Crack Propagation In Composites Research Articles

An anisotropic gradient damage model with energy limiter for brittle crack propagation in composites

This work presents a novel anisotropic implicit gradient-enhanced damage model for directional fracture in composites with a single family of fibers. The improvement of anisotropy into the new smeared crack damage model is necessary and meaningful to adequately capture the typical orientation-dependent behavior of cracks in anisotropic media. Under the setting, the relationship between cracks and fiber direction is described through the introduction of a second-order structural tensor. This tensor depends on an anisotropic coefficient and the orientations of the fibers, which in turn control the direction of the simulated cracks. Consistently, the standard isotropic strain energy density function as the damage-driving term is replaced by the anisotropic SED function for the fiber-reinforced composites. With the use of the anisotropic SED function, a proper energy splitting technique is adopted for avoiding nonphysical damage under compression. The final governing equations of the equilibrium and anisotropic diffusive damage evolution equation are solved by means of the standard FEM with the aid of a staggered algorithm. The accuracy and modeling capacity of the developed direction-dependent fracture formulation are demonstrated through a set of representative numerical experiments. It shows that the anisotropic damage model can predict complex directional failure in transversely isotropic materials.

Numerical studies of crack propagation in composites reinforced by irregular particles

The study of crack-particle interaction and its impact on a material's fracture toughness are important investigations in composite materials. The micromechanical deformations that occur in the area of the embedded particles can lead to crack initiation and affect the overall macroscopic properties. It is a known fact that in composites with stiff brittle particles and weak plastic matrix, during the process of tensile deformation, microcracks are first formed at the defects and weak interfaces. Many such fine cracks converge to form large cracks leading to the fracture propagation on the particle-matrix boundary and in the matrix. Crack propagation in particle-reinforced composites can be significantly influenced by parameters such as particle size, geometry, distribution, and interface to the surrounding matrix. This article studies the effect of these parameters on crack initiation and growth by simulating various 2D models of uniaxial tensile tests through finite element modeling. A typical part of a tensile test specimen is used for 2D modeling. It is observed that the irregular shape of the particles plays a crucial role in the crack propagation and trajectory of the crack path, as particles with sharp corners that are oriented perpendicular to the tensile loading define the sites of stress concentration, which eventually leads to the crack formation. Furthermore, the irregular particles are approximated by circular and elliptical shapes with the same surface area. The tangential behavior between the particles and the matrix has been modeled as zero friction. Finally, the tensile strengths for different microstructure realizations have been evaluated in this study.

1D higher-order theories for quasi-static progressive failure analysis of composites based on a full 3D Hashin orthotropic damage model

This work investigates the crack propagation in composites by adopting a novel full three-dimensional (3D) Hashin-based orthotropic damage model combined with higher-order one-dimensional (1D) finite elements based on the Carrera Unified Formulation (CUF). Previous literature has proven that CUF provides structural formulations with great accuracy and improved computational efficiency. Moreover, a Layer-Wise (LW) formulation can be implemented within the CUF framework, allowing an accurate description of the 3D stress state in composite laminate, representing crucial information for progressive failure analysis. A Newton–Raphson predictor–corrector algorithm is used for the numerical solution of classical case tests, i.e., compact tension and three-point bending tests. The obtained results are compared with experimental outcomes and with solutions from well-established 2D damage models and a 3D Abaqus numerical model, demonstrating the capability of the proposed method to efficiently capture both the failure load and shape of the crack pattern.

Effects of graphene size and arrangement on crack propagation of graphene/aluminum composites

Aluminum-based composite material is one of the most important candidate materials in the mechanical industry and aerospace engineering due to its light weight and high strength. Graphene is an ideal reinforcement for composite materials for its excellent mechanical properties. Till-now, the contribution of graphene sheets in the process of crack propagation in composites is not clear. In present work, the effects of graphene size and distribution in graphene/aluminum composites are explored using molecular dynamics simulation methods. It is found that when the length of graphene flake is less than 3.35 nm, the generated sub-cracks in the composite is benefit to the crack propagation. This effect reduces the mechanical properties of composite. When the length of graphene flake is greater than 3.35 nm, graphene sheet impedes the crack propagation and dislocates slip at sub-cracks. In addition, the distribution of graphene flakes angle changes the crack propagation path. Our findings also provide insights into ways to optimize mechanical properties of graphene/aluminum composites.

A multiscale modeling on fracture and strength of graphene platelets reinforced epoxy

A novel multiscale simulation framework was proposed to investigate the mechanical properties of single layer graphene platelets reinforced crosslinked epoxy. Crosslinking reactions in composites were simulated with the molecular dynamics (MD) method in the nanoscale, and the mechanical properties of bulk epoxy and interfaces between unfunctionalized graphene and epoxy were obtained. These mechanical properties from MD method were used in FEM simulation in the microscale. The crack propagation in composites was investigated with the finite element method (FEM) based phase-field method (PFM). The influence of several morphologic factors of graphene platelets on mechanical properties, including volume fractions, distributions of graphene orientations and waviness of graphene, was investigated. Results showed that the increasing graphene volume fraction would lead to the decrease of mechanical properties of composites due to the weak interfacial strength in the present model. Meanwhile, aligned graphene platelets improve all the mechanical properties simultaneously. In addition, the graphene platelets with higher curvatures provide improvement of the overall mechanical properties of the composites because they can block interfacial sliding. The present research suggested that the interfacial strength can be the bottleneck in the graphene reinforced epoxy.

Quasi-static crush modelling of carbon/epoxy composites with discontinuous Galerkin/anisotropic extrinsic cohesive law method

Carbon/epoxy composites demonstrate significant promising improvements of weight to performance in the automotive industry. However, the design of carbon/epoxy composite components for crashworthiness remains challenging and normally requires laborious and repeated experimental work. This study adopts a predictive crush model of carbon/epoxy composites, which can partially replace the experimental work. The discontinuous Galerkin (DG) method with extrinsic cohesive laws is employed to simulate the failure patterns in the composite structures. The application of DG distinguishes the fracture model from the conventional approach where preset cohesive elements are used on the location where cracks are expected. The mixed mode cohesive laws are used to simulate the delamination between each layer. To capture different crack propagations in different layups, the anisotropic cohesive law is used to simulate the intralaminar crack propagation in composites. To verify the adopted model, circular composite tube specimens with different layups have been simulated and compared with tests under quasi-static crush loadings. The comparisons of numerical results with experimental data show that the DG crush model can reproduce the experimental results with relatively high accuracy.

Sandwich-structured bamboo powder/glass fibre-reinforced epoxy hybrid composites – Mechanical performance in static and dynamic evaluations

A layer of woven E-glass fibre was embedded each at top and bottom layer of bamboo-filled epoxy, producing sandwich-structured hybrid composites. The incorporation of woven glass fibre was intended to slow down the crack propagation in composites. Different bamboo powder loading was applied to analyse its effect on the static and dynamic mechanical properties of composites. The composite with the lowest bamboo powder loading of 10% marked the highest tensile strength, where the strength decreased as the loading increased. Poor bamboo-epoxy adhesion, observed from the SEM, leads to more chances of pull out fibres when tensile load was applied. Opposite trend was observed in flexural strength, where the highest loading of 30% marked the highest value of flexural strength. The dynamic evaluation was carried out with respect to temperature, which ranged from 25°C to 150°C, and at a fixed frequency of 1 Hz. Effective stress transfer between the fibre and the matrix takes place in composites with 30% bamboo powder loading, shown by the lowest peak height of the Tanδ curves. The significant increase in the storage modulus values for the composites at low temperature compared to the rubbery plateau region at high temperature suggested the high utility of the composites at low temperature regardless of the effect of the percentage increment in bamboo powder loading. These results showed that the bamboo powder inclusion helps in bestowing stiffness to the composites with 30% as the optimum percentage in this dynamic mechanical evaluation. It can be suggested that the introduction of woven-typed fibre into short fibre composites in sandwich structure, as discussed in this study, can slow down the failure of composites, and thus notify users before the total failure.

A new multiscale phase field method to simulate failure in composites

In this paper, a new multiscale phase field method (MsPFM) has been proposed to simulate crack propagation in composites. The MsPFM inherits the merits of anisotropic phase field method and multiscale finite element method. It is known that phase field simulation requires dense meshing to represent a sharp crack, thus the main aim of the MsPFM is to achieve mesh refinement in the vicinity of diffused crack/cracks. The proposed method is also used to study the interaction of a pre-existing crack with weak or strong interfaces (between matrix-fibre or between laminates) in terms of crack arrest, crack deflection, crack coalescence, and multiple cracks initiation in composites. Various numerical experiments are performed to demonstrate the effectiveness of proposed MsPFM to simulate the aforementioned failure characteristics of the composites. The crack growth trajectory obtained by the MsPFM for few test cases is validated through standard extended finite element method.

A time-domain reflectometry method for automated measurement of crack propagation in composites during mode I DCB testing under cold, hot, and hot/wet conditions

This article describes an automated method for the measurement of crack initiation and propagation in composite materials during modeI double cantilever beam (DCB) testing under different environmental conditions. The method uses the time-domain reflectometry (TDR)-DCB system, which transmits a high-frequency pulse through a transmission line integrated within the composite test coupon and measures impedance discontinuities generated due to the presence of a crack. Using this system, real-time crack propagation in the specimen can be monitored, and the critical fracture toughness parameters ( GIC) can be calculated in a variety of environmental conditions. TDR-DCB test method was used for the measurement of GIC for dry and wet (water-saturated) DCB samples made from E-glass fiber/vinyl ester composites under dry conditions (room temperature (RT) at 94°C) and wet conditions (RT at 60°C). For all test conditions, TDR signals showed that crack initiation and propagation was the dominant mechanism in identifying impedance changes in the material. Changes in dielectric properties of the specimen due to the test conditions, whether from water uptake, temperature, or a combination of the two, did not significantly affect signal quality.

A two-dimensional in situ fatigue cohesive zone model for crack propagation in composites under cyclic loading

In this paper a two-dimensional fatigue cohesive zone model (CZM) for crack propagation in composites under cyclic loading has been formulated and validated through successful predictions of fatigue crack growth under pure and mixed mode conditions for several different composites. The proposed fatigue CZM assumes simple power-law functions for fatigue damage accumulation of which the damage parameters can be calibrated from simple fatigue tests under pure mode I and mode II conditions. The model relies solely on the in situ cohesive responses for fatigue damage rate calculation, enabling the differentiation of the local elemental load history from the global load history. An effective cycle jump strategy for high-cycle fatigue has also been proposed. It has been demonstrated that once calibrated, the fatigue CZM can predict the Paris laws for the pure modes. Furthermore, it can predict the Paris laws of any mixed-mode conditions without the need of additional empirical parameters. This is of significant practical importance because it leads to greatly reduced experimental needs for mixed mode crack propagation widely observed in composites under cyclic loads.

XFEM analysis of fiber bridging in mixed-mode crack propagation in composites

In this work, the extended finite element method (XFEM) is further generalized to study the fiber bridging phenomenon in fracture analysis of unidirectional composites. Treating composites as a biphase material, fibers effects on increasing fracture toughness are modeled by non-linear springs integrated in the XFEM formulation of displacement discontinuity. Combining the capability of XFEM in modeling arbitrary crack path with the traction-separation representation of the fracture process zone in the crack-bridged zone model, this formulation allows for simulation of fiber bridging in a crack propagation process without a priori knowledge of the crack path. Moreover, the criterion originally proposed for predicting the crack propagation path in orthotropic solids is modified to incorporate the effects of fiber orientation. Several numerical simulations of mode I and mixed-mode problems are provided, and the corresponding force–displacement curves are analyzed to address the accuracy and efficiency of the proposed method.

Crescimento subcritico de trinca e previsão de vida em fadiga do compósito cerâmico ZrO2-Al2O3

Cerâmicas apresentam excelente durabilidade química, resistência ao desgaste, biocompatibilidade, respeito ao meio ambiente e estética. Uma das propriedades mais importantes a ser considerada em implantes dentários totalmente cerâmicos é a fadiga cíclica, devido às solicitações mecânicas cíclicas as quais os implantes estão subjugados durante processos de mastigação, que pode induzir milhares de ciclos de tensão por dia em uma restauração, com isso exibir significativo crescimento subcrítico de trinca e assim poder diminuir a resistência de componentes cerâmicos, ao longo do tempo. Nesse trabalho, a previsão de vida em fadiga cíclica do compósito ZrO2-Al2O3 foi investigada. Mistura de pós contendo 80% de ZrO2 e 20% de Al2O3 foi compactada e sinterizada a 1600 °C. As amostras sinterizadas foram caracterizadas por difração de raios X e microscopia eletrônica de varredura. Dureza, tenacidade e resistência à fratura por flexão foram determinadas, e os resultados utilizados na determinação dos parâmetros de fadiga. Os testes de fadiga foram realizados em dispositivo de flexão em 4 pontos, sob freqüência de 25 Hz e razão de tensão de 0,1. Um aumento do nível de tensão levou à redução do tempo de vida sob fadiga. Baseado nos parâmetros determinados pelos ensaios mecânicos e de fadiga, e utilizando-se a estatística de Weibull, associada a modelos de determinação de crescimento subcrítico de falha, a velocidade de propagação de trincas nesse compósito é determinada e relacionada com os mecanismos de transformação martensítica e tensão residual entre as fases. Os componentes submetidos ao carregamento cíclico exibiram propagação subcrítica de trinca, em níveis de tensão significativamente menores do que o KIC. Apesar desta susceptibilidade ao crescimento subcrítico de trinca, cálculos com base nos parâmetros de fadiga e nas tensões aplicadas indicam que os componentes com estruturas do compósito ZrO2-Al2O3 podem exibir vidas maiores que 20 anos, se o diâmetro do componente estrutural é adequadamente projetado.

Dynamic crack propagation in matrix involving inclusions by a time-domain BEM

The dynamic crack propagation in composites with inclusions is analyzed by a time-domain boundary element method (BEM) in conjunction with the sub-region technique. The crack-growth direction and the crack-tip instantaneous velocity are determined by the maximum circumferential stress criterion. The instantaneous velocity is well smoothed by a bisection technique. New crack-tip elements of inconstant length are added to the active crack-tip to simulate the fast crack growth. Square root shape functions are adopted as to describe the proper asymptotic behavior in the vicinity of the crack-tips. The computation time for the dynamic fracture problems in composites with multiple inclusions is reduced by a numerical method. The influences of the inclusions on the shielding ratio, the crack growing path and the crack-tip instantaneous speed are well investigated.

Simulation of crack propagation in anisotropic structures using the boundary element shape sensitivities and optimisation techniques

Using the boundary element shape sensitivities of multi-region domains coupled with an optimisation algorithm and an automatic mesh generator, the crack kink angle and propagation path in anisotropic elastic solids are predicted. The maximum strain energy release rate criterion, best suited for the composite structures, has been employed. In contrast to the J-integral method, which would require the computation of stresses and strains at a series of internal points, here by direct differentiation of the structural response the strain energy release rates at the existing crack tip and new cracks for the period of crack growth are determined. The length of each kinked crack is treated as the shape design variable. The shape variable is then associated with the coordinates of a series of boundary nodes located on the new crack surface. Thus, the relevant velocity terms are applied together in the sensitivity analysis with respect to that variable to determine the energy release rate, which is the derivative of the total strain energy with respect to the crack length extension. Wherever possible the results are compared with the existing experimental, analytical and/or numerical results reported in the literature, in which good agreement is observed. It is shown that the present method is computationally more accurate and efficient. Two example problems with different anisotropic material properties are presented to validate the applications of this formulation. The results show that material anisotropy has a profound influence on the crack propagation of composites.

Investigations on synthesis of ZrB 2 and development of new composites with HfB 2 and TiSi 2

This paper presents the results of experimental investigations carried out on the synthesis of pure ZrB 2 by boron carbide reduction of ZrO 2 and densification with the addition of HfB 2 and TiSi 2. Process parameters and charge composition were optimized to obtain pure ZrB 2 powder. Monolithic ZrB 2 was hot pressed to full density and characterized. Effects of HfB 2 and TiSi 2 addition on densification and properties of ZrB 2 composites were studied. Four compositions namely monolithic ZrB 2, ZrB 2 + 10% TiSi 2, ZrB 2 + 10% TiSi 2 + 10% HfB 2 and ZrB 2 + 10% TiSi 2 + 20% HfB 2 were prepared by hot pressing. Near theoretical density (99.8%) was obtained in the case of monolithic ZrB 2 by hot pressing at 1850 °C and 35 MPa. Addition of 10 wt.% TiSi 2 resulted in an equally high density of 98.9% at a lower temperature (1650 °C) and pressure (20 MPa). Similar densities were obtained for ZrB 2 + HfB 2 mixtures also with TiSi 2 under similar conditions. The hardness of monolithic ZrB 2 was measured as 23.95 GPa which decreased to 19.45 GPa on addition of 10% TiSi 2. With the addition of 10% HfB 2 to this composition, the hardness increased to 23.08 GPa, close to that of monolithic ZrB 2. Increase of HfB 2 content to 20% did not change the hardness value. Fracture toughness of monolithic sample was measured as 3.31 MPa m 1/2, which increased to 6.36 MPa m 1/2 on addition of 10% TiSi 2. With 10% HfB 2 addition the value of K IC was measured as 6.44 MPa m 1/2, which further improved to 6.59 MPa m 1/2 with higher addition of HfB 2 (20%). Fracture surface of the dense bodies was examined by scanning electron microscope. Intergranular fracture was found to be a predominant mode in all the samples. Crack propagation in composites has shown considerable deflection indicating high fracture toughness. An oxidation study of ZrB 2 composites was carried out at 900 °C in air for 64 h. Specific weight gain vs time plot was obtained and the oxidized surface was examined by XRD and SEM. ZrB 2 composites have shown a much better resistance to oxidation as compared to monolithic ZrB 2. A protective glassy layer was seen on the oxidized surfaces of the composites.

평직 CFRP 복합재료의 섬유 배열각도별 피로 균열 성장 평가

많은 연구자들이 평직 탄소섬유강화플라스틱에 대해서 연구해왔지만 피로 균열 진전에 관한 연구는 아직도 미지한 상태이다. 그리고 하중과 섬유 배열 각도에 따라 균열 진전 양상이 다름을 알 수 있다. 본 연구에서는 서로 다른 두 개의 섬유 배열각도(0°, 45°)에서 평직 탄소섬유강화플라스틱의 피로 균열 진전에 대해 연구하였다. 평직 탄소섬유강화플라스틱의 피로 균열 진전 테스를 하중비 0.1에 10㎐로 수행하였다. 그 시험 결과로써, 피로 균열 진전 속도(da/dN)와 에너지해방률(ΔG)과의 그래프를 도출하였고, 섬유 배열 각도에 따른 균열 진전 양상을 0°의 경우에는 Mode I를 적용하였고, 45°의 경우에는 Mixed Mode를 적용하였다.

Investigations on synthesis of HfB2 and development of a new composite with TiSi2

Abstract This paper presents the results of investigation carried out on synthesis and densification of monolithic HfB 2 and the effect of TiSi 2 as sinter additive. Pure phase HfB 2 was prepared by boron carbide reduction of HfO 2 and hot pressed to full density with the addition of TiSi 2 . Isothermal oxidation study of this composite was carried out at 850 °C up to 64 h. Formation of HfB 2 was seen at 1200 °C but pure HfB 2 was formed at a much higher temperature of 1875 °C in vacuum. Hot pressing of HfB 2 at 1850 °C and 35 MPa pressure gave a compact of 80% TD. Addition of TiSi 2 helped in achieving a much higher density at a lower temperature of 1600 °C and a pressure of 20 MPa. A fully dense composite of HfB 2 and TiSi 2 was obtained with 15% TiSi 2 . Hardness and fracture toughness of this composite were 27.4 ± 1.9 GPa and 6.6 ± 0.2 MPa m 1/2 , respectively. Considerable deflection was observed in the crack propagation in composites. Oxidation studies indicated the formation of HfO 2 , SiO 2 , TiO 2 and HfSiO 4 with some glassy phase and the composite with 15% TiSi 2 was seen to be completely covered with a protective glassy layer.

A Time-domain Reflectometry Method for Automated Measurement of Crack Propagation in Composites during Mode I DCB Testing

This article describes a new technique for automated measurement of crack initiation, growth, and propagation in composite materials during mode I double cantilever beam (DCB) testing. The proposed method uses time-domain reflectometry (TDR) to detect changes in geometry and electromagnetic properties (dielectric or magnetic) along a transmission line that can be embedded in or bonded to the surface of the specimen. Two types of transmission line TDR sensors are evaluated (IM7 carbon fiber and ARACON) during DCB tests. A P-SPICE transmission-line simulation model is used to verify the baseline signal response for the DCB sensor and the sensitivity for crack detection, with good agreement. Comparison with standard visual methods in DCB testing showed excellent correlation in crack location, crack propagation (LC), and the interlaminar fracture toughness (GIC) values. The TDR sensor design and model-based parametric studies are carried out to determine optimal sensor geometry and configuration. The results demonstrate that the TDR-based method can measure crack propagation parameters at high resolution and accuracy, in an automated manner using low-cost sensors.

A Micromechanical Model for the Fiber Bridging of Macro-Cracks in Composite Plates

Recent experimental studies on the propagation of transverse cracks in composites have shown that fiber bridging is frequently present, and can be considered as the cause of increased toughness. This paper presents a model that is capable of quantifying this effect and explaining the decrease in the crack growth rate in either a monotonic or a cyclic load profile. Both Modes I and II are considered. The model is based on the elastic loading of a fiber located on the macro-crack face close to the tip and under dominantly plane strain conditions. Two fundamental cases of fiber bridging configurations are distinguished, namely when the fiber-matrix interface is intact and when the fiber-matrix interface has partially failed. Following the single fiber analysis, the model is extended to the case of multiple fibers bridging the faces of the macro-crack. The analysis is for a generally anisotropic material and the fiber lines are at arbitrary angles. Results are presented for the case of an orthotropic material with unidirectional fibers perpendicular to the crack faces. Specifically, the reduction in the stress intensity factor (relative to the nominal value) is investigated for the glass fibers in a glass/epoxy composite system. The effects of fiber debonding and pullout with friction as well as fiber breaking are accounted for in the analysis, and results with respect to a parameter representing the fiber-matrix interface friction are presented. Results are also presented regarding the partial or full fracture of the fiber bridging zone. The model can also be used to analyze the phenomenon of fiber nesting, which is similar to fiber bridging, and occurs with growing delaminations.

A micromechanical analysis of fiber crack propagation in composite materials due to transverse tensile loads

The fiber crack propagation in composites due to transverse tensile loads is studied using a micromechanical model and Linear Elastic Fracture Mechanics. To approach the problem, a three domain cylindrical model is introduced to simulate the fiber cracking. The model problem is then solved by the dislocation and singular integral equation techniques. The stress intensity factors of the fiber crack are calculated for various situations. It is found that fiber anisotropy has hardly any effect on the fiber crack propagation; “reverse composites” (composites in which fiber is less stiff than the matrix, such as Nicalon/SiC ceramic composite) virtually eliminate fiber crack propagation.