Crack Depth Ratio Research Articles

Phase field thermal shock analysis of rotating porous cracked pretwisted FGM microblade using exact shear correction factor

The present work is an attempt to develop a simple and accurate finite element formulation for the thermal shock analysis of the rotating porous cracked pretwisted functionally graded material (FGM) microblade using modified coupled stress theory in conjunction with phase-field and first-order shear deformation theory (FSDT). The physical neural surface is taken as the reference plane and the exact value of the shear correction factor is calculated from the shear stiffness. The elastic properties are assumed to be temperature-dependent and the upper ceramic layer is subjected to a high thermal shock whereas the bottom metallic layer is maintained at room temperature or is thermally insulated. The governing differential equation for the present analysis is derived using Hamilton’s principle and Newmark average acceleration method is used to obtain the transient response of the rotating porous cracked pretwisted FGM microblade subjected to thermal shock. The results obtained from the present finite element formulation are first validated with several benchmark examples available in the literature. New results are presented investigating the effect of crack depth, crack location, crack angle, rotational velocity and material scale ratio on the transient response of the cracked rotating porous pretwisted FGM microblade subjected to thermal shock. It is shown here that the parameters like crack depth, crack location and crack angle have a significant influence on the transient response of the rotating porous cracked pretwisted FGM microblade.

Analytical solution of nano-concrete-epoxy interaction area considering static equilibrium

This research proposes an analytical solution of the nano-concrete-epoxy interaction area within nano crack region of the reinforced concrete beam by applying Newton’s third law in static equilibrium. For deriving the governing equation, the imaginary beam with free ends (no support) is considered within nano crack region. This imaginary beam is acted along the imaginary line of concrete-epoxy interface. Newton’s third law is applicable for deriving the governing equation because of assuming the absence of frictional and other external forces. The parametric study is performed for implementing the proposed formula of nano interactive area considering variable nano crack depths and thicknesses. The nano interactive area is increased gradually with the increment of depths and thicknesses based on the parametric study because of linear functionality of interactive area and geometry of nano crack region. The maximum interactive area is found to be 314 nm2 at 0.6 ratio of depths and thicknesses of the nano crack. The incremental differences in interactive area between the crack depth or thickness ratios of 0.1 and 0.6 are found to be 25.4% and 1.6% for variations of the crack depth and thickness ratios, respectively. So, the crack depth shows higher impact on the interaction area compared to the thickness of the crack. However, there is a scope for enhancing this research in future by deriving closed-formed analytical formulations to consider appropriate boundary conditions.

Potential of Non-Contact Dynamic Response Measurements for Predicting Small Size or Hidden Damages in Highly Damped Structures.

Vibration-based structural health monitoring (SHM) is essential for evaluating structural integrity. Traditional methods using contact vibration sensors like accelerometers have limitations in accessibility, coverage, and impact on structural dynamics. Recent digital advancements offer new solutions through high-speed camera-based measurements. This study explores how camera settings (speed and resolution) influence the accuracy of dynamic response measurements for detecting small cracks in damped cantilever beams. Different beam thicknesses affect damping, altering dynamic response parameters such as frequency and amplitude, which are crucial for damage quantification. Experiments were conducted on 3D-printed Acrylonitrile Butadiene Styrene (ABS) cantilever beams with varying crack depth ratios from 0% to 60% of the beam thickness. The study utilised the Canny edge detection technique and Fast Fourier Transform to analyse vibration behaviour captured by cameras at different settings. The results show an optimal set of camera resolutions and frame rates for accurately capturing dynamic responses. Empirical models based on four image resolutions were validated against experimental data, achieving over 98% accuracy for predicting the natural frequency and around 90% for resonance amplitude. The optimal frame rate for measuring natural frequency and amplitude was found to be 2.4 times the beam's natural frequency. The findings provide a method for damage assessment by establishing a relationship between crack depth, beam thickness, and damping ratio.

Study on calcium dissolution of concrete specimens with surface cracks

The effects of crack width, crack depth and water-cement ratio (w/c) on calcium dissolution resistance of cracked concrete were evaluated. Results show that the degradation in physical properties and mechanical properties of concrete after dissolution increase with the increasing crack width, crack depth and w/c. In the case of concrete with w/c of 0.40 and dissolution age of 100 d, the degradation of splitting tensile strength of specimens with crack widths of 0.1, 0.2 and 0.3 mm was 1.27 times, 1.39 times and 1.54 times that of uncracked specimens. Dissolution resistance of cracked concrete is obviously lower than that of uncracked concrete, and the effect of crack width on it is more significant than that of crack depth, and the higher the w/c of concrete, the more significant the effect of crack width. Dissolution damage increasing coefficient of cracked concrete can be used to quantitatively characterise the effect of cracks on the dissolution damage of concrete, and its maximum value is approximately 1.08 corresponding to the crack width of 0.3 mm. The results of this study can be used as a reference for the accurate evaluation of calcium dissolution resistance and service life of the water-related concrete structures.

Finite Element Analysis based Stress Intensity Factor Solutions for Surface Cracks

The stress intensity concept is important in termsof crack extension as critical values of the stress intensityfactors govern crack initiation. Therefore, the present workdetermines stress intensity factors for semielliptical shallowand deep surface cracks as a function of parametric angle,crack depth, and aspect ratio for tension and bending loads.The stress intensity factors are obtained from a threedimensional finite-element analysis of semielliptical surfacecracks in finite plates subjected independently to tensionand bending loads under elastic conditions. The obtainedstress intensity factor is used to predict the crack growthunder linear elastic conditions. Results show that the stressintensity factor varies along the crack front for shallow anddeep cracks. At the deepest point in bending and tension thestress intensity factor increases as the ratio of the crackdepth to the crack length at surface decreases. However, atthe free surface the stress intensity factor becomesmaximum when the crack depth equals crack length. Asurface crack in tension loading is predicted to break thewall thickness with a relatively small amount of crackgrowth at surface. While in bending the crack breaksthrough with large amount of crack growth in the widthdirection.

Fracture mechanics analysis of gas pipeline with circumferential crack under the action of transverse landslide

The whole process of pipeline–soil interactions between a landslide and a gas pipeline was simulated using the strength reduction method. The main purpose is to investigate how pipeline internal pressure, landslide displacement, crack depth ratio (the ratio of crack depth to wall thickness), crack aspect ratio (the ratio of crack depth to crack half-length), and reinforcement with anti-slide piles influence the J-integral of a circumferential crack in the pipeline under landslide impact. The simulation showed that increases in the landslide displacement, crack depth ratio, and pipeline internal pressure led to an increase in the maximum value of the J-integral at the crack leading edge. An increase in the crack aspect ratio reduced the maximum value of the J-integral. In addition, in the process in which the crack shape changed from semi-elliptical to semicircular, there was a critical crack aspect ratio at which the J-integral at the deepest point of the crack was equal to the J-integral at a point on the surface. The study also found that an increase in the number of anti-slide piles affected the location and distribution of the zone of maximum slippage and effectively reduced the maximum von mises stress and the J-integral at the crack tip. However, when the number and cross-sectional size of anti-slide piles exceed a certain threshold, further increasing or enlarging them barely affects the J-integral.

Experimental and Numerical Studies on the Vibration of Hybrid Composite with an Edge Crack

The hybrid composite plate is increasingly used in marine, robotic arm, and other applications. Edge crack is the greatest common fault in the structural systems during its working time. In this research, the successful fabrications of a hybrid composite of epoxy-based composites reinforced with bamboo and glass fibers have been done to examine the vibration characteristics under free vibration. First-order shear deformation theory is used to study the fundamental natural frequencies of asymmetrically hybrid composite beam with edge cracks for cantilever beam boundary conditions. Both numerical (FEM) using ABAQUS software and experimental investigations are done for the vibration analysis of unidirectional bamboo/glass fiber epoxy hybrid composite (BGHC) beam with edge cracks using fracture mechanics theory. It is observed that implications edge crack with different crack depth and various fiber weight ratio parameters have a major effect on vibration analysis. Also, it is clear that the natural frequencies of the hybrid composite are significantly affected due to the fiber weight ratio and crack depth of the hybrid composite materials. So, crack lengths are playing a vital role in the dynamic or vibration characteristics of the hybrid composite materials. The results of natural frequencies have been shown that they are decreased with an increase in crack depth and an increase in the bamboo fiber weight. Thus, BGHC-2 made from 30% bamboo and 10% glass fiber can be a viable candidate for applications that will produce good vibration properties. Generally, the first-third natural frequency of the hybrid composite beam decreases within the increase of bamboo fiber and decreases in glass fiber. The composite materials having 60% of epoxy with 20% bamboo and 20% glass fiber, and 60% of epoxy with 10% glass and 30% bamboo fibers, are observed with a gradual decrease in the values of natural frequencies with respect to increasing in crack depth. A fine agreement was accomplished between the simulation and experimental results. Therefore, the present approach can be used to identify cracks for mechanical health monitoring by linking the variation in natural frequencies of the hybrid composite beams.

A deep neural network-based method to predict J-integral for surface cracked plates under biaxial loading

As surface cracks may cause potential failure for engineering structures, it is of vital significance to carry out the fracture assessment for cracked structures. The crack driving force in the form of J-integral is an important input parameter in fracture assessment. This paper focuses on the determination of J-integral for surface cracked plates under biaxial loading. A method for predicting the J-integral based on the deep neural network (DNN) is proposed to estimate J-integral efficiently and accurately. Firstly, extensive three-dimensional (3D) elastic–plastic finite element (FE) analysis is conducted to compute the J-integral along the crack front for developing a FE J-integral datasets containing 1600 cases. Various crack aspect ratios, crack depth ratios, strain hardening exponents, ratios of the loading perpendicular to the crack plane to yield stress, and biaxial ratios, are strategically considered. Secondly, DNN models for predicting the J-integral are constructed and trained according to the obtained datasets by FE analysis. Then, the evaluation criteria for DNN models and the grid search method are utilized to determine the optimal DNN model structure. Finally, test cases are employed to verify the feasibility and prediction accuracy of the determined DNN model. Based on validation results, the determined DNN model exhibits sufficiently accurate prediction performance. This research provides an idea for engineering applications, through building software based on continuously optimized DNN models, the J-integral for surface cracked plates under biaxial loading can be accurately and efficiently predicted for performing fracture assessments.

The effect of beam width and crack-depth ratio on mode I fracture toughness of RCB: an experimental and numerical study

In the present work, the fracture performance of pre-cracked reinforced concrete beams was investigated numerically and experimentally. Experimental and numerical programs were designed to examine the effect of beam width, b, (120 and 250 mm) and crack-to-depth ratio, a/d, (0.1, 0.2 and 0.3) for concrete strength, fc, (40 MPa), on the behavior of stress intensity factor, K1C, and fracture energy, G, for reinforced concrete, RC, beams. The work utilized beams with three-point loading conditions experimentally. Through the use of the ANSYS program, a comprehensive 3-D finite element analysis was conducted with utmost precision to simulate and idealize all experimental specimens. It has been confirmed through numerical and experimental outcomes that the stress intensity factor for RC concrete beams experiences a significant increase as the a/d increases. Furthermore, the fracture toughness values in this study show a slight increase due to the utilization of RC concrete beams with wider width. The validity of the presented concept was demonstrated by comparing the experimentally measured load vs. deflection values to the predicted numerical values and finding them to be acceptable.

Analytical study of CFRP strengthening steel plates with a semi-elliptical surface crack

Flaws and defects are unavoidable in the manufacturing process of steel members. Surface cracks are a common type of defect in steel structures that can introduce fatigue failure under cyclic loading. In this study, stress analysis of carbon fiber reinforced polymer (CFRP) repaired specimens with a semi-elliptical surface crack was conducted by theoretical analysis. The analysis was used to calculate stress intensity factors at crack tips. Finite element analysis was carried out to verify the proposed equations considering CFRP strengthening. Both single-sided and double-sided strengthening methods were considered. Thereafter, a modified Paris Law model was adopted to predict fatigue crack propagation life. Several parameters, which are crack aspect ratio, crack depth ratio, layers of CFRP, CFRP width and stress range are considered to analyze their influence on fatigue life. It was found that the augmentation of crack aspect ratio, layers of CFRP and CFRP width can significantly increase fatigue crack propagation life of repaired specimens. Furthermore, single-sided repairing on cracked side is better than double-sided repairing.

Residual stresses effects on fatigue crack growth behavior of rib-to-deck double-sided welded joints in orthotropic steel decks

Rib-to-deck (RTD) innovative double-sided welded joints have the potential to enhance the fatigue resistance of orthotropic steel decks (OSDs). However, welding residual stress (WRS) has been reported to be a contributing factor to fatigue cracking of steel bridges. This paper performed fatigue crack growth of the RTD innovative double-sided welded joints of OSD considering WRS. Firstly, a thermal-mechanical sequential coupling finite element model (FEM) of the RTD double-sided welded joints was established. The WRS distribution along the direction of deck thickness was analyzed. Secondly, the FEM of the OSD segment with crack was established. The fatigue crack behavior of RTD double-sided welded joints under the combined action of vehicle load and WRS was studied. Finally, the influences of initial crack on fatigue life was analyzed. Results indicate the distribution of the transverse WRS along the direction of deck thickness is tension-compression-tension stress, which has the characteristics of the sinusoidal function. The ∆ Keff value increases significantly considering WRS than without considering WRS during crack growth. WRS has a significant effect on fatigue life, and the fatigue life of the weld toe without considering WRS is about twice that of considering WRS. The crack depth and aspect ratio ( a0/ c0) of the initial crack affect the fatigue life of RTD double-sided welded joints.

Analytical solutions for buckling analysis of cracked plates under in-plane compressive loads: 2D refined modeling

Two refined two-dimensional (2D) crack models are developed to deal with rectangular isotropic and orthotropic plate problems with all-over part-through surface cracks under in-plane compressive loads. In the refined models, the crack terms are directly incorporated into the governing equations of cracked plates. In particular, the effect of internal in-plane forces can be investigated by theoretical analysis. The critical buckling loads of thin plates with uni-directional or bi-directional part-through cracks under uni-axial or bi-axial compressive loads can be determined analytically. In this work, different material properties, including steel, tempered glass, glass-fibre-reinforced composite, and graphite-epoxy composite, are considered. The influence of crack depth ratio and plate aspect ratio on the critical buckling loads of these structures is also presented. The analytical results are compared with those results obtained by the line-spring model and three-dimensional finite element method to verify their correctness and accuracy. The proposed models are highly effective for the buckling analysis of plates with part-through cracks.

Dynamic characteristics of cracked simply supported bidirectional functionally graded Rayleigh beam

This paper investigates the dynamic behavior of cracked Rayleigh beams constructed from bidirectional functionally graded (BDFG) materials under simple boundary conditions. A torsional massless spring is employed to model the beam's open crack type. The vibration equations are obtained using Hamilton's principle. The graded beam material properties are varied throughout the thickness based on the power-law distribution and in the longitudinal direction using the exponential material distribution. To solve the dynamic equations, Galerkin's approach is employed. The paper evaluates the impacts of the axial index, gradient property index, beam modulus ratio, and crack parameters on the natural frequencies of the FG beam. The results indicate that the dimensionless natural frequencies of intact graded beams decrease with increased gradient index k. In contrast, they increase with a rise in the modulus ratio. Additionally, the results demonstrate that an increase in the crack depth ratio decreases dimensionless natural frequencies.

Numerical Investigation of Fatigue Crack Propagation Behaviour of 550E High-Performance Steel

The fatigue crack propagation behaviour of Q550E high-performance steel (HPS) is studied in this paper. Static tensile testing and fatigue crack propagation testing were carried out, and the results were compared with those of Q235. Finite element models were developed and verified against the experimental results. The impacts of the initial crack angle, crack depth ratio, stress ratio, thickness, and corrosion pitting on the fatigue crack propagation behaviour of the HPS were analysed. The results show that the fatigue life of Q550 was reduced by 18% due to the corrosion pitting, but it did not change the crack propagation path. When the stress intensity factor is higher than a certain value, the fatigue performance of Q235 is better than that of Q550E. The initial crack angle of 52.5° is the critical angle of the crack stress intensity factor. The steel tends to fracture as the crack depth ratio increases, and more attention should be paid to the effective crack length in engineering practice. An increasing stress ratio leads to a smaller stress intensity factor, and the thickness affects the stress intensity factor in the later stage. The crack stress intensity factor around the corrosion pits gradually decreases along the thickness direction, and the crack tips around the corrosion pits tend to reach the yield state initially, accelerating the fatigue fracture of the specimen and ultimately leading to a decrease in fatigue life.

Investigation of Constraint Effect and Fracture Mode for Mixed Mode Inclination Surface Crack in Infinite Plate Under Compression

Abstract The stress field, constraint effect, and fracture mode transition at crack tip of mixed mode I-II-III inclination surface crack under compression have been investigated. The effects of geometrical configurations (relative crack depth and aspect ratio), friction coefficient, and biaxial scale factor on stress intensity factor (KII and KIII) and in-plane constraint parameter T-stress are quantitatively studied, the stress field at different crack inclination angles under tension and compression are compared, the failure mode at special locations along crack front of inclination surface crack is analyzed according to the generalized maximum tangential stress criterion (GMTS). The relative crack depth has slight effect on stress intensity factor and T-stress, and aspect ratio has a significant effect on stress intensity factor and T-stress. The friction coefficient decreases the magnitude of stress intensity factor and increases the magnitude of T-stress, the greater the crack inclination angle is, the more pronounced the effect is when crack inclination angle greater than 30 deg. The stress distribution around crack tip under tension and compression is completely different. At free surface, the crack will failure in-plane shear mode II sliding crack, and at the deepest part of crack, the crack will start as out-plane shear mode III tearing crack under compression.

Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models

Based on the equivalent bending stiffness of the viscoelastic cracked beam with open cracks, the corresponding complex frequency characteristic equations of a Timoshenko viscoelastic cracked beam are obtained by using the method of separation of variables and the Laplace transform. The vibration characteristics of a viscoelastic Timoshenko cracked beams with the standard linear solid model and Kelvin-Voigt model are investigated. By numerical examples, the effects of the crack location, crack number, crack depth, and slenderness ratio on the vibration characteristics of the viscoelastic cracked beams are revealed.

Predicting crack growth of paving materials under indirect tensile fatigue loads

Cracking of paving materials affects the reliability and safety of pavement structures, and indirect tension (IDT) test is commonly used to investigate the cracking behavior of the paving materials. However, the existing studies usually adopted a reduced modulus or strength to indirectly quantify cracking damage under the IDT fatigue loads. A direct analysis method for the crack growth under the IDT fatigue loads is still missing. The objective of this study is to propose a crack growth prediction model under the IDT fatigue loads based on continuum damage mechanics (CDM), which can directly quantify and predict the crack growth of the paving materials. Two types of paving materials, cement-treated aggregates and asphalt mixtures, were investigated. A damage density model based on CDM was proposed to quantify the crack growth under the IDT fatigue loads. The model coefficients are obtained by the IDT horizontal tensile stress, material surface energy, resilient modulus, and the size of the IDT specimen. The surface crack length of the IDT specimen is obtained using the solved damage density with introducing a crack depth ratio. Results show that the cement-treated aggregates show relatively more brittle cracking where the cracks are penetrative and going through the whole thickness of the IDT specimen. In contrast, the asphalt mixtures exhibit more ductile cracking where multiple cracks present and are nonpenetrative. The cracks of the asphalt mixture penetrate only 48% and 46% of the specimen thickness when the IDT fatigue loads are 540 kPa (1 Hz) and 700 kPa (10 Hz), respectively. The damage density calculated by the CDM-based model can accurately predict the crack lengths for both the cement treated aggregates and the asphalt mixtures, which are found consistent with the measured crack lengths from the IDT tests. This study provides a mechanics model for determining the crack growth under the IDT fatigue loads that can serve as a tool for evaluating the fatigue crack resistance of the paving materials like the asphalt mixtures and cement treated aggregates.

Effect of repair welding on the fatigue behavior of AA6082-T6 T-joints in marine structures based on FFS and experiments

In this study, the effect of repair welding on the fatigue behavior of AA6082-T6 welded T-joints in marine structures was investigated based on experiments and the fitness-for-service (FFS) assessment in BS7910. Repair welding led to an increase in residual stress and a decline in fatigue life according to fatigue tests and FEA. Meanwhile, repair welding changed the crack initiation site (CIS) and crack shape factor (CSF, the ratio of crack depth a to length 2c; i.e., a/2c), as indicated by fatigue fractography. In addition, when FFS assessment was performed, two methods for characterizing the CSF under different repair welding lengths during fatigue crack growth were presented: fixed and non-fixed a/2c. The results showed that repair welding led to a transition from ductile fracture to brittle fracture. For a fixed CSF, the critical crack depth and crack opening area of T-joints with repair welding lengths of 30 mm were greatly reduced by 63–66% and 86–89%, respectively, compared to T-joints without repair welding. However, the corresponding reductions for the non-fixed a/2c method were approximately 40% and 90%. The comparison indicated the results obtained with a non-fixed CSF were more consistent with the experiments, with a deviation below 15%.

Role of Dynamic Response in Inclined Transverse Crack Inspection for 3D-Printed Polymeric Beam with Metal Stiffener.

This paper aims to quantify the relationship between the dynamic response of 3D-printed polymeric beams with metal stiffeners and the severity of inclined transverse cracks under mechanical loading. Very few studies in the literature have focused on defects starting from bolt holes in light-weighted panels and considered the defect's orientation in an analysis. The research outcomes can be applied to vibration-based structure health monitoring (SHM). In this study, an acrylonitrile butadiene styrene (ABS) beam was manufactured through material extrusion and bolted to an aluminium 2014-T615 stiffener as the specimen. It simulated a typical aircraft stiffened panel geometry. The specimen had seeded and propagated inclined transverse cracks of different depths (1/1.4 mm) and orientations (0°/30°/45°). Then, their dynamic response was investigated numerically and experimentally. The fundamental frequencies were measured with an experimental modal analysis. The numerical simulation provided the modal strain energy damage index (MSE-DI) to quantify and localise the defects. Experimental results showed that the 45° cracked specimen presented the lowest fundamental frequency with a decreased magnitude drop rate during crack propagation. However, the 0° cracked specimen generated a more significant frequency drop rate with an increased crack depth ratio. On the other hand, several peaks were presented at various locations where no defect was present in the MSE-DI plots. This suggests that the MSE-DI approach for assessing damage is unsuitable for detecting cracks beneath stiffening elements due to the restriction of the unique mode shape at the crack's location.

Fatigue cracking characteristics of components stiffened with vertical ribs under eccentric loading in steel bridge deck

The components in orthotropic steel decks are generally in an eccentrically loaded state for the nonuniformly distributed wheel loads. By conducting numerical simulation and fatigue tests of components stiffened by the vertical rib (CVR) with single butt weld, the propagation law of CVR cracks under eccentric loading were analyzed. By comparing with components stiffened by U-ribs (CUR), the difference of crack-growth characteristics between components with single and multi butt welds under eccentric loading was explored. The results show that CVR cracks will initiate at the eccentrically loaded side of the weld and propagate obliquely, but still perform the bilateral cracking mode as that under symmetric loading. The CUR and CVR cracks present the same three-stage characteristics of fast-slow-rapid growth and components will accelerate to failure in the third stage, which shall be avoided. The section-damage rate of CUR will be greatly relieved for the unilateral cracking under eccentric loading compared with that of bilateral cracking under symmetric loading, which delays the crack to enter the rapid-growth stage. Since there’s little effect of eccentric loading on the demarcations of crack-growth stages in CVR, it is reasonable to take the demarcation 80 mm between the second and third crack-growth stages as the warning length for maintenance. The semi-elliptical CVR cracks will quickly penetrate base metal after extending to 75 % of thickness with the average ratio of crack depth to length being 0.09, which can be treated as the operation timing of maintenance methods for non-penetrating cracks.