom. Converters transform tonnes into thousands of square meters of finished corrugated packaging.

Sourcing decisions balance lower grammage costs against process waste generated by web rupture, score cracking, and packaging failure on automated packing lines.

Downgauging testliner from 175 grams per square meter to 140 grams per square meter reduces nominal raw material mass by 20 percent. Recycled mills often achieve this grammage reduction by compensating with higher filler loads or increasing surface starch sizing to preserve nominal burst index. This operational substitution masks fundamental shifts in network mechanics.

The resulting lighter sheet exhibits lower strain-to-failure thresholds and reduced fracture process zones under optical digital image correlation analysis.

A commercial model reveals the real cost impact of downgauged furnish when web performance degrades. Take an industrial corrugated packaging plant converting 3,000 tonnes of testliner monthly across three continuous corrugating lines. Assume a benchmark 175 grams per square meter recycled linerboard purchased at 620 euros per tonne, running with a baseline converting waste rate of 1.8 percent across the wet and dry ends.

Consider a downgrade to a 150 grams per square meter multi-ply testliner priced at 640 euros per tonne. The lower basis weight increases theoretical area yield per tonne from 5,714 square meters to 6,667 square meters, a theoretical yield gain of 16.7 percent. The downgauged sheet incorporates 14 percent mineral ash in its middle ply to maintain caliper, alongside a reduced refining profile to control dewatering limits on the paper machine wire.

Optical strain mapping of this 150 grams per square meter sheet demonstrates severe strain localization, with local strain peaks exceeding 3.8 percent during scoring and fluting adhesion. During high-speed converting, this structural brittleness causes web breaks, score cracking, and flute delamination. The real converting waste jumps from 1.8 percent to 4.6 percent due to score-line tears and line stoppages.

A formal commercial trade-off analysis defines the operational parameters:

• Parent reel yield increases the surface area produced per metric tonne, lowering nominal paper cost per thousand square meters from 108.50 euros to 96.00 euros.
• Unscheduled web breaks incur direct mechanical downtime costs averaging 450 euros per incident in lost production time and operator intervention.
• Corrugator waste scrap strips out gross yield savings through unrecoverable starch, energy, and labor embedded in non-conforming converted board.
• Customer box rejects trigger commercial chargebacks and transportation claims when score lines fracture on high-speed automated packing equipment.

The arithmetic proves that a 2.8 percent increase in plant scrap completely erodes the theoretical paper cost savings whenever running speeds drop by more than 12 percent. Optical strain analysis provides the objective qualification standard to predict whether a lightweight recycled sheet can withstand machine conversion dynamics prior to purchasing hundreds of tonnes of paperboard stock.

A specification clause referencing only Mullen burst or ring crush test values fails to protect the buyer from brittleness caused by excessive ash loading in secondary plies.

Audit

Verifying multi-ply recycled linerboard calls for structural mechanical testing at goods-in, replacing reliance on standard mill test certificates. Mills test paper under ideal conditions, reporting averaged data from tambours that hide cross-machine directional basis weight swings and internal ply delamination risks. A comprehensive quality audit inspects the raw material for hidden furnish substitutions and localized embrittlement.

The sampling protocol must follow ISO 186 guidelines, pulling test specimens across the entire reel width while discarding outer wraps exposed to warehouse atmospheric fluctuations. Condition all specimens in accordance with ISO 187 at 23 degrees Celsius and 50 percent relative humidity for a minimum of 24 hours. Failure to equilibrate specimens invalidates optical strain mapping by introducing transient hygroscopic curling and local swelling artifacts.

Goods-in verification combines standard physical testing with rapid full-field digital image correlation screening on calibrated tensile frames. The following checklist details the mandatory mechanical verification sequence for every new linerboard delivery:

1. Verify basis weight across the cross direction using ISO 536 to confirm compliance within a plus or minus 2.5 percent tolerance band.
2. Measure absolute sheet caliper and calculate apparent sheet density following ISO 534 to identify excessive wet pressing.
3. Determine mineral ash content at 525 degrees Celsius under ISO 1762 to detect middle-ply mineral loading exceeding specification limits.
4. Measure inter-ply internal bond strength using TAPPI T 569, rejecting any stock registering below 160 joules per square meter.
5. Execute uniaxial tensile testing combined with digital image correlation optical mapping under ISO 1924-3 to verify local strain distribution across the gauge field.

Optical strain mapping acts as the decisive qualification gate. Technicians record tensile tests while running digital image correlation software to measure the local strain concentration factor, calculated as peak localized strain divided by average far-field strain. Sheets displaying a local strain concentration factor greater than 2.8 at 50 percent of ultimate failure load carry severe fiber network defects and will perform poorly during scoring and folding operations.

The contract framework between the board buyer and the paper mill must enshrine these physical mechanical thresholds. A standard delivery clause must define clear acceptance criteria that link laboratory verification to commercial settlement:

A delivered lot exhibiting an ash content exceeding 11 percent or a Scott Bond internal strength below 150 joules per square meter authorizes immediate commercial rejection without sorting penalty.

When mills dispute optical strain results, citing adherence to nominal burst and tensile indices, cross-sectional scanning electron microscopy resolves the disagreement. Microscopic imaging reveals the distribution of mineral fillers and adhesive starches across individual plies, confirming whether middle-ply dilution caused localized network failure.

Rigorous mechanical verification protects the converter from absorbing the financial costs of papermaking shortcuts. By measuring localized strain evolution and inter-ply rupture behavior, packaging engineers ensure that high-recycled multi-ply liners meet the performance demands of modern packaging lines.

The open technical question remains whether high-speed online optical strain mapping can be integrated directly into the dry end of paper machines to reject defective web sections before slitting and dispatch to converters.