[Paper Review] A Novel Physics-Based and Data-Supported Microstructure Model for Part-Scale Simulation of Laser Powder Bed Fusion of Ti-6Al-4V

Jonas Nitzler, Christoph Meier+3 more|arXiv (Cornell University)|Jan 14, 2021

Additive Manufacturing Materials and Processes80 references22 citations

TL;DR

This paper presents a physics-based, data-supported phenomenological microstructure model for Ti-6Al-4V in laser powder bed fusion that predicts phase fractions of β, αs, and αm phases via energy and mobility-driven transformations, eliminating heuristic criteria. It enables accurate, part-scale simulations of selective laser melting with validated predictions of critical cooling rates and martensite formation, confirmed by continuous cooling and large-scale quenching simulations.

ABSTRACT

The elasto-plastic material behavior, material strength and failure modes of metals fabricated by additive manufacturing technologies are significantly determined by the underlying process-specific microstructure evolution. In this work a novel physics-based and data-supported phenomenological microstructure model for Ti-6Al-4V is proposed that is suitable for the part-scale simulation of selective laser melting processes. The model predicts spatially homogenized phase fractions of the most relevant microstructural species, namely the stable $\\beta$-phase, the stable $\\alpha_{\ ext{s}}$-phase as well as the metastable Martensite $\\alpha_{\ ext{m}}$-phase, in a physically consistent manner. In particular, the modeled microstructure evolution, in form of diffusion-based and non-diffusional transformations, is a pure consequence of energy and mobility competitions among the different species, without the need for heuristic transformation criteria as often applied in existing models. The mathematically consistent formulation of the evolution equations in rate form renders the model suitable for the practically relevant scenario of temperature- or time-dependent diffusion coefficients, arbitrary temperature profiles, and multiple coexisting phases. Due to its physically motivated foundation, the proposed model requires only a minimal number of free parameters, which are determined in an inverse identification process considering a broad experimental data basis in form of time-temperature transformation diagrams. Subsequently, the predictive ability of the model is demonstrated by means of continuous cooling transformation diagrams, showing that experimentally observed characteristics such as critical cooling rates emerge naturally from the proposed microstructure model, instead of being enforced as heuristic transformation criteria.

Motivation & Objective

• To develop a physically consistent microstructure model for Ti-6Al-4V that avoids heuristic transformation criteria common in existing models.
• To enable accurate part-scale simulations of selective laser melting by integrating thermodynamically consistent phase evolution with realistic thermal histories.
• To determine model parameters via inverse identification using comprehensive experimental time-temperature transformation (TTT) and transient heating data.
• To demonstrate the model's predictive capability for critical cooling rates and microstructure distributions in realistic SLM and quenching scenarios.
• To support future integration with nonlinear elasto-plastic constitutive models for full thermo-mechanical simulation of SLM parts.

Proposed method

• The model uses rate-form ordinary differential equations for phase fraction evolution, driven by thermodynamic driving forces and temperature-dependent mobility.
• Phase transformations are modeled as energy-competition-driven processes, with no heuristic criteria for martensite formation.
• Diffusion coefficients and phase fractions are updated in time using numerically integrated rate equations, enabling arbitrary temperature profiles and time-dependent parameters.
• Model parameters are identified via inverse optimization using a broad experimental data basis, including TTT and transient heating diagrams.
• The model is coupled with a macroscale thermal simulation of SLM to predict microstructure evolution in realistic geometries.
• Validation is performed against continuous cooling transformation (CCT) experiments and large-scale quenching simulations of a 10 cm Ti-6Al-4V cube.

Experimental results

Research questions

• RQ1 Can a physics-based microstructure model predict critical cooling rates naturally, without enforcing them as heuristic thresholds?
• RQ2 How accurately can the model reproduce experimentally observed phase fractions in continuous cooling and TTT diagrams?
• RQ3 What microstructure distribution emerges in a realistic SLM process with localized heat sources and layer-by-layer deposition?
• RQ4 How does preheating the base plate affect martensite formation in SLM-fabricated parts?
• RQ5 Can the model predict the formation of a martensitic surface layer and a stable αs-phase core in large-scale quenching scenarios?

Key findings

• The model successfully predicts critical cooling rates for martensite formation without heuristic criteria, showing strong agreement with experimental observations.
• In a 1 mm cube SLM simulation, martensite dominates due to high cooling rates, consistent with experimental findings.
• Preheating the base plate to 900 K significantly reduces martensite fraction and increases stable αs-phase formation.
• In a 10 cm cube quenching simulation, near-surface regions develop a martensitic coating of several millimeters due to high cooling rates, while the core remains dominated by αs-phase.
• The model accurately reproduces continuous cooling transformation (CCT) behavior, including long-term equilibria and characteristic transformation kinetics.
• The use of rate-form evolution equations enables consistent simulation of time- and temperature-dependent diffusion coefficients and multiple coexisting phases.