Attachment 1- SOW.pdf

Naval Research Laboratory 4555 Overlook Avenue SW

Washington DC, 20375-5329 Code 0000

Phenomenological model relating the crack growth rate to stress intensity factors

Statement of Work (SOW)

25 June 2025

N00173-25-RFI-MR37

Attachment 1-SOW

Attachment 1- SOW

STATEMENT OF WORK

Phenomenological model relating the crack growth rate to stress intensity factors

Table of Contents Section 1 Background

Section 2 Objective/ Scope

Section 3 - Requirements

Section 4 Assumptions

Section 5 Key Personnel

Section 6 GFM/GFP

Section 7 Data Rights Assertions:

Section 8 Deliverables

Section 1 Background.

Predicting fatigue crack growth plays a central role in computational modeling and design meth-ods. This task involves the selection of a, e.g., phenomenological model relating the crack growth rate to stress intensity factors. Of particular interest in this project is the so-called Hartman-Schijve (HS) model. An important challenge lies in the identification of the set of parameters of this model.

Besides the selection of an appropriate optimization framework, including both the definition of the loss function and solver, this calibration task also requires handling substantial noise in the data, as well as intrinsic variability across samples, and potentially violation of physical con-sistency.

To address the multi-modality of the data in the space of the HS model parameters, NRL has tested a regularized approach using a multivariate Gaussian mixture model. This model represents the distribution of data as a combination of multiple multivariate Gaussian distributions. While this mixture model delivers satisfactory results in terms of cross-component statistical moments and spread, it involves the selection of parameters (specifically, the number of high-dimensional com-ponents used and a regularization value), the selection of which dramatically affects the sampled crack growth results.

Section 2 Objective/ Scope.

The aim of this project is to expand the toolkit available at NRL, by developing a state-of-the-art modeling and generation framework for crack propagation datasets, using model encoding and stochastic methods capturing both the underlying mathematical and physical constraints, and the dependence, correlation, and concentration trends exhibited by the data. Option years will involve implementation and refinement of sampling algorithms and verification and validation tasks. Also, applications of developed modeling and generation framework will be applied to material made by additive manufacturing as well as polymer-based composites.

Section 3 - Requirements.

The Contractor shall conduct research in the following three major task areas:

1. Implementation of a Statistical Calibration Method for HS Model Parameters,

2. Implementation of Sampling Algorithms, Verification and Validation Tasks,

3. Application of Algorithms and Models;

Task 1 Implementation of a Statistical Calibration Method for HS Model Parameters

The first task will be concerned with the development of a Bayesian calibration approach for the parameters in the Hartman-Schijve model. Given the (relatively small) expected number of data points, we anticipate that the definition of the multivariate prior model will be critical for the deployment of a Bayesian approach. This task will involve an infor-mation-theoretic approach to construct a prior model with minimized bias. Statistical tests need to be conducted to inform the underlying model for the noise term.

Task 2 Implementation of Sampling Algorithms, Verification and Validation Tasks The second task will be concern sampling methods. Given the multi-model nature of the experimental data, it is anticipated, that vanilla non-parametric kernel-based methods will perform poorly. To address this, two approaches need to be implemented (1) adaptive score-based methods that automatically refine kernel parameters to capture structure and concentration, and (2) diffusion-based sampling techniques.

Task 3 Application of Algorithms and Models The third task will focus on the application of the developed algorithms and models to datasets provided by NRL. This will include material made by additive manufacturing as well as polymer-based composites.

Section 4 Assumptions.

The publication and/or presentation of UNCLASSIFIED results at professional conferences and peer reviews journals will be subject to approval by U.S. NRL.

Section 5 Key Personnel

The required qualifications of the key personnel are:

1. Principal Investigator: Key Personnel

a. PhD in computational mechanics.

b. Expertise in materials modeling, statistical methods, and uncertainty quantifica-tion.

c. Experience in developing and deploying algorithms for Naval applications.

2. Scientist/Researcher: Key Personnel

a. a. MS in computational engineering/mechanics.

b. Background in probabilistic modeling and statistical methods.

c. Experience in code development.

Section 6 GFM/GFP

No government equipment will be provided.

Section 7 Data Rights Assertions:

The Government shall have unlimited rights in source codes, computer software, software docu-mentation, and technical data developed under this requirement.

Section 8 Deliverables

8.1 A001 Contractor Labor and Financial Report Bi-Annually

8.2 A002 Technical and Data Analysis, Reports, Procedures, Presentation Materials, including software developed herein Bi-Annually