ABSTRACT The shear stress difference method (SDM) plays a central role in photoelastic stress separation. Direct compatibility with standard experimental setups enables straightforward full‐field recovery of stress components. The practical application of SDM is constrained by pronounced fringe streak artefacts and non‐physical discontinuities in recovered normal‐stress maps. These shortcomings arise from three interrelated challenges: (i) irregular fluctuations of the shear‐stress component perpendicular to numerical integration paths that accumulate during integration, producing path‐to‐path discrepancies; (ii) boundary residual stresses that introduce bias in initial‐value determination; and (iii) cumulative errors when integration paths traverse low‐quality measurement zones. To overcome these limitations, we developed a mechanism‐driven framework: it combined (a) a directional smoothing operator targeting perpendicular shear fluctuations while preserving legitimate stress gradients; (b) an informed initial‐value selection rule and a low‐temperature annealing protocol to mitigate boundary bias; and (c) a partitioned reconstruction workflow that prioritized high‐quality regions and propagated interface results into lower quality zones to limit error growth. This framework was validated against an analytical solution for a radially compressed disk and a numerical simulation of a radially compressed ring. The results demonstrated substantial suppression of streak artefacts, restored continuity and strong quantitative agreement with reference fields. This approach was robust and practically implementable, and it provided a reliable foundation for broader photoelastic stress separation tasks.
The CANDU (CANadian Deuterium Uranium) nuclear reactors are pressure tube reactors. The fuel channels of the reactor comprise a calandria tube and a smaller diameter pressure tube (pressure boundary) concentric within the calandria tube. The pressure tube, made from a zirconium alloy, Zr-2.5wt.%Nb, contains the nuclear fuel and pressurized coolant. In some scenarios, such as a postulated loss of coolant accident, the horizontally oriented pressure tube gets heated to high temperatures (above 650 degrees C) and deforms into contact with the calandria tube either through primarily downward deformation under its weight (sagging) or primarily radial deformation under internal pressure (ballooning). This deformation establishes a more direct path to remove heat from the fuel to the heavy water moderator that surrounds the calandria tube. A method was developed to apply stereo digital image correlation paired with thermography images to measure deformation of prototypical biaxial stress tests and Zr-2.5wt.%Nb pressure tubes demonstrating ballooning behaviour and compare experimental measurements to predictive deformation models developed from tests on uniaxially stressed specimens. The experiments were performed at an internal pressure of 3.5 MPa and a heating rate of 7.5 degrees C/s representing low heating rates of a pressure tube in a CANDU accident scenario and provided transient surface deformation and temperature for comparison against models. The model predictions were in good agreement with the experimental measurements especially when the uncertainty in the temperature measurements is considered.
At present, a multibeam optical stress sensor (MOSS) is the preferred instrument for measuring thin-film stress in situ and in real time. The thin-film stress-induced curvature is measured using the reflection from the substrate of an array of parallel laser beams, while the curvature is converted to the thin-film stress using Stoney's equation. To accurately track the displacements on the detector, each laser spot is fitted with a Gaussian intensity profile, a method that requires a few, narrow, isolated laser spots and, consequently, most of the detector area remains unused. To increase the accuracy, this work proposes an alternative method named the speckle stress sensor (SSS). It is based on (i) integrated digital image correlation (IDIC), known for its high displacement field accuracy for non-optimal brightness patterns if an accurate description of the actual kinematics is incorporated, and (ii) a suitable pattern of a large number of overlapping spots, created with a simple LED and perforated plate. First, it is shown that IDIC is a more robust and more accurate method, even for analysing images with isolated laser spots. Next, a simple SSS LED set-up has been developed that generates high-quality images with overlapping spots, resulting in at least a twofold increase in stress sensor accuracy. Suggestions for further improvements are also proposed.
Digital Image Correlation (DIC) is a popular camera-based, non-contacting method to obtain full-field displacement and strain measurements. In a vibration-based fatigue test, DIC is desirable because DIC can continue to monitor strain after a strain gage would have failed. When applied to vibration-based testing, one of the major challenges of DIC is maintaining sufficient lighting. Large out-of-plane displacements necessitate small apertures for improved depth of field while high frequency oscillation requires short exposure times to reduce motion blur. In this work, the tradeoffs in aperture, exposure time, gain, and external lighting are examined. First, a Design of Experiment (DOE) response surface test matrix is generated for each light source and aperture size. Second, strains are estimated using a laser vibrometer for which there is a pre-determined relationship between its measured displacement and the strains measured by a strain gauge at lower amplitudes. Third, strains are additionally measured by fitting an analytical solution to full-field deformation obtained using DIC. Further, a Monte Carlo Method uncertainty propagation was performed to determine the uncertainty between the two strain measurements. The strobe lights provided the most accurate and stable strain measurements while the ring lights provided the smallest tolerance range. In most cases, the use of Gain was found to be relatively harmless, which runs counter to the common wisdom that it should be generally avoided in DIC. In some extreme cases, Gain even produced less error than leaving the Gain as zero, but there are also counter-examples for which increased Gain produced worse outcomes. Thus, although in some situations Gain may be the least-worst option based on the needs of the experiment, DIC users should be cautioned not to over-rely on Gain without careful consideration of other lighting methods.
ABSTRACT The assessment of ductile damage at high strain rates poses challenges both at an experimental and numerical modelling levels. Indeed, testing requires special facilities, such as the split‐Hopkinson bar (SHB), through which it is not trivial to reproduce the multiaxial stress states that are mandatory for a robust material characterisation and tuning of numerical damage models. The paper proposes the use of a minimal but effective set of cylindrical, notched and shear‐tension specimens which can be tested using a conventional SHB only to investigate material strains to fracture at different (low) triaxialities and Lode angles. The materials investigated are a 17‐4PH steel and a Ti6Al4V titanium alloy. Experimental ultimate fracture strains corresponding to the different stress states are shown, along with the results of damage model calibration. It is proved that the approach can lead to an accurate dynamic characterisation, and that two widely used damage models can provide effective predictions even when high strain rates are involved. Finally, a comparison between dynamic and quasi‐static ductile fracture behaviour for the two materials is presented and discussed.
ABSTRACT In the present work, mappings of two invariants of the true strain tensor, that measures the magnitude of the distortion and that quantifies the mode of distortion, are used to investigate the multiaxial fatigue of AE2 and AE42 diabolo samples under tension/torsion conditions. These mappings are used to set up two types of experimental tests. The first is called unimodal because it ensures a constant value of ; therefore, the mode of distortion remains the same along the cycles; three modes have been chosen: uniaxial tension (), simple shear () and a mix mode (). The second is called multimodal because the value of changes along a cycle, oscillating between simple shear and uniaxial tension with a constant magnitude of the distortion . Experimental results show large difference between the fatigue lifetime of the two samples: For both unimodal and multimodal tests, failure of AE42 samples occurs earlier than failure of AE2 samples for the same conditions. Numerical analysis show that, under the same conditions, the principal stresses and stretch ratios are identical for the two samples questioning the relevance of these quantities for multiaxial fatigue lifetime predictions. Finally, it appears that the stress gradient differs from one geometry to another, and it could be an important mechanical quantity to take into account. This experimental work highlights one of the weaknesses of the fatigue criteria proposed in the past in the literature: The geometry of the test specimens must be taken into account. Here, we emphasize that this can be accounted for using the spatial stress gradient.
Identification of damage using dynamic measurements has been a continued area of research. Defects or damaged regions within a structure can result in an apparent change to the dynamic response of the system. Typical damage detection methods use changes in displacement responses as an indication of damage. However, displacement is relatively insensitive to minor structural variations. Strain-based damage detection methods are more sensitive to minor structural variations but regularly suffer from poor resolution, which hinders their detection capabilities. To improve on the damage detection process, a strain-based technique has been developed that uses full-field data obtained via displacement-strain expansion from a sparse set of measurement points. This expansion method incorporates both strain-based mode shapes and displacement-based mode shapes obtained from either a finite element model (FEM) or experimental modal data. In this work, two laboratory structures with a localised structural modification are excited to obtain sparse displacement and strain response measurements. Sparse test measurements are then used to obtain the full-field strain response, which is compared with the simulated strain response of an undamaged structure subjected to an equivalent excitation. Differences between the damaged and undamaged strain responses are then analysed in the time domain to identify and locate damage within the structures.
This study introduces a novel approach to characterising the mechanical properties of polymeric multilayer films used in photovoltaic (PV) backsheets through nanoindentation (NI). While traditional methods, like tensile testing, measure overall mechanical performance, NI enables layer-specific analysis, which is essential for understanding multilayer structures. Here, we employ the structural compliance correction method to address challenges of specimen-scale flexing and edge effects in NI, enabling accurate measurements of hardness and elastic modulus across distinct film layers. Fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC) and Raman spectroscopy were used to identify the different film layers, which included polyamide (PA), polyvinyl fluoride (PVF), polyethylene terephthalate (PET) and an aromatic polyester-based urethane adhesive. The NI results reveal substantial variation in mechanical properties across layers, with PET showing the highest hardness (200-250 MPa) and modulus values (4-5 GPa). PA offered a hardness of 100-150 MPa and a modulus of 2-3 GPa, followed by PVF with 50-100 MPa hardness and 1-2 GPa modulus. The adhesive layer had the lowest hardness (1.2-1.4 MPa) and modulus (200-400 MPa). Importantly, the structural compliance correction reduced measurement errors caused by specimen-scale flexing and edge effects. Additionally, we observed a small indentation size effect in PET and the adhesive. This study highlights the importance of the structural compliance correction in NI of multilayer films and paves the way for more precise degradation mapping and longevity predictions in polymeric film applications.
This study presents a comprehensive experimental-numerical investigation of the load-bearing behaviour of octahedral and pillar-reinforced octahedral lattice structures fabricated via stereolithography (SLA) using a bio-based UV-curable KS408B (PAR-based) resin. Lattice specimens were produced with three nominal strut thicknesses (300, 400 and 500 mu m), enabling systematic variation of infill density and architectural stiffness. Mechanical performance was evaluated under compression, shear and torsional loading to capture geometry-dependent responses across multiple deformation modes. Experimental results reveal a pronounced nonlinear sensitivity of mechanical properties to slight variations in infill density at low porosity. At a strut thickness of 300 mu m, a modest increase of 1.7 percentage points in infill density resulted in a 255% increase in elastic modulus and a 63% increase in compressive yield stress. Under shear loading, pillar-reinforced lattices exhibited enhancements of up to 86% in shear modulus and 33% in yield stress compared to the pure octahedral topology. Torsional tests further demonstrated geometry-dependent trade-offs: pillar reinforcement generally improved torque capacity, whereas the octahedral architecture exhibited greater deformation tolerance and stress homogenization. Finite element analysis (FEA), incorporating experimentally measured bulk material properties, showed good agreement with experimental data, particularly for yield-related parameters, with deviations of 3%-14%, while stiffness-related deviations remained within 16%-26%. Stress distribution analyses highlighted increased rigidity and localized stress concentrations in pillar-reinforced structures, in contrast to the more uniform stress fields observed in pure octahedral lattices. Overall, this work establishes a unified multi-loading experimental-numerical framework for evaluating SLA-fabricated porous lattices and provides new quantitative insights into the interplay between lattice geometry, infill density and mechanical efficiency. The findings offer practical design guidelines for tailoring architectured polymeric structures for load-bearing biomedical scaffolds and lightweight structural applications, where balancing stiffness, strength and deformation capability is critical.
Performing well-controlled warm formability experiments on metal sheets is a topical industrial challenge as vehicle lightweighting turns to higher strength aluminium alloys. A number of difficulties with warm forming are tackled in this paper using both an experimental and a numerical approach. The sensitivity of the material behaviour to temperature and strain rate was first studied using tensile testing. It is shown that the strain rate does not have a significant impact on the material response below 180 degrees C. At 180 degrees C, the yield stress and the strain hardening are higher at faster strain rates. Nakazima experiments were then carried out on a forming press to study the formability of the material at different temperatures. The impact of several parameters on the results was investigated in order to conduct and analyse properly warm formability experiments (e.g., friction and filtering methods). A finite element model was also developed to support this sensitivity study. A comparison between the forming limit diagrams obtained experimentally and numerically is presented.
Accurate identification of nonlinear material parameters from three-dimensional full-field deformation data remains a challenge in experimental mechanics. The virtual fields method (VFM) provides a powerful, computationally efficient approach for material model calibration; however, its success depends critically on the choice of virtual fields and the informativeness of available kinematic data. In this work, we advance the state-of-the-art discrete formulation of the sensitivity-based virtual fields (SBVF) method by systematically developing and comparing alternative variational and analytical SBVFs within a strain-invariant-based modeling framework. A central contribution of this work is the implementation and assessment of variation-based SBVFs (vSBVFs), formulated using directional G & acirc;teaux derivatives, as well as virtual fields derived from analytical differentiation (aSBVFs) which provide explicit, model-tailored virtual displacement fields for parameter identification. Using simulated noisy volumetric datasets, we demonstrate that vSBVFs and aSBVFs enable procedural, automated construction of optimal virtual fields for each material parameter, substantially enhancing the robustness and efficiency of calibration without the need for manual field selection or high temporal resolution in the data acquisition. We quantify data richness-the effective diversity of sampled kinematic states-showing that increased data richness via sample geometry and loading protocols leads to improved parameter identifiability. These findings establish a pathway for automated, noise-robust material model calibration suitable for future deployment with experimental full-field imaging of soft, complex materials.
Digital image correlation (DIC) is a widely used experimental technique for measuring full-field deformation, but its application to complex scenarios involving large deformations, discontinuities, or intricate geometries is often hampered by the need for manual region of interest (ROI) definition. This limitation is particularly acute for incremental tracking strategies, where frequent ROI updates create a significant bottleneck and require substantial user intervention. To overcome this challenge, we present a machine learning-aided workflow that automates and accelerates the analysis pipeline. Our approach leverages the Segment Anything Model 2 (SAM 2) for rapid initial mask generation, followed by novel spatial and temporal smoothing filters to denoise and refine the ROI sequence. These high-quality masks are then seamlessly integrated into our SpatioTemporally Adaptive Quadtree-mesh DIC (STAQ-DIC) method, which performs automated adaptive meshing and subset splitting near complex boundaries. Through multiple challenging case studies, we demonstrate that our method reduces processing time by one to two orders of magnitude compared to manual methods and shows superior scalability over other automated techniques. The workflow enables robust and accurate full-field measurements in scenarios that were previously intractable or required extensive manual effort. To facilitate broad adoption and benefit the experimental mechanics community, we have integrated the entire pipeline into a user-friendly, open-source code package with graphical user interfaces (GUIs).
Full-field strain measurement is a critical technique for evaluating the mechanical properties and fracture behaviour of diverse materials. Imaging methodologies based on the sampling moir & eacute; (SM) method, which employ digital camera and grating patterns, offer remarkable versatility and effectiveness in strain analysis. In this study, we propose an improved SM method incorporating an image scaling technique for comprehensive strain measurement under varying deformation conditions. The proposed method was validated through simulations and tensile tests on angle-ply carbon fibre reinforced polymer (CFRP) laminates, effectively capturing strain distributions during large deformation events, such as necking. Key results include precise strain distribution measurements beyond 2%, identification of necking deformation within the 2.5%-17% strain range and determination of material failure above 26.4% strain. These findings demonstrate the method's effectiveness and potential for advanced strain analysis, addressing limitations of conventional SM approaches in large deformation scenarios.
This paper reviews the current state of the art in high-speed (HS) and ultrahigh-speed (UHS) digital image correlation (DIC) techniques, emphasizing their critical role in experimental research across various scientific domains. HS and UHS DIC have evolved significantly, driven by advancements in camera systems, image processing algorithms and experimental methodologies. These developments have opened new avenues for capturing and analysing dynamic events with unprecedented temporal and spatial detail, but not without introducing challenges such as optical distortions, motion blur and lighting issues that can affect measurement quality. This review advocates for standardized reporting practices in HS/UHS DIC methodologies to improve reproducibility and reliability across studies, drawing on guidelines from the International Digital Image Correlation Society (iDICs). Through a comprehensive analysis of over 150 articles, this review identifies key advancements in imaging technology and their application in six research domains: material characterization, test development, fracture mechanics, model validation, ballistic and explosive phenomena assessment and measurement uncertainties. Distinctions between two-dimensional (2D) and stereo-DIC applications are explored, offering insights into their practical implementation and trade-offs. Good practices for HS/UHS DIC applications are proposed along with suggestions for future directions for this evolving field, highlighting the indispensable role of technological innovation in expanding the capabilities of optical metrology.
The combination of digital image correlation with infrared thermography (DIC-IRT) in heterogeneous thermomechanical tests enables the simultaneous measurement of temperature and deformation fields and can be used to identify thermomechanical constitutive parameters using inverse identification methods. However, two major challenges remain. The first is the quantification of experimental uncertainties on identification results. The second is the design of optimal test configurations that allow a single heterogeneous DIC-IRT experiment to be reliably exploited for the inverse identification of unknown constitutive parameters. To address the first challenge, this paper presents the first developments towards a digital virtual twin (DVT) able to simulate heterogeneous thermomechanical tests integrating DIC-IRT. The proposed methodology relies on virtual image deformation, which mimics kinematic field measurements with DIC. To include thermal field measurements, a numerical measurement chain is added to simulate the acquisition of infrared images and the spatial synchronization with kinematic data. Based on this approach, a metrological study has enabled the characterization of parameters required to reproduce the experimental uncertainties in the measurement chain. The DVT was then used to simulate a thermomechanical test, which consists of a thick steel sample subjected to heterogeneous thermal strain and temperature fields. The test is designed to identify the thermal expansion coefficient and thermophysical properties from a single experiment using finite element model updating (FEMU). By processing virtual DIC-IRT data with FEMU, the confidence intervals on the identified parameters were predicted based on random and systematic errors in DIC-IRT measurements. Finally, the main limitation hampering the use of the proposed DVT for optimizing the design of heterogeneous thermomechanical tests is discussed, along with potential strategies to overcome it.
The CuCrZr alloy has garnered significant interest as a promising material for additive manufacturing, particularly in applications requiring high strain rate performance. Such applications include vertical targets like heat sinks in the ITER divertor and actively cooled plasma-facing components, where these alloys serve as structural materials. Although the dynamic behaviour of additively manufactured materials is an expanding area of study, the high strain rate properties of CuCrZr remain not exhaustive and require further investigation. This study presents the results of quasi-static and dynamic tension-compression tests conducted at various strain rates on CuCrZr alloy specimens in their as-built condition. The alloy was fabricated using laser powder bed fusion (L-PBF) with selective laser melting (SLM) technology. Compression samples were designed with standard cylindrical shapes, whereas tensile sample geometry was tailored to meet dynamic testing requirements. The study involves the calibration of an improved Johnson-Cook constitutive model through inverse analytical and numerical procedures. Dynamic increase factors (DIFs) were also evaluated using phenomenological and physical model parameters. The findings indicate that CuCrZr alloy exhibits strain rate sensitivity, which activates above a certain threshold. This was confirmed by a reconstructed dynamic fracture locus, which was consistently higher than the quasi-static locus across all stress triaxiality values.
This paper revisits the effects of plasticity-induced crack closure on the experimental determination of the stress intensity factor using an experimental-numerical approach based on the displacement field measurements obtained via digital image correlation (DIC). The study focuses on the application of the CJP model, an advanced linear-elastic crack-tip stress-field model that incorporates plasticity-induced shielding effects into fatigue crack propagation analysis. For comparison, a second approach based on the J-integral method was employed. The experimental stage involved fatigue crack growth tests under constant-Delta K conditions, a key requirement for isolating crack-shielding effects and validating crack growth models. For this purpose, disk compact tension (DC(T)) specimens made from 6351-T6 aluminium and AISI 1020 steel were used. Two different loading conditions were examined, including a low-high Delta K block loading sequence. The findings highlight the importance of incorporating crack-shielding effects through advanced analytical models like the CJP for more accurate fatigue crack growth assessments.
The present study investigates the compressive mechanical behaviour of a newly developed solid propellant under high temperatures and different strain rates. Quasi-static and dynamic uniaxial compression tests of the energetic solid propellant were conducted under high temperatures and different strain rates. Based on the test results, there exists a significant correlation between temperature, strain rate and the mechanical characteristics of energetic solid propellants. As temperature increases, both compressive strength and compressive modulus of the solid propellants exhibit a decreasing trend. The damage mechanisms of the solid propellant under various loading conditions were systematically analyzed. A thermoviscoelastic constitutive model was established to characterize the mechanical behaviour of solid propellants under various high strain rates and across an extensive temperature range. The multipopulation genetic algorithm (MPGA) was employed to optimize the model parameters. The constitutive model demonstrates excellent applicability in accurately capturing the mechanical responses of both the elastic and reinforcing phases of solid propellants.
In this paper, we chart a path to a method that enables us to extract temporal and spatially varying pressure loading effects on the transient response of steel plates under near-field blast loading, employing ultra-high-speed cameras and DIC to measure the transient deformation field. The study addresses the challenges of obtaining full-field, high-fidelity DIC measurements in extreme blast environments by conducting small-scale detonations in close proximity to steel target plates using two ultra-high-speed camera systems. A comprehensive error analysis of these systems is reported and challenges the historic norms of reported accuracy and repeatability in such testing, showing that errors as low as 0.01 mm can be achieved in transient measurements. Pressure measurements obtained via non-contact DIC are compared with data from Hopkinson pressure bar measurements, providing cross-validation of the methods. This research highlights the critical influence of several factors on the reliability of the results, including the chosen camera system, the geometry of the target plate and the errors introduced during DIC processing. The study demonstrates that, with careful attention to experimental design, short exposure times, thorough error evaluation for each camera system and consideration of the structural response, blast test results from DIC can be independent of the camera system used. Furthermore, the study finds that the design of the plate for obtaining accurate impulse distributions is more critical than the inherent camera system uncertainties. Within these limitations, the spatial distribution and temporal development of the impulse loading inferred from the DIC velocity data shows excellent correlation with direct measurements of impulse applied to a nominally rigid target by an identical explosive detonation. This offers a path to a method that could achieve the hitherto impossible task of extracting accurate data on the blast load applied in the extreme nearfield to deforming targets.
In the biomedical field, accurate measurement of mechanical properties of small-sized soft tissue samples such as coagulation, thrombosis and plaques has always been a challenge. This paper proposes a method for measuring Young's modulus. The main idea of the method is to excite the sample's resonance through an external magnetic field and then use optical coherence technology to detect the resonance frequency, from which Young's modulus is derived. The verification results show that this method can accurately obtain Young's modulus within the range of 1-120 kPa, with a sensitivity of +/- 0.1 kPa. For precise measurements, the microbead-to-sample mass ratio must be maintained below 0.5%. The measurement results across different geometric samples exhibit a deviation of less than +/- 5%, while the relative error of Young's modulus measurements at various locations on the sample surface is under +/- 3%. This method effectively assesses the elastic modulus (ranging from 1 to over 100 kPa) of small samples (millimetre scale) with various geometries (e.g., prism, cuboid), demonstrating significant potential for clinical applications in bleeding risk diagnosis and disease staging.
