Multiscale Theory of Dislocation Plasticity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a theory that unifies dislocation plasticity within a thermodynamic/free energy framework. Its significance lies in connecting existing concepts (damage mechanics, dislocation density, and scaling analysis) into a consistent thermodynamic approach.

Several original aspects can be highlighted: the incorporation of dislocation density via a “damage parameter,” the use of gradient terms to account for inhomogeneous deformation, and the application of scaling/renormalization group analysis, linking the model to experimental similitude principles. The theory successfully predicts the equilibrium and evolution of dislocation structures, including cell walls and slip bands.

I recommend this paper for publication without reservation. Nonetheless, several improvements regarding the manuscript’s style and structure would be beneficial, as outlined below.

The presentation is sometimes difficult to follow due to dense wording and heavy notation. The English would benefit from careful editing to improve clarity and remove stylistic flaws.

For instance, the sentence on lines 20-22 repeats the word “describe,” resulting in an awkward construction: “To describe the strain hardening of soft metals, Kocks, Mecking and Estrin [1-3] developed phenomenological models, which made it possible to describe plastic behavior of materials both under dynamic loading and creep.”

Lines 39-42 contain a long and, at the same time, incomplete sentence: “Gavazza and Barnett [8] considered the elastic energy stored in the material outside a tube region surrounding the dislocation line and calculated the self-force on a planar dislocation loop by computing the first variation of the loop self-energy during an arbitrary virtual planar change in the loop configuration.”

It would improve readability to split this sentence into two parts. The first part could explicitly introduce the notion of the dislocation core, which would be particularly helpful for readers new to plasticity research.

The notions of back and residual strains are introduced on page 2 (lines 72 and 83), but their physical meaning remains unclear until page 5, particularly in the case of the back strain. Clarity would be improved if the link between these strains and geometrically necessary and statistically stored dislocations were mentioned from the outset.

The sentence on lines 220-221: “A popular model of plasticity for many metals and alloys, called ideal or perfect, describes a quasistatic, homogeneous, monotonic, and uniaxial deformation by the following stress-strain relation:” requires supporting references to substantiate the statement.

The Discussion section is very short and does not contain substantial discussion, except for the last paragraph. The title “Concluding Remarks” would therefore be more appropriate. Indeed, the first paragraph summarizes the overall content of the paper, while the second briefly recapitulates the discussion presented in the previous section. The last paragraph resembles a discussion because it refers to figures and equations; however, its main purpose is to present prospects for further research. In my view, the predictions discussed in this paragraph (presented in a very telegraphic style) could be integrated into the main text and reiterated in the final section in a more conclusion-oriented manner.

Comments on the Quality of English Language

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Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article advances a thermodynamically consistent multiscale theory of dislocation-mediated plasticity, expands it to include spatial gradients of independent variables, obtains low-energy dislocation structures (LEDS) via renormalization group scaling analysis as ordinary solutions to equilibrium equations without arbitrary assumptions, matches these theoretical structures with experimental observations, and makes several related experimental predictions, but further improvements are needed in the following aspects:

• The paper should provide more detailed discussions on the experimental methods to determine the gradient energy coefficients (κₑ and κω), as their values significantly affect the calculation of dislocation structure parameters but are only briefly mentioned as adjustable parameters for copper.
• It would be beneficial to supplement the verification of the proposed theory with experimental data from more materials (e.g., aluminum or steel) instead of solely relying on phosphorus-alloyed copper, to enhance the theory’s universality.
• The limitations of the ideal plasticity assumption adopted in the model, especially its impact on the discrepancy between theoretical cell size evolution and experimental observations (e.g., opposite trends with plastic deformation), need to be further analyzed and discussed.
• Some parameters in the figures (e.g., the "χ" (mechanical potential) in Figs. 2, 3, 10) lack explicit in-figure annotations or concise explanations in the caption, which may cause confusion for readers unfamiliar with the theory’s notation.
• Since the authors mention plans to include multiaxial deformation in future work, a brief preliminary discussion on the potential challenges or modifications required for extending the current uniaxial deformation theory to multiaxial cases would strengthen the paper’s forward-looking value.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

This version looks fine and I suggest it for the publication.