Micromechanical Damage Model Research Articles

A unified nonlinear yield criterion for fracture and fault slip in quasi-brittle rocks

The micromechanical damage model has been developed to better describe multiscale fracture behavior in quasi-brittle rocks. While the deduced yield criterion under tension and compression has been carefully investigated in different stress spaces, it fails to capture a smooth transition from extension to shear fracture and overestimates the tensile strength of the rock. This paper introduces a unified nonlinear yield criterion based on a stress-dependent fracture energy parameter. In particular, the effect of the intermediate principal stress is encapsulated. The proposed yield criterion is then validated in the principal stress space based on a detailed parameter calibration procedure. Subsequently, four verification examples corresponding to Beishan granite, Lac du Bonnect granite, Carrara marble and Berea sandstone are carried out to show a desirable predictive capacity of the proposed yield criterion on progressive failure, extension to compressive-shear fracture transition and fault slip in quasi-brittle rocks.

Deformation and fracture of SiCp/Al composites under complex loading conditions: A simulation study

An accurate depiction of the deformation and fracture mechanisms of metal matrix composites is the key to their rational structure and property design. In the present work, the Advanced Guerson Tvergaard Needleman (AGTN) constitutive model is firstly combined with an algorithm to reconstruct realistic 3D microstructures within the finite-element framework. We employ this model to probe the elastoplastic response and fracture behaviors of aluminum matrix composites with different volume fractions of reinforcing particles (7, 14, and 21 %) and under various loading conditions (tension, compression and shear). Real microstructures are referred to reconstruct the three-dimensional model of the composites. The AGTN constitutive model is integrated with the micromechanical damage model, which is capable of independently describing the constitutive behavior of various components, including the elastoplastic damage of the metal matrix, particle-enhanced elastic-brittle failure, and the interfacial traction separation. By using the conventional SiCp/Al composite system as a model material, we examine the stress state of the matrix and fracture mechanisms under different loading conditions by using triaxiality, Lode angle and statistical analysis. In general, the damage of SiCp/Al composites can be attributed to interfacial debonding and particle fracture, whereas the latter dominates when the volume fraction of SiCp is high. Furthermore, the critical volume fraction for the transition of damage mechanisms is found to be largely dependent on the loading conditions. Our work provides a comprehensive understanding of particle-reinforced aluminum matrix composite under in-service conditions.

A Combined Experimental and Numerical Calibration Approach for Modeling the Performance of Aerospace-Grade Titanium Alloy Products

Finite element modeling for designing and optimizing lightweight titanium aerospace components requires advanced simulation tools with adequate material modeling. In this sense, a hybrid strategy is proposed in this work to identify the parameters of the Johnson–Cook plasticity and damage laws using a combined direct-inverse method. A direct calibration method for plasticity law is applied based on the literature-reported data of strain-stress curves from experimental tensile tests at different temperatures and strain rates. The triaxiliaty-dependent fracture parameters of the Johnson–Cook damage law at reference conditions of strain rate and temperature (d1, d2, and d3) are calibrated with the direct method based on new data of experimental evolution of computed average fracture strain with the average stress triaxiality. The validation is performed with numerical results from an accurate micromechanics-based Ti64 model. The inverse calibration method is used to determine the strain rate and temperature-dependent damage parameters (d4 and d5) through large strain simulations of uniaxial tensile tests. The numerical results, including average strain and necking profile at fracture, are then utilized to calculate stress triaxiality by the Bridgman criterion for adjusting parameters d4 and d5. The calibrated model yields a 2.1% error for plasticity and 3.4% for fracture predictions. The experimental and simulated load-bearing capacity using the micromechanics damage model differed by only 1%. This demonstrates that the SC11–TNT model of Ti64 is reliable for identifying the Johnson–Cook damage law through the accurate use of inverse methods. The hybrid calibration strategy demonstrates the potential capability of the identified Johnson–Cook model to accurately predict the design load-carrying capacity of Ti64 aerospace components under different deformation rates and temperatures while accounting for material damage effects.

Predicting the forming limits in the tube hydroforming process by coupling the cyclic plasticity model with ductile fracture criteria

This study presents a one-surface plasticity constitutive model combined with phenomenological and micromechanical damage models to be applied to the large plastic deformation during tube hydroforming. These factors lead to simulating the Bauschinger effect and transient behavior in large plastic strain ranges and predicting fracture onset. By using the integration approach, a numerical integration algorithm of implementation by explicit schemes was carried out. A comparison of several cyclic loading tests between experiments and numerical simulation was accomplished. The accuracy of these models is verified, which could be expanded to a large strain range forming process. Adopting the proposed models, finite element modeling is performed in the tube hydroforming process. The simulation and experimental results comparison showed that the proposed framework accurately predicted the tube formability in the hydroforming process.

A new micromechanical damage model for quasi-brittle geomaterials with non-associated and state-dependent friction law

In this paper, we shall present a new micromechanical damage model for capturing the mechanical behaviors of quasi-brittle geomaterials under a wide range of compressive stress. Two essential coupled non-linear mechanisms are taken into account: plastic deformation related to frictional sliding along the microcrack surfaces, and microscopic damage induced by the initiation and propagation of microcracks. Within the framework of thermodynamics and Mori–Tanaka homogenization scheme, free energy and thermodynamic forces, including the local stress applied on the microcracks and damage driving force are deduced. The main novelty of this work lies in presenting a new physically based non-associated and state-dependent friction law to capture the plastic distortion, in which the friction coefficient is no longer a constant but a state-dependent variable varying with the surface asperities of microcracks. The relationship between the friction coefficient and mean local stress, as well as microscopic damage is subtly defined. Intriguingly, a macroscopic strength criterion is derived as an inherent part of the proposed model without rotation of the principal stress. Moreover, semi-analytical stress–strain–damage relationships of the proposed model can be derived under conventional triaxial compression. These up-scaling analyses provide a powerful tool for parameter calibration. For application, the semi-implicit return mapping algorithm with plasticity-damage decoupling correction procedure (SRM-PDDC) is adopted for numerical implementation. To demonstrate the performance of the micromechanical model, we compare the model predictions with experimental data of quasi-brittle rocks in literature as well as the results obtained by Zhu et al. (2016). Finally, the applicable condition of the SRM-PDDC algorithm is discussed in detail.

Microstructure-based prediction of UHPC's tensile behavior considering the effects of interface bonding, matrix spalling and fiber distribution

Ultra-high performance concrete (UHPC) is an ideal construction material to cut down carbon emissions due to its superior mechanical performance and durability. It is important to clarify the relationship between the microstructure and the overall tensile response of UHPC. In this paper, a microstructure-based multiscale framework is proposed to predict the stress-strain curve of UHPC under tensile load. The linear elastic stage is obtained by estimating the effective properties with the multi-level homogenization scheme based on the microstructure. The strain hardening and tension softening processes in the tensile curve are predicted with a statistical micromechanical damage model, where the characteristics of steel fibers are considered, including the effects of slip-softening, residual bonding strength of the fiber/matrix interface, matrix spalling and fiber orientation distribution. Comparisons with existing test results and previous models demonstrate the feasibility of using this multiscale framework to predict the overall tensile response of UHPC, especially the tension softening branch. Finally, the effects of interface parameters, matrix spalling degree, fiber orientation distribution, hydration degree and water/binder ratio on the tensile response of UHPC are evaluated and discussed with the proposed framework.

Mechanical Behavior of Titanium Alloys at Moderate Strain Rates Characterized by the Punch Test Technique

Material characterization at moderate strain rates is an important factor for improving the adequacy and accuracy of analysis of structures operating under extreme conditions. In this paper, the deformation and fracture of Ti-5Al-2.5Sn alloys were studied utilizing the punch test at strain rates up to several hundred per second. Loading velocities from 0.0003 to 15 m/s were realized during the spherical body penetration through a thin titanium plate. To describe the plastic flow and fracture of the Ti-5Al-2.5Sn alloy at strain rates ranging from 0.001 to 103 s-1, a micromechanical damage model was coupled with a viscoplastic constitutive model based on the dislocation dynamics. Numerical simulations of the punch test at 15 and 2 m/s were carried out to validate used constitutive relations. It was verified that the simulated fracture shape and deflections were similar to experimental ones. It was found that dynamic punch test is suitable for validation of damage kinetics under complex stress states.

Coupled crystal plasticity and micromechanics damage model based on viscoplastic self-consistent theory and X-ray computed tomography

In recent years, coupled crystal plastic and micromechanics damage models have been applied to effectively deal with the complex interactions between the polycrystalline environments and void behaviors. The classical viscoplastic self-consistent (VPSC) model, as a widely used analytical model with excellent computational efficiency, has been extended to the dilatational-VPSC (DVPSC) model. However, as proposed by the model developers (Lebensohn et al., 2004), there are two main challenges hindering the further extension of the DVPSC model, including (1) the lack of the void nucleation and coalescence and (2) the effective experimental verification. Aiming at the above challenges, a modified-DVPSC model considering the void nucleation and coalescence was proposed and experimentally verified in this work. Accordingly, some improvements were made on the original DVPSC model including the linearization method, the self-consistent equations, and also the volume update equations. Then, with the support of the X-ray computed tomography (CT) technique, the void evolution and fracture mode were analyzed and revealed during the uniaxial tension deformation of 2055 aluminum alloy, through which the essential parameters of the modified model were calibrated. Compared to the previous VPSC and DVPSC models, this modified model accurately describes the stress-strain state, the porosity evolution, and fracture behaviors. Finally, the modified model was applied to investigate the effects of the different loading directions, exhibiting a substantial influence of texture on the void evolution. This research is thereby an innovative attempt for the improvement of the DVPSC model, which can provide inspirations for the future extensions of this theoretical system.

Prediction of mechanical behavior of rocks with strong strain-softening effects by a deep-learning approach

Rock materials exhibit various mechanical characteristics, and it is difficult to describe the strain–stress relation with strong strain-softening behavior by a single constitutive law. In the present study, a long short term memory (LSTM) deep learning method is proposed to predict the material’s deformation under different loading conditions. Unlike the traditional analysis method focusing on the determination of effective tangent stiffness tensor, the constructed LSTM-based procedure requires only the strain–stress values in certain cases to predict the future mechanical behaviors, even for rock materials with strong strain-softening, indicating that the loading history can be taken into account as time sequence data. In order to validate the accuracy, two applications are provided with the established LSTM model: predicting the deformation of granite and sandstone in conventional triaxial compression tests without introducing any elastoplastic parameters or constitutive laws, where the dataset for training the LSTM model is collected alternatively from an analytical micromechanical damage model and from laboratory experiments by considering a wide range of confining pressure. Comparisons of accuracy and convergence rate with different neural network structures are also carried out to check the best performance of the procedure. Implementation method of the trained LSTM model in Finite Element program as a constitutive relation is also provided and applied to the simulation of sandstone. Comparisons show that the LSTM-FEM method provides a good capacity to predict the mechanical behavior of rocks.

Coupling of a phase-field method with a nonlocal micro-mechanical damage model for simulating ductile fracture

Coupling of a phase-field method with a nonlocal micro-mechanical damage model for simulating ductile fracture

A micromechanical damage model for oxide/oxide ceramic matrix composites with hierarchical porosity under thermomechanical loading

This work presents a micromechanical damage model to describe the microstructural damage behaviors of ceramic matrix composites with hierarchical porosity during thermomechanical loading. The microstructure evolution may cause the nonlinear constitutive behavior, and a hierarchical porosity-based elasto-plastic constitutive model was developed. Damage mechanisms of matrix-crack, hierarchical pore nucleation and fiber-breaking are incorporated into the formulation of the damage model to describe various micromechanical damage modes of ceramic matrix composites accurately. Two damage variables are proposed for the damage evolution of matrix and fiber bundles. The main damage mechanisms in the matrix are matrix-cracking, and fibers breaking in the fiber bundles. The performance of the proposed damage model is verified by comparing with the existing experimental data. The proposed damage model outperforms the existing counterparts by capturing the microstructural damage mechanism and integrated into the damage model, and the contribution of different damage mechanisms can be quantified. The present work will provide a robust tool for describing the damage behaviors of matrix and fiber bundles in the ceramic matrix composites under thermomechanical loading, as well as allow a more accurate characterization of microstructural damage for a large extent of ceramic matrix composites.

A Micromechanical Anisotropic Damage Model for Brittle Rocks With Non-Associated Plastic Flow Rule Under True Triaxial Compressive Stresses

A micromechanical anisotropic damage model with a non-associated plastic flow rule is developed for describing the true triaxial behaviors of brittle rocks. We combine the Eshelby’s solution to the inclusion problem with the framework of irreversible thermodynamics. The main dissipative mechanisms of inelastic deformation due to the frictional sliding and damage by microcrack propagation are strongly coupled to each other. A Coulomb-type friction criterion is formulated in terms of the local stress applied onto the microcracks as the yielding function. The back-stress term contained in this local stress plays a critical role in describing the material’s hardening/softening behaviors. With a non-associated flow rule, a potential function is involved. Some analytical analysis of the non-associated micromechanical anisotropic damage model are conducted, which are useful for the model parameters calibration. The proposed model is used to simulate the laboratory tests on Westerly granite under true triaxial stresses. Comparing the numerical simulation results provided by the models with associated/non-associated plastic flow rule and experimental results, it is clear that the proposed non-associated model gives a better prediction than the previous associated model.

Micromechanical Modeling on Compressive Behavior of Foamed Concrete

Much attention has recently been paid to investigating the internal mechanisms between the void structures of foamed concrete and its mechanical behavior. This study adopted the X-ray computed tomography (X-CT) technique to build three-dimensional (3D) internal void structures of foamed concrete before conducting the unconfined compression test. A sensitivity analysis was conducted to evaluate the influence of the void structure on the mechanical properties. The results showed that the contacts between voids had a primary influence on the residual strength, and the void size was the major influence factor on the modulus. A micromechanical model was developed to simulate the mechanical behavior of the foamed concrete under compression, and good agreements were found with the test results. A simple equation was proposed to predict the mechanical properties of the foamed concretes considering the effects and variations of the void structures on the mechanical properties. Combining the equation with the micromechanical damage model, the variations of the mechanical behavior due to the difference in void structures can be well predicted.

Deterioration of concrete due to ASR: Experiments and multiscale modeling

The process of ASR (Alkali-Silica Reaction) induced expansion and damage in pavement concrete specimens is investigated using laboratory experiments and computational modeling. In the experimental program, the concrete specimens are subject to CS-CPT (climate simulation concrete prism test) to obtain ASR induced expansion with and without external supply of alkali. The dissolution rates of the granodiorite used in the concrete mix and the gel formation rates are determined under concrete-like conditions (pH 13.8, with/without Ca(OH)2 and NaCl) at different temperatures. A micromechanics based computational model with aggregate-scale diffusion and reaction kinetics coupled to an Eigenstrain based micromechanics damage model is developed for the simulation of ASR induced expansion and damage. Data from the experimental program are used to calibrate and validate the computational model. Model predictions show that for the given concrete mixture, ASR induced expansion in the specimen exposed to water is predominantly governed by microcracking in the aggregate, while the expansion in the specimen subjected to external alkali supply is governed by microcracking in both the aggregates and the cement paste.

Experimental and numerical study of the interaction between dynamically loaded cracks and pre-existing flaws in edge impacted PMMA specimens

Dynamic fracture tests are carried out for four groups of hole-containing edge impacted PMMA specimens. The crack growth velocity, crack path, and dynamic toughness are extracted from the experiments using high-speed photography and digital image correlation. The importance of the interaction between the in-coming stress wave and the pre-existing hole is revealed and analyzed. We found that the location and size of the pre-existing holes have a significant effect on the rate and spatial distribution build-up of strain energy near the crack tip due to wave scattering effects from the holes. A micromechanical damage model is calibrated to the experimental data from two of the specimens' designs and evaluated for its predictive capabilities using the other experimental configurations. The studied model is shown to be in reasonable agreement with the experimental data, and its limitations are discussed.

Identification and validation of an extended Stewart-Cazacu micromechanics damage model applied to Ti–6Al–4V specimens exhibiting positive stress triaxialities

In this research, the Stewart-Cazacu micromechanics coupled damage model is extended and validated adding nucleation and coalescence models as new damage mechanisms. The Ti–6Al–4V titanium alloy is chosen as a suitable hcp ductile material to be modeled using this extended damage law. The characterization of the damage evolution in this alloy is addressed throughout a quasi-static experimental campaign. Damage characterization relies on in situ X-ray tomography data and scanning electron microscopy imaging technique. The validation procedure consists in the implementation into the finite element research software Lagamine of ULiège and in the comparison of numerical predictions and experimental results. Load–displacement curves and damage-related state variables at fracture configuration from smooth and notched bar specimens submitted to tensile tests are analyzed. The nucleation and coalescence model extensions as well as an accurate elastoplastic and damage material parameter identification for Ti–6Al–4V samples are essential features to reach a validated model. The prediction capabilities exhibited for large strains are in good agreement with experimental results, while the near-fracture strains can still be improved.

Statistical micromechanical damage model for SH-SFRC under tensile load considering the interfacial slip-softening and matrix spalling effects

Strain hardening behavior can be observed in steel fiber reinforced concretes under tensile loads. In this paper, a statistical micromechanical damage framework is presented for the strain hardening steel fiber reinforced concrete (SH-SFRC) considering the interfacial slip-softening and matrix spalling effects. With a linear slip-softening interface law, an analytical model is developed for the single steel fiber pullout behavior. The crack bridging effects are reached by averaging the contribution of the fibers with different inclined angles. Afterwards, the traditional snubbing factor is modified by considering the fiber snubbing and the matrix spalling effects. By adopting the Weibull distribution, a statistical micromechanical damage model is established with the fracture mechanics based cracking criteria and the stress transfer distance. The comparison with the experimental results demonstrates that the proposed framework is capable of reproducing the SH-SFRC’s uniaxial tensile behavior well. Moreover, the impact of the interfacial slip-softening and matrix spalling effects are further discussed with the presented framework.

Strain response of fiber-reinforced ceramic-matrix composites subjected to stress-rupture with stochastic load at intermediate temperature

To ensure the reliability and safety of ceramic-matrix composites (CMCs) hot-section components used in the aero engines, it is necessary to perform the strain response of CMCs at intermediate temperatures (600 to 1000 °C) under stress-rupture with stochastic loading. In this paper, the strain response of SiC/SiC composite under stress-rupture with stochastic load at intermediate temperatures is investigated. Multiple damage mechanisms of matrix cracking, interface debonding and oxidation, and fiber’s oxidation and fracture are considered. Matrix crack spacing, interface oxidation and debonding length, fiber’s broken probability, and intact fiber’s stress are determined using micromechanical damage models. Experimental strain response and internal damage evolution of SiC/SiC composite under constant and stochastic stress are predicted. Effects of stochastic stress level and stochastic time, material properties, damage state and environment temperature on composite’s strain response and stress-rupture life are discussed. When stochastic stress level and environment temperature increase, the composite’s strain at the stochastic stress increases, the time for the interface complete debonding and oxidation decreases, and the stress-rupture life decreases.

Α numerical evaluation of various damage models for thermoplastic composite materials subjected to quasi-static tensile loading

In the present work, damage propagation in thermoplastic composite laminates subjected to quasi-static tensile loading was numerically simulated using different damage models. The simulation was performed using the commercial finite element suite LS-Dyna, where various material models were evaluated based on their ability to simulate the thermoplastic composite behavior. More specifically, material models based on Tsai-Wu failure criteria (MAT_055), progressive damage modeling (MAT_162), micromechanical material modeling (MAT_215) and continuum damage modeling (MAT_261) were implemented, comparing the output failure strength and load – displacement curve with experimental data available in the literature. The approach of damage evolution and failure type for each model was taken under consideration as well. Overall, the progressive damage model (MAT_162) presented the most accurate prediction of the material’s failure behavior.

Perturbed First Order State Dependent Moreau's Sweeping Process

In this paper, we deal with the state-dependent nonconvex sweeping process motivated through quasi-variational inequalities arising in the evolution of sandpiles, quasistatic evolution problems with friction, micromechanical damage models for iron materials. We prove the existence of absolutely continuous solution for the problem in presence of a perturbation, that is an external force applied on the system. The perturbation considered here is general and take the form of a sum of a single-valued Carath'eodory mapping and a set-valued unbounded mapping.