Elastic-plastic Damage Research Articles

Influence of loading rate on failure property of concrete twin fibers pull-out test

Under the premise of considering the mesoscopic heterogeneity of each phase material, we use the dynamic finite element analysis software RFPA^3D-dynamics to establish a three-dimensional dynamic numerical model of concrete twin fibers pull-out test and study the effect of different loading rates on fracture performance of concrete twin fibers pull-out specimens. Based on the elastic damage constitutive relation of mesoscopic elements, the failure diagram of the whole process, distribution curve of interfacial shear stress, acoustic emission (AE) histogram, accumulative AE curves and AE energy analysis of each specimen have been obtained. The results show that the fracture process of concrete twin fibers pull-out specimens under different loading rates goes through the following stages: elastic stage, elastic-plastic damage stage, interface debonding stage and steel fiber pull-out stage. The higher the loading rate, the faster the crack propagation and the interfacial shear stress transmission, and the higher the cumulative acoustic emission counts and the total acoustic emission energy.

An elasto-plastic damage accumulation model for fatigue life predication of ductile metals at the yield stress

From the analysis of massive fatigue test data, we find a mismatch between the fatigue life predictions done by stress-life method (SN) and those by strain-life method (εN) around the yield stress of ductile metals. Since the SN and εN methods are widely used in engineering applications, this work aims to explain such mismatch and thereby to address the fatigue life prediction at material’s yield stress, at which the material’s elastic damage and plastic damage are comparable. Based on a normalized damage concept, we propose an elasto-plastic damage accumulation model, a data-driven approach, to evaluate the fatigue damage at the yield stress. By differentiating the damage caused by the elastic from the plastic, the damage of each loading cycle is formulated as a function of both stress and strain amplitudes to accurately capture the material’s response state. With introducing the strain-energy-density based weighting factor, the proposed model can accord well with the classical methods from low-cycle fatigue to high-cycle fatigue. When it comes to the yield stress, the fatigue life estimated by the proposed model compares favorably with the fatigue test data. Therefore, beyond clarifying the mismatch between the classical approaches, the proposed model is expected to improve the accuracy in fatigue damage evaluation of ductile metals at the yield stress.

Stochastic fatigue life prediction of Fiber-Reinforced laminated composites by continuum damage Mechanics-based damage plastic model

In this paper, the evolution of elastic–plastic damage in the composite laminates under fatigue conditions is modeled. Continuum damage mechanics (CDM) has been coupled with the bridge micromechanics model to estimate the fatigue damage and life for laminated composite structures. Based on the elastic–plastic bridging model, three damage variables are defined. These variables estimate the fiber, matrix, and fiber/matrix damage response at the ply scale. To model the beginning of plastic deformation, a yield function is utilized, and evolution equations of the damage variables are obtained. Then the developed deformation plastic model is calculated. The model parameters are calibrated by experimental data. The proposed model is implemented in Abaqus by a subroutine. The capability of the developed model under multiaxial loading is investigated. The constitutive behavior of composite laminates in different conditions is compared with experimental data. The estimated fatigue life of the CDM-plastic damage approach for different layups is in accordance with the experimental data. Numerical results confirm the plastic deformation model leads to more accurate fatigue life prediction, especially in low‐cycle fatigue. Finally, a stochastic model is applied to predict the fatigue life of composite laminates. In the stochastic approach, fiber volume fraction, critical damage parameters, and mechanical properties are modeled as random variables with normal distribution. The stochastic model emphasizes the importance of variations of mechanical properties.

Modeling and simulation of interface failure in metal-composite hybrids

The application of hybrid composites in lightweight engineering enables the combination of material-specific advantages of fiber-reinforced polymers and classical metals. The interface between the connected materials is of particular interest since failure often initializes in the bonding zone. In this contribution the connection of an aluminum component and a glass fiber-reinforced epoxy is considered on the microscale. The constitutive modeling accounts for adhesive failure of the local interfaces and cohesive failure of the bulk material. Interface failure is represented by cohesive zone models, while the behavior of the polymer is described by an elastic-plastic damage model. A gradient-enhanced formulation is applied to avoid the well-known mesh dependency of local continuum damage models. The application of numerical homogenization schemes allows for the prediction of effective traction-separation relations. Therefore, the influence of the local interface strength and geometry of random rough interfaces on the macroscopical properties is investigated in a numerical study. There is a positive effect of an increased roughness on the effective joint behavior.

Orthotropic elastic–plastic–damage model of beech wood based on split Hopkinson pressure and tensile bar experiments

The hardwood is a natural composite, which finds applications in many fields such as an important building material. Attention was paid to the accurate description of the European beech wood under high strain rates in order to constitute a reliable input for the finite element method. It was done on the basis of split Hopkinson tensile bar tests, taking also into consideration the previously reported pressure bar tests to capture the tensile–compressive failure asymmetry, which was incorporated through the stress triaxiality. Strains measured on the steel bars for specimens oriented in all principal loading directions were used to calibrate the fully orthotropic behaviour of elasticity, plasticity and fracture. The concept of continuum damage mechanics was applied to the damage accumulation in order to simulate the crack propagation within explicit finite elements realistically.

Failure Mechanism and Numerical Simulation of Splitting Failure for Deep High Sidewall Cavern Under High Stress

With the increase of the depth of the underground engineering, the phenomenon of splitting failure of the deep rock will appear, which is very different from the shallow cavern. In order to reveal the formation mechanism of splitting failure, mechanical model test and numerical simulations of splitting failure were carried out respectively. Using the Pubugou Hydropower Station as the engineering background, a three-dimensional (3D) geomechanical model test was conducted relying on a high stress three-dimensional load test system. The splitting failure phenomenon of high sidewall cavern was observed, and the oscillation variations of displacement and stress were measured. Based on strain gradient theory and continuum damage mechanics, an elastic–plastic damage softening model for splitting damage was established. The relationship between rock damage and energy dissipation was analyzed. Based on the strain energy density theory, the splitting failure criterion based on the strain gradient is established. A numerical analysis method for splitting damage was proposed, and a regional disintegration calculation program was developed based on a commercial finite element code. The numerical simulation results are in basic agreement with the 3D geomechanical model test.

Numerical simulation and experimental verification studies on a unified strength theory-based elastoplastic damage constitutive model of shale

The purpose of this study is to establish an elastic–plastic damage constitutive model of shale and simulate the elastic–plastic damage characteristics of shale under stress. Based on the unified strength theory and the mechanics of shale rock samples characterized in laboratory tests, a new elastic–plastic damage constitutive model for shale is established by introducing compression factors and damage variables. The main considerations include the compressibility of primary fractures and pores in the shale core, and the formation of secondary cracks in the rock matrix under stress. A fully implicit backward Euler regression mapping algorithm has been used to solve the model, and the numerical simulation results are in good agreement with the experimental results. The results show that the model established in this paper can accurately simulate the elastic–plastic damage characteristics of shale under stress, and that it provides a new numerical simulation method for describing the elastic–plastic damage in shale.

Experimental and numerical studies of T-shaped reinforced concrete members subjected to combined compression-bending-shear-torsion

The study of reinforced concrete members subjected to combined loads always has been an important research topic in the field of engineering, but the torsional behavior of T-shaped reinforced concrete members subjected to combined loads has yet to be determined. This paper is focused on providing a detailed explanation of the torsional behavior of T-shaped reinforced concrete members subjected to combined compression-bending-shear-torsion. From the perspective of experimental tests and numerical analyses, in this paper, we discuss the effects of combined loads on the torsion bearing capacity, the development of cracks and the failure mode, strains of key points in the concrete and longitudinal reinforcement, and the relation of torsion and angular displacement. We conducted experiments and numerical analyses of four groups of reinforced concrete members by using the main variables of the axial pressure ratio and the bending moment. Also, the experimental and calculated results are compared based on the elastic-plastic damage constitutive model of concrete. Based on the test data and the existing formula, we also extended the formula used to calculate the torsion bearing capacity and provided diagrams of the interaction when combined loads were applied. In addition, the results of this study highlight the turning point from torsion failure to compression-bending-torsion failure. The test results demonstrated that torsion capability increases in the specified range of axial pressure ratio and decreases as bending increases. The test results also indicate the importance of considering the effects of compression-shear-bending on the torsion bearing capacity in the engineering design.

Nonlocal plasticity-based damage modeling in quasi-brittle materials using an isogeometric approach

PurposeThis paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented.Design/methodology/approachIn this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented.FindingsThe proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables.Research limitations/implicationsThe method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work.Practical implicationsThe nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.Social implicationsThe nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.Originality/valueThe present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

Ductile failure analysis of epoxy resin plates containing multiple circular arc cracks by means of the equivalent material concept

Ductile failure of polymeric samples weakened by circular arc cracks is studied theoretically and experimentally in this research. Various arrangements of cracks with different arc angles are considered in the specimens such that crack tips experienced the mixed mode I/II loading conditions. Fracture tests are conducted on the multi-cracked specimens and their fracture loads are achieved. To provide the results, the equivalent material concept (EMC) is used in conjunction of dislocation method and a brittle fracture criterion such that there is no necessity for performing complex and time-consuming elastic-plastic damage analyses. Theoretical and experimental stress intensity factors are computed and compared with each other by employing the fracture curves which demonstrate the appropriate efficiency of proposed method to predict the tests results.

STUDY ON DAMAGE CONSTITUTIVE MODEL OF RECYCLED AGGREGATE CONCRETE IN CODE FOR DESIGN OF CONCRETE STRUCTURES AND DEVELOPMENT IN ABAQUS

Based on the damage constitutive of ordinary concrete in code for Design of Concrete Structures and considering the similarity of mechanical properties between recycled aggregate concrete and ordinary concrete, a uniaxial damage constitutive of recycled concrete was proposed. At the same time, the above model was programmed as a subroutine by FORTRAN language, and the subroutine was embedded into finite element analysis software ABAQUS to simulate and analyze the uniaxial compression mechanical properties of recycled concrete. The results of finite element simulation and test are compared from the aspects of stress-strain curve and damage evolution curve. The results show that the proposed elastic-plastic damage constitutive model can effectively represent the mechanical properties of recycled aggregate concrete under uniaxial compression at different substitution rates.

Research on viscoelastic-plastic damage characteristics of cement asphalt composite binder

In order to study the viscoelastic-plastic damage of cement asphalt composite binder (simplified as CACB) and the relationship between plastic damage and viscoelastic damage, a viscoelastic-plastic constitutive model (VE-P model) was constructed, and the viscoelastic-plastic damage process of CACB was analyzed. Effects of material composition and microstructure on viscoelastic-plastic damage were studied. During creep test, with the increase of stress ratio, the proportion of plastic strain and unrecoverable strain increases, and the ability of CACB to resist deformation and deformation recovery decreases. Stress ratio has different effects on elastic damage, viscous damage, delayed elastic damage and plastic damage. Temperature has little effect on elastic damage and delayed elastic damage, but has a greater effect on plastic damage. With the increase of initial plastic damage, the damage of elasticity, viscosity and delayed elasticity intensified. When A/C = 0.8, CACB can form a more reasonable microstructure, the mechanical properties of CACB are least affected by damage, and its mechanical properties are more stable. The research results in this paper provide a theoretical basis for CACB’s material design and performance evaluation.

Creep hardening damage constitutive model of coal with fracture proppant

Abstract Fracture is the flow channel of gas (fluid) body in the exploitation of coalbed methane and other energy sources. It has a great influence on gas (fluid) production and work efficiency. Creep results in the proppant embedded in the coal seam leading to fracture damage, reducing fracture permeability. However, there are few studies on a creep model considering proppant embedding in fractures. In this paper, a creep test of proppant embedment in a fracture of a coal seam is carried out, and a creep model considering the damage to proppant embedment is established. The results show that with an increase of closure stress, the range of strain rate first increases and then decreases, and the mean value of strain rate increases slowly and then increases rapidly when the closure stress levels increases in the stable creep stage. During the creep of coal with a fracture proppant, there is not only the hardening and damage of coal, but there is also the damage to proppant embedding. A creep hardening damage model considering the viscosity damage factor of coal, the stress hardening model, the elastic-plastic damage factor, proppant compaction and the embedded viscosity loss factor is established. The creep hardening damage model can better describe the whole process of decelerating creep, stable creep and accelerating creep of coal with proppant fracture.

Three-dimensional elastic-plastic damage constitutive model of wood

Abstract A 3D combined elastic-plastic damage constitutive model for wood is proposed within the theoretical framework of classical plasticity and continuum damage mechanics (CDM). The model is able to describe the various behavior of wood under loading, including the orthotropic elasticity, strengths inequality under tension and compression in each orthotropic direction, ductile softening under longitudinal compression, brittle failure under transverse tension, and parallel shearing, densification hardening under transverse compression. Hoffman criterion and a set of eight separate failure criteria were used to define wood yielding and damage initiation, respectively. Isotropic hardening was assumed after yielding and defined by an exponential type function. The constitutive model was implicitly discretized using backward Euler method, solved through the return mapping algorithm and implemented into ABAQUS through the user-defined material subroutine (UMAT). The proposed model was firstly verified by material property tests considering different stress states: monotonic and repeated tension and compression (in both parallel and perpendicular-to-grain directions), parallel-to-grain shearing, and the interactions between perpendicular-to-grain compression/tension and parallel-to-grain shearing, etc. Mechanical behavior of typical structural elements was further simulated to validate the proposed constitutive model.

Experimental and numerical analysis on the limited ductility of H-shaped concrete cable-stayed bridge tower

When a cable-stayed bridge is subjected to strong ground motions during an earthquake, the vibration of the tower column is much stronger and more severe in the transverse direction than the longitudinal direction, due to the lateral restriction between the tower and the main girder. To address this issue, the current seismic design of cable-stayed bridge recommends that a larger reinforcement ratio in tower column be used to achieve the target seismic performance (i.e., remaining elastic). This entails an increased number of the piles and the reinforcement volume as well and thus such a design is often not cost-effective. Alternatively, the tower column can be designed to have allowable ductile behaviour for saving costs. Therefore, this study aimed to verify the ductility margin and the allowable ductile performance of the H-shaped concrete tower, by studying its lateral elastic-plastic behaviour and damage mechanism through incremental dynamic analysis, and its limited ductility against the lateral inertial forces based on quasi-static test.

A three-dimensional elastic-plastic damage model for predicting the impact behaviour of fibre-reinforced polymer-matrix composites

A three-dimensional (3-D) Finite Element Analysis (FEA) model incorporating an elastic-plastic (EP) damage model, which was implemented as a user-defined material (‘VUMAT’) sub-routine in a FEA code (‘Abaqus/Explicit’), is developed to simulate the impact response of carbon-fibre reinforced-plastic (CFRP) composites. The model predicts the load versus time and the load versus displacement responses of the composite during the impact event. Further, it predicts the extent, shape and direction of any intralaminar damage and interlaminar delaminations, i.e. interlaminar cracking, as a function of the depth through the thickness of the impacted CFRP test specimen, as well as the extent of permanent indention caused by the impactor striking the composite plate. To validate the model, experimental results are obtained from relatively low-velocity impact tests on CFRP plates employing either a matrix of a thermoplastic polymer, i.e. poly(ether-ether ketone), or a thermosetting epoxy polymer. The 3-D EP model that has been developed is shown to model successfully the experimentally-measured impact behaviour of the CFRP composites.

An Experimental Study of Dynamic Compression Performance of Self-Compacting Concrete.

To investigate the dynamic performance of self-compacting concrete (SCC), the dynamic uniaxial compression tests at eight different loading strain rates were performed on the ordinary concrete and SCC cubic specimens. Based on the tests, the compression failure patterns and stress–strain curves of both kinds of concrete were obtained. The results show that SCC performs more brittle than ordinary concrete by showing the diagonal crack failure pattern of SCC at a high strain rate. Besides, with the increase of loading strain rate, the peak compressive stress of SCC is slightly lower than that of ordinary concrete, but the increase of elastic modulus is slightly higher than that of ordinary concrete. The peak compressive strains of the two kinds of concrete are discrete under the influence of loading strain rate, thus putting forward the relation equation for the loading strain rate and peak compressive stress increase coefficient of the two kinds of concrete. Besides, based on the theory of elastic–plastic damage and considering the dynamic extension of damage, the dynamic constitutive relation with good applicability between ordinary concrete and SCC was established.

Tailoring ductile-phase toughened tungsten hierarchical microstructures for plasma-facing materials

Biological materials, such as bones, nacre, etc., have been found to exhibit attractive and unique combinations of stiffness, strength and fracture toughness. Research has been conducted in various engineering areas to mimic the naturally hierarchical microstructures or nanostructures of these materials to produce materials with optimum stiffness, high strength and fracture toughness for their intended structural applications. In the same objective, this work applies a multiscale microstructural approach recently developed (J. Nucl. Mater., (2018) 508: 371–384) to investigate the deformation and fracture behavior of ductile phase toughened tungsten (W) materials such as tungsten-nickel/iron (W-Ni/Fe) composites that possess lamellar-like and hierarchical “brick-and-mortar” (BAM) microstructures. First, the approach is used to simulate tensile loading of W-Ni/Fe specimens cut out from hot-rolled W-Ni/Fe plates which possess lamellar-like microstructures. The finite element model of the gage section of the specimen consists of a W-Ni/Fe dual-phase microstructural domain in which the constitutive behaviors of W and Ni/Fe phases are described by an elastic-plastic damage model. The predicted material stress-strain response and crack pattern development as a function of loading are then compared to the corresponding experimental results to determine the constitutive model parameters for W and Ni/Fe. Subsequently, the model parameters are used to analyze W-Ni/Fe BAM microstructures that are artificially created to investigate the effects of microstructural features and morphologies on the composite stress-strain response, damage, and fracture patterns. The modeling shows that regular BAM microstructures that experience bridging mechanism combined with crack penetration across W-phase regions exhibit significantly higher strengths than the rather random lamellar-like microstructures. More significantly, however adjusting the brick’s length-to-height ratio, the BAM microstructure can be designed to allow a more distributed damage zone which leads to increased strength, ductility and fracture energy.

Effects of Impactor Geometry on the Low-Velocity Impact Behaviour of Fibre-Reinforced Composites: An Experimental and Theoretical Investigation

Carbon-fibre/epoxy-matrix composites used in aerospace and vehicle applications are often susceptible to critical loading conditions and one example is impact loading. The present paper describes a detailed experimental and numerical investigation on the relatively low-velocity (i.e. <10 m/s) impact behaviour of such composite laminates. In particular, the effects of the geometry of the impactor have been studied and two types of impactor were investigated: (a) a steel impactor with a hemispherical head and (b) a flat-ended steel impactor. They were employed to strike the composite specimens with an impact energy level of 15 J. After the impact experiments, all the composite laminates were inspected using ultrasonic C-scan tests to assess the damage that was induced by the two different types of impactor. A three-dimensional finite-element (FE) model, incorporating a newly developed elastic-plastic damage model which was implemented as a VUMAT subroutine, was employed to simulate the impact event and to investigate the effects of the geometry of the impactor. The numerical predictions, including those for the loading response and the damage maps, gave good agreement with the experimental results.

A three-scale micro-mechanical model for elastic–plastic damage modeling of shale rocks

This paper is devoted to study the elastic–plastic damage behavior of heterogeneous shale rocks. The representative microstructure of this kind of rocks is first studied in order to define the representative elementary volume for the implementation of homogenization procedure. Three relevant material scales are considered. Inter-particle pores are distributed at the nanoscopic scale. Fine grains of calcite and kerogen are immersed at the microscopic scale. Large grains of minerals are embedded at the mesoscopic scale. Effective elastic properties of shale rocks are first determined by using a three-step linear homogenization procedure. The plastic damage behavior is estimated by developing a three-step nonlinear homogenization method. The effective plastic behavior of porous clay matrix with nanoscopic pores is described by an analytical model. The effects of small and large grains of various mineral inclusions are investigated by using a two-step incremental model. The damage due to progressive debonding of mineral inclusions is taken into account. After the implementation of the proposed model, comparisons between numerical results and experimental data are presented.