Maximum Principal Tensile Stress Research Articles

Mechanisms for the control of the complex propagation behaviour of hydraulic fractures in shale

The complex propagation behaviours of hydraulic fracture (HF) at bedding planes (BPs) and the produced complicated fracture geometry are essential to enhance the production of shale gas reservoirs. To better understand the complex propagation behaviour of HF at BPs with different bond strengths, the propagation behaviour, including arrest, crossing, and deviation, was identified first from post-fracturing shale specimens. The discontinuous stress and displacement fields on both sides of a BP ahead of an HF were then determined using the numerical simulation method. Finally, three mechanisms—principal stress jump, Cook–Gordon debonding or Poisson effect, and elastic dissimilarity—were explored in detail to interpret the complex propagation behaviour. The results revealed that HF is arrested/deviated only at extremely weakly cemented or fully opened BPs, whereas HF crosses strongly cemented BPs. The high heterogeneity of the BPs in cementing strength is responsible for the complex propagation behaviour of HF. The principal stress jump at a BP is caused by the difference in stiffness between the BP and the rock matrix. The maximum tensile principal stress ahead of the HF cannot be transmitted across the weakly cemented or fully opened BPs, suggesting that the HF cannot cross BPs. The principal stresses may rotate at a weakly cemented BP, and the rotated principal stresses tend to terminate or deviate an HF. Because of Cook–Gordon debonding and the Poisson effect, if a weakly cemented BP is present and is roughly normal to an advancing HF, the BP may break at some distance ahead of the fracture tip and induce a secondary fracture along the BP. The HF then reaches the opened BP and deviates towards the BP. The propagation process of L- or T-shaped fractures can be interpreted both by the Cook–Gordon debonding and Poisson effect from the viewpoints of stress and displacement. The three mechanisms often operate together when an HF deviates towards a weak BP; while for a special case, there may be only one dominant mechanism.

Finite Element Analysis of the Cutting Balloon With an Adequate Balloon-to-Artery Ratio for Fracturing Calcification While Preventing Perforation

Background: The appropriate balloon-to-artery ratio (BAR) for cutting balloons (CBs), to expand calcified lesions without increasing the risk of coronary artery perforation is unknown. This study investigated the effects of BAR on stress levels in the calcification and at the borders of the coronary artery adjacent to the calcification to determine an appropriate BAR.Methods and Results: A custom-designed folding process of the CB model was developed. The CB models were deployed in a coronary artery model with a reference diameter of 3.0 mm, length of 24 mm, and wall thickness of 0.8 mm equipped with a 50% diameter stenotic, 360° concentric, 400-µm, and 5-mm-long calcification. Finite element analysis of the expansion of CBs with diameters increasing from 2.0 to 3.0 mm in 0.25-mm increments, corresponding to BARs from 0.67 : 1 to 1 : 1, was conducted with pressures up to 12 atm. Decreasing the CB by 0.25 and 0.5 mm (relative to the reference diameter of 3 mm) preserved maximum principal tensile stress levels comparable to that of a CB with a BAR of 1 : 1 while distinctly reducing the stress at the border of the artery adjacent and calcification.Conclusions: Selecting a CB that is 0.25 or 0.5 mm lower than the 3-mm reference diameter may be the first choice to effectively fracture calcifications without increasing the risk of severe artery dissection and perforation.

Effect of Thermal Parameters on Hydration Heat Temperature and Thermal Stress of Mass Concrete

To explore the influence of concrete thermal parameters on the hydration heat temperature and thermal stress of mass concrete, four feature positions of a dam foundation were chosen to analyze the changing process of temperature and stress by varying the thermal parameters, including the thermal conductivity, specific heat, surface heat diffusion coefficient, temperature rise coefficient, solar absorption coefficient, and thermal expansion coefficient. Some conclusions were obtained as follows. Increasing the thermal conductivity and reducing the specific heat and temperature rise coefficient of concrete can effectively reduce the maximum temperature of the central concrete structure. Increasing the solar absorption coefficient, specific heat, and thermal expansion coefficient and reducing the thermal conductivity, surface heat diffusion coefficient, and temperature rise coefficient of concrete can reduce the maximum principal tensile stress in the structure to a certain extent. The maximum principal tensile stress at different positions of the structure has a linear functional relationship with the thermal conductivity, specific heat, and thermal expansion coefficient and has a quadratic function relationship with the surface heat diffusion coefficient, temperature rise coefficient, and solar absorption coefficient. Besides, this study also proposed a series of related anticracking measures. This study was expected to provide a theoretical reference for the design, construction, and cracking disease prevention of mass concrete structures.

Study on the subsurface damage mechanism of optical quartz glass during single grain scratching

The single grain scratching SPH simulation model was established to study the subsurface damage of optical quartz glass. Based on the analysis of the stress, strain and scratching force during scratching, the generation and propagation of subsurface cracks were studied by combining with the scratch elastic stress field model. The simulation results show that the cracks generate firstly at the elastic-plastic deformation boundary in front of the grain (φ = 28°) due to the influence of the maximum principal tensile stress. During the scratching process, the median crack closes to form the subsurface damage by extending downward, the lateral crack promotes the brittle removal of the material by extending upward to the free surface, and microcracks remain in the elastic-plastic boundary at the bottom of the scratch after scratching. The depth of subsurface crack and plastic deformation increases with rising scratching depth. The increase of scratching speed leads to the greater dynamic fracture toughness, accompanied by a significant decrease of the maximum depth of subsurface crack and the number of subsurface cracks. The subsurface residual stress is concentrated at the bottom of the scratch, and the residual stress on both sides of the scratch surface would generate and propogate the Hertz crack. When the scratching depth is less than 1.5 μm or the scratching speed is greater than 75 m/s, the residual stress value and the depth of residual stress are relatively small. Finally, the scratching experiment was carried out. The simulation analysis is verified to be correct, as the generation and propagation of the cracks in the scratching experiment are consistent with the simulation analysis and the experimental scratching force indicates the same variation tendency with the simulation scratching force. The research results in this paper could help to restrain the subsurface damage in grinding process.

Stresses State and Mechanical Behaviors of the Green Body During Die Compaction and Ejection Process

Finite element simulations for metal powder compaction of a clutch plate were performed to examine the stresses during compaction, unloading, and ejection. To describe the mechanical behavior of compacted green body, a modified density-dependent Drucker–Prager Cap model was utilized to predict the stress and density distribution of the compacted clutch plate during loading and ejection stages. The results indicate that maximum tensile principal stress was a main driving force for the tensile crack initiation during ejection stage, and shear stress may be another driving force in both compaction and ejection stages for shear crack initiation. There were peak value of the stresses during ejection stage, and the stresses are in compressive state only during compaction stage. Therefore, the tensile crack initiation is not possible during compaction except shear crack. Hoop stress in the clutch plate is of less contribution to the crack initiation during compaction, unloading and ejection. Study of criteria of the crack initiation and fracture is necessary in order to obtain uniform density and crack-free components in the manufacturing of metal powder compaction.

Evaluation of Stress Distribution in Tooth-Supported Fixed Dental Prostheses Made of Translucent Zirconia with Variations in Framework Designs: A Three-Dimensional Finite Element Analysis.

To evaluate the influence of the framework designs on the stress distribution within tooth-supported partially veneered fixed dental prostheses (FDPs) made of translucent zirconia under simulated loads using a three-dimensional finite element analysis (3D-FEA). For a linear 3D-FEA, simplified 3D solid models of prepared abutment teeth (first premolar and first molar) with different 3-unit FDPs were created. The models with different FDP designs-monolithic zirconia (control); semi-monolithic zirconia with 0.3 mm veneer thickness (SM0.3); semi-monolithic zirconia with 0.5 mm veneer thickness (SM0.5); semi-monolithic zirconia with 0.5 mm veneer thickness supported with cap design (SMC), and semi-monolithic zirconia with 0.5 mm veneer thickness supported with wave design (SMW)-were analyzed using 3D-FEA. The elastic properties of the components (bone, dentine, cement, translucent zirconia, and veneering porcelain) were obtained from the published data for FEA. Simulated static loading forces (300 N) were applied at 10° oblique direction over six points in the occlusal surfaces of the FDPs. Maximum principal stress, shear stress, and safety factor were calculated and analyzed among the different models. Semi-monolithic with cap design showed the smallest maximum principal stress levels in the veneering porcelain compared to all other models (SM0.3, SM0.5, SMW). The SM0.3 had lower maximum principal stress levels in the veneering porcelain compared to SM0.5. Regarding stresses in the zirconia framework, all models had comparable results in maximum principal tensile stresses, except SMW had a lower value. Maximum principal stress levels were located in the veneer component of SM0.3, SM0.5, and SMW, whereas, such levels were observed in the cervical areas of the zirconia frameworks of SMC and control. The SM0.3 had the highest maximum shear stress levels at the zirconia-veneer interface, while SMW had the lowest shear values. The 3D-FEA models with different FDP designs showed different minimum safety factor levels. Framework and veneer designs play a significant role in the stress distribution of the partially veneered zirconia FDPs under loading. The FDPs with zirconia frameworks with cap design minimize the maximum principal tensile stress in the veneering porcelain. The FDPs with 0.3-mm-veneering porcelain show low maximum principal tensile stress in the veneering porcelain, but highest maximum shear stress at the zirconia-veneer interface. The FDPs with wave design of zirconia frameworks minimize the maximum shear stress considerably.

The Effect of Shear Sliding of Vertical Contraction Joints on Seismic Response of High Arch Dams with Fine Finite Element Model

The contraction joints of arch dams with and without shear keys are simplified to be with no‐slip condition and with relative sliding condition, respectively. Based on the Lagrange multiplier method, a contact model considering the manner of independent cantilever dead load type with no‐slip condition and relative sliding condition is proposed to model the nonlinearities of vertical contraction joins, which is special to the nonlinear analysis of arch dams considering the manner of dead load type. Different from the conventional Gauss iterative method, the strategy of the alternating iterative solution of normal force and tangential force is employed. The parallelization based on overlapping domain decomposition method (ODDM) and explicit message passing using distributed memory parallel computers is employed to improve the computational efficiency. An existing high arch dam with fine finite element model is analyzed to investigate the effect of shear sliding of vertical joints on seismic response of the arch dam. The result shows that the values of maximum principal tensile stress under relative sliding condition are significantly greater than those under no‐slip condition.

Multi-criteria shape optimization of open-spandrel concrete arch bridges: Pareto front development and decision-making

PurposeThis paper aims to study the shape of the concrete arched bridge by particle swarm optimization algorithm.Design/methodology/approachFinite element model of open-spandrel concrete arch bridges was constructed using a number of parameters. Design variables of optimization problem include height of skewback abutment, height of arch crown, position of crown with respect to global axes and left and right radius of up and down arches. After parametric modeling of bridge geometry and application of multi-objective particle swarm optimization, the shape optimization of bridge arch was determined. The concrete volume used in bridge substructure construction and maximum principal tensile stress of concrete arch body was adopted as two objective functions in this study. The optimization problem aims to minimize the two objective functions. Geometric and stress constraints are also included in the problem.FindingsBased on the results presented in the paper, the Pareto front is generated which helps the decision-maker or designer to pick the compromise solution from among 20 optimum designs according to their subjective preferences or engineering judgment, respectively. Moreover, to help the decision-maker, the two multiple objective decision-making methods were used for selection of the best solution from among nondominated solutions.Originality/valueThis research aims to solve an interesting optimization problem in structural engineering. Optimization of arch bridges structure was done for reducing construction costs and increasing safety for the first time.

Study on the composite mechanism of large Rubber-Sleeved Stud connector

Abstract The Ordinary Headed Stud (OHS) connector whose diameter is 25 mm or larger is regarded as the large OHS connector, which possesses greater shear stiffness and ultimate capacity. Therefore, it is expected that the required number of OHS connectors can be reduced by applying the large OHS connectors in the steel-concrete interface, which have its construction advantages over smaller ones. However, the great stiffness could also cause the shear force of the large OHS connector at the interface edge exceeding the design allowable value. Hence, the large Rubber-sleeved Stud (RSS) connector was proposed by wrapping rubber sleeve at the root of large OHS connector to decrease its stiffness, making the shear force in the steel-concrete interface more evenly distributed. In this study, push-out tests and numerical simulation were carried out to reveal the composite mechanism of the large RSS connector. Based on the verified modeling method, parametric analysis was performed to investigate the influence of different parameters on the shear stiffness of RSS connectors. The results show that the shear stiffness of large RSS connector is decreased to 41.5% of the large OHS connector. RSS connectors exhibit better deformation recovery and accumulation compared with OHS connectors under cyclic loading. Furthermore, the maximum principal tensile stress of concrete could be decreased and concrete damaged areas are reduced when the large OHS connectors are wrapped with rubber sleeves. The shear stiffness of RSS connector is positively related to the rubber shearing coefficient C10 and concrete compressive strength fcm while negatively related to the rubber sleeve thickness tr, rubber sleeve height hr and rubber compressibility coefficient D1.

Investigations on web-shear behavior of deep precast, prestressed concrete hollow core slabs

Shear tests were conducted on four precast, prestressed concrete hollow core (PCHC) slabs with depths ranging from 320 mm to 500 mm, resulting in two distinct modes of failure, i.e., web-shear and flexural-shear. Shear strength results of the specimens obtained from the experimental program were compared to those predicted by EN 1168 and ACI 318-14. The comparisons showed that in some instances, these codes overpredict shear capacity of the tested specimens. Furthermore, an finite element (FE) model aimed to simulate web-shear responses of PCHC slabs was developed using Abaqus/Explicit (2014). Concrete Damage Plasticity model (CDP model) was employed to model nonlinear behavior of concrete. The sensitivity of the numerical analyses was calibrated against four plastic parameters in the CDP model. The calibrations showed that web-shear behavior of PCHC slabs is not sensitive to three out of the four plastic parameters. However, the last parameter, dilation angle, significantly affects the predicted failure loads. The validity of the developed FE model was verified by 2 shear tests in the experimental program and another 8 shear tests from the literature. Parametric studies based on the verified model were then performed. The influence of design variables including concrete strength, slab geometry, and level of prestressing force, on web-shear behavior of PCHC slabs was examined. The parametric studies showed that concrete strength plays a dominant role in the web-shear performance. However, the choice of angular or smoother-surface void shapes does not lead to a noticeable difference in web-shear capacity. Besides, web-shear strength increases with web thickness. Most importantly, a high level of prestressing force increases additional shear stresses in concrete webs due to changes in strand stress within the transmission length region. In addition, it leads to higher compressive forces in concrete diagonal struts. The presence of such a higher compression force reduces the resistance in tension of concrete webs in the direction of maximum principal tensile stress. As a result, the web-shear strength of PCHC slabs decreases with increasing prestressing force.

Local Tensile Stress in the Development of Posttraumatic Osteoarthritis.

The pathogenesis of posttraumatic osteoarthritis (PTOA) remains unrevealed. We speculate that cartilage crack caused by joint trauma will induce local abnormal tensile stress, leading to change in extracellular matrix (ECM) expression of chondrocytes, cartilage degeneration, and initiation of osteoarthritis. Finite element model was used to examine whether the local tensile stress could be produced around the crack. Cell experiments were conducted to test the effect of tensile strain on chondrocyte ECM expression. Animal tests in rabbits were carried out to examine the change around the cartilage crack. The results indicated that the local tensile stress was generated around the crack and varied with the crack angles. The maximum principal tensile stress was 0.59 MPa around the 45° crack, and no tensile stress was found at 90°. 10% tensile strain could significantly promote type I collagen mRNA expression and inhibit type II collagen and aggrecan (the proteoglycan core protein) mRNA expression. Type I collagen was detected around the 45° crack region in the cartilage with no change in type II collagen and proteoglycan. We conclude that the local tensile stress produced around the cartilage crack can cause the change in cartilage matrix expression which might lead to cartilage degeneration and initiation of osteoarthritis. This study provides biomechanical-based insight into the pathogenesis of PTOA and potentially new intervention in prevention and treatment of PTOA.

On modeling fracture of ferritic steels due to hydrogen embrittlement

Experimental studies in the literature show that the fracture of ferritic steels in the presence of hydrogen occurs primarily perpendicular to the direction of the maximum principal tensile stress, is transgranular in nature, and has fracture surfaces which show “quasi-cleavage” features. Such features are cleavage-like but not along any known cleavage plane or grain boundaries. While the precise micromechanisms which lead to a transition from regular plastic deformation of the steel to “quasi-brittle” fracture are at present unclear, in this paper we have formulated a continuum theory for the diffusion of hydrogen coupled with the elastic-viscoplastic response of metals, together with a simple model which leads to quasi-brittle fracture in the presence of hydrogen. We assume that when an internal variable φ of the theory reaches a critical value φcr, then the inelastic deformation transitions from (a) a volume-preserving plastic stretching which occurs in the direction of the stress deviator — as in standard Mises-type plasticity, to (b) a different form of inelastic stretching which occurs in the direction of the maximum principal stress, and which is dilational in nature. We call this latter form of inelastic deformation craze inelasticity. We view the strain produced due to crazing as a “quasi-brittle” form of inelastic deformation. We allow only a small amount of inelastic craze-strain before the process of craze-breakdown and fracture sets in. To model craze-breakdown we introduce a damage variable d∈[0,1]; if d=0 at a point then that point is intact, while if d=1 at some point then that point is fractured. With the aim of “regularizing” the strain-softening behavior during craze-breakdown, and to avoid mesh-dependency related issues during finite element simulations, we develop a damage theory which depends not only on d but also its gradient ∇d, which is considered to be a measure of the spatial inhomogeneity of the damage during the craze-breakdown process. We have numerically implemented our coupled diffusion-deformation-damage theory in a finite element program, and we present representative numerical examples which show the ability of the simulation capability to qualitatively replicate the process of fracture due to hydrogen embrittlement in some technically relevant geometries.

Crevasses as Indicators of Surge Dynamics in the Bering Bagley Glacier System, Alaska: Numerical Experiments and Comparison to Image Data Analysis

One of the largest sources of uncertainty in sea level rise prediction is glacial acceleration, of which the surge phenomenon is the least understood type. The surge of the Bering Bagley Glacier System (BBGS), Alaska, in 2011–2013 has provided a rare opportunity to study the surge phenomenon in a large and complex glacier system. A surge results in widespread crevassing throughout the glacier system complicating many traditional techniques used to study glacier dynamics. In this paper, we utilize crevassing as a means to investigate the recent BBGS surge through numerical modeling and geostatistical data analysis. Following the principles of structural glaciology, image‐based crevasse characterizations are obtained through geostatistical methods applied to Landsat‐7 data, supplemented by airborne field observations. On the modeling side, a 3‐D full‐Stokes finite element model of the BBGS is developed and applied to investigate ice dynamics and surface structures during the recent surge. A von Mises criterion is adopted to simulate crevassing at the glacier surface, oriented along the axes of maximum principal tensile stress. To facilitate evaluation of model‐ and data‐derived crevasse characteristics, three different comparison methods are introduced. General agreement in the model‐data comparisons indicates that the model has the ability to represent the BBGS system during peak acceleration. The crevasse‐based approach is also employed to optimize the basal sliding parameter and the von Mises stress threshold in the model. Results further indicate that bed topography is an important constraint in modeling the surge process.

Effects of Crack Surface Diffusion on Central Crack Evolution in Active Particle of Li-Ion Batteries

The active particle fracture is one of the major reasons for capacity fading in lithium ion batteries (LIBs). In this study, a model that couples Li-ion diffusion, stress evolution, and extended finite element method (X-FEM) is proposed to investigate the effects of central crack surface diffusion (CSD) in active particle. The different initial central crack length is adopted to simulate the crack evolution. The simulation results show the fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. When the influence of CSD is considered, the maximum principal tensile stress near the crack tip decreases and fracture of active particle becomes more difficult.

Numerical computation of central crack growth in an active particle of electrodes influenced by multiple factors

Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithium-ion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles $$(\hbox {LiMn}_{2}\hbox {O}_{4})$$ by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling.

Multi-objective optimization of an arch dam shape under static loads using an evolutionary game method

ABSTRACTThis article attempts to evaluate the safety and economic performance of an arch dam under the action of static loads. The geometric description of a crown cantilever section and the horizontal arch ring is presented. A three-objective optimization model of arch dam shape is established based on the arch dam volume, maximum principal tensile stress and total strain energy. The evolutionary game method is then applied to obtain the optimal solution. In the evolutionary game technique, a novel and more efficient exploration method of the game players’ strategy space, named the ‘sorting partition method under the threshold limit’, is presented, with the game profit functions constructed according to both competitive and cooperative behaviour. By way of example, three optimization goals have all shown improvements over the initial solutions. In particular, the evolutionary game method has potentially faster convergence. This demonstrates the preliminary proof of principle of the evolutionary game method.

Nucleation from a cluster of inclusions, leading to void coalescense

A cell model analysis is used to study the nucleation and subsequent growth of voids from a non-uniform distribution of inclusions in a ductile material. Nucleation is modeled as either stress controlled or strain controlled. The special clusters considered consist of a number of uniformly spaced inclusions located along a plane perpendicular to the maximum principal tensile stress. A plane strain approximation is used, where the inclusions are parallel cylinders perpendicular to the plane. Clusters with different numbers of inclusions are compared with the nucleation and growth from a single inclusion, such that the total initial volume of the inclusions is the same for the clusters and the single inclusion. After nucleation, local void coalescence inside the clusters is accounted for, since this makes it possible to compare the rate of growth of the single larger void that results from coalescence in the different clusters. Nucleation parameters leading to rather early nucleation, or to later nucleation, are considered. Also, different transverse stresses on the unit cell are considered to see the influence of different levels of stress triaxiality, and results are shown for different levels of strain hardening in the material.

Finite Element Analysis of Screw-Tightening Torque Applied to Custom and Conventional Abutment

The aim of this study was to design an abutment with an esthetic emergence profile contour using CAD technology and compare the stress distribution within the structure between the custom abutment and conventional abutment according to the screw tightening torque using 3D finite element analysis (FEA). The maximum tensile principal stress was found in the endpoint of the screw head and the start point of the screw line with regard to the application of the tightening torque of the screw. A similar pattern was observed in all of the following screws: 10N·cm, 20N·cm, and 30N·cm. The tightening torque of the screw had a significant impact on the changes in the stress of the abutment and screw fixture. This study also found that the condition in which the screw load was applied showed a more realistic description of the behavior of a single fixed dental implant than the condition in which the screw load was not applied. This study examined the optimal tightening torque value of the screw for the denture used in this study at a location slightly higher than 20N·cm. The difference in the custom abutment and conventional abutment did not have a significant impact on the supporting bone with regard to the external load. In regard to the stress occurring in the screw, the custom abutment had a lower degree of stress than the conventional type. Therefore, a screw fracture would occur less frequently in a custom abutment than a conventional abutment.

Axisymmetric torsional fretting contact between a spherical punch and an FGPM coating

• The maximum tensile principal stress increases with the increase of the gradient index. • The maximum Mises stress occurs at the end of slip annulus where the severest state of stress happens. • The FGPM coating can be used to resist the fretting contact damage at smart devices. The axisymmetric torsional fretting contact between a rigid conducting spherical punch and a functionally graded piezoelectric material (FGPM) coating is studied in this paper. The exponential model is used to simulate the inhomogeneous electro-mechanical properties of the FGPMs coating. The conducting spherical punch with a constant surface electric potential is considered in the contact. A normal force and a cyclic torque are applied to the two contact bodies. The applied torque produces an outer annular slip area and an inner stick area. The torsion angle is produced within the inner stick area as a rigid body. With the aid of the Hankel integral transform technique, we can reduce the contact problem to the singular integral equations of the Cauchy type. Then the unknown electro-mechanical fields and stick/slip area can be obtained numerically. The effect of the gradient index on the surface electro-mechanical fields is discussed at loading and unloading phases. The Mises stress and principal stress at the contact surface are also discussed to predict the possible location of fretting damage and failure.

Multiple cohesive cracking during nanoindentation in a hard W-C coating/steel substrate system by FEM

Stress evolution and subsequent cohesive cracking in the hard and stiff W-C coating on steel substrate during nanoindentation have been investigated using finite element modelling (FEM) and eXtended FEM (XFEM). The FEM simulations showed that the maximum principal stresses in the studied system were tensile and always located in the coating. They evolved in several stages. At indentation depths below 15% of the relative indentation depth, the maximum principal tensile stresses of ∼3GPa developed at the top surface of the coating along the indenter/coating interface. At relative depths range 15–60%, the maximum tensile stresses of ∼6–8GPa concentrated under the indenter tip in the coating along the interface with the substrate. At relative depths exceeding 60%, the maximum stresses gradually increased up to 10GPa and they were located in the sink-in zone outside the indent as well as below the indenter tip. The first and subsequent cohesive cracks developed when the maximum tensile stresses in the sink-in zone at the top surface of the coating (and at the coating/substrate interface under the indenter) repeatedly reached the ultimate tensile strength of the coating. The hardness profile as well as cohesive cracking is controlled by the deformation of the substrate defined by the ration of the yield stresses of the coating and substrate. Very good correlation between the experimentally obtained cracks and multiple cracks predicted by XFEM confirmed the ability of the applied modelling in the prediction of fracture behavior of the studied coating/substrate system.