[Paper Review] Modeling strength and failure variability due to porosity in additively manufactured metals

Mohammad Khalil, Gregory H. Teichert+5 more|arXiv (Cornell University)|Dec 23, 2019

Probabilistic and Robust Engineering Design48 references4 citations

TL;DR

This paper develops a Bayesian uncertainty quantification framework that combines high-resolution CT scans with a pseudo-marginal likelihood approach to model strength and failure variability in additively manufactured 17-4PH stainless steel due to porosity. It distinguishes between resolvable voids and sub-threshold porosity, revealing that the latter dominates mechanical response variability, enabling robust inference of constitutive model parameters and process quality assessment.

ABSTRACT

To model and quantify the variability in plasticity and failure of additively manufactured metals due to imperfections in their microstructure, we have developed uncertainty quantification methodology based on pseudo marginal likelihood and embedded variability techniques. We account for both the porosity resolvable in computed tomography scans of the initial material and the sub-threshold distribution of voids through a physically motivated model. Calibration of the model indicates that the sub-threshold population of defects dominates the yield and failure response. The technique also allows us to quantify the distribution of material parameters connected to microstructural variability created by the manufacturing process, and, thereby, make assessments of material quality and process control.

Motivation & Objective

• To quantify the variability in plasticity and failure of additively manufactured metals due to microstructural imperfections, particularly porosity.
• To develop a computationally efficient uncertainty quantification (UQ) methodology that handles both resolvable and sub-threshold porosity in a physically consistent way.
• To calibrate constitutive damage models using experimental stress-strain data and CT scans, enabling inference of material parameters linked to manufacturing variability.
• To distinguish between epistemic uncertainty (limited data) and aleatory uncertainty (intrinsic microstructural variability), especially from unresolved porosity.
• To enable robust design and process control by quantifying the distribution of material parameters arising from manufacturing-induced microstructural variability.

Proposed method

• The method employs a hybrid finite element modeling approach that explicitly resolves observable voids from X-ray CT scans while modeling sub-threshold porosity via a constitutive damage model.
• It uses Karhunen-Loève expansion (KLE) to represent the 3D stochastic porosity field with reduced dimensionality, minimizing the number of random coefficients for efficient UQ.
• A pseudo-marginal likelihood approach is applied to perform Bayesian calibration, treating the high-dimensional KLE coefficients as nuisance parameters.
• The framework integrates experimental stress-strain data from dogbone tensile specimens to infer posterior distributions of key damage model parameters such as initial hardening and initial damage.
• The method accounts for aleatory uncertainty from unresolved microstructural features by embedding them within the constitutive model, avoiding direct inference of high-dimensional parameters.
• It enables uncertainty propagation through multiscale simulations, linking microstructural variability to macroscopic performance metrics like yield strength and strain-to-failure.

Experimental results

Research questions

• RQ1 To what extent does sub-threshold porosity (below CT resolution) dominate the variability in yield and failure response of additively manufactured 17-4PH stainless steel?
• RQ2 How can a Bayesian framework with pseudo-marginal likelihood be used to infer constitutive model parameters when the number of nuisance parameters (e.g., KLE coefficients) is extremely high?
• RQ3 Can a hybrid modeling approach that explicitly resolves large voids while implicitly modeling small-scale porosity accurately predict macroscopic failure variability in AM metals?
• RQ4 How does the distribution of material parameters (e.g., initial hardening, initial damage) reflect underlying microstructural variability from the manufacturing process?
• RQ5 What is the relative contribution of resolvable versus sub-threshold porosity to the observed scatter in stress-strain response across multiple AM test specimens?

Key findings

• The sub-threshold porosity population—below the 7.5 µm resolution limit of the CT scans—was found to dominate the variability in yield strength and failure strain in 17-4PH stainless steel specimens.
• The proposed pseudo-marginal likelihood method enabled effective Bayesian calibration despite the high dimensionality (~10^4 to 10^5) of the KLE-based porosity representation.
• The framework successfully quantified the full posterior distribution of key constitutive parameters, including initial hardening and initial damage, linking them to microstructural variability.
• The method demonstrated convergence with relatively few sample realizations, indicating computational efficiency for uncertainty propagation in complex microstructures.
• The embedded uncertainty approach enabled physically meaningful inference of material parameters and provided a pathway to assess material quality and process control in AM manufacturing.
• The study confirms that the dominant source of mechanical response variability in this AM process is not the explicitly resolved voids but the implicit, sub-threshold porosity captured by the damage model.