Implementation Question: Explicit Precipitates in DAMASK CPFEM

[cjyehnycu]

Dear all,

I am using the dislocation-based CPFEM in DAMASK to model precipitation-strengthened aluminum alloys, with precipitates explicitly resolved (element size smaller than precipitate size). The precipitate phase is assigned a higher elastic modulus or higher initial CRSS (τ₀) than the aluminum matrix.

However, the macroscopic stress–strain response of the alloy with precipitates is lower than that of a pure alloy without precipitates, contrary to expected strengthening (rule of mixtures). The stress–strain curve of aluminum alloys containing precipitates shows a noticeable difference compared with that of pure aluminum, even though the volume fraction of precipitates is very low (less than 1%). In addition, the stress–strain responses of individual elements within the matrix grains show significant variability.

I would appreciate insights into possible causes, such as load partitioning, dislocation density evolution, phase interaction, or parameter consistency in the dislocation-based model, and any guidance on correctly implementing precipitate strengthening in DAMASK.

Thank you for your help.

[nikprabhu]

Dear @cjyehnycu,

Thanks for your question. Could you please provide more information on your simulation setup?

It would be especially helpful to know more about your post‑processing workflow. One common pitfall is that the volume-averaged quantities are taken only from the aluminum matrix phase and not from the precipitate phase. This often leads to an apparent reduction in macroscopic response, even when the precipitates are intended to be harder.

From my own experience with modeling hard particles embedded in a softer matrix, it is also important to remember that if your model is fully local, it cannot capture effects such as dislocation pileups at the precipitate--matrix boundary. Even so, the overall macroscopic response should still follow the expected rule of mixtures, especially when you assign a higher elastic modulus or higher initial CRSS to the precipitates.

To understand the underlying reason, it would help to know more about your configuration.

Best regards,
Nikhil

[cjyehnycu]

Dear @nikprabhu

sorry for the late response.

I observe an unexpected deviation in the macroscopic stress–strain response of a DAMASK simulation with a very small precipitate volume fraction (0.679%).

Model setup

Mesh: 20 × 20 × 20 (grid.vti)

Phases:

Al matrix: 7,946 elements

Precipitates: 4 clusters (8, 8, 10, 28 elements), total VF = 0.679%

Solver: spectral_basic

Loading: uniaxial tension, F₁₁ = 1.1, free lateral deformation

Time discretization: t = 10.0, N = 700

Cases

Case A (material_caseA.yaml): Pure Al reference; matrix and precipitate phases share identical material parameters (homogeneous behavior).

Case B (material_caseB.yaml): Precipitate phase assigned τ₀ = 10× matrix; all other parameters identical. Intended to suppress plasticity in precipitates.

Observation

Despite the extremely low precipitate volume fraction, Case B shows a noticeable deviation in the macroscopic stress–strain curve compared to Case A. Based on a rule-of-mixtures expectation, the response should be close to that of pure Al.

Post-processing

Macroscopic stress obtained by volume-averaging true stresses converted from element-level deformation gradients. Post-processing script and results summary (Overview.ppt) are attached.

You can access the data via the following link:
https://drive.google.com/drive/folders/1Pr_v8EwqDwHl-xxHugiEHLpf5XTs4tDe?usp=sharing

Question

What mechanisms or modeling aspects (e.g., load partitioning, dislocation density evolution, numerical artifacts, phase interaction) could explain this pronounced deviation at such a low precipitate volume fraction?