Crack propagation and damage evolution of metallic cylindrical shells under internal explosive loading

This paper investigates the three-dimensional crack propagation and damage evolution process of metallic column shells under internal explosive loading.The calibration of four typical failure parameters for 40CrMnSiB steel was conducted through experiments and subsequently applied to simulations.The numerical simulation results employing the four failure criteria were compared with the differences and similarities observed in freeze-recovery tests and ultra-high-speed tests.This analysis addressed the critical issue of determining failure criteria for the fracture of a metal shell under internal explosive loads.Building upon this foundation,the damage parameter D_(c),linked to the cumulative crack density,was defined based on the evolution characteristics of a substantial number of cracks.The relationship between the damage parameter and crack velocity over time was established,and the influence of the internal central pressure on the damage parameter and crack velocity was investigated.Variations in the fracture modes were found under different failure criteria,with the principal strain failure criterion proving to be the most effective for simulating 3D crack propagation in a pure shear fracture mode.Through statistical analysis of the shell penetration fracture radius data,it was determined that the fracture radius remained essentially constant during the crack evolution process and could be considered a constant.The propagation velocity of axial cracks ranged between 5300 m/s and 12600 m/s,surpassing the Rayleigh wave velocity of the shell material and decreasing linearly with time.The increase in shell damage exhibited an initial rapid phase,followed by deceleration,demonstrating accelerated damage during the propagation stage of the blast wave and decelerated damage after the arrival of the rarefaction wave.This study provides an effective approach for investigating crack propagation and damage evolution.The derived crack propagation and damage evolution law serves as a valuable reference for the development of crack velocity theory and the construction of shell damage evolution modes.

Detection of internal crack growth in polyethylene pipe using guided wave ultrasonic testing

Despite the success of guided wave ultrasonic inspection for internal defect detection in steel pipes,its application on polyethylene(PE)pipe remains relatively unexplored.The growth of internal cracks in PE pipe severely affects its pressure-holding capacity,hence the early detection of internal cracks is crucial for effective pipeline maintenance strategies.This study extends the scope of guided wave-based ultrasonic testing to detect the growth of internal cracks in a natural gas distribution PE pipe.Laboratory experiments and a finite element model were planned to study the wave-crack interaction at different stages of axially oriented internal crack growth with a piezoceramic transducer-based setup arranged in a pitch-catch configuration.Mode dispersion analysis supplemented with preliminary experiments was performed to isolate the optimal inspection frequency,leading to the selection of the T(0,1)mode at 50-kHz for the investigation.A transmission index based on the energy of the T(0,1)mode was developed to trace the extent of simulated crack growth.The findings revealed an inverse linear correlation between the transmission index and the crack depth for crack growth beyond 20%crack depth.

Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression

Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

An Estimation of Internal Soliton Forces on a Pile in the Ocean

Internal soliton forces on oil-platform piles in the ocean are estimated with the Morison Formula. Different from sur- face wave forces, which change only in magnitude along a pile, internal soliton forces can be distributed over the entire pile in the water and they change not only in magnitude but also in direction with depth. Our calculations show that the maximum total force caused by a soliton with its associated current of 2.1 m s-1 is nearly equal to the maximum total force exerted by a surface wave with a wavelength of 300 m and a wave-height of 18 m. The total internal soliton force is large enough to affect the operations of marine oil platforms and other facilities. Therefore, the influence of internal solitons should not be neglected in the design of oil platforms.

Electro-elastic Fields of Piezoelectric Materials with An Elliptic Hole under Uniform Internal Shearing Forces

The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields inside and outside the elliptic hole are considered.

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.

Depression and elevation internal solitary waves in a two-layer fluid and their forces on cylindrical piles

Both large amplitude depression and elevation internal solitary waves （ISWs） were observed on the continental shelf of the northwest South China Sea （SCS） during the Wenchang Intemal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries （EKdV） theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly fi＇om that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.

Internal Force Distribution in Steel-Concrete Composite Structure for Pylon of Cable-Stayed Bridge

Adopting a steel-anchor beam and steel corbel composite structure in the anchor zone on pylon is one of the key techniques for the design of Jintang bridge, a cable-stayed bridge in Zhoushan, China. In order to ensure the safety of the steel-concrete composite structure, a stud connector model for the joint section was put forward. Experiments were conducted to obtain the relation between load and slip of specimen, the failure pattern of stud connector, the yield bearing capacity and ultimate bearing capacity of a single stud, etc. The whole process of the structural behavior of the specimen was comprehensively analyzed. The features of the internal force distribution in the steel-concrete composite structure and the strain distribution of stud connector under different loads were emphatically studied. The test results show that the stud connector is applicable for the steel-concrete composite structure for pylon of Jintang bridge. The stud has a good ductility performance and a obvious yield process before its destruction. The stud connector basically works in a state of elasticity under a load less than the yield load.

Three Dimensional Numerical Simulation for the Driving Force of Weld Solidification Cracking

The double ellipsoidal model of heat source is used to analyze the thermal distributions with a three dimensional finite element method (FEM). In the mechanical model, solidification effects are treated by a dynamic element rebirth scheme. The driving force is obtained in the cracking susceptible temperature range. Moreover, this paper presents the effect of solidification shrinkage, external restraint, weld start locations and material properties on the driving force. The comparison between the simulated driving force and the experimental measurements of the material resistance predicts the susceptibility of weld metal solidification cracking.

Internal Force Analysis Due to the Supporting Translation in Statically (Indeterminate) Structures for Different Elastic Modulus

For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.

A Study of the Mechanical Characteristics of a Mandibular Parasymphyseal Fracture with Internal Fixation Device Subject to Variable Bite Forces: Finite Element Analysis

In recent times, research into mandibular fracture has gained momentum from advances in scanning techniques, software/algorithm developments and improvements, and numerical structural modeling using the finite-element method (FEM). In this work, the FEM is used to model a mandibular fracture (using an inhomogeneous and orthotropic jaw model) simulating the effect of different bite tasks/forces on the stability of the fixated fracture. Specifically, bilateral and unilateral clenches (using muscle data) were studied using a low-profile 3D 4 × 2 hole mini-plate deployed for fracture fixation. Here, the mandible bone was treated as orthotropic and spatially inhomogeneous. Although the results of stress and displacement analyses, for this fixation hardware, indicate sufficient fixation under normal biting conditions, the results show that the unilateral and ipsilateral bites develop, in general, the highest stresses or displacements. Such results can guide post-surgery recommendation on bite behavior.

Analysis and Calibration of Internal Flow Force of EjectorPowered Engine Simulator System in Wind Tunnels

The ejector-powered engine simulator(EPES)system is an important piece of equipment in conducting an influence test of the intake and jet flow in low-speed wind tunnels.In this work,through the analysis of the structure and principle of EPES,three parts of the internal flow force were obtained,namely,the additional resistance before the inlet,the internal flow force in the inlet and the thrust produced by the ejector.On the assumption of one-dimensional isentropic adiabatic flow,the theoretical formulae for calculating the forces were derived according to the measured total pressure,static pressure and total temperature of the internal flow section.Subsequently,a calibration tank was used to calibrate the EPES system.On the basis of the characteristics of the EPES system,the process and method of its calibration were designed in detail,and the model installation interface of the calibration tank was reformed.By applying this method,the repeatability accuracy of the inlet flow rate calibration coefficient was less than0.05%,whereas that of the exhaust flow rate and velocity was less than 0.1%.Upon the application of the calibration coefficients to the correction of the wind tunnel experiment data,the results showed good agreement with the numerical simulation results in terms of regularity and magnitude before stall,which validates the reasonableness and feasibility of the calibration method.Analysis of the calibration data also demonstrated the consistency in the variation law and trend between the theoretical calculation and actual measurement of internal flow force,further reflecting the rationality and feasibility of the theoretical calculation.Nevertheless,the numerical difference was large and further widened with a higher ejection flow rate mainly because of the accuracy of flow measurement and the inhomogeneity of internal flow.The thrust deflection angle of EPES is an important factor in correcting this issue.In particular,the thrust deflection angle becomes larger with small ejection flow and becomes smaller with an increase in flow rate,essentially exhibiting a general change of less than 10°.

Calculation and Analysis of Internal Force in Arch Structure of Frozen Soil

Aimed at the frozen soil arch reinforcement form of upside shed used for the shield machine launching in tunneling the internal force of the structure was calculated with the aid of the structural mechanics theory. Considering the space characteristics of the structure, this calculating method is suitable for practical engineering. Moreover, the behavior of the freezing arch reinforcement structure was analyzed combined with an engineering case.

A Study of the Radial Compressive Cracking Force of Two Cassava Varieties

Radial compressive cracking force of two cassava varieties （TMS 30572 and TMS 4（2）1425） was determined. Tubers from plants about 1.5 years old, freshly harvested from the Teaching and Research Farm of Obafemi Awolowo University, Ile-Ife, Nigeria, were used for this study. The tubers were cleaned and sliced into different lengths ranging from 25 mm to 150 mm in steps of 25 mm. For each species, slices of a particular length were sorted into 8 diameter groups： 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-90 and 91-100 ram. The cracking force of the sliced tubers was determined using an adapted tensometer. Generally, the cracking force increases with increase in tuber slice length. While the average value across all diameters ranges from 504.65 N to 1,770.19 N as the tuber length varies from 25 mm to 150 mm for TMS 30572, it ranges from 428.32 N to 1,721.95 N for TMS 4（2）1425. Within the same diameter group, the compression cracking force for tubers of small lengths was significantly lower than that required for large tuber lengths. Further, while the average cracking force for TMS 30572 varies between 894.54 N and 1,287.16 N across varying diameter ranges, it varies between 715.47 N and 1,268.82 N for TMS 4（2）1425. The highest values for both varieties occur at diameter range 71-80 mm. The data generated would be useful for the development of an efficient cassava peeling machine, based on the principle of peel-flesh separation by compression and peel removal with knives.

New Insights on the Deflection and Internal Forces of a Bending Nanobeam

Nanowires, nanofibers and nanotubes have been widely used as the building blocks in micro/nano-electromechanical systems, energy harvesting or storage devices, and small-scaled measurement equipment. We report that the sur- face effects of these nanobeams have a great impact on their deflection and internal forces. A simply supported nanobeam is taken as an example. For the displacement and shear force of the nanobeam, its dangerous sections are different from those predicted by the conventional beam theory, but for the bending moment, the dangerous section is the same. Moreover, the values of these three quantities for the nanobeam are all distinct from those calculated from the conventional beam model. These analyses shed new light on the stiffness and strength check of nanobeams, which are beneficial to engineer new-types of nano-materials and nano-devices.

AN ANALYTICAL METHOD FOR SOLVING INTERNAL FORCES AND DEFORMATIONS OF BAR-SYSTEM STRUCTURE IN SPACE

In this paper, based on the idea of finite element method, the initial parametric method in bending, problem of a beam is extended to analyse the bar-system structure by employing Dirac function and llcavisidc step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.

RESEARCH ON THE FORMATION MECHANISM OF INTERNAL CRACK IN THE CONTINUOUS CASTING SLAB

In view of the periodic bending deformation of solid-liquid interface in the solidification process for continuous casting slab, the variation of temperature gradient and dendritic spacing in the front edge of the solid-liquid interface, and the nucleation and propagation process of crack were studied. It is shown that the bending deformation of the interface results in the temperature field change in the front edge of solid-liquid interface, and the occurrence of temperature gradient along drawing direction results in the growth of secondary dendrites. The initial crack formed during the middle and final stage of solidification may extend to the surface of the casting slab and become an internal crack. The results of the theoretical analysis are basically in agreement with that of the experiment.

Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing

Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.

Formation of internal cracks during soft reduction in rectangular bloom continuous casting

To investigate the formation of internal cracks in GCrl 5 bearing steels during the soft reduction process in rectangular bloom con- tinuous casting, fully coupled thermomechanieal finite element models were developed using the commercial software MSC.MARC, and microstructures and fractographs were also observed. With the finite element models, the contours of temperature, equivalent plastic strain, and equivalent vun Mises stress were simulated. It is observed that the fracture surfaces of internal cracks are covered by cleavage or quasi-cleavage facets. The region of internal cracks in the intergranular brittle fracture mode is in the mushy zone between the zero ductility temperature （ZDT） and the zero strength temperature （ZST）. The simulated equivalent plastic strain in the crack region is 2.34%-2.45%, which is larger than the critical strain （0.4%-1.5%）, and the equivalent von Mises stress is 1.84-5.05 MPa, which is within the range of criti- cal stress （3.9-7.2 MPa）, thus resulting in the occurrence of internal cracks. Reducing the soft reduction amount from 3 to 2 mm can lower the stress under the critical value.

Formation mechanism of internal cracks in continuously cast slab

In order to make clear the formation mechanism of centerline cracks incontinuously cast slabs, the form, distribution and other characteristics of the cracks wereanalyzed. The final solidification point, surface temperature of the slabs and strain in solidifyingshell were investigated. The results were that: (1) Five relatively low temperature zones exist onslab surface below the three water spraying nozzles and near the two edges, respectively, whichcorresponds to the places of centerline cracks and triangle-zone cracks. (2) Centerline cracks andtriangle-zone cracks occur because of weak secondary cooling, uneven cooling along slab width, andlarge variation of roll gap. (3) After minimizing the variation of roll gap and applying the newsecondary cooling pattern, the occurring frequency of centerline and triangle-zone cracks minimizesto zero.