Simulated Ultrasound and Machine Learning Probe Hidden Fatigue Cracks in Titanium

Fatigue cracks in microtextured titanium alloys are notoriously difficult to find with ultrasound, and a simulation study published in Frontiers in Materials examines why, and what a learned detector can and cannot do about it. The paper, authored by Shicheng Hu, Shuo Chen and Caifeng Wang of Jiangsu Aviation Technical College in Zhenjiang, China, builds a physics-based forward model of pulse-echo ultrasonic inspection whose material constants are those of mill-annealed Ti-6Al-4V. The study is explicitly a simulation exercise: no experimental validation on Ti-6Al-4V or any other titanium alloy is presented, and no qualification is claimed.

The physical problem the model addresses is twofold. In microtextured titanium, backscatter from alpha colonies, modulated by microtextured regions, mimics the echo of a small flaw, burying a genuine crack signal in grain noise. At the same time, crack faces held in contact by residual stress reflect far less energy than their area would suggest, so a metallurgically real crack can be acoustically almost invisible. Both effects inflate false calls from microstructure while suppressing true calls from tight cracks.

To make these effects computable, the model solves a bilinear contact law at the crack interface, coupling the linear and nonlinear scattering paths in a single calculation. The same partial contact that weakens the ordinary reflected echo also generates harmonic distortion, because the crack opens and closes nonlinearly under the interrogating pulse. The forward model was verified against closed-form solutions on 15 quantities, a check intended to establish that the simulated records behave like the analytical limits before any learning is layered on top.

On top of this model sits the detector. A small dilated residual encoder reads both the drive-frequency band and the second-harmonic band of each simulated pulse-echo record. Crucially, the encoder is trained on simulated records only; no measured titanium data enter training. The network’s raw score is converted into a call or no-call decision by split conformal calibration, which provides a false-call guarantee under exchangeability. The authors state that this guarantee is not claimed under distribution shift: if real data depart from the simulated distribution, the statistical promise lapses.

The headline numbers come from simulated test specimens with crack half-lengths from 0.05 to 1.0 millimetres. On the hardest cases, cracks with low contact fractions, the encoder called 73 of 84 cracks while producing no false calls on 180 defect-free specimens, a false-call rate whose 95 percent upper bound is 0.017. The fitted crack half-length at 90 percent detection came out at 0.138 millimetres, with a bootstrap interval of 0.088 to 0.181 millimetres, a threshold that exists only inside the simulation.

Perhaps the most sobering result concerns what the learning itself contributes. A second-harmonic peak measured with no learning achieved the highest part-level area under the curve among the methods compared, and the four leading methods were not separable on that measure. An input ablation went further: an encoder reading only the second-harmonic envelope matched or exceeded the full model reading both bands. The conclusion is that the harmonic band carries the performance. Over five training seeds, the low-contact detection count ranged from 73 to 82 of 84, quantifying how much depends on training stochasticity.

Where the encoder does earn its keep is decision efficiency at the operating point. Against the simple second-harmonic peak rule, the learned detector added nine additional low-contact detections while losing one, in a paired comparison yielding p equal to 0.02. The authors frame this precisely: the encoder adds decision efficiency at the operating point, not information absent from the measurement. The nonlinear harmonic content already contains nearly everything the network extracts; the learning reorganises it into a sharper decision boundary.

The study also maps its boundaries. Detection is confined to contact fractions between 0.05 and 0.30, so cracks that are almost fully open or almost fully closed fall outside the characterised regime. The conformal calibration’s exchangeability assumption adds a second boundary: the false-call guarantee is a statement about the simulated world.

As a methodological case study, the decision layer alone was applied to measured guided-wave data from an aluminium plate cycled to 100,000 cycles. There, the second-harmonic channel produced 4 false calls in 370 angle tests, while the drive band produced 9. This demonstrates that the conformal decision machinery can be ported to measured data, but it does not validate the titanium forward model.

The paper’s contribution, then, is less a deployable inspection tool than a disciplined characterisation of what learned ultrasonic crack detection can deliver under a physically grounded model. It shows that a compact network trained purely in simulation can approach the information limit set by the second-harmonic band, that its advantage over a simple harmonic peak rule is real but narrow, and that the hardest, most tightly closed cracks remain the limiting case.

Subject of Research: Machine-learning ultrasonic detection of fatigue cracks in microtextured titanium alloys using a physics-based simulation model

Article Title: Machine-learning ultrasonic detection of fatigue cracks: a physics-based simulation study

Article References: Hu, S., Chen, S., & Wang, C. (2026). Machine-learning ultrasonic detection of fatigue cracks: a physics-based simulation study. Frontiers in Materials, 13, Article 1961699. https://doi.org/10.3389/fmats.2026.1961699

Image Credits: AI Generated

DOI: 10.3389/fmats.2026.1961699

Keywords: fatigue cracks, ultrasonic testing, Ti-6Al-4V, microtextured regions, second harmonic, machine learning, conformal calibration, probability of detection, simulation study, nonlinear scattering, guided waves, structural materials