Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

A thermo-mechanical damage constitutive model for deep rock considering brittleness-ductility transition characteristics

This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.

Modeling asymmetric fracture mechanics of Mg alloy wire in drawing process

In this study,a numerical analysis was conducted on the ductile fracture of a 2-mm diameter Mg-1Zn-0.5Mn-0.5Sr-0.1Ca alloy wire during drawing.The hexagonally close-packed crystal structure of Mg alloys causes asymmetric fracture behavior,especially in the compression region.The aim of this study is to develop a comprehensive damage model for Mg alloy wire that accurately predicts ductile fracture,with a focus on the compression region.A novel experimental method was introduced to measure the ductile fracture of Mg alloy wires under different stress states.The wire drawing process was simulated using the Generalized Incremental Stress-State dependent damage(GISSMO)Model and the Semi-Analytical Model for Polymers(SAMP)model.The damage model's prediction and the experimental results were found to be in excellent agreement,especially in determining crack initiation.Computational analysis established a safe zone diagram for die angle and reduction ratio,and experimental validation confirmed the feasibility of this approach.The proposed damage model can provide a practical and reliable analysis for optimizing the drawing process of Mg alloy wire.

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

A model of continuum damage mechanics for high cycle fatigue of metallic materials

A non-linear continuum damage model was presented based on the irreversible thermodynamics framework developed by LEMAITRE and CHABOCHE. The proposed model was formulated by taking into account the influence of loading frequency on fatigue life. The parameters H and c are constants for frequency-independent materials, but functions of cyclic frequency for frequency-dependent materials. In addition, the expression of the model was discussed in detail at different stress ratios （R）. Fatigue test data of AlZnMgCu1.5 aluminium alloy and AMg6N alloy were used to verify the proposed model. The results showed that the model possesses a good ability of predicting fatigue life at different loading frequencies and stress ratios.

Thermal damage constitutive model for rock considering damage threshold and residual strength

With the gradual depletion of mineral resources in the shallow part of the earth,resource exploitation continues to move deeper into the earth,it becomes a hot topic to simulate the whole process of rock strain softening,deformation and failure in deep environment,especially under high temperature and high pressure.On the basis of Lemaitre’s strain-equivalent principle,combined with statistics and damage theory,a statistical constitutive model of rock thermal damage under triaxial compression condition is established.At the same time,taking into account the existing damage model is difficult to reflect residual strength after rock failure,the residual strength is considered in this paper by introducing correction factor of damage variable,the model rationality is also verified by experiments.Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure,initiation,expansion,penetration,and the formation of macro-cracks under coupled effect of temperature and confining pressure.Rock thermal damage shows logistic growth function with the increase of temperature.Under the same strain condition,rock total damage decreases with the rise of confining pressure.By studying the electron microscope images(SEM)of rock fracture,it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite.The model parameter F reflects the average strength of rock,and M reflects the morphological characteristics of rock stress–strain curves.The physical meanings of model parameters are clear and the model is suitable for complex stress states,which provides valuable references for the study of rock deformation and stability in deep engineering.

DAMAGE MODEL OF CONTROL FISSURE IN PERILOUS ROCK

Hitherto, perilous rock is the weakest topic in disasters studies. Specially, damage of control fissure under loads is one key technique in study of develop mechanism of perilous rock. Damage division of end area of control fissure was defined by authors, then calculation methods of timed-Poisson＇s ratio and timed-Young＇s modulus were established in damage mechanics theory. Further, the authors set up damage constitutive equation of control fissure, which founds important basis to numerical simulation for control fissure to develop.

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.

An interface shear damage model of chromium coating/steel substrate under thermal erosion load

The Cr-plated coating inside a gun barrel can effectively improve the barrel’s erosion resistance and thus increase the service life.However,due to the cyclic thermal load caused by high-temperature gunpowder,micro-element damage tends to occur within the Cr coating/steel substrate interface,leading to a gradual deterioration in macro-mechanical properties for the material in the related region.In order to mimic this cyclic thermal load and,thereby,study the thermal erosion behavior of the Cr coating on the barrel’s inner wall,a laser emitter is utilized in the current study.With the help of in-situ tensile test and finite element simulation results,a shear stress distribution law of the Cr coating/steel substrate and a change law of the interface ultimate shear strength are identified.Studies have shown that the Cr coating/steel substrate interface’s ultimate shear strength has a significant weakening effect due to increasing temperature.In this study,the interfacial ultimate shear strength decreases from 2.57 GPa(no erosion)to 1.02 GPa(laser power is 160 W).The data from this experiment is employed to establish a Cr coating/steel substrate interface shear damage model.And this model is used to predict the flaking process of Cr coating by finite element method.The simulation results show that the increase of coating crack spacing and coating thickness will increase the service life of gun barrel.

Evaluation of Blast-Resistant Performance Predicted by Damaged Plasticity Model for Concrete

in order to evaluate the capacity of reinforced concrete （RC） structures subjected to blast Ioadings, the damaged plasticity model for concrete was used in the analysis of the dynamic responses of blast-loaded RC structures, and all three failure modes were numerically simulated by the finite element software ABAQUS. Simulation results agree with the experimental observations. It is demonstrated that the damaged plasticity model for concrete in the finite element software ABAQUS can predict dynamic responses and typical flexure, flexure-shear and direct shear failure modes of the blast-loaded RC structures.

Non-linear creep damage model of sandstone under freeze-thaw cycle

To study rock damage characteristics under long-term freeze-thaw cycles and loads,rock freeze-thaw and creep damage factors were defined based on nuclear magnetic resonance porosity and volume strain,respectively.The damage factor is introduced into the basic rheological element,and the non-linear creep damage constitutive model and freeze-thaw rock equation are established to describe non-linear creep characteristics under a constant load.Simultaneously,the creep test of freeze-thaw rock under step loading is performed.Based on the test data,the applicability and accuracy of the creep damage freeze-thaw rock model are analyzed and verified.The results show that freeze-thaw cycles result in continuous rock pore structure damage and deterioration,and nuclear magnetic resonance porosity enhancement.The constant load induces increasing rock plastic deformation,volume,and creep aging damage.As the loading stress increases,the instantaneous rock elastic parameters increase,and the rheological elastic and viscosity parameters decrease.Furthermore,the damage degradation of freeze-thaw cycles weakens the rock viscoplasticity,resulting in a rapid decrease in the viscosity parameter with an increase in freeze-thaw cycles.Generally,the continuous damage of the rock is degraded,and the long-term strength decreases continuously.

Experimental investigation on dynamic response and damage models of circular RC columns subjected to underwater explosions

Reinforced concrete(RC) columns are widely used as supporting structures for high-piled wharfs.The study of damage model of a RC column due to underwater explosion is a critical issue to assess the wharfs antiknock security.In this study,the dynamic response and damage model of circular RC columns subjected to underwater explosions were investigated by means of scaled-down experiment models.Experiments were carried out in a 10.0 m diameter tank with the water depth of 2.25 m,under different explosive quantities(0.025 kg-1.6 kg),stand-off distances(0.0 m-7.0 m),and detonation depths(0.25 m-2.0 m).The shock wave load and dynamic response of experiment models were measured by configuring sensors of pressure,acceleration,strain,and displacement.Then,the load distribution characteristics,time history of test data,and damage models related to present conditions were obtained and discussed.Three damage models,including bending failure,bending-shear failure and punching failure,were identified.In addition,the experie nce model of shock wave loads on the surface of a RC column was proposed for engineering application.

A NEW DAMAGE MODEL FOR MICROCRACK-WEAKENED BRITTLE SOLIDS

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically in- creasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given.

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

To describe the deformation and strength characteristics of the corroded rock-like specimens containing a single crack under uniaxial compression,a damage constitutive model combining hydro-chemical damage with coupling damage of micro-flaws and macro-cracks is proposed.Firstly,based on phenomenological theory,the damage variable of the rock-like specimens subjected to water environment erosion and chemical corrosion is obtained.Secondly,a coupled damage variable for cracked rock-like specimens is derived based on the Lemaitre strain equivalence hypothesis,which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for a macro single crack.Then,considering the residual strength characteristics of the rock-like materials,the damage variable is modified by introducing the correction coefficient,and the damage constitutive model of the corroded rock-like specimens with a single crack under uniaxial compression is established.The model is verified by comparing the experimental stress−strain curves,and the results are in good agreement with those provided in the literature.Finally,the correction coefficient of the damage variable proposed in this paper is discussed.The damage constitutive model developed in this paper provides an effective method to describe the stress−strain relationship and residual strength characteristics of the corroded rock-like specimens with a single crack under uniaxial compression.

Acoustic emission activity in directly tensile test on marble specimens and its tensile damage constitutive model

For understanding acoustic emission （AE） activity and accumulation of micro-damage inside rock under pure tensile state, the AE signals has been monitored on the test of directly tension on two kinds of marble specimens. A tensile constitutive model was proposed with the damage factor calculated by AE energy rate. The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition. With increasing of loading, the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing. In repeated loading cycle, the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading. It means the linear weakening occurring in the specimens. The AE activity was corresponding with occurrence of nonlinear deformation. In the initial loading stage which only elastic deformation happened on the specimens, there were few AE events occurred; while when the nonlinear deformation happened with increasing of loading, lots of AE events were generated. The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus. The Kaiser effect of AE activity could be clearly observed in tensile cycle loading. Based on the theory of damage mechanics, the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants. The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.

MICROMECHANICAL DAMAGE MODEL FOR ROCKS AND CONCRETES SUBJECTED TO COUPLED TENSILE AND SHEAR STRESSES

Based on the analysis of the deformation in an infinite isotropic elastic matrix with an embedded elliptic crack under far field coupled tensile and shear stresses, the energy release rate and a mixed fracture criterion are obtained using an energy balance approach. The additional compliance tensor induced by a single opening elliptic microcrack in a representative volume element is derived, and the effect of microcracks with random orientations is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes is obtained and is verified with experimental results.

A Damage Model of Concrete under Freeze-Thaw Cycles

The frost durability of concrete is considered from structural engineering points of view.Specific failure process is analyzed and a damage model is established,which can describe the deterioration of concrete during the whole freeze thawing process.The model is verified by test data.The parameters of model can explain the effect of pore structures or water to binder ratio on frost durability of concrete.

Prediction of fracture limits of Ni-Cr based alloy under warm forming condition using ductile damage models and numerical method

The stretch forming and the deep-drawing processes were carried out at 300 and 673 K to determine the safe forming and fracture limits of IN625 alloy.The experimentally obtained strain-based fracture forming limit diagram(FFLD)was transformed into a stress-based(σ-FFLD)and effective plastic strain(EPS)vs triaxiality(η)plot to remove the excess dependency of fracture limits over the strains.For the prediction of fracture limits,seven different damage models were calibrated.The Oh model displayed the best ability to predict the fracture locus with the least absolute error.Though the experimentally obtained fracture limits have only been used for the numerical analysis,none of the considered damage models predicted the fracture strains over the entire considered range of stress triaxiality(0.33<η<0.66).The deep drawing process window helped to determine wrinkling,safe and fracture zones while drawing the cylindrical cups under different temperature and lubricating conditions.Further,the highest drawing ratio of 2 was achieved at 673 K under the lubricating condition.All the numerically predicted results of both stretch forming and deep drawing processes using the Hill 1948 anisotropic yielding function were found to be good within the acceptable range of error.

Mesomechanics coal experiment and an elastic-brittle damage model based on texture features

To accurately describe damage within coal, digital image processing technology was used to determine texture parameters and obtain quantitative information related to coal meso-cracks. The relationship between damage and mesoscopic information for coal under compression was then analysed. The shape and distribution of damage were comprehensively considered in a defined damage variable, which was based on the texture characteristic. An elastic-brittle damage model based on the mesostructure information of coal was established. As a result, the damage model can appropriately and reliably replicate the processes of initiation, expansion, cut-through and eventual destruction of microscopic damage to coal under compression. After comparison, it was proved that the predicted overall stress-strain response of the model was comparable to the experimental result.