PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finitediscrete element approach

Deep underground excavations within hard rocks can result in damage to the surrounding rock mass mostly due to redistribution of stresses.Especially within rock masses with non-persistent joints,the role of the pre-existing joints in the damage evolution around the underground opening is of critical importance as they govern the fracturing mechanisms and influence the brittle responses of these hard rock masses under highly anisotropic in situ stresses.In this study,the main focus is the impact of joint network geometry,joint strength and applied field stresses on the rock mass behaviours and the evolution of excavation induced damage due to the loss of confinement as a tunnel face advances.Analysis of such a phenomenon was conducted using the finite-discrete element method (FDEM).The numerical model is initially calibrated in order to match the behaviour of the fracture-free,massive Lac du Bonnet granite during the excavation of the Underground Research Laboratory (URL) Test Tunnel,Canada.The influence of the pre-existing joints on the rock mass response during excavation is investigated by integrating discrete fracture networks (DFNs) of various characteristics into the numerical models under varying in situ stresses.The numerical results obtained highlight the significance of the pre-existing joints on the reduction of in situ rock mass strength and its capacity for extension with both factors controlling the brittle response of the material.Furthermore,the impact of spatial distribution of natural joints on the stability of an underground excavation is discussed,as well as the potentially minor influence of joint strength on the stress induced damage within joint systems of a non-persistent nature under specific conditions.Additionally,the in situ stress-joint network interaction is examined,revealing the complex fracturing mechanisms that may lead to uncontrolled fracture propagation that compromises the overall stability of an underground excavation.

FINITE ELEMENT ANALYSIS ON EVOLUTION PROCESS FOR DAMAGE MICROCRACK HEALING

Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled by surface diffusion. Two kinds of typical models for microcrack splitting are proposed, i.e., the grain boundary energy existing on the crack surface and residual stresses applying on the crack surface. And the conditions of microcrack splitting in the two models are given as a function of the microcrack aspect ratio. The microcrack with traction-free surfaces will directly evolve into a spheroid.

Stress-corrosion coupled damage localization induced by secondary phases in bio-degradable Mg alloys:phase-field modeling

In this study,a phase-field scheme that rigorously obeys conservation laws and irreversible thermodynamics is developed for modeling stress-corrosion coupled damage(SCCD).The coupling constitutive relationships of the deformation,phase-field damage,mass transfer,and electrostatic field are derived from the entropy inequality.The SCCD localization induced by secondary phases in Mg is numerically simulated using the implicit iterative algorithm of the self-defined finite elements.The quantitative evaluation of the SCCD of a C-ring is in good agreement with the experimental results.To capture the damage localization,a micro-galvanic corrosion domain is defined,and the buffering effect on charge migration is explored.Three cases are investigated to reveal the effect of localization on corrosion acceleration and provide guidance for the design for resistance to SCCD at the crystal scale.

Damage smear method for rock failure process analysis

Damage smear method(DSM)is adopted to study trans-scale progressive rock failure process,based on statistical meso-damage model and finite element solver.The statistical approach is utilized to reflect the mesoscopic rock heterogeneity.The constitutive law of representative volume element(RVE)is established according to continuum damage mechanics in which double-damage criterion is considered.The damage evolution and accumulation of RVEs are used to reveal the macroscopic rock failure characteristics.Each single RVE will be represented by one unique element.The initiation,propagation and coalescence of meso-to macro-cracks are captured by smearing failed elements.The above ideas are formulated into the framework of the DSM and programed into self-developed rock failure process analysis(RFPA)software.Two laboratory-scale examples are conducted and the well-known engineering-scale tests,i.e.Atomic Energy of Canada Limited’s(AECL’s)Underground Research Laboratory(URL)tests,are used for verification.It shows that the simulation results match with other experimental results and field observations.

Cross spectral energy method for damage assessment of the cable-stayed bridge under operational conditions

The new cross spectral energy method(CSEM)is proposed for maintaining cable-stayed bridge safe-ty by the measurable output-only vibration response.Damage assessment of real structures is limited by aseries of problems such as unknown ambient excitation forces,errors introduced by system identification,incomplete dynamic measurements,etc.Thus the methodology based on cross spectral energy of eachsubstructure member is derived to meet these challenges.The novel damage index does not require anymodal or parameter identification technology.It can be calculated directly from vibration test data.In or-der to evaluate the efficiency of the presented methodology,a three dimensional(3D)actual cable-stayedbridge model with one or more damaged positions under operational conditions was studied.In order totestify the reliability of damage detection method,the response data was polluted by the random noise.Itis proved that the proposed method can successfully localize all damage cases even in noisy data.Withthe help of examples,the CSEM can potentially be applied as a nondestructive evaluation technique(NDT)for on-line health monitoring of cable-stayed bridges with minimum disruption of its operations.

Numerical study of fatigue damage of asphalt concrete using cohesive zone model

In order to investigate the fatigue behavior of asphalt concrete, a new numerical approach based on a bi-linear cohesive zone model （CZM） is developed. Integrated with the CZM, a fatigue damage evolution model is established to indicate the gradual degradation of cohesive properties of asphalt concrete under cyclic loading. Then the model is implemented in the finite element software ABAQUS through a user-defined subroutine. Based on the proposed model, an indirect tensile fatigue test is finally simulated. The fatigue lives obtained through numerical analysis show good agreement with laboratory results. Fatigue damage accumulates in a nonlinear manner during the cyclic loading process and damage initiation phase is the major part of fatigue failure. As the stress ratio increases, the time of the steady damage growth stage decreases significantly. It is found that the proposed fatigue damage evolution model can serve as an accurate and efficient tool for the prediction of fatigue damage of asphalt concrete.

Aero-engine Blade Fatigue Analysis Based on Nonlinear Continuum Damage Model Using Neural Networks

Fatigue life and reliability of aero-engine blade are always of important significance to flight safety.The establishment of damage model is one of the key factors in blade fatigue research.Conventional linear Miner＇s sum method is not suitable for aero-engine because of its low accuracy.A back propagation neutral network（BPNN） based on the combination of Levenberg-Marquardt（LM） and finite element method（FEM） is used to describe process of nonlinear damage accumulation behavior in material and predict fatigue life of the blade.Fatigue tests of standard specimen made from TC4 are carried out to obtain material fatigue parameters and S-N curve.A nonlinear continuum damage model（CDM）,based on the BPNN with one hidden layer and ten neurons,is built to investigate the nonlinear damage accumulation behavior,in which the results from the tests are used as training set.Comparing with linear models and previous nonlinear models,BPNN has the lowest calculation error in full load range.It has significant accuracy when the load is below 500 MPa.Especially,when the load is 350 MPa,the calculation error of the BPNN is only 0.4%.The accurate model of the blade is built by using 3D coordinate measurement technology.The loading cycle in fatigue analysis is defined from takeoff to cruise in 10 min,and the load history is obtained from finite element analysis（FEA）.Then the fatigue life of the compressor blade is predicted by using the BPNN model.The final fatigue life of the aero-engine blade is 6.55 104 cycles（10 916 h） based on the BPNN model,which is effective for the virtual design of aero-engine blade.

Modeling and simulation of bullet-barrel interaction process for the damaged gun barrel

In this paper,the influences of bore damage on the bullet-barrel interaction process and the mechanism of how bore damage results in the end of a machine gun barrel’s service life were studied,which had seldom been paid attention to in the past several decades.A novel finite element mesh generation method for the damaged barrel and a new transient coupled thermo-mechanical finite element(FE)model,which were based on the damage data obtained through barrel life tests,were developed to simulate the interior ballistics process of a coupled bullet-barrel system.Additionally,user subroutine VUAMP was developed in the FE model in order to take the bullet base pressure brought by propellant gas into account.Good consistency between the simulation results and the experimental results verified the preciseness of the proposed mesh generation method and the FE model.The simulation results show that the increase of bullet’s initial disturbance at the muzzle and the variation of its surface morphology caused by bore damage are primarily responsible for the life end of this 12.7 mm machine gun barrel.

A SINGULAR VALUE DECOMPOSITION BASED TRUNCATION ALGORITHM IN SOLVING THE STRUCTURAL DAMAGE EQUATIONS

The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods. Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.

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.

ON RESIDUAL COMPRESSIVE STRENGTH PREDICTION OF COMPOSITE SANDWICH PANELS AFTER LOW-VELOCITY IMPACT DAMAGE

This paper introduces a nonlinear finite element analysis on damage propagation behavior of composite sandwich panels under in-plane uniaxial quasi-static compression after a low velocity impact. The major damage modes due to the impact, including the residual indentation on the impacted facesheet, the initially crushed core under the impacted area, and the delamination are incorporated into the model. A consequential core crushing mechanism is incorporated into the analysis by using an element deactivation technique. Damage propagation behavior, which corresponds to those observed in sandwich compression after impact （SCAI） tests, has been successfully captured in the numerical simulation. The critical far field stress corresponding to the onset of damage propagation at specified critical locations near the damage zone are captured successfully. They show a good correlation with experimental data. These values can be used to effectively predict the residual compressive strength of low-velocity impact damaged composite sandwich panels.

Revised damage evolution equation for high cycle fatigue life prediction of aluminum alloy LC4 under uniaxial loading

The fatigue life prediction for components is a difficult task since many factors can affect the final fatigue life. Based on the damage evolution equation of Lemaitre and Desmorat, a revised two-scale damage evolution equation for high cycle fatigue is presented according to the experimental data, in which factors such as the stress amplitude and mean stress are taken into account. Then, a method is proposed to obtain the material parameters of the revised equation from the present fatigue experimental data. Finally, with the utilization of the ANSYS parametric design language （APDL） on the ANSYS platform, the coupling effect between the fatigue damage of materials and the stress distribution in structures is taken into account, and the fatigue life of specimens is predicted. The outcome shows that the numerical prediction is in accord with the experimental results, indicating that the revised two-scale damage evolution model can be well applied for the high cycle fatigue life prediction under uniaxial loading.

Effects of Stacking Sequence and Impactor Diameter on Impact Damage of Glass Fiber Reinforced Aluminum Alloy Laminate

The methods of numerical simulation and test are combined to analyze the impact behavior of glass fiber reinforced aluminum alloy laminate(GLARE).A new failure criteria is proposed to obtain the impact failure of GLARE,and combined with material progressive damage method by writing code of LS-DYNA.Low velocity impact test of GLARE is employed to validate the feasibility of the finite element model established.The simulation results have been shown that progressive damage finite element model established is reliable.Through the application of the finite element model established,the delamination of GLARE evolution progress is simulated,various failure modes of GLARE during impact are obtained,and the effects of stacking sequence and impactor diameter on the impact damage of GLARE are obtained.

Analysis of the damage mechanism of strainbursts by a global-local modeling approach

Strainburst is the most common type of rockbursts.The research of strainburst damage mechanisms is helpful to improve and optimize the rock support design in the burst-prone ground.In this study,an improved global-local modeling approach was first adopted to study strainburst damage mechanisms.The extracted stresses induced by multiple excavations from a three-dimensional(3D)global model established by fast Lagrangian analysis of continua in 3 dimensions(FLAC3D)are used as boundary conditions for a two-dimensional(2D)local model of a deep roadway built by universal distinct element code(UDEC)to simulate realistic stress loading paths and conduct a detailed analysis of rockburst damage from both micro and macro perspectives.The results suggest that the deformation and damage level of the roadway gradually increase with the growth of surrounding rock stress caused by the superposition of mining-or excavation-induced stresses of the panel and nearby roadways.The significant increase of surrounding rock stresses will result in more accumulated strain energy in two sidewalls,providing a necessary condition for the strainburst occurrence in the dynamic stage.The strainburst damage mechanism for the study site combines three types of damage:rock ejection,rock bulking,and rockfall.During the strainburst,initiation,propagation,and development of tensile cracks play a crucial role in controlling macroscopic failure of surrounding rock masses,although the shear crack always accounts for the main proportion of damage levels.The deformation and damage level of the roadway during a strainburst positively correlate with the increasing peak particle velocities(PPVs).The yielding steel arch might not dissipate kinetic energy and mitigate strainburst damage effectively due to the limited energy absorption capacity.The principles to control and mitigate strainburst damage are proposed in this paper.This study presents a systematic framework to investigate strainburst damage mechanisms using the global-local modeling approach.

NUMERICAL STUDY ON CREEP DAMAGE OF COMPOSITES AT HIGH TEMPERATURE

A unit cell model is applied to study the creep damage behavior after fiber fractures in the fiber-reinforced composites at high temperature. The user subroutine CREEP has been programmed for ABAQUS. The fiber breakage results in a new crack. The results show that the stress concentration factor resulted from the fiber breakage increases with the creep time. The creep damage takes place near the crack, and then grows in the matrix along a certain angle, up to the total failure. The influences of the ratio of modulus of the fiber to the matrix (Ef/Em) on the creep deformation, damage and stress distributions have been studied. With the increasing Ef/Em, the damage in the matrix increases. Analysis on the different ductility of matrix shows that the creep damage of low ductile matrix composites is higher than high ductile matrix composites.

Micromechanical analysis of damage evolution in splitting test of asphalt mixtures

A methodology was presented relating the microstructure of asphalt mixtures to their damage behavior. Digital image techniques were used to capture the asphalt mixture microstructure, and the finite element method was used to simulate the damage evolution of asphalt mixture through splitting test. Aggregates were modeled to be linearly elastic, and the mastics were modeled to be plastically damaged. The splitting test simulation results show that the material heterogeneity, the properties of aggregates and air voids have significant effects on the damage evolution approach. The damage behavior of asphalt mixture considering material heterogeneity is quite different from that of the conventional hypothesis of homogeneous material. The results indicate that the proposed method can be extended to the numerical analysis for the other micromechanical behaviors of asphalt concrete.

F E M ANALYSIS OF DELAMINATION BUCKLING IN COMPOSITE PLATES AND SHELLS

The purpose of the present study is to develop a new finite element method far analyzing buckling of delaminated composite plates and shells. This is achieved by establishing a new finite element called the reference-surface element. By use of the compatibility condition under Mindlin assumptions, the formulation of the reference-surface element was derived from whichever plate-element or shell-element being capable of analyzing composite plates and shells. This method assures a reasonable description of displacement field and the satisfaction of compatibility conditions for delamination problem. Numerical results for linear delamination buckling of axially compressed shells are presented to validate the method.

FATIGUE DAMAGE AND LIFETIME PREDICTION OF AERONAUTIC WELDED STRUCTURES UNDER HIGH TEMPERATURE

The fatigue damage evolution equations and the relation of fatigue damage parameter with maximum cyclic stress of superalloy GH150 and its welded structures are established. The fatigue damage evolution equations in a multiaxial stress state are also given. By use of cyclic thermal elastoplastic damage constitutive relations, the fatigue damage and lifetime predictions are carried out for the welded combustion chamber of aeroengine.

COMPUTER SIMULATION OF CREEP DAMAGE AT CRACK TIP IN SHORT FIBRE COMPOSITES

Creep damage at crack tip in short fibre composites has been sim- ulated by using the finite element method(FEM).The well-known Schapery non- linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material.A modified recurrence equation was adopted to accelerate the iteration.Kachanov-Rabotnov's damage evolution law was employed.The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called 'digit photo',which was produced by the printer.