Mixed-mode Bending Test Research Articles

Mixed Mode‐I/II interlaminar fracture toughness Characterization of woven Carbon–Kevlar interyarn hybrid textile composites

AbstractIn actual service conditions, the composite structures are subjected to the combined effect of Mode‐I and Mode‐II loadings. It has great significance in the aerospace, defense, military, automobile, and marine sectors. This study aims to determine the Mixed Mode‐I/II interlaminar fracture toughness (ILFT) of plain and twill woven carbon, Kevlar monolithic, and interyarn hybrid textile composites under several hybridization schemes. The tailored properties are obtained using the interyarn hybridization of high stiff carbon yarn and high tough Kevlar yarn. The effect of individual yarn in the length direction in different hybrid composite laminates is carefully investigated. The Mixed Mode‐I/II ILFT characterization is experimentally performed using a mixed mode bending (MMB) test specimen on the Instron 8862 system under 45%, 55%, and 65% Mixed Mode ratios (MMRs). The increase in mode mixture percentage decreases the lever length, increases the load‐bearing capacity, and increases the Mixed Mode‐I/II ILFT of the MMB test specimen. Plain woven composites exhibited a higher ILFT than twill woven textile composites. The plain woven carbon–Kevlar hybrid composite laminate with carbon yarn‐in‐length direction shows the highest Mixed Mode‐I/II ILFT after CP laminates. Hybridization significantly increases the Mixed Mode‐I/II ILFT compared to monolithic Kevlar fabric‐reinforced composites. Moreover, the failure mechanisms are investigated using scanning electron microscopy.Highlights Mixed Mode‐I/II ILFT of carbon–Kevlar interyarn hybrid textile composites. ILFT at nonlinearity (NL), VIS, and 5%/Max load points for 45%, 55%, and 65% MMR. Advantage of placing carbon yarn‐in‐length direction in hybrid configurations. Effect of carbon–Kevlar interyarn hybridization on Mixed Mode‐I/II ILFT. Fractography of tested specimens to investigate several failure mechanisms.

Dual-actuator mixed-mode bending tests on structural adhesive joints

In this article, a novel mixed-mode bending (MMB) test setup is presented and used to investigate the fracture behavior of the structural adhesive SikaPower®-498. The novelty lies in the implementation of two actuators that can be controlled independently of each other. This opens up investigation possibilities that go beyond those of the MMB standard configuration. For example, a varying mode-mixity can be prescribed during testing, allowing identification of an entire fracture envelope from a single experiment. Additionally, an optical fiber strain measurement (OFS) system is used to determine the curvatures of the substrates, allowing for a detection of the actual crack tip position and an analysis of the loading conditions behind the crack tip. The presented work focuses on the experimental calibration of the compliance change during crack growth, on tests performed at constant (external) mode-mixity using a mode partitioning approach based on the J-integral, as well as on tests carried out under varying mode-mixity. Additional aspects of the test setup such as stable crack growth regime or differences between the results of different evaluation methods are discussed. Finally, the obtained fracture envelopes are compared with references from literature, including for the first time a comparison between mixed-modes I+II and I+III.

A comprehensive study on the fracture behavior modeling of adhesively bonded composite joints using a compliance-based beam method

In this study, the fracture response of adhesively bonded composite joints under different modes of I, II and mixed-mode I/II conditions was characterized by employing the double cantilever beam (DCB), end notched flexure (ENF), and mixed-mode bending (MMB) tests, respectively. In addition, various mechanical tests were executed for determining the mechanical properties of the glass fiber/epoxy composite substrates. The flexural modulus and equivalent crack length relations for the MMB specimen were derived using the compliance-based beam method (CBBM). This method enabled the determination of strain energy release rate (SERR) and fracture energy only using the load-displacement curve. Furthermore, the proposed method simplified the process of obtaining resistance curves (R-curves), as the crack length did not need to be measured during the test and considered the effects of energy loss in the fracture process zone that are neglected in classical methods. The R-curves obtained from the proposed method were compared with the direct beam theory for pure mode I and corrected beam theory for pure mode II and mixed mode loadings. According to this comparison between the classical methods and CBBM, SERR achieved by the proposed method was higher than that obtained by classical methods. The cohesive zone model and corresponding traction-separation laws developed by a direct method were used in conjunction with the finite element method to validate the acquired experimental data. Moreover, the failure patterns occurred during testing was determined after investigating the fracture surfaces under the loading modes of I, II, and mixed I/II.

Mode I, mode II and mixed mode I-II delamination of carbon fibre-reinforced polyamide composites 3D-printed by material extrusion

Continuous carbon fibres can greatly improve the properties of 3D-printed polymer parts made by material extrusion. However, like all laminated composites, 3D-printed parts are susceptible to delamination damage. In addition, the printing process does not include a consolidation at high temperatures and pressure, unlike conventional manufacturing methods, which can lead to poor interlayer cohesion. Due to the combination of the susceptibility to delamination and a weak interface, the assessment of the interlaminar properties of 3D-printed parts is critical. This work experimentally investigates the delamination behaviour of carbon fibre-reinforced polyamide laminates under mode I, mode II and mixed mode I-II loading, using the double cantilever beam (DCB), end-loaded split (ELS), end-notched flexure (ENF) and mixed-mode bending (MMB) tests. An interlaminar fracture toughness at crack initiation of 1.5 kJ/m2 was found in mode I, 2.1 (ELS) and 1.8 (ENF) kJ/m2 in mode II, and 1.0 kJ/m2 in mixed mode I-II with GII/Gtotal = 0.5. Several analytical and numerical models are employed to validate the experimental results. Scanning electron microscopy revealed the micro-mechanical origins of the crack in the different loading configurations.

Geometrical imperfection sensitivity on in-plane compressive modulus and strength of honeycomb core and deviations from isotropy

Honeycomb core sandwich may suffer from face/core debonding. Candidate debond fracture test specimens such as End-Notch Flexure (ENF) and Mixed Mode Bending (MMB) contain unbonded regions of the sandwich where the core is required to carry in-plane com-pressive load. In-plane modulus and compressive strength of honeycomb core are not pro-vided by core producers and must be estimated from unit cell models assuming perfect hexagonal cells. In this study it is shown that geometrical imperfections, such as deviations in the angle between cell walls and curved cell walls have a strong influence on modulus and strength because of deviations from transverse isotropy. A range of Nomex honeycomb cores were tested under in-plane compression. Modulus and strength ratios ( L/W) were found to vary from 0.3 to 3.24 and 0.96 to 1.8, respectively. Analysis based on unit cell models verified that deviations of the inclined cell wall angle, θ, from 30 ◦ is a major cause for orthotropy. Rounded corners and curved walls were analyzed using finite element analysis. Both principal elastic moduli of the core ( E L and E W) were reduced by the curvature while the Poisson’s ratios remained largely unaffected. Implications of the results for design of MMB and ENF fracture test specimens are discussed.

From High Strain Rates to Elevated Temperatures: Investigating Mixed-Mode Fracture Behaviour in a Polyurethane Adhesive.

The investigation of the behaviour of adhesive joints under high strain rates is an active area of research, primarily due to the widespread use of adhesives in various industries, including automotive manufacturing. Understanding how adhesives perform when subjected to high strain rates is crucial for designing vehicle structures. Additionally, it is particularly important to comprehend the behaviour of adhesive joints when exposed to elevated temperatures. Therefore, this study aims to analyse the impact of strain rate and temperature on the mixed-mode fracture characteristics of a polyurethane adhesive. To achieve this, mixed-mode bending tests were conducted on test specimens. These specimens were subjected to three different strain rates (0.2 mm/min, 200 mm/min, and 6000 mm/min) and tested at temperatures ranging from -30 °C to 60 °C. The crack size was measured using a compliance-based method during the tests. For temperatures above Tg, the maximum load supported by the specimen increased with an increasing loading rate. GI increased by a factor of 35 for an intermediate strain rate and 38 for a high strain rate from low temperature (-30 °C) to room temperature (23 °C). GII also increased for the same conditions by a factor of 25 and 95 times, respectively.

Crack self-sensing capability of glass fiber reinforced polymer composites embedded with magnetostrictive fibers in mixed-mode bending

Glass fiber reinforced polymer (GFRP) composites integrated with sensors have received attention because the composite material can transmit information about the structural condition during operation. This study investigated the crack self-sensing capability of GFRP composites with magnetostrictive Fe–Co fibers under mixed-mode bending. The mixed-mode bending (MMB) test was performed using GFRP composites with a certain number of Fe–Co fibers introduced. Three different mixed-mode I/II ratios for MMB tests were selected and tested. The self-sensing capability of crack propagation was discussed by measuring the magnetic flux density induced by the inverse magnetostrictive effect using Hall probes. The GFRP composites with Fe–Co fibers fabricated in this study are a promising monitoring technology for non-contact sensing.

Accurate simulation of delamination under mixed-mode loading using a multilinear cohesive law

The complex failure mechanisms involved in failure of interfaces requires the use of an accurate description of the cohesive law. In recent years, there have been many developments to determine the full shape of the cohesive law. However, most of the existing cohesive zone models assume a simplified shape, such as bilinear, trapezoidal or exponential, which are usually simple to model. Their accuracy is found to be rather limited, especially in the presence of a large fracture process zone due to either plastic deformation or fibre bridging. In this work, a new cohesive element description is proposed to formulate a general cohesive zone model to overcome these limitations. The benefit of the new approach is that it allows for convenient implementation of any arbitrary shape of the cohesive law obtained experimentally. The authors present a new procedure based on the superposition of n-bilinear cohesive zones to obtain an equivalent multilinear cohesive law that fits any experimental measurement. The new element formulation has been implemented in the commercial finite element software ABAQUS, using user element subroutine. Verification of the methodology is performed at the single element level and the approach is validated for different material systems (adhesives and composites) using the double cantilever beam, end-notched flexure and mixed-mode bending tests. Excellent correlation between all numerical predictions and experimental results is obtained, demonstrating the robustness of the proposed methodology.

Cohesive-zone based fracture mechanics model of an edge delamination in bimaterial beam under mixed-mode bending test

The problem of an edge-split bilayer beam consisted of bonded dissimilar materials under mixed-mode bending (MMB) is investigated by using a structural mechanics procedure. In this analytical procedure, the bilayer beam is modeled as two Timoshenko beams joined by using interface tensile and shear springs, and the fracture mechanics parameters including the strain energy release rate and phase angle are estimated from the spring responses. Numerical examples of bilayer beams consisted of isotropic or orthotropic bimaterials and with symmetric or asymmetric dimensions are presented and compared to continuum based finite-element solutions with either cohesive-zone or perfectly-bonded interface models. It is shown that the strain energy release rates obtained from these models are in good agreement. The phase angles obtained from the analytical model and the cohesive-zone-interface based continuum model are also consistent with each other, and agree to the crack-tip deformation. On the other hand, the phase angles obtained from the oscillating crack-tip fields related to the perfectly-bonded interface do not match to the crack-tip deformation as well as the cohesive-zone interface models. Consequently, it is recommended to characterize the mode-mixity dependent interfacial adhesion and fatigue responses by using the fracture mechanics parameters obtained by using the analytical solution for the MMB fracture problem.

An elastoplastic damage model of concrete under cyclic loading and its numerical implementation

A novel elastoplastic damage model describing the complex mechanical behaviors such as stiffness degradation and irreversible deformation of concrete under cyclic loading is constructed and the complete procedure for numerical implementation is presented. To solve the key problems including multi-axial stress states, asymmetry in tension and compression and conversion between tension and compression under cyclic loading, a series of approaches are put forward. A scalar equivalent strain based on the Hsieh-Ting-Chen strength criterion in the framework of strain space is used to convert the complex multiaxial stress state to the simple uniaxial one. Correspondingly, the equivalent strain obtained by the characteristic strength curve addresses the asymmetry in tension and compression, so that the stress–strain relationship in both uniaxial tension and uniaxial compression can be represented by the same curve, and a single damage scalar is available to characterize both tensile damage and compressive damage. To overcome the difficulty of conversion between tension and compression owing to the non-negative equivalent strain, a net equivalent strain is defined to keep the curve proceeding in the first quadrant under reverse loading. Meanwhile, a nominal damage variable is proposed to ensure that the reloading curve can return to the original stress–strain envelope. A new framework of the model with a concise mathematical form has been numerically implemented and is independent of the selection of fundamental governing equations. Typical experimental tests involving three-point bending test, mixed-mode bending test, cyclic uniaxial test, and reciprocating loading test are used for verification. The results calculated by the proposed model are all in good agreement with the tests. As a result, the correctness and reliability of the novel model are demonstrated.

Experimental evaluation of cohesive laws components of mixed-mode I + II fracture characterization of cortical bone

Mixed-mode I + II fracture characterization of cortical bone tissue is addressed in this work. The mixed-mode bending test was used to impose different mode ratios. An equivalent crack length data reduction method was considered to obtain the strain energy release rate components. Crack opening and shear displacements were measured by means of digital image correlation. These quantities were then integrated to propose a direct evaluation of cohesive laws. The components of the cohesive laws for each mixed-mode loading were obtained by the uncoupled and Högberg’s methods. The later provided consistent evolution of strain energy release rate and peak stresses components in function of mode-ratio, revealing its appropriateness regarding the fracture characterization of cortical bone under mixed-mode I + II loading.

Predicting fatigue damage in composites subjected to general loading conditions

A computationally efficient fatigue analysis methodology is proposed that uses a cycle jump approach to drive the accumulation of fatigue damage and a unified local fatigue cohesive zone model that can predict the initiation and propagation of cracks using a reduced set of model parameters. A new definition of the stress ratio is proposed for general loading conditions, which include negative load ratios, unsynchronized loads, and problems where the mode mixity changes during a cycle. The cycle jump procedure was verified by performing analyses of standard double cantilever beam and mixed mode bending tests. Then, the model was validated by performing analyses of double notch shear tests and initiation of transverse matrix cracking in a [0/90] laminate using models that account for residual thermal stresses. The results indicate that the analysis methodology can reproduce experimentally measured fatigue damage initiation and evolution for a variety of different configurations and load combinations.(Keywords: C. Cohesive interface modelling, B Fatigue, B. Delamination, A. Polymer-matrix composites (PMCs))

Design and validation of mixed-mode device for fracture toughness analysis of adhesive joints

In real applications, adhesive joints are subjected to mixed mode I+II loading. The tests developed for mixed-mode loading are complex but considered highly relevant for fracture characterization. There are several mixed-mode tests, of which the Mixed-Mode Bending (MMB) test stands out for its capacity to allow the variation of the mixed-mode ratio practically without limitations. However, although there are several proposals for MMB test device configurations, this test is still considered complex, and some of the current solutions do not allow performing the test on stiffer materials. In this work, the main objective is to design, numerically model and experimentally validate an MMB test equipment to perform structural adhesive tests. Experimentally, it is intended to design and manufacture the MMB test equipment, and subsequently carry out the respective tests. The end result should be an equipment that enables obtaining various mixed-mode combinations, using a single equipment and the same type of test specimen, for further application in the design of adhesively-bonded joints. The equipment was validated by fabricating and testing adhesive joints, although further validation should contemplate estimating the mixed-mode behaviour of adhesive joints and comparing it with literature data.

Mixed Mode Cohesive Law of Adhesive Joints

This work presents an experimental method to determine the cohesive law of thin adhesive joints in mixed mode. The proposed method is based on the MMB (Mixed Mode Bending test). The Energy release Rate and Crack Tip Relative Displacement are determined based on a compliance variation data reduction method by processing the global load displacement curve, without monitoring the crack length and the crack tip relative displacement during the test. Representing the energy release rate versus relative displacement the cohesive law is determined by numerical differentiation. The method is validated numerically by virtual tests including the cohesive zone model. The results reveal that the proposed data reduction scheme is suitable to obtain the mixed mode cohesive law using only the load and displacement data obtained from the testing machine, without any external displacement measurement technique and without any assumption of the form of the cohesive law.

Improved Mixed-Mode Bending Test Apparatus through Analytical Modeling and Finite-Element Optimization for Improved Characterization

AbstractThe compliance of the mixed-mode bending (MMB) test fixtures can influence the interlaminar fracture toughness measurements for different mixed-mode ratios in an unpredictable way. The purp...

Influence of the test methodology on the fatigue behaviour of a composite subjected to a mixed fracture mode I/II

Composite materials manufactured by means of the superposition of layers and some specific morphologies, are susceptible to losing part of their resistant capacity due to the presence of delaminations between their  layers. The objective of this work is to evaluate experimentally the generation and propagation of these interlaminar cracks in a carbon-epoxy composite subjected to dynamic stress under mixed fracture mode I/II, using for this purpose two different test methodologies, on the one hand the standardized MMB (Mixed-Mode Bending) and on the other hand the ADCB (Asymmetric Double Cantilever Beam), with the intention of exploring the viability of the ADCB test as a simpler alternative of execution, especially in fatigue tests, to the MMB test. For this purpose and after a previous static characterization of the material in which the critical values of the energy release rate were determined in both test methods, the energy release rate levels to be applied in the fatigue tests were defined for two GII/Gc mixed mode grades of 0.2 and 0.4(0,33 ADCB)   and a ratio of stress levels to fatigue of R= Gmin/Gmax=0.1.DG-N fatigue initiation curves were obtained from these experimental data. The most relevant result of the work is that, in general, the MMB mixed mode provides different fatigue limits depending on the degree of mixed mode, whereas in the ADCB type test the fatigue limits tend to have the same value.

Embedding artificial neural networks into twin cohesive zone models for composites fatigue delamination prediction under various stress ratios and mode mixities

This paper presents for the first time a novel numerical technique for modelling fatigue delamination growth in fibre reinforced composites, which is based on coupling two twin cohesive zone models with a single-hidden-layer artificial neural network. The simulation approach proposed here can describe composites fatigue delamination under negative & positive stress ratios and the full range of mode mixities. In the modelling strategy, each segment of a composites interface is described by two twin cohesive elements, which jointly provide local fracture mechanics parameters into a feedforward single-hidden-layer neural network, without the need to know the global load R ratio. In turn, the neural network algorithm feeds the fatigue crack propagation rate da/dN back into the twin cohesive elements, which follow a static and fatigue cohesive law in a synchronous fashion. The novel modelling methodology has been implemented in an explicit finite element scheme. The modelling strategy is first verified and validated by several benchmark cases, involving mode I Double Cantilever Beam tests, mode II End Loaded Split tests with and without reversal, as well as Mixed-Mode Bending tests. A relevant application of the modelling technique is demonstrated considering a tapered laminate, which experiences non-proportional loading due to the presence of combined static tension and cyclic bending.

Evaluation of the strain-based partitioning method for mixed-mode I+II fracture of bi-material cracks

ABSTRACT The goal of this paper is to evaluate the strain-based partitioning method (SBM), an analytical method based on beam analysis, for the mixed-mode fracture characterization of asymmetric cracks. The fracture energy is calculated at the crack tip of mixed-mode bending (MMB) test with asymmetric geometry and asymmetric material parameters. The fracture energy obtained using SBM is benchmarked against the widely applied Williams’ partitioning method (WM) and numerical results from finite element models using the virtual crack closure technique (VCCT). Results show that WM produces inaccurate fracture modes in asymmetric conditions. However, if using SBM, the fracture mode ratio of bi-material cracks was obtained with accuracy. SBM describes a coupling function between mode I and mode II fracture that allows the mode partitioning as long the specimen complies with a simple design criterion based on the longitudinal strain equivalence between arms. Experimental results of composite-to-metal bonded joints validate the results of the parametric study. SBM proves to be an easy and reliable solution for the mixed-mode fracture characterization of bi-material cracks.

A reduced-input cohesive zone model with regularized extended finite element method for fatigue analysis of laminated composites in Abaqus

A cohesive zone model (CZM) for fatigue crack propagation was integrated within the Regularized eXtended Finite Element Method (Rx-FEM) discrete damage modeling framework. This CZM constitutive model, which is formulated in terms of S-N stress-life curves rather than the more usual rates of crack propagation described with a Paris law, can predict both crack initiation and propagation by relying on the intrinsic relationships between S-N and the Paris law. This feature of the model is of significant practical interest since S-N curves can be synthesized with few parameters and simple engineering assumptions, while the experimental characterization of the Paris law parameters for all required stress ratios, mode mixities, and material interfaces in a composite structure is very difficult and often impractical. Used in combination with the Rx-FEM method, this CZM can predict mesh-independent crack networks in composite structures subjected to cyclic or quasi-static loads. The Rx-FEM methodology for fatigue damage was implemented in Abaqus using two superimposed sets of standard Abaqus elements to represent the enriched displacement field. The capabilities of the proposed methodology are demonstrated by comparing the experimental and predicted response of a mixed-mode bending (MMB) test, as well as a Clamped Tapered Beam (CTB) sub-element designed to study matrix crack initiation, delamination propagation, and subsequent delamination migration from one ply interface to another.

Influence of interface ply orientation on delamination growth in composite laminates

The standard experimental procedures for determining the interlaminar fracture toughness are designed for delamination propagation in unidirectional specimens. However, in aerospace structural components, delamination usually occurs between plies at different orientations resulting in different damage mechanisms which can increase the value of the fracture toughness as the delamination propagates. Generally, numerical analyses employ the value measured at the delamination onset, leading to conservative results since the increase resistance of the delamination is neglected. In this paper, the fracture toughness and the R-curves of carbon/epoxy IM7/8552 are experimentally evaluated in coupons with delamination positioned at 0°/0° and 45°/−45° interfaces using Double Cantilever Beam (DCB) and Mixed-Mode Bending (MMB) tests. A simplified numerical approach based on the Virtual Crack Closure Technique (VCCT) is developed to simulate variable fracture toughness with the delamination length within a Finite Element code using a predefined field variable. The results of the numerical analyses compared with the experimental data in terms of load-displacement curves demonstrate the effectiveness of the proposed technique in simulating the increase resistance in delamination positioned between plies at 45°/−45° interface.