Crack Opening Research Articles

Digital-image Correlation and Cohesive Fracture Analysis of Fibre-reinforced Concrete Experiments: The Sergipe Test

Fibres are added to the concrete mix to improve its tensile strength and fracture properties, and they are used in several engineering applications. Therefore, fracture energy is a well-known quantity worth measuring. Some experiments in the technical literature are designed to quantify fracture energy. This paper proposes a new experiment to analyze the mechanical properties of fibre-reinforced concrete, named the Sergipe test. Such experiment consists of a square hollowed specimen submitted to a flexural test, where tensile cracks appear in different locations. Digital image correlation was used to analyze the cracking behaviour and crack opening displacement (COD). Regarding the experimental results of the Sergipe test, both specimens reached similar force-displacement and force-COD results despite different cracking locations at the specimens’ bottom. Such characteristics might indicate the suitability of the proposed experiment for fracture energy measurement. Regardless, the proposed experiment may be a benchmark for future non-linear models. To analyze such conditions, the well-established cohesive fracture model implemented in ABAQUS® is used to reproduce the experimental observations numerically, achieving good accuracy. Keywords: Cohesive fracture, Digital image correlation, Fracture energy, Fibre-reinforced concrete, Sergipe test.

Numerical Investigation of Fracture Behavior for Glass Fiber Composite Concretes

Waste aggregate-based composite cementitious materials preserve natural resources and reduce environmental concerns throughout green concepts. In this view, recycled waste aggregate-based concrete and its innovative design require advanced computational modeling techniques. Accordingly, this comprehensive and computational research is conducted to investigate the fracture behavior of notched glass fiber reinforced concrete beam modeled with finite element method. The impacts of substitution ratios of the waste on strains and crack opening displacements of validated beam models are investigated and argued.

Automated high-resolution asphalt pavement crack segmentation using deep convolutional neural networks with repeated hierarchical feature fusion

ABSTRACT Automated collection and detection of asphalt pavement crack conditions are essential for evaluating road conditions and maintenance planning. However, determining crack conditions accurately and efficiently has been challenging due to their small object-to-background information ratio, poor contrast with defect-free regions, and vulnerability to noise, such as stains and shadows. We approach this challenge by developing a series of methods that generate high-resolution asphalt pavement crack segmentation, the HRCrack series, which attends to hairline cracks by repeatedly fusing hierarchical features learned using convolutional neural networks. We validated and compared the models with ten widely used models on six open crack datasets. The results demonstrated that our models outperformed the considered methods on the self-made and six open-source datasets. Our best-performing model, HRCrack48, achieved an optimal dataset scale (ODS) F1 score of 0.948 on the self-made dataset. Our smallest model, HRCrack18s, was the fastest (25 FPS) while still providing competitive performance.

Numerical study on the dynamic characteristics of the drive shaft system with diaphragm crack

The diaphragm coupling is widely used in the drive shaft system, which suffer from the crack at the waist of the diaphragm in long-term and high-speed working environments. However, the effect of the diaphragm crack (DC) on the dynamic characteristics of the drive shaft system. To solve the above issues, this paper researched the effect of the DC on the dynamic characteristics of the drive shaft system. The time-varying stiffness of the diaphragm group (DG) with crack was calculated considering friction. The calculation results indicated that the DC causes a decrease in the stiffness of the DG and introduces multiple higher-order harmonic components into the stiffness of the DG. The effect of the DC on the dynamic characteristics of the system was conducted. The accuracy of the system model is verified by comparing the critical speed results of the software and theory. The DC caused 2×, 4× super-harmonic resonance phenomenon. Meanwhile, the frequency-domain response of the system included a significant 2× super-harmonic component and also a significant 4× super-harmonic component at low speed. The super-harmonic components in the system response are introduced by the higher-order harmonic components in the time-varying stiffness of the DG, then leading to the super-harmonic resonance and irregular axis trajectory. The effect of the DC is significantly different from that of the open and breathing cracks in the rotor system. In engineering, it is possible to comprehensively observe the axis trajectory, super-harmonic resonance phenomenon, 2× and 4×super-harmonic components, and the 180° flip of the axis trajectory through the 1/2 first critical speed is used to determine whether the diaphragm has a crack.

Numerical study on the evolution characteristics of contact and fluid flow in shear-induced rough joint

In order to investigate the influence of shear on contact characteristics and fluid flow evolution of rough rock fractures, a series of shear-flow tests were carried out by numerical experiments. Firstly, a sandstone specimen with a rough fracture was made in the laboratory, and the numerical model of the fracture was reconstructed in FLAC3D software. Experiments were conducted to investigate the depth of penetration of the fracture under different normal stress (1, 3, and 5 MPa) and shear displacement (2, 4, 6, 8, and 10 mm). By establishing the relationship between the shear direction and the apparent inclination of the fracture asperity, the effects on the asperity contact characteristics and seepage properties are explored. The results of the study indicated that the larger the normal stress the larger the surface contact section and the smaller the aperture, showing the opposite trend with increasing shear displacement. Positive apparent inclination distribution can effectively predict the location of shear damage during the shear process. Negative apparent dip implies that those regions increase permeability after shear, and decrease with increasing crack opening. Fracture seepage shows obvious nonlinear characteristics, where the nonlinear coefficients are 5–6 orders of magnitude larger than the linear coefficients. The critical Reynolds number Rec is used to distinguish the linear and nonlinear categories of fluid flow, and the calculated results show that the range of Rec is between 0.0081 and 0.11.3, and the Rec increases with shear displacement and decreases with normal stress.

Regularized X‐FEM Modeling of Arbitrary 3D Interacting Crack Networks

ABSTRACTAn extension to the Regularized eXtended Finite Element Method (RX‐FEM) is proposed that allows arbitrary 3D cracks through a novel hierarchical enrichment algorithm. The technique avoids geometric consideration of how a crack cuts elements or intersects other cracks. Each crack is described separately in terms of its sign distance function and regularized step function, which are only recorded for nodes in the region where the gradient of the regularized step function is non‐zero. The algorithm creates a set of superimposed nodes, referred to as node twins, and elements, referred to as twinned elements, for each crack and determines the connectivity of the element twins using the involved crack indices. The displacement jump is calculated between each pair of element twins corresponding to the same crack, and a cohesive zone model (CZM) is formulated for each pair of twins to model crack opening. Following the theory for the novel method, several examples are presented that illustrate capabilities of the new method that the traditional RX‐FEM formulation lacked. A quasi‐2D example of offset crack propagation is considered and successfully compared with published results. Additionally, two 3D examples involving perpendicularly intersecting cracks are considered, illustrating the intersection of two crack fronts and correct partitioning of the domain into eight fragments due to three crossing cracks, respectively.

Features of failure with cleavage after ctod tests of low-carbon microalloyed marine steel S460MLO during crack opening tests

Features of failure with cleavage after ctod tests of low-carbon microalloyed marine steel S460MLO during crack opening tests

Fibre Optic‐Based Patch Sensor for Crack Monitoring in Concrete Structures

ABSTRACTIn the context of the necessity to monitor civil engineering structures for accident prevention, this paper presents the performance of an innovative optical fibre patch sensor that can be embedded or glued on the concrete's surface. The sensor is composed of a fabric comprising an optical fibre network. When employed in concrete structures, it is capable of detecting opening cracks in the order of 0.01 mm, thereby satisfying the regulatory standards for limit states (Eurocode 2). This sensor is capable of accurately tracking the evolution of crack, including cyclic changes, by sensing both the increase and decrease in crack width. The procedure outlined in this paper includes a preliminary investigation into the influence of fibre diameter and density within the patch, which has revealed that fibres of 750 μm in diameter exhibit optimal performance, as well as the attachment method to concrete surfaces. Subsequently, the process of calibration is detailed, followed by numerous laboratory tests that were conducted on reinforced concrete samples of varying sizes. Comparisons and validations of optical fibre patch sensor measurements were performed using digital image correlation, resulting in a sensitivity of the sensors reaching 0.01 mm/K, and an accuracy ranging between 0.1% and 1%. The discussion within this paper considers the installation of this new sensor both externally and internally within real reinforced concrete structures.

Development of the reinforced concrete resistance theory in the zone about reinforcement

The actual problem of resistance of near-reinforcement zone of concrete is solved as a problem of volumetric stress-strain state with "closure" of output integral parameters of this zone on the rod scheme of the whole reinforced concrete element synthesizing hypotheses and dependencies of various disciplines of mechanics of solid deformation body, including fracture mechanics. The calculation model of the reinforced concrete element takes into account the effect of reinforced concrete of prof. Vl.I. Kolchunov describing the mechanism of formation and development of transverse and longitudinal cracks. In this case, generalized hypotheses of linear and angular deformations for warping and gradients of jumps of relative mutual displacements of reinforcement and concrete are adopted. New functionals of reinforced concrete are constructed, which are consistent with the ideas about resistance of crosssections of rod elements in near-reinforcement zones. Physical equations for a concrete matrix modeled between transverse cracks are written. The displacement components for the near-reinforcement area are found in relation to the crack opening width at the boundary of the "concrete-reinforcement" contact in transverse, longitudinal and radial cracks, respectively. The use of the accepted assumptions and multi-level calculation scheme for the near-reinforcement region significantly brings the calculation model closer to a real assessment of physical phenomena.

Experimental Study on the Size Effect of Compression-Shear Fracture Characteristics of Rock-like Materials Containing Open Cracks.

Understanding fracture mechanics in rock-like materials under compression-shear condition is critical for predicting failure mechanisms in various engineering applications, such as mining and civil infrastructure. This study conducted uniaxial compression tests on cubic gypsum specimens of varying sizes (side lengths of 75 mm, 100 mm, 125 mm, and 150 mm) and crack inclination angles (ranging from 0° to 90°) to assess the size effect on fracture behavior. The effects of specimen size and crack inclination on fracture characteristics, including strength, failure mode, and crack initiation angle, were analyzed based on the maximum tangential stress (MTS) criterion and the generalized maximum tangential stress (GMTS) criterion, with relative critical size (α) and relative openness (η). Results indicate that the crack initiation angle increases with crack inclination, while compressive strength decreases significantly with increasing specimen size. For example, at a 30° crack inclination, the peak compressive strength of 75 mm specimens was 2.53 MPa, whereas that of 150 mm specimens decreased to 1.05 MPa. Crack type and failure mode were found to be primarily influenced by crack inclination rather than specimen size. The experimental crack initiation angle aligned with the theoretical crack initiation angle at inclinations below 50° but diverged at higher inclinations. A linear relationship was established between rc and specimen size (L) under compression-shear stress, expressed as rc=-0.01772L+3.54648; larger specimens exhibited increased tangential stress at the crack tip, leading to earlier macroscopic crack formation, while rc decreased as specimen size increased. These results underscore the significant influence of size on fracture behavior in quasi-brittle materials under compression-shear stress, providing essential insights for predicting material failure in rock-like structures.

The seismic signature and geothermal potential of the Schwechat Depression in the Vienna Basin, Austria, from ambient noise tomography

The Schwechat depression, in the Vienna Basin (VB) is currently the main target area for deep geothermal exploration in eastern Austria. Knowledge of the subsurface heavily relies on active seismic reflection profiling experiments that are expensive and logistically demanding. Affordable geophysical prospecting methods are needed to reduce subsurface uncertainty over large spatial areas. Over recent years, seismic ambient noise tomography (ANT) has proven to be a cost-effective and environment-friendly exploration technique fulfilling this need. Here, we present an ANT study of the central Vienna Basin revealing the shear-wave velocity, and shear-wave radial anisotropy structure down to 5 km beneath the surface. We deployed an array of 100 seismic nodal instruments during 5 weeks over summer 2023. We measured fundamental-mode Rayleigh and Love-wave group velocity dispersion from seismic noise correlations, and employed transdimensional Bayesian tomography to invert for isotropic Rayleigh and Love group velocity maps at periods ranging from 0.8 to 5.5 s. We then extracted Rayleigh and Love group velocity dispersion curves from the maps at all locations, and jointly inverted them for shear-wave velocity and radial anisotropy as a function of depth using a transdimensional Bayesian framework.Our shear-wave velocity model reveals a basin-like low-velocity feature, interpreted as the seismic signature of the Schwechat depression. Another low-velocity feature is observed beneath the city of Vienna, which could be of great interest for geothermal exploration. The shear-wave velocity radial anisotropy structure indicates a thin negative anisotropy layer in the top 150 meters, likely associated with water-saturated open cracks. Between 150 meters and 1.5 km depth, we observe widespread positive radial anisotropy across the entire study area, corresponding to sub-horizontal layering within the Neogene basin. At greater depths, the Schwechat depression is characterized by positive radial anisotropy, while the edges of the Schwechat depression exhibit negative radial anisotropy due to steeply dipping strata and normal faults responsible for the formation of this major depocenter in the Vienna Basin.

Flexural tensile behaviour of alkali-activated slag-based concrete and Portland cement-based concrete incorporating single and multiple hooked-end steel fibres

In this study, three-point bending tests on notched beams according to EN 14651 have been performed to evaluate the flexural post-cracking behaviour of alkali-activated slag-based concrete (AASC) and Portland cement-based concrete (PCC) incorporating single (3D) and multiple (4D, 5D) hooked-end steel fibres in different volume fractions up to 0.75%. According to the experimental results, the post-cracking residual flexural strength increases with the increase in the fibre volume fraction for each fibre and concrete matrix type. AASC mixes incorporating 3D and 4D fibres show higher values of residual flexural strength for the same crack opening than PCC mixes with the same fibre type and dosage. Only for the mixes incorporating 5D fibres, steel fibre-reinforced PCC (SFRPCC) mixes outperform steel fibre-reinforced AASC (SFRAASC) mixes in terms of post-cracking behaviour. According to EN 14651, the values of the residual strengths and , corresponding to a crack mouth opening displacement (CMOD) of 0.5 mm and 2.5 mm, respectively, and their corresponding characteristic values and , respectively, can be derived from the experimental load-CMOD curves. Following the fib Model Code 2020, each mix can then be classified according to the values of and the ratio. As a result, empirical models have been developed for SFRPCC to predict the values of and and the applicability of such models to SFRAASC is evaluated in this study. Once the values of and are known, tensile constitutive models can be derived according to the fib Model Code 2020 and used as input parameters for finite element modelling. In this study, the accuracy of the code-based constitutive model to predict the flexural behaviour of SFRAASC and SFRPCC is evaluated using the concrete damage plasticity (CDP) model available in ABAQUS. The numerical model based on the tensile stress-strain curve in the fib Model Code 2020 can qualitatively capture the post-cracking behaviour of SFRAASC and SFRPCC incorporating 3D, 4D and 5D at 0.25% fibre volume fraction, despite overestimating their tensile strength. For higher fibre volume fractions, the CDP model, in conjunction with the mode I parameters derived from the fib Model Code 2020, is unable to adequately describe the post-hardening behaviour exhibited by the composites.

In-situ formation of molybdenum disulfide nanoparticle and its catalytic performance in heavy oil long-term aquathermolysis

Heavy oil is an important unconventional petroleum resource due to its abundant reserve, but the reduction of viscosity is a prerequisite for its effective exploitation. Researchers are trying to develop heavy oil catalytic aquathermolysis technologies for their merit of irreversible viscosity reduction through in-situ upgrading. The key point of catalytic aquathermolysis is the in-situ formation of high active catalytic phase. In this study, we have demonstrated that the precursor (NH4)2MoS4 was fully decomposed into MoS2 nanoparticles at relatively low temperature of 200°C after 90 minutes. The decomposition of (NH4)2MoS4 in aquathermolysis was significantly different from its decomposition process under hydrogen and vacuum atmospheres. The laboratory experimental results showed that the heavy oil viscosity reduction rate was above 85 % with the action of in- situ formed MoS2 nanoparticles after aquathermolysis. The sulfur content of heavy oil and asphaltene, asphaltenes and aromatics contents of heavy oil were decreased significantly, indicating that the cracking and ring opening reactions did take place. In the oilfield experiment, the precursor (NH4)2MoS4 was injected into the reservoir along with steam. After one-time injection, the catalytic effect could be sustained for at least four months. The maximum viscosity reduction rate was as high as 90 % during the first week, and still around 70 % in the 4th month. The molecular structural analysis of the produced heavy oil proved that the asphaltenes has been effectively cracked during the in-situ catalytic aquathermolysis. Both the laboratory and oilfield experimental results demonstrated that (NH4)2MoS4 precursor could form MoS2 nanoparticle and effectively catalyze the upgrading reactions of heavy oil. We hope that this study will provide a new catalyst development strategy for the catalytic aquathermolysis exploitation technology of heavy oil.

Tensile Fracture Initiation and Propagation of Granite and Gneiss at Wedge Splitting Tests: Part 2—Fracturing Studies Based on Digital Image Correlation and Thin Section Analysis

AbstractThe crack development in quasi-brittle granite and brittle gneiss under mode I loading condition was monitored using digital image correlation (DIC) technique during wedge splitting tests. The cracking behavior was studied on granite specimens that were split in one material direction, perpendicular to the rift plane, and gneiss specimens that were split in three different material directions, parallel and perpendicular to the foliation (along and across a lineation). The granite specimens had a saw cut 5 mm-wide notch and a blunt round notch in form of a 32 mm borehole. The gneiss specimens had a saw cut notch. The results from the DIC measurements revealed a meandering and branching crack path for the granite, whereas a smoother crack path for the gneiss with almost no branching. This behavior was confirmed by microscopy images from thin sections taken from specimens after testing. The thin sections showed that the fractures were prone to propagate across grains in the more coarse-grained granite than in the fine-grained gneiss, where the fractures propagated almost entirely along grain boundaries. The crack initiation occurred mainly in the corner of the saw cut notches and centrally in the round notch. However, the initiation locations in the granite were affected by the medium- to coarse-grained microstructure with grains preventing initiation and propagation which yielded displaced positions out from the ideal ones with respect to the highest stress in some cases. The crack opening displacement was determined along the crack path from the DIC measurements at 12 stages on each specimen of the advancing crack during the splitting progress. The critical crack opening displacement and length of the fracture process zone were assessed and the crack front position yielding the crack length along the tests was determined. The results showed a critical crack length when the deformations in the ligament (also called plastic hinge) affected the cracking process. The average crack velocity in gneiss during the test was more than twice as high as in the granite. This is attributed to a combined effect of the higher brittleness in the gneiss and the effect of a too large elastic energy in the specimen and test setup in relation to the dissipated fracture energy which made the initial crack propagation in the gneiss specimens nearly unstable. The strain energy release rate was calculated along the crack propagation and showed a lower value when the crack lengths were less than 40–60 mm. The calculation of the strain energy release rate was made on crack length measurements from DIC results. The results from the investigation were discussed in relation to the few other similar results found in the literature. The findings give an insight and understanding of the cracking process via both qualitative and quantitative results. Several used methods were novel or not used together in a single study as in this one.

Purification of Vein Quartz Using a New Fluorine-Free Flotation: A Case from Southern Anhui Province, China

High-purity quartz is an emerging strategic material that has been extensively used in the semiconductor and photovoltaic fields. Taking vein quartz from southern Anhui Province as an example, raw materials were processed by ultrasonic scrubbing-desliming, magnetic separation, flotation, high-temperature calcination, water quenching, hot-press acid leaching, and deionized water cleaning to prepare high-purity quartz sand. At the same time, the microscopic structure, inclusions, phase, mineral morphology, water content in inclusions, and trace impurities of the gangue samples were analyzed using an optical microscope, a laser Raman spectrometer, an X-ray diffractometer, a scanning electron microscope, an infrared spectrum analyzer, and an inductively coupled plasma mass spectrometer. The results showed that feldspar and muscovite were the main impurities. After purification, the total amount of 13 impurities in quartz sand was reduced to 28.66 μg/g, and the contents of the main impurity elements Al, Na, and Fe were 12.81 μg/g, 12.80 μg/g, and 0.52 μg/g, respectively. The mass fraction of SiO2 increased from 99.06% to 99.9972%. This shows that flotation, high-temperature calcination, and hot-pressing acid leaching are the keys to obtaining high-purity quartz sand. Fluoride-free flotation with the new collector XK02 can effectively realize the deep separation of quartz and mineral impurities. High-temperature calcination can form more cracks on the surface of quartz sand particles, and the mixed acid enters the open crack channels to effectively remove impurities from the inclusions. This method provides technical support for the preparation of high-purity quartz sand with high value and for the efficient utilization of quartz ore.

An analytical model based on cross-sectional geometric characteristics for calculating crack opening displacement in reinforced concrete beams

To accurately calculate crack opening displacement (COD) in reinforced concrete beams, this study establishes a relationship between COD, cross-sectional rotation, and strain distribution by utilizing the geometric relationships of deformation in the cracked region. Based on the varying bond characteristics between the reinforcement and concrete, a method is developed to calculate COD by analyzing the nonlinear strain distribution in both materials and determining the sectional rotation of the cracked beam. This proposed method was validated through experimental tests on a cracked reinforced concrete beam model. The results indicate that, as the load increases, the bond stiffness between the reinforcement and concrete diminishes, leading to nonlinear changes in the tensile strain of the reinforcement. This results in an increasing slope of the crack opening displacement with increasing load, showing a clear nonlinear trend, even under small loads. However, a linear relationship is observed between crack opening displacement and structural deflection. The proposed method, based on the geometric relationship of sectional deformation, accurately predicts these nonlinear deformations, offering a novel approach for calculating crack opening displacements.

Evaluation of the stress-strain state of the RC beam with the use of DIC

Abstract The article presents the results of adapting the digital image correlation method for the possibility of diagnosing reinforced concrete structures. Reinforced concrete (RC) bending elements are the most widely used in construction practice, which determines the importance of reliable estimation of their stress-strain state. The purpose of this study includes reliable theoretical and experimental investigation of the strength and deformability parameters of the RC beam. The experimental study was conducted using digital image correlation and sub-micron contactless gauges. Experimental data was verified with the calculation of the stress-strain state of the RC beam according to DBN V.2.6-98:2009 and Eurocode 2 and the finite-element modelling (FEM). As a result, the values of deflections, concrete and rebar strains were obtained and presented as corresponding diagrams. The results of all the methods are within the same ranges. Also, the form and character of corresponding diagrams are very similar. The indicated deviations were within acceptable limits. It was noted that the theoretical calculation generally provides lower strain values, which is a satisfactory result, as it indicates the bearing capacity reserves provided by the current regulations. The propagation of cracks was monitored during the experiment and the measured cracks opening was compared with theoretical assumptions. Theoretical values are higher than experimental, which shows certain conservativity of valid normative regulations. The experimental and theoretical results were in good correspondence, which confirms their reliability. It was concluded, that the proposed in the study complex theoretic-experimental approach provides essential information about the strength and deformability of the structure.

Interaction mechanism of radial collinear cracks on a high-speed train brake disc

This article focuses on the problem of multiple crack damage in brake discs. Using the extended finite element analysis method, the interaction mechanism between radially collinear multiple cracks in brake discs is analyzed, and the influence of crack spacing and length ratio on the propagation behavior of multiple cracks is further investigated. The results indicate that the interaction mechanism between multiple radial collinear cracks on the brake disc is complex, not only influenced by the crack spacing and crack length ratio but also related to the location of the cracks on the brake disc. The interaction of radial collinear cracks on the brake disc is mainly concentrated in the stress field at the vicinity of the adjacent tips between the cracks and has little effect on the crack opening displacement field. When the distance between cracks is less than half the length of the crack of interest, the two collinear radial cracks have a significant mutual influence and tend to merge into a longer crack. The length ratio between cracks has a significant impact on the stress transmission path around the cracks, and increasing the length ratio accelerates the crack-to-crack coalescence.

Plasticity-induced crack closure identification during fatigue crack growth in AA2024-T3 by using high-resolution digital image correlation

Fatigue crack growth in ductile materials is primarily driven by the interaction between damaging and shielding mechanisms. In the Paris regime, the predominant mechanism for retardation is plasticity-induced crack closure (PICC). However, some of the mechanisms behind this phenomenon are still unclear. Identifying and separating the three-dimensional aspect from other shielding aspects during experiments is extremely complex. In this paper, we analyze the crack opening kinematics based on local crack opening displacement measurements in both 2D high-resolution digital image correlation data and 3D finite element simulations. The results confirm that the crack opening stress intensity factor Kop differs along the crack path. we present a new method to determine Kop at the crack front allowing to identify PICC as the predominant shielding mechanism in fatigue crack growth experiments. Furthermore, this work contributes to the discussion on the damage-reducing effect of PICC, since we find that the influence on fatigue damage in the plastic zone remains negligible when the crack is closed and crack surface contact is directed towards the surface.

COD and CSD based model for in-plane stiffness of symmetric laminates with cracks in plies and local delaminations: Analysis of crack face sliding

In-plane thermo-elastic constants of symmetric damaged laminates containing transverse cracks in plies and local delaminations starting from crack tip are predicted using a crack opening (COD) and crack sliding displacement (CSD) based approach. An exact elastic analysis shows that the displacement gap on the delamination crack surfaces does not enter the stiffness expressions explicitly. The delamination affects the stiffness via larger COD and CSD of the intralaminar crack. This means that the same expressions for cracked laminates with and without delaminations can be used but with different expressions for COD and CSD. Finite element method is used to analyze the CSD dependence on delamination length and crack density. The obtained approximative expressions for CSD are in a good agreement with FEM. It is shown that in cases when it depends on CSD only, the predicted shear modulus of laminates is in an excellent agreement with direct FEM calculations. The used homogenization over couples of off-axis plies (monoclinic materials) in CSD expressions for balanced laminates is validated.