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.

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor （DSIF） at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Compressive Strength of Tubular Members with Combined Pitting Corrosion and Crack Damage

Tubular members subject to combined pitting corrosion and crack damage were numerically studied to clarify the reduction of ultimate strength and failure behavior,based on numerical models validated against available experi-ments.The effects of length,location and inclined angle of a crack under combined damage were studied to disclose the mechanism of interaction between the crack and corrosion pits.The methods,named as linear superposition directly accumulating the effects of solo crack and solo pitting damage,as well as crack projection transferring an inclined crack to a transverse one,were discussed and verified in the view of assessing ultimate strength of tubular members with combined damage.It was shown that the former is practical but complex while the next always over-estimates the residual strength.Besides,the location and inclined angle of a crack have a subtle effect on the reduction of ultimate strength under combined damage,especially at higher level of pitting damage,due to the synergistic effect between corrosion pits and cracks.Such effect can lead to early occurrence of plasticity and local buckling by inducing stress interaction between crack tips and pits,and causing more significant strength reduction compared with a solo type of damage.A practical method was proposed to determine the loss ratio of cross-sectional area on the equivalent weakest section of a damaged member.Based on the loss ratio,a formula was presented to predict the ultimate strength of damaged members with combined damage,showing good applicability.

Prediction of edge cracks and plastic-damage analysis of Mg alloy sheet in rolling

A thermal-mechanical-damage coupled finite elements model was established to investigate temperature changes, edge cracks and rolling force during roiling of magnesium alloy sheet. A cuneal sheet was also adopted to study the influence of reduction on temperature, damage and rolling force. The results show that with increasing the reduction, the rolling force increases, and the temperature of the Mg sheet decreases. Edge cracks occur when the reduction is above 51.6%, with the damage value of above 0.49. The plastic-damage in Mg sheet rolling is a result of hole development, shearing deformation and accumulative plastic strain.

Experimental evaluation of asphalt mixtures with emerging additives against cracking and moisture damage

The objective of this study was to evaluate and recommend an asphalt mixture design with emerging additive technologies that would provide superior performance against asphalt concrete(AC)stripping and cracking.To achieve this objective,a laboratory test program was developed to evaluate the use of nanomaterials(nanoclay and graphene nanoplatelet),an emerging anti-stripping agent(adhere),and warm-mix asphalt technologies(ZycoTherm,Sasobit,and EvoTherm).Two mix types were evaluated,which were a stone-matrix asphalt(SMA)and a dense-graded binder mix.In addition,the modified Lottman test(AASHTO T 283)and the indirect tensile asphalt cracking test(IDEAL-CT)test were used as performance indicators of moisture damage resistance and cracking susceptibility.Results were analyzed statistically to identify and quantify the effects of the design variables and selected additives on the performance,moisture damage resistance,and durability of asphalt mixes.Based on the cracking test results,a superior cracking resistance performance was observed with ZycoTherm,irrespective of the mix type.Adhere had the lowest average cracking indices for both mix types,which suggest that it would not perform as well as the other additives in terms of cracking resistance.Overall,SMA mixes displayed greater cracking resistance than the dense-graded mixtures,which may have been the result of the reclaimed asphalt pavement(RAP)material used in the dense-graded mix and its lower asphalt binder content.In terms of moisture resistance,both nanomaterials(graphene nanoplatelet and nanoclay)did not perform well as they did not meet the minimum required tensile strength ratio(TSR)criterion(>0.80).In addition,nanomaterials showed the lowest TSR values in both mix types suggesting that their effectiveness against moisture-induced damage may not be as good as warm-mix additives.On the other hand,warm-mix additives were expected to show enhanced performance in terms of moisture resistance as compared to the other additives evaluated in this study.

ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity.The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure.The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage, which is related to the piezoelectric properties.

Correlation analysis of longitudinal cracks and vertical deformation within asphalt pavement of cold regions

The asphalt pavement longitudinal crack is a common distress in cold regions,resulting from uneven deformation of the subgrade.Analysis of the correlation law between uneven deformation and crack distress is of positive significance for understanding the mechanism of crack initiation,and putting forward treatment measures.In view of the complexity of longitudinal crack inducement and road surface deformation,the grey relational method was used to analyze this relationship.Through long-term monitoring of the vertical deformation data of typical road sections,the vertical deformation law of the pavement surface and its deformation characteristics under the action of temperature field are analyzed.Parameters such as vertical relative deformation,vertical relative deformation rate and vertical differential deformation VDSr were constructed to describe vertical deformation characteristics.Typical distribution characteristics of longitudinal fractures and their length and distribution characteristics are also described.The grey correlation analysis theory was utilized to analyze the relationship between deformation characteristics of sections,cross sections and monitoring points and longitudinal crack characteristics(length and location).The analysis reveals a linear positive correlation or a high correlation between several indicators.This study can provide a deeper understanding of the occurrence and development mechanism of longitudinal cracks in asphalt pavement of cold areas,and give references for the research of road engineering structure,materials and distress prevention.

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.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

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.

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.

ANTIPLANE SHEAR FIELDS NEAR A CRACK-TIP IN A BRITTLE DAMAGED MATERIAL

In this paper,a simplified brittle damage model is proposed according to the Mazars-Lemaitre damage model for concrete.A closed-form solution for a mode Ⅲ crack is obtained based on the simplified model under small scale damage conditions,which allows for discontinuities of displacement-gradient and tangential stress on the damage boundary.It is pointed out that the discontinuities of field variables near the tip region exist for the brittle damaged material induced by the softening effect of the material.

THE CHARACTERISTICS OF SHORT CRACKS AND EQUIVALENT PARAMETER OF FATIGUE DAMAGE

In order to understand which parameters, such as the number of cracks and the total crack length is the useful indicators of fatigue damage, rotatory bending fatigue tests are carried out using smooth specimens of a medium-carbon steel. The behavior of short crock propagation and the evolution of surface cracks during fatigue are examined. The aim of this paper is to study how these damage parameters are correlated with the process of fatigue in order to evaluate the effectiveness of damage detection methods.

Feature extraction and damage alarming using time series analysis

Aiming at the problem of on-line damage diagnosis in structural health monitoring （SHM）, an algorithm of feature extraction and damage alarming based on auto-regressive moving-average （ARMA） time series analysis is presented. The monitoring data were first modeled as ARMA models, while a principalcomponent matrix derived from the AR coefficients of these models was utilized to establish the Mahalanobisdistance criterion functions. Then, a new damage-sensitive feature index DDSF is proposed. A hypothesis test involving the t-test method is further applied to obtain a decision of damage alarming as the mean value of DDSF had significantly changed after damage. The numerical results of a three-span-girder model shows that the defined index is sensitive to subtle structural damage, and the proposed algorithm can be applied to the on-line damage alarming in SHM.

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.

Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking

In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.

Monitoring and analysis of nonlinear dynamic damage of transport roadway supported by composite hard rock materials in Linglong Gold Mine

The study concentrates mainly on the development of failure process incomposite rock mass. By use of acoustic emission (AE), convergence inspection, pressure monitoring,level measurement techniques and the modem signal analysis technology, as well as scan electronmicroscopy (SEM) experiment, various aspects of nonlinear dynamic damage of composite rock masssurrounding the transport roadway in Linglong gold mine are discussed. According to the monitoringresults, the stability of the rock mass can be synthetically evaluated, and the intrinsic relationbetween the damage and the characteristic parameters of acoustic emission can be determined. Thelocation of the damage of rock mass can also be detected based on the acoustic emission couplemonitoring signals. Finally, the key factors which influence the stability of the transport roadwaysupported by composite hard rock materials are found out.

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.

A 3-D DDA damage analysis of brick masonry buildings under the impact of boulders in mountainous areas

In mountainous areas, geological disasters carrying large boulders can cause severe damage to the widely used masonry buildings due to the high impact forces. To better understand the damage of brick masonry buildings under the impact of boulders, a "block-joint" model is developed using threedimensional discontinuous deformation analysis(3-D DDA) to simulate the behaviour of the "brick-mortar" structure. The "block-joint" model is used to capture not only the large displacement and deformation of individual bricks but also the large-scale sliding and opening along the mortar between the bricks. The linear elastic constitutive model is applied to account for the non-plastic deformation behaviour of brick materials. Furthermore, the mechanical characteristics of the mortar are represented using the Mohr-Coulomb and Drucker-Prager criteria. To propose safe structural design schemes and effective reinforcement for brick masonry buildings, seven construction techniques are considered, includingdifferent grades of brick and mortar, effective shear areas and reinforced members. The proposed 3-D DDA model is used to analyse the velocity distribution and the key point displacements of the brick masonry building under the impact of boulders. The results show that upgrading the brick and mortar, increasing the wall thickness, making full use of the wall thickness, and adding a circular beam and structural column are very effective approaches for improving the impact resistance of brick masonry buildings.