Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Correlation Analysis between Fruit Cracking and Influencing Factors in Apricot

In this study, 14 representative apricot cultivars in the production were selected as the experimental materials, and their fruit cracking characteristics, as well as the correlations between fruit cracking and influencing factors （e.g., pedcarp structure, mineral elements contents, DW/FW ratio and soluble sugar content） were analyzed to provide some reference for systematic study on fruit cracking mecha- nism of apricot. The results showed the cultivars with small orderly-and compactlyarranged epidermal cells were difficult to crack, while the cultivars with big disorderly-and loosely-arranged epidermal cells were easy to crack. There was no significant correlation between pericarp thickness and cracking index. The correlations between cracking and mineral elements contents of apricot fruit were in the order as Ca 〉 Zn 〉 Mn 〉 Fe 〉 K 〉 Mg 〉 Cu. The cracking index of apricot fruit was significantly negatively correlated with Ca content, was weakly correlated with Zn and Mn contents, and was uncorrelated with Fe, K, Mg and Cu contents. Ca deficiency was the main factor affecting the fruit cracking in apricot. Under the same conditions, the higher the water content is, the lower the cracking index is; and the higher the soluble sugar content is, the higher the cracking index is.

Experimental and Numerical Analysis of Restrained Early Age Cracking based on Electrical Resistivity Using Eccentric Sample

Crack potential and hydration processes of the cement pastes were monitored using an upto-date eccentric steel cracking frame(ESCF), associated with the non-contact electrical resistivity apparatus, independently. The objective of employing the ESCF is to give a new method determining cracks of concrete at early age. The findings indicate that the lowest water-cement ratio paste reveals highest resistivity values, compasses an earlier inflection point and obtained higher stress. The eccentric restrained cracking test exhibited that lower water-cement ratio paste cracked at the earliest time, accordingly confirms cracking tendency is the highest. Tensile strength test and stresses utilizing ABAQUS simulation was performed. The crack initiation ages obtained are consistent with the experimental program results, which indicates that ABAQUS numerical analysis can well be utilized to predict the crack tendency of cement.

NEAR CRACK LINE ELASTIC－PLASTIC ANALYSIS FOR A CRACK LOADED BY ANTIPLANE POINT FORCES

In this paper, the improved near crack line analysis method proposed in Refs. [1]and [2] is used to investigate a mode Ⅲ crack loaded by antiplane point forces in aninfinite plate in an elastic-perfectly plastic solid. The solutions of this paper aresufficiently precise near the crack line region because. the assumptions of the smallscale yielding theory have not been used and no other assumptions have been taken.

The Effects of Fatigue Cracks on Fastener Loads during Cyclic Loading and on the Stresses Used for Crack Growth Analysis in Classical Linear Elastic Fracture Mechanics Approaches

High strength threaded fasteners are widely used in the aircraft industry, and service experience shows that for structures where shear loading of the joints is significant, like skin splices, fuselage joints or spar caps-web attachments, more cracks are initiated and grow from the edges of the fastener holes than from features like fillets radii and corners or from large access holes. The main causes of this cracking are the stress concentrations introduced by the fastener holes and by the threaded fasteners themselves, with the most common damage site being at the edge of the fastener holes. Intuitively, it is easy to visualize that after the crack initiation, during the growth stages, some of the load transferred initially by the fastener at the cracked hole will decrease, and it will be shed to the adjacent fasteners that will carry higher loads than in uncracked condition. Using currently available computer software, the method presented in this paper provides a relatively quick and quantitatively defined solution to account for the effects of crack length on the fastener loads transfer, and on the far field and bypass loads at each fastener adjacent to the crack. At each location, these variations are determined from the 3-dimensional distribution of stresses in the joint, and accounting for secondary bending effects and fastener tilt. Two cases of a typical skins lap splice with eight fasteners in a two rows configuration loaded in tension are presented and discussed, one representative for wing or fuselage skins configurations, and the second case representative for cost effective laboratory testing. Each case presents five cracking scenarios, with the cracks growing from approx. 0.03 inch to either the free edge, next hole or both simultaneously.

SIMULATION OF CRACK DIAGNOSIS OF ROTOR BASED ON MULTI-SCALE SINGUUR-SPECTRUM ANALYSIS

In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.

APPLICATION OF WAVELET TIME-FR EQUENCY ANALYSIS TO IDENTIFICA-TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.

Near Crack Line Elastic-Plastic Analysis for an Infinite Plate Loaded by a Pair of Point Shear Forces

The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.

FAILURE ANALYSIS AND INSPECTION OF CRACKING OF IN-SERVICE CATALYTIC REGENERATOR

The special subject 'research on life prediction technology of important in-service pressure' mainly analyzes the failure mechanism of large-sized important and criticalin-service pressure vessels under the action of working medium and investigates safety assessmentand life prediction technology with a view to enhance the operation reliability of in-servicepressure vessels in China. Based on a series of accident investigation and test & measuringresearch, the cause of cracking of catalytic regenerator is analyzed and the in-line non-destructiveexamination method and failure prevention measures for the cracking of catalytic regenerator areproposed.

Element Analysis of Ceramic Coatings under Spherical Indentation with Metallic Interlayer: PartⅡRing Crack

Spherical indentation of ceramic coatings with metallic interlayer was performed by means of axisymmetric finite element analysis （FEA）. Two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel were considered. The fracture mechanics of the ceramic coatings mechanisms due to occurrence of surface ring cracks extending traverse the coating thickness under spherical indentation are investigated within the framework of linear fracture mechanics. The J-integral associated to such cracks was computed. The evolution of J-integral vs the crack length and the indentation depth was studied. The effects of the interlayer, the coating and the substrate on the J-integral evolution were discussed. The results show that a suitable metallic interlayer can improve the fracture resistance of the coating systems under the same indentation conditions through reducing the J-integral.

Probabilistic Model Checking-Based Survivability Analysis in Vehicle-to-Vehicle Networks

Probabilistic model checking has been widely applied to quantitative analysis of stochastic systems, e.g., analyzing the performance, reliability and survivability of computer and communication systems. In this paper, we extend the application of probabilistic model checking to the vehicle to vehicle(V2V) networks. We first develop a continuous-time Markov chain(CTMC) model for the considered V2V network, after that, the PRISM language is adopted to describe the CTMC model, and continuous-time stochastic logic is used to describe the objective survivability properties. In the analysis, two typical failures are considered, namely the node failure and the link failure, respectively induced by external malicious attacks on a target V2V node, and interrupt in a communication link. Considering these failures, their impacts on the network survivability are demonstrated. It is shown that with increasing failure strength, the network survivability is reduced. On the other hand, the network survivability can be improved with increasing repair rate. The proposed probabilistic model checking-based approach can be effectively used in survivability analysis for the V2V networks, moreover, it is anticipated that the approach can be conveniently extended to other networks.

Correlation Analysis between Cracking and Mineral Element Content of Apricot Fruit

This study aimed to clarify the effectsof mineral nutrient contents on fruit cracking so as to provide certain reference for further study on fruit cracking in apricot and basis for reasonable fertilization in the production. The 39-year-old apricot trees, with plant and row spacing of 3.0 m×4.0 m, were selected as the test materials, and the effects of contents of 7 kinds of mineral elements on the fruit cracking in apricot were analyzed. The results of variance analysis showed the intensity of correlation between mineral element content and apricot fruit cracking ranked as Ca＇s 〉 Zn＇s 〉 Mn＇s 〉 Fe＇s 〉 K＇s 〉 Mg＇s 〉 Cu＇s, The content of Ca was negatively correlated with cracking index, and the correlation ,coefficient was larger; the correlations between the contents of Zn and Mn and cracking index were weaker; and the correlations between the contents of Fe, K, Mg and Cu and cracking index were extremely weak. In conclusion, Ca deficiency is the main factor affecting fruit cracking in apricot.

Elastoplastic analysis for infinite plate with centric crack loaded by two pairs of point shear forces

The near crack line analysis method was used to investigate a crack loaded by two pairs of point shear forces in an infinite plate in an elastic-perfectly plastic solid, and the analytical solution was obtained. The solutions include: the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line, law that the length of the plastic zone along the crack line is varied with an external loads, and the bearing capacity of an infinite plate with a center crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been made and no other assumption have been taken.

Cracking analysis of fracture mechanics by the finite element method of lines(FEMOL)

The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.

Cause Analysis of Crack Formation in HRB400 Screw-Thread Steel

The analysis of the crack on the HRB400 screw-thread steel surface has been carried out by means of metallographic microscope, scanning electron microscope and EDAX. It is shown that the type of inclusions in the crack steel samples is mainly class B oxide, C silicate, and the inclusion size of the majority below 10 μm, and a small number of large inclusions are observed. The content of oxygen in the steel is high, and the carbon segregation is the main reason of the crack formation of HRB400 screw-thread steel. The measures to improve the crack formation of HRB400 screw-thread steel are put forward, which provides a powerful basis for the practical production.

CRACKING BEHAVIOR AND MECHANICAL ANALYSIS ON DUPLEX STRUCTURE UNDER CYCLIC LOADING

On the basis of stress-strain analysis under cyclic loading,the mechanism,origin and cyclic number of microcraek nucleation of duplex structure materials,saying ferrite plus martensite, have been experimentally studied and calculated.Both results are in fair mutual agreement. The morphology,distribution,size and relative quantities of the constitutional phase,especial ly strengthening phase,as well as the stress-strain distribution and variation in micro-region are directly influential in the origin of microcracks in duplex structure materials.

HIGHER-ORDER ANALYSIS OF NEAR-TIP FIELDS AROUND AN INTERFACIAL CRACK BETWEEN TWO DISSIMILAR POWER LAW HARDENING MATERIALS

By means of an asymptotic expansion method of a regular series, an exact higher-order analysis has been carried out for the near-tip fields of an in- terfacial crack between two different elastic-plastic materials. The condition of plane strain is invoked. Two group of solutions have been obtained for the crack surface conditions: (1) traction free and (2) frictionless contact, respectively. It is found that along the interface ahead of crack tip the stress fields are co-order continuous while the displacement fields are cross-order continuous. The zone of dominance of the asymptotic solutions has been estimated.

AN IMPEDANCE ANALYSIS FOR CRACK DETECTION IN THE TIMOSHENKO BEAM BASED ON THE ANTI-RESONANCE TECHNIQUE

An alternative technique for crack detection in a Timoshenko beam based on the first anti-resonant frequency is presented in this paper. Unlike the natural frequency, the anti-resonant frequency is a local parameter rather than a global parameter of structures, thus the proposed technique can be used to locate the structural defects. An impedance analysis of a cracked beam stimulated by a harmonic force based on the Timoshenko beam formulation is investigated. In order to characterize the local discontinuity due to cracks, a rotational spring model based on fracture mechanics is proposed to model the crack. Subsequently, the proposed method is verified by a numerical example of a simply-supported beam with a crack. The effect of the crack size on the anti-resonant frequency is investigated. The position of the crack of the simply-supported beam is also determined by the anti-resonance technique. The proposed technique is further applied to the ＂contaminated＂ anti-resonant frequency to detect crack damage, which is obtained by adding 1-3% noise to the calculated data. It is found that the proposed technique is effective and free from the environment noise. Finally, an experimental study is performed, which further verifies the validity of the proposed crack identification technique.

Determination of Coke,Pitch and Pores/Cracks in Green Anode by Image Analysis

Carbon anodes are an essential part of the primary aluminum production. They are made of coal tar pitch, calcined petroleum coke, recycled anodes and butts. As pitch acts as a binder for the anode, its proper distribution in a green anode has a great impact on the properties of the baked anode. Information on cracks in anodes is important for the quality of the baked anode. There is presently no reliable method available to analyze and quantify the amount of coke, pitch and pores/cracks in a green anode sample. In this article, an image analysis technique has been described, that can analyze as well as quantify the area percentage of pores/cracks and weight percentages of pitch and coke. The novelty of the method is its capacity to differentiate the different components of anode.

Numerical stress analysis of crack at welded beam-to-column connection

In the past, brittle fracture of steel structure was reported rarely under earthquake. However, recent earthquakes, especially Northridge Earthquake (USA) and Hyogoken Nanbu earthquake (Japan), astonished engineers in the field of construction. The experience from recent earthquakes of USA and Japan shows that brittle fracture of welded steel structure always starts from high stress zone with welded crack [1～5] . As backing bar for grooved weld on beam flange exists, artificial crack is formed because of lack of fusion at the root of flange weld. In this paper stress distribution of connection is computed with FEM, and stress concentration at the root of flange weld is also analyzed. Stress intensity factors (SIFs), K I, at the root of flange weld are computed in the method of fracture mechanics. The computation shows that stress intensity factor on bottom flange weld is obviously higher than that on top flange weld. It is proved by the fact that brittle fracture is liable to start at the root of bottom flange weld on actual earthquake [1,4] . Finally measures are brought forward to avoid fracture of weld structure against earthquake.