Forecasting Damage Mechanics By Deep Learning

We in this paper exploit time series algorithm based deep learning in forecasting damage mechanics problems.The methodologies that are able to work accurately for less computational and resolving attempts are a significant demand nowadays.Relied on learning an amount of information from given data,the long short-term memory(LSTM)method and multi-layer neural networks(MNN)method are applied to predict solutions.Numerical examples are implemented for predicting fracture growth rates of L-shape concrete specimen under load ratio,single-edge-notched beam forced by 4-point shear and hydraulic fracturing in permeable porous media problems such as storage-toughness fracture regime and fracture-height growth in Marcellus shale.The predicted results by deep learning algorithms are well-agreed with experimental data.

Fracture behaviors of columnar jointed rock mass using interface mechanics theorem

For a special geological structure of columnar jointed rock mass(CJRM),its mechanical properties are strongly affected by the columnar joints.To describe the fracture behaviors of CJRM using the basic theories of interface mechanics for composite materials,the interface stresses of the vertical and horizontal joints,which are the two primary joints in the CJRM under triaxial compression,are studied,and their mathematical expressions are derived based on the superposition principle.Based on the obtained interface stresses of the vertical and horizontal joints in the CJRM,the crack initiation of the joint interface in the CJRM is studied using the maximum circumferential stress theory in fracture mechanics.Moreover,based on this investigation,the fracture behaviors of CJRM are analyzed.According to the results of similar material physical model tests for the CJRM,the theoretical study is verified.Finally,the influence of the mechanical parameters of the CJRM on the joint interface stress is discussed comprehensively.

A Hybrid Local/Nonlocal Continuum Mechanics Modeling of Damage and Fracture in Concrete Structure at High Temperatures

This paper proposes a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures.In this model,we introduce the thermal expansion into peridynamics and then couple it with the thermoelasticity based on the Morphing method.In addition,a thermomechanical constitutive model of peridynamic bond is presented inspired by the classic Mazars model for the quasi-brittle damage evolution of concrete structures under high-temperature conditions.The validity and effectiveness of the proposed model are verified through two-dimensional numerical examples,in which the influence of temperature on the damage behavior of concrete structures is investigated.Furthermore,the thermal effects on the fracture path of concrete structures are analyzed by numerical results.

Creep life assessment of aero-engine recuperator based on continuum damage mechanics approach

The creep life of an aeroengine recuperator is investigated in terms of continuum damage mechanics by using finite element simulations.The effects of the manifold wall thickness and creep properties of brazing filler metal on the operating life of the recuperator are analyzed.Results show that the crack initiates from the brazing filler metal located on the outer surface of the manifold with the wall thickness of 2 mm and propagates throughout the whole region of the brazing filler metal when the creep time reaches 34900 h.The creep life of the recuperator meets the requirement of 40000 h continuous operation when the wall thickness increases to 3.5 mm,but its total weight increases by 15%.Decreasing the minimum creep strain rate with the enhancement of the creep strength of the brazing filler metal presents an obvious effect on the creep life of the recuperator.At the same stress level,the creep rupture time of the recuperator is enhanced by 13 times if the mismatch between the minimum creep rate of the filler and base metal is reduced by 20%.

COMBINED DAMAGE FRACTURE CRITERIA FOR PIEZOELECTRIC CERAMICS

Mechanical and electrical damages are introduced to study the fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are established using the method of least squares combined with a damage analysis of the well-known piezoelectric fracture experiments of Park and Sun’s. One is based on a linear combination of the mechanical and electrical damages and the other on their nonlinear combination. When the combined damage D is up to its critical value Dc, piezoelectric fracture occurs. It is found from the qualitative comparison of the numerical results with the experimental data that the nonlinearly combined damage fracture criterion can give a better prediction of piezoelectric fracture. And it is concluded from the nonlinearly combined damage fracture criterion that a negative electric feld impedes fracture whereas the efect of a positive electric feld on fracture depends on its magnitude.

Damage and fracture mechanism of 6063 aluminum alloy under three kinds of stress states

To study the damage and fracture mechanism of 6063 aluminum alloy under different stress states,three kinds of representative triaxial stress states have been adopted,namely smooth tensile,notch tensile,and pure shear.The results of the study indicate the following.During the notch tensile test,a relatively higher stress triaxiality appears in the root of the notch.With the applied loading increasing,the volume fraction of microvoids in the root of the notch increases continuously.When it reaches the critical volume fraction of microvoids,the specimen fractures.During the pure shear test,the stress triaxiality almost equals to zero,and there is almost no microvoids but a shear band at the center of the butterfly specimen.The shear band results from nonuniform deformation constantly under the shear stress.With stress concentration,cracks are produced within the shear band and are later coalesced.When the equivalent plastic strain reaches the critical value（equivalent plastic fracture strain）,the butterfly specimen fractures.During the smooth tensile test,the stress triaxiality in the gauge of the specimen remains constant at 0.33.Thus,the volume of microvoids of the smooth tensile test is less than that of the notch tensile test and the smooth specimen fractures due to shearing between microvoids.The G-T-N damage model and Johnson-Cook model are used to simulate the notch tensile and shear test,respectively.The simulated engineering stress-strain curves fit the measured engineering stress-strain curves very well.In addition,the empirical damage evolution equation for the notch specimen is obtained from the experimental data and FEM simulations.

The law of strength damage and deterioration of jointed sandstone after dry-wet cycles

Under the periodic rise and fall of the water level in the Three Gorges Reservoir in China,the rock mass in the ebb and flow zone of the slope is always in a state of a dry-wet cycle.In order to explore the influence of dry-wet cycle on mechanical properties of jointed sandstone,the triaxial and uniaxial compression tests of dry-wet cycle of jointed sandstone were carried out.For the experiment,four groups of samples with different numbers of joints were set up,and the jointed rock samples were subjected to 20 dry-wet cycles.Using both the triaxial compression test and the Mohr-Coulomb(M-C)rock fracture criterion,the strength envelope of the sandstone samples was fitted,and their strength degradation was further analyzed and studied.The results show that:(1)The peak intensity and elastic modulus of the sandstone samples decrease with increased number of dry-wet cycles.(2)The total deterioration of mechanical properties of intact rock samples is bigger than that of jointed sandstone samples as the number of dry-wet cycles increases.(3)With the increase of confining pressure,the peak intensity of intact sandstone samples increases much more than that of jointed sandstone samples,which indicates that joints and their numbers have obvious influence.(4)Joints and their numbers play an important role in guiding the damage effects of sandstone samples,which weaken the damage caused by dry-wet cycles.Therefore,the envelope of the M-C strength criterion of intact sandstone samples moves more than that of jointed sandstone samples.

Recent Developments on Damage and Fracture of Thin-Walled Complex Components Produced by Spinning

The spinning technique has been widely used in the manufacture of aerospace thin-walled axisymmetric components because of its excellent formability. Damage and fracture,as the important defects that often occur and must be avoided in the forming and service stages of components,have attracted much attention of researchers. In this paper,the fracture behavior and laws of spinning components such as conical parts,tubular parts,and components with inner ribs are summarized,the typical coupled and uncoupled ductile fracture models are introduced,and their applications in spinning are analyzed. Meanwhile,the recent developments on the modified ductile fracture model in analyzing damage and fracture mechanisms of spinning are emphatically introduced. The results could provide guidance for the selection and establishment of appropriate ductile fracture models in the finite element simulation for the accurate prediction and analysis of fracture moment,location,form,damage mechanism,and evolution law,and help the development of precision spinning techniques for high-performance thin-walled complex components.

Fracture and Damage Behaviors of Concrete in the Fractal Space

The fracture toughness, the driving force and the fracture energy for an infinite plate with a fractal crack are investigated in the fractal space in this work. The perimeter-area relation is adopted to derive the transforma-tion rule between damage variables in the fractal space and Euclidean space. A plasticity yield criterion is introduced and a damage variable tensor is decomposed into tensile and compressive components to describe the distinct behaviors in tension and compression. A plastic damage constitutive model for concrete in the Euclidean space is developed and generalized to fractal case according to the transformation rule of damage variables. Numerical calculations of the present model with and without fractal are conducted and compared with experimental data to verify the efficiency of this model and show the necessity of considering the fractal effect in the constitutive model of concrete. The structural response and mesh sensitivity of a notched unre-inforced concrete beam under 3-point bending test are theoretical studied and show good agreement with the experimental data.

Microdynamic mechanical properties and fracture evolution mechanism of monzogabbro with a true triaxial multilevel disturbance method

The far-field microdynamic disturbance caused by the excavation of deep mineral resources and underground engineering can induce surrounding rock damage in high-stress conditions and even lead to disasters.However,the mechanical properties and damage/fracture evolution mechanisms of deep rock induced by microdynamic disturbance under three-dimensional stress states are unclear.Therefore,a true triaxial multilevel disturbance test method is proposed,which can completely simulate natural geostress,excavation stress redistribution(such as stress unloading,concentration and rotation),and subsequently the microdynamic disturbance triggering damaged rock failure.Based on a dynamic true triaxial test platform,true triaxial microdynamic disturbance tests under different frequency and amplitudes were carried out on monzogabbro.The results show that increasing amplitude or decreasing frequency diminishes the failure strength of monzogabbro.Deformation modulus gradually decreases during disturbance failure.As frequency and amplitude increase,the degradation rate of deformation modulus decreases slightly,disturbance dissipated energy increases significantly,and disturbance deformation anisotropy strengthens obviously.A damage model has been proposed to quantitatively characterize the disturbance-induced damage evolution at different frequency and amplitude under true triaxial stress.Before disturbance failure,the micro-tensile crack mechanism is dominant,and the micro-shear crack mechanism increases significantly at failure.With the increase of amplitude and frequency,the micro-shear crack mechanism increases.When approaching disturbance failure,the acoustic emission fractal dimension changes from a stable value to local large oscillation,and finally increases sharply to a high value at failure.Finally,the disturbance-induced failure mechanism of surrounding rock in deep engineering is clearly elucidated.

Effects of dry-wet cycles on the mechanical properties of sandstone with unloading-induced damage

Sandstone is the fundamental material in various engineering and construction projects.However,the mechanical integrity of sandstone can be compromised by initial unloading damage resulting from activities such as engineering excavations.Furthermore,this degradation is further exacerbated under periodic dry-wet environmental conditions.This study investigated the effects of dry-wet cycles and unloading on the mechanical properties of jointed fine sandstone using uniaxial and triaxial compression tests.These tests were performed on rock samples subjected to varying unloading degrees and different numbers of dry-wet cycles.The results demonstrate that with an increase in the unloading degree from 0%to 70%,there is a corresponding decrease in peak stress ranging from 10%to 33%.Additionally,the cohesion exhibits a reduction of approximately 20%to 25%,while the internal friction angle experiences a decline of about 3.5%to 6%.These findings emphasize a significant unloading effect.Moreover,the degree of peak stress degradation in unloading jointed fine sandstone diminishes with an increase in confining pressure,suggesting that confining pressure mitigates the deterioration caused by dry-wet cycles.Additionally,as the number of dry-wet cycles increases,there is a notable decline in the mechanical properties of the sandstone,evidencing significant dry-wet degradation.Utilizing the Drucker Prager criterion,this study establishes a strength criterion and fracture criterion,denoted as σ_(1)(m,n) and K_(T)^(Ⅱ)(m, n), to quantify the combined impacts of dry-wet cycles and unloading on jointed fine sandstone,which provides a comprehensive understanding of its mechanical behavior under such conditions.

Shear mechanical properties and fracturing responses of layered rough jointed rock-like materials

This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n)) ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.As σ_(n) increases,the peak stress shows an increasing trend,with correlation coefficients R² ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,as σ_(n) increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.

Damage evolution model of strain hardening cementitious composites under the uniaxial stress state

The deformation and damage behaviors of strain hardening cementitious composites （SHCC） under the uniaxial stress state were investigated in this paper. Two ductile failure-based constitutive models were introduced to describe the uniaxial tension and compression properties of SHCC only using a few parameters. The computation method of model parameters was developed to ease the simulation procedures. Damage evolution of the SHCC was simulated by the formulation of continuum damage mechanics subsequently. The results show that the proposed models fit the stress-strain curves reasonably well, and the damage variables show different growth rules under uniaxial tension and compression. It is concluded that the proposed method can not only simply simulate the constitutive behavior of SHCC with the reasonable accuracy but also capture the characteristic of material degradation.

A NEW DUCTILE FRACTURE THEORY AND ITS APPLICATIONS

This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characteriz;e various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility Of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness values J(1c) and delta(c) with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameters J(dc) and delta(dc) are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.

Multi-fracture interactions during two-phase flow of oil and water in deformable tight sandstone oil reservoirs

Tight oil reservoirs are complex geological materials composed of solid matrix,pore structure,and mixed multiple phases of fluids,particularly for oil reservoirs suffering from high content of in situ pressurized water found in China.In this regard,a coupled model considering two-phase flow of oil and water,as well as deformation and damage evolution of porous media,is proposed and validated using associated results,including the oil depletion process,analytical solution of stress shadow effect,and physical experiments on multi-fracture interactions and fracture propagation in unsaturated seepage fields.Then,the proposed model is used to study the behavior of multi-fracture interactions in an unsaturated reservoir in presence of water and oil.The results show that conspicuous interactions exist among multiple induced fractures.Interaction behavior varies from extracted geological profiles of the reservoir due to in situ stress anisotropy.The differential pressures of water and that of oil in different regions of reservoir affect interactions and trajectories of multi-fractures to a considerable degree.The absolute value of reservoir average pressure is a dominant factor affecting fracture interactions and in favor of enhancing fracture network complexity.In addition,difference of reservoir average pressures in different regions of reservoir would promote the fracturing effectiveness.Factors affecting fracture interactions and reservoir treatment effectiveness are quantitatively estimated through stimulated reservoir area.This study confirms the significance of incorporating the two-phase flow process in analyses of multifracture interactions and fracture trajectory predictions during tight sandstone oil reservoir developments.

Fatigue properties analysis of cracked rock based on fracture evolution process

Fracture evolution process (initiation, propagation and coalescence) of cracked rock was observed and the force- displacement curves of cracked rock were measured under uniaxial cyclic loading. The tested specimens made of sandstone-like modeling material contained three pre-existing intermittent cracks with different geometrical distributions. The experimental results indicate that the fatigue deformation limit corresponding to the maximal cyclic load is equal to that of post-peak locus of static complete force?displacement curve; the fatigue deformation process can be divided into three stages: initial deformation, constant deformation rate and accelerative deformation; the time of fracture initiation, propagation and coalescence corresponds to the change of irreversible deformation.

Statistical damage model for quasi-brittle materials under uniaxial tension

Based on the parallel bar system, combining with the synergetic method, the catastrophe theory and the acoustic emission test, a new motivated statistical damage model for quasi-brittle solid was developed. Taking concrete for instances, the rationality and the flexibility of this model and its parameters-determining method were identified by the comparative analyses between theoretical and experimental curves. The results show that the model can simulate the whole damage and fracture process in the fracture process zone of material when the materials arc exposed to quasi-static uniaxial tensile traction. The influence of the mesoscopic damage mechanism on the macroscopic mechanical properties of quasi-brittle materials is summarized into two aspects, rupture damage and yield damage. The whole damage course is divided into the statistical even damage phase and the local breach phase, corresponding to the two stages described by the catastrophe theory. The two characteristic states, the peak nominal stress state and the critical state are distinguished, and the critical state plays a key role during the whole damage evolution course.

Investigation on microscopic invasion characteristics and retention mechanism of fracturing fluid in fractured porous media

Reservoir damage caused by guar gum fracturing fluid and slick water seriously affects the subsequent oil and gas production. However, the invasion characteristics and retention mechanisms of fracturing fluids in the fracture-matrix zone are still unclear. In this work, a microscopic model reflecting the characteristics of the fracture-matrix zone was designed. Based on the microfluidic experimental method, the process of fracturing fluid invasion, flowback and retention in the fracture-matrix zone was investigated visually and characterized quantitatively. The factors and mechanisms affecting fracturing fluid retention in the fracture-matrix zone were analyzed and clarified. The results indicated that in the invasion process, the frontal swept range of slick water was larger than that of the guar gum fracturing fluid, and the oil displacement efficiency and damage rate were lower than those of the guar gum fracturing fluid under the same invasion pressure. With the increase in invasion pressure, the damage rate of slick water increased from 61.09% to 82.77%, and that of the guar gum fracturing fluid decreased from 93.45% to83.36%. Before subsequent oil production, the invaded fracturing fluid was mainly concentrated in the medium-high permeability area of the fracture-matrix zone. The main resistance of slick water was capillary force, while that of the guar fracturing fluid was mainly viscous resistance. The fracturing fluid retention was most serious in the low permeability region and the region near the end of the fracture.The experimental and numerical simulation results showed that increasing the production pressure difference could improve the velocity field distribution of the fracture-matrix zone, increase the flowback swept range and finally reduce the retention rate of the fracture fluid. The retention mechanisms of slick water in the fracture-matrix zone include emulsion retention and flow field retention, while those of the guar gum fracturing fluid include viscous retention and flow field retention. Emulsion retention is caused by capillary force and flow interception effect. Viscous retention is caused by the viscous resistance of polymer, while flow-field retention is caused by uneven distribution of flowback velocity.

Failure Patterns and Mechanisms of Hydraulic Fracture Propagation Behavior in the Presence of Naturally Cemented Fractures

In this study,we use the extended finite element method(XFEM)with a consideration of junction enrichment functions to investigate the mechanics of hydraulic fractures related to naturally cemented fractures.In the proposed numerical model,the lubrication equation is adopted to describe the fluid flow within fractures.The fluid-solid coupling systems of the hydraulic fracturing problem are solved using the Newton-Raphson method.The energy release rate criterion is used to determine the cross/arrest behavior between a hydraulic fracture(HF)and a cemented natural fracture(NF).The failure patterns and mechanisms of crack propagation at the intersection of natural fractures are discussed.Simulation results show that after crossing an NF,the failure mode along the cemented NF path may change from the tensile regime to the shear or mixed-mode regime.When an advancing HF kinks back toward the matrix,the failure mode may gradually switch back to the tensile-dominated regime.Key factors,including the length of the upper/lower portion of the cemented NF,horizontal stress anisotropy,and the intersection angle of the crack propagation are investigated in detail.An uncemented or partially cemented NF will form a more complex fracture network than a cemented NF.This study provides insight into the formation mechanism of fracture networks in formations that contain cemented NF.

A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study,an analytical method is developed to determine the deformation modulus of jointed rock masses,which considers the mechanical properties of intact rocks and joints based on the superposition principle.Due to incorporating the variations in the orientations and sizes of joint sets,the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints.In addition,an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses.The range of AIdmis from 0 to 1,and the more anisotropic the rock mass is,the larger the value of AIdmwill be.To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC).For each experimental group,the deformation modulus in 24 directions are obtained by UDEC(numerical value)and the proposed method(predicted value),and then the mean error rates are calculated.Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction,the error rate is equal to the ratio of numerical value minus predicted value to the numerical value.The results show that(i)for different experimental groups,the mean error rates vary between 5.06%and 22.03%;(ii)the error rates for the discrete fracture networks(DFNs)with two sets of joints are at the same level as those with one set of joints;and(iii)therefore,the proposed method for estimating the deformation modulus of jointed rock masses is valid.