Crack Growth Angle Research Articles

Crack propagation analysis of slewing bearings in wind turbines applying a modified sub-model technology

As slewing bearings in wind turbines are exposed to complex operational environments, they are prone to crack initiation, propagation and evolution that can lead to contact fatigue problems. Reliable crack extension prediction is a critical requirement. With the goal of obtaining more accurate crack characteristics, this study proposes a crack initiated contact finite element model (CI-CFEM) targeted at the raceway of slewing bearings by introducing a modified sub-model. In the application of the global finite element model (G-FEM) to the slewing bearing system, the rolling displacements of the ball and the boundary displacements are employed in CI-CFEM to take account of external ring deformations and the support conditions. The crack is embedded using FRANC3D, and the stress intensity factor distribution and propagation characteristics of the crack front are investigated. Furthermore, the effect of external load and the design parameters of the slewing bearing on crack propagation are explored, providing insight for optimizing the design of slewing bearings to extend service life. The results reveal that changing external loads and bearing parameters are an effective means of retarding crack propagation rate, while have relatively minor influence on crack growth angle.

Thermally nonlinear analysis of propagating cracks under generalized thermal shock

In this paper, the thermally nonlinear response of stationary and moving cracks in isotropic media subjected to a hyperbolic thermal shock in the framework of the eXtended Finite Element Method (XFEM) is examined. For this purpose, the thermally nonlinear fully coupled Lord-Shulman (LS) model is considered as governing equations. In addition, two cases of material properties, temperature-dependent (TD) and temperature-independent (TID), are assumed. The geometry, including a predefined crack, is modeled using the XFEM for spatial discretization. For modeling the dynamic crack growth within the XFEM, the Maximum Tangential Stress (MTS) criterion is modified based on the stress field near the tip of a growing crack to calculate the dynamic crack growth angle. Besides, the nonlinear form of the Newmark integration scheme is implemented for the numerical integration in the time domain. Finally, a method based on one of the Barnet-Lothe tensors for isotropic materials is employed to extract the stress intensity factors (SIFs). In the provided examples, the effects of thermal nonlinearity, the temperature-dependency of material properties, and the LS relaxation time on the crack propagation path are explored.

Three-Dimensional Fracture Analysis of Large Opening Box Girder With Crack Damage Under Bending and Torsion Loads

Abstract This work aims to investigate the complex fracture behavior of a large opening box girder (LOBG) using three-dimensional (3D) finite element method (FEM). A numerical model is developed to simulate the fracture of LOBG under individually or jointly applied torsion and bending loads. The crack damage is introduced into the side plate and bottom plate of LOBG. The influencing factors such as crack angles, crack locations, and load types are emphatically discussed. Additionally, the crack growth angles are also predicted during the analysis. The results present that the large opening can generate significant effects on the crack growth of the side plate crack (SPC) and the bottom plate crack (BPC). Under the condition of torsion or hogging, SPC grows more easily than BPC, while BPC is relatively prone to grow under sagging condition. Compared with the torsion condition, the initial crack angle can significantly reduce the stress intensity factor (SIF) under the bending condition. Furthermore, the cracks that gradually approach transverse frames are also more likely to induce mode I fracture under torsion conditions. These findings from the present study can reveal insights for a better understanding of fracture behavior for LOBG.

Study on fracture behavior of pipeline girth weld based on CTOD-Am method and Gurson ductile damage model

The mechanical properties of the materials in different regions of the pipeline girth weld are sometimes quite different, which will produce a more significant material constraint effect and complicate the fracture behavior of the girth weld. Therefore, this work adopts the finite element method combined with the material damage model to study the ductile tearing process of the weld. The results of the single edge notched bending (SENB) specimens with the weld center crack show that for the welds with different mismatch conditions, with the increase of the weld mismatch coefficient, the crack tip constraint decreases gradually, and the fracture toughness increases gradually. The smaller weld width will make this effect more significant. When the ratio of the weld width to the specimen width is larger than or equal to 0.43, the BM will basically no longer affect the crack tip constraint and the fracture toughness of the weld. The results of the SENB specimens with the interface crack show that for the overmatched weld, with the increase of the weld mismatch coefficient, the crack first grows along the interface and then deflects into the heat affected zone (base metal). When the weld mismatch coefficients are 1.44 and 1.86, the corresponding deflection angles are 14.84° and 24.61°. For undermatched weld, with the decrease of the weld mismatch coefficient, the crack growth will deflect into the weld metal. When the weld mismatch coefficients are 0.69 and 0.6, the corresponding crack growth deflection angles are 14.04° and 25.36°. The larger the degree of the weld mismatch, the more significant the deflection of the distribution of the equivalent plastic strain and the stress triaxiality ahead of the crack tip. The effect of the specimen thickness on the deflection angle of the interface crack growth is small. The verification shows that the numerical analysis results of this study are valid.

Glass laminate aluminum reinforced epoxy under non-proportional multiaxial fatigue loading: Experimental testing and new fatigue apparatus development

Predominately, the structures and components in aeronautic, automotive and other important implementations suffer from non-proportional multi-axial fatigue loading. One of the best selected materials to fabricate these structures and components are fiber metal laminates (FML). In this research, fatigue crack-propagation in glass-laminate aluminum reinforced-epoxy (GLARE) specimen under the effect of special case of multi-axial fatigue loading (constant shear with repeated tensile stresses) has been studied analytically, numerically and experimentally. GLARE_2 A 2/1 specimen was fabricated using vacuum assisted resin transfer molding technique after special preparation aluminum surface procedure. New multi-axial fatigue apparatus including mechanical, hydraulic and control systems was manufactured to investigate crack growth experimentally. Analytical model using Paris relation was adopted to predict crack growth through aluminum layers of GLARE specimen. The rate of crack propagation is related to the mixed-mode equivalent stress intensity factor, which is estimated by the superposition for both fiber-bridging and far-field stress intensity factors. The crack opening contour, distribution of fiber-bridging stress, delamination growth and its shape were evaluated in simultaneous manner to find the fiber-bridging stress intensity factor. ABAQUS 2021 software has been used to simulate crack and delamination growth in GLARE specimen with the aforementioned fatigue loading. The extracted results from analytical and numerical models such as crack growth, crack opening, delamination shape and crack angle have been compared with that measured experimentally. The comparison indicates that there is good agreement between the calculated and measured results (with maximum deviation of 8.74% for crack growth).

On fatigue crack growth testing and analysis of non-crystallising rubber using planar tension specimen

Rubber fatigue crack growth tests are one method of characterising fatigue behaviour. Due to the possibility of using one specimen to measure fatigue at multiple load levels, it is often considered a faster and less expensive method compared to the time-consuming fatigue crack initiation tests. In this work, the possibility of a new specimen grip geometry for crack growth tests was investigated, enabling the use of specimens cut from compression moulded plates. Several variations of a crack growth predictor parameter for tests with different mean strain levels were investigated. In addition, the optimum variation of the crack growth angle with respect to the loading direction was evaluated using test measurements. The results show that the use of the simplified crack growth predictor can provide the same results as the commonly used tearing energy. Using the Euclidean length of the crack growth increments gives better results than their horizontal projection, with the possibility of using angle deviations up to 90° without major drawbacks.

Investigation of the thermomechanical behavior of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading

For mixed-mode, thermal shock crack problems with thermal lagging behaviors, it is difficult to obtain the transient thermal stress intensity factors (TSIFs). This paper aims to develop a method combining the Newmark method and the transient interaction energy integral method (IEIM) to extract the transient, mixed-mode TSIFs of nonhomogeneous, layered materials with mixed-mode cracks. The transient temperature field obtained by non-Fourier heat conduction theory is discretized in the spatial and temporal domains through the finite element method (FEM) and Newmark method, respectively. The effect of the continuity of thermomechanical parameters at the dual interface on the transient, mixed-mode TSIFs of nonhomogeneous, layered materials is discussed, then the fracture resistance of nonhomogeneous, layered materials is evaluated. Moreover, the maximum hoop stress criterion is utilized to obtain the crack growth angle and the equivalent, transient TSIFs of nonhomogeneous, layered materials. The influences of the interface on crack growth angle and equivalent transient TSIFs of nonhomogeneous layered materials are also studied. The present work is beneficial for the thermal design of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading.

Study on Mechanical and Acoustic Emission Characteristics of the Influence of Rock Bridge Length on Rock Failure

Abstract Rock bridge of jointed rock plays a key role in its instability failure and has great influence on underground engineering. In this paper, the direct shear tests of jointed rocks with different rock bridge lengths are carried out, and the mechanical properties, acoustic emission (AE) characteristics, and fracture mechanism during the failure of rock bridge are studied. The results show that the shear strength increases with the increase of normal stress. When the rock bridge is long, cohesion c plays a leading role to control the failure of jointed rock; on the contrary, the internal friction angle φ plays a leading role. AE count rate, cumulative AE counts, and peak AE energy rate increase with the increase of rock bridge length. With the increase of rock bridge length, peak AE energy rate and AE count rate occur earlier. Considering the influence of rock bridge length, the fracture criterion and crack growth angle of shear fracture are derived based on linear elastic fracture mechanics. The theoretically calculated result is consistent with the experimental result. The research in this paper can provide relevant theoretical basis and useful reference for the instability and failure analysis of jointed rock.

Mixed Mode Fracture Assessment for Box Girder with Crack Damage under Combined Loads

The box girder is an important structure which is widely used in the ship and marine engineering but has not extensively investigated fracture problem. The paper adopts the stress intensity factor (SIF) as the crack tip parameter to carry out the mixed mode fracture assessment of the box girder structure with crack damage. The bending load, torsion load and side load are firstly introduced to study box girder crack propagation. And the related influencing factors of crack length, crack type, combined loads, etc. are investigated emphatically. In analysis, crack growth angle is also analyzed to evaluate the crack growth. The results show that different load types have different contributions to crack propagation. And combined bending and torsion loads effect may be considered adopting a linear superposition principle under transverse cracks and larger angle cracks. When the side load is added, the area near the crack upper surface will be easy to occur unstable expansion. These conclusions will provide a guiding significance to evaluate the crack propagation of box girder.

Investigation of the fracture problem of functionally graded materials with an inclined crack under strong transient thermal loading

In this paper, a special method for solving transient thermal stress intensity factors (TSIFs) in functionally graded materials (FGMs) with inclined cracks under strong, transient thermal shock loading is established based on the hyperbolic heat conduction equation. First, the Newmark method is employed to obtain the strong transient temperature field of FGMs containing inclined cracks. Then, the transient interaction energy integral method (IEIM) is used to solve the TSIFs for inclined cracks. In addition, the influences of the distribution patterns of the thermal relaxation parameter, the crack length and the crack angle on the TSIFs, and the crack growth angle are investigated. Moreover, we discuss the difference between using the hyperbolic heat conduction theory and the classical, Fourier heat conduction theory in calculating the TSIFs of FGMs with inclined cracks. The results show that the present, combined IEIM-Newmark method can be used to solve strong transient thermal shock crack problems with high efficiency. This work can be used for the thermal design, evaluation, and engineering applications of FGM structures.

3-Dimentional Elucidation of Fatigue Characteristics and Fracture Morphologies in Spot Welding Joints of High Strength Steel

In order to investigate the three-dimensional fatigue properties of resistance spot welded joints made of high strength steel, this study was carried out observed three-dimensional fatigue cracks and calculated stress intensity factors using fem analysis. In addition, this study was conducted under shear mode and pure shear mode to investigate the influence of loading mode during fatigue testing. As a result, it was found that a new crack growth behavior branched in the welding circumferential and width direction under the low loading force range. However, all the cracks leading to final fracture were of the same type, and it was confirmed that the fatigue strength was not affected by a new crack growth behavior. Moreover, the results of observed initial fatigue crack growth angles and the calculated stress intensity factor, KIθ, were in close agreement, which proved that the fatigue crack growth behavior was strongly influenced by the fracture mechanics.

In-situ optical approach to predict mixed mode fracture in a polymeric biomaterial

The present article promotes the usage of the digital image correlation (DIC) technique to determine the in‑situ stress and predict the onset of fracture in a cracked dental biomaterial sample. For this purpose, the elastic and fracture properties of the dental material are measured via the DIC method. To perform mixed mode fracture experiments, a modified single edge notched bend (SENB) specimen with varying crack length is introduced and utilised. From the theoretical point of view, we next implement a stress-based fracture criterion and combine it with two different critical distance models. In this regard, the in‑situ stress is formulated using the data from the DIC analysis conjugated with a supervised learning algorithm. Finally, the crack growth angle and fracture load for the tested biomaterial specimens are estimated, the comparison of which with the experimental measurements reveals good correlation.

Calibration and uniqueness analysis of microparameters for DEM cohesive granular material

The differential evolution (DE) algorithm was deployed to calibrate microparameters of the DEM cohesive granular material. 4 macroparameters, namely, uniaxial compressive strength, direct tensile strength, Young’s modulus and Poisson’s ratio, can be calibrated to high accuracy. The best calibration accuracy could reach the sum of relative errors REsum < 0.1%. Most calibrations can be achieved with REsum < 5% within hours or REsum < 1% within 2 days. Based on the calibrated results, microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material: (1) microparameters effective modulus, tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth, (2) microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress, and (3) microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour. Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study. The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.

Crack growth angle prediction of an internal crack under mixed mode load for unfilled elastomer using the strain energy density factor

ABSTRACTThis article investigates the prediction of the crack growth angle of an existing internal crack under mixed mode loading at the crack tip for an unfilled ethylene propylene diene terpolymer rubber (EPDM). For the realization of mixed mode loading, the cracks of the uniaxial loaded specimens were oriented with different angles to the loading direction. The energy density factor was used as a potential criterion for determining the crack growth angle. The determination of the strain energy density factor was carried out simulatively in Abaqus. The second‐order Ogden model was used to describe the rubber‐like material behavior. The relative local minimum of the strain energy density factor provides the possible growth angle. The experimental investigations show that the initial cracks grow orthogonally to the loading direction for the different crack orientation angles. For the crack orientation angle parallel to the load direction, the crack growth was observed because the strong stretching of the specimen caused strong necking in the crack region. The crack growth for the remaining crack orientation angles were induced due to shear loading at the crack tip. The predictive angle of different crack orientation angles shows very good accordance to the measured crack growth angles.

Experimental investigation on uniaxial compressive mechanical characteristics of red-sandstone containing single fissure after rainfall infiltration

The fissure flawed red-sandstone under dynamic rainfall infiltration is one of the key factors determining the safety and reliability of red-sandstone embankment and slope. However, there is still a lack of investigations considering the combined influence of rainfall infiltration and flaw geometry on the mechanical behavior of fissure flawed red-sandstone. Therefore, the effects of rainfall intensity, rainfall duration, as well as prefabricated fissure inclination angle on the uniaxial compressive mechanical behavior of red-sandstone containing a prefabricated fissure were investigated by rainfall infiltration and uniaxial compression tests. The results show that fissure inclination angle, rainfall intensity, and duration have significant influences on the axial stress-strain characteristics of the red-sandstone specimen under uniaxial compression. The quantitative expression of the unconfined compressive strength, peak strain, modulus with fissure inclination angle, rainfall intensity, and duration are obtained. The unconfined compressive strength, deformation modulus, and elastic modulus of the red-sandstone specimen present negative relationships with rainfall intensity and duration, while a positive trend is observed for its peak strain. The unconfined compressive strength, deformation modulus, and elastic modulus of the red-sandstone specimen attain the minimums when the prefabricated fissure inclination angle is 45°, while its peak strain reaches the maximum at this time. The ultimate failure modes, crack characteristics, and types of the red-sandstone specimen under uniaxial compression after rainfall infiltration are discussed according to the photographic monitoring in uniaxial compression tests. The meso-level failure mechanism of the red-sandstone specimen under uniaxial compression after rainfall infiltration is evaluated on the basis of the meso-morphology of the specimen’s fractured surface. The influences of prefabricated fissure inclination, rainfall intensity, and duration on the variations of the red-sandstone specimen’s crack growth angle under axial compression are also analyzed.

A graph-theoretic approach for multiscale modeling and prediction of crack propagation in polycrystalline materials

A multiscale graph theory-based approach is introduced here to predict the microscale crack path in polycrystalline materials. The crack path is represented as the boundary of the partition of a geometric graph. The partitioning is carried out by optimizing an Ising-type hamiltonian. The hamiltonian parameters are chosen such that each partition cost is the same as the energy of the corresponding crack. The interplay of the loading conditions on the specimen and the microstructure of the material near the crack tip determines the crack growth angle in polycrystalline materials. Two different length scales of macro and micro is incorporated for the crack path by defining the crack total energy as the summation of macroscopic energy release and microscopic surface energy. The former term represents the macroscopically favorable crack growth angle by directing the crack to propagate from the crack tip along the direction of the maximum energy release. The latter term guides the microscopic crack path along the macroscopically preferred direction. At this scale, the crack path naturally accommodates both the intergranular and transgranular fractures. In the case of intergranular fracture, the crack propagates along the grain boundaries, while in the case of transgranular fracture, the crack propagates along the crystallographic cleavage planes. The mixed-mode fracture in a thin foil specimen is studied, and the effect of the dihedral angle of the 2D crack is included in defining the effective surface energy. The model is validated using the analytical results for mixed-mode fracture in an isotropic medium and mode-I fracture in a medium with a preferred crack direction. The proposed method can be used to design materials microstructure with optimal fracture resistance.

Coupled numerical analysis for in-plane elastic T-stress evaluation in isotropic FG solids

This contribution establishes a coupled numerical method to show its effectiveness in the simulation of LEFM problems. The semi-meshless method uses the MLPG1 meshfree theory to discrete governing equations while geometry is modeled by simple CPS3 triangular cells. The cells help to propose an efficient neighboring method for meshfree interpolations. Three benchmark homogeneous cases are considered whose analytical solutions are available to carefully examine the accuracy of this method and validate the numerical implementation by comparing relative errors in terms of error norms, crack onset angle and also fracture parameters, i.e. KI, KII and T-stress that characterize the crack tip condition. Good computational accuracy is observed in this article. Three FG structures by simple linear, exponential and complex hyperbolic-tangent gradations are taken from the literature and investigated under thermo-mechanical conditions. A thermal barrier coating with an FG structure is also modeled. Then, fracture parameters and crack growth angles with and without considering T-stress are compared with FE solutions. Generalized maximum tangential stress (GMTS) criterion and interaction integral method are used to respectively compute crack growth angle and capture T.

Experimental and numerical investigation of the weld geometry effects on Type IV cracking behaviour in P91 steel

The focus of the present study is on creep crack growth behaviour in Type IV region of P91 steel weldments at 650 °C. In the experimental studies on small- and large-scale single-edge notched specimens in tension, SENT, the effects of weld dimensions and specimen size on the creep crack growth behaviour of the material are investigated. The experimental results demonstrate that the crack starts to propagate at an angle normal to the loading direction, subsequently deviates towards the Type IV region and the specimen eventually ruptures when the crack growth angle becomes parallel to the loading direction. The creep rupture data for SENT specimens compared well with those of the round bar specimens for P91 welded joints. In addition, the data for crack growth rates from the deviating crack path were correlated with the C* fracture mechanics parameter and showed good agreement with standard compact tension test data. To predict the creep crack growth behaviour in the Type IV region, finite element simulations were performed in conjunction with a multiaxial ductility damage criterion at the weld/base metal interface. Given that a lower failure strain along the Type IV region is prominent, it is shown that the cracking, in line with the experiments, followed the HAZ region and led to the final creep rupture in the net section.

Evaluation of Critical Crack Orientations and Crack Growth Analysis in Compressor Blade Root Subjected to Fatigue

Abstract Aero-engine compressor blade and disk assemblies are subjected to radially outward centrifugal force due to blade rotation and the bending of the blade due to gas pressure. Static analysis is done initially to find the critical crack orientation at the root of the blade. With simulated initial cracks, the cracks are allowed to grow in low cycle fatigue (LCF) and isochromatics are captured at selected intervals. Using digital photoelasticity, isochromatic images are used along with an over-deterministic least-squares approach to find the fracture parameters. As the stress fields are very complex, a multiparameter solution with a higher number of parameters was needed to model the stress field. Crack growth angles are evaluated using maximum tangential stress (MTS), strain energy density (SED), and generalized MTS (GMTS) criteria. It is observed that the GMTS criterion predicted closer results to that of experimental values, which implied the significance of T-stress in predicting the crack growth angle.

Corrosion effect, constraint and path orientation estimated in cracked gas turbine blade

The severe damage of gas turbine is due to the failure of the blade, in which the occurrence of a serious pitting occurred on the blade surfaces was evidence of fatigue marks in the fracture surface. This paper deals with the effect of semi-elliptical crack propagation on the crack path using a basic approach in predicting crack paths, namely, incremental methods. The crack position was chosen at the node coordinate where we have the maximum principal stresses. In this node, we have created a semi-elliptical crack and we have compared the results with the Stress Intensity Factors and T-stress values. The local fracture criterion of the maximum average tangential stress in the vicinity of fracture process zone including two terms of the Williams series solution for the mixed mode I/II loading has been used for predicting the angle of surface crack growth. The volumetric method (VM) for the compression-sensitive materials is described by a linear combination of the effective stress and the effective stress intensity factor. The results of our finite element computations based on a two-parameter fracture mechanics formulation showed that the T-stress has significant effects on the crack path.