Ductile Damage Research Articles

Research on cracking characteristics and failure modes of semi-flexible pavement materials

Semi-flexible pavement (SFP) is designed for heavy traffic but its susceptibility to cracking hinders its development and application. This study aims to investigate the cracking characteristics and failure modes of SFP materials through macroscopic tests and image processing, thereby guiding anti-cracking technology. First, the effects of gradation and bitumen content on cracking process curves were analyzed using three-point bending tests across a wide temperature range. Second, the variations in maximum tensile strain, tensile strength, and fracture energy were comparatively examined. Finally, the morphology of specimens at crack initiation and after complete fracture was analyzed using image processing techniques to quantify the failure modes. The results indicate that the SFP material exhibits elastic development and brittle damage at the low temperature, and viscoelastic development and ductile damage at medium and the high temperature. At the low temperature, the changes in maximum tensile strain and fracture energy are consistent. The primary weak points at crack initiation include internal cement failure, cement-bitumen interface failure, and bitumen-aggregate interface failure. After complete fracture, internal cement damage and bitumen-bitumen/aggregate interface damage are dominant. To improve low-temperature cracking resistance of SFP, it is recommended to increase the maximum aggregate size, add fine aggregates, and increase the bitumen content. Additionally, enhancing the internal cohesion and external bonding properties of bitumen can mitigate the negative effects of increased bitumen consumption. This study provides guidance on designing the SFP material to enhance its crack resistance.

A thermodynamically‐based fractional model combined viscoelastic‐viscoplastic‐ductile damage with application to fiber‐reinforced polymer composites

AbstractA thermodynamically‐based fractional viscoelastic‐viscoplastic‐damage constitutive model combined with continuous damage mechanics (CDM) theory was established, in order to describe the rate‐dependent nonlinear behavior of fiber‐reinforced polymer composites (FRPCs). The fractional Helmholtz free energy consists of four contributions: viscoelastic (VE), viscoplastic (VP), hardening and damage, in which the VE and VP parts are constructed by fractional Zener and Scott‐Blair (SB) element forms respectively. The constitutive equation is obtained through Helmholtz free energy for the fractional Zener model, and plastic flow and hardening evolution law are all derived in the process. The ductile damage, coupled to both VE and VP free energy parts, is introduced through fractional damage energy release rates to model the degradation of material properties. The corresponding strain energy release rate and dissipation contributions are also derived. The fractional implicit time integration algorithms of proposed model are presented. The model is applied to validate tests of FRPCs under various loading conditions. The model validation and comparison are presented by simulating experimental data and existing models in the literature. And the corresponding evolution of dissipated energy is discussed to further valid the characterization ability of the model.Highlights A thermodynamical fractional constitutive model was developed for FRPCs. The Helmholtz free‐energy potential for fractional Zener model is adopted. The physical significance of fractional order parameters is explored. Fractional implicit integration algorithm of proposed model is implemented. The validation and comparison of the model are presented under various loads.

Phase Field Coupled Finite Deformation Plasticity Formulation of Ductile Fracture With Nonlinear Kinematic Hardening and Modified Energy Release Function

ABSTRACTA ductile damage theory is presented by coupling the covariant formulation of finite deformation plasticity with the phase field modeling of fracture, including kinematic hardening for the ductile response of the materials. A phase field coupled nonlinear kinematic hardening equation is proposed in the reference configuration having equivalent representation through the Lie derivative of the kinematic hardening tensor by push‐forward operation in the spatial configuration, thus ensuring the satisfaction of frame invariance. To capture the correct physical response of the material by the phase field evolution equation, the fracture driving function, that is, the difference between the sum of elastic and plastic energies and threshold energy, after the damage initiation is modified by an energy release controlling function, which is an empirical relation of equivalent plastic strain. In defining the energy release controlling function, well‐defined points with physical significance in the experimental load versus displacement curve are used. To simulate the response of the material in relatively large time steps, a modified staggered scheme is presented, evaluating the fracture driving and energy release controlling functions from the previous converged step and using the updated phase field variable in the weak form of the momentum balance equation. To quantify different material parameters from available experimental results in the literature, the developed phase field coupled elasto‐plastic model uses a neural network optimization procedure consisting of neural network training together with optimization in MATLAB and finite element model evaluation in Abaqus user element subroutine UEL. Model capabilities are demonstrated by simulating the crack propagation in complex 3D geometries such as the second and third Sandia Fracture Challenges.

Comparison of FE Simulation and Experiment on Tensile Test of TWB-HPF 22MnB5 Steel

Finite element (FE) analysis of the tensile test of TWB-HPF 22MnB5 steel was performed and compared with the experimental results. To improve the accuracy of the simulation, the damage theory of FLD and ductile damage theory were used in 2D and 3D simulations. The tensile strength of 22MnB5 steel was determined under various welding heat inputs for FE simulation. Crack propagation of the welded region indicated that the fracture was observed in the base metal under normal welding conditions. Also, the crack propagated along the HAZ region due to higher heat input of the welding, and lead fractures have been highlighted as a potential complication.

Effect of Surface Morphology and Internal Structure on the Tribological Behaviors of Snake Scales from Dinodon rufozonatum.

Snakes can move freely on land, in lakes, and in other environments. During movement, the scales are in long-term contact with the external environment, providing protection to the body. In this study, we evaluated the mechanical properties and scratching performance of the ventral and dorsal scales from Dinodon rufozonatum, a generalist species that moves on both land and in streams under wet and dry conditions. The results showed that the elastic modulus and hardness of the dry scales were greater than those of the wet scales. The average scale friction coefficient under wet conditions (0.1588) was 9.3% greater than that under dry conditions (0.1453). The scales exhibit brittle damage in dry environments, while in wet environments, ductile damage is observed. This adaptation mechanism allows the scales to protect the body by dissipating energy and reducing stress concentration, ensuring efficient locomotion and durability in both terrestrial and aquatic environments. Understanding how this biomaterial adapts to environmental changes can inspire the development of bionic materials.

An alternative finite element formulation to predict ductile fracture in highly deformable materials

Abstract An alternative finite element formulation to predict ductile damage and fracture in highly deformable materials is presented. For this purpose, a finite-strain elastoplastic model based on the Gurson-Tvergaard-Needleman (GTN) formulation is employed, in which the level of damage is described by the void volume fraction (or porosity). The model accounts for large strains, associative plasticity and isotropic hardening, as well as void nucleation, coalescence and material failure. To avoid severe damage localization, a nonlocal enrichment is adopted, resulting in a mixed finite element whose degrees of freedom are the current positions and nonlocal porosity at the nodes. In this work, 2D triangular elements of linear-order and plane-stress conditions are used. Two systems of equations have to be solved: the global variables system, involving the degrees of freedom; and the internal variables system, including the damage and plastic variables. To this end, a new numerical strategy has been developed, in which the change in material stiffness due to the evolution of internal variables is embedded in the consistent tangent operator regarding the global system. The performance of the proposed formulation is assessed by three numerical examples involving large elastoplastic strains and ductile fracture. Results confirm that the present formulation is capable of reproducing fracture initiation and evolution, as well as necking instability. Convergence analysis is also performed in order to evaluate the effect of mesh refinement on the mechanical response. In addition, it is demonstrated that the nonlocal parameter alleviates damage localization, providing smoother porosity fields.

Prediction of Ductile Damage in Composite Material Used in Type IV Hydrogen Tanks by Artificial Neural Network and Machine Learning with Finite Element Modeling Approach

This study investigates the degradation process of composite materials used in high‐pressure hydrogen storage vessels by employing advanced computational techniques. A recurrent neural network, specifically a bidirectional long short‐term memory (Bi‐LSTM) network, is utilized to predict the temporal evolution of ductile damage. The key degradation features are extracted from finite element modeling (FEM) computations using group method of data handling algorithms and treated as time‐series data. Results demonstrate that the Bi‐LSTM network can accurately undergo both elastic and plastic behaviors of the composite under tensile strength. Additionally, traditional machine learning (ML) algorithms such as extreme gradient boosting and random forest are employed to forecast strain degradation, showing promising results. This hybrid approach combining FEM, ML, and deep learning provides a comprehensive method for predicting the degradation of composite materials, offering significant potential for optimizing the design and durability of hydrogen storage vessels.

Influence of printing orientation on power-law hardening and ductile damage parameters for 3D-printed SS316L steel: experimental and FEA approach

In the present investigation, the selective laser melting (SLM) technique has been utilized for the 3-dimensional printing (tensile test specimens) of SS316L steel powder at 00 (horizontal) and 900 (vertical) angles. Further, an experimental and finite element analysis approach has been made to analyse the effect of printed orientation or direction on the Hollomon power law parameters (strain hardening exponent (n) and strength coefficient (K)) and ductile damage parameters (fracture strain (εf), stress triaxiality (η) and strain rate ( ε ̇ )). The influence of printing orientation on plastic deformation behavior has also been analysed. The results revealed that 00 angle 3D-printed specimens exhibited 11.05%, 21.97% and 9.50% more yield strength, tensile strength and elongation than 900 angle 3D-printed tensile test specimens. Further, the strain hardening exponent (n) and strength coefficient (K) (Hollomon power law hardening model parameters) for 00 angle 3D-printed specimens are 35.80% and 32.47% more than the 900 angle 3D-printed tensile test specimens respectively. The fracture strain for 00 angle 3D-printed specimens is 37.82% less than the 900 angle 3D-printed tensile test specimens. The percentage difference between FEA and experimental results is less than 5% which shows the good prediction capability of estimated Hollomon power law parameters and ductile damage model parameters with developed FEA model for 00 and 900 3D printed specimens.

4D printing of polylactic acid (PLA)/PLA-thermoplastic polyurethane (TPU)-based metastructure: examining the mechanical, thermal, and shape memory properties

Abstract In the present day and age, increasing demand concerning the enhancement of the mechanical performance of Shape Memory Polymer (SMP) based structures has paved the way for developing newer metastructures of enhanced load-bearing, damping capacity, and durability. The present study focuses on developing SMP-based metastructures made of commercially available Polylactic Acid (PLA) and 30% by wt. of Thermoplastic Polyurethane (TPU) blended PLA. The designed metastructures are initially analyzed using numerical modeling to prevent lateral deformation, acute stress concentration zones, and row-wise collapse. Mechanical tests reveal that blending TPU with PLA enhances the material's flexibility and ductility, further improving the toughness and fracture resistance of the built metastructures. Loading-unloading and shape recovery tests (under compression mode) of the s-shape metastructure reveal that the PLA/TPU metastructure withstands ≅ 170 N load, less than neat PLA's ≅ 223 N due to TPU's flexibility. PLA/TPU endures 30 cycles, while PLA fails after the 9th cycle. In shape recovery plots, PLA/TPU metastructures exhibit a lower standard deviation (~0.32%) than PLA (~1.4%), attributed to the entropy decrease and cross-linkage disentanglements of PLA. Furthermore, a Dynamic Mechanical Analyzer (DMA) assesses glass transition temperature, energy storage capability, and dissipation in variation with the temperature. The nephograms of ABAQUS result divulge accurate fracture initiation locations of the metastructure unit cells, which involves implementing ductile damage behavior modeling by employing damage initiation and evolution parameters. Finally, assessing compression tests and shape recovery behavior results elucidates that these SMP-based metastructures are promising for load-bearing pallets in the transporting and packaging industries, providing superior damping and self-repairing capabilities during significant plastic deformations.

Plastic deformation and damage modeling of AA7075 synthetic 3D microstructure created using generative AI

3D microstructures provide valuable insight into material behavior which is essential in elucidating microstructural phenomena, such as particle morphology and void damage, and consequent macroscopic material response. However, creating 3D microstructures is extremely laborious and expensive, requiring complex microstructural characterization and imaging techniques such as Focussed-Ion Beam based Scanning Electron Microscopy (FIB-SEM) or X-ray Computed Tomography (XCT). To this end, synthetic 3D microstructures were rapidly generated from orthogonal 2D images using SliceGAN, which proved a practical and cost-effective method. In this study, multiple synthetic microstructures of AA7075-O, a complex microstructure of various strengthening precipitates within a softer aluminum matrix, were post-processed, meshed, and modeled for different damage behavior in FEA using advanced constitutive material models. Subsequently, the synthetic and real microstructures were qualitatively and quantitatively analyzed for their elastoplastic deformation and ductile void damage responses.This study illustrates the viability of an integrated AI-FE methodology in studying microstructural micromechanics, demonstrating that synthetic microstructures exhibited a very similar stress-strain response, especially when using a free boundary condition, and comparable stress distribution and void damage, albeit with some discrepancies. Also, it emphasizes the influence of particle morphology on strength and damage, where highly irregular particles play a dual role in increasing strain hardening by restricting matrix flow at the cost of increased ductile damage induced by decohered particles. Lastly, the more advanced FE models, with multiple voiding mechanisms, reduced the discrepancy between real and synthetic microstructures compared to simpler models

A finite element framework for thermo‐mechanically coupled gradient‐enhanced damage formulations

AbstractThe solution of coupled multi‐field problems by means of commercially available finite element codes such as Abaqus constitutes an important part in the study of industrial processes. Against this background, a comprehensive implementation framework for a gradient‐enhanced continuum damage formulation in a thermo‐mechanically coupled finite deformation setting is proposed in this contribution. To assess the applicability of the implementation framework to industrial processes, a thermo‐mechanically coupled, gradient‐enhanced ductile damage model is exemplarily employed. The resulting three‐field problem, consisting of the balance of linear momentum, the heat equation and the balance of micromorphic momentum, is implemented based on an Abaqus user material by making use of a novel two‐instance formulation. Representative simulation results are discussed, with the specific focus lying on the application to manufacturing processes involving complex contact interactions. The Abaqus framework is made available as an open‐source code on GitHub, see Sobisch et al., Finite Elements in Analysis and Design 232 (2024) 104105.

Implementation of a finite element framework coupling chemo‐mechanics and the Gurson‐Tvergaard‐Needleman model

AbstractHydrogen embrittlement in ductile metals, such as steel, is a significant concern, for instance, in the safety assessment of existing pipeline infrastructure intended for hydrogen transport. The ductile damage mechanism in steels is characterized by the nucleation, growth, and coalescence of microvoids, which is further enhanced by the presence of hydrogen. This leads to material damage and premature failure in components. Mechanisms contributing to hydrogen‐induced reduction of strength in steels include hydrogen‐enhanced decohesion (HEDE), hydrogen‐enhanced local plasticity (HELP), and hydrogen‐enhanced strain‐induced vacancies (HESIV). The HEDE mechanism leads to a principal stress‐controlled brittle failure mode. Conversely, the HELP and the HESIV mechanisms, which are dominated by plastic deformation, alter the ductile damage behavior as they lead to accelerated void growth and coalescence. Furthermore, interstitial diffusion of hydrogen leading to lattice expansion, commonly referred to as swelling, also contributes to hydrogen‐induced embrittlement. Hydrogen embrittlement is therefore a stress‐diffusion process that involves chemo‐mechanical coupling, where hydrogen atoms primarily diffuse toward areas with high hydrostatic stress. In this regard, we propose a framework using the finite element method and combining coupled chemo‐mechanics and the well‐known Gurson‐Tvergaard‐Needleman (GTN) damage model. The framework is motivated by mixed rate‐type potentials, that account for the influence of hydrogen concentration on the damage behavior. An additional dependence of the fracture strain and evolution of the void volume fraction on hydrogen is included. A comparison of the fully‐coupled model to simplified versions is conducted to individually assess the role of hydrogen concentration on damage evolution and the stress state on diffusion.

GTN poroplastic damage model construction and forming limit prediction of magnesium alloy based on BP-GA neural network

During plastic deformation processes, the ductile solids damage and fracture at the microscopic level originate from the evolution of micro -voids, including nucleation, growth and coalescence of voids. In this study, the fracture caused by damage of the AZ31 magnesium alloy sheet is analyzed using the Gurson-Tvergaard-Needleman (GTN) model. The damage parameters of the GTN model are determined by statistical void volume fractions (VVF) in three damage stages during uniaxial tensile experiments with scanning electron microscopy (SEM). The damage parameters are then optimized by the Back Propagation-Genetic Algorithms (BP-GA) neural network. According to the result, the main GTN damage parameters: the initial void volume, the critical volume fraction, the void volume fraction of the nucleation part, and the void volume fraction when the material finally fails are obtained, respectively. Comparing the simulation with the test, the results of the optimized parameters fit better. The void growth reflects the damage during the deformation process, and the GTN model can accurately predict the ductile damage. Furthermore, the experimental forming limit diagrams (FLDs) of the AZ31 sheet at 200℃ are accurately predicted using the parameters obtained by the GTN model. Good agreement has been observed between the experimental and predicted FLDs.

Enhanced spall strength of an Al0.1CoCrFeNi high-entropy alloy by the pre-strain method

The effects of pre-strain on spallation damage of an Al0.1CoCrFeNi high-entropy alloy are investigated with plate impact loading. During the pre-strain process, Kink bands and dislocations are generated in the microstructures. Pre-strain smears elastic–plastic transition upon shock loading and improves spall strength via dislocation strengthening. Although the level of pre-strain does not affect the ductile damage mode, it has a pronounced effect on damage evolution.

The discontinuous strain method: accurately representing fatigue and failure

AbstractFatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable—which leads to unphysical behavior during unloading. This unphysical behavior stems from the continued accumulation of plastic strains after failure, resulting in an incorrect stress state at crack closure. As a remedy, we introduce a discontinuous strain in the additive elasto-plastic strain decomposition, which absorbs the excess strain after failure. This allows representing pre- and post-cracking regimes in a fully continuous setting, wherein the transition from the elasto-plastic response to cracking can be triggered at any arbitrary stage in a completely smooth manner. Moreover, the presented methodology does not exhibit the spurious energy release observed in hybrid approaches. In addition, our approach guarantees mesh-independent results by relying on a characteristic length scale—based on the discretization’s resolution. We name this new methodology the discontinuous strain method. The proposed approach requires only minor modifications of conventional plastic-damage routines. To convey the method in a didactic manner, the algorithmic modifications are first discussed for one- and subsequently for two-/three-dimensional implementations. Using a simple ductile constitutive model, the discontinuous strain method is validated against established two-dimensional benchmarks. The method is, however, independent of the employed constitutive model. Elastic, plastic, and damage models may thus be chosen arbitrarily. Furthermore, computational efforts associated with the method are minimal, rendering it advantageous for accurately representing low-cycle fatigue but potentially also for other scenarios requiring a discontinuity representation within a plastic-damage framework. An open-source implementation is provided to make the proposed method accessible.

Seismic behavior of CFDST frame with metallic dampers: Damage-controlled design and performance assessment

Current investigations on performance-based seismic design of structures generally employed story drift as performance objectives. However, the story drift could only partially reveal the global damage of a structure and not control the damage of important components. In order to control the damage of various components in a structure, this paper proposed a new damage-controlled seismic design method using the Park & Ang indexes of components. Firstly, the Park & Ang damage index was simplified as an equivalent ductility damage index for various components. The energy balance concept was used to observe the hysteretic energy demand which was subsequently distributed to all stories. Thus, the components of each story could be designed based on their damage indexes under design-based and maximum-considered earthquakes. Four concrete filled double skin tubular (CFDST) moment resisting frames equipped with metallic dampers with various layouts were designed based on the proposed design method. Time history analyses on these four structures were performed after validating the accuracy of nonlinear model by Opensees. Analysis results showed that the components in four structures exhibited expected damage states as illustrated by the design method. It also verified that proposed seismic design method was effective to control the damage of various components, which was beneficial for protecting the important components in a structure by setting low damage indexes for them. The seismic design method and analysis results also provided a reference for the design of moment resisting frame with energy devices.

Material Parameter Identification for a Stress-State-Dependent Ductile Damage and Failure Model Applied to Clinch Joining

Similar to bulk metal forming, clinch joining is characterised by large plastic deformations and a variety of different 3D stress states, including severe compression. However, inherent to plastic forming is the nucleation and growth of defects, whose detrimental effects on the material behaviour can be described by continuum damage models and eventually lead to material failure. As the damage evolution strongly depends on the stress state, a stress-state-dependent model is utilised to correctly track the accumulation. To formulate and parameterise this model, besides classical experiments, so-called modified punch tests are also integrated herein to enhance the calibration of the failure model by capturing a larger range of stress states and metal-forming-specific loading conditions. Moreover, when highly ductile materials are considered, such as the dual-phase steel HCT590X and the aluminium alloy EN AW-6014 T4 investigated here, strong necking and localisation might occur prior to fracture. This can alter the stress state and affect the actual strain at failure. This influence is captured by coupling plasticity and damage to incorporate the damage-induced softening effect. Its relative importance is shown by conducting inverse parameter identifications to determine damage and failure parameters for both mentioned ductile metals based on up to 12 different experiments.

Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification

The open-source parameter identification tool ADAPT (A diversely applicable parameter identification Tool) is integrated with a machine learning-based approach for start value prediction in order to calibrate a Gurson–Tvergaard–Needleman (GTN) and a Lemaitre damage model. As representative example case-hardened steel 16MnCrS5 is elaborated. An artificial neural network (ANN) is initially trained by using load–displacement curves derived from simulations of a boundary value problem—instead of using data generated for homogeneous states of deformation at material point or one-element level—with varying material parameter combinations. The ANN is then employed so as to predict sets of material parameters that already provide close solutions to the experiment. These predicted parameter sets serve as starting values for a subsequent multi-objective parameter identification by using ADAPT. ADAPT allows for the consideration of input data from multiple scales, including integral data such as load–displacement curves, full-field data such as displacement and strain fields, and high-resolution experimental void data at the micro-scale. The influence of each data set on prediction quality is analyzed. Using various types of input data introduces additional information, enhancing prediction accuracy. The validation is carried out with respect to experimental void measurements of forward rod extruded parts. The results demonstrate, by incorporating void measurements in the optimization process, that it is possible to improve the quantitative prediction of ductile damage in the sense of void area fractions by factor 28 in forward rod extrusion.

Ice-Induced Vibration Analysis of Fixed-Bottom Wind Turbine Towers

This research tackles the challenge of ice-induced vibrations in fixed-bottom offshore wind turbines, particularly the risk of frequency lock-in (FLI), a critical loading condition arising from slow ice movement against structures. We introduce an innovative FLI analysis process grounded in the ductile damage–collapse (DDC) mechanism, which offers a more accurate and significantly lower probability of FLI occurrence than conventional methods. Through dynamic evaluations employing a time-domain ice load model and FLI displacement analyses, we demonstrate that FLI can lead to higher structural vibrations than those caused by continuous brittle ice crushing. A case study of a 5 MW monopile wind turbine tower utilising Abaqus confirms the necessity for incorporating FLI considerations into structural design to ensure safety and performance in ice-prone environments. Comparing the DDC mechanism with the ISO method, our study reveals that the DDC approach predicts higher displacement and acceleration values during FLI, nearly an order of magnitude greater than those induced by ice loads with a 50-year return period. The research underscores the importance of robust ice-load integration in design strategies for offshore wind turbines, especially in regions susceptible to ice. It highlights the DDC mechanism as a novel strategy for enhancing structural resilience against ice-induced hazards.

Ductile shear damage micromechanisms studied by correlative multiscale nanotomography and SEM/EBSD for a recrystallized aluminum alloy 2198 T8

The damage mechanisms of ductile fracture under shear loading of an aluminum alloy 2198T8R were studied using flat thin-sheet samples. One sample was loaded until 85% of the failure displacement and then unloaded, and another one was loaded up to failure. To overcome the inherent shortcomings of nanotomography concerning the investigation of flat samples, synchrotron nano-laminography was applied to the pre-loaded sample and provided structural information down to the nanometer scale, allowing ductile damage nucleation and evolution to be studied. The damage features, including flat cracks and intermetallic particle-related damage, were visualized in 3D from the highly-deformed shear band region. Using nano-laminography, no nano-voids were found. The damaged shear ligament was also observed after polishing via destructive correlative scanning electron microscope (SEM) and electron back-scatter diffraction (EBSD) which suggests that the detrimental flat cracks were both intergranular and transgranular. The flat cracks were related to highly-deformed bands. No nano-voids could be found using SEM analysis. Fractography on the second broken sample revealed that the flat cracks contained hardly observable nanometer-sized dimples. The final coalescence region was covered by sub-micrometer-sized dimples, inside which dispersoid particles were present. The fact that no nano-void was found for the pre-deformed sample implies that the nucleation, growth and coalescence of these sub-micrometer-sized voids occur at late stages of the loading history.