Deformation Field Measurement Research Articles

Energy Dissipation during Crack Growth in Rubbers with Mullins Softening

The modulus and toughness of rubbers can be improved by incorporating fillers into the rubber matrix. Filled rubbers exhibit a strain‐induced softening phenomenon known as the Mullins effect. Upon deformation, filled rubbers can dissipate strain energy, which results in enhanced resistance to crack growth. An in‐depth understanding of the energy dissipation accompanying crack growth is important for the predictive modeling of rubber fracture. Herein, an experimental study on the fracture toughness of filled and unfilled rubbers with a focus on characterizing the energy dissipation caused by the Mullins effect during crack growth is presented. A particle tracking method is used to measure the nonlinear deformation fields in notched rubber specimens when subjected to monotonic tensile loading. Using the measured deformation fields and an independently calibrated constitutive model, the evolution of stress fields during crack growth is quantitatively evaluated, based on which the energy dissipation and intrinsic toughness are determined with the assumption of steady‐state crack growth. It is found that the filled rubber exhibits more energy dissipation during crack growth than the unfilled rubber. More importantly, the intrinsic toughness of the filled rubber (5000–8000 J m−2) is also much higher than that of the unfilled rubber (150–300 J m−2).

Локальное изменение напряженного состояния в образцах горных пород перед разрушением по данным коэффициента Лоде–Надаи

In this paper, the relationship of the Lode–Nadai coefficient, which determines the shape of the stress ellipsoid, with the nature of brittle fracture in sandstone, pyrophyllite and dolomite samples for a rigid loading machine is investigated. The measurement of the inhomogeneous deformation field in the samples and the observation of the internal fracture process were performed using strain gauges and acoustic sensors. It is shown that the formation of the main crack is preceded by the evolution of local deformations in the sample, recorded by the strain gauge method. Special processing of strain gauge data, taking into account the free lateral surface of the samples, made it possible to calculate the principle deformations and three invariants of the strain tensor: maximum shear deformation, volume change deformation and the Lode–Nadai coefficient. It has been established that at the final stage of deformation, when a main crack is formed in local sections of the sample, the axes of the principal deformations are reindexed, which is expressed in the achievement of the maximum values of +1 and -1 by the Lode–Nadai coefficient. A comparison with field observations was made.

Dual-Modal Sensing Skin Adaptive to Daylight, Darkness, and Ultraviolet Light for Simultaneous Full-Field Deformation Measurement and Mechanoluminescence Responses.

Mechanoluminescence (ML) and digital image correlation (DIC) have emerged as promising optical methods to visualize and measure deformation fields. In this study, a dual-modal sensing skin, called the ML-DIC skin is introduced, that is capable of emitting ML and facilitating DIC measurements under various lighting conditions, including daylight, night or darkness, and UV irradiation. Four ML-DIC skins are fabricated with or without carbon nanotubes (CNTs) using a composite powder consisting of SrAl2O4: Eu,Dy (SAO), and acrylic resin, with CNT milling times of 48, 72, and 96h for three of four skins, respectively. DIC measurements are performed under multiple lighting conditions for measuring photoluminescence, persistence luminescence, and reflection. Uniaxial tension tests demonstrate the superior performance of ML-DIC skins with CNTs compared with pristine SAO skins, with the skin subjected to 48h of CNT dispersion exhibiting optimal performance. Further investigations focus on ML emission and DIC measurements near the crack-tip vicinity of static and propagating cracks as well as on surfaces above subsurface cracks. The integration of ML and DIC techniques offers a versatile approach for comprehensive deformation analysis applicable to diverse environments, with implications for materials science, engineering, and structural health monitoring.

High lift devices using compliant surfaces

Stall delay and lift enhancement play a crucial role in modern aircraft performance. This is commonly achieved by devices such as slats or flaps located at the leading edge or trailing edge of an aircraft's wing. In this paper, we report a feasibility study of using light-weight compliant surfaces for novel high lift devices. The effects of compliant flags with one end fixed or both ends fixed near the leading edge and trailing edge of an airfoil were studied by force, flag deformation, and flow field measurements in a wind tunnel. When a flag is placed near the leading edge, the excitation of the separated shear layer from the leading edge is the main mechanism in increasing the lift at the post-stall angles of attack. In contrast, the trailing-edge flag with an excess length and both ends fixed could increase the effective camber and the circulation around the airfoil in a time-averaged sense. The mechanism is similar to that of the conventional Gurney flap effect, and equally effective at pre-stall and post-stall angles of attack. When used together, the compliant flags can delay stall angle by 8° and increase the maximum lift coefficient by 67% in the parameter range tested presently. Compliant surfaces require no external power as a passive method. If they are to be used as active methods, they are light weight, and can be stored and deployed easily.

Full-scale tests of two-storey precast reinforced concrete shear walls: Investigation of strength and deformation capacity

Precast concrete structures behave differently than equivalent in-situ cast solutions mainly because of the narrow connections between the precast elements. In this context, the keyed shear connections are of particular interest, as they have to ensure structural integrity in order to transfer shear- and normal stresses between adjacent elements. Extensive experimental studies (based on push-off tests) of this type of connection have been conducted in the past. These tests typically showed significant softening in the post-peak regime of the shear-slip relationship. It is for this reason important to study how effectively such connections can be utilised on the level of structural systems, where redistribution of internal forces is often required to reach the global load carrying capacity. This paper presents results from full-scale testing of two precast shear wall structures. The structures were two stories high and simulated a typical segment of precast buildings in practice. Each test structure was composed of 12 precast elements (decks and walls) and tested to failure under a combination of vertical and horizontal loads. The main varying parameter between the two tests is the design shear capacity of the keyed connections, which was doubled from test T2 to test T3 by increasing the diameter and the yield strength of the U-bar loops. Both structures displayed a ductile failure with significant deformation capacity. However, despite the higher strength in the keyed connections, the load carrying capacity of test T3 was not increased compared to test T2. This behaviour can be explained by a comprehensive analysis of the measured deformation field obtained from 2D Digital Image Correlation. By comparing the deformations with information obtained from independent component push-off tests with equivalent connections, it is possible to pinpoint the different stress regimes that the critical connection experienced, when the test structure reached its load carrying capacity. The results show that at that point in time, large parts of the critical connection were still in the pre-peak shear-slip regime, while another part located between two window openings was already at the end of the post-peak regime with practically no residual strength left. The findings indicate that the effective design strength of connections should be chosen with caution when modern numerical rigid-plastic methods are used to calculate the load carrying capacity of precast structural systems.

Geometric phase analysis of magnetic skyrmion lattices in Lorentz transmission electron microscopy images

Magnetic skyrmions are quasi-particles with a swirling spin texture that form two-dimensional lattices. Skyrmion lattices can exhibit defects in response to geometric constraints, variations of temperature or applied magnetic fields. Measuring deformations in skyrmion lattices is important to understand the interplay between the lattice structure and external influences. Geometric phase analysis (GPA) is a Fourier-based image processing method that is used to measure deformation fields in high resolution transmission electron microscopy (TEM) images of crystalline materials. Here, we show that GPA can be applied quantitatively to Lorentz TEM images of two-dimensional skyrmion lattices obtained from a chiral magnet of FeGe. First, GPA is used to map deformation fields around a 5–7 dislocation and the results are compared with the linear theory of elasticity. Second, rotation angles between skyrmion crystal grains are measured and compared with angles calculated from the density of dislocations. Third, an orientational order parameter and the corresponding correlation function are calculated to describe the evolution of the disorder as a function of applied magnetic field. The influence of sources of artifacts such as geometric distortions and large defoci are also discussed.

Mapping deformation and dissipation during fracture of soft viscoelastic solid

Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel.

Deformation Field Analysis of Small-Scale Model Experiment on Overtopping Failure of Embankment Dams

There are a large number of reservoir dams in China, of which embankment dams account for more than 90%, and public safety will be seriously endangered in case of dam failure. Overtopping is the leading cause of dam failure, and the existing research mainly focuses on the study of the failure process, with less research on the change in the deformation field during the failure process. In this study, the measured deformation field data of a modeled embankment dam during the whole process of impoundment, operation, and failure were obtained by carrying out indoor small-scale model experiments of overtopping failure, embedding inclinometers inside the dam body, and setting vertical displacement measurement markers on the surface. A refined analysis of the measured deformation data shows that the dam body displaces vertically downward during the impoundment stage and the vertical displacement at the dam crest has the largest amplitude; the internal horizontal displacement changes to the left bank and downstream side, and the amplitude of the internal horizontal displacement (upstream and downstream direction and dam axis direction) on the right dam sections is more significant than that in the middle of the dam; during the breaching stage, the time sequence of the sudden change in each internal horizontal displacement measuring point is from the downstream side to the upstream side and from the higher elevation to the lower elevation, which is basically consistent with the process of overtopping of embankment dams; and the overall sudden change in left and right bank horizontal displacements within the downstream side of the dam crest and the downstream side of the dam body gauges is significant, and the sudden change in upstream and downstream horizontal displacement (U&D HD) within the downstream side of the dam crest gauges is significant. The experimental analysis results can support the disaster mechanism of embankment dam failure and the theory of early warning of failure.

MCNN-DIC: a mechanical constraints-based digital image correlation by a neural network approach

Digital image correlation (DIC) is a widely used photomechanical method for measuring surface deformation of materials. Practical engineering applications of DIC often encounter challenges such as discontinuous deformation fields, noise interference, and difficulties in measuring boundary deformations. To address these challenges, a new, to the best of our knowledge, DIC method called MCNN-DIC is proposed in this study by incorporating mechanical constraints using neural network technology. The proposed method applied compatibility equation constraints to the measured deformation field through a semi-supervised learning approach, thus making it more physical. The effectiveness of the proposed MCNN-DIC method was demonstrated through simulated experiments and real deformation fields of nuclear graphite material. The results show that the MCNN-DIC method achieves higher accuracy in measuring non-uniform deformation fields than a traditional mechanical constraints-based DIC and can rapidly measure deformation fields without requiring extensive pre-training of the neural network.

Photo-crosslinking speckle patterns for large deformation measurement of hydrogels using digital image correlation

Hydrogels often undergo large or inhomogeneous deformation when they are used in soft electronic devices, adhesives, or biological implants. To avoid the potential risk of damage and failure in service, the mechanical response of hydrogels, especially subjected to large deformation, requires meticulous evaluation. Digital image correlation (DIC) has been increasingly employed in the mechanical tests of hydrogels due to non-contact measuring the deformation field by tracking speckle patterns motion on the specimen. However, measuring large deformation of hydrogels using DIC is challenging because the speckle patterns painted on the wet surface suffer various issues, such as bleeding when water is squeezed out, fragmentation or debonding if the stress transferred from hydrogel exceeds the strength or adhesion of painting. In this work, we developed a UV lithography-based speckle pattern preparation method to overcome these difficulties. Speckle patterns are generated by curing a polymer on the surface of hydrogels through chemical-crosslinked bonds, making them an integral part of the hydrogel surface. Experiments indicate that the speckle patterns work as reliable information carrier for DIC to measure large deformation up to strain of 580% and highly concentrated localized strain field within specimen. The speckle patterns show good durability in cyclic loading tests with peak strain up to 150%, achieving low relative deviation (<6%) of the measured deformation field in different cycles. Furthermore, our method allows the optimization of speckle patterns by controlling the shape, size, and coverage of speckles through well designed masks, which guarantees the accuracy and robustness of DIC measurement.

Semi-Analytical Prediction of Ground Surface Heave Induced by Shield Tunneling Considering Three-Dimensional Space Effect

The ground surface deformation induced by shield tunnels passing through enclosure structures of existing tunnels is a particular underground construction scenario that has been encountered in Wuhan Metro Line 12 engineering cases in China. Timely ground deformation prediction is important to keep shield tunneling safe. However, the classic ground deformation theory is difficult to accurately predict for this ground deformation. This paper develops a semi-analytical method to predict ground heave considering the space effect in this engineering condition. Based on the improved ground deformation theory, a novel deformation prediction method for the ground and enclosure structure is derived and combined with Kirchhoff plate theory. Comparing with field deformation measurements, the maximum difference between the measured and calculated deformation is 14.6%, which demonstrates that the proposed method can be used to predict the ground heave induced by shield tunnels passing through the enclosure structure of existing tunnels. The parameters of the underground diaphragm wall used in Wuhan Metro Line 12 are further studied in detail. The results show that the ground heaves have a positive correlation with the embedded ratio of the diaphragm wall, but a negative correlation with its elastic modulus and thickness. However, the thickness and embedded ratio have a limited effect on ground heaves. This study provides a technical reference for optimizing the setting of enclosure structures in order to protect existing buildings.

Element-removal global digital image correlation for accurate discontinuous deformation field measurement in fracture mechanics

We propose an element-removal (ER) global digital image correlation (DIC) method to improve the measurement accuracy of discontinuous deformation fields, such as crack propagation. The occurrence of cracks in materials or structures inevitably deteriorates the tracking accuracy, and, consequently, the strain field accuracy obtained by regular subset and global DIC. The proposed ER-global-DIC algorithm iteratively identifies and removes all the elements covering the crack, during the updating of displacement fields. In the remaining elements, the continuous shape function is applicable for accurate deformation measurement. In principle, although elements that contain the cracks are removed, the algorithm preserves the same number of nodes since the nodes are retained by the remaining elements. Synthetically deformed images based on analytical discontinuous displacement fields validate the effectiveness and accuracy of the proposed method. The ER-global-DIC is further applied to measure the discontinuous displacement fields containing a crack deflection, generated from a finite element model with a cohesive zone model. The results demonstrate the potential of the proposed method for discontinuous deformation measurement on advanced materials, e.g., fiber-reinforced composites.

Creep and shrinkage monitoring and modelling of CFST columns in a super high-rise under-construction building

Concrete-filled steel tube (CFST) giant columns have been widely used in super high-rise structures. However, there is a major shortage of field measurements of shrinkage and creep deformation from actual projects. Existing experimental results and derived models cannot reflect the actual on-site conditions where sustained loading is an incremental process during construction and the facing environments vary. In this study, the deformations of giant CFST columns in a super-high-rise under-construction building were monitored for more than 400 d. For comparison, a scaled experiment was conducted in a laboratory. The strains measured in the laboratory and on-site show a good changing trend over time and could be used for model verification. The existing CEB-FIP (2010) model is improved in two ways: 1) introducing a reduction factor in the calculation of shrinkage strains and 2) considering the stress history and stress redistribution in the calculation of creep strains. With parameters determined from the experimental results, the modified model could predict the shrinkage and creep strains of CFST columns in the actual project well with sufficient accuracy.

3D deformation and strain fields in drying kaolinite obtained from tracking internal bubbles using X-ray CT and ANN

AbstractDrying fine-grained sediments experience shrinkage and desiccation cracking that may dramatically alter their mechanical and hydraulic properties. This study adopts X-ray computed tomography (CT) to monitor the three-dimensional (3D) internal deformation and strain fields, and their relationships with desiccation crack formation, for drying kaolinite samples contained in plastic containers. Two kaolinite samples, one dried at room temperature and the other oven-dried at 60 °C, were CT scanned at several intervals during the drying process. From sequential CT scans for the same sample, entrained gas bubbles were extracted and used as tracking markers for deformation and strain field measurements. Since the bubble morphology continuously changed during the drying process, an artificial neural network (ANN) model was developed to link bubbles in sequential scans for the same sample. The tracking algorithm was trained with manually linked bubbles and optimised by comparing different combinations of bubble information, e.g. bubble location, size and shape. The drying samples experienced primarily vertical displacement before the air-entry value, while horizontal displacement occurred during vertical crack formation. Internal vertical and horizontal strains were generally uniform, indicating a limited impact of non-uniform sample drying and substrate constraint.

Mirror-assisted multi-view high-speed digital image correlation for dual-surface dynamic deformation measurement

Based on the recently proposed mirror-assisted multi-view digital image correlation (MV-DIC), we establish a cost-effective and easy-to-implement mirror-assisted multi-view high-speed digital image correlation (MVHS-DIC) method and explore its applications for dual-surface full-field dynamic deformation measurement. In contrast to the general requirement of four expensive high-speed cameras for dual-surface dynamic deformation field measurement, the established mirror-assisted MVHS-DIC halves the cost by involving only two synchronized high-speed cameras and two planar mirrors. The two synchronized highspeed cameras can dynamically measure the front and rear surfaces of a sheet sample simultaneously through the reflection of the two mirrors The results on the two surfaces are then transformed into the same coordinate system, leading to the required dual-surface 3D dynamical deformation fields. The effectiveness and accuracy of the established system are validated through modal tests of a cantilever aluminum sheet. The vibration measurement of a drum and dual-surface transient deformation measurement of a smartphone in the drop-collision process further prove its practicability. Benefiting from the attractive advantages of multiview dynamic deformation measurement in a cost-efficient way, the established mirror-assisted MVHS-DIC is expected to encourage more comprehensive dynamic mechanical behavior characterization of regular-sized materials and structures in vibration and impact engineering fields.

Ordinary Kriging Interpolation Method Combined with FEM for Arch Dam Deformation Field Estimation

The deformation characteristic of the arch dam can directly reflect its service performance, which can be analyzed on the basis of the dam deformation field. However, restricted by the limited number of dam monitoring points and the inhomogeneity of materials, an accurate measurement of arch dam deformation field is difficult to estimate by using the existing common methods, such as the spatial interpolation methods and the finite element method (FEM). With the aim of ensuring arch dam structure safety, the ordinary kriging interpolation method, combined with FEM, is proposed for arch dam deformation field estimation, in this study. Given the inversion of the computation parameters of the arch dam, FEM is used to calculate the basic arch dam deformation. Subsequently, the ordinary kriging interpolation method is introduced to estimate the spatial variance deformation at each point of the arch dam. One superhigh arch dam in China is selected as a case study; two additional methods are introduced as comparisons that are based on a numerical experiment and the actual monitoring data. The experimental results show that the proposed method considerably improves the accuracy and computational efficiency of the arch dam deformation field estimation and that it is of great practical importance for characterizing the deformation behavior of arch dams.

Numerical modelling of enhancement of the capacity of buried metal culverts by using geogrids

This paper presents a two-dimensional numerical modelling analysis of a flexible buried corrugated metal arch culvert in Enkoping, Sweden. The numerical results of this study are validated against field measurements of the culvert crown deformation, thrust, and bending moments recorded during backfilling. To model the backfill soil, the hardening soil with small strains (HSs) material model is used because of its efficiency in simulating the soil-structure interaction. Furthermore, in a numerical investigation of the stress distribution at the culvert invert, it is found that weakness of the foundation soil has an insignificant impact, due to stress dissipation resulting from arching actions. The numerical modelling analysis also investigates the use of geogrid layers with dead end bolts in the soil cover above the culvert crown during the application of static surface loads, as an innovative technique to improve the load capacity of the soil-culvert system. The results show a reduction in culvert crown deformation and internal forces when geogrid layers are used. This indicates the efficiency of geogrid layers in improving the load capacity of existing buried culverts or overcoming deficiencies in culvert serviceability by reducing the impact of applied loads.

Bearing capacity and deformation behavior of rigid strip footings on coral sand slopes

Porous coral sands formed by the remains of marine organisms are important foundation-filling materials for artificial island construction and other marine geotechnical projects. A typical situation is that the significantly reduced bearing capacity of a rigid footing adjacent to coral sand slopes threatens the safety and stability of the upper structures. In this study, a series of model-scale tests were conducted to investigate the bearing capacity and deformation behavior of a rigid strip footing resting on the top of coral sand slopes with consideration of the effects of edge distance, slope height, slope angle, number of geogrid layers, burial depth and spacing of the geogrid layer. The measured deformation field based on particle image velocimetry (PIV) technology indicates that the unreinforced coral sand slope is dominated by unilateral sliding patterns, and its bearing area is significantly smaller than that of the geogrid reinforced coral sand slope (GRCSS). The bearing capacity in unreinforced coral sand slopes increases with the increasing edge distance, and the decreasing slope height and angle. Although the geogrid reinforcement significantly improves the bearing capacity, it is also affected by the number of layers, burial depth and spacing between reinforcement layers. Besides, the reduction coefficient of bearing capacity (RCBC), the bearing capacity factor (Nγq) and the normalized bearing capacity (Nγq/NγqR) were further calculated and discussed based on the test results and classical bearing capacity theory.

Simultaneous measurement of depth-resolved refractive index field and deformation field inside polymers during the curing process

A method based on phase-sensitive optical coherence tomography (PhS-OCT) has recently been used to visualize curing process inside polymers [Appl. Phys. Lett. 116: 054103 (2020)]. Based on this proven method, we further proposed a refractive index model to determine curing induced displacements. For validation, the curing process of a light-cured resin droplet was first monitored by recording a time series of spectral images. Amplitude images and phase difference maps were then calculated from the spectral images. Finally, according to the proposed refractive index model, amplitude and phase information were used together to simultaneously measure refractive index fields and displacement fields. The results show that the time-dependent refractive index field is generalized by a piecewise function consistent with the polymerization kinetics; only the displacements with the piecewise functional feature, similar to the refractive index change, can characterize polymerization shrinkage.

Multi-modal Dataset of a Polycrystalline Metallic Material: 3D Microstructure and Deformation Fields

The development of high-fidelity mechanical property prediction models for the design of polycrystalline materials relies on large volumes of microstructural feature data. Concurrently, at these same scales, the deformation fields that develop during mechanical loading can be highly heterogeneous. Spatially correlated measurements of 3D microstructure and the ensuing deformation fields at the micro-scale would provide highly valuable insight into the relationship between microstructure and macroscopic mechanical response. They would also provide direct validation for numerical simulations that can guide and speed up the design of new materials and microstructures. However, to date, such data have been rare. Here, a one-of-a-kind, multi-modal dataset is presented that combines recent state-of-the-art experimental developments in 3D tomography and high-resolution deformation field measurements.