Crack Spacing Research Articles

Load-bearing behavior of short-fiber-reinforced textile-reinforced concrete for a wrapping process

In the research project titled Wrapping process for highly fiber-reinforced concrete using the example of a pump sump (WiFaPu), a new production process for components made of short-fiber-reinforced textile-reinforced concrete was developed. The idea of wrapping concrete continuously around a formwork evokes high-level requirements on the workability of concrete while matching reinforcement properties. In this study, the load-bearing behavior of wrappable short-fiber-reinforced textile-reinforced concrete with an uncoated textile reinforcement made of AR-glass is investigated via tensile and bending tests. The concrete inserted into the wrapped layers by casting, laminating or spraying and the short fiber content and warp/weft direction of the uncoated fabric have a major influence on the load-bearing behavior of the tested specimens with regard to the utilized tensile strength and crack spacing. Members produced by inserting the concrete in a spraying or laminating process showed low tensile strength and unsatisfactory cracking patterns in the warp direction of the fabric due to the lacing of rovings, which led to lower matrix penetration. For rovings in the weft direction without lacings, higher utilized tensile strengths and fine crack patterns are observed. The casting of specimens leads to significantly higher utilized textile tensile strengths if the reinforcement is slightly tightened in the formwork. Compacting fine-grained concrete leads to better roving penetration than does the spraying process. The addition of short fibers generally benefits the cracking pattern and partially compensates for the negative effects of the textile weave on the utilized tensile strength as well as on the warp direction of the crack pattern. The load increase in tensile and bending tests is proportional to the increase in short fiber content and fiber length. Finally, the influence of different coatings is examined for another uncoated textile reinforcement made of AR-glass with a more favorable textile weave. The utilized tensile strength of the reinforcement is almost doubled when impregnated with a fine cement suspension and directly installed in the formwork and cast. An impregnation process such as this can also be integrated into the wrapping process.

Flexural cracking behaviour and crack width calculation of steel-plate-reinforced ribbed UHPFRC deck panels

Ribbed ultra-high performance fiber reinforced concrete (UHPFRC) deck panels have been designed and implemented in buildings and bridges due to being increasingly slender, lightweight and tough. To further improve the crack resistance, this paper studies a neotype ribbed UHPFRC deck panel using steel plates and headed studs to reinforce the ribs. Bending tests were conducted to reveal the various crack and strain developments at different specimen parts with an aim to selecting the interesting primary-crack position and spacing. Then, theoretical calculation equations were proposed and verified on the differential strain, crack spacing and crack width for the interesting primary crack. The test results showed that the maximum crack width was invariably located at the rib instead of the top slab, and the primary-crack spacing varied from 52.1 mm to 151.2 mm after the cracks penetrated the whole rib into the top slab. The theoretical study showed that the tensile property of UHPFRC can be taken account by a two-line model, the shrinkage strain of UHPFRC as 556.5 με herein should be amended in the equation of the differential strain between reinforcement and UHPFRC. Besides, the crack spacing before and after the cracks penetrated the whole rib can be predicted by the standard AFNOR: 2016 and the headed-stud spacing, respectively. Finally, the theoretical crack-width calculation method was verified to have a satisfactory accuracy by comparing the calculated and test results with a percentage error within 4.0 %.

Estimation of the bar stress based on crack width measurements in reinforced concrete structures

AbstractEstimating the stress of reinforcing bars and its variations in service conditions can be useful to determine the reserve capacity of structures or to assess the risk of fatigue in the reinforcement. This paper investigates the use crack width measurements to estimate the stress in the bars. In existing structures, crack width formulations can be used to estimate the stress in the reinforcement from crack width measurements, profiting from additional information that can be measured in‐situ, such as the crack spacing. Recent experimental results show that the values of the mean bond stress typically considered in code formulations overestimate the actual bond stresses activated in cracked concrete specimens. This paper presents the results of an experimental program consisting of reinforced concrete ties and beams instrumented with Digital Image Correlation and fiber optical measurements. The results confirm the differences with typically assumed bond stresses. A formulation to estimate the bond stresses in service conditions is derived from the results of the numerical integration of a previously developed local bond–slip relationship. Their pertinence for the estimation of the stress in the reinforcement from the measured crack width is evaluated with satisfactory results for monotonic loading and for the maximum force in cyclic tests.

Numerical and experimental study of Yellow River sand in engineered cementitious composite

Engineered cementitious composites (ECCs) represent a significant advancement in concrete technology, addressing the issues and limitations of conventional concrete and environmental challenges related to sedimentation in rivers such as the Yellow River in China. This study investigates the integration of Yellow River sand (YRS) into ECC mix designs for sustainable development. YRS replacement rates (0, 25, 50, 75 and 100%) with quartz sand are systematically analysed through flexural, compressive, uniaxial tensile and four-point bending tests. In addition, scanning electron microscopy and mercury intrusion porosimetry tests are conducted to investigate the micro-mechanical properties. The results reveal that the optimal mechanical performance with 100% YRS substitution improves the compressive and flexural strengths to 26.4 and 11.5 MPa, respectively. These values are 6.20% lower than the those of the 0% substitution rate. Notably, a 100% replacement maintains an ultimate tensile strain of 3.71%, improving the crack width and spacing compared with those at 0%. The average crack width and spacing decrease by 4.87 and 11.2%, respectively, compared with those of 0% substitution. The four-point bending test results show the highest ductility at a 75% substitution rate. Furthermore, a finite-element method model of ECC beams with YRS is developed and validated under the same loading conditions as the experimental data. This study recommends an analytical method for predicting flexural strength compared with the experimental data, enhancing its suitability for sustainable engineering applications.

Flexural durability of BFRP bars reinforced geopolymer-based coral aggregate concrete beams conditioned in marine environments

Geopolymer is an environmentally friendly material that utilizes industrial solid waste, boasting reduced greenhouse gas emissions and energy consumption. It exhibits superior performance in terms of corrosion resistance and thermal stability compared to ordinary Portland cement (OPC). These excellent properties are crucial for marine engineering construction, offering significant value and application potential in marine engineering materials. In this study, geopolymer was employed as the cementitious material, with marine resources like seawater and coral aggregates sourced from remote island areas effectively utilized, and basalt fiber-reinforced polymer (BFRP) bars were incorporated as reinforcements to develop BFRP bars reinforced geopolymer-based coral aggregate concrete (GPCAC) beams. Laboratory aging procedures were employed to investigate the deterioration patterns and damage mechanisms affecting the flexural behavior of GPCAC beams under seawater immersion and dry-wet cycling conditions, comparing them with cement-based coral aggregate concrete (CAC) beams. The experimental results indicated that both CAC and GPCAC beams under simulated marine environments experienced a reduction in the number of cracks upon damage, but their crack spacing and width increased. Moreover, the flexural stiffness of CAC and GPCAC beams after seawater attacks tended to increase, but this increased stiffness did not translate to a higher loading capacity. Conversely, as the corrosion age increased, the ultimate load and deflection values of both CAC and GPCAC beams decreased to varying extents, with the load-carrying capacity degradation more pronounced in seawater dry-wet cycling environments than in seawater immersion conditions. Compared to CAC beams, GPCAC beams exhibited superior resistance to seawater erosion. Following 12 months of seawater dry-wet cycling, the ultimate loading capacity of CAC beams decreased by 12.2%, while that of GPCAC beams only degraded by 9.5%. Predictions of the flexural capacity of GPCAC beams using equations from existing FRP-reinforced normal aggregate concrete (NAC) specifications indicated slightly higher values than the experimental values, with an error margin of less than 15%. Overall, the formulas for the flexural capacity of NAC beams in existing FRP-reinforced NAC codes remained applicable to CAC and GPCAC beams.

Features of bond-slip relations: 3D finite element analysis based on tests of short RC ties

The interaction between concrete and reinforcement is highly complex and is of fundamental importance for predicting the behaviour of reinforced concrete (RC) structures. While the interaction of the two materials is often characterised by a bond – slip law, there are currently no such laws capable of accurately predicting serviceability characteristics, such as deflection, crack spacing, and width. This paper examines the effect of various parameters on the shape of bond – slip relation at loads before yielding of reinforcement. The study is based on a mesoscopic numerical analysis, utilizing the finite element method along with a friction cohesive zone model to explore the bond-slip phenomena in short RC ties. The numerical model is combined with an experimental campaign involving six short concrete ties reinforced with 20 mm bars. Steel strain profiles were monitored within the reinforcement using electrical strain gauges. These experimental steel strain profiles served as a robust tool for controlling and calibrating numerical models. The numerical models employed solid finite elements to simulate both reinforcement and concrete, with special zero-thickness plain elements applied to simulate the friction cohesive contact at the steel-concrete interface. Bond-slip relations were obtained from the numerically modelled reinforcement strain profiles. It was shown that concrete strains can be ignored when assessing slip. The effect of the embedded length of reinforcement under the fully confined conditions was demonstrated to have little effect on bond-slip relations. It was also shown that the maximum bond stress is strongly related to the thickness of the concrete cover. The effect of load intensity on the bond – slip behaviour was investigated. It was shown that under full confinement, the initial bond stiffness was not affected by load intensity. However, degradation of bond stiffness with increasing load due to internal cracking took place in the RC ties with a small cover/diameter ratio.

Reinforcement effects on the tensile properties of seawater sea-sand engineered cementitious composites reinforced with multi-scale hybrid fibers

The preparation of seawater sea-sand engineered cementitious composites (SS-ECC) holds great potential for development in coastal and marine infrastructure. To improve its compressive strength and tensile properties, this study investigated the crack characteristics, micro-mechanics, fibers reinforcement index, and micro-structure of SS-ECC using a multi-scale hybrid fibers system consisting of CaCO3 whiskers, PE fibers, and stainless steel fibers (SSF). The aim was to gain an in-depth understanding of the reinforcement effects of multi-scale hybrid fibers. The results showed that CaCO3 whiskers increased the number of cracks and the stability of crack evolution in SS-ECC during the ultimate tensile state by bridging the matrix micro-cracks, improving the matrix micro-structure, and filling the interfacial transition zones between the macroscopic fibers (PE fibers and SSF) and the matrix. Additionally, it reduced the crack width and spacing. These combined effects increased the compressive strength, tensile strength, and tensile strain capacity of SS-ECC by 12.8%, 15.7%, and 11.9%, respectively. Finally, the reinforcement effects of multi-scale hybrid fibers were analyzed based on the pseudo-strain hardening performance indices, fibers reinforcement index, and hybrid coefficient. This analysis provides reference and insight for the design of multi-scale hybrid fibers SS-ECC with a high comprehensive performance (σcσtε/w) index.

Behaviour of FRC Beams with Different Combination of Fibers

The use of fibers in reinforced concrete (RC) beams mainly improves both the bearing capacity and the cracking control. In this way, positive effects on the service life of RC structures can be expected. In this paper, the fiber influence on the flexural behaviour of RC beams with different longitudinal reinforcement ratios (0.5% ≤ρs≤ 1.2%) is analyzed by testing small-scale RC beams. Concretes incorporating 0, 25 and 50 kg/m3 of steel, 6 and 12 kg/m3 of glass macro fibers, and 5 and 10 kg/m3 of polymer macro fibers were studied. Crack and deflection control, as well as bearing capacity and crack localization were evaluated for a broad range of fiber-reinforced concrete (FRC) toughness. It is verified that fibers, in the longitudinal reinforcement ratio considered, improve the bending behaviour at serviceability limit state (SLS) and ultimate limit state (ULS) of RC beams, without limiting the structure ductility. It was also confirmed the philosophy of the fib Model Code 2010, such that FRC can be considered as a composite material where performance parameters govern its mechanical behaviour. Finally, the several data available allowed to deeply analyze fib Model Code 2010 formulations (mean crack spacing and flexural bearing capacity) and to propose modifications where needed.

Phase-field simulation and coupled criterion link echelon cracks to internal length in antiplane shear

This paper provides a comprehensive numerical analysis of daughter crack localization in pure antiplane shear. Although antiplane shear fracture is important in various industrial applications, understanding the morphology of the resulting fragmentation remains challenging. The paper develops innovative phase-field models to induce the facets using a small spatial variation in the toughness field and examines the impact of numerical and material parameters on the newly formed daughter cracks’ shape and spacing. Through meticulous comparison to the coupled criterion, the paper reveals a compelling connection between the internal length-scale of damage regularization, Irwin’s length and the facet crack spacing. Furthermore, the effect of Poisson’s ratio on the crack form and spacing is investigated: the results reveal a significant influence and showcase comparable initiation distances between the numerical simulations and experimental measurements in pure antiplane loading.

Flexural and Shear Deformation of Basement-Clamped Reinforced Concrete Shear Walls.

For a precise analysis of buildings under earthquake effects, the load-deformation behaviour of the bracing walls must be comprehensively known. The horizontal bracing walls are often clamped in the basement; however, less attention has been paid to these walls' clamping parts in the past. This study presents three shear wall experiments (NW 1, NW 2, NW 3) with heights up to six meters in a scale of 1:1.5 to the real size. Measured were the force-displacement curve, the curvature distribution over the height, the crack pattern, and the crack opening and spacing. Twelve displacement transducers, an optical measurement system with eight cameras, and a manual crack measurement were utilised. Out of the measurements, the impact of the tension shift effect on the load-displacement curves could be quantified for the cantilever part of the walls. Additionally, it was found out that a sliding failure in the clamping part must be considered if the aspect ratio of H/L is equal to or less than one.

High fatigue performance and microscopic mechanisms of in-situ TiB2/7050Al composite at different temperatures

In this work, the fatigue properties of in-situ TiB2 particle-reinforced 7050 Al-matrix (TiB2/7050Al) composites at room temperature (RM), 100 ℃ and 150 ℃ were studied, respectively, and the microstructure changes, fatigue fracture characteristics and fracture mechanism were analyzed. The results indicate that when the fatigue temperature increased, the amount of S phase precipitation along grain boundaries increases, forming a banded distribution with TiB2 particles near the grain boundary regions. The RM fatigue limit of the composite is high up to 307.5 MPa. Under the same fatigue strength, TiB2/7050 composites can withstand fatigue cycles far greater than 7050Al alloy. With the increase of temperature, the fatigue performance of the composite gradually decreased, and unlike at RM and 100 ℃, the use of Weibull three-parameter model is necessary to obtain a satisfactory S-N curve at 150 ℃. In some locations of the steady-state crack propagation stage, the direction and spacing of fatigue striations were influenced by grain orientation, grain boundaries and TiB2 particle bands. Therefore, the effects of TiB2 particles, grain boundaries, and precipitations on the fatigue processes were analyzed to reveal the strengthening mechanisms of the composite.

Mott waves and fragment size in viscoplastic metals

Previous ductile fragmentation analysis involves unloading wave (Mott wave) propagations in rate-independent rigid-plastic materials. This paper studies the dynamic fragmentations of a rigid-viscoplastic material in which there exists a rigid unloading zone and a viscoplastic unloading zone. A linear diffusion equation incorporating a moving boundary condition for the viscoplastic unloading zone is presented. The fracture process of an isolated crack in the infinite medium, and that of an array of equally spaced cracks, are investigated numerically. The crack array problem reveals an optimal crack spacing upon which the material fails and unloads most rapidly. Based on the 'principle of the rapidest unloading (PRU)', this crack spacing is regarded as the measure of fragment size. Systematic numerical calculations are conducted to obtain the fragment size data as functions of strain rate and viscosity coefficient. A modified Grady-Kipp fragment size formula is proposed to accommodate the viscous effect. In the case of non-viscous material, the formula returns to the classical Grady-Kipp fragment size model. Finite element simulations using rate-dependent constitutive model show similar trend of viscous effect on the fragment sizes, and the modified fragment size formula yields better agreement with the simulated data.

A silicone rubber packaged distributed optical fiber sensing tape for strain-crack monitoring based on OFDR technique

A novel silicone rubber (SR)-packaged distributed optical fiber sensor (DOFS) tape based on optical frequency domain reflectometry (OFDR) technique was developed to effectively monitor substrate cracking. The analytical strain distribution of this sensor tape is derived based on the current strain transfer model and then used to determine the parameter sensitivity to provide a scientific basis for the selection of packing parameters and bond length. A calibration test of the sensor tape on steel plates was performed, and the feasibility of the sensing tape for accurately measuring the substrate strain and crack width was demonstrated. A test is conducted to monitor adjacent double cracks, and the test results show that the sensor tape has the ability to identify crack positions with crack spacings greater than 40 mm. The sensor tape is applied to the monitoring of concrete cracking induced by corrosion, and the test results demonstrate that the DOFS sensing tape has advantages for monitoring large cracks. Both the analytical and experimental results show that the novel SR-packaged DOFS tape is effective and feasible.

Research on the flexural behavior of polypropylene fiber reinforced concrete beams with hybrid reinforcement of GFRP and steel bars

To study the flexural behavior of glass fiber (GFRP) bars and steel bars hybrid reinforced polypropylene fiber concrete (Hybrid-PFRC) beams, one GFRP-PFRC beam, one Steel-PFRC beam, and five Hybrid-PFRC beams were designed and fabricated. The effects of the different area ratio (Af/As\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{A_{f} } \\mathord{\\left/ {\\vphantom {{A_{f} } {A_{s} }}} \\right. \\kern-0pt} {A_{s} }}$$\\end{document}) of GFRP to steel bars and polypropylene fiber (PP) volume fraction on the flexural behavior of Hybrid-PFRC beams were investigated through experiments. The research results indicated that the Hybrid-PFRC beams’ load–deflection curves exhibited trilinear characteristics with specimen cracking and steel bars yielding as turning points. As Af/As\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{A_{f} } \\mathord{\\left/ {\\vphantom {{A_{f} } {A_{s} }}} \\right. \\kern-0pt} {A_{s} }}$$\\end{document} increased, the flexural bearing capacity of Hybrid-PFRC beams increased, the deflection decreased, the crack spacing and width decreased, and the ductility decreased. The addition of PP did not significantly improve the flexural bearing capacity and cracking moment of Hybrid-PFRC beams, but it greatly enhanced the ductility of the beam. Moreover, PP had good advantages in controlling crack propagation in the beam. The article also used the theoretical model to predict and analyze the flexural behavior of Hybrid-PFRC beams. When predicting the maximum crack width of Hybrid-PFRC beams, when PP is not added to the beam, the bonding coefficient kb should be greater than 1.4; When PP is added to the beam, it is recommended that the bonding coefficient kb should not exceed 1.4.

Position‐based fluid simulation for robotic injection sealing of pavement cracks

AbstractAutomated crack sealing could significantly benefit the maintenance of road pavements, but there is difficulty in depositing the correct volume of sealant material into the hidden crack space. A simulated model of the material flow within a crack space would allow the development of a predictive control scheme, such that the repair robot can apply suitable trajectories and operational parameters to accomplish neatly sealed surfaces. For the first time, the position‐based fluid (PBF) method, a computationally cheap and fast but approximate model of fluid flows, is studied for its feasibility for sealant flow simulation in the robotic injection crack sealing scenario. A Real‐to‐Sim experiment is performed, in which a PBF simulation of sealant in a virtual robotic crack sealing environment is mirrored from the physical lab setup. The fluid simulation is tuned to match the real‐world dynamics through comparison with 132 simulation runs, varying the artificial viscosity parameters (fluid–fluid viscous interaction) and (fluid–wall viscous interaction). It was found that had a varied three‐stage influence on the simulation error while 's negative influence on the simulation error only effectively applied to fluids satisfying . Through comparing the physical and virtual crack sealing results, the simulation was validated with an average fluid level error of 1.26 mm along a 3.1 mm wide, 16 mm deep and 80 mm long artificial crack, which shows the usefulness of the PBF method for robotic injection sealing. The accuracy and computational requirements of the PBF method are also discussed.

Tensile damage evolution and mechanical behaviour of SiCf/SiC mini-composites through 4D in-situ micro-CT and data-driven modelling

Damage evolution of SiCf/SiC ceramic matrix mini-composites (CMMCs) was characterised by using a 4D in-situ micro-computed tomography (CT) tensile test and digital volume correlation (DVC) technique. Additionally, a CT damage data-driven shear lag model was developed to predict its tensile stress-strain response. A 4D in-situ X-ray CT tensile test of a unidirectional SiCf/SiC mini-composite was first carried out. Then two ad-hoc deep-learning image segmentation models were developed to automatically identify its microstructure and damages induced by tension, respectively. Damage evolution was quantitively characterised by visualising the initiation and propagation of matrix cracks in three-dimensions (3D). A two-step approach was employed to evaluate its 3D internal strain distributions at various loading levels, which further revealed strain concentrations and helped establishing the tensile stress-strain response of the CMMCs. It was observed that transverse cracking is the predominant damage mode, and the average crack opening displacement increases with loading. A high-fidelity X-ray CT data-driven shear lag model was developed, incorporating inputs of transverse matrix crack spacing calculated by the 4D in-situ CT test data. The predicted stress-strain response showed a good correlation with the experimental results.

Flexural behaviour of post-tensioned precast beams manufactured with basalt-fibre-reinforced recycled concrete–conventional concrete

To promote the sustainable development of the ecological environment, facilitate the recycling of recycled concrete and explore efficient approaches to enhance the performance of structural components, this study proposes a post-tensioned precast beam model manufactured with basalt-fiber-reinforced recycled concrete–conventional concrete. Flexural performance tests were conducted on 12 beams with different concrete strength grades (C40, C50, C60), basalt-fiber-reinforced recycled concrete layer thicknesses (200 mm, 250 mm, 300 mm), and basalt fiber volume fractions (0%, 0.1%, 0.2%). The results show that the incorporation of basalt fiber can effectively inhibit crack development, and improve the stiffness and flexural strength of components. Through theoretical analysis, the factors affecting the ultimate stress formula for high-strength prestressing steel strands are attributed to the comprehensive reinforcement index and prestressed reinforcement index, thereby obtaining a flexural strength formula. Coefficients describing the influences of basalt fiber and recycled coarse aggregate were introduced and combined with average crack spacing and width measurements to derive a post-tensioned precast beam model of average crack spacing and width. Based on the derived calculation model, the average deviation between the tested and calculated results of the ultimate bending moment is less than 6%, and the average deviation between the tested and calculated results of the average crack width is less than 9%. The proposed model has good prediction accuracy for evaluating the flexural strength and average crack width, which provides a theoretical basis for assessing the flexural performance of composite beams.

Simplified Procedure to Determine the Cohesive Material Law of Fiber-Reinforced Cementitious Matrix (FRCM)-Substrate Joints.

Fiber-reinforced cementitious matrix (FRCM) composites have been largely used to strengthen existing concrete and masonry structures in the last decade. To design FRCM-strengthened members, the provisions of the Italian CNR-DT 215 (2018) or the American ACI 549.4R and 6R (2020) guidelines can be adopted. According to the former, the FRCM effective strain, i.e., the composite strain associated with the loss of composite action, can be obtained by combining the results of direct shear tests on FRCM-substrate joints and of tensile tests on the bare reinforcing textile. According to the latter, the effective strain can be obtained by testing FRCM coupons in tension, using the so-called clevis-grip test set-up. However, the complex bond behavior of the FRCM cannot be fully captured by considering only the effective strain. Thus, a cohesive approach has been used to describe the stress transfer between the composite and the substrate and cohesive material laws (CMLs) with different shapes have been proposed. The determination of the CML associated with a specific FRCM-substrate joint is fundamental to capture the behavior of the FRCM-strengthened member and should be determined based on the results of experimental bond tests. In this paper, a procedure previously proposed by the authors to calibrate the CML from the load response obtained by direct shear tests of FRCM-substrate joints is applied to different FRCM composites. Namely, carbon, AR glass, and PBO FRCMs are considered. The results obtained prove that the procedure allows to estimate the CML and to associate the idealized load response of a specific type of FRCM to the corresponding CML. The estimated CML can be used to determine the onset of debonding in FRCM-substrate joints, the crack number and spacing in FRCM coupons, and the locations where debonding occurs in FRCM-strengthened members.

Influence of debonding and substrate plasticity on thin film multicracking

Multicracking of a thin brittle layer deposited on a substrate with an intermetallic layer is studied using finite fracture mechanics. Nonlinear implementation of the coupled criterion is used to predict the initiation and successive subdivisions of a periodic network of cracks considering intermetallic layer plasticity and interface debonding. Plasticity has a moderate influence on the cracking kinetics whereas debonding length has a strong influence on the saturation crack spacing. The cracking kinetics predicted numerically is more abrupt than in experiments because of the periodicity assumption, however crack spacing at saturation similar to those measured experimentally are obtained. The tensile strength and critical energy release rate of the thin brittle layer are determined by inverse identification based on the crack density variation as a function of the imposed loading. The proposed approach also enables the accurate determination of the interface critical energy release rate based on the experimentally measured debonding lengths.

Development of craquelure patterns in paintings on panels

Panel paintings are multi-layer structures composed of humidity-sensitive materials. Preventing or limiting stresses in these structures, generated by the loss or gain of moisture, requires an understanding of the relevant processes and risks. A three-dimensional elastic model of a panel painting was used to analyse surface stresses and understand how crack patterns are developed in the two-layer structure of the pictorial layer—the gesso and the paints. Two historically important paint types were considered—egg tempera and oil paints, laid on a gesso produced following historical procedures. Two scenarios of stress development were analysed: permanent cumulative drying shrinkage of paints or gesso, owing to gradual loss of water or evolution of the molecular composition of the binders, and moisture-induced cyclic swelling of the wood substrate. Ratios of distances between cracks in the tangential and longitudinal directions of a wood panel to the layer thickness were estimated for increasing magnitudes of materials’ dimensional change in the two scenarios. The critical values of the ratios for which stress in the midpoint between the cracks dropped below the value inducing strain at break in the materials and saturation of the crack patterns occurred, was approximately 3–4 or 5–6 for the paints and the gesso, respectively. The critical distance normalized to the gesso thickness between cracks parallel to the wood grain induced by cyclic swelling of the wood substrate due to relative humidity variation in the range of 50–70% was 6. The study demonstrated that crack spacings in the fully developed crack systems remain sensitive only to the thicknesses of paint or gesso layers which, therefore, can be derived from the crack pattern geometry. Existing flaws in gesso were found not to increase the risk of new crack development.