1. Introduction
In critical fields such as aerospace, automotive engineering, and large-scale civil infrastructure, structural components are subjected to complex dynamic loads under multi-field coupled environments throughout their service life. The reliability of their mechanical performance not only directly affects the overall operational efficiency of equipment systems but also plays a vital role in ensuring personnel safety. Therefore, the accurate and real-time monitoring of the stress state and deformation behavior of key components holds significant engineering value for preventing structural failure and extending service life. Among them, strain, as a key mechanical parameter characterizing the local deformation and damage evolution of materials [
1], has become an indispensable technical indicator in structural health monitoring (SHM) systems for its precise measurement.
Current strain measurement techniques are mainly categorized into contact and non-contact methods [
1]. Contact methods include strain gauges [
2], fiber Bragg grating (FBG) sensors [
3,
4], and piezoelectric sensors [
5,
6]. Although strain gauges are small in size and low in cost, they provide only point measurement data and are susceptible to temperature-induced drift. FBG sensors have the advantages of anti-electromagnetic interference and multi-point series measurement, but they are relatively expensive and rely on professional demodulation equipment. Among non-contact methods, digital image correlation (DIC) [
7] has emerged as a widely adopted optical technique. It reconstructs full-field strain by tracking the grayscale distribution of random speckle patterns. Due to its high measurement accuracy and flexible experimental arrangement, DIC has been increasingly applied in the field of SHM. The research focus has transferred from controlled laboratory environments to long-term monitoring of real, large-scale infrastructure, such as long-span bridges [
8], wind turbine blades [
9,
10], and historic buildings [
11]. However, DIC also has certain limitations, including sensitivity to outdoor lighting, weather, and vibration conditions, and reliance on computationally intensive image processing algorithms.
To overcome the limitations of the aforementioned strain-sensing techniques, a novel optical detection method based on mechanoluminescent (ML) materials [
12,
13] has become a research hotspot in the field of direct strain visualization. Compared with DIC, ML measurement has the advantages of high spatial resolution, passive operation, and strong environmental adaptability. In the field of SHM, sensing technologies based on ML have demonstrated significant application potential, such as in impact damage detection of composite materials [
14,
15] and the dynamic visualization of crack propagation [
16,
17]. Notably, recent research highlights a key trend: integrating ML optical sensing with machine learning algorithms to develop next-generation intelligent SHM systems. For instance, existing studies have proposed hybrid architectures that integrate full-field ML information sensing, deep learning-based data analysis, and finite element simulation [
18]. This approach enables multimodal sensing, automated damage diagnosis, and real-time validation of structural conditions.
Despite the remarkable progress in qualitative analysis, the quantitative application of ML technology still faces several challenges. First, photoluminescence (PL) afterglow induced by ultraviolet (UV) excitation can interfere with the strain signal. This issue can be addressed either by maintaining a stable PL background through continuous UV illumination [
19,
20] or by allowing the sample to rest for several minutes under stress-free conditions after ceasing UV illumination to allow the afterglow to naturally decay, thereby obtaining a relatively constant PL background [
21,
22]. Second, how to achieve precise calibration of the strain field while maintaining the luminescent properties of ML remains a core issue that urgently needs to be addressed.
Currently, two complementary solutions have emerged in this field. The first method involves integrating ML films onto the surface of the test specimen, utilizing its highly sensitive light intensity response characteristics to obtain full-field strain information, and combining finite element analysis (FEA) to establish a light intensity-strain mapping relationship [
23,
24]. The advantage of this method lies in its simple experimental setup, which enables non-contact measurement without additional optical markers, making it particularly suitable for strain monitoring of complex geometric components. However, since FEA simulations are based on idealized material constitutive relationships and boundary conditions, their computational results exhibit systematic deviations from the actual physical strain field, thereby limiting calibration accuracy to some extent. To overcome this limitation, the second method innovatively utilizes the luminescent particles in the ML film as a natural speckle field, directly calculating the true strain distribution on the specimen surface via DIC algorithm [
19,
24]. The prominent advantage of this technical approach lies in establishing calibration relationships entirely based on experimental measurement data, thereby avoiding uncertainties introduced by theoretical models. It should be noted that a basic assumption of the DIC algorithm is that speckle serves as a deformation marker, and the brightness remains constant or linearly changes. However, the brightness of ML particles is different before and after deformation compared to traditional DIC speckles, so that the normalized cross-correlation coefficient (NCC) of ML particles is significantly below the NCC precision threshold of 0.98–0.99 required by the traditional DIC algorithm. Additionally, this method is highly sensitive to the film fabrication process, with even minor variations in particle distribution uniformity or surface morphology potentially significantly affecting measurement reliability. Current research status indicates that both methods have their own advantages: the former offers the advantage of a simple system but is limited by model accuracy, while the latter can obtain true strain but faces challenges in measurement stability. Therefore, developing a new calibration method that combines theoretical rigor and experimental reliability remains an important research direction for advancing the engineering application of ML technology.
To overcome these challenges, this study introduces a dual-sided synchronous measurement methodology that spatially decouples the functions of DIC and ML sensing. In contrast to the integrated-film approach of Shin et al. [
19], a high-contrast speckle pattern is applied on one side of the specimen for high-fidelity DIC strain measurement, while an ML film is coated on the opposite side to capture luminescent response under identical loading conditions. This configuration preserves the advantages of both techniques: the DIC side provides an accurate, model-free strain reference, while the ML side enables full-field, passive sensing. The establishment of the light intensity-strain mapping relation is, therefore, based on direct experimental correlation rather than numerical simulation, significantly improving reliability and traceability. The accuracy of this calibration is rigorously validated through tensile testing of notched specimens, with detailed precision analysis performed on the calibration curves. This method combines the high accuracy of DIC with the high resolution and passive characteristics of ML, potentially enabling a distributed, passive, and traceable strain measurement system that meets both the requirements for large-area online monitoring and local detail imaging.
2. Brief Principle of Three-Dimensional DIC
Three-dimensional DIC (3D-DIC) is a non-contact optical technique that combines binocular stereo vision with two-dimensional DIC (2D-DIC) to measure full-field surface deformations and strains. The method begins with the calibration of the binocular vision system to determine the intrinsic and extrinsic parameters of the left and right cameras. Once calibrated, the system captures a pair of reference images of the specimen surface before deformation. Subsequently, during mechanical loading or deformation, a series of deformed images is recorded synchronously by both cameras.
In the left reference image, a region of interest (ROI) is selected, and it is subdivided into small square subsets for analysis. Each subset serves as a tracking unit. Using 2D-DIC, the corresponding position of each subset in the right reference image is identified through correlation matching, enabled by extreme geometric constraints after stereo rectification. This initial matching, combined with the calibrated camera parameters, allows reconstruction of the 3D coordinates of surface points via triangulation, establishing the undeformed 3D coordinate field.
As shown in
Figure 1 [
25], when deformation occurs, the same subsets in the left camera’s deformed images are matched using a correlation criterion—typically the normalized cross-correlation (NCC) function—to determine their new positions and, thus, the in-plane displacement components. Simultaneously, the corresponding subsets in the right camera’s deformed images are matched to maintain stereo correspondence. The updated image coordinates from both views are then used to reconstruct the deformed 3D positions of the points. By comparing the 3D coordinates before and after deformation, the full-field 3D displacement field is computed. Strain fields can subsequently be derived through spatial differentiation of the displacement data.
4. Methods
4.1. Data Extraction
During the acquisition of ML and DIC images, the use of different imaging systems—industrial cameras for ML and specialized instruments for 3D-DIC—resulted in inconsistent image coordinate systems, preventing direct spatial registration. To ensure accurate correlation in the light intensity-strain relationship, data points from both datasets had to correspond to the same physical location on the specimen. To achieve this, a physical scale calibration was implemented by marking the four corner points of a predefined ROI directly on both front and back surfaces of the specimen. These physical markers defined an identical ROI area visible to both imaging systems. By referencing these shared spatial landmarks, image coordinates from both ML and DIC were converted into a common physical coordinate system, enabling precise spatial alignment, cross-system data matching, and reliable joint analysis.
4.2. Image Processing
To quantitatively characterize the evolution of the ML response during the tensile process of aluminum alloy specimens, image processing and analysis were performed using custom Python scripts (Python Software Foundation, version 3.12). The algorithm mainly implemented the following three core processing steps, with its overall workflow illustrated in
Figure 4:
- (1)
Background average light intensity calculation: since the ML film exhibited a certain degree of self-luminescence when exposed to UV light without loading, background light intensity had to be corrected to ensure data accuracy. The algorithm first extracted the grayscale image of the specified ROI area from the initial frame image and calculated the average grayscale value within that area as the background average light intensity , which was used for background subtraction in subsequent images.
- (2)
Background subtraction: for each frame of the image, its grayscale matrix within the same ROI range was extracted, and background subtraction processing was performed according to the following formula:
The resulting image data retained only the luminescence enhancement caused by mechanical loading.
- (3)
Visualization: each frame of background-corrected image data was visualized in the form of a false-color image, facilitating analysis of the distribution of light intensity and its evolution with load.
Strain data was directly calculated using a commercial 3D-DIC software (RDIC-STD-DH1200, Hefei Zhongke Junda Vision Technology Co., Ltd., Hefei, China) and served as reference information for ML image data, which was used to establish and analyze the subsequent light intensity-strain mapping relationship.
4.3. Numerical Modeling
To gain deeper insight into the stress concentration phenomenon around the defect and to provide a theoretical basis for interpreting the experimental ML response, a finite element model was established using the commercial software ABAQUS (version 2024). The geometric model replicated the dimensions of the notched 6061 aluminum alloy specimen. The material was modeled as an isotropic, linear elastic solid, with properties including Young’s modulus and Poisson’s ratio provided in
Table 3.
The model was meshed using structured hexahedral elements (C3D8R), which help avoid mesh distortion issues near the notch and ensure computational accuracy in the stress concentration region. A suitable global seed size was defined, with local refinement applied around the notch to capture stress gradients effectively.
The response of this discretized system is governed by the fundamental principles of linear elastic statics. From a computational mechanics perspective, the mechanical behavior of the specimen is governed by the classical equations of linear elasticity. The fundamental system consists of the equilibrium equation, the strain-displacement relation, and the constitutive law. Specifically, the infinitesimal strain tensor is defined as
, and the stress–strain relationship follows Hooke’s law for isotropic materials [
26]:
where
λ and
μ are the Lamé constants, related to Young’s modulus
E and Poisson’s ratio
ν by
and
. The governing equation is solved subject to appropriate boundary conditions, including prescribed displacements and traction loads.
Within this theoretical framework, a static general analysis step was employed to simulate the quasi-static tensile process. The boundary conditions replicated the experimental setup: one end of the specimen was fully fixed, while a prescribed displacement of 6 mm—matching the final displacement achieved in the physical experiment—was applied to the opposite end along the axial direction.
The primary objective of the simulation was to compute the full-field strain distributions for quantitative correlation with the ML intensity patterns. It should be noted that the current model assumes linear elasticity and does not account for plasticity or damage at higher strain levels.
Therefore, it is important to acknowledge the limitations of the current finite element model. Firstly, the material was modeled as perfectly linear elastic, which does not capture the potential plastic deformation or damage initiation that may occur in the aluminum alloy at higher stress levels near the notch. Secondly, the model assumed a perfectly bonded interface between the ML film and the substrate, neglecting the potential influence of interfacial shear or debonding effects on strain transfer that may occur during actual experiments. Lastly, the simulations were conducted under quasi-static conditions and did not account for any strain-rate-dependent material behavior. These simplifications were necessary to establish a baseline understanding but suggest avenues for future work.
6. Conclusions
This study successfully achieved non-contact, full-field visualization and quantitative monitoring of the stress–strain state of aluminum alloy specimens under elastic loading conditions by combining ML film sensors with DIC. The experiment employed a dual-sided synchronous measurement scheme, with ML films adhered to the front surface of the specimen and a speckle field prepared on the back surface. An industrial camera and DIC system were used to separately capture ML images and surface deformation images, ensuring spatiotemporal consistency. By spatially aligning and region-matching the light intensity during the elastic stage with the strain field measured by DIC, a pixel-level data-based light intensity-strain calibration relationship was established. The results showed a significant linear correlation between the two within the studied range.
The calibration relationship was further validated on specimens with an artificial notch defect. By substituting the light intensity data from the ML images into the established linear model, the calculated strain cloud map was reconstructed. Its spatial distribution trend highly matched the DIC-measured strain field and finite element simulation results, particularly maintaining good morphological consistency in the high-strain concentrated regions near the notch tip, verifying that the method retains high quantitative accuracy even in local high-strain regions.
Quantitatively, the method demonstrated high accuracy and reliability. The calibration yielded a strong linear relationship (R2 = 0.92) between ML intensity and strain. Residual analysis confirmed that most errors were confined within ±0.7, while relative errors were predominantly within ±2.5%, with a mean relative error of 0.23% and a standard deviation of 3.53%. These quantitative metrics affirm the robustness of the proposed approach for strain field reconstruction.
This method establishes a conversion pathway from the ML intensity field to the physical strain field while retaining the spatial resolution of the original image, thereby facilitating a transition of ML technology from qualitative observation toward quantitative characterization. The operational compatibility between ML films and DIC algorithms in data acquisition and processing suggests that the approach can be adapted to various ML material systems. However, it is important to note that the present validation is confined to static elastic loading under well-controlled laboratory conditions.
To improve the credibility and mechanistic depth of the methodology, future work will focus on: (1) extending the technique to nonlinear and plastic deformation regimes to establish a unified elastoplastic constitutive model correlating luminescence and strain; (2) integrating multi-modal measurement techniques, including Raman spectroscopy for local crystal structure and strain analysis, XPS mapping for chemical state evolution under stress, and high-speed imaging for transient luminescence dynamics. Such synergistic validation will significantly enhance the interpretation of ML mechanisms and strengthen the reliability of strain field reconstruction under complex mechanical conditions; (3) testing the method in real structural environments to evaluate its practicality and limitations beyond idealized settings.