Biaxial Failure Envelope Research Articles

A machine learning-based prediction of biaxial failure envelope of a short fiber-reinforced polymer composite

A machine learning-based prediction of biaxial failure envelope of a short fiber-reinforced polymer composite

A novel three-dimensional modified Griffith failure criterion for concrete

This study proposes a three-dimensional failure criterion based on the Griffith criterion, which accounts for the nonlinear influences of hydrostatic pressure and Lode angle on the failure strength of concrete. Two approaches are utilized in the proposed criterion to describe the Lode-dependence, one is to use the biaxial compressive envelopes to derive each meridian directly, and the other is to employ a scaling function between the compressive and tensile meridians. Besides, the proposed criterion can be expressed by the principal stresses in the form of f(σ1, σ2, σ3) = 0 as well as by the stress invariants in the form of J2 = f(P, θ). To comprehensively validate the proposed criterion, it collects 37 groups of tests with nearly 1000 test data conducted on concrete under biaxial and triaxial stress states. It demonstrates that predictions of the proposed criterion, including biaxial failure envelope, compressive meridian, tensile meridian, deviatoric section, and multiaxial strength, are close to the corresponding experimental observations. The proposed criterion requires four parameters, three of which have clear physical meaning, namely the tensile, compressive, and equal-biaxial compressive strength (ft, fc, and fbc), and the rest parameter n can be determined by the triaxial compressive strength. Aimed at elaborating the physical meaning of n, it interprets the proposed criterion as a combination of the original Griffith, Mohr-Coulomb, and Rankine criteria. In addition, a simple modification based on the proposed criterion is also suggested to describe the transformation from shear failure to ductile failure of concrete with the increase of pressure. Compared with the existing Ottosen and Willam-Warnke criteria, the proposed criterion is simple in determining parameters, convenient in the application, and diverse in describing the Lode-dependence.

Investigation of Biaxial Properties of CFRP with the Novel-Designed Cruciform Specimens.

The biaxial loading properties of carbon-fiber-reinforced polymer (CFRP) are critical for evaluating the performance of composite structures under the complex stress state. There are currently no standardized specimens for the CFRP biaxial experiments. This work developed a new design criterion for the cruciform specimen coupled with the Hashin criterion. The finite element analysis was conducted to investigate the effect of geometric parameters on the stress distribution in the test area. The embedded continuous laying method (ECLM) was proposed to achieve the thinning of the center of the test region without introducing defects. The manufacturing quality of the cruciform specimens was verified by the ultrasonic C-scanning test. The biaxial test platform consisting of the biaxial loading system, digital image correlation (DIC) system, strain electrical measurement system, and acoustic emission detection system was constructed. The biaxial tensile tests under different biaxial loading ratios were conducted. The results showed that the biaxial failure efficiently occurred in the test area of the cruciform specimens designed and manufactured in this paper. The failure modes and morphology were characterized using macro/microscopic experimental techniques. The biaxial failure envelope was obtained. The results can be used to guide the design of composite structures under biaxial stress.

Modelo mecánico para la resistencia a cortante de vigas de hormigón armado reforzado con fibras, sin armadura de cortante

Es bien conocido que la adicion de fibras de acero mejora la resistencia a cortante y ductilidad de las vigas de hormigón armado. Sin embargo, a pesar de los numerosos estudios existentes, las normativas y recomendaciones de diseño se basan en modelos empiricos que presentan mucha dispersion cuando se comparan sus resultados con los de ensayos. Ello es fundamentalmente debido a las incertidumbres asociadas al comportamiento del hormigon con fibras debido a la orientcion, ditsribucion y adherencia de las fibras con el hormigón, entre otros factores. Por ello, la caracterizacion del hormigon con fibras se asocia a parametros de ensayos a flexión, a pesar de que las tensiones post-fisuracion obtenidas no son directamente utilizables como tensiones transmitidas a través de la fisura crítica. Por otra parte, la mayoría de los ensayos existentes no disponen de estos parametros experimentales. Por ello se detecta la necesidad de disponer de modelos mecánicos (no empíricos) que partan de los parametros usados en el dise´ño del hormigón con fibras (tipo, geometria y cuantia de las fibras, etc)
 A tal fin, en esta ponencia se presenta un modelo mecánico de resistencia a cortante, obtenido extendiendo el modelo "Multi-Action Shear Model" previamente desarrollado en las universidades UPC y UIB, incorporando los efectos de las fibras , tanto a puenteando la fisura crítica como aumentando la resistencia de la cabeza de compresión. Por otra parte, la tension residual a través de la fisura crítica se obtiene mediante una formulación desarrollada en funcion de las caracteristicas de las fibras (geometria, forma, caracteristicas de adherencia, volumen de fibras) y de la resistencia a traccion del hormigón. Los resultados del modelo, comparados con los de 488 tensayos a cortante incluidos en una reciente base de datos de vigas de hormigon con fibras, sin cercos, han mostrado una dispersión menor que cualquiera de los modelos existentes hasta el momento, siendo por tanto muy adecuado (por sencillez y precision) para el diseño de estas estructuras.

Parametric failure manifolds for laminated composites

The failure modes of laminated composites are complex and varied, being strongly dependant on layup and loading conditions. In this paper, a novel representation of damage initiation in laminated composites on the structural scale is presented. The proposed approach combines the knowledge of the composite design space with detailed meso-scale models to generate a complete representation of damage initiation under all possible combinations of bi-axial loading and for any layup in the composite design space. The 2D bi-axial failure envelopes are then combined with the knowledge of the composite’s physical behaviour and the surface compatibility conditions to generate 3D failure manifolds using Gauss surface equations. The resulting system is a complete parametric description of damage initiation in laminated composite for any layup under general loading conditions. The proposed manifolds are accurate and computationally efficient tools for structural (macro) scale analyses, design and optimisation.

On the prediction of the bi-axial failure envelope of a UD CFRP composite lamina using computational micromechanics: Effect of microscale parameters on macroscale stress–strain behavior

A computational micromechanics based Finite Element (FE) analysis methodology is presented to predict the bi-axial failure envelope of a unidirectional (UD) carbon-epoxy composite ply. In order to estimate the effect of various microscale parameters that are influencing the macroscopic stress–strain behavior, under individual load cases, detailed numerical studies are conducted using a 3D RVE (Representative Volume Element) model. The constituent epoxy matrix plastic deformation in the RVE is captured using the linear Drucker-Prager plasticity model.The effect of the fiber–matrix interface damage, followed by frictional sliding of the constituent materials on the computed interface tractions is captured using the cohesive zone damage model combined with the Coulomb friction law, which is implemented into Abaqus using VUMAT. From the detailed FE analysis of the RVE under individual load cases, it is observed that the predicted macroscopic stress–strain behavior is sensitive to the fiber–matrix interface properties as well as the in-situ epoxy stress–strain behavior. Hence, using a coupled experimental-computational micromechanics approach the interface and the in-situ epoxy material properties are calibrated and validated. Using the calibrated interface and in-situ epoxy material properties, the bi-axial (transverse tension/transverse compression – in-plane shear) failure envelope of a UD composite ply is estimated. Comparing the predicted damage profiles and the failure envelope with the experimental results leads to good agreement and validates the proposed numerical methodology.

Numerical study of the biaxial compressive strength of high strength concrete based on a yield design micromechanical approach

SummaryThis paper presents a numerical study of high strength concrete microstructure effects on its uniaxial and biaxial compressive strengths. Concrete is first represented as a set of angular aggregates interacting within a cement paste matrix. Then, a yield design kinematic approach is conducted at the mesoscopic scale in order to determine the concrete compressive strength for a given loading path. The proposed model, having a low computational cost, is able to capture the main microstructure effects already observed in literature on concrete uniaxial compressive strength, in particular, the aggregates volume fraction and maximal size effects. Finally, the proposed model also predicts the biaxial failure envelope of high strength concrete and confirms some experimental trends observed in literature.

Behaviour of Plain Concrete and Steel Fibre Reinforced Concrete (SFRC) under Biaxial Stresses- A Review

This paper provides general overview on the development of biaxial behaviour of plain concrete and steel fibre reinforced concrete (SFRC) under various types of loading conditions, namely, biaxial compression, biaxial tension-compression and biaxial tension. The biaxial behaviour including failure envelope, ultimate strength, failure mode and stress-strain relationship of plain concrete and SFRC are reported and compared. The effects of fibre volumetric fraction of fibre in SFRC on the biaxial behaviour are also discussed. Overall, previous researchers show that the inclusion of fibre enhance the biaxial behaviour of the concrete, agreed with the biaxial failure envelope developed. However, further experimental works and investigation is required to determine the relationship between the biaxial behaviour of SFRC and its fracture toughness, in addition to prove the analytical prediction of biaxial behaviour of SFRC especially in biaxial tension-compression and biaxial tension.

First-ply failure prediction of glass/epoxy composite pipes using an artificial neural network model

An artificial neural network (ANN) model was developed to predict the onset of failure of glass fibre reinforced epoxy composite pipes under multiaxial loadings. The developed ANN model used input/output experimental data for training and classification. The model was expected to predict the first-ply failure within the pipe composite laminates under various biaxial stress ratios. The biaxial failure envelope was then illustrated by plotting the failure points in a graph showing axial stress versus hoop stress. During the model’s construction, the best entire mean classification accuracy rate achieved was within the range of 95%–99.66%. Validation with experimental findings indicated good agreement with the model’s predictions, with less than 30% variation. The results suggest that the ANN model can be extended to yield useful predictions of the onset of failure in composite pipes under a range of stress conditions. This can be utilised as an internal means for pipe rating prior to the required standard ASTM qualification process.

Nonlinear finite element modelling of high bond thin-layer mortared concrete masonry

This paper presents a finite element technique for high bond strength, thin-layer mortared-masonry through material and interface modelling to simulate the behaviour of masonry. Constituent material blocks and mortar and their interfaces, affect the behaviour of masonry significantly. A finite element technique to represent these constituent materials and their interfaces is presented in this paper, and is shown that the technique predicts the behaviour of thin-layer mortared-concrete-masonry appropriately, and provides good insight into the failure characteristics of masonry under different loading conditions. The properties of the unit and the mortar are modelled using the principles of concrete damage plasticity, and the characteristics of the interfaces are modelled using the traction separation damage principles. The finite element model is applied to masonry subject to shear, flexure, compression and combined shear-compression. The numerical results are validated with experimental test results; good agreement is found. The predicted biaxial failure envelope of the high bond strength thin-layer mortared-concrete-masonry is presented.

Working temperature variation effect on the failure envelope of continuous fiber-reinforced composites

In this study, a micromechanical method is presented to study working temperature variation effect on biaxial failure envelopes of continuous fiber-reinforced composites with imperfect interfacial bonding. Generalized viscoplastic potential structure model is used to describe nonlinear response of composites. The interfacial debonding model is incorporated into the micromechanical model for describing the interfacial damage evolution. Theoretical results show good consistency with experimental data. On this basis, a series of numerical examples are performed to investigate working temperature variation and interfacial debonding effect on macroscopic tensile response and biaxial loading failure, respectively. The results indicate that the stress–strain responses and failure strength are closely dependent on working temperature. And biaxial compressive loadings in axial-transverse and transverse–transverse, as well as axial tensile and compressive loadings, do not generate interfacial debonding.

Biaxial Specimen Design for Structures Subjected to Multi-Axial Loads

The ability to optimise structures requires a thorough understanding of the loadsthat they are subjected to. Many composite materials in use today are subjectedto complex loading patterns that exhibit multi-axial stress and straincharacteristics. It is not sufficient to model material data for thesestructures based purely on uniaxial information. Unlike the well understoodfailure criteria of materials when subjected to uniaxial loads; biaxial failureenvelope has not been defined with sufficient experimental data particularly inthe tensile load region. There has not been any standard specimen geometrydefined for biaxial testing. Also the effective area when subjected to loadingis not as easily known as is the case in uniaxial loading. Thus biaxial testspose a greater level of difficulty when establishing failure stresses for thematerial. The authors look at establishing a specimen geometry that is suitablefor use preliminarily in isotropic materials. These specimen geometries must beable to ensure failure at the anticipated gauge region. Investigation into thefirst quadrant of the biaxial failure envelope under tension-tension is lookedat with insight into matrix failure as the dominant mode of failure. Numerical resultsand preliminary experimental results for FM355 epoxy specimens are presentedand compared with existing failure models such as Von Mises criterion and thefailure criterion used in Strain Invariant Failure Theory.

Numerical modelling of woven composites: Biaxial loading

A numerical model of a 2×2 twill reduced Unit Cell was developed. The elasto-plastic response of the matrix and possibility of tow/matrix debonding were modelled. The material is assumed to fail after failure of the tows is detected using maximum-stress and/or physically-based failure criteria. The support provided by the adjacent layers was accounted for considering two idealised cases of support: In-Phase (IP) and Out-of-Phase (OP); which bound the support a given layer can have within a laminate.The difference in results between IP and OP provides an estimate of the expected variation in strength due to the support. Additionally, the failure strength predictions obtained averaging the IP and OP results agree well with experimental results for uniaxial tension/compression.The in-plane biaxial failure envelope was also determined. A strong correlation was found between the loading ratio and the effect of support provided by the adjacent layers on the failure strength.

Prediction of biaxial failure envelopes for composite laminates based on Generalized Method of Cells

Macro/micromulti-scale analysis based on the efficient implementation of the Generalized Method of Cells coupled with classical lamination theory was conducted to predict failure of composite laminates, applying failure criteria at the constituent level, including fiber, matrix and interface. Representative unit cells with different fiber arrays were constructed in order to study the effect of reinforcement architecture and failure criteria on strength prediction of composite laminates. In order to compare the micromechanics model’s accuracy with commonly-used macroscopic failure theories, the experimental data obtained from the Worldwide Failure Exercise (WWFE) was utilized, and a quantitative assessment method for failure envelopes was developed to evaluate the model’s performance. Finally, the types of representative unit cell architectures and failure theories which are applicable for different layups were identified. The results indicate that the predictive performance of the employed micromechanics-based model is closest to the three leading macroscopic failure criteria of Puck, Cuntze and Tsai–Wu, and better than all other microscopic-based failure criteria (Chamis, Mayes, Huang), employed in the WWFE study.

Ab initio elastic properties and tensile strength of crystalline hydroxyapatite

We report elastic constant calculation and a “theoretical” tensile experiment on stoichiometric hydroxyapatite (HAP) crystal using an ab initio technique. These results compare favorably with a variety of measured data. Theoretical tensile experiments are performed on the orthorhombic cell of HAP for both uniaxial and biaxial loading. The results show considerable anisotropy in the stress–strain behavior. It is shown that the failure behavior of the perfect HAP crystal is brittle for tension along the z-axis with a maximum stress of 9.6 GPa at 10% strain. Biaxial failure envelopes from six “theoretical” loading tests show a highly anisotropic pattern. Structural analysis of the crystal under various stages of tensile strain reveals that the deformation behavior manifests itself mainly in the rotation of the PO 4 tetrahedron with concomitant movements of both the columnar and axial Ca ions. These results are discussed in the context of mechanical properties of bioceramic composites relevant to mineralized tissues.

Comparison of MCT Failure Prediction Techniques and Experimental Verification for Biaxially Loaded Glass Fabric-reinforced Composite Laminates

The inability to accurately predict the onset of failure in modern fabric-reinforced composite materials has hindered the implementation of these materials into the mainstream applications. Excessive qualification and structural testing must be performed on composite members as a result of uncertainty in the performance of the material, resulting in significantly higher expenses associated with these materials. This situation can only be improved through the rigorous development of both improved failure and material response prediction capabilities and improved experimental verification. The current study addresses these issues, as well as explores recent developments in numerical predictions and experimental techniques. A combined numerical investigation of damage initiation mechanics and experimental verification of predicted results for a woven glass–vinyl ester composite material is performed. More specifically, 18-oz biased (5 warp/4 fill rovings) plain weave E-glass–vinyl ester laminate with warp rovings oriented in [0/90]s and [0/90/±45]s configurations are investigated. Experimental data for the E-glass–vinyl ester [0/90]s laminate is summarized in a two-dimensional biaxial failure envelope. The feasibility of using thickness-tapered cruciform specimens for generating the experimental biaxial test data is also addressed. Finally, numerical predictions of failure of the fabric-reinforced laminate are developed and compared against the experimental failure envelope for the cross-ply laminate.

The predictive capability of failure mode concept-based strength criteria for multidirectional laminates

This contribution is a post-runner to the ‘failure exercise’. It focuses on two aspects of the theoretical prediction of failure in composites [1–3]: the first is the derivation of failure conditions for a unidirectional (UD) lamina with the prediction of initial failure of the embedded lamina, and the second the treatment of non-linear, progressive failure of 3-dimensionally stressed laminates until final failure. The failure conditions are based on the so-called Failure Mode Concept (FMC) which takes into account the material-symmetries (by the application of invariants) of the UD-lamina homogenized to a ‘material’, and on a strict failure mode thinking. The results of the investigation are stress–strain curves for the various given GFRP-/CFRP-UD-laminae, biaxial failure stress envelopes for the UD-laminae, and initial as well as final biaxial failure envelopes for the laminates. In addition a brief comparison between Puck's and Cuntze's failure theory is presented by the authors themselves.

A further assessment of the predictive capabilities of current failure theories for composite laminates: comparison with experimental evidence

This paper presents supplementary conclusions from an international exercise to establish the current status of failure prediction theories for polymer composite laminates. In previous stages of the exercise leading theoreticians in the field used 15 different approaches to predict a range of biaxial failure envelopes and stress–strain curves for composite laminates. The theoretical predictions were compared with experimental results and their performance was assessed using a process designed by the organisers Hinton, Soden and Kaddour [Compos Sci Technol 62 (2002) 1725]. During the course of the exercise four additional theories have emerged that add to the overall picture. The performance of the new theories is assessed here and compared with that of the other fifteen theories, using an identical methodology. The theories are ranked according to their abilities to predict the experimental results for failure of a unidirectional fibre reinforced lamina, initial and final failure of multi-directional laminates and large deformation of laminates under biaxial loads. An attempt is made to identify the most accurate approaches for use in a wide range of applications. The predictions of the four most highly ranked theories, which included two of the new approaches, were within ±50% (i.e. a factor of 2) of the experimental results in more than 75% of the test cases.

Application of progressive fracture analysis for predicting failure envelopes and stress–strain behaviors of composite laminates: a comparison with experimental results

The theoretical predictions, published in Part A of the failure exercise, are compared with experimental results provided by the organizers of the exercise. Two computer codes, ICAN and CODSTRAN, developed at NASA (Glenn Research Center at Lewis Field), were applied to predict the damage initiation, damage growth and global structural fracture in a wide range of multidirectional laminates. CODSTRAN was employed to predict (I) seven biaxial failure envelopes of [0°] unidirectional and [0°/±45°/90°] s, [±30°/90°] s and [±55°] s multi-layered composite laminates and (II) seven stress–strain curves for [0°/±45°/90°] s, [±55°] s, [0°/90°] s and [±45°] s laminates under uniaxial and biaxial loadings. In general, CODSTRAN gave reasonable predictions for cases where final failure was dominated by fibre fracture. There was, however, large discrepancy between the predicted and measured failure strengths and strains for cases where failure was dominated by matrix failure. Some of the discrepancy is attributed to (a) the effect of residual matrix stiffness that is discounted in simulations and (b) sensitivity of the specimens to the presence of biaxial stress state in certain cases.

An experimental investigation of the biaxial strength of IM6/3501-6 carbon/epoxy cross-ply laminates using cruciform specimens

Abstract Several variations of a thickness-tapered cruciform specimen have previously been used to experimentally determine the biaxial strength of an AS4/3501-6 carbon/epoxy cross-ply laminate. The present work represents a follow-up study of the original specimen design, and incorporates numerous specimen improvements made in an attempt to generate more accurate biaxial results. A total of 52 tests were performed at numerous biaxial stress ratios, utilizing six different specimen configurations. The experimental data generated in the present study for all specimen geometries, as well as a complete biaxial failure envelope in σ1–σ2 stress space for this laminate configuration, are presented. A desirable failure mode in the gage section of the specimen was achieved for all specimens tested in the present study, indicating that accurate biaxial stress states were being generated at ultimate specimen failure. The ability of the thickness-tapered cruciform specimen to determine the biaxial strength of composite materials at any stress ratio has been demonstrated.