High Strain Rate Dynamic Shear Energy Threshold Models for Recycled Ply Bonding Failure

Shock

Delamination in multi-ply recycled paperboard occurs when converting machinery subjects the sheet to shear displacement rates orders of magnitude above laboratory test speeds. Modern rotary die-cutters, high-speed folder-gluers, and automated packaging lines exert localized web accelerations where interfacial strain rates surpass 1,000 reciprocal seconds. Standard mill certificates quote internal bond strength through pendulum impact methods such as TAPPI T 569 or ISO 16260.

These values establish static compliance at velocities near two meters per second. They fail to reflect the brittle shear transition that occurs when converting knives and scoring rules strike the board at line speeds exceeding 400 meters per minute.

The mechanical response of a recovered fibre network changes sharply under transient stress. Dry hornified fibres and short-chain recycled fines exhibit negligible viscoelastic relaxation at millisecond durations. When a rotary anvil strikes a crease line, the middle plies absorb the impulse without sufficient time to redistribute shear stresses through hydrogen bond rotation.

The interface between the virgin top liner and the recovered waste pulp core experiences a severe Mode II shear concentration. If the localized kinetic energy density exceeds the fracture toughness of the starch-fibre matrix, delamination propagates instantly along the web direction. Packaging blanks split laterally at the folder-gluer feed nip, producing blisters and structural collapse before the carton receives an adhesive bead.

A laboratory Scott bond value of 210 Joules per square meter measured under TAPPI T 569 drops below 110 Joules per square meter when shear displacement rates exceed five hundred reciprocal seconds at 23 degrees Celsius and 50 percent relative humidity.

Specifying board based purely on static z-directional tensile strength exposes converters to catastrophic line stoppages. Virgin bleached kraft plies sustain localized shear through plastic micro-fibril pullout. Recycled chipboard cores undergo brittle crack initiation.

The difference stems from the shear energy threshold, defined as the critical energy release rate per unit area required to advance an interfacial fracture under rapid mechanical excitation. Packaging lines running recycled grades encounter delamination spikes whenever web tension spikes combine with high-velocity mechanical tooling impacts.

Higher converting speeds demand greater interfacial shear compliance rather than higher static density.

Fines

Secondary pulp contains fragmented cell walls, ray cells, and mineral particulate grouped collectively as fines. These elements dominate the interfacial zone between plies in white-lined chipboard and recycled folding boxboard. During fourdrinier or multi-vat cylinder forming, dewatering draws fines toward the wire and suction interfaces.

This concentration alters the physical density and hydrogen bonding topography at the ply boundary. Short recycled fibres possess reduced micro-fibrillar surface area, restricting mechanical interlocking across the couching line.

Where Does Shear Dissipation Collapse under Speed?

Fibre-to-fibre contact in recycled networks relies heavily on added wet-end native or cationic starches to offset the bonding loss caused by irreversible drying hornification. Under quasi-static loading, starch bridges deform plastically, redistributing local shear over many adjacent fibre crossings. Rapid transient loading suppresses this plastic accommodation.

At strain rates above 800 reciprocal seconds, the cross-linked starch networks behave elastically until reaching a critical shear yield stress. Beyond this yield stress, the starch adhesive fails adhesively at the fibre wall rather than cohesively within the binder volume.

Filler minerals aggravate this failure pattern. Calcium carbonate and talc particles accumulate at the couching interface, interrupting fibrillar hydrogen bonding networks. High filler ratios reduce raw material furnish costs.

The economic saving introduces micro-voids along the shear plane. These micro-voids serve as stress concentrators during high-rate converting actions. When an impact shear wave traverses the board thickness, these voids initiate micro-cracks that coalesce into an extensive delamination plane.

The table displays the performance drop observed when recovered mechanical and chemical pulps replace virgin fibres. The secondary fines fraction, measured under TAPPI T 261, directly correlates with the severity of high-rate bond degradation. Coated recycled board retains less than half its static energy dissipation capability when tested under high-velocity shear regimes.

• Hornified lumen collapse reduces transverse fibre flexibility and limits the contact surface area available for hydrogen bridging during rapid couching.
• Secondary starch precipitation creates localized glassy zones that shatter under impact shear rather than deforming viscoelastically.
• Ash particulate agglomeration interrupts continuous cellulose networks, establishing micro-crack pathways along the couched ply boundary.
• Shortened average fibre length limits the critical pullout length, preventing bridge formation behind advancing shear crack tips.

Mill representatives explain delamination rejects by asserting that the converter tooling applies excessive clearance pressure or improper anvil penetration depths during production runs.

Apparatus

Standardized paperboard laboratory instruments fail to reproduce the strain velocities encountered during commercial converting. The Scott internal bond apparatus relies on a falling pendulum to delaminate a double-backed specimen. The pendulum decelerates throughout the impact process, obscuring the velocity dependence of energy dissipation.

Translating laboratory Scott bond readings into predictive converting performance demands specialized high-velocity instrumentation capable of maintaining constant strain rates during specimen fracture.

Modified split-Hopkinson pressure bars and electro-hydraulic high-speed tensile rigs permit controlled shear displacement rates from 10 to 1,500 reciprocal seconds. Specimens mount between hardened steel grips using high-shear cyanoacrylate films to prevent elastomeric peel compliance from confounding board response. Displacement sensors track real-time crack extension across the delamination front.

Load transducers measure the instantaneous traction vector along the z-direction and the shear plane simultaneously.

DIN 53121 scoring verification guarantees crease profile uniformity but omits dynamic shear threshold verification under rapid folding velocities.

Instrument stiffness dictates measurement integrity. Frame resonance frequencies must exceed 50 kilohertz to separate mechanical rig vibration from stress relaxation transients within the paperboard specimen. Accelerometers positioned behind the substrate interface isolate the energy absorbed by the fibre network from inertial mass acceleration of the steel clamps.

The mill sales agreement specifies TAPPI T 569 compliance as the sole metric for ply adhesion, releasing the board supplier from defect claims resulting from high-speed die-cutting delamination.

Boundary

Predicting interfacial delamination requires a mathematical description of the crack propagation front. Cohesive zone models define the relationship between interfacial traction and separation displacement across a damaged ply boundary. For recycled paperboard operating under high shear velocities, the traction-separation law requires rate-dependent parameters.

The constitutive formulation couples shear displacement with z-directional tensile peeling to account for mixed-mode loading during rotary converting.

What Velocity Governs the Core Failure?

A bilinear traction-separation formulation represents the initial elastic response followed by linear softening due to fibre bridging pullout. The penalty stiffness governs the non-damaged state. As shear stress reaches the rate-dependent peak traction value, micro-cracks form within the secondary fines matrix.

The area under the traction-separation curve corresponds to the critical Mode II strain energy release rate.

Let the critical strain energy release rate under high strain rates follow an empirical power-law attenuation model:

G_IIc(gamma_dot) = G_IIc_0 (1 – beta ln(gamma_dot / gamma_dot_0))

Here, G_IIc_0 represents the quasi-static shear energy threshold measured at a reference strain rate gamma_dot_0 of 0.1 reciprocal seconds. The rate sensitivity coefficient beta captures network embrittlement caused by hornified fibre fractions and starch glass transitions. For virgin bleached kraft plies, beta typically ranges between 0.02 and 0.05.

In recycled chipboard cores containing high secondary fines and mineral ash, beta escalates to values between 0.12 and 0.18.

Assume a converting run processing 400 gram per square meter coated recycled board with an initial quasi-static fracture energy of 210 Joules per square meter. At a machine speed generating an interfacial shear strain rate of 1,000 reciprocal seconds with a beta coefficient of 0.15, the actual high-rate energy threshold collapses:

G_IIc(1000) = 210 (1 – 0.15 ln(1000 / 0.1))

The logarithmic ratio evaluates to 9.21. Multiplying by the beta value yields 1.38. The calculation indicates complete material threshold exhaustion prior to reaching steady-state converting speed.

The furnish cannot absorb the mechanical work applied by the knife. Delamination occurs as a brittle wave ahead of the cutting edge.

The constitutive values above demonstrate that recycled substrates display lower peak traction and lower critical separation displacements. The combination restricts total energy absorption capacity during high-velocity knife penetration. The interface fractures with minimal post-peak plastic deformation.

1. Substrate conditioning verification checks that board samples equilibrate under standard conditions specified by ISO 187 prior to destructive evaluation.
2. Specimen coupon mounting positions the board between rigid aluminum test blocks using rapid-setting structural adhesives cured under uniform pressure.
3. Velocity acceleration control programs the dynamic test actuator to achieve constant shear velocity within the first two millimeters of crosshead displacement.
4. Traction data acquisition records force-displacement histories at sampling rates exceeding one megahertz to resolve high-frequency crack propagation fronts.
5. Constitutive curve regression fits measured force decays to extract cohesive penalty stiffness and rate-dependent fracture energy thresholds.

Higher secondary ash fractions accelerate interfacial micro-void coalescence under rapid shear loading.

The critical unanswered question remains whether cross-linking chemical retention aids can suppress beta sensitivity without compromising the repulpability requirements established by European standard EN 13430.

Penalty

Converting failures rooted in deficient dynamic shear thresholds generate immediate operational downtime and packaging line rejects. When high-speed folder-gluers process recycled cartons with brittle interfacial boundaries, blanks split internally along the main crease lines. Carton erectors fail to erect the blanks cleanly.

Vacuum suction cups tear delaminated outer liners away from the grey core, triggering automatic optical inspection rejections and machine jams. In automated filling plants running at 600 cartons per minute, a single defective pallet generates hours of unscheduled line downtime.

Substrate selection balances raw material costs against potential packaging line losses. Coated recycled board trades at a discount of 220 to 350 dollars per metric tonne compared to virgin solid bleached sulphate. A plant converting 1,000 tonnes monthly saves significant raw material expense on paperboard purchases.

If that recycled board exhibits a dynamic shear threshold below 100 Joules per square meter, folder-gluer running speeds drop from 450 meters per minute to 260 meters per minute to prevent scoreline blistering. The speed reduction eliminates the raw material cost advantage by increasing machine-hour costs and reducing plant throughput.

A packaging substrate chosen without high-rate shear verification transfers material savings directly into folder-gluer waste and machine-hour inflation.

Sourcing engineers address this operational exposure by modifying technical delivery specifications. Contracts specifying recycled board grades must incorporate dynamic shear performance floors alongside traditional basis weight, caliper, and Cobb sizing metrics. Goods-in inspection teams should subject incoming lots to rate-dependent mechanical screening before releasing stock to high-speed die-cutting assets.

Procuring low-cost recycled multi-ply board without high-rate shear thresholds results in recurring carton delamination, elevated converting waste rates, and complete forfeiture of production capacity.