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.

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pith.paper-citation-record.v1
2608.04781 v1

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measured 31 of 31 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-06T16:57:12.471331Z

measured 31 of 31 standing notices

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

31 of 31 outbound references displayed

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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

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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

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:16.265504Z

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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

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:16.103367Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.908623Z

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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: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.685956Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.498271Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.413848Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.261799Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.193444Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:15.062466Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.968265Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.848839Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.744422Z

Source-reported events for the cited work

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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: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.642521Z

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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: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.515437Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.424324Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.331726Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.212551Z

Source-reported events for the cited work

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:14.055425Z

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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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:13.899198Z

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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

Resolution: verified fuzzy; 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 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; 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 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; 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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:13.112987Z

Source-reported events for the cited work

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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

Resolution: verified fuzzy; 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 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; 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 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; 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 2026-08-13T06:32:02.005865+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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:57:12.522688Z

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