Multiscale Damage Model Research Articles

Multiscale modeling of deformation and damage of elasticplastic particle reinforced composites

A model is proposed for the deformation of elastic-plastic particle reinforced composite materials of a periodic structure with allowance for the damage. The model is based on a variant of the deformation theory of plasticity under active loading, in which the damage parameter is introduced, taking into account the difference in the accumulation of damage in phases during shear, tension and compression. The method of asymptotic homogenization of periodic structures was used to model the effective characteristics of elastic-plastic composites. Examples of numerical calculation are carried out for particle-reinforced metal composite - aluminum matrix filled with SiC particles.

A multiscale modeling for failure predictions of fiber reinforced composite laminates

A three-dimensional multiscale damage modeling, based on the parametric High Fidelity Generalized Method of Cells (HFGMC) micromechanics and integrated with a finite-element (FE) code, is proposed to predict the mechanical response, including damage evolution, as well as to generate failure envelopes of composite laminates. A hexagonal repeating unit-cell (RUC) is used to represent explicitly the fiber and matrix phases of a lamina at the microscale level. Failure of a lamina is determined by using both strain-based and stress-based failure theories. This modeling approach is implemented as a user material subroutine (UMAT) within displacement-based Solid FE models, where each solid element is represented by one material point. When the modeled damage is propagating within the macroscale FE model, the material points are eliminated from the FE calculations by using the element deletion approach. The efficiency of the proposed multiscale modeling is demonstrated by a comparison of simulated results with measured data available in the literature.

Multi-scale damage modeling of 3D orthogonal woven carbon-carbon composite at elevated temperatures

This paper presents a multi-scale structure modeling scheme to analyze the damage behaviors of three-dimensional orthogonal Carbon/Carbon (C/C) composites subject to uniaxial tension at high temperatures. The multi-scale structure model includes a micro-scale and a meso-scale structure model with periodic boundary conditions to homogenize the heterogeneous fiber/matrix system into unit cells. The micro-scale model predicts the mechanical properties at the fiber tow scale in the three orthogonal directions (x, y and z). The output results by the micro-scale simulations are then incorporated in the meso-scale model to demonstrate the locations of stress propagation and the progressive failure behavior of the 3D C/C composite. Based on the numerical approaches, uniaxial tensile strengths of the 3D C/C composite are calculated from 300 to 2500 K, and its temperature dependences are discussed. The current applied multi-scale models provide an efficient approach to predict the tensile strength of 3D textile composites, and will give some highlights for the design of 3D C/C composite components.

Microstructure and damage evolution of SiCf/PyC/SiC and SiCf/BN/SiC mini-composites: A synchrotron X-ray computed microtomography study

Abstract SiCf/PyC/SiC and SiCf/BN/SiC mini-composites comprising single tow SiC fibre-reinforced SiC with chemical vapor deposited PyC or BN interface layers are fabricated. The microstructure evolutions of the mini-composite samples as the oxidation temperature increases (oxidation at 1000, 1200, 1400, and 1600 °C in air for 2 h) are observed by scanning electron microscopy, energy dispersive spectrometry, and X-ray diffraction characterization methods. The damage evolution for each component of the as-fabricated SiCf/SiC composites (SiC fibre, PyC/BN interface, SiC matrix, and mesophase) is mapped as a three-dimensional (3D) image and quantified with X-ray computed tomography. The mechanical performance of the composites is investigated via tensile tests. The results reveal that tensile failure occurs after the delamination and fibre pull-out in the SiCf/PyC/SiC composites due to the volatilization of the PyC interface at high temperatures in the air environment. Meanwhile, the gaps between the fibres and matrix lead to rapid oxidation and crack propagation from the SiC matrix to SiC fibre, resulting in the failure of the SiCf/PyC/SiC composites as the oxidation temperature increases to 1600 °C. On the other hand, the oxidation products of B2O3 molten compounds (reacted from the BN interface) fill up the fracture, cracks, and voids in the SiC matrix, providing excellent strength retention at elevated oxidation temperatures. Moreover, under the protection of B2O3, the SiCf/BN/SiC mini-composites show a nearly intact microstructure of the SiC fibre, a low void growth rate from the matrix to fibre, and inhibition of new void formation and the SiO2 grain growth from room to high temperatures. This work provides guidance for predicting the service life of SiCf/PyC/SiC and SiCf/BN/SiC composite materials, and is fundamental for establishing multiscale damage models on a local scale.

Multi-scale fatigue damage model for steel structures working under high temperature

In order to better understand the fatigue mechanisms of steel structures working under high temperature, a multi-scale fatigue damage model at high temperature is developed. In the developed model, the macroscopic fatigue damage of metallic materials due to the collective behavior of micro-cracks is quantified by using the generalized self-consistent method. The influence of temperature on fatigue damage of steel structures is quantified by using the previous creep damage model. In addition, the fatigue damage at room temperature and creep damage is coupled in the multi-scale fatigue damage model. The validity of the developed multi-scale damage model is verified by comparing the predicted damage evolution curve with the experimental data. It shows that the developed model is effectiveness. Finally, the fatigue analysis on steel crane runway girders (CRGs) of industrial steel melt shop is performed based on the developed model.

Multiscale modeling of fiber recruitment and damage with a discrete fiber dispersion method

Recently, we introduced a discrete fiber dispersion model based on triangular discretization of a unit sphere with a finite number of elementary areas. Over each elementary area, we define a representative fiber direction and an elementary fiber density based on the fiber dispersion. The strain energy of fibers distributed in each elementary area is then approximated by the deformation of the representative fiber direction weighted by the corresponding elementary fiber density. A summation of fiber contributions of all elementary areas yields the resultant fiber strain energy. However, in that study we did not consider fiber recruitment, softening and damage. The goal of this study is to incorporate these important properties of collagen fibers into the constitutive model. We first define a fiber recruitment stretch at which the fiber becomes straightened. Then, we adopt the continuum damage mechanics method for modeling fiber softening and damage. We implemented the proposed model in a finite element program and verified it with three representative examples including a uniaxial extension test of a dog-bone shaped specimen up to failure. The computational solution agrees well with the experimental result. In conclusion, the proposed model is able to capture fiber recruitment, softening, and damage. Future studies with more complex boundary conditions are necessary to verify this approach.

Development and implementation of a multi-scale model for matrix micro-cracking prediction in composite structures subjected to low velocity impact

In this paper, a novel multi-scale damage model has been developed to predict the progression of matrix micro-cracking in a prototype car bumper under low-velocity impact. The methodology is based on FE micro-damage modelling to calibrate the parameters of a Synergistic Damage Mechanics model considering multi-axial loading, combined with a matrix micro-crack multiplication model. Python scripting was used to model a series of micro-mechanical FE models to determine the damage parameters, which were then used to simulate damage evolution at the structural scale, using a VUMAT subroutine. Following validation, the effects of the impactor's initial velocity, stacking sequence, rate-dependency and bumper's cross sectional profile have been evaluated for different material systems. The patterns of damage progression show that the damage model can accurately predict the progression of matrix micro-cracking, paving the way for the utilization of accurate multi-scale analysis tools in composite structures.

Multiscale Modeling of Tip-Formation and Damage of Red Blood Cells Squeezing through Submicron Slits

Multiscale Modeling of Tip-Formation and Damage of Red Blood Cells Squeezing through Submicron Slits

Assessing progressive failure in long wind turbine blades under quasi-static and cyclic loads

Predicting progressive failure and consequential loss in the load-bearing capability of large-scale composite wind blades is vital for accurately assessing their service life and maintenance. A physics-based multi-scale damage model describing progressive ply cracking and joint adhesive debonding in blades under both quasi-static and cyclic loading is presented. The complete structure of the blade was considered including the shell-spar adhesive joint and shell-root adhesive joint. For quasi-static loading, the geometrical transition region of the blade was observed as the critical ply crack damage region, which was in agreement with previous experimental results. The matrix micro-cracking damage was mainly caused by high gale wind speeds, and adhesive debonding ultimately initiated at the shell-spar joint. The blade tip deflection increased nonlinearly with increasing wind speeds, reaching 29.0% of the blade length at 19 m/s. For cyclic loading, sub-critical damage grew along the length of the blade with increasing cycles, gradually increasing the normal and shear stresses in the joint adhesive layer as the crack density increased, eventually leading to local shell-spar adhesive debonding. The simulation methodology presented here will be useful for assessing the durability and increasing the safety and accuracy of service life prediction of large-scale blade structures.

A damage model of mechanical behavior of porous materials: Application to sandstone

In this work, a multiscale model based on the Fast Fourier Transform (FFT) technique is applied to describe the mechanical behavior of porous materials. The effects of the microstructures (such as pore shape, number, size, distribution and orientation) on the overall strength of the porous medium and its microstress distribution are fully studied. The elastoplastic model is further extended by including a damage process. The influences of microstructure on the damage evolution of the porous medium are discussed and illustrated numerically. Then the proposed multiscale damage model is applied to study the macroscopic behavior of porous sandstone. According to the microstructure of the studied material, a representative elementary volume with randomly distributed spherical pores is considered. The solid phase of the sandstone is assumed to obey the Drucker–Prager criterion. Taking advantage of the FFT-based method, the evolution of generated damage is clearly illustrated during the loading process at the microscopic level. Comparisons between numerical results and experimental data show the efficiency of the proposed numerical model.

Multi-scale Modeling of Radiation Damage: Large Scale Data Analysis

Modification of materials in nuclear reactors due to neutron irradiation is a multiscale problem. These neutrons pass through materials creating several energetic primary knock-on atoms (PKA) which cause localized collision cascades creating damage tracks, defects (interstitials and vacancies) and defect clusters depending on the energy of the PKA. These defects diffuse and recombine throughout the whole duration of operation of the reactor, thereby changing the micro-structure of the material and its properties. It is therefore desirable to develop predictive computational tools to simulate the micro-structural changes of irradiated materials. In this paper we describe how statistical averages of the collision cascades from thousands of MD simulations are used to provide inputs to Kinetic Monte Carlo (KMC) simulations which can handle larger sizes, more defects and longer time durations. Use of unsupervised learning and graph optimization in handling and analyzing large scale MD data will be highlighted.

Multi-scale damage modelling in a ceramic matrix composite using a finite-element microstructure meshfree methodology.

The problem of multi-scale modelling of damage development in a SiC ceramic fibre-reinforced SiC matrix ceramic composite tube is addressed, with the objective of demonstrating the ability of the finite-element microstructure meshfree (FEMME) model to introduce important aspects of the microstructure into a larger scale model of the component. These are particularly the location, orientation and geometry of significant porosity and the load-carrying capability and quasi-brittle failure behaviour of the fibre tows. The FEMME model uses finite-element and cellular automata layers, connected by a meshfree layer, to efficiently couple the damage in the microstructure with the strain field at the component level. Comparison is made with experimental observations of damage development in an axially loaded composite tube, studied by X-ray computed tomography and digital volume correlation. Recommendations are made for further development of the model to achieve greater fidelity to the microstructure. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

A simplified multiscale damage model for the transversely isotropic shale rocks under tensile loading

A simplified multiscale damage model is proposed for the transversely isotropic shale rocks under tensile loading. In this framework, the multiscale representations for the shale rocks are presented by introducing the microcrack-weakened equivalent solid with hierarchical microstructures, whose transversely isotropic properties are obtained by performing multilevel homogenization procedures. To simplify the calculation process for the damage-induced properties, the equivalent isotropic medium is attained by applying the Voigt–Reuss–Hill averaging process to the transversely isotropic solid. Subsequently, the microcrack-induced inelastic compliances are approximately derived in terms of microcrack opening displacements in the equivalent isotropic medium of the shale rock under tensile loading. The sizes and orientations of microcracks are taken as random variables. Both stationary and evolutionary damage models are considered. Microcrack kinetic equations are characterized through the use of a fracture mechanics-based stability criterion and microcrack geometry within a representative volume element. Numerical examples including experimental validations and comparisons with existing micromechanical models are presented to verify the proposed multiscale damage model. Finally, the influences of the silt inclusions and porosity on the material intrinsic and damage-induced properties are discussed.

Explicit multiscale modelling of impact damage on laminated composites – Part II: Multiscale analyses

This work describes a multiscale impact damage prediction methodology for laminated composite structures which is based on the HFGMC micromechanical model and the MMCDM damage formulation. The numerical approach is intended for application within explicit finite element analyses and has been employed for modelling of high-velocity impact damage in laminated composite structures. Structural-scale applications and the multiscale framework of the method are presented in this paper whereas introduction and validation of the methodology have been presented in Part I of the paper.By applying the described method, the micromechanical model calculates the local stress/strain fields within the unidirectional composite material, whereas the structural-scale computations have been performed employing Abaqus/Explicit. The Mixed Mode Continuum Damage Mechanics (MMCDM) theory has been utilised as to model the damage and failure modes of the composite material at the micromechanical level. As demonstrated in the Part I paper, the HFGMC and MMCDM model enable modelling of the microdamage nonlinearities at in-plane shear and transverse compressive loading of the composite plies. The micromechanical damage modelling approach has been employed at high-velocity soft-body impact on CFRP and GFRP composite plates in this work. Results of the multiscale damage model have been validated using available experimental data and by comparison with the numerical results obtained using the commonly used ply-level failure criteria and damage models.

Multi-scale damage modelling of 3D woven composites under uni-axial tension

This paper presents a detailed numerical analysis of two types of 3D woven composite architecture. a unit cell, full finite element meso model, and a mosaic macro model are developed to simulate the elastic and damage progression behaviour of the two weave types. Both models predicted the tensile modulus and strength within 20% of the experimentally measured values, and the predicted failure sequence was similar to the experimental observation.

Critical stiffness damage envelopes for multidirectional laminated structures under multiaxial loading conditions

Load-bearing laminated structures undergo complex crack evolution processes and consequent stiffness degradation, which leads to a decline in their overall performance. Thus, consideration of damage evolution is important for stiffness critical applications. In this study, a multi-scale damage model combining synergistic damage mechanics (SDM) with an energy-based damage evolution model is developed for multidirectional laminated structures. The SDM approach combines computational finite element-based micromechanics with continuum damage mechanics, enabling the evaluation of the laminate stiffness. The damage model predicts evolution of sub-critical matrix cracks in different plies under multiaxial loading. Model predictions, which include ply crack density evolution and laminate stiffness degradation, correlate well with available experimental data, while model results for various CFRP and GFRP multidirectional laminates demonstrate its robustness. Additionally, damage envelopes corresponding to pre-selected critical stiffness degradation levels are developed to serve as an alternative to current approaches of final failure envelopes, and are regarded as a useful design tool for stiffness critical composite structures in practical applications.

Progressive damage and failure response of hybrid 3D textile composites subjected to flexural loading, part II: Mechanics based multiscale computational modeling of progressive damage and failure

A mechanics based multiscale computational model is presented to predict the deformation, damage and failure response of hybrid 3D textile composites (H3DTCs) subjected to three-point bending. The geometry of the textile architecture was incorporated in a mesoscale finite element (FE) model, while the H3DTC was homogenized at the macroscale. The mesoscale model is a collection of repeat unit cells (RUCs) that are composed of different types of fiber tows embedded in a surrounding matrix. Matrix microdamage was modeled by a (pre-peak) nonlinear stress versus strain response, using a modified J2 deformation theory of plasticity incorporating a secant-modulus approach. Fiber tow pre-peak nonlinear response was computed using a novel, two-scale model, in which the subscale micromechanical analysis was carried out in closed-form based upon a unit cell of a fiber–matrix concentric cylinder. Consequently, the influence of matrix microdamage developing at the microscale manifests as the progressive degradation of fiber tow stiffness at the mesoscale. The smeared crack approach (SCA) was employed to model the post-peak softening of the constituents due to failure, including matrix macro-cracking, tow kinking, and tow breaking. This method offers a mesh objective result by relating the post-peak softening response to a traction–separation law that is associated with each failure mechanism through a characteristic length. Thus, the total energy release rate during failure in a continuum element is related to the fracture toughness of the material.The load–deflection responses, along with the progressive damage and failure events, including fiber tow kinking and rupture, are successfully predicted through the proposed computational model. In addition, the textile architecture-dependent effect, observed in the asymmetric H3DTCs, is also captured, demonstrating the predictive capability of the proposed modeling scheme. Since all the inputs are from the constituent level, the model is useful in understanding how the macroscopic response of H3DTCs is influenced by textile architecture and constituent properties. The experimental studies are presented in Part I of this two-part sequence (Zhang et al., 2015).

Condition-based prediction of time-dependent reliability in composites

This paper presents a reliability-based prediction methodology to obtain the remaining useful life of composite materials subjected to fatigue degradation. Degradation phenomena such as stiffness reduction and increase in matrix micro-cracks density are sequentially estimated through a Bayesian filtering framework that incorporates information from both multi-scale damage models and damage measurements, that are sequentially collected along the process. A set of damage states are further propagated forward in time by simulating the damage progression using the models in the absence of new damage measurements to estimate the time-dependent reliability of the composite material. As a key contribution, the estimation of the remaining useful life is obtained as a probability from the prediction of the time-dependent reliability, whose validity is formally proven using the axioms of Probability Logic. A case study is presented using multi-scale fatigue damage data from a cross-ply carbon-epoxy laminate.

Multiscale damage modeling with the “Morphological Approach” to highlight particle size and interaction effects in highly-filled particulate composites

Abstract This paper concerns the modeling of interfacial damage in highly-filled particulate composites (e.g. solid propellants), thanks to a specific multi-scale approach recently developed, called “Morphological Approach”. This approach was shown to provide both the homogenized and local responses of the composite taking into account heterogeneity of the strain field within the matrix. In this paper, the M.A. ability to deal with particle size and complex interaction effects expected in highly-filled composites is studied. Considering for simplicity the constituents (particles and matrix) as linear elastic, numerical computations are performed on simple periodic microstructures, monomodal random microstructures and finally a bimodal random microstructure. Particle/matrix debonding chronology is analyzed with respect to the particle size as well as the influence of interactions between particles. The role of interfaces orientation is also addressed. The M.A. is shown to account for preferential damage on the largest particles. Moreover, M.A. estimates show that the more important the particle volume fraction, the earlier the first nucleations. Results are in accordance with experimental studies and full-field simulations available in the literature.

Accelerated time integrator for multiple time scale homogenization

SummaryThis manuscript presents an accelerated time domain homogenization methodology for prediction of material and structural failure under fatigue loading. The methodology is based on mathematical homogenization theory applied to the time domain. The method addresses the computational challenge associated with the scale disparity between the characteristic fatigue load period and the overall fatigue life. Cycle sensitive continuum damage mechanics modeling is used to describe the progressive damage accumulation under fatigue loading. The original initial boundary value problem is decomposed into coupled fast and slow time scale problems. A quasilinear approximation to the fast time scale problem is introduced to efficiently evaluate the response under a fatigue load cycle. The effect of the new time integrator on the thermodynamic consistency of the resulting system of discrete equations is demonstrated for a general class of continuum damage mechanics models. The proposed method is numerically verified based on a scalar damage model and a spatially multiscale damage model used for predicting fatigue life of composite materials. The proposed accelerated time integrator is shown to have reasonable accuracy and is orders of magnitude more computationally efficient when compared with previously proposed time homogenization methods. Copyright © 2015 John Wiley & Sons, Ltd.