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Size effects in tension and constrained bending of paperboard

Borgqvist, Eric LU orcid ; Claesson, Filip ; Wallin, Mathias LU ; Ristinmaa, Matti LU orcid and Engqvist, Jonas LU orcid (2026) In Engineering Fracture Mechanics 345.
Abstract

This study investigates fracture initiation in tension and constrained bending of a three-ply paperboard. Size effects in tension are examined using two complementary approaches: Digital Image Correlation (DIC) based strain mapping on separated plies and tensile tests with varying gauge lengths. DIC of the tensile tests reveals persistent Localized Strain Zones (LSZ) with characteristic widths cf≈1.5–2.5 mm and peak local strains roughly twice the average tensile strain at failure. Tensile tests shows that nominal strength increases as length decreases and approaches a constant level when the specimen length becomes comparable to the LSZ-width. A constrained bending setup is developed to study fracture initiation under... (More)

This study investigates fracture initiation in tension and constrained bending of a three-ply paperboard. Size effects in tension are examined using two complementary approaches: Digital Image Correlation (DIC) based strain mapping on separated plies and tensile tests with varying gauge lengths. DIC of the tensile tests reveals persistent Localized Strain Zones (LSZ) with characteristic widths cf≈1.5–2.5 mm and peak local strains roughly twice the average tensile strain at failure. Tensile tests shows that nominal strength increases as length decreases and approaches a constant level when the specimen length becomes comparable to the LSZ-width. A constrained bending setup is developed to study fracture initiation under bending-dominated loading. Different pressing tool radii is used in the constrained bending test to investigate size dependency. Finite element simulations reproduce the global force–displacement response for the different bending cases but predict higher local strains than those obtained in tensile tests. For constrained bending, the simulated local strains at failure vary depending on pressing tool radius, implying that a failure criterion based solely on local strain cannot predict fracture initiation. The overall investigation indicates that fracture initiation in bending depends on how deformation localizes rather than on a peak local strain alone.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Constrained bending, Fracture initiation, Localized Strain Zone (LSZ), Paperboard, Size effect
in
Engineering Fracture Mechanics
volume
345
article number
112510
publisher
Elsevier
external identifiers
  • scopus:105046717472
ISSN
0013-7944
DOI
10.1016/j.engfracmech.2026.112510
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2026 The Authors.
id
80c45006-e24a-43aa-a5ff-94ac90246873
date added to LUP
2026-08-17 08:31:21
date last changed
2026-08-18 15:30:36
@article{80c45006-e24a-43aa-a5ff-94ac90246873,
  abstract     = {{<p>This study investigates fracture initiation in tension and constrained bending of a three-ply paperboard. Size effects in tension are examined using two complementary approaches: Digital Image Correlation (DIC) based strain mapping on separated plies and tensile tests with varying gauge lengths. DIC of the tensile tests reveals persistent Localized Strain Zones (LSZ) with characteristic widths c<sub>f</sub>≈1.5–2.5 mm and peak local strains roughly twice the average tensile strain at failure. Tensile tests shows that nominal strength increases as length decreases and approaches a constant level when the specimen length becomes comparable to the LSZ-width. A constrained bending setup is developed to study fracture initiation under bending-dominated loading. Different pressing tool radii is used in the constrained bending test to investigate size dependency. Finite element simulations reproduce the global force–displacement response for the different bending cases but predict higher local strains than those obtained in tensile tests. For constrained bending, the simulated local strains at failure vary depending on pressing tool radius, implying that a failure criterion based solely on local strain cannot predict fracture initiation. The overall investigation indicates that fracture initiation in bending depends on how deformation localizes rather than on a peak local strain alone.</p>}},
  author       = {{Borgqvist, Eric and Claesson, Filip and Wallin, Mathias and Ristinmaa, Matti and Engqvist, Jonas}},
  issn         = {{0013-7944}},
  keywords     = {{Constrained bending; Fracture initiation; Localized Strain Zone (LSZ); Paperboard; Size effect}},
  language     = {{eng}},
  month        = {{10}},
  publisher    = {{Elsevier}},
  series       = {{Engineering Fracture Mechanics}},
  title        = {{Size effects in tension and constrained bending of paperboard}},
  url          = {{http://dx.doi.org/10.1016/j.engfracmech.2026.112510}},
  doi          = {{10.1016/j.engfracmech.2026.112510}},
  volume       = {{345}},
  year         = {{2026}},
}