# Probability of Detection and Defect Distribution Modeling of Porous Hard-Alpha Inclusions in Titanium Aero-Engine Disks

## TL;DR

This paper introduces a method to create and study porous hard-alpha inclusions in titanium aero-engine disks, improving defect detection and modeling.

## Contribution

The paper proposes a novel method to fabricate real porous hard-alpha inclusions and establishes the first POD model for them.

## Key findings

- A method to fabricate real porous hard-alpha inclusions in TC4 titanium alloy disks was successfully implemented.
- A probability of detection model for porous hard-alpha inclusions was established for the first time.
- A defect distribution model with a cubic polynomial relationship was derived, differing from traditional linear models.

## Abstract

A major quality challenge in the application of titanium alloys is the persistence of substances known as “hard-alpha inclusions”. Although hard-alpha inclusions are extremely rare and typically small in size in high-quality titanium alloys for aero-engine disks, their hard and brittle nature poses a non-negligible threat to the structural integrity of the disks. Due to the extreme scarcity of natural hard-alpha inclusions, most previous studies have focused on “synthetic dense hard-alpha particles” rather than “real porous hard-alpha inclusions”, inevitably over-looking the differences between them. In this work, a method of introducing titanium nitride sponge preforms into the electrode preparation step of the smelting process is proposed and implemented, successfully fabricating real porous hard-alpha inclusions in TC4 titanium alloy disks. On this basis, the detection characteristics of ultrasonic non-destructive testing for such porous hard-alpha inclusions are investigated, and a probability of detection (POD) model for these defects is established for the first time. A defect distribution model of porous hard-alpha inclusions for the probabilistic damage tolerance assessment of disks is also derived. This work reveals that, unlike the “linear” behavior of traditional models, the new defect distribution model adheres to a “cubic polynomial” relationship.