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.

The dynamic response and damage models of rebar reinforced polymer slabs subjected to contact and near-field explosions

Non aqueous reactive polymer materials produced by the reaction of isocyanate and polyol have been widely used in infrastructure construction,which may be subjected to explosion loads during complex service conditions.The blast response of composite materials is a crucial aspect for applications in engineering structures potentially subjected to extreme loadings.In this work,damage caused to rebar reinforced polymer slabs by surface explosive charges was studied experimentally and numerically.A total of 6 field tests were carried out to investigate the performances of the failure modes of rebar reinforced polymer slabs under contact and near-field explosions.The influence of explosive quantity(10-40 g)and stand-off distances(0-20 cm)at the damage modes were studied.The results show that the failure modes of rebar reinforced polymer slabs under near-field explosion mainly were bending and surface spalling,while under the impact of contact explosion,the failure modes were craters of the top surface,spalling of the bottom surface,and middle perforation.Furthermore,a detailed fully coupled model was developed and validated with the test data.The influences of explosive quantity and slab thickness on rebar reinforced polymer slabs under contact explosion were studied.Based on this,the calculation formula between breach diameter,explosive quantity,and slab thickness is fitted.

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.

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.

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 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.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.

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.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Triaxial creep damage characteristics of sandstone under high crustal stress and its constitutive model for engineering application

The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone under high crustal stress,this study constructed nonlinear creep damage(NCD)constitutive mode based on the triaxial graded loading‒unloading creep test of sandstone in the Yuezhishan Tunnel.A numerical NCD constitutive model and a breakable lining(BL)model were developed based on FLAC3D and then applied to the stability analysis of the Yuezhishan Tunnel.Based on the creep test results of sandstone,a power function of creep rate and stress level was constructed,by which the long‐term strength was solved.The results show that the long‐term strength of the red sandstone based on the related function of the steady‐state creep rate and stress level is close to the measured stress value in engineering.The NCD model considering damage factors reflects the instantaneous and viscoelastic plasticity deformation characteristics of the red sandstone.The numerical NCD constitutive model and the BL model can reflect surrounding rock deformation characteristics and lining failure characteristics in practical engineering.The research results provide theoretical references for long‐term stability analysis of rock engineering and the deformation control of surrounding rock under high crustal stress.

Deformation and damage properties of rock-like materials subjected to multi-level loading-unloading cycles

In the process of engineering construction such as tunnels and slopes,rock mass is frequently subjected to multiple levels of loading and unloading,while previous research ignores the impact of unloading rate on the stability of rock mass.A number of uniaxial multi-level cyclic loading-unloading experiments were conducted to better understand the effect of unloading rate on the deformation behavior,energy evolution,and damage properties of rock-like material.The experimental results demonstrated that the unloading rate and relative cyclic number clearly influence the deformation behavior and energy evo-lution of rock-like samples.In particular,as the relative cyclic number rises,the total strain and reversible strain both increase linearly,while the total energy density,elastic energy density,and dissipated energy density all rise nonlinearly.In contrast,the irreversible strain first decreases quickly,then stabilizes,and finally rises slowly.As the unloading rate increases,the total strain and reversible strain both increase,while the irreversible strain decreases.The dissipated energy damage was examined in light of the aforementioned experimental findings.The accuracy of the proposed damage model,which takes into account the impact of the unloading rate and relative cyclic number,is then confirmed by examining the consistency between the model predicted and the experimental results.The proposed damage model will make it easier to foresee how the multi-level loading-unloading cycles will affect the rock-like materials.

A Compensation Algorithm for Large Element Characterizing the Damage Evolution Process and Its Application to Structure Collisions

When simulating the process from elastic–plastic deformation,damage to failure in a metal structure collision,it is necessary to use the large shell element due to the calculation efficiency,but this would affect the accuracy of damage evolution simulation.The compensation algorithm adjusting failure strain according to element size is usually used in the damage model to deal with the problem.In this paper,a new nonlinear compensation algorithm between failure strain and element size was proposed,which was incorporated in the damage model GISSMO(Generalized incremental stress state dependent damage model)to characterize ductile fracture.And associated material parameters were calibrated based on tensile experiments of aluminum alloy specimens with notches.Simulation and experimental results show that the new compensation algorithm significantly reduces the dependence of element size compared with the constant failure strain model and the damage model with the linear compensation algorithm.During the axial splitting process of a circular tubular structure,the new compensation algorithm keeps the failure prediction errors low over the stress states ranging from shear to biaxial tension,and achieves the objective prediction of the damage evolution process.This study demonstrates how the compensation algorithm resolves the contradiction between large element size and fracture prediction accuracy,and this facilitates the use of the damage model in ductile fracture prediction for engineering structures.

A Modified Model for Soil–Structure Interface Considering Random Damage of Mesoscopic Contact Elements

The interaction between soil and marine structures like submarine pipeline/pipe pile/suction caisson is a complicated geotechnical mechanism process.In this study,the interface is discretized into multiple mesoscopic contact elements that are damaged randomly throughout the shearing process due to the natural heterogeneity.The evolution equation of damage variable is developed based on the Weibull function,which is able to cover a rather wide range of distribution shapes by only two parameters,making it applicable for varying scenarios.Accordingly,a statistical damage model is established by incorporating Mohr–Coulomb strength criterion,in which the interfacial residual strength is considered whereby the strain softening behavior can be described.A concept of“semi-softening”characteristic point on shear stress–displacement curve is proposed for effectively modeling the evolution of strain softening.Finally,a series of ring shear tests of the interfaces between fine sea sand and smooth/rough steel surfaces are conducted.The predicted results using the proposed model are compared with experimental data of this study as well as some results from existing literature,indicating that the model has a good performance in modeling the progressive failure and strain softening behavior for various types of soil–structure interfaces.

Predicting the electromechanical properties of small caliber projectile impact igniter using PZT dynamic damage constitutive model considering crack propagation

Block piezoelectric ceramics(PZTs)are often used in impact igniters to provide activation energy for electric initiators.Under the action of strong impact stress,PZTs release electric energy accompanied by crack initiation,propagation and crushing.At present,the electrical output performance of PZTs in projectile is usually calculated by quasi-static piezoelectric equation without considering the dynamic effect caused by strong impact and the influence of crack propagation on material properties.So the ignition parameters are always not accurately predicted.To tackle this,a PZT dynamic damage constitutive model considering crack propagation is established based on the dynamic impact test and the crack propagation theory of brittle materials.The model is then embedded into the ABAQUS subroutine and used to simulate the electromechanical response of the impact igniter during the impact of a small caliber projectile on the target.Meanwhile,the experiments of projectile with impact igniter impact on the target are carried out.The comparison between experimental and numerical simulation results show that the established dynamic damage model can effectively predict the dynamic electromechanical response of PZTs in the missile service environment.

Damage Identification of Wind Turbine Blades–A Brief Review

The increasing size of these blades of wind turbines emphasizes the need for reliable monitoring and maintenance.This brief review explores the detection and analysis of damage in wind turbine blades.The study highlights various techniques,including acoustic emission analysis,strain signal monitoring,and vibration analysis,as effective approaches for damage detection.Vibration analysis,in particular,shows promise for fault identification by analyzing changes in dynamic characteristics.Damage indices based on modal properties,such as natural frequencies,mode shapes,and curvature,are discussed.

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.

NMR-based analysis of the effect of moisture migration on sandstone pore structure under alternating wetting and drying conditions

The wetting-drying(W-D)cycle is a type of water–rock interaction.The pore structure of rock,such as shape,size,distribution and pore throat,affects fluid storage and transport.Fractal theory and experimental research on the evolution characteristics of pore damage during the wet-dry erosion process are highly important for determining W-D damage.The mass and velocity of liquid migration are related to the pore size,porosity,fluid properties,etc.Experimental data show that the water absorption quality and velocity in rocks decrease with the number of wet-dry cycles.At the same test time,the mass and velocity of the SI water absorption method are smaller than those of the FI method.Under these two conditions,the amount and rate of water absorption represent the degree of water–rock interaction.Considering the pore evolution during the wet-dry cycling,an equation describing the motion of liquid in porous media was derived based on the imbibition-type separation model.The experimental data are in excellent agreement with the calculated values of the model.Permeability characteristics can affect the area and degree of rock deterioration as well as the development rate of pores and microcracks.Based on the interaction between permeability and pores,quantitative analysis of the weakening process(local damage)of rocks under W-D cycles can provide good reference indicators for evaluating the stability of geotechnical engineering.

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.

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.

Seismic damage of mountain tunnels during the 5.12 Wenchuan earthquake

A number of mountain tunnels suffered significant damage to various extent during the 2008 Wenchuan earthquake in China.Damage ranging from small to heavy cracking was observed both at the portal and inside the tunnels,while some sections close to the faults completely collapsed.A summary of qualitative data collected from reports and papers is presented regarding the behavior of the 55 mountain tunnels near the epicenter during the earthquake.Based on the seismic investigation and data collection of mountain tunnels,the tunnel damage is classified into six most common damage models involving cracking,spalling,shear failure,dislocation,pavement uplift and collapse.Detailed study and discussion are then carried out on the damage models.In order to examine the influencing factors of the damage magnitude of the mountain tunnels,the correlations between epicentral distance,earthquake intensity,overburden depth,geological condition and damage levels are analyzed.The relationships between earthquake parameters and different damagemodels are developed and discussed.Also,suggestions are provided to improve the seismic resistance of mountain tunnels.