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arxiv: 2510.03713 · v2 · submitted 2025-10-04 · ❄️ cond-mat.mtrl-sci

In situ elucidation of mechanisms governing crack transition to plasticity arrest

Abdalrhaman Koko , Bemin Sheen , Caitlin Green , Fionn Dunne This is my paper

Pith reviewed 2026-05-18 10:36 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords crack arrestenergy release rateSEM-DICelastoplasticaluminum alloyprocess zonemixed-mode fracture
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The pith

Cracks arrest in aluminum when elastic energy release rate at the tip equals or exceeds the elastoplastic rate and the process zone grows beyond grain boundaries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes an experimentally measurable energy-partition criterion for crack arrest by tracking how elastic and elastoplastic energy contributions evolve at the crack tip in cold-worked AA-5052. Using high-resolution SEM-DIC to reconstruct local displacement fields and EBSD for microstructure, the authors extract mode I and II stress intensity factors along with elastic (ΔJE) and elastoplastic (ΔJP) energy release rates. They show that short, microstructure-sensitive cracks begin in mixed mode at low driving force but transition to load-aligned plasticity arrest once ΔJE diverges above ΔJP, accompanied by crack blunting, slip-band emission, and expansion of the plastic process zone across multiple grains. A sympathetic reader cares because this supplies a direct, in-situ observable for when propagating cracks stop growing instead of continuing under load. The work fills the prior gap in experimental quantification of energy evolution during the short-to-long crack transition.

Core claim

Reconstructing local crack-tip fields from measured displacement data shows that microstructure-sensitive cracks propagate in a mixed-mode manner at low driving force and transition to plasticity-dominated and load-aligned arrest as the crack-tip process zone develops and expands multiple grains, identified through the divergence of elastic and elastoplastic energy measures (ΔJE >= ΔJP), crack-tip blunting, slip-band emission, and the emergence of localised plastic deformation.

What carries the argument

The energy-partition criterion given by divergence of elastic energy release rate (ΔJE) and elastoplastic energy release rate (ΔJP) reconstructed from SEM-DIC displacement fields, with arrest occurring when ΔJE >= ΔJP together with process-zone expansion beyond grain-scale dimensions.

If this is right

  • Crack arrest coincides with a measurable transition in crack-tip energy partitioning.
  • Process-zone expansion beyond grain-scale dimensions marks the arrest of microstructure-sensitive cracks.
  • The transition appears through crack-tip blunting, slip-band emission, and localised plastic deformation.
  • Fracture regime transition is governed by the energy-partition criterion.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same energy-partition signature might serve as a practical indicator for arrest in other ductile alloys if the reconstruction method generalizes.
  • Coupling this in-situ approach with cyclic loading tests could test whether the criterion also governs fatigue crack arrest.
  • Direct comparison of the measured zone sizes against crystal-plasticity simulations of the same grain structure would check if grain-boundary crossing is required for arrest.

Load-bearing premise

The local crack-tip fields reconstructed from measured displacement data accurately yield mode I and II stress intensity factors together with elastic and elastoplastic energy release rates, without major artifacts from imaging resolution, surface preparation, or the DIC correlation algorithm.

What would settle it

Observation of crack arrest occurring while ΔJE remains below ΔJP or while the process zone remains confined within single-grain dimensions would contradict the claimed energy-partition criterion.

read the original abstract

Despite extensive theoretical treatment of short- to long-crack transitions, direct experimental quantification of how elastic and plastic energy contributions evolve at the crack tip during arrest has remained absent. In this study, we present an in situ investigation of crack propagation in cold-worked AA-5052 using high-resolution scanning electron microscopy digital image correlation (SEM-DIC) and electron backscatter diffraction (EBSD). By reconstructing local crack-tip fields from measured displacement data, we extract mode I and II stress intensity factors and both elastic and elastoplastic energy release rates ({\Delta}JE and {\Delta}Jp). The results show that microstructure-sensitive cracks propagate in a mixed-mode manner at low driving force and transition to plasticity-dominated and load-aligned crack, arrested as the crack-tip process zone develops and expands multiple grains. This transition is identified through the divergence of elastic and elastoplastic energy measures ({\Delta}JE >= {\Delta}JP), crack-tip blunting, slip-band emission, and the emergence of localised plastic deformation. These findings demonstrate that crack arrest coincides with a measurable transition in crack-tip energy partitioning and with process-zone expansion beyond grain-scale dimensions. The results establish an experimentally measurable energy-partition criterion for crack arrest and demonstrate that fracture regime transition is governed by

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an in situ SEM-DIC and EBSD study of crack propagation in cold-worked AA-5052. By reconstructing local crack-tip fields from measured displacements, the authors extract mode-I/II stress intensity factors together with elastic and elastoplastic energy release rates (ΔJ_E and ΔJ_P). They observe that microstructure-sensitive cracks transition to plasticity-dominated, load-aligned growth and arrest when ΔJ_E ≥ ΔJ_P coincides with crack-tip blunting, slip-band emission, and process-zone expansion beyond grain-scale dimensions, proposing this energy-partition divergence as an experimentally measurable arrest criterion.

Significance. If the quantitative fidelity of the reconstructed fields is confirmed, the work supplies direct experimental evidence for the evolution of elastic versus plastic energy contributions during crack arrest, filling a noted gap in short-to-long crack transition studies. The combination of high-resolution in situ imaging with EBSD for microstructure correlation is a clear strength and could support falsifiable predictions in fracture-mechanics modeling of aluminum alloys.

major comments (2)
  1. [Abstract / field-reconstruction description] Abstract and description of field reconstruction: the central claim that crack arrest is identified by the divergence ΔJ_E ≥ ΔJ_P rests on the accuracy of mode-I/II SIFs and partitioned energy release rates extracted from SEM-DIC displacements. No validation against analytical fields, finite-element benchmarks, or sensitivity checks to subset size, correlation parameters, or surface preparation is reported, leaving open the possibility that imaging resolution or grain-boundary relief artifacts mimic the reported energy-partition transition.
  2. [Results] Results presentation: the manuscript states that the transition is identified through measurable divergence of energy measures together with process-zone expansion, yet supplies no quantitative plots, error bars, sample statistics, or explicit description of how the J-integral evaluations separate elastic and elastoplastic contributions from the displacement data.
minor comments (2)
  1. [Abstract] Notation: the abstract uses the LaTeX fragment {Δ}JE; this should be rendered consistently as ΔJ_E (elastic) and ΔJ_P (elastoplastic) throughout the text and figures for clarity.
  2. [Abstract] The abstract sentence ends abruptly at “governed by”; the final clause should be completed in the revised manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments highlight important aspects of quantitative validation and presentation that will strengthen the manuscript. We respond to each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract / field-reconstruction description] Abstract and description of field reconstruction: the central claim that crack arrest is identified by the divergence ΔJ_E ≥ ΔJ_P rests on the accuracy of mode-I/II SIFs and partitioned energy release rates extracted from SEM-DIC displacements. No validation against analytical fields, finite-element benchmarks, or sensitivity checks to subset size, correlation parameters, or surface preparation is reported, leaving open the possibility that imaging resolution or grain-boundary relief artifacts mimic the reported energy-partition transition.

    Authors: We acknowledge that the original manuscript does not present explicit validation of the DIC field reconstruction or sensitivity analyses. In the revised version we will add a dedicated subsection (and supplementary material) that includes: (i) reconstruction of synthetic displacement fields with known analytical mode-I/II SIFs and J-integrals, (ii) comparison against finite-element elastoplastic benchmarks, and (iii) systematic sensitivity tests to subset size, correlation parameters, and surface-preparation effects. These additions will quantify the uncertainty in ΔJ_E and ΔJ_P and directly address the possibility of grain-boundary or imaging artifacts. revision: yes

  2. Referee: [Results] Results presentation: the manuscript states that the transition is identified through measurable divergence of energy measures together with process-zone expansion, yet supplies no quantitative plots, error bars, sample statistics, or explicit description of how the J-integral evaluations separate elastic and elastoplastic contributions from the displacement data.

    Authors: The referee correctly identifies that the current results section lacks the requested quantitative detail. We will revise the manuscript to include: (i) plots of ΔJ_E and ΔJ_P versus crack extension with error bars derived from DIC displacement uncertainty and multiple contour integrals, (ii) a clear description of the elastic–elastoplastic partitioning procedure (based on decomposition of the measured displacement field into elastic and residual plastic components), and (iii) summary statistics across multiple crack instances and specimens to demonstrate reproducibility of the ΔJ_E ≥ ΔJ_P condition at arrest. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript is an observational experimental study that reconstructs crack-tip fields directly from SEM-DIC displacement measurements and reports measured quantities (mode I/II SIFs, ΔJE, ΔJP, process-zone size) without any derivation chain that reduces a claimed result to a fitted parameter, self-citation, or ansatz by construction. No equations are presented that equate a 'prediction' to its own input data, and the central energy-partition criterion is stated as an empirical observation rather than a theoretically derived necessity. The work therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work is experimental and relies on standard domain assumptions of digital image correlation and linear-elastic fracture mechanics rather than new free parameters or postulated entities.

axioms (2)
  • domain assumption Displacement fields measured by SEM-DIC accurately represent the in-plane deformation at the crack tip.
    Invoked when reconstructing local crack-tip fields from measured displacement data.
  • domain assumption Standard mode-I and mode-II stress-intensity-factor extraction formulas apply to the reconstructed fields.
    Used to obtain the reported stress intensity factors and energy release rates.

pith-pipeline@v0.9.0 · 5763 in / 1404 out tokens · 52051 ms · 2026-05-18T10:36:09.960927+00:00 · methodology

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Works this paper leans on

115 extracted references · 115 canonical work pages

  1. [1]

    Mechanisms and micromechanics of intergranular ductile fracture

    Sénac C. Mechanisms and micromechanics of intergranular ductile fracture. Int J Solids Struct 2024;301:112951. https://doi.org/10.1016/j.ijsolstr.2024.112951

    work page doi:10.1016/j.ijsolstr.2024.112951 2024

  2. [2]

    Enhanced grain boundary cohesion mediated by solute segregation in a dilute Mg alloy with improved crack tolerance and strength

    Yang A, Liu Y-J, Wang C, Gao Y , Chen P , Ju H, et al. Enhanced grain boundary cohesion mediated by solute segregation in a dilute Mg alloy with improved crack tolerance and strength. Int J Plast 2024;176:103950. https://doi.org/10.1016/j.ijplas.2024.103950

    work page doi:10.1016/j.ijplas.2024.103950 2024

  3. [3]

    Void nucleation during ductile rupture of metals: A review

    Noell PJ, Sills RB, Benzerga AA, Boyce BL. Void nucleation during ductile rupture of metals: A review. Prog Mater Sci 2023;135:101085. https://doi.org/10.1016/j.pmatsci.2023.101085

    work page doi:10.1016/j.pmatsci.2023.101085 2023

  4. [4]

    Localized brittle intergranular cracking and recrystallization -induced blunting in fatigue crack growth of ductile tantalum

    Huang R, Zhou Y , Yang Q, Yang X, Wei K, Qu Z, et al. Localized brittle intergranular cracking and recrystallization -induced blunting in fatigue crack growth of ductile tantalum. Int J Plast 2025;186:104262. https://doi.org/10.1016/j.ijplas.2025.104262

    work page doi:10.1016/j.ijplas.2025.104262 2025

  5. [5]

    Microstructure -interacting short crack growth in blocky alpha Zircaloy-4

    Wan W , Dunne FPE. Microstructure -interacting short crack growth in blocky alpha Zircaloy-4. Int J Plast 2020;130:102711. https://doi.org/10.1016/J.IJPLAS.2020.102711

    work page doi:10.1016/j.ijplas.2020.102711 2020

  6. [6]

    Fatigue crack growth behavior of an additively manufactured titanium alloy: Effects of spatial and crystallographic orientations of α lamellae

    Liu Z, Dash SS, Zhang J, Lyu T, Lang L, Chen D, et al. Fatigue crack growth behavior of an additively manufactured titanium alloy: Effects of spatial and crystallographic orientations of α lamellae. Int J Plast 2024;172:103819. https://doi.org/10.1016/j.ijplas.2023.103819

    work page doi:10.1016/j.ijplas.2023.103819 2024

  7. [7]

    Effect of precipitate phase on the plastic deformation behavior of Alloy 718: In -situ tensile experiment and crystal plasticity simulation

    Guo G, Zhang W , Zhang B, Xu J, Chen S, Ye X, et al. Effect of precipitate phase on the plastic deformation behavior of Alloy 718: In -situ tensile experiment and crystal plasticity simulation. Int J Plast 2025;187:104286. https://doi.org/10.1016/j.ijplas.2025.104286

    work page doi:10.1016/j.ijplas.2025.104286 2025

  8. [8]

    Microstructural effects on short fatigue crack propagation in cast Al -Si alloys

    Ren P , Withers PJ, Zuo Z, Feng H, Huang W. Microstructural effects on short fatigue crack propagation in cast Al -Si alloys. Int J Fatigue 2023;175:107788. https://doi.org/10.1016/j.ijfatigue.2023.107788

    work page doi:10.1016/j.ijfatigue.2023.107788 2023

  9. [10]

    Tensile Deformation and Fracture Behavior of AA5052 Aluminum Alloy under Different Strain Rates

    Fang J, Zhu Z, Zhang X, Xie L, Huang Z. Tensile Deformation and Fracture Behavior of AA5052 Aluminum Alloy under Different Strain Rates. J Mater Eng Perform 2021;30:9403–11. https://doi.org/10.1007/S11665-021-06112-5/METRICS

    work page doi:10.1007/s11665-021-06112-5/metrics 2021

  10. [11]

    The influence of residual stress on fatigue crack growth rates of additively manufactured Type 304L stainless steel

    Smudde CM, D’Elia CR, San Marchi CW , Hill MR, Gibeling JC. The influence of residual stress on fatigue crack growth rates of additively manufactured Type 304L stainless steel. Int J Fatigue 2022;162:106954. https://doi.org/10.1016/j.ijfatigue.2022.106954

    work page doi:10.1016/j.ijfatigue.2022.106954 2022

  11. [12]

    Fatigue crack growth prediction for shot-peened steel considering residual stress relaxation

    Gao Z, Gan J, Liu H, Liu X, Wu W. Fatigue crack growth prediction for shot-peened steel considering residual stress relaxation. Mater Des 2023;234:112301. https://doi.org/10.1016/j.matdes.2023.112301

    work page doi:10.1016/j.matdes.2023.112301 2023

  12. [13]

    Microstructure-sensitive computational modeling of fatigue crack formation

    McDowell DL, Dunne FPE. Microstructure-sensitive computational modeling of fatigue crack formation. Int J Fatigue 2010;32:1521 –42. https://doi.org/10.1016/j.ijfatigue.2010.01.003

    work page doi:10.1016/j.ijfatigue.2010.01.003 2010

  13. [14]

    Direct comparison of microstructure - sensitive fatigue crack initiation via crystal plasticity simulations and in situ high-energy X-ray experiments

    Prithivirajan V, Ravi P , Naragani D, Sangid MD. Direct comparison of microstructure - sensitive fatigue crack initiation via crystal plasticity simulations and in situ high-energy X-ray experiments. Mater Des 2021;197:109216. https://doi.org/10.1016/J.MATDES.2020.109216

    work page doi:10.1016/j.matdes.2020.109216 2021

  14. [15]

    A mechanistic modelling methodology for microstructure - sensitive fatigue crack growth

    Wilson D, Dunne FPE. A mechanistic modelling methodology for microstructure - sensitive fatigue crack growth. J Mech Phys Solids 2019;124:827 –48. https://doi.org/10.1016/j.jmps.2018.11.023

    work page doi:10.1016/j.jmps.2018.11.023 2019

  15. [16]

    Is stored energy density the primary meso-scale mechanistic driver for fatigue crack nucleation? Int J Plast 2018;101:213 –29

    Chen B, Jiang J, Dunne FPE. Is stored energy density the primary meso-scale mechanistic driver for fatigue crack nucleation? Int J Plast 2018;101:213 –29. https://doi.org/10.1016/J.IJPLAS.2017.11.005

    work page doi:10.1016/j.ijplas.2017.11.005 2018

  16. [17]

    The Role of Cnidaria in Drug Discovery

    Kramer S, Boyce B, Jones A, Gearhart J, Salzbrenner B. The Sandia Fracture Challenge: How Ductile Failure Predictions Fare, 2019, p. 25 –9. https://doi.org/10.1007/978 -3- 319-95879-8_6. Page 33 of 44

    work page doi:10.1007/978 2019

  17. [18]

    Study on quasi -in-situ tensile microstructure evolution law of 5052 -O aluminum alloy based on EBSD

    Zhao G, Sun M, Li J, Li H, Ma L, Li Y . Study on quasi -in-situ tensile microstructure evolution law of 5052 -O aluminum alloy based on EBSD. Mater Today Commun 2022;33:104572. https://doi.org/10.1016/j.mtcomm.2022.104572

    work page doi:10.1016/j.mtcomm.2022.104572 2022

  18. [19]

    Ductile tearing of aluminium plates: experiments and modelling

    Espeseth V, Morin D, Tekoğlu C, Børvik T, Hopperstad OS. Ductile tearing of aluminium plates: experiments and modelling. Int J Fract 2023;242:39 –70. https://doi.org/10.1007/s10704-023-00701-2

    work page doi:10.1007/s10704-023-00701-2 2023

  19. [20]

    Influence of orientation on crack propagation of aluminum by molecular dynamics

    Ma L, Deng Y , Ren Y , Hu W. Influence of orientation on crack propagation of aluminum by molecular dynamics. Eur Phys J B 2022;95:25. https://doi.org/10.1140/epjb/s10051- 022-00285-1

    work page doi:10.1140/epjb/s10051- 2022

  20. [21]

    Fatigue crack growth in an aluminum alloy: Avalanches and coarse graining to growth laws

    Lomakin I V., Mäkinen T, Widell K, Savolainen J, Coffeng S, Koivisto J, et al. Fatigue crack growth in an aluminum alloy: Avalanches and coarse graining to growth laws. Phys Rev Res 2021;3:L042029. https://doi.org/10.1103/PhysRevResearch.3.L042029

    work page doi:10.1103/physrevresearch.3.l042029 2021

  21. [22]

    Size -effect method to determine mode -I fracture toughness of aluminium alloys

    Gattu M, Aala S. Size -effect method to determine mode -I fracture toughness of aluminium alloys. Eng Fract Mech 2021;242:107504. https://doi.org/10.1016/j.engfracmech.2020.107504

    work page doi:10.1016/j.engfracmech.2020.107504 2021

  22. [23]

    Plasticity-induced crack closure identification during fatigue crack growth in AA2024 -T3 by using high -resolution digital image correlation

    Paysan F, Melching D, Breitbarth E. Plasticity-induced crack closure identification during fatigue crack growth in AA2024 -T3 by using high -resolution digital image correlation. Int J Fatigue 2025;192:108703. https://doi.org/10.1016/j.ijfatigue.2024.108703

    work page doi:10.1016/j.ijfatigue.2024.108703 2025

  23. [24]

    Investigation of grain boundary and orientation effects in polycrystalline metals by a dislocation-based crystal plasticity model

    Hu J, Zhuang Z, Liu F, Liu X, Liu Z. Investigation of grain boundary and orientation effects in polycrystalline metals by a dislocation-based crystal plasticity model. Comput Mater Sci 2019;159:86–94. https://doi.org/10.1016/j.commatsci.2018.12.010

    work page doi:10.1016/j.commatsci.2018.12.010 2019

  24. [25]

    An Ex-Situ Study on Epitaxial Growth of Nickel on Copper Substrate in Electrodeposition

    Huang Y-C, Hou Y-C, Chang L, Yan T. An Ex-Situ Study on Epitaxial Growth of Nickel on Copper Substrate in Electrodeposition. ECS Trans 2017;80:713 –21. https://doi.org/10.1149/08010.0713ecst

    work page doi:10.1149/08010.0713ecst 2017

  25. [26]

    Micromechanical Modeling of Crack Initiation and Propagation in the Ductile -Brittle Transition Region

    Anh GN, Hütter G, Kuna M. Micromechanical Modeling of Crack Initiation and Propagation in the Ductile -Brittle Transition Region. Key Eng Mater 2016;713:58 –61. https://doi.org/10.4028/www.scientific.net/KEM.713.58. Page 34 of 44

    work page doi:10.4028/www.scientific.net/kem.713.58 2016

  26. [27]

    High resolution digital image correlation measurements of strain accumulation in fatigue crack growth

    Carroll JD, Abuzaid W , Lambros J, Sehitoglu H. High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. Int J Fatigue 2013;57:140–50. https://doi.org/10.1016/j.ijfatigue.2012.06.010

    work page doi:10.1016/j.ijfatigue.2012.06.010 2013

  27. [28]

    On the mechanistic driving force for short fatigue crack path

    Long DJ, Dunne FPE. On the mechanistic driving force for short fatigue crack path. J Mech Phys Solids 2023;179:105368. https://doi.org/10.1016/j.jmps.2023.105368

    work page doi:10.1016/j.jmps.2023.105368 2023

  28. [29]

    Cyclic microstructure analysis, crack propagation and life prediction of Inconel 750H considering the slip fracture energy

    Wang K, Song K, Xin R, Zhao L, Xu L. Cyclic microstructure analysis, crack propagation and life prediction of Inconel 750H considering the slip fracture energy. Int J Plast 2023;167:103660. https://doi.org/10.1016/j.ijplas.2023.103660

    work page doi:10.1016/j.ijplas.2023.103660 2023

  29. [30]

    An efficient phase -field model for fatigue fracture in ductile materials

    Seiler M, Linse T, Hantschke P , Kästner M. An efficient phase -field model for fatigue fracture in ductile materials. Eng Fract Mech 2020;224:106807. https://doi.org/10.1016/j.engfracmech.2019.106807

    work page doi:10.1016/j.engfracmech.2019.106807 2020

  30. [31]

    Simulation of fracture behaviors in hydrogenated zirconium alloys using a crystal plasticity coupled phase -field fracture model

    Zan XD, Guo X, Weng GJ. Simulation of fracture behaviors in hydrogenated zirconium alloys using a crystal plasticity coupled phase -field fracture model. Int J Plast 2025;188:104304. https://doi.org/10.1016/j.ijplas.2025.104304

    work page doi:10.1016/j.ijplas.2025.104304 2025

  31. [32]

    Anisotropic phase -field crystal plasticity modelling of fracture in nickel -based superalloy

    Xu Q, Pan K, Chen Y , Zhang Z. Anisotropic phase -field crystal plasticity modelling of fracture in nickel -based superalloy. Int J Plast 2025;190:104368. https://doi.org/10.1016/j.ijplas.2025.104368

    work page doi:10.1016/j.ijplas.2025.104368 2025

  32. [33]

    On the mechanistic basis of fatigue crack nucleation in Ni superalloy containing inclusions using high resolution electron backscatter diffraction

    Jiang J, Yang J, Zhang T, Dunne FPE, Britton T Ben. On the mechanistic basis of fatigue crack nucleation in Ni superalloy containing inclusions using high resolution electron backscatter diffraction. Acta Mater 2015;97:367 –79. https://doi.org/10.1016/j.actamat.2015.06.035

    work page doi:10.1016/j.actamat.2015.06.035 2015

  33. [34]

    Microstructural causes and mechanisms of crack growth rate transition and fluctuation of additively manufactured titanium alloy

    Wang X, Cao M, Zhao Y , He J, Guan X. Microstructural causes and mechanisms of crack growth rate transition and fluctuation of additively manufactured titanium alloy. Int J Plast 2024;179:104034. https://doi.org/10.1016/j.ijplas.2024.104034

    work page doi:10.1016/j.ijplas.2024.104034 2024

  34. [35]

    In-situ experiment and numerical modelling of the intragranular and intergranular damage and fracture in plastic deformation of Page 35 of 44 ductile alloys

    Cai W , Sun C, Wang C, Qian L, Fu MW. In-situ experiment and numerical modelling of the intragranular and intergranular damage and fracture in plastic deformation of Page 35 of 44 ductile alloys. Int J Plast 2025;185:104217. https://doi.org/10.1016/j.ijplas.2024.104217

    work page doi:10.1016/j.ijplas.2024.104217 2025

  35. [36]

    Microstructural insights into fatigue short crack propagation resistance and rate fluctuation in a Ni -based superalloy manufactured by laser powder bed fusion

    Li J, Huang Q, Wang Z, Zhang N, Chen G, Qian G. Microstructural insights into fatigue short crack propagation resistance and rate fluctuation in a Ni -based superalloy manufactured by laser powder bed fusion. Int J Plast 2023;171:103800. https://doi.org/10.1016/j.ijplas.2023.103800

    work page doi:10.1016/j.ijplas.2023.103800 2023

  36. [37]

    The influence of microstructure on short fatigue crack growth rates in Zircaloy -4: Crystal plasticity modelling and experiment

    Long DJ, Wan W , Dunne FPE. The influence of microstructure on short fatigue crack growth rates in Zircaloy -4: Crystal plasticity modelling and experiment. Int J Fatigue 2023;167:107385. https://doi.org/10.1016/j.ijfatigue.2022.107385

    work page doi:10.1016/j.ijfatigue.2022.107385 2023

  37. [38]

    Micro -strain and cyclic slip accumulation in a polycrystalline nickel -based superalloy

    Black RL, Anjaria D, Genée J, Valle V, Stinville JC. Micro -strain and cyclic slip accumulation in a polycrystalline nickel -based superalloy. Acta Mater 2024;266:119657. https://doi.org/10.1016/j.actamat.2024.119657

    work page doi:10.1016/j.actamat.2024.119657 2024

  38. [39]

    Zirconium δ-hydrides: Strain localisation, ratcheting, and fatigue crack propagation

    Long DJ, Dessolier T, Britton T Ben, Pedrazzini S, Dunne FPE. Zirconium δ-hydrides: Strain localisation, ratcheting, and fatigue crack propagation. Int J Plast 2025;190:104344. https://doi.org/10.1016/j.ijplas.2025.104344

    work page doi:10.1016/j.ijplas.2025.104344 2025

  39. [40]

    Aluminum and Aluminum Alloys

    Davis JR. Aluminum and Aluminum Alloys. ASM International; 1993

    work page 1993

  40. [41]

    Microstructural evolution and mechanical properties of a 5052 Al alloy with gradient structures

    Li Y , Li L, Nie J, Cao Y , Zhao Y , Zhub Y . Microstructural evolution and mechanical properties of a 5052 Al alloy with gradient structures. J Mater Res 2017;32:4443 –51. https://doi.org/10.1557/JMR.2017.310/METRICS

    work page doi:10.1557/jmr.2017.310/metrics 2017

  41. [42]

    Solidification cracking test of aluminium alloy 5052

    Soysal T, Kou S. Solidification cracking test of aluminium alloy 5052. Science and Technology of Welding and Joining 2022;27:301 –8. https://doi.org/10.1080/13621718.2022.2051410

    work page doi:10.1080/13621718.2022.2051410 2022

  42. [43]

    High -resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity

    Wilkinson AJ, Meaden G, Dingley DJ. High -resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity. Ultramicroscopy 2006;106:307–13. https://doi.org/10.1016/j.ultramic.2005.10.001. Page 36 of 44

    work page doi:10.1016/j.ultramic.2005.10.001 2006

  43. [44]

    Grain detection from 2d and 3d EBSD data — Specification of the MTEX algorithm

    Bachmann F, Hielscher R, Schaeben H. Grain detection from 2d and 3d EBSD data — Specification of the MTEX algorithm. Ultramicroscopy 2011;111:1720 –33. https://doi.org/10.1016/j.ultramic.2011.08.002

    work page doi:10.1016/j.ultramic.2011.08.002 2011

  44. [45]

    An iterative method for reference pattern selection in high -resolution electron backscatter diffraction (HR -EBSD)

    Koko A, Tong V, Wilkinson AJ, Marrow TJ. An iterative method for reference pattern selection in high -resolution electron backscatter diffraction (HR -EBSD). Ultramicroscopy 2023;248. https://doi.org/10.1016/j.ultramic.2023.113705

    work page doi:10.1016/j.ultramic.2023.113705 2023

  45. [46]

    Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

    Wilkinson AJ, Randman D. Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction. Philosophical Magazine 2010;90:1159 –77. https://doi.org/10.1080/14786430903304145

    work page doi:10.1080/14786430903304145 2010

  46. [47]

    Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation

    Di Gioacchino F, Quinta da Fonseca J. Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation. Exp Mech 2013;53:743 –54. https://doi.org/10.1007/s11340-012-9685-2

    work page doi:10.1007/s11340-012-9685-2 2013

  47. [48]

    An experimental study of the polycrystalline plasticity of austenitic stainless steel

    Di Gioacchino F, Quinta da Fonseca J. An experimental study of the polycrystalline plasticity of austenitic stainless steel. Int J Plast 2015;74:92 –109. https://doi.org/10.1016/j.ijplas.2015.05.012

    work page doi:10.1016/j.ijplas.2015.05.012 2015

  48. [49]

    Tensile Behaviour of Al5052 Alloy Sheets Annealed at Different Temperatures

    Mugendiran V, Gnanavelbabu A, Ramadoss R. Tensile Behaviour of Al5052 Alloy Sheets Annealed at Different Temperatures. Adv Mat Res 2013;845:431 –5. https://doi.org/10.4028/www.scientific.net/AMR.845.431

    work page doi:10.4028/www.scientific.net/amr.845.431 2013

  49. [50]

    Effect of annealing on formability and crystallographic textures of aluminium 5052 alloy sheets

    Ravindran R, Manonmani K, Narayanasamy R. Effect of annealing on formability and crystallographic textures of aluminium 5052 alloy sheets. International Journal of Materials Research 2010;101:877–86. https://doi.org/10.3139/146.110347

    work page doi:10.3139/146.110347 2010

  50. [51]

    A Good Practices Guide for Digital Image Correlation

    Bigger R, Blaysat B, Boo C, Grewer M, Hu J, Jones A, et al. A Good Practices Guide for Digital Image Correlation. 2018. https://doi.org/10.32720/idics/gpg.ed1

    work page doi:10.32720/idics/gpg.ed1 2018

  51. [52]

    A simple and effective way to evaluate the accuracy of digital image correlation combined with scanning electron microscopy (SEM -DIC)

    Glushko O. A simple and effective way to evaluate the accuracy of digital image correlation combined with scanning electron microscopy (SEM -DIC). Results in Materials 2022;14:100276. https://doi.org/10.1016/j.rinma.2022.100276. Page 37 of 44

    work page doi:10.1016/j.rinma.2022.100276 2022

  52. [53]

    Yield behavior beneath hardness indentations in ductile metals, measured by three -dimensional computed X-ray tomography and digital volume correlation

    Mostafavi M, Collins DM, Cai B, Bradley R, Atwood RC, Reinhard C, et al. Yield behavior beneath hardness indentations in ductile metals, measured by three -dimensional computed X-ray tomography and digital volume correlation. Acta Mater 2015;82:468–

    work page 2015

  53. [54]

    https://doi.org/10.1016/j.actamat.2014.08.046

    work page doi:10.1016/j.actamat.2014.08.046 2014

  54. [55]

    Exploring Short Crack Behaviour and Fracture Transition in 5052 Aluminium Alloy

    Koko A, Salim D, Leung N, Spetsieris N, Smith S, England D, et al. Exploring Short Crack Behaviour and Fracture Transition in 5052 Aluminium Alloy. Results in Engineering 2025:105303. https://doi.org/10.1016/j.rineng.2025.105303

    work page doi:10.1016/j.rineng.2025.105303 2025

  55. [56]

    Extracting fracture properties from digital image and volume correlation displacement data: A review

    Becker TH. Extracting fracture properties from digital image and volume correlation displacement data: A review. Strain 2023. https://doi.org/10.1111/str.12469

    work page doi:10.1111/str.12469 2023

  56. [57]

    DIC2Abaqus: Calculating mixed -mode stress intensity factors from 2D and 3D -stereo displacement fields

    Koko A, Marrow J. DIC2Abaqus: Calculating mixed -mode stress intensity factors from 2D and 3D -stereo displacement fields. SoftwareX 2025;31:102231. https://doi.org/10.1016/j.softx.2025.102231

    work page doi:10.1016/j.softx.2025.102231 2025

  57. [58]

    J -Integral Calculation by Finite Element Processing of Measured Full -Field Surface Displacements

    Barhli SM, Mostafavi M, Cinar AF, Hollis D, Marrow TJ. J -Integral Calculation by Finite Element Processing of Measured Full -Field Surface Displacements. Exp Mech 2017;57:997–1009. https://doi.org/10.1007/s11340-017-0275-1

    work page doi:10.1007/s11340-017-0275-1 2017

  58. [59]

    An approach to calculate the J -integral by digital image correlation displacement field measurement

    Becker TH, Mostafavi M, Tait RB, Marrow TJ. An approach to calculate the J -integral by digital image correlation displacement field measurement. Fatigue Fract Eng Mater Struct 2012;35:971–84. https://doi.org/10.1111/j.1460-2695.2012.01685.x

    work page doi:10.1111/j.1460-2695.2012.01685.x 2012

  59. [60]

    A 117 Line 2D Digital Image Correlation Code Written in MATLAB

    Atkinson D, Becker T. A 117 Line 2D Digital Image Correlation Code Written in MATLAB. Remote Sensing 2020, Vol 12, Page 2906 2020;12:2906. https://doi.org/10.3390/RS12182906

    work page doi:10.3390/rs12182906 2020

  60. [61]

    J -integral analysis: An EDXD and DIC comparative study for a fatigue crack

    Koko A, Earp P , Wigger T, Tong J, Marrow TJ. J -integral analysis: An EDXD and DIC comparative study for a fatigue crack. Int J Fatigue 2020;134:105474. https://doi.org/10.1016/j.ijfatigue.2020.105474

    work page doi:10.1016/j.ijfatigue.2020.105474 2020

  61. [62]

    Mixed-mode fracture: Combination of Arcan fixture and stereo-DIC

    Koko A, Becker TH. Mixed-mode fracture: Combination of Arcan fixture and stereo-DIC. Theoretical and Applied Fracture Mechanics 2024:104724. https://doi.org/10.1016/j.tafmec.2024.104724. Page 38 of 44

    work page doi:10.1016/j.tafmec.2024.104724 2024

  62. [63]

    Mode I -III Decomposition of the J -integral from DIC Displacement Data

    Molteno MR, Becker TH. Mode I -III Decomposition of the J -integral from DIC Displacement Data. Strain 2015;51:492–503. https://doi.org/10.1111/str.12166

    work page doi:10.1111/str.12166 2015

  63. [64]

    Small-Specimen Testing, with Image-Based Analysis, for Crack Propagation Resistance in Polygranular Nuclear Graphite

    Marrow J, Scotson D, Jin X, Chen H, Chen Y , Koko A, et al. Small-Specimen Testing, with Image-Based Analysis, for Crack Propagation Resistance in Polygranular Nuclear Graphite. Graphite Testing for Nuclear Applications: The Validity and Extension of Test Methods for Material Exposed to Operating Reactor Environments, ASTM International100 Barr Harbor Dri...

    work page doi:10.1520/stp163920210051 2022

  64. [65]

    3-Dimensional analysis of fatigue crack fields and crack growth by in situ synchrotron X -ray tomography

    Koko A, Singh S, Barhli S, Connolley T, Vo NT, Wigger T, et al. 3-Dimensional analysis of fatigue crack fields and crack growth by in situ synchrotron X -ray tomography. Int J Fatigue 2023;170:107541. https://doi.org/10.1016/j.ijfatigue.2023.107541

    work page doi:10.1016/j.ijfatigue.2023.107541 2023

  65. [66]

    Procedure for accurate calculation of the J -integral from digital volume correlation displacement data

    Becker TH, Molteno MR, Marrow TJ. Procedure for accurate calculation of the J -integral from digital volume correlation displacement data. Strain 2020;56. https://doi.org/10.1111/str.12337

    work page doi:10.1111/str.12337 2020

  66. [67]

    Second Edition

    Crystal Structures. Second Edition. Interscience Publishers, New York Note: Aluminum Cubic Closest Packed Structure. Crystal Structure 1963;1:7–83

    work page 1963

  67. [68]

    Uncertainty quantification of residual stress evaluation by the FIB –DIC ring-core method due to elastic anisotropy effects

    Salvati E, Sui T, Korsunsky AM. Uncertainty quantification of residual stress evaluation by the FIB –DIC ring-core method due to elastic anisotropy effects. Int J Solids Struct 2016;87:61–9. https://doi.org/10.1016/j.ijsolstr.2016.02.031

    work page doi:10.1016/j.ijsolstr.2016.02.031 2016

  68. [69]

    Lengthscale -dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys

    Dunne FPE, Rugg D, Walker A. Lengthscale -dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys. Int J Plast 2007;23:1061–83. https://doi.org/10.1016/j.ijplas.2006.10.013

    work page doi:10.1016/j.ijplas.2006.10.013 2007

  69. [70]

    Thermodynamic analysis of dislocation glide controlled by dispersed local obstacles

    Gibbs GB. Thermodynamic analysis of dislocation glide controlled by dispersed local obstacles. Materials Science and Engineering 1969;4:313 –28. https://doi.org/10.1016/0025-5416(69)90026-3. Page 39 of 44

    work page doi:10.1016/0025-5416(69)90026-3 1969

  70. [71]

    Micromechanistic study of textured multiphase polycrystals for resisting cold dwell fatigue

    Zhang Z. Micromechanistic study of textured multiphase polycrystals for resisting cold dwell fatigue. Acta Mater 2018;156:254 –65. https://doi.org/10.1016/j.actamat.2018.06.033

    work page doi:10.1016/j.actamat.2018.06.033 2018

  71. [72]

    Crystal plasticity extended models based on thermal mechanism and damage functions: Application to multiscale modeling of aluminum alloy tensile behavior

    Hu P , Liu Y , Zhu Y , Ying L. Crystal plasticity extended models based on thermal mechanism and damage functions: Application to multiscale modeling of aluminum alloy tensile behavior. Int J Plast 2016;86:1 –25. https://doi.org/10.1016/j.ijplas.2016.07.001

    work page doi:10.1016/j.ijplas.2016.07.001 2016

  72. [73]

    Interaction integral method for computation of crack parameters K–T – A review

    Yu H, Kuna M. Interaction integral method for computation of crack parameters K–T – A review. Eng Fract Mech 2021;249:107722. https://doi.org/10.1016/j.engfracmech.2021.107722

    work page doi:10.1016/j.engfracmech.2021.107722 2021

  73. [74]

    Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the ‘equivalent domain integral’ method

    Nikishkov GP , Atluri SN. Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the ‘equivalent domain integral’ method. Int J Numer Methods Eng 1987;24:1801–21. https://doi.org/10.1002/nme.1620240914

    work page doi:10.1002/nme.1620240914 1987

  74. [75]

    The virtual crack extension method for nonlinear material behavior

    Parks DM. The virtual crack extension method for nonlinear material behavior. Comput Methods Appl Mech Eng 1977;12:353 –64. https://doi.org/10.1016/0045 - 7825(77)90023-8

    work page doi:10.1016/0045 1977

  75. [76]

    The J -integral and geometrically necessary dislocations in nonuniform plastic deformation

    Shi MX, Huang Y , Gao H. The J -integral and geometrically necessary dislocations in nonuniform plastic deformation. Int J Plast 2004;20:1739 –62. https://doi.org/10.1016/J.IJPLAS.2003.11.013

    work page doi:10.1016/j.ijplas.2003.11.013 2004

  76. [77]

    Resolving the fundamentals of the J-integral concept by multi-method in situ nanoscale stress-strain mapping

    Meindlhumer M, Alfreider M, Sheshi N, Hohenwarter A, Todt J, Rosenthal M, et al. Resolving the fundamentals of the J-integral concept by multi-method in situ nanoscale stress-strain mapping. Commun Mater 2025;6:35. https://doi.org/10.1038/s43246 - 025-00752-z

    work page doi:10.1038/s43246 2025

  77. [78]

    The M -integral for Computing Stress Intensity Factors in Generally Anisotropic Materials

    Wawrzynek PA, Carter BJ, Banks-Sills L. The M -integral for Computing Stress Intensity Factors in Generally Anisotropic Materials. Hanover, MD: 2005

    work page 2005

  78. [79]

    Advantages of the J -integral approach for calculating stress intensity factors when using the commercial finite Page 40 of 44 element software ABAQUS

    Courtin S, Gardin C, Bézine G, Ben Hadj Hamouda H. Advantages of the J -integral approach for calculating stress intensity factors when using the commercial finite Page 40 of 44 element software ABAQUS. Eng Fract Mech 2005;72:2174 –85. https://doi.org/10.1016/j.engfracmech.2005.02.003

    work page doi:10.1016/j.engfracmech.2005.02.003 2005

  79. [80]

    https://doi.org/10.1520/E1820-25

    ASTM E1820 -18: Test Method for Measurement of Fracture Toughness 2025. https://doi.org/10.1520/E1820-25

    work page doi:10.1520/e1820-25 2025

  80. [81]

    Alan F. Liu. Mechanical Properties Data for Selected Aluminum Alloys. Mechanics and Mechanisms of Fracture: An Introduction, Materials Park, Ohio: ASM International; 2005, p. 397–409

    work page 2005

Showing first 80 references.