Plastic Damage Behavior Research Articles

Predicting the rutting behaviour of asphalt concrete in the modified wheel tracking test using DEM and a cohesive viscoelastic–elastoplastic-damage contact model

AbstractThis study used an advanced modelling approach capable of capturing the complex behaviour of asphalt concrete to model the modified wheel tracking test using a recent advanced experimental test set-up in accordance with ASTM D8292-20. The modelling approach uses the discrete element method (DEM) to naturally produce the heterogeneous internal structure and governs the behaviour of asphalt concrete at the grain level by an interparticle contact model. The contact model used is capable of characterising the rate and time dependency, viscoelastic-damage, and plastic-damage behaviour of asphalt concrete utilising the coupling of an elastoplastic-damage law with a viscoelastic-damage law. Unlike the conventional wheel tracking tests run in a fixed boundary condition (fully confined), the modified wheel tracking test considers the effect of boundary conditions on the rutting behaviour of asphalt mixes. Through comparisons and verifications with laboratory data of the rutting test at different boundary conditions (fully confined and unconfined), the modelling approach shows its capability of capturing the rutting behaviour of asphalt concrete in the modified wheel tracking test. Micromechanics analysis shows that the third (tertiary) stage of rutting behaviour is due to the weakening of the internal structure of the asphalt samples with contact bond breaks over time, which is found in the unconfined test. Meanwhile, the tertiary stage hardly occurs in the fully confined test once densification leads to contact of the aggregate–aggregate skeleton, forming a rigid structure to resist the load with lateral support from the fixed boundary condition. Finally, a parametric study was also conducted to provide further insight into the current testing set-up, including the effect of the sample size and boundary condition on the rutting behaviour of asphalt concrete.

The strain-rate-dependent tensile failure and energy-absorbing behavior of sheet molding compounds

Sheet molding compounds (SMCs) as an alternative material for low-cost and lightweight automotive structural components require special attention to their failure behavior and collision safety. This study aims to analyze the energy-absorbing response and variability of unsaturated polyester matrix SMCs under the range of strain rates from 10−3/s to 500/s through quasi-static and dynamic tensile tests. Additionally, the tensile process and fracture morphology were characterized using Digital Image Correlation and Scanning Electron Microscopy to reveal the underlying rate-dependent failure mechanism. The results demonstrate a pronounced positive correlation between the tensile strength and absorbed energy of SMCs with strain rates. Specially, the absorbed energy exhibits substantial variability, primarily attributable to the plastic damage behavior during the nonlinear phase. A transition in the failure mode from debonding to pseudo-delamination, accompanied by a more extensive failure area at high strain rates, serves as the main mechanism for enhancing the material energy absorption capacity.

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.

Assessing 3D Seismic Plastic Damages of Arch Dams Considering Optimum Mesh Spaces Based on FOS Analyses and 2023 Kahramanmaraş, Hatay, Malatya, and Gaziantep Earthquakes in Turkey

In this paper, the three-dimensional (3D) seismic plastic damage performance of the Ermenek Arch Dam (220 m), which was built in Karaman, Turkey, in 2009, is investigated by including different gallery spaces. 3D modeling of the dam is performed using the finite-difference method, and four various gallery spaces are added to the dam model considering their original oval geometries. WIPP-Drucker (WD) material model is utilized for the dam’s concrete material in creep and seismic damage analyses. Moreover, the Mohr–Coulomb material model is utilized for the foundation. Quiet nonreflecting and free-field boundary conditions are taken into account in the earthquake analyses, and reflecting (fix) boundary condition is used in the factor of safety (FOS) analyses in order to minimize the reflection of earthquake waves at the boundaries. First, the FOS analyses of the Ermenek Dam are performed considering the WD material model, and the optimum mesh space is determined according to FOS analyses. Then, 3D earthquake analyses are performed for 10 important strong ground motions that occurred in Kahramanmaraş, Hatay, Malatya, and Gaziantep in 2023. As a result of the FOS analyses, it is suggested that the mesh length of arch dams should not be chosen randomly while performing the earthquake analyses, and the FOS analyses of arch dams should be carried out using the WD material model before choosing the mesh space. Besides, it is concluded that selected ground motions for seismic analyses have created significant plastic damage around the galleries of the Ermenek Arch Dam, and gallery spaces are of great importance for the seismic plastic damage behavior of arch dams.

Study of Hydrogen-Induced Plastic Damage Response of 7085-T7651 High-Strength Aluminum Alloy

The hydrogen-induced plastic loss behavior of titanium alloys is often reported, but there are relatively few studies on high-strength aluminum alloys. In this article, the hydrogen-induced plastic damage behavior of 7085-T7651 high-strength aluminum alloy was investigated using a tensile specimen with pre-charging hydrogen, and the microstructure was characterized by transmission electron microscopy, scanning electron microscopy and time-of-flight secondary ion mass spectrometry. The results showed that 7085-T7651 high-strength aluminum alloy material has certain hydrogen embrittlement sensitivities, and with the increase of hydrogen-charging time, the hydrogen content and sensitivity of the material increases significantly. For the first time, the theoretical analysis and intuitive quantitative characterization of the hydrogen-induced plastic loss behavior mechanism on 7085-T7651 high-strength aluminum alloy is stated as the formation of Mg and H segregation formed at the crystal boundary, which will result in the weakening of the crystal boundary.

Nonlinear FE-analysis and testing of light-frame timber shear walls subjected to cyclic loading

Light-frame timber shear walls have been used as load-bearing elements in buildings for several decades. To predict the performance of such structural elements under loading, numerous analytical and numerical models have been developed. However, little focus has been on the prediction of the plastic damage behaviour and unloading of the walls. In this paper, a parametric Finite Element (FE) model is further developed by introducing elasto-plastic connectors to simulate the mechanical behaviour of the sheathing-to-framing connections. To verify the accuracy of the elasto-plastic model, full-size walls were tested and compared with results from simulations. The numerical results, from a few loading cycles, indicate that the model achieves reasonable accuracy in predicting both the nonlinear elastic and plastic deformations. Both experimental and simulation results demonstrate the importance of opening locations relating to the external racking force. The results also indicate that for a double-layer wall, its racking strength can be achieved by summation of the separate contribution from each layer. Furthermore, the internal layer was observed to contribute significantly less than the external layer since its nail pattern was based on the sheathing pattern of the external layer.

Experimental and finite element studies of prefabricated timber-concrete composite structures with glued perforated steel plate connections

To evaluate the feasibility of adopting glued perforated steel plate (GSP) connections in prefabricated timber-concrete composite (PTCC) structures, two series of tests were conducted in this study: push-out tests on prefabricated GSP (PGSP) connections and bending tests on PTCC beams. The same experimental programmes on cast-in-situ timber-concrete composite (TCC) structures with this type of connection were also performed. For validation, the three-dimensional finite element (FE) models considering the orthotropic elastic–plastic damage behavior of the timber, damage plasticity characteristics of the concrete, fracture of the adhesive, and the nonlinear shear-slip behavior of the connections were developed. The test results demonstrated that the glued perforated steel plate connections have excellent slip stiffness and shearing capacity but low ductility due to the brittle fracture of the adhesive. Owing to the high anchorage performance of the grouting cements and low shrinkage behavior of the dry construction method, the connection stiffness and load-carrying capacity of PGSP are higher than those of GSP. The PTCC beams showed better bending performance than the cast-in-situ TCC beams as a result of the higher slip stiffness of PGSP than that of GSP. Additionally, the FE numerical results are in good agreement with the test results in terms of the failure modes, shear-slip behavior of the connections, and bending performance of the composite beams.

Multi-scale modeling method for polycrystalline materials considering grain boundary misorientation angle

Grain boundaries (GBs) are microstructures in polycrystalline materials, which influence the mechanical properties of materials significantly. Simulation is an indispensable means to study GBs due to its high flexibility. However, the existing GB simulation models mostly focus on a single simulation scale, lack the consideration of the grain boundary misorientation angle (GBMA) characteristic and fail to describe the coupled elastic–plastic damage behavior between grains and GBs accurately. To describe the influence mechanism of GB on the mechanical behavior of materials accurately, a GBMA-considered multi-scale modeling method for polycrystalline materials is proposed in this paper. The method is based on molecular dynamics (MD), the crystal plasticity finite element method and the cohesive zone model, which considers the GBMA information at grain and atomic scales comprehensively. Firstly, a GB geometric model containing GBMA characteristic is generated at grain scale through EBSD information. Then the GB cohesive parameters are obtained at the atomic scale by MD simulation. Finally, some experiments are performed for verification, which indicates the high accuracy of the proposed method. Furthermore, three models with the same geometric shape and different grain orientation and GBMA are established to study the influence of GBMA on the mechanical properties of polycrystalline materials.

A cohesive viscoelastic-elastoplastic-damage model for DEM and its applications to predict the rate- and time-dependent behaviour of asphalt concretes

Asphalt concrete is a composite heterogeneous material comprised of aggregates bonded together by bitumen binder. The mechanical behaviour of this material shows great dependence on loading rates and time (e.g., creep, relaxation). Such heterogeneity in the internal structure and complex behaviour of asphalt concrete present a challenge for numerical methods to fully capture its responses under different loading rates and durations, especially when large deformation and crack development are present in the material. This study proposes a modelling approach capable of capturing the behaviour of asphalt concrete under different loading rates and durations. In this approach, the heterogeneous internal structure of asphalt concrete is naturally reproduced by the discrete element method (DEM). In parallel, a new inter-particle contact model is developed for the DEM to describe the grain-level behaviour of asphalt concrete. This contact model couples a viscoelastic-damage law with a cohesive-elastoplastic-damage law, enabling the contact model to characterise the rate and time dependency, viscoelastic damage, and plastic-damage behaviour of asphalt concrete. Moreover, thanks to the use of DEM, the proposed approach can naturally capture crack initiation and development. Through comparisons and verifications with a wide range of experiments on asphalt concrete, including the relaxation test, creep test, and dynamic semi-circular bending test, the proposed approach shows its capability of overcoming the limitations of previous DEM models in reproducing the complex behaviours of asphalt material under various loading conditions. Insights into the failure mechanisms of asphalt material under complex loading conditions and its transitional behaviours from diffuse to localised failure can be thus naturally derived from the proposed DEM approach. This study demonstrates the effectiveness of the proposed approach for investigating the behaviour of asphalt concrete.

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.

Strain-controlled fatigue and fracture of AISI 410 stainless steel

Microstructural characteristics, monotonic and strain-controlled cyclic axial behaviors of AISI 410 stainless steel were investigated. Grain size and distribution is uniform throughout the alloy's microstructure. Tensile behavior is characterized with high ductility yet mild strain hardening. Strain-controlled fatigue testing was conducted at strain amplitudes ranging from 0.3% to 0.9%. Cyclic stress softening was observed at all applied strain amplitudes. Hysteresis loops show that stress-strain stabilization was not reached by the alloy. Cyclic softening rate decreases with fatigue life and its ratio was independent of strain amplitude above 0.5%. An accumulating plastic damage behavior was exhibited by the alloy. Fatigue life data were well correlated with Coffin-Manson and plastic energy density damage equations. Multiple cracks were observed in specimens under monotonic and cyclic loadings.

Parametric Study of Cohesive ITZ in Meso-scale Concrete Model

Modelling of concrete at the meso-scale provides an effective way to analyse the effects of its constituents on damage initiation and evolution, leading to better understanding and predicting structural integrity. Majority of works to date focus on models calibration and validation with experiments in either tension or compression, leaving open the question of how such models perform under complex stress states. This work presents a modelling approach that includes all key constituents of the concrete meso-structure: coarse aggregates, represented by inclusions with elastic-brittle behaviour, mortar (including cement, sand and fine aggregates), represented with plastic-damage behaviour, interfacial transition zones (ITZ) between aggregates and mortar, represented by zero-thickness cohesive interfaces, and air voids or pores. Tension and compression experiments with mortar specimens are conducted to obtain its plastic-damage constitutive law. Similar experiments with concrete with several aggregate volume fractions are conducted to obtain stress-strain behaviours for further calibration of cohesive laws and model validation. Numerical simulations show that the proposed approach with pre-calibration of mortar behaviour leads to very good agreements between the predictions of the concrete meso-structural models and the experimental results under both tension and compression. The calibration of ITZ cohesive laws is performed by a parametric study of the effects of critical stress and fracture energy on the predicted stress-strain curves and fracture patterns. The results are used to propose a practical set of ITZ cohesive parameters.

A stable finite element method for computing combined plastic and damage behaviour

Abstract Metals exhibit both plasticity and fracture behaviour. These behaviour both dissipate stresses and are driven by the loads applied on the material. Although much development effort has improved material models derived from first principles, numerical efficacy keeps empirical descriptions attractive. A key difficulty, however it capturing the path-dependent aspects of behaviour, in particular in the case of strong localisation. Provided empirical descriptions of each behaviour, we propose an unconditionally stable algorithm which guarantees their effects are combined in a thermodynamically admissible way. During a simulation, the algorithm compute the instant irreversible mechanisms are triggered and the appropriate increment of e.g. damage or plasticity. We demonstrate the algorithm using a numerical examples of plastic and plastic-damage behaviour. These examples show how numerical instability can be overcome using the algorithm proposed.

2D-lattice modelling of crack propagation induced by fluid injection in heterogeneous quasi-brittle materials

Characterizing the path of a hydraulic fracture in a heterogeneous medium is one of the challenges of current research on hydraulic fracturing. We present here a 2D lattice hydro-mechanical model for this purpose.Natural joints are represented introducing elements with a plastic-damage behaviour. The action of fluid pressure on skeleton is represented using Biot’s theory. The interactions of cracks on fluid flow are represented considering a Poisueille’s flow between two parallel plates. The model is simplified by neglecting the effect of deformation in the equation governing fluid flow. Numerical coupling is achieved with a staggered coupling scheme.We consider first the propagation of fracture restricted to the homogeneous case. The numerical model is compared to analytical solutions. It is found that the model is consistent with LEFM in the pure mechanical case, and with analytical solutions from the literature in the case where the leak off is dominant. In very tight formations, deviations are observed, as expected, because of the assumption in the flow model.Finally, the influence of a natural joint of finite length crossed by the fracture is shown. Two cases are considered, the case of a joint perpendicular to the crack and the case of an inclined joint. In the first case, the crack passes through the joint, which is damaged due to the intrusion of the fluid. In the second case, the crack follows the joint and propagation starts again from the tip.

Computational modeling of the plastic-damage behavior of porous MAX phase with aligned ellipsoid-like pores under uniaxial compression

The mechanical properties of porous MAX phase, namely porous Ti2AlC with aligned ellipsoid-like pores is studied in this study. Micromechanics based representative element volume (RVE) and finite element (FE) method are adopted in modeling porous Ti2AlC. A damage-plasticity coupled constitutive model considering different tensile and compressive behaviors is used in modeling the inelastic behavior of porous Ti2AlC under uniaxial compression. The effects of porosity volume fraction and pore size on elastic moduli and compressive behavior of the porous Ti2AlC systems are investigated. Numerical results show that unlike typical porous ceramic, porous Ti2AlC behaves like a quasi-brittle material under uniaxial compression, and the damage of porous Ti2AlC is mainly driven by localized tensile failure.

Effects of microstructure and concavity on damage behavior of laser beam welded Ti-2Al-1.5Mn titanium alloy joints

Pulsed laser beam welding (PLBW) and continuous fiber laser beam welding (CFLBW) of Ti-2Al-1.5Mn titanium alloy thin sheets were proceeded in the given welding conditions, and the unfilled and undercut defects were found in the weld joints, separately. The finite element simulation result shows that there is great geometrical discontinuity in joints due to the concavity defects. The microstructure observation indicates that strong nonlinear distributions of microstructures exist both in the same joint from base metal (BM) to fusion zone (FZ) and in different joints under different welding conditions. Furthermore, effects of microstructure and concavity on plastic damage behavior were investigated using a multispecimen tensile method. The results show that the plastic damage behavior relates to both the microstructure and the tensile stress level. Existence of concavity accelerates the plastic damage nearby the concavity area while decelerates the plastic damage of fusion line area.

Investigation into plastic damage behavior of the CO2 laser deep penetration welded joint for Ti–6Al–4V alloy

There are great nonlinear gradient distributions of microstructures in CO2 laser deep penetration welded joints of Ti–6Al–4V alloy. Although there are great developments on the damage behavior of titanium alloy, there is a few to investigate the plastic damage behavior of the laser welded joint with heterogeneous microstructures. In order to understand the effects of nonlinear microstructures on the plastic damage behavior of CO2 laser deep penetration welded joint, a multi-specimen tensile method by measuring the microvoid density was applied to estimate the plastic damage behavior for Ti–6Al–4V alloy. The damage mechanism presents the pattern of microvoid nucleation, growth and coalescence. The microvoid density under different loading has a great relationship with the gradient distribution of microstructure in the welded joint. The growth rate of microvoids in the weld metal, heat affected zone and base metal is also related to the loads. When the load is lower, the damage in the weld metal is larger than that in the heat affected zone and base metal, and when the load is higher, the growth rate of the microvoid in heat affected zone and base metal is higher than that in weld metal. The grain size in weld metal has small effects on plastic damage, but the great gradient of the grain size in heat affected zone may delay the plastic damage evolution.

Incremental damage theory of particulate-reinforced composites with a ductile interphase

This paper deals with a new micromechanics model of particulate-reinforced composites (PRCs) describing the evolution of debonding damage, matrix plasticity and particle size effect on the deformation. A ductile interphase was considered in the frame of incremental damage theory to analyze the dependence of elastic–plastic–damage behavior on particle size. Progressive debonding damage was controlled by a critical energy criterion for particle–matrix interfacial separation. The equivalent stresses of the matrix and interphase were determined by field fluctuation method. The influences of progressive debonding damage, particle size and interphase properties on the overall stress–strain response of PRC were explained simultaneously. Due to the existence of a ductile interphase, stress transfer and plastic initiation in PRC become very complicated, and thus a unit-cell (UC) based FEM was used to simulate their evolutions and demonstrate the role of the interphase. Finally, particle size effect on the mechanical behaviors of composites was interpreted.

A continuum damage model for ductile fracture of weld heat affected zone

In this paper, the ductile plastic damage behaviour of weld heat affected zone (HAZ) is studied by use of continuum damage mechanics (CDM). Based on a continuum damage variable, D, the effective stress concept and the thermodynamics, a general continuum damage model for Isotropie ductile fracture is derived from a new dissipation potential chosen by the author herein. A comparison between the damage model and experimental results is presented and a good agreement is found. The model is also used to analyse the ductile plastic damage evolution in thermally simulated welding coarse-grained HAZ of a low alloy steel. The effects of stress triaxiality on plastic damage evolution and on ductile fracture of the coarse-grained HAZ are discussed.