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Source: paper_references, paper_reference_links, observed 2026-08-06T16:57:12.471331Z
Paper Citation Record · LEDGER
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening
As of 13 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2608.04781.
A citation records a reference. It does not transfer a finding from one paper to another.
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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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Source: cited_works
Reference resolution
31 of 31 outbound references displayed
- verified exact0
- verified fuzzy29
- unresolved2
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- malformed identifier0
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Outbound references
Observation 1b6a7ebc-c117-45c4-a237-5aba90d1794f · outbound
This paper cites Approximation of functionals depend- ing on jumps by elliptic functionals viaΓ-convergence.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Approximation of functionals depend- ing on jumps by elliptic functionals viaΓ-convergence
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:16.621556Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5497c68e-cef5-4137-b1bb-0ce40b75a994 · outbound
This paper cites Dislocation nucleation and work hard- ening in anti-plane constrained shear.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Dislocation nucleation and work hard- ening in anti-plane constrained shear
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:16.478213Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f995ab6f-9b01-417c-81ed-c65ddf09be73 · outbound
This paper cites Types of dislocation source, in: Report of Bristol Confer- ence on Defects in Crystalline Solids (Bristol 1954, London: The Physical Society), pp.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Types of dislocation source, in: Report of Bristol Confer- ence on Defects in Crystalline Solids (Bristol 1954, London: The Physical Society), pp
Reference 3
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- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:16.265504Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 77f07c45-7c70-4e47-8c6e-6880e02bf572 · outbound
This paper cites Numerical experiments in revisited brittle fracture.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Numerical experiments in revisited brittle fracture
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:57:10.255828Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3331b9c7-205a-41c2-8796-9d0757a30062 · outbound
This paper cites Distributed optimization and statistical learning via the alternating direction method of multipliers.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Distributed optimization and statistical learning via the alternating direction method of multipliers
Reference 5
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- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:16.103367Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4711b8ef-3b79-45d9-866a-ab06abd714e4 · outbound
This paper cites A discrete dislocation analysis of mode I crack growth.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening A discrete dislocation analysis of mode I crack growth
Reference 6
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- raw_fallback, observed 2026-08-06T16:57:15.908623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 66f80bda-abdc-42c4-b05d-c1a611cf53ff · outbound
This paper cites Effect of grain size on the lower yield and flow stress of iron and steel.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Effect of grain size on the lower yield and flow stress of iron and steel
Reference 7
- Resolution
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- raw_fallback, observed 2026-08-06T16:57:15.685956Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 72791531-a964-4874-9568-ed859fe7c1e1 · outbound
This paper cites Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size
Reference 8
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- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:15.498271Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 88cf5b5d-7ce1-43b4-a612-d873116dc8de · outbound
This paper cites Revisiting brittle fracture as an energy minimization problem.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Revisiting brittle fracture as an energy minimization problem
Reference 9
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- raw_fallback, observed 2026-08-06T16:57:15.413848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5ad19d88-84f6-4074-a011-e4727a861f63 · outbound
This paper cites The phenomena of rupture and flow in solids.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening The phenomena of rupture and flow in solids
Reference 10
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- raw_fallback, observed 2026-08-06T16:57:15.261799Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8efa5a30-954d-4a6a-919e-f382a4426bdc · outbound
This paper cites Control- ling factors for the brittle-to-ductile transition in tungsten single crystals.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Control- ling factors for the brittle-to-ductile transition in tungsten single crystals
Reference 11
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- raw_fallback, observed 2026-08-06T16:57:15.193444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d97fd19c-31d8-4458-81a0-2cad7425e67e · outbound
This paper cites The deformation and ageing of mild steel: III Discussion of results.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening The deformation and ageing of mild steel: III Discussion of results
Reference 12
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- raw_fallback, observed 2026-08-06T16:57:15.062466Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 255a519b-82f1-4a08-9a50-e1681c521881 · outbound
This paper cites Effective toughness of heterogeneous media.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Effective toughness of heterogeneous media
Reference 13
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- raw_fallback, observed 2026-08-06T16:57:14.968265Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2924c0a6-6d8c-458a-83e4-b3b5dff11a3c · outbound
This paper cites A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittle- ment.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittle- ment
Reference 14
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- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:14.848839Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c1a3e8a3-61e5-4836-89de-a7f89c6c5707 · outbound
This paper cites Fracture toughness of crystalline solids.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Fracture toughness of crystalline solids
Reference 15
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- raw_fallback, observed 2026-08-06T16:57:14.744422Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5ccce49d-3130-4d1f-8de3-6254b760e40a · outbound
This paper cites Thermodynamic dislocation theory for non-uniform plastic deformations.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Thermodynamic dislocation theory for non-uniform plastic deformations
Reference 16
- Resolution
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- raw_fallback, observed 2026-08-06T16:57:14.642521Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6814ebb8-7b26-4da7-af1b-e3e3b653685b · outbound
This paper cites Theory of transition from brittle to ductile fracture.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Theory of transition from brittle to ductile fracture
Reference 17
- Resolution
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- raw_fallback, observed 2026-08-06T16:57:14.515437Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 59921f4a-f2ee-4935-b009-f12d32e8b16c · outbound
This paper cites Analytical solution of plane constrained shear problem for single crystals within continuum dislocation theory.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Analytical solution of plane constrained shear problem for single crystals within continuum dislocation theory
Reference 18
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- raw_fallback, observed 2026-08-06T16:57:14.424324Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation dadf1b02-e943-4684-a943-82d3c7d8690e · outbound
This paper cites Petch relation and grain boundary sources.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Petch relation and grain boundary sources
Reference 19
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- raw_fallback, observed 2026-08-06T16:57:14.331726Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 063a7e3a-3b99-48e5-9ca6-3b06a6512105 · outbound
This paper cites Some geometrical relations in dislocated crystals.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Some geometrical relations in dislocated crystals
Reference 20
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- raw_fallback, observed 2026-08-06T16:57:14.212551Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 14babd26-2834-43ca-841c-751d730beac0 · outbound
This paper cites Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations
Reference 21
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- raw_fallback, observed 2026-08-06T16:57:14.055425Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e067d625-a293-4d27-b40d-9fc6085ba974 · outbound
This paper cites The cleavage strength of polycrystals.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening The cleavage strength of polycrystals
Reference 22
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- raw_fallback, observed 2026-08-06T16:57:13.899198Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1bebbe5f-2dd2-4935-8902-fc0c76eac7c4 · outbound
This paper cites Apathindependentintegralandtheapproximateanalysisof strain concentration by notches and cracks.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Apathindependentintegralandtheapproximateanalysisof strain concentration by notches and cracks
Reference 23
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- raw_fallback, observed 2026-08-06T16:57:13.734488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ba96c676-6df3-4c20-b55a-805736871036 · outbound
This paper cites Ductile versus brittle behaviour of crystals.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Ductile versus brittle behaviour of crystals
Reference 24
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- raw_fallback, observed 2026-08-06T16:57:13.599077Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b7e24e90-4fa9-49ba-9995-6154375ea88e · outbound
This paper cites The conflicts between strength and toughness.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening The conflicts between strength and toughness
Reference 25
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- raw_fallback, observed 2026-08-06T16:57:13.459432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6a1e14d4-7331-45cf-8337-15ca89383b79 · outbound
This paper cites an unresolved cited work.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:57:13.277264Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 232c5005-f950-4720-a338-a903a018d6c5 · outbound
This paper cites A phase field model for damage in elasto-viscoplastic materials.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening A phase field model for damage in elasto-viscoplastic materials
Reference 27
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- verified fuzzy
- raw_fallback, observed 2026-08-06T16:57:13.112987Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 86316cb1-a4fb-48ae-885c-1bea74417d40 · outbound
This paper cites Elasto- viscoplastic phase field modelling of anisotropic cleavage fracture.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Elasto- viscoplastic phase field modelling of anisotropic cleavage fracture
Reference 28
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- raw_fallback, observed 2026-08-06T16:57:12.899101Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d4f63f65-b419-462e-9313-e017b186fb71 · outbound
This paper cites Variational principles of nonlinear fracture me- chanics.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Variational principles of nonlinear fracture me- chanics
Reference 29
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- raw_fallback, observed 2026-08-06T16:57:12.713549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 13358792-cc74-4f6e-981a-e96534cf5665 · outbound
This paper cites Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface
Reference 30
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- raw_fallback, observed 2026-08-06T16:57:12.612390Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 632d3f54-23a0-47c1-98b6-2046352c0ed5 · outbound
This paper cites Stability and crack nucleation in variational phase-field models of fracture: effects of length-scales and stress multi- axiality.
A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening Stability and crack nucleation in variational phase-field models of fracture: effects of length-scales and stress multi- axiality
Reference 31
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- raw_fallback, observed 2026-08-06T16:57:12.522688Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
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