Cracks Of Different Lengths Research Articles

Structural integrity of polymers processed by additive manufacturing techniques using residual strength diagrams

Motivated by the increasingly important role that polymers have in structural applications, this study aims to analyse the structural integrity of polymers through residual strength diagrams. The polymers analysed have been thermoplastics, Polylactic acid (PLA), Polyethylene terephthalate glycol-modified (PET-G) and Polyamide 12 (PA-12), as well as a thermosetting resin, processed through different additive manufacturing techniques: Fused Deposition Modelling (FDM) in the case of PLA, PET-G, Selective Laser Sintering (SLS) for PA-12 and Digital Light Processing (DLP) for the thermosetting resin. In addition, PA-12 manufactured by injection moulding was also included in this study. To obtain the residual strength diagrams, mechanical tests have been carried out on smooth specimens and on specimens with cracks of different lengths. From the analysis of the results, a prediction has been obtained by fitting a semi-empirical model that describes the structural integrity in the areas of microstructurally short cracks, long cracks and physically short cracks.

Longitudinal Shear of a Composite Material in Which the Binder and Inclusions are Weakened by Cohesive Cracks

Background: An elastic medium is considered that is weakened by a doubly periodic system of round holes filled with washers made of a homogeneous elastic material and has cohesive cracks, the surface of which is uniformly covered with a cylindrical non-metallic film. The binder (medium) is weakened by two doubly periodic systems of rectilinear cohesive cracks, directed parallel to the abscissa and ordinate axes, and the length of the crack and their dimensions are not the same (different). General concepts are constructed that describe a class of problems with doubly periodic stress distribution outside circular holes and cohesive cracks under longitudinal shear. The analysis of the limit equilibrium of cracks within the framework of the end zone model is performed on the basis of a nonlocal failure criterion with a force condition for the advancement of the crack tip and a deformation condition for determining the advance of the edge of the end zone of the crack. In solving the problem, the main resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations. The equations obtained in each approximation were solved by the Gaussian method with the choice of the main element for different order values depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing crack growth. Objective: In the considered problem, the problem of longitudinal slip weakened by cracks parallel to the x axis in the filling medium with two pairs of two periodic cracks weakened by 2 periodic circular holes is considered. In the problem, the boundary problem along the contour of the circular holes is determined, and at the same time, the surface problem is established for the cracks parallel to the x and y axes. The solution of the problem is sought analytically, and taking into account the boundary condition, a system of linear algebraic equations for circular holes and 3 singular integral equations for cracks is obtained. Theoretical Framework: The problem is solved analytically, as the system of linear algebraic equations obtained for circular holes and the system of linear integral equations are jointly solved, and the stress intensity factor at the end of the cracks is determined. Method: The problem was solved using "Kolosova Muskhalashvili" functions and "Collondia's method of solving singular integral equations". Results and Discussion: The main essence of the considered issue is that the stress intensity factor at the end of the cracks is determined according to Fig. 1. Research Implications: For the first time, the stress intensity factor was calculated in composite materials with two pairs of biperiodic cracks of different lengths weakened by biperiodic round holes. Originality/Value: For the first time, the stress intensity coefficient was determined in composite materials with two periodic two pairs of cohesive cracks.

Empirijski model koji integriše dimenzionu analizu i Bok-Behnken dizajn za detekciju pukotina u lopaticama ventilatora rotora

Due to continuous operations and manufacturing errors, fatigue cracks can emerge after hours of service; this causes a fan blade failure and potentially ruins an entire engine, turbo machinery, or rotating machinery of a similar kind. This paper focuses on the condition monitoring of the fan blade for detecting cracks occurring in these blades by analyzing the vibration responses. The mathematical formulation is carried out using the matrix method of dimensional analysis, which is dependent on the fundamental quantities of force, Length, Time, and Temperature (FLTƟ) systems of units. Numerical analysis in ANSYS software is done to comprehend the blade harmonic response for the cracked blade condition. Experimentation is also carried out on Tiera fault simulation machinery equipment, where vibration responses are measured and analyzed for crack detection in the blades. The tests were performed for three different cracks of different lengths and analyzed by varying parameters such as load speed, for which experiments are planned using a Box-Behnken design method. The test results were confirmed with the model equations developed, and notable similarities were seen between the analytical, numerical, and experimental analyses. Thus, the proposed study will help detect the cracks in the blades, thus reducing the serious accidents or failure of the machinery.

Optimizing structural topology design through consideration of fatigue crack propagation

This paper presents an advanced approach for structural topology optimization by incorporating fatigue crack propagation analysis. The extended finite element method (X-FEM) is employed to model initial crack propagation, while the Paris model serves as the basis for simulating fatigue crack growth. The proposed methodology aims to optimize the structural design by minimizing compliance while considering volume and fatigue constraints. The proposed method employs the developed bi-directional evolutionary structural optimization (BESO) algorithm. The accuracy of the proposed technique is validated through the solution of benchmark problem and is further demonstrated in its effectiveness and robustness by examining several numerical examples. The optimization process considers various crack conditions, including the absence of cracks, horizontal and vertical cracks of different lengths. The optimized topologies obtained through the proposed algorithm clearly demonstrate the impact of crack presence, crack direction, and crack length on the material distribution. Furthermore, the convergence histories of the objective function, represented by mean compliance, highlight the influence of crack length on the stiffness and converged compliance of the structure. The results demonstrate its ability to adapt the material distribution based on fatigue cracks propagation conditions and achieve optimal topologies that balance structural integrity and performance.

Non-destructive evaluation of internal cracks in glass fiber reinforced composites using the laser shearing interferometry method

Laser shearing interferometry is one of the new methods of non-destructive testing, which is based on the interference of monochromatic waves reflected from the surface of the sample. This method can evaluate the entire surface of the sample with high accuracy and speed, by directly measuring the out-of-plane displacement gradient. In this paper, the possibility of detecting subsurface cracks with various lengths and angles in composite samples has been investigated using the shearing method and thermal stimulation system. To this aim, artificial and controlled cracks of different lengths and angles were created in the manufactured composites. After validating the performance of the shearing arrangement, two radiation heat sources were used to apply the load on the samples. The effect of loading size variables, shearing size and direction, crack length, and their angle on the quality of the results was investigated. The results show that the change in loading size plays a more important role than the change in shearing size in correct crack detection. To achieve the best results in crack detection on the selected samples, optimal loading in thermal mode equal to 12 and 15 seconds from the front of the sample was obtained. Moreover, the optimal size of the shearing in the examined composite samples was estimated to be about 10% of the width of the image recorded by the camera. Using the optimized values, all subsurface cracks were identified.

Evaluation of fatigue cracks on rail material based on laser nonlinear wave modulation and adaptive particle swarm optimization - support vector machines

ABSTRACT The evaluation of fatigue cracks is essential for the detection of early damage to railway tracks. Laser nonlinear wave modulation spectroscopy using broadband excitation is an effective method for fatigue crack detection that can solve the problem of frequency combination optimisation. However, due to the complex components of laser nonlinear ultrasonic signals, the evaluation of fatigue cracks using laser nonlinear ultrasonic signals remains a challenge. In this study, wavelet packet decomposition and principal component analysis were used to extract various features of nonlinear ultrasonic signals in the frequency domain, and four new combinations of features were obtained. These new features were used as input for the evaluation model. Finally, a fatigue crack evaluation model based on adaptive particle swarm optimisation-support vector machines was proposed to accurately evaluate fatigue cracks of different lengths. The experiments conducted showed that the fourth new combination of features and evaluation model proposed in this paper can improve the accuracy of evaluating rail fatigue cracks of different lengths, reaching a classification accuracy of 97%.

Experimental Study on the Crack Initiation and Propagation of Unequal Cracks in Rock-Like Materials

The crack in the rock is a system that coexists with multiscale and interaction cracks, and it is necessary to evaluate the deformation, stability, and strength of rock mass in many engineering projects and the failure of rock are related to the distribution of cracks in the rock. Cracks of different lengths were set in rock-like materials, and uniaxial loading experiments were carried out under 30 test conditions by changing the length of the rock bridge and the short crack as well as the crack angle. During the experiment, a high-speed camera system was used to record the failure process of the specimens. The following conclusions were obtained: when the crack angle is in the range of 30°to 60° with the loading direction, the shorter cracks are more likely to propagate and coalesce. Most of the specimens initiate cracking from the outer tip of the longer crack and the key point of crack instability is the outer tip of the longer crack. The coalescence mode of the cracks is mainly related to the length of the rock bridge length and the crack angle.

Mechanism of crack propagation in penta-graphene

Penta graphene has attracted much attention due to its unique carbon atom topology and novel properties in these years. In this paper, we study the crack growth and material fracture mechanism of penta graphene under uniaxial tension systematically via molecular dynamics simulation. We explore the mechanism of stress field and influencing factors during crack growth on penta graphene. The mechanical properties of penta graphene and graphene are compared and analyzed. The effect of temperature on the mechanical properties of penta graphene is analyzed by comparing the strain-stress curves at various temperatures. The Young's modulus of penta graphene at fracture time are discussed, and we reveal that the temperature influence on Young's modulus before fracture. By designing initial cracks of different lengths on penta graphene, we investigate into the variation of stress field at both crack tips on penta graphene under stress stretching. The mechanism of crack growth and propagation on penta graphene is uncovered with more details from atomic perspective. It is found that the stress fields are concentrated on various parts on penta graphene with the different crack length. During the growth of short cracks, the stress field mainly concentrates on the crack tip during all the process. In the process of the growth of longer cracks, the stress field will first focus on the section of the crack, and then transfer to the crack tip and begin to grow and propagate around. By analyzing the reduced energy release rate during crack growth and fracture, it is suggested that the lower atomic binding energy weakens the fracture strength of penta graphene, and thus affects the mechanical properties of penta graphene.

INTEGRITY ASSESSMENT OF AN AIRCRAFT CYLINDER ASSEMBLY WITH A CRACK

The repeatability of the air-cooled piston engine cylinder assembly failure due to a crack in the cylinder head, as well as its severity from the aspect of crew and passenger safety were the main motives for our research. In this paper an integrity assessment of a cylinder assembly with a crack was performed. By modeling cracks of different lengths in the cylinder head and considering the values of stress intensity factors and J-integral values at a given crack length on the one hand and determining the critical values of these fracture mechanics parameters on the other hand, the stability of the crack was examined. As part of the research, the dependence of the crack length on the stress intensity factor was established. The methodology proposed in this paper can be adapted to assess the integrity of other similar structural elements.

Effect of hexagonal stringer design on bulging factor and stress intensity factor of cracks in the skin of pressurized aircraft fuselage

Aircraft structural fatigue is a serious issue. Untreated, it could lead to failure. Several aircraft accidents were caused by widespread fatigue damage. For cracks in the fuselage, the stress state is due to the bulging around the crack caused by applied internal pressure. This condition is characterized by a parameter called the bulging factor; it compares the stress intensity factor of a crack in curved shell to its counterpart in a plate. Bulging factor expressions are available for longitudinal and circumferential cracks but less for slanted cracks. The underlying structure that stiffens the skin of the fuselage has a direct impact on the stress intensity factor and the bulging factor of the crack. A hexagonal grid stiffening pattern has been shown to provide sufficient stiffening to the fuselage skin while using a lesser amount of material compared to the traditional orthogonal grid design. However, the response of this grid pattern in the presence of a cracked fuselage has not been studied. The current paper aims to estimate the effect of the hexagonal grid pattern on the bulging factor and stress intensity factor of cracks of various lengths and orientations in the skin of the fuselage. Results obtained are compared to the conventional orthogonal grid stiffening pattern of a fuselage structure. Several patterns were considered. Results show that cracks of different lengths and orientations in hexagonal grid stiffened panels had stress intensity factors and bulging factors that are comparable to the base case within a margin of 2%–8%.

On the Design and Development of Planar Monopole Antenna for Bone Crack/Void Detection

In this study, the design of a compact narrowband monopole antenna for bone crack detection is presented. The proposed antenna consists of a modified hexagon-shaped radiator with six triangular slits integrated on its bottom periphery, a rectangular-shaped ground plane, and a microstrip feed line of 50 Ω. The antenna is fabricated on the FR-4 substrate with a thickness of 1.6 mm, an overall size of 32 mm × 30 mm, and electrical dimensions of 0.13λ0 × 0.122λ0, where λ0 is the free space wavelength at 2.45 GHz. The resonant frequency of the designed antenna is 2.45 GHz. The antenna offers a gain of 1.68 dB and an efficiency of 85.3%. The presence of a crack in the bone is detected by observing the shift in the peak resonating frequency of the antenna. This method can detect bone fractures in a noninvasive manner. The human arm model is constructed, and the effect of bone cracks of different lengths on the resonating frequency is investigated. The pig bone and tissues are used to validate the simulated results. The simulated results are in agreement with the measured outcomes. Also, the specific absorption rate (SAR) of the antenna is calculated and found to be less than 0.57 W/kg. The designed monopole antenna has several advantages, including a small footprint, straightforward design, low cost, and easy integration with other devices. The proposed method is suitable for primary-level bone crack diagnosis.

Environmentally assisted growth of multiple cracks grouped in stacked configurations

The effect of interaction of rectilinear cracks of different lengths, grouped into stacks, under uniaxial tension normal to the cracks, on their stress-corrosion growth is studied. We examine whether the circular relaxation zone around a pre-existing crack may suppress the growth of other cracks inside the zone. It is found that the farther away neighbors may affect the growth of the considered crack not only quantitatively but, also, in a qualitative way.

Fracture Toughness Analysis of Aluminum (Al) Foil and Its Adhesion with Low-Density Polyethylene (LPDE) in the Packing Industry

Liquid food packages consist of various polymers films, which are bonded together with Aluminum foil (Al-foil) using adhesion or by direct heat. The main aim of this research was to define important material properties such as fracture toughness and some FE-simulation material model parameters such as damage initiation, damage evolution, and the adhesion between Al-foil and low-density polyethylene (LDPE) film. This investigation is based on both physical experiments and FE simulations in ABAQUS with and without initial cracks of different lengths for comparison purposes. The final FE model in ABAQUS was used to compare the numerical input parameters in an extensive study with the ambition to investigate the materials’ parameters in cases with or without adhesion between laminates. Finally, the relation between the theoretical and experimental results for Al-foil using linear elastic fracture mechanics and modified strip yield model were shown, and the fracture toughness was calculated for two different thicknesses of Al-foil.

Experimental study on damage evolution characteristics of segment structure of shield tunnel with cracks based on acoustic emission information

Cracks are constantly observed in segments due to adverse geological conditions and loads during shield construction. However, crack propagation can have a negative impact on the stress deformation of the segment structures in the long run. Revealing the characteristics of energy release during crack propagation can effectively reflect the damage evolution process. Based on an investigation of segment cracks in a subway tunnel project, this paper conducts an in-depth analysis of AE data of segments through similar model tests, and explores the influence of cracks of different lengths, quantities and positions on the damage evolution of segments of shield tunnels. The results show that cracks reduce the overall stiffness of the structure when compared with that of a segment ring with no prepared cracks, and the elastic bearing range increases slightly, while the plastic bearing range decreases obviously. With the increase of the length and number of prepared cracks, the number of ladders of AE events decreases and the height of ladders increases, and the number of AE events of segments increases continuously at the critical point of instability. The damage of segments appears earlier, and the development process of the damage and is relatively gentle if cracks are located at the arch waist. By contrast, the damage of segments is more serious if cracks are located at the arch roof and arch bottom. The results provide theoretical basis for design optimization, disease analysis and evaluation of shield tunnel.

Solution of Spur Gear Meshing Stiffness and Analysis of Degradation Characteristics

The computational model of spur gear meshing stiffness is established by using the hypothesis of cantilever beam of the gear. The meshing stiffness of spur gear is calculated by analytical method, and the distributional curve of meshing stiffness is obtained by comparison with FEM. Experimental verification of simulated results is performed by mechanical test-bed of closed flow. The experimental results show that the simulation results are in good agreement with the experimental results. Based on the FEM models of gear tooth with cracks of different lengths, the comparison between degradation trends in different meshing regions that shows that the degree of degradation in a single tooth meshing area is much higher than in a double teeth meshing region. In the FEM models of gear tooth with cracks of different lengths, the stiffness degradation rate of the double tooth indentation area increases first and then decreases, and the crack length is most obvious between 4 and 8 mm.

The Influence of Laser Shock Peening on Fatigue Properties of AA2024-T3 Alloy with a Fastener Hole

The objective of the present study was to estimate the influence of laser shock peening on the fatigue properties of AA2024-T3 specimens with a fastener hole and to investigate the possibility to heal the initial cracks in such specimens. Fatigue cracks of different lengths were introduced in the specimens with a fastener hole before applying laser shock peening. Deep compressive residual stresses, characterized by the hole drilling method, were generated into the specimens by applying laser shock peening on both sides. Subsequently, the specimens were subjected to fatigue tests. The results show that laser shock peening has a positive effect regarding the fatigue life improvement in the specimens with a fastener hole. In addition, laser shock peening leads to a healing effect on fatigue cracks. The efficiency of this effect depends on the initial crack length. The effect of laser shock peening on the fatigue life periods was determined by using resonant frequency graphs.

Identification of Crack Length and Angle at the Center Weld Seam of Offshore Platforms Using a Neural Network Approach

The reconstruction algorithm for the probabilistic inspection of damage (RAPID) is aimed at localizing structural damage via the signal difference coefficient (SDC) between the signals of the present and reference conditions. However, tomography is only capable of presenting the approximate location and not the length and angle of defects. Therefore, a new quantitative evaluation method called the multiple back propagation neural network (Multi-BPNN) is proposed in this work. The Multi-BPNN employs SDC values as input variables and outputs the predicted length and angle, with each output node depending on an individual hidden layer. The cracks of different lengths and angles at the center weld seam of offshore platforms are simulated numerically. The SDC values of the simulations and experiments were normalized for each sample to eliminate external interference in the experiments. Then, the normalized simulation data were employed to train the proposed neural network. The results of the simulations and experimental verification indicated that the Multi-BPNN can effectively predict crack length and angle, and has better stability and generalization capacity than the multi-input to multi-output back propagation neural network.

Crack healing and strength recovery of Al2O3/TiC/TiB2 ceramic tool materials

Because ceramic tool materials are sensitive to defects such as microcracks, this paper develops ceramic tool materials with crack healing function to solve this problem. In this paper, Al2O3/TiC/TiB2 ceramic tool materials were prepared by vacuum hot pressing sintering technology. Cracks of different lengths are prefabricated on the surface of the material through Vickers hardness tester. The crack healing of the material was studied by high temperature air heat treatment. According to the recovery of material strength after heat treatment and the change of microstructure, the crack healing effect of the material was judged. The effects of different heat treatment temperature, heat treatment time and crack length on the healing behavior of ceramic materials were mainly studied. Research shows that the surface crack of the material is completely filled and healed by oxidation products. The flexural strength of the specimen with pre-cracked surface is only 24.50% of that of the smooth specimen. After heat treatment at 700 °C for 60 min, the strength of the cracked specimen returns to 91.35% of that of the smooth specimen. The maximum effective crack length for crack healing of this ceramic material is 500 μm. Through micro-morphology and elemental analysis, it is found that the main mechanism of surface crack healing is the filling and healing of cracks by liquid phase oxidation products of titanium diboride, namely boron trioxide and titanium dioxide, thus restoring the flexural strength of the material.

Study of Simulation Test in Inclusion Rockburst

Based on the existing classification research of rockburst dynamic disasters, a new rockburst model is introduced. The model specimens with inclusion rock are designed and produced, and the indoor test of inclusion rockburst with or without cementation, different inclusion angles, and prefabricated cracks of different lengths is carried out. The failure process and displacement variation of rock specimens are recorded and measured by the high‐speed camera system and digital image correlation method, and based on this, the characteristics and laws of rockburst are analyzed. The results show that the failure process of inclusion rock can be divided into several periods, such as crushing and extrusion of the cement body, and the cracks in the upper left tip, the lower right tip, the lower left tip, and the upper tip are expanded and broken in different orders. The dynamic ejection failure of the rock fragments occurs when the degree of failure is severe, and the static failure occurs when the degree of failure is weak. The inclusions have cementation, and the better the cementation, the greater the stress loading required in the failure, the greater the energy accumulated, the more severe the failure, and the higher the fractal dimension of the fragments. The larger the angle of the inclusion tip, the greater the stress loading in failure; the greater the change of the u and v displacements, the more the displacement of the inclusions changed; and the more the energy accumulated, the higher the fractal dimension of the fragment. The smaller the crack length, the greater the stress loading in failure, and the more the energy accumulated, the higher the fractal dimension of the fragments in failure. With more number of cracks and the more severe expansion before failure, the failure of rock mass can be transformed from the dynamic to the static.

Experimental and numerical assessment of the work of fracture in injection-moulded low-density polyethylene

The fracture mechanics properties of injection-moulded low-density polyethylene (LDPE) sheets were investigated both experimentally and numerically. The total work of fracture was determined experimentally, by means of fracture mechanics testing of sheets of injection-moulded LDPE with side cracks of different lengths. A multi-specimen method, proposed by Kim and Joe (1987), was employed. The total work of fracture was estimated to 13 kJ/m2. The experiments were simulated numerically using the finite element method. Crack growth was enabled by inclusion of a cohesive zone, and the constitutive response of this zone was governed by a traction-separation law. The local (or essential) work of fracture was estimated through numerical analyses, where the initiation of crack growth was simulated and the outcome was compared to the experimental results. The local (i.e. essential) work of fracture was estimated to 1.7 kJ/m2, which is consistent with previous experimental measurements for the material in question. The total work of fracture, retrieved from the present experiments, agreed well with the far field values of the J-integral in the numerical analyses.