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A New Failure Criterion for Nonlinear Composite Materials
Abstract
A new failure criterion based on the total strain energy density approach is introduced for an equivalent linear elastic material. The total strain energy is composed of the elastic strain energy and the plastic strain energy. The proposed criterion can be used to predict failure of fibrous composite materials subject to uniaxial, biaxial, or multiaxial stress state. The proposed criterion takes into account the different behavior of bimodular composites in tension and compression. Given the stress-strain diagrams in the principal material directions, the failure of the material at any fiber orientation angle under an imposed stress state can be predicted. The results are compared with the corresponding available experimental data. In addition, the predicted failure stresses are compared with those obtained using available failure criteria.
... Equations were formulated using the secant model (non-linear model) mentioned in Abu-Farsakh [3]. A reasonable approach to estimate the crack-density ratios for any fiber-orientation loaded up to failure was introduced based on total strain energy approach of an equivalent linear elastic system as mentioned in Abu-Farsakh et al. [8]. Results of damage-factor and crack-density ratios were compared with experimental data for Boron-Epoxy, Graphite-Epoxy, [0/90] s and [±45] s metal-matrix laminates. ...
... (12) and (13). In the case of shear damage-factor ðF 12 Þ, it is expressed in Eq. (8), which can be considered as pure shear case, since there is no local shearextension coupling in an orthotropic material (i.e. Q 16 ¼ 0). ...
In the present paper, a new macro-mechanical model for tracing damage-evolution in composite materials is proposed. The present model represents a new extension and a new approach to a previous model (Ghazi-Farid model), which can be applied for a general state of stress. The model is verified by comparing its results with those corresponding to Ghazi-Farid model for different composite materials and it seems to give very close correlations. The proposed model can be applied to both elastic and inelastic materials as well as generally orthotropic fibrous composite nonlinear-materials.
It was concluded that shear damage is always higher than any other damage types due to the high nonlinear-material shear behavior, which causes high plastic strain-energy density. Damage in a composite lamina causes a reduction in its stiffness. Therefore, a new quantum-damage variable is proposed: '' tangential quantum-damage variable '' to quantify the overall-damage in a composite lamina. Percentage reduction of composite stiffness depends mainly on the amount of resulting damage irrespective of fiber-orientation angle. So, a new trend for the behavior of composite materials is introduced which states that the relation between damage-evolution and corresponding stiffness-reduction follows a certain behavior and it is independent of fiber-orientation. Each composite material has a unique trend which is verified using three different composite materials; Boron-Epoxy-Narmco 5505, Graphite-Epoxy 4617/Modmore-II, and Carbon-Epoxy AS4/3501–6.
A new damage-term is introduced as: "directional damage-variable", to simplify tracing damage in the case of a uniaxial off-axis loading. The new damage-variable was used to predict damage-evolution in the three laminas made of the indicated composite materials. It is concluded that, Graphite-Epoxy 4617/Modmore-II has the minimum damage at all stress levels and Boron-Epoxy-Narmco 5505 has the maximum damage. The importance of the new damage-term makes it easier to predict damage and make preferences between several composite materials subjected to uniaxial off-axis loading.
... A very similar approach with degradation factors assigned to different failure modes was developed by Camanho and Matthews [22] and implemented in the 3D finite element framework in ABAQUS. The cited examples are just two of the many examples of ISM in earlier literature [23][24][25][26][27][28][29][30][31][32][33]. A comparison of ISM-based models against the experimental results confirmed that the predicted failure occurs at a substantially lower load than the experimentally determined one, underestimating the laminate strength and neglecting the fact that the damage is indeed localized and a failed lamina still has a residual load-carrying capability. ...
This paper presents the original incorporation of the smeared crack band (SCB) damage model within the full layerwise theory (FLWT) framework, to contribute to the increase of the computational efficiency of the progressive failure analysis of open-hole laminar composites loaded in tension, simultaneously preserving the accuracy of the conventional 3D finite element models. The developed FLWT-SCB prediction model was implemented into an original FLWTFEM framework allowing for the accurate 3D stress fields and excellent visualization capacity. The response of damaged lamina, in both fiber and matrix directions, was described by distinct bilinear strain-softening curves. The mesh dependency problem was minimized by scaling the fracture energy using a characteristic element length.
Both the failure initiation and failure modes were determined using the Hashin failure criterion. To verify the model effectiveness, the obtained results were compared against the experimental and benchmark data from the literature. Mesh dependency was analysed to confirm the benefits of suggested model, as well. The obtained results agreed with the experimental ones and those from the literature.
According to the numerical results, FLWT-SCB allows for coarser meshes than those used in the standard finite element models, leading to improved computational efficiency without compromising the accuracy. The model also demonstrated the weak dependency between the size of the structure and the mesh. The advantages of using FLWT-SCB damage model in achieving significant improvements in computational efficiency are highlighted.
... Método del Ply Discount [83,84] Modelo Matzenmiller [85] Modelo Ladevèze [86][87][88][89][90] Modelo Linde [91] Modelo Barbero [92,93] Modelo Williams [94] Modelo Chang-Chang [95] En este sentido, muchos de los trabajos encontrados en bibliografía acerca de los modelos para la simulación de estructuras de impacto de materiales compuestos se han basado en diferentes criterios de daño y degradación del material. Feraboli et al. [63] citados, todos consiguieron buenas correlaciones con los resultados experimentales por lo que no hay argumentos para poder decir cuál es el modelo más preciso y fiable. ...
La preocupación medio-ambiental va en aumento en diversos sectores de la industria, en especial en la industria automovilística. Por un lado se está trabajando en la reducción de emisiones de CO2 mediante el desarrollo de motores más eficientes. Por otra parte, en el desarrollo de vehículos eléctricos que contaminen el medio ambiente en menor medida. Con este mismo fin, todos los grandes fabricantes de automóviles han adoptado la estrategia de intentar reducir el peso de los vehículos. En el caso particular de los vehículos eléctricos, una de las mayores limitaciones es la falta de autonomía, que en parte es debido al elevado peso de las baterías. Sin embargo, la seguridad de los pasajeros no debe verse afectada debido a la reducción del peso del vehículo. Es por ello por lo que en las últimas décadas se está investigando sobre el uso de materiales más ligeros con mejores propiedades para reducir el peso y aumentar la seguridad de los pasajeros. Entre estos materiales se encuentran los materiales compuestos de matriz polimérica, en los cuales se centra la presente investigación.
Las actuales estructuras de impacto de los vehículos son de materiales metálicos como el acero y el aluminio. En esta tesis se analizan y se desarrollan estructuras de impacto o crash box de materiales compuestos reforzados con fibra contínua de manera que se consigue reducir considerablemente el peso del componente y aumentar la capacidad de absorber energía en caso de un accidente.
Por un lado se realiza un análisis de tipo de refuerzo y la influencia de la secuencia del laminado en la capacidad de absorción de energía de la estructura. Se trabaja con fibras de vidrio unidireccionales, bidireccionales y fibras de basalto bidireccionales para intentar maximizar la energía absorbida y elegir el material de refuerzo más adecuado.
Otro de los aspectos trabajados es el efecto que tiene el porcentaje de volumen de fibra en el comportamiento a colapso de las estructuras. Se ha podido ver que existe un porcentaje óptimo en el cual la estructura es capaz de absorber mayores cantidades de energía.
La mayoría del trabajo se ha centrado en analizar las propiedades a colapso de un perfil unitario semi-hexagonal cambiando diferentes parámetros. Sin embargo, la idea es utilizar la combinación de estos perfiles siguiendo el concepto de nido de abeja para poder diseñar estructuras de impacto modulares que se puedan adaptar a las diferentes especificaciones que tienen los vehículos distintos. Para ello, también se ha analizado el efecto que tienen las diferentes geometrías que se obtienen después de combinar estos perfiles en términos de absorción de energía. Se ha podido comprobar que aumentando el nivel de corrugación se consiguen disipar mayores cantidades de energía.
Debido a los costes que suponen los ensayos experimentales, hoy en día la mayor parte del desarrollo se efectúa mediante simulaciones numéricas. Es por ello por lo que se ha trabajado en el desarrollo de una herramienta numérica capaz de predecir con exactitud el comportamiento a colapso analizado experimentalmente. Una vez que el modelo ha sido validado, se ha realizado una optimización de la geometría de la sección del perfil semi-hexagonal mediante el método de los elementos finitos.
Una de las mayores limitaciones de estos materiales es la falta de productividad de los procesos de fabricación. Por ello, se han querido analizar las propiedades a colapso del material fabricado por un nuevo proceso que está en fase de desarrollo en Mondragon Unibertsitatea. Este proceso está basado en la pultrusión tradicional pero con un curado alternativo de ultravioleta fuera del molde, el cual es capaz de fabricar de manera automatzada, en continuo y en cadecias suficientemente altas para hacer frente a los requisitos de productividad exigidas por la industria de la automoción. De este modo, se han analizado y comparado las propiedades del material del nuevo proceso con el mismo material fabricado por los procesos tradicionales de infusión con bolsa de vacío y el método de contacto a mano. Los resultados demuestran que las propiedades están al mismo nivel o que incluso son mejores.
Por último, se han fabricado estructuras reales de impacto con los perfiles fabricados por el nuevo proceso de pultrusión y se han integrado en el chasis de un prototipo de un vehículo eléctrico para realizar un crash test en condiciones reales de impacto. Los resultados muestran la validez de este material y de estas estructuras para esta aplicación. Las cantidades de energías absorbidas por unidad de peso son significativamente mayores que las estructuras metálicas que se emplean actualmente.
Description
This comprehensive new ASTM publication examines state-of-the-art multiaxial testing techniques and methods for characterizing the fatigue and deformation behaviors of engineering materials. 25 analytical, peer-reviewed papers, written by experts from academia, industry, and government, are divided into the following sections:
Multiaxial Strength of Materials--addresses multiaxial strength, stress, and failure modes of materials.
Multiaxial Deformation of Materials--investigates constitutive relationships and deformation behavior of materials under multiaxial loading conditions.
Fatigue Life Prediction under Generic Multiaxial Loads--examines the challenging task of estimating fatigue life under general multiaxial loads.
Fatigue Life Prediction under Specific Multiaxial Loads--describes biaxial and multiaxial fatigue and life estimation under combinations of cyclic loading conditions, such as axial tension/compression, bending, and torsion.
Multiaxial Fatigue Life and Crack Growth Estimation--covers crack growth monitoring under cyclic mulitaxial loading conditions and determination of fatigue life.
Multiaxial Experimental Techniques--explores state-of-the-art experimental methods to generate mulitaxial deformation and fatigue data to develop and verify both constitutive models used to describe the flow behavior of materials and fatigue life estimation models.
In the present paper, a novel combined damage-based failure criterion is being proposed for predicting failure stresses in unidirectional fibrous composite laminas or laminates having a nonlinear material behavior. The present model incorporates the effect of a quantitative damage factor on the final stresses at failure. This is achieved through a new term called the quantitative directional damage-index (QDD-I) which assesses the contribution and effectiveness of damage in each principal material direction on the present failure criterion. From the QDD-I, it is proved that the principal material-direction with a linear or nonlinear stress-strain behavior showed a quantitative damage response on the proposed failure criterion. In a composite lamina, the contribution of fiber-damage and matrix transverse-damage are proved to have minor effects on the failure criterion, while in-plane shear-damage has the major effect. In order to verify the suitability and applicability of the criterion, results are tested using various theoretical and experimental data available from the literature. Furthermore, the model is compared with other failure criteria under both uniaxial and biaxial loading cases from a worldwide comparison, which showed reasonable accuracy and good agreement. Three types of fibrous composite materials are used; Graphite/Epoxy 4617/Modmore-II, Carbon/Epoxy AS4/3501-6, and Boron/Epoxy Narmco 5505.
p>This thesis is concerned with the damage assessment of composite structures under static loading case with geometric non-linearity. Both the finite element method and the boundary element method are studied for this purpose. A finite element based computational damage model is developed for predicting the nonlinear response, first-ply failure and ultimate collapse strength of uni-directional laminated composite plates. The damage model is implemened into the finite element program ABAQUS. It contains theory of large deformation and large strain. The model is then extended to laminated composite structures with woven fabric piles. A simplified model is developed for prediction of stiffness properties of woven fabric composite plates. In both the cases numerical results are compared against test values. It is demonstrated that excellent correlation with experimental results can be achieved. In the context of the boundary element method (BEM) the present research focuses on stress analysis of 2-D orthotropic structures. A novel technique is proposed for accurately computing the singular integrals in the 2-D boundary element method.</p
The purpose of this paper is to investigate the effect of nonlinear material behavior on four layered, symmetric; angle-ply laminated composite plate with various fiber-orientation angles; (θ = 30°, 45° and 60°). The plate has a central square-hole and subjected to out-of-plane uniformly distributed load. The effect of Stress Concentration Factor (SCF) resulting from redistribution of in-plane stresses (σx, σy, τxy) around the hole was taken into consideration. Square plates with simply supported boundary conditions were considered in the present study. The analysis was carried out utilizing the ANSYS-computer program. The presence of a central hole was found to concentrate the maximum stresses at the corners of the hole. The nonlinear material behavior was found to redistribute the in-plane stresses more reasonably and smoothly around the hole-perimeter and hence resulting in smaller SCF-values.
This paper reviews important published literature on composite material failures. the reviewed publications were mainly taken from journals and conference proceedings. The period covered is from 1986-1996. This literature review concludes that the problem of composite material failures is quite serious and requires a systematic effort. Eventhough, researchers in the area have developed various useful mathematical models and theories, the general approaches are sill missing in their strength.
The main objective of this study is to investigate the crack propagation in laminated plates made of fibrous composite materials. A rectangular type finite element having an in-plane displacement field with eight degrees of freedom, is used. A finite element computer program is developed which incorporates the Tsai-Hill failure criterion. Failure stresses are compared with the stresses obtained using AF-AJ failure criterion and the related experimental results. Two composite materials are considered; glass-epoxy, and boron-epoxy. The laminates are of two types; three-layered angle-ply with stacking sequence [0°/-0°/0°] and three layered cross-ply with stacking sequence [0°/90°/0°]. The results are obtained for laminates with different elastic properties, thicknesses, and orientation angles. A comparison between the results of finite element technique and available experimental data from literature is carried out.
The failure analysis composites remains a topic still open to discussion. Indeed, despite the of progress of the research, none of the available failure theories is still able to accurately predict the failure at all levels of analysis, for all the loading and boundary conditions, failure modes, lay-ups, relative thickness and constituent materials. The criteria suited for specific classes of applications and the range of variation of their predictions with the variation of the design parameters are still unknown. In this paper, a bibliographical review that collects the most recent failure theories of composites with continuous reinforcement fibers, the recent improvements to existing theories and their applications is presented, together with a numerical assessment of their accuracy. Various criteria are compared considering various lay-ups, constituent materials, loading configurations, relative thickness and boundary conditions for which experimental results are available for comparisons. The analysis is carried out by a recently developed mixed, solid element whose nodal d.o.f, are the three displacement and the three interlaminar stress components, because it provides more accurate predictions with respect to displacement-based elements with a reasonably fine in-plane and through-the-thickness discretization. In the regions where the failure analysis is carried out, the fiber and matrix phase-averaged stresses are is used. It appears that the criteria can be accurate in a particular and inaccurate in other cases. In certain cases, the generalized failure criteria can be as accurate like the physically based failure criteria; the opposite can occur in other cases. However a group of criteria was identified that could be used for reciprocal checks.
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