Evolution Of Damage Variable Research Articles

A 3D objective material model for elastic–plastic damage behavior of fiber reinforced polymer composites

To simulate the plastic deformation and the progressive failure process of fiber reinforced polymer composites under 3D stress conditions, a new elastic–plastic damage model is proposed to satisfy the objectivity of 3D stress conditions. A new two-parameter 3D plasticity criterion and a simple non-associated flow potential, expressed by stress invariants of a transversely isotropic unidirectional (UD) lamina, are developed to characterize plastic deformation in an objective way. Moreover, the material degradation model and damage evolution laws are constructed on a matrix fracture angle-dependent coordinate system to ensure the objectivity of the continuum damage mechanics (CDM) approach. In addition, a new linear law alleviating mesh dependence is derived to govern the damage variable evolution in the elastic–plastic damage process. ​The effectiveness and objectivity of the proposed material model are demonstrated by a series of test cases.

Fractional Calculus-Based Statistical Damage Model of Unsaturated Soil under the Coupling Effect of Moistening and Stress Fields

Unsaturated soil exhibits extremely complex engineering mechanical properties under the coupling effect of moistening and stress fields. Firstly, the effective stress principle and limit equilibrium conditions of unsaturated soil under the coupling effect of moistening and stress fields were discussed based on the basic principles of unsaturated soil. Secondly, a fractional-order model considering the viscoelasticity and strain hardening of unsaturated soil was established based on the fractional calculus theory. Then, based on the principle of damage mechanics, the damage variable evolution equation under the coupling effect of moistening and stress fields was established, and the fractional calculus-based statistical constitutive damage model of unsaturated soil under the coupling effect of moistening and stress fields was developed. In turn, parameters of the developed model were solved using a triaxial test of unsaturated loess, and the calculated data using the developed model were compared with the experimental data, which demonstrated that the developed model in this paper performed well in describing the whole strain hardening process of unsaturated soil under the coupling effect of moistening and stress fields. Finally, the sensitivity of the main parameters of the developed model was discussed under the coupling effect of moistening and stress fields, which showed that the proposed model performed well in reflecting the main mechanical properties of unsaturated loess.

Modeling description of interface shear deformation: A theoretical study on damage statistical distributions

The shear constitutive model is important for the analysis of the interface shear deformation mechanism. In this study, five statistical distributions, including four that have never been applied in interface shear deformation, are introduced to describe the damage evolution of the interface. The corresponding statistical damage constitutive models are developed, and they have been validated using a series of experimental data (both laboratory and in-situ tests) at the rock-concrete interface. The comparison results with laboratory data show that the Mitscherlich model has the lowest prediction accuracy. By comparing with in-situ data, the Weibull model shows the best-predicted performance. Based on the Akaike information criterion metric, the Morgan-Mercer-Flodin (MMF) model performs much better than the other models in the laboratory tests, which indicates the MMF model can be introduced for a comprehensive analysis of interface shear deformation. In addition, the similarities between the MMF model and the Weibull model are found through the canonical transformation of the MMF model. And the analysis of the two unknown parameters of the MMF model shows that they are related to the yield characteristics and strength characteristics of the interface, respectively. Based on the damage variable evolution, the shear deformation of the interface can be divided into three phases, i.e., damage initiation phase, damage acceleration phase and damage slowing phase. And the parameters of the MMF model have an important influence on the damage variable curves.

Mechanical properties and acoustic emission response of carbonate fault breccias: a study from Greece

The present study aims to investigate the mechanical properties and acoustic emission (AE) response of carbonate fault rocks in Lefkada Island, Greece. In the aforementioned region, tectonic processes have resulted in the formation of fault breccias with poor mechanical properties and complex behaviour. In these weak formations, conventional laboratory testing methods are restricted due to disintegration during sampling and specimen preparation. A novel sample preparation and laboratory testing technique are used jointly with a back-analysis of a co-seismic landslide that occurred during a M w 6.5 earthquake in 2015. These two approaches are employed to characterize and predict the mechanical behaviour of these formations. The uniaxial compressive strength (UCS) of the fault breccias, determined in the laboratory, has a wide range due primarily to the complex nature of the material. The back-analysis, using a 3D limit equilibrium method, proves that the shear strength of the in situ material is significantly lower than that determined in the laboratory. Finally, the acoustic emission response of fault breccias was different compared to that of brittle rocks. Both b -value analysis and the damage variable evolution indicate that the accumulated damage within fault breccias is higher than expected, and thus they are more prone to fatigue. Thematic collection: This article is part of the Leading to Innovative Engineering Geology Practices collection available at: https://www.lyellcollection.org/topic/collections/leading-to-innovative-engineering-geology-practices

Meso-macro damage deterioration of weakly cemented red sandstone under the coupling effect of high-humidity and uniaxial loading

The physical and mechanical damage of surrounding rock caused by water–rock interaction and excavation disturbance has an important influence on the stability of the chamber. Water absorption test was conducted for the weakly cemented red sandstone in the mine under high-humidity environment. Five rock samples with different water contents were obtained through different curing times. The microstructure variation characteristics and microfracture extension and penetration mechanism of rock samples with different water contents were analyzed by scanning electron microscopy (SEM). Combined with acoustic emission monitoring, comprehensive damage variables under two contiguous states of rock samples in high-humidity environment, i.e., initial damage induced by water absorption and hydraulic coupling damage, were constructed, and the stress–strain curve variation characteristics, damage evolution law, and macroscopic failure mode of red sandstone under uniaxial compression were analyzed. The results show that the water content of red sandstone in a high-humidity environment increased logarithmically with the water absorption time. The meso-fabric changes caused by water absorption can cause initial damage, resulting in subsequent significant variation characteristics, including mechanical loading stress–strain curve characteristics, energy evolution, and macroscopic failure modes. The comprehensive damage variable evolution law constructed by acoustic emission monitoring information reflected the coupling effect of initial damage and mechanical loading damage.

Determination of crack closure stress under constant-fatigue loading based on damage variable evolution

Crack closure stress is a key stress threshold of rocks under various loading. The determination of which plays essential roles in deformation behavior and gas seepage characteristics of overlying strata. However, considering damage indicators evolution of rock under the constant-fatigue loading has rarely been studied under constant-fatigue unloading conditions. In this study, a series of uniaxial decreasing amplitude stress constant-fatigue tests were conducted on sandstone specimens to determine crack closure stress. The evolution of damage indicators depended strongly on the applied stress level. In addition, the influence of cycle numbers on the deformation and crack damage parameters was investigated. The results show that irreversible strain, elastic moduli, and load-unload response ratio show two-phase evolution characteristics. The energy evolution illustrates linear evolution when the stress level exceeds crack closure stress. However, when the stress level approaches crack closure stress, damage indicators show a three-phase evolution stage, and the energy evolution fluctuates greatly. Apart from those, the crack closure stress is a range rather than a specific value. It may be due to the progressive pre-existing or stress invasion cracks reopen. The proposed method can effectively complement existing methods to determine the crack closure stress and evaluate the stress relief extent, which is vital to improve gas drainage efficiency in overlying strata.

Damage characteristics of coal under different loading modes based on CT three-dimensional reconstruction

Due to the heterogeneous characteristics of coal materials, it is difficult to carry out repetitive tests and quantitative analysis of internal damage of coal. Therefore, the damage characteristics of coal under uniaxial and true triaxial loading was studied by numerical simulation based on 3D reconstruction modeling, and the corresponding mechanics experiment was used for auxiliary parameter validation. Firstly, the CT scanning system was used to scan the coal specimen, and the Otsu method was used to segment the original CT images to extract the three-dimensional fracture network and the distribution characteristics of mineral components. Secondly, the internal fracture and mineral distribution network model of the coal was reconstructed and imported into FLAC3D for modeling, and the numerical model was validated by fractal geometry method. The average error of fractal dimension between the original CT image and the corresponding numerical model is 1.422%, showing that the numerical model is basically consistent with the CT image of the coal, and the numerical model could reflect the distribution characteristics of the internal fractures and mineral components of the coal. Then, the basic mechanical parameters and acoustic emission (AE) response characteristics of CT reconstructed coal samples were obtained. And the mechanical parameters of the numerical model were calibrated. It can be concluded that the stress–strain curve of the coal is basically consistent with that of the numerical model, and the AE response characteristics of the coal are basically consistent with the evolution of the plastic zone of the numerical simulation, indicating that the numerical model and parameters are reasonable in this work. Moreover, the damage variable evolution of coal specimen in uniaxial compression and true triaxial loading was studied. Finally, the damage equation of coal under uniaxial compression and the relationship between damage variable and body strain energy under true triaxial loading were established.

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin, China

Shale, as a kind of brittle rock, often exhibits different nonlinear stress‐strain behavior, failure and time‐dependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10−6 s−1 to 1×10−3 s−1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate‐dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value (about 0.1 to 0.2), soon reaches its minimum (about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut‐off point and considering damage variable evolution, a new measure of micro‐mechanical strength is proposed. Based on the Lemaitre's equivalent strain assumption and the new measure of micro‐mechanical strength, a statistical strain‐rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back‐calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.

Uniaxial ratchetting and low-cycle fatigue failure behaviors of adhesively bonded butt-joints under cyclic tension deformation

Ratcheting and low-cycle fatigue failure behaviors of the adhesively bonded hollow cylindrical butt-joints has been experimentally investigated. A series of uniaxial cyclic tension experiments were carried out under stress-controlled mode. The effects of stress amplitude, mean stress and cycle time on the uniaxial ratcheting response, fatigue damage variable evolution and fatigue life of the adhesively bonded butt-joints were analyzed. The results show that the ratcheting strain, ratcheting strain rate and fatigue damage variable all increase with the increase of stress amplitude and mean stress. The shorter cycle time results in the increase of fatigue damage variable and the degradation of the stiffness of the adhesive material. It is also found that the increase of stress amplitude and mean stress can reduce the low-cycle fatigue life. Meanwhile, the fatigue life increases with the increase of cycle time for the adhesively bonded butt-joints.

Numerical Study of the Mechanical and Acoustic Emissions Characteristics of Red Sandstone under Different Double Fracture Conditions

Natural rock masses have many internal joints, fractures and faults, which greatly influence their mechanical properties during geological processes. In this paper, considering different joint angles and rock-bridge angles, uniaxial compression numerical tests on double-fractured red sandstone based on particle flow code (PFC) were carried out. The influence laws of the mechanics, acoustic emission (AE) and damage evolution characteristics of double-fractured sandstone under different crack geometry conditions were analysed. The results indicated that the peak stress and elastic modulus increase with increasing fracture angle. The peak stress and elastic modulus of rock samples first increase and then decrease with the increase in the rock-bridge angle, exhibiting a nonlinear distribution; when the angle β (rock-bridge angle) is less than or equal to 45°, the peak strain differs only slightly and decreases gradually with the increase in the rock-bridge angle. There are three stages in the AE evolution of fractured red sandstone: The initial emission of AE, the increase in AE and the decline in AE. The influences of different fracture angles and rock-bridge angles on the AE characteristic rule of rock samples vary. The damage evolution process of sandstone specimens with different joints can be divided into four stages: Initial damage, stable increase, accelerated development and stable damage. The fracture angle mainly affects the damage stage. The smaller the angle of the crack is, the greater the strain value in this stage. The rock-bridge angle mainly influences the damage variable evolution during the stable increase, accelerated damage development and stable damage stages.

Influence of liquid nitrogen cryotherapy on mechanic properties of coal and constitutive model study

ABSTRACTLiquid nitrogen (LN2) cryotherapy can lead to fracture propagation, and affect the macroscopic mechanical property of coal. To explore the influence of LN2 cryotherapy on coal mechanics, LN2 cryotherapy was applied for the anthracite and coking coal samples. Then, the stress-strain curves of non-cryogenic coal samples and LN2 cryogenic coal samples were acquired based on uniaxial compression test. Based on damage variable evolution rule, the strength statistical damage (SSD) constitutive model considering the whole process of stress-strain curve was established. The results showed that the elasticity modulus, compressive strength, brittleness index of LN2 cryogenic anthracite and coking coal were decreased compared with the non-cryogenic coal samples, respectively. Based on the test results the damage evolution rule was obtained and the constitutive model parameters were calculated. The rationality of SSD constitutive model was verified through comparison of SSD modeling results, Mazars modeling results, and test results. After LN2 cryotherapy, the coal samples changed from brittleness to ductility, which is mainly due to that the cohesive force decreased and friction force increased in loading process. In the SSD model, parameter m represents the brittle characteristics. The brittleness index decreased with the decreased of m value. This study provides a theoretical support for LN2 cryogenic technology.

Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6

The whole-life ratchetting and fatigue failure, as well as the ratchetting-fatigue interaction, of polyamide-6 (PA6) were investigated by performing a set of uniaxial stress-controlled cyclic tests at room temperature and with different stress levels. The effects of mean stress, stress amplitude and stress ratio on the evolution of ratchetting strain and the fatigue life of PA6 are discussed. Simultaneously, the evolution of damage variable, which is defined as a function of equivalent modulus, is summarized to reflect the interaction of ratchetting and fatigue damage. The experimental results show that the uniaxial whole-life ratchetting and fatigue life of PA6 are sensitive to the mean stress, stress amplitude and stress ratio. The evolution of damage variable and its dependence on the stress level are similar to that of whole-life ratchetting, and present a tri-phased feature with respect to the damage rate. By comparing the fatigue lives obtained in the asymmetrical and symmetrical tests, a detrimental effect of ratchetting deformation on the fatigue life of PA6 is found.

Experimental and Modelling Investigations of the Coupled Elastoplastic Damage of a Quasi-brittle Rock

Triaxial compression tests are conducted on a quasi-brittle rock, limestone. The analyses show that elastoplastic deformation is coupled with damage. Based on the experimental investigation, a coupled elastoplastic damage model is developed within the framework of irreversible thermodynamics. The coupling effects between the plastic and damage dissipations are described by introducing an isotropic damage variable into the elastic stiffness and yield criterion. The novelty of the model is in the description of the thermodynamic force associated with damage, which is formulated as a state function of both elastic and plastic strain energies. The latter gives a full consideration on the comprehensive effects of plastic strain and stress changing processes in rock material on the development of damage. The damage criterion and potential are constructed to determine the onset and evolution of damage variable. The return mapping algorithms of the coupled model are deduced for three different inelastic corrections. Comparisons between test data and numerical simulations show that the coupled elastoplastic damage model is capable of describing the main mechanical behaviours of the quasi-brittle rock.

RC structures cyclic behavior simulation with a model integrating plasticity, damage, and bond‐slip

SummaryThe behavior of reinforced concrete structures under severe demands, as strong ground motions, is highly complex; this is mainly due to the complexity of concrete behavior and to the strong interaction between concrete and steel, with several coupled failure modes. On the other hand, given the increasing awareness and concern on the worldwide seismic risk, new developments have arisen in earthquake engineering; nonetheless, some developments are mainly based on simple analytical tools that are widely used, given their moderate computational cost. This research aims to provide a solid basis for validation and calibration of such developments by using computationally efficient continuum mechanics‐based tools. Within this context, this paper presents a model for 3D simulation of cyclic behavior of RC structures. The model integrates a bond‐slip model developed by one of the authors and the damage variable evolution methodology for concrete damage plastic model developed by some authors. In the integrated model, a new technique is derived for efficient 3D analysis of bond‐slip of 2 or more crossing reinforcing bars in beam‐column joints, slabs, footings, pile caps, and other similar members. The analysis is performed by implementing the bond‐slip model in a user element subroutine of Abaqus and the damage variable evolution methodology in the original concrete damage plastic model in the package. Two laboratory experiments consisting of a column and a frame subjected to cyclic displacements up to failure are simulated with the proposed formulation.

Numerical Modeling and Simulation of Delamination Crack Growth in CF/Epoxy Composite Laminates under Cyclic Loading Using Cohesive Zone Model

This paper presents the mathematical modelling of fatigue damage able to carry out simulation of evolution of delamination in the laminated composite structures under cyclic loadings. A new elastic fatigue damage evolution law is proposed here. A classical interface damage evolution law, which is commonly used to predict static debonding process, is modified further to incorporate fatigue delamination effects due to high cycle loadings. The proposed fatigue damage model is identified using Fracture Mechanics tests like DCB, ENF and MMB. Simulations of delamination under fatigue loading are performed and results are successfully compared with reported experimental data on HTA/6376C unidirectional material. Delamination crack growth with variable fatigue amplitude is also performed and simulation results show that the proposed fatigue damage law can also accommodate this variable amplitude phenomenon. A study of crack tip behaviour using damage variable evolution is also carried out in this paper. Finally the effect of mesh density on crack growth is also discussed.

Ultrasonic Propagation Characteristics and Damage Evolution of Recycled Concrete under Dynamic Loading

Four types of recycled concrete specimens were made for dynamic loading tests in laboratory, in order to research the ultrasonic propagation characteristics and damage evolution of recycled concrete under dynamic loading. Ultrasonic propagation parameters such as ultrasonic propagation wave time, ultrasonic velocity and ultrasonic amplitude of recycled concrete were tested synchronously while recycled concrete were loaded. Tests results show that ultrasonic propagation wave time increased with the rise of cyclic times, while ultrasonic amplitude decreased in the same time. Damage variable evolution of recycled concrete lived through obvious three stages during the loading process. The development of inner cracks of recycled concrete in loading process accordingly were the stage of the growing of original cracks, the stage of the expansion of cracks and the stage of the linkage of cracks.

Fold zone analysis in wiping die bending process by using experimental and numerical approaches

AbstractThis paper deals with an analysis of the fold zone of bent parts within the sheet thickness by means of micro hardness measurement and numerical modelling. The failure risk has to be accurately predicted by using a continuum damage mechanics in order to avoid some expensive experiments. In this reason, a 3D numerical model, based on Lemaitre damage formulations, has been developed. The scalar damage variable D as well as the hardening law are taken to be isotropic within the sheet. The numerical approach is based on an incremental integration scheme of the constitutive equations coupled with ductile damage and von Mises criteria. The corresponding numerical algorithm is implemented into ABAQUS/Standard code. During bending operation, the damage variable evolution is computed and the hydrostatic stress effect is investigated within the sheet thickness. The hardening and plastic strain evolutions have been compared with the micro hardness one deduced from experimental tests. The comparison between experimental and numerical results illustrates the capability of the model in 3D process simulation, particularly in bending processes. Copyright © 2004 John Wiley & Sons, Ltd.