Progressive Damage Model Research Articles

Bird strike simulation on a bonded Ti/CFRP leading edge of an engine fan blade

Bird strike represents a critical loading scenario for aeronautical structures, especially for engine fan blades. It is, therefore, of great importance both to protect the leading edge of the fan blade from impact damage and to be able to detect impact damage directly. In the present study, an explicit finite element (FE) model was developed using the LS-DYNA software to simulate bird strike on the leading edge of a CFRP fan blade protected by an adhesively bonded Ti layer. The model accounts for damage on the CFRP blade through a progressive damage modeling scheme and for debonding through a cohesive zone modeling scheme but not for damage on the Ti layer. For the modeling of the bird, the smooth particle hydrodynamics (SPH) method was used, due to the large deformations that were expected. Using the model, a parametric study on the effects of bird mass and impact energy was performed. The numerical results show that impact damage depends more on impact velocity than the bird mass. In all cases, debonding of the tip of the leading edge was predicted, while for combinations of small bird mass and large impact velocity a more extensive debonding of the protective layer was predicted. Regarding damage in the CFRP, only matrix cracking on the leading edge has been predicted. Aiming to assess the effectiveness of FBGs to detect debonding of the Ti layer due to bird strike, an FBG network has been modeled into the bondline and a study was performed on the correlation of the measured strains with impact damage.

Effect of forced assembly on bearing performance of single-lap, countersunk composite bolted joints – Part Ⅱ: Numerical investigation

A progressive damage model with the combination of 3D Hashin criterion and exponential material degradation was developed and validated according to the experimental results of the Part Ⅰ. The effect of forced assembly on stress distribution and bearing damage of single-lap, countersunk composite bolted joints were revealed by utilizing the present model. It is found that the joints with forced assembly show higher contact stress levels. The stress distribution of the countersunk hole tends to be uniform, while that of the non-countersunk hole is more uneven, and the maximum contact stress occurs at the non-countersunk hole. Furthermore, the forced assembly made a bolt sustain additional axial tensile load, introducing high failure risks to the bolts. With forced assembly, the fiber compressive damage and in-plane matrix compressive damage are more serious, and the most serious damage is transferred from the countersunk hole to the non-countersunk hole.

A progressive damage model for quasi-static tension of 2D woven composites and FEM implementation

We tested the quasi-static tension behavior of the high-strength glass fiber four-Harness stain woven composite, Kevlar fiber plain woven composite, and their laminated hybrid composite. Their representative volume element models are established based on mesoscopic cross-section photographs combined with voxel mesh. A progressive damage model for predicting the damage initiation and evolution of the 2D woven composites is proposed. The crimping effect of plain-woven composites has been considered. The 3D Hashin and the maximum stress criterion are used as the fiber yarn and matrix's damage initiation criterion, respectively. The exponential model is used as the damage evolution model of the fiber yarn. A combination of exponential and reverse tangential damage models has been proposed to describe the damage evolution of the matrix. The proposed damage model is realized using user-defined subroutine UMAT and VUMAT. Abaqus/Standard performs the uniaxial tensile simulation of the two kinds of 2D woven composites with UMAT. Abaqus/Explicit solver simulates the laminated hybrid composite with VUMAT. The simulation results highly agree with the experiment results.

Nonlinear progressive damage model for woven patch-repaired laminate composites

Laminated fiber-reinforced composite materials are vulnerable to damages arising due to impact events like accidental tool drops, bird strikes, etc., which significantly reduce the structural integrity of these materials. Therefore, one of the popular adhesively bonded repair techniques, i.e. patch repair is employed in this work. The present work focuses on developing a three-dimensional energy-based gradual degradation model for patch-repaired laminates, including the effects of shear non-linearity under tensile load. The model utilizes modified Hashin failure criteria for plain woven laminate and maximum shear stress criteria for the adhesive. Using the nonlinear model, the failure strengths for different pristine, drilled and repaired specimens with double-sided patches of [0]2 and [45]2 are studied. Tensile experiments in accordance with ASTM-D3039/D3039M are performed using Digital Image Correlation (DIC) and Acoustic Emission (AE) to validate numerical results. The simulated results based on the proposed model and experimental observations are used to compare the damage mechanisms of pristine, drilled, and patch-repaired laminates. It is observed that matrix cracking is majorly responsible for damage initiation. Subsequently, fiber–matrix debonding and fiber breakage account for the ultimate failure of pristine, drilled and repaired specimens. The developed model is used for studying the effect of different patch sizes of repaired specimens under tensile load.

Multiscale damage modelling of notched and un-notched 3D woven composites with randomly distributed manufacturing defects

This work proposes a stochastic multiscale computational framework for damage modelling in 3D woven composite laminates, by considering the random distribution of manufacturing-induced imperfections. The proposed method is demonstrated to be accurate, while being simple to implement and requiring modest computational resources. In this approach, a limited number of cross-sectional views obtained from micro-computed tomography (µCT) are used to obtain the stochastic distribution of two key manufacturing-induced defects, namely waviness and voids. This distribution is fed into a multiscale progressive damage model to predict the damage response of three-dimensional (3D) orthogonal woven composites. The accuracy of the proposed model was demonstrated by performing a series of finite element simulations of the un-notched and notched tensile tests (having two different hole sizes) for resin-infused thermoplastic (Elium®) 3D woven composites. Excellent correlation was achieved between experiments and the stochastic finite element simulations. This demonstrates the effectiveness of the proposed stochastic multiscale model. The model successfully captured the stochastic nature of tensile responses (ultimate tensile strength and stiffness), damage modes (matrix damage and fibre failure), and initiation and propagation of transverse cracks in thermoplastic 3D woven composites, consistent with experimental observation. The stochastic computational framework presented in this paper can be used to guide the design and optimization of 3D textile composite structures.

Temperature-Moisture-Mechanical coupling fatigue behaviours of screwed Composite-Steel joints

This paper seeks to probe temperature-moisture-mechanical coupling fatigue behaviours of screwed composite-steel joints by using experimental and numerical methods. Novel temperature-moisture-mechanical (TMM) coupling constitutive model, fatigue failure criterion and progressive fatigue damage algorithm (PFDA) are first devised for simulating fatigue failure mechanisms and modes and for predicting fatigue lives of single-lap screwed composite-metal joints (CMJs) in arbitrary temperature-moisture environment. In order to validate the presented model and algorithm, tension–tension fatigue tests are then conducted on the CMJs in four representative environments: low temperature of −40 °C and dry (LTD), room temperature of + 23 °C and dry (RTD), room temperature of + 23 °C and wet (RTW) and elevated temperature of + 55 °C and wet (ETW), respectively. Finally, the TMM coupling fatigue behaviors of the CMJs are analyzed and discussed from the experiments and progressive fatigue damage modelling, and predicted results agree well with experimental findings, demonstrating the feasible and practical usage of the proposed model.

Revealing the coupled effects of hygrothermal environment and geometrical parameters on the failure of double-lap, single-bolt composite joints

Coupled effects of hygrothermal environment and geometrical parameters on the failure of a double-lap, single-bolt composite joint are investigated numerically. The studied geometrical parameters include the ratio of end distance to hole diameter (e/D) and that of width to hole diameter (w/D). Three representative environmental conditions, including −55 °C/dry (CTD), 23 °C/dry (RTD) and 70 °C/wet (ETW), are considered. Numerical progressive damage models (PDMs) that consider hygrothermal effects are established to predict the failure load and failure mode of the joints. Good agreement between the predicted and experimental results confirm the applicability of the established PDMs. The results indicate that the CTD condition increases the failure load of the joint, whereas the ETW condition decreases it. The extent of the hygrothermal effect changes with e/D, but is insusceptible to w/D. Further, the relationship between the failure load and e/D is affected by the hygrothermal condition. Under the CTD condition, the failure load reaches a plateau at a smaller critical value of e/D, compared with that under the ETW condition. However, the relationship between the failure load and w/D is unaffected by the hygrothermal condition. The failure mode depends on e/D and w/D, and is not affected by the hygrothermal condition.

Lay-up effect on the open-hole shear strength of composite laminates

The effect of lay-up on the open-hole shear (OHS) strength of quasi-isotropic carbon fibre/epoxy composite laminates was investigated. It was found that laminates with equivalent specific stiffness but different laminate lay-up, i.e. with different arrangements of plies and ply thicknesses, exhibit significant differences in ultimate OHS strength of up to 16.3% and 27.9% for the prepreg material systems IM7/8552 and T800/epoxy, respectively. Using Digital Image Correlation (DIC), X-ray Computed Tomography (CT), and Finite Element Analysis (FEA), it is shown that the lay-up dependent OHS strengths were associated with distinctly different failure modes. These lay-up dependent failure modes are challenging to predict. It is therefore proposed that the OHS test could be used for material screening, and as a new benchmark case for the development and validation of advanced progressive damage modelling frameworks for laminated composites, complementing the commonly used open-hole tensile (OHT) test.

Numerical investigation on the mechanical behaviors of 2D woven composites under complex in-plane stress states

Using finite element method (FEM), the mechanical behaviors of 2D woven composites with different weave structures are investigated with considering the complex in-plane stress states. Periodic boundary conditions for arbitrary off-axis loading scenarios are established, and a progressive damage model based on Linde criterion is proposed, which is subsequently validated by the previous experiments. In addition, the failure envelopes predicted by classical failure criteria are compared to the results obtained by FEM. The effects of woven structures on elastic properties and failure behavior are also discussed, which demonstrates that the plain woven composites have inferior mechanical performance than twill and satin woven composites. Based on the assessment of the failure criteria, this study provides recommendations for selecting relevant failure criteria to anticipate mechanical properties under various loading conditions. The findings in this paper are expected to encourage the development of damage constitutive models and their engineering applications for 2D woven composites.

Multiscale image-based modeling of progressive damage in 3D5D braided composites with yarn-reduction

The special-shape fiber-reinforced composites are improbable to be represented by the representative volume element (RVE). Hence, a multiscale image-based model is proposed to reveal the progressive damage in 3D5D braided composites with/without yarn-reduction. The microscale and mesoscale models of the materials are reconstructed by Micro-CT, considering the yarns’ twists, global compression, and yarns’ misalignment. Subsequently, the continuous damage method and the cohesive-zone model are proposed to characterize the damage behavior of the microscale and mesoscale constituents. These constitutive models are implemented by a user-defined subroutine UMAT in ABAQUS. Finally, based on the homogenization procedure and the multiscale analysis method, the effects of structures on microscale, mesoscale, and macroscale properties of 3D5D braided composites without/with yarn-reduction are analyzed sequentially. The results show that cross-section variations and twists in the yarns modify the damage initiation. The wedge-shaped stress migration phenomenon occurs near the yarn-reduction point. Besides, the macroscopic simulation of strain fields and the damage morphology agrees well with the DIC measurements and Micro-CT results. The established multiscale framework is expected to predict the progressive damage of 3D5D braided composites with/without yarn-reduction and provide the theoretical basis for the structure design.

A progressive damage model to predict the shear and mixed-mode low-cycle impact fatigue life of adhesive joints using cohesive elements

A progressive damage model to predict the shear and mixed-mode low-cycle impact fatigue life of adhesive joints using cohesive elements

A progressive damage model for ceramic matrix mini-composites with thick interphases

Toughness enhancement in ceramic matrix composites (CMCs) with brittle matrix and fiber phases is often accomplished by introducing a weak finite-thickness interphase between the fiber and matrix. The current work presents a progressive damage model to predict the tensile response of single tow CMCs (mini-composite) representative of a unidirectional composite at the microscale. Implementation of a 3-phase shear-lag model for a geometrically accurate representation of the underlying microstructure in CMCs with finite thickness interphase has been highlighted. A probabilistic progressive modeling approach has been adopted, accounting for multiple matrix cracking, interfacial debonding, and fiber failure in 3-phase mini-composites. The predicted tensile response of CMCs from the progressive damage modeling approach agrees with experimental results obtained for C/BN/SiC mini-composites validating the approach.

A bond-based peridynamics model based on variable material properties for modeling elastoplastic behavior

Crack tip singularities and material discontinuities are taken to be the main challenges for analyzing cracks in fracture mechanics problems. Peridynamic (PD) theory has been recently introduced as a nonlocal extension of continuum mechanics capable of improved modeling of progressive damage and rupture in cracked structures. In this theory, the internal forces have been characterized by nonlocal interaction between the pairs of the material points whose displacements or displacement derivatives are discontinuous. Given that the bond-based PD (BB-PD) has not been satisfactorily employed for predicting ductile fracture, the main purpose of this work is to present a new PD plasticity model in conjunction with the Variable Material Property (VMP) method, aiming to provide the possibility of elastoplastic modeling in BB-PD. In the present work, the quasi-static loading has been selected for simulation and the von-Mises yield criterion has been utilized for describing the plastic deformation. The loadings are applied as the displacement is controlled and outputs from the PD model are compared with the results achieved from ABAQUS software based on the continuum mechanic assumptions. To validate the accuracy of the present formulation, two example problems of the plate with a central crack and a central hole subjected to tensile load are examined. The results of von-Mises stress, the plastic zone size, horizontal and vertical displacement, and equivalent plastic strain have been verified in comparison with the outputs calculated by the finite element method (FEM), evidencing good accuracy of the VMP-based PD elastoplastic model in predicting the desired parameters. To predict the formation of spontaneous cracks and crack growth trajectory, two more examples that include a plate with a central hole, as well as, a plate with two edge cracks and a double hole are discussed. The obtained results are in good agreement with those from the experiment and ABAQUS software.

A new strategy for generating regional random fiber-reinforced polymer composite

This paper proposes a novel method of random fiber distribution inspired by the finite element mesh technique. It solves the problem of fiber interference when generating the Representative Volume Element (RVE) with a high volume fraction and prevents fiber cluster formation at low volume fractions. Theoretically, the method can produce Fiber-Reinforced Polymer (FRP) composites with volume fractions up to 90.7%. The mechanical properties of FRP composites are then predicted using a progressive damage model that considers the failure of the matrix and interface. The experimental results in the literature verify the rationality of the numerical model. Finally, the effect of varying volume fractions and cell-cutting methods on the mechanical characteristics of unidirectional FRP composites under transverse loading was studied. The results show that the elastic modulus increases with increasing fiber volume fraction, while the tensile strength shows an opposite trend. The hexagonal cell-cutting method can alleviate the adverse effect of the decrease in tensile strength with the increase in fiber volume fraction. Meanwhile, the hexagonal cell-cutting method is reliably reproducible, and the coefficient of variation for the 30 renditions is only 0.05%. It illustrates that the hexagonal cell-cutting method can generate composites with higher tensile strength compared to other methods.

Progressive damage analysis in an open hole compression of FRP laminates including fiber kinking and pre-existing damage

Progressive damage and strength analysis in an open hole compression (OHC) test is crucial in designing components made of fiber reinforced plastics (FRPs) composites. In this work, a continuum damage mechanics based 3D progressive damage model (PDM) incorporating LaRC05 failure criteria is developed. It considers identification of fracture and kink-band plane, shear non-linearity, in-situ strengths, and mixed-mode fracture in the formulation. The proposed PDM is validated through single element tests and applied to analyze the damage patterns and strength during open hole compression (OHC) tests of three different layups with two different hole sizes and a pre-existing damage. It is observed that fiber kinking in 0∘ plies initiates at the location of maximum in-plane shear stress and propagates due to a combined action of longitudinal compression and in-plane shear stress. The final failure of 0∘ dominant and quasi-isotropic layup is governed by fiber kinking in 0∘ plies, whereas matrix cracking in ±45∘ plies is responsible for the final failure of the shear dominant layup. Furthermore, OHC strength of the layups reduces by 15%–20%, when the hole size increases from 6.35 mm to 9.525 mm. In the presence of a pre-existing kink or matrix damage, fiber kinking initiates at locations of the pre-existing damage. A small pre-existing damage reduces OHC strength of the layups up to 7%–11%. The results predicted by the model match well with the experimental results in the literature.

Experimental and numerical investigation on the failure behavior of Bouligand laminates under off-axis open-hole tensile loading

The Bouligand structure is a fibrous laminate with uniaxial layers assembled periodically into a helicoidal pattern. Compared to other types of laminates, its resistance to in-plane damage still lacks clarification. The failure behavior of Bouligand laminates under off-axis open-hole tensile (OHT) loading was investigated compared to cross-ply and quasi-isotropic structures using experiment and numerical simulation. After verifying the progressive damage model based on Hashin criteria, the numerical predictions from various off-axis loadings were compared between these three structures. The results show that Bouligand laminates exhibit low but nearly stable OHT strength. In comparison, the cross-ply structure exhibits high OHT strength variation when loaded in different directions. With the change of off-axis angle, the OHT strength of the Bouligand structure changes by 10.1 % from 405.2 MPa to 364.1 MPa, while it changes by 69.1 % from 533.8 MPa to 165.1 MPa for the cross-ply structure. Besides, the Bouligand structure exhibits higher OHT strength when the off-axis angle exceeds 5°. It also exhibits a more stable OHT strength than the quasi-isotropic structure. It is shown that the failure of fiber and matrix is the primary factor affecting the OHT strength of the laminate, while the delamination has little effect on the OHT strength.

History effects in the creep of a disordered brittle material

We study the creep behavior of a disordered brittle material (concrete) under successive loading steps, using acoustic emission and ultrasonic sensing to track internal damage. The primary creep rate is observed to follow a (Omori-type) power-law decay in the strain rate, the number of acoustic emission events, as well as the amplitudes of the ultrasonic beams, supporting a brittle-creep mechanism. The distribution of acoustic emission event energies is observed to have a scale-free power-law distribution instead of a truncated one expected for a system approaching a critical point at failure. The main outcome is, however, the discovery of unexpected history effects that make the material less prone to creep when it has been previously deformed and damaged under primary creep. With the help of a progressive damage model implementing thermal activation, we interpret this as an aging-under-stress phenomenon: During an initial creep step at relatively low applied stress, the easy-to-damage sites are exhausted first, depleting the excitation spectrum at low stress gap values. Consequently on reloading, although previously damaged, the primary creep restarts but the material creeps (and damages) less than it would under the same stress but without precreeping. Besides shedding a new light on the fundamental physics of creep of disordered brittle materials, this has important practical consequences in the interpretation of some experimental procedures, such as stress-stepping experiments.

High-fidelity simulation of low-velocity impact damage in fiber-reinforced composite laminates using integrated discrete and continuum damage models

A high-fidelity finite element (FE) model based on integrated discrete and continuum damage modeling techniques was developed to predict damage modes, locations, sizes, and damage occurrence sequence in a composite laminate during a low-velocity impact event. Fiber breakage and transverse matrix cracking were captured using the three-dimensional Hashin’s criteria, and delamination was captured by inserting a layer of cohesive elements between every adjacent composite ply. Delamination progression from one layer to another was captured by embedding cohesive elements inside each composite ply aligned with the fiber orientation and with a 45° angle to the thickness direction. The refined mesh and intralaminar cohesive elements were only used in the predicted damage region based on an analytical solution. The FE model predicted impact response was validated by drop-weight tests, and the layer-by-layer damage areas were validated and characterized by X-Ray CT inspections on 254 mm by 304.8 mm IM7/977-3 laminates with a stacking sequence of [0/45/90/-45]4s. The absorbed energy, damage areas, maximum deflection, contact time, and peak load were predicted with less than 10% error. The detailed damage occurrence sequence during the impact event was predicted through histories of energies dissipated by different damage modes. The modeling methodology developed in this work highlights the effects of modeling parameters on convergence, solution accuracy and computational efficiency, and provides an effective approach for progressive damage modeling of composite laminates.

Experimental and numerical studies on the tensile behaviors of thin-ply and thick-ply open-hole laminates

Laminated composites with thin-ply unidirectional prepregs are popular due to their higher in-situ strength as compared with thick-ply laminates due to different failure mechanisms. Thin-ply and thick-ply open-hole laminates were fabricated and the tensile failure characteristics were studied by combining experimental and numerical simulation approaches. Charge-coupled device camera and de-ply technology were used to obtain failure morphologies of open-hole specimens under tensile loading. A finite element model considering progressive damage and bilinear cohesive model was built based on ABAQUS to study the damage mechanism of open-hole laminates. In thin-ply laminates, the damage plane was relatively neat while in thick-ply laminate broom-shaped damage morphologies were observed. Based on de-ply experiments and numerical prediction, it was found that thin-ply laminates had delamination suppression effect and could restrain the propagation of delamination along the loading direction, which explains the distinct damage patterns existed in thin-ply and thick-ply laminates. Based on numerical prediction, it was found that drilling-induced delamination did not affect the tensile strength of open-hole laminates. Propagation of drilling-induced delamination was also restrained in thin-ply laminates. The results of this research suggested that thin-ply prepregs should be considered when delamination poses critical threat to the structural integrity of laminated composite structures.

Four-point bending behaviors of CFRP trapezoidal corrugated sandwich plates

The stiffness, failure load and failure mechanism of carbon fibre reinforced plastic (CFRP) composite trapezoidal corrugated sandwich plates (CTCSPs) subjected to four-point bending load were studied by experiment, modelling prediction and parametric analysis. With orthogonal anisotropic lay-ups containing ± θ plies (θ = 15°, 45° and 90°), three all-CFRP specimens were fabricated by mold hot pressing and secondary bonding. The four-point bending behaviors of specimens were tested and compared, and the analytical expressions of stiffness and failure load were provided. Four buckling failure modes and four strength failure modes were analytically considered. The spatial location and time sequence of eight failure modes were revealed by numerical linear buckling and progressive damage models established in ABAQUS. The modelling stiffness, failure load and failure process agreed with the four-bending experimental results. By increasing θ, the limit load of the specimens first increases and then decreases while the stiffness decrease. Correspondingly, the initial failure modes are shear corrugation fracture, debonding and face fracture. The variations in stiffness parameters and failure mechanism maps were presented; the latter can simultaneously predict the limit load and failure mode. The limit load and stiffness of CTCSPs can be improved more obviously by increasing the number of the face plies than by expanding the core plies.