Mixed-mode Fracture Energy Research Articles

Measurement of the interfacial energy release rate (ERR) and cohesive law parameters of polyvinyl butyral laminated glass using a novel beam-type test specimen

The polyvinyl butyral (PVB) laminated glass (LG) structures are widely used in architectural and automotive sectors. Determination of the interfacial fracture energy (i.e. G) between the PVB layer and glass is one of the most vital procedures for ensuring the structural safety and fracture resistance of these kinds of components. The present study investigates the adhesion characteristics between glass and PVB interface in a LG composite structure. A new simple test fixture is introduced to measure the mixed-mode fracture energy from pure mode I (i.e. GI) to pure mode II (i.e. GII). By making use of the concept of Equivalent material Concept (EMC), linear elastic fracture mechanics (LEFM) formulations together with finite element (FE) analysis can be used to compute the compliance parameter of the system and pure modes I/II fracture energies. Besides, the interaction of cohesive forces between the PVB layer and glass are simulated by using a FE method based on a bi-linear cohesive zone model (CZM) technique. In this regard, the cohesive law parameters are computed for mode I and mode II in an iterative process. Then, the obtained pure mode cohesive law parameters are utilized to predict the mixed-mode load–displacement diagrams. The obtained results demonstrate the satisfactory accuracy of the cohesive law parameters and fracture energies in predicting the mixed-mode loading results across four different loading rates (i.e. LR = 2, 5, 10, and 15 mm/min).

Ply-Blocking Phenomenon and Hole Size Effects in Modeling Progressive Damage in Fiber-Reinforced Plastics Laminates

Abstract This work presents a 3D progressive damage model based on Puck’s failure theory and linear damage evolution in fiber-reinforced plastic (FRP) laminates. It includes shear nonlinearity, in situ strengths, equivalent stress–strain, and mixed-mode fracture energy, and is implemented in abaqus/explicitTM through VUMAT subroutine. Various test cases were performed to validate the model and demonstrate its applications. The shear nonlinearity test shows that transverse compression retards matrix microcracking while transverse tension accelerates it. The open hole tension (OHT) test of laminates shows that delamination initiates around the holes and free edges, spreads the most, and propagates in different directions at different interfaces. Later, interfiber damage in 45 deg or −45 deg plies initiates and spreads at a slight inclination to the tip of the hole. Finally, fiber damage in 0 deg plies initiates at the tip of the hole, spreads the least, and propagates perpendicular to the loading direction. The ply-blocked laminates show around 30% higher strength and fracture strain than non-ply-blocked laminate due to delay in damage propagation, and are less sensitive to the hole size. Accordingly, their OHT strength reduces by 14.3% as opposed to 21.14% in the non-ply-blocked laminates, when the hole size increases from 6 to 9 mm. The damage location, magnitude, and propagation were corroborated with experimental findings in the literature.

Finite element modeling of debonding failure in CFRP-strengthened steel beam using a ductile adhesive

Carbon fiber-reinforced polymer (CFRP) composites externally bonded to the tensile flange of the steel beam are an effective strengthening technique. Due to the apparent effect of the adhesive toughness on the debonding behavior between the CFRP and steel, this paper focuses on the CFRP-strengthened steel beam using a ductile adhesive and the adhesive selection in the strengthening work. Three-dimensional (3-D) finite element (FE) models were proposed to simulate the mechanical response of the CFRP-strengthened steel beam under a static four-point bending load. The failure of a ductile adhesive was modeled using the trapezoidal mixed-mode cohesive zone model (CZM) coded in the user subroutine (UMAT) of ABAQUS. The effectiveness of the trapezoidal CZM was validated by the experiment in the literature, and the debonding characteristics using different laminate thicknesses and lengths were clarified by the stress and damage analysis. In terms of plate-end debonding failure mode, the ductile adhesive is more appropriate for the CFRP-strengthened steel beam due to its reduced normal stress, increased mixed-mode fracture energy, and more uniform stress distribution.

Mixed-mode I + II fracture characterisation of a honeycomb/carbon-epoxy sandwich panel using the asymmetric single-leg bending test

The Asymmetric Single-Leg Bending (ASLB) test was employed to obtain the fracture energy of a honeycomb/carbon-epoxy sandwich panel under mixed-mode I + II loading. A data reduction method lying on beam theory, specimen compliance and equivalent crack length concepts was employed to get the experimental Resistance-curve (R-curve), which allows determination of the mixed-mode fracture energy. Numerical analysis including cohesive zone modelling was used for validation and as a suitable partition method useful to estimate the mode ratio. In view of the observed non-linear behaviour, a mixed-mode I + II trapezoidal cohesive zone model and the quadratic energetic criterion were considered in the simulations. Overall, it can be concluded that the ASLB test is appropriate for mixed-mode I + II fracture characterisation of sandwich panels under predominant mode I.

Effect of notch depth ratio on mode I and mixed mode I-II fracture properties of engineered cementitious composites (ECC)

The effect of initial notch depth ratios (a/h) on the mode I and mixed mode I-II fracture properties of ECC was studied by using three-point bending test and four-point shear test, respectively. For mode I fracture, the initial fracture toughness KICini and unstable fracture toughness KICun- and KICun+ instead of KICun based on double-K fracture criterion are calculated. The mode I fracture energy GI is calculated by load-crack mouth opening displacement curve (P-CMOD). For mixed mode I-II fracture, the initial effective stress intensity factor (Keffini) are calculated by using nonlinear finite element software and the mixed mode fracture energy GI–II is analyzed. Also, crack propagation mechanism of ECC under mixed mode I-II fracture is analyzed from P-CMOD curve and load-crack mouth sliding displacement (P-CMSD) curve, and mixed mode I-II crack propagation of ECC is divided into six stage. It is found that when 0.3 ≤ a/h ≤ 0.8, the KICini does not change. While, KICun increases when a/h increases from 0.1 to 0.3, decreases when a/h increases from 0.3 to 0.7 and GI decreases with the a/h increasing from 0.3 to 0.8. GI–II is much larger than GI due to an obvious inclined fracture process zone with many micro-cracks dissipating energy in the mixed mode I-II fracture. The GI–II increases with the a/h increasing from 0.1 to 0.6 and decreases with the increase of the a/h from 0.6 to 0.8. While, the crack initiation angle increases with the increase of a/h in the mode I-II fracture.

A Finite Element Method Study of Polymer Exchange Membrane Fuel Cell End Plate Materials by Using Arcan Specimen

In the current days, fuel cells are more preferred to generate electricity due to their positive sides. Because, if they use hydrogen and oxygen as fuel, they only produce electricity, heat, and water. This property of fuel cells is significant because of preventing environmental and chemical pollution so, they contribute to the environment positively. In addition, they have more positive points such as no moving or rotating parts. Therefore, they are no required for mechanical maintenance and not make noise. Besides, they can be used used in a wide range of areas as mobile and stationary power sources for electricity generation. There are many fuel cell types but, proton exchange membrane fuel cell (PEMFC) is more common than the other fuel cell types. It consists of parts such as an endplate, bipolar flow plate, gas diffusion layer, catalyst layer, and membrane. End plates are located on the outer side of PEMFC and hold together its stacks. In the design of the endplates, the state of fracture energy should be considered in the different loading conditions. Because the material may fail if it is designed only by the strength of materials concepts. This paper investigated pure mode I, pure mode II and mixed mode fracture energy behavior of different materials numerically by using Arcan specimen.

Damage Behavior Prediction of Repaired Composite Laminates Subjected to Oblique Penetrate Loading

To predict the effect of oblique impact on the damage and performance of perforation resistance of repaired composite laminates, a three-dimensional continuum damage model (CDM) is used to simulate and calculate the low-velocity impact process of repaired laminates. In the established finite element model, several different types of failure modes are considered. The damage model is based on the modified 3D-Hashin failure criterion to predict the initial damage of the fiber and matrix. The linear-exponential law and the exponential law are used to simulate the tensile and compressive softening process of the material. The triangle traction-separation law and mixed-mode fracture energy method are applied to simulate interface debonding damage between patch/lamina, patch/patch and lamina/lamina. A comparison of the numerical results of several different offsets with the experimental results shows that the simulated failure modes and impact responses are very close to the experiment, which verifies the validation of the finite element model (FEM). The increase of the impact angle can enhance the residual velocity of the projectile in the laminate and reduces the energy absorption. At the same time, it has a great influence on the failure modes, especially the interface debonding damage of the patch.

Mixed mode (I/II) fracture energy of cement emulsified asphalt mortar under intermediate temperature

Being a combination of sand, cement, water, and asphalt emulsion, Cement Emulsified Asphalt Mortar (CEAM) has better toughness and flexibility properties than cement mortar. Given the multiphase nature of CEAM, it is susceptible to micro-cracking during the setting process and also due to other factors such as traffic loads, undesirable atmospheric conditions. Given the typical direction of loading and cracking in these mortars, they are likely to experience mixed-mode fractures. Therefore, this study investigated the fracture properties of CEAM at service temperature in mixed mode I&II fractures. For this investigation, the mixed-mode fracture energy was determined through experiments on Semi-Circular Bending (SCB) specimens with the volume fractions of mortar treated as independent variables and the material behavior assumed to be viscoelastic at ambient temperature. Considering the need to investigate the effect of mix design ratios and their interactions, to reduce the number of experiments, and to limit these ratios to the ranges that produce acceptable rheological and mechanical properties, the D-Optimal mixture design method at 5% significance level was used to optimize the design of experiments and related analyses. Next, a regression model was developed for the relationship between fracture energy in each mode (I, II, I&II) and the mortar constituents. Also, the optimum mix design range to reach maximum fracture energy in all three modes was determined by graphical optimization. Analysis of the results with ternary contour plots showed the dependence of fracture energy and the optimum mix design range in the studied modes on the mix ratios of the CEAM constituents. The Cement and asphalt were identified as the independent variables with greatest effects on fracture energy variations and the optimum mix design. The results also revealed that as the asphalt emulsion-to-cement ratio increased, the maximum carried force decreased and the deformation corresponding to this force increased.

Mixed mode fracture characterization of brittle and semi-brittle adhesives using the SCB specimen

Fracture mechanics and damage mechanics are widely used to predict the mechanical behavior of adhesive joints. The critical energy release rate is one of the most important parameters in these models. In practice, most adhesive joints experience mixed mode loading conditions. Therefore, mixed mode fracture energy measurement plays an important role in adhesive joint failure analysis. A new test method for mixed mode fracture energy measurement of brittle and semi-brittle adhesive joints is presented in this paper using semi-circular bend specimens. A data reduction scheme based on a finite element analysis is suggested and finite element results are validated by digital image correlation strain measurement technique. The fracture envelops obtained from the proposed specimen are compared to double cantilever beam (DCB), single leg bending (SLB) and, end-notched flexure (ENF) test results. Good agreement between the new specimen and the classic energy measurement methods is observed.

Damage and perforation resistance behaviors induced by projectile impact load on bonding-patch repaired and scarf-patch repaired composite laminates

A three-dimensional continuum damage model is proposed to analyze the damage and perforation resistance behaviors of bonding-patch and scarf-patch repaired composite laminates under projectile impact load. Coupling with modified 3D-Hashin failure criteria, a linear-exponential law due to fiber pull-out failure and an exponential law are used to predict tensile and compressive softening processes of materials, respectively. A cohesive interaction based on triangle traction–separation law and mixed-mode fracture energy method is applied for interface debonding damages between patch/lamina, patch/patch and lamina/lamina. Comparisons are made between numerical results and several available test data for different impact offsets. The perforation resistance and interface debonding damage mechanisms are extensively discussed using finite element analysis. Further, perforation resistance behaviors of laminate with six different patch-repair patterns are assessed. Effects of initial velocity of projectile on residual velocity and energy-absorption are discussed. A residual velocity error within 7.3% and energy-absorption error within 9.2% is found between simulations and tests. Consistent failure modes including fiber fracture, matrix cracking, delamination and interface debonding are also identified. As the projectile invades patches, interface debonding damage in patches is accumulated rapidly, especially for larger impact offset. The combined patch-repairs show a reduction of at the most 48.3% in velocity and higher ballistic limit velocities which implies better perforation resistance capacity. The energy-absorption almost increases with increasing the initial velocity and a decreasing trend in average energy-absorption is found with the increase of impact offset.

The applicability of J-integral approach in the determination of mixed-mode fracture energy in a ductile adhesive

In this work, a J-integral-based data reduction approach was used for fracture characterisation of a ductile two-component epoxy adhesive with steel adherends under mixed-mode loading. The applied method is a closed-form relation which requires only rotation angle of the load introduction points and the applied load as input. Double Cantilever Beam (DCB) tests as well as Mixed Mode Bending (MMB) tests (with different mixed-mode ratios) were carried out to achieve a wide range of mode-mixity. Based on the measured values of fracture toughness Gc, the full fracture envelope of the adhesive was developed by using the Benzeggagh-Kenane (B-K) fracture criterion. Good agreement between the FE and experimental load-displacement curves proved that the applied method is accurately capable of determining the fracture toughness of the adhesive. The proposed approach shows high potential to account the dissipated energy in the fracture process zone in the ductile adhesives.

Characterising bonded joints with a thick and flexible adhesive layer–Part 1: Fracture testing and behaviour

Adhesively bonded structural joints have increasingly found applications in automotive primary structures, joining dissimilar lighter-weight materials. Low-modulus rubbery adhesives are attracting rising interest as an alternative to conventional rigid structural adhesives due to benefits such as the excellent impact resistance they provide. This paper is the first of two parts that investigate, both experimentally and numerically, the mechanical behaviour of a rubbery adhesive and the bonded joints to be used in a lightweight automobile structure. This part 1 paper characterises the fracture behaviour of the flexible adhesive layer with thick bondlines and presents a way to reliably determine the fracture mechanics parameters under a range of loading modes. Assessment of the various fracture tests indicated that DCB and SLB should provide mode I and mixed mode fracture energies but that the conventional ENF for mode II would not be practical for such compliant adhesive layers. Instead a cracked thick adherend shear specimen was developed and used. Reliable fracture energies were obtained from these specimens and a mixed mode fracture criterion developed for application in the part 2 paper.

Comparison of solder joint fracture behavior in Arcan and DCB specimens

The mixed-mode fracture energies of copper–SAC305–copper solder joints were measured using both an Arcan-type specimen and a double-cantilever beam (DCB) specimen. The critical strain energy release rate, Jci, values obtained from Arcan-type specimens were in the range of 10–80J/m2, depending on the strain rate and phase angle of loading, while those obtained from DCB specimens were much higher, in the range of 380–2300J/m2. This large difference in the measured Jci values, which is consistent with the literature, was explained in terms of the stress distributions, constraint and plastic zone sizes in the solder layers in these two specimens.

Constitutive law of adhesive layer measured with mixed mode bending test

New analytical theory is presented in this paper to measure the mixed mode constitutive law of adhesive bonding. The theory is on the basis of the J-integral theory and the mixed mode bending test. The fracture energy and the mode I/II constitutive law components were obtained at different mode mixity ratios. A comprehensive discussion is carried out with focus on the plastic yielding and initiation of localized damage. In situ SEM was used to analyse the tension/shear deformation mechanisms. The mixed mode fracture energy is found to increase significantly as the mode mixity ratio increased. The tension stress started to decrease after plastic yielding, while the shear stress kept increasing until the emergence of localized damage. This difference was attributed to the anisotropy of the adhesive material, caused by shear banding. The plastic deformation consisted of cavitation caused by tension and shear banding caused by shear. The present method is verified with numerical simulations. The constitutive law measured with the present method can be used to develop new cohesive zone models, and may produce a more accurate analysis of adhesive bonded structures than existing methods do.

A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode I and mode II fracture energies

Abstract The present paper deals with the derivation of an interface model characterized by macroscopic fracture energies which are different in modes I and II, the macroscopic fracture energy being the total energy dissipated per unit of fracture area. It is first shown that thermo-dynamical consistency for a model governed by a single damage variable, combined with the choice of employing an equivalent relative displacement and of a linear softening in the stress-relative displacement law, leads to the coincidence of fracture energies in modes I and II. To retrieve the experimental evidence of a greater fracture energy in mode II, a micro-structured geometry is considered at the typical point of the interface where a Representative Interface Element (RIE) characterized by a periodic arrangement of distinct inclined planes is introduced. The interaction within each of these surfaces is governed by a coupled damage-friction law. A sensitivity analysis of the correlation between micromechanical parameters and the numerically computed single-point microstructural response in mode II is reported. An assessment of the capability of the model in predicting different mixed mode fracture energies is carried out both at the single microstructural interface point level and with a structural example. For the latter a double cantilever beam with uneven bending moments has been analyzed and numerical results are compared with experimental data reported in the literature for different values of mode mixity.

Adhesion Improvement of Glass-Fibre-Reinforced Polyester Composites by Gliding Arc Discharge Treatment

A gliding arc is a plasma that can be operated at atmospheric pressure and applied for plasma surface treatment for adhesion improvement. In the present work, glass-fibre-reinforced polyester plates were treated using an atmospheric pressure gliding arc discharge with an air flow to improve adhesion with a vinylester adhesive. The treatment improved wettability and increased the polar component of the surface energy and the density of oxygen-containing polar functional groups at the surfaces. Double cantilever beam specimens were prepared for fracture mechanics characterisation (fracture resistance as a function of nominal mode mixity) of the laminate adhesive interface. It was found that gliding arc treatment significantly increases the interfacial fracture energy and fracture resistance in comparison with a standard peel ply treatment, although the mixed mode fracture energy of the gliding arc treated specimen was not as high as that of the laminate itself.

Application of the end loaded split and single-leg bending tests to the mixed-mode fracture characterization of wood

Abstract This work describes the application of end loaded split and single-leg bending tests to the mixed-mode fracture characterization of wood. Experimental tests and numerical validation analyses were performed. A new data reduction scheme based on the crack equivalent concept is proposed. The method overcomes the difficulties inherent to these tests, such as crack length monitoring during propagation and influence of clamping conditions. The single-leg bending test is simpler to execute and provided accurate results. The obtained mixed-mode fracture energy is associated with the pure mode values and the obtained trend point to a linear fracture criterion as a candidate to describe the fracture behavior of the Pinus pinaster Ait. wood.

Observations of Decreased Fracture Toughness for Mixed Mode Fracture Testing of Adhesively Bonded Joints

In contrast to fracture in monolithic materials, where cracks naturally grow in a mode I manner, fracture in laminated or adhesively bonded joints often involves cracks growing under mixed mode conditions. In many cases, the mixed mode fracture energy increases as the fracture mode changes from mode I to mode II, but exceptions have been noted for several practical engineering adhesives. In some cases, G IIc may be less than G Ic, while in other situations, failure may occur at total energy release rate (G T = G I + G II) values that are smaller than either of the pure mode fracture energies. Several examples of this behavior are reported along with possible explanations for the behavior, which often involves the propagation of the growing debond into regions where less energy is dissipated by the fracture process. These examples showing that mixed mode fracture energies of adhesive joints may be lower than pure mode fracture energies remind us of the importance of developing fracture envelopes over a wide range of mode mixities for engineering design.

Rotational interface formulation for delamination analysis of composite laminates

In this paper, delamination progression in a composite laminate is modelled by interface elements within a geometrically non-linear FE analysis setting. With the assumption of small continuum deformations, a rotational interface formulation is obtained from a recently proposed formulation based on the concept of a regularised strong discontinuity, cf. [Int. J. Numer. Meth. Eng. 54 (2002) 473]. The degradation of the stress vector in the cohesive zone is described by a damage-plasticity coupling, which is calibrated analytically against experimental data of mixed-mode fracture energies. The paper is concluded by a couple of numerical examples that describe the predictive capabilities of the interface formulation.

Strain-Rate Effects on Unidirectional Carbon-Fiber Composites

Strain-rate effects on mode I fracture of unidirectional carbon-e ber tow composites corresponding to crack propagation parallel to the e ber tow direction was investigated. Precracked unidirectional stitched carbon-e ber specimensweresubjected to a staticandlow-velocity-impactthree-pointbend test.Thecrack position asa function oftime and hencethecrack-propagation velocity were measured with thehelp ofspecial crack-propagation gauges and a high-resolution digital camera. Load vs load point displacement was measured for every test. The effect of strain rate on fracture energy was characterized. The Iosipescu shear test under static and low-velocity-impact loading conditions wasused to characterizetherate-dependent shearresponse ofthematerial. In addition, tension and compression responses were characterized using American Society for Testing and Materials standard test cone gurations. It is found that the mode I fracture energy decreases with an increase in the rate of loading. with the failure event. The resin used for the tubes is slightly rate sensitive; however,thisindicatesthat theresin isstiffer and stronger under dynamic conditions. Yet, the dynamically crushed tubes con- sistently absorblessenergythan thestatically crushedtubes,always atalowermeanplateauload.Thus,itappearsthattheratesensitivity of the fracture events warrant a careful examination. The basic building block of braided composite plaques are e ber tows that are braided into different microstructural architectures prior to being infused with resin. Different types of braided archi- tectures are summarized in the text. 1 Prior to studying the fracture propertiesofthebraidedplaques (thebraidedplaquescontainacom- plex internal microstructure ), it is prudent to understand the various fracturemechanisms andfractureproperties of thetows themselves. Fundamental issues related to mode I, mode II, and mixed mode fracture of stitched tow-reinforced composites need investigation. The mode I, mode II, and mixed mode fracture energies are fun- damental properties of a e ber-reinforced composite. Consequently, measurement of these fracture energies is necessary for properly characterizing the response and failure of structures made of these composites. In this paper we present the results of an experimental study that examined the mode I fracture of unidirectional carbon- e ber tow composites with crack propagation along the e ber tow direction. The present investigation of crack growth is limited to low ve- locity impact (LVI) conditions. Under these conditions the dy- namic stress e eld produced by the impact loading subsides, and this transient e eld occurs at the very early stages of loading. In the present experiments the maximum impactor velocity is 4.6 m/s, re- sulting in maximum crack-propagation velocities on the order of 350 m/s. These velocities are a small fraction of the shear wave speed (1540 m/s) and Rayleigh wave speed of the material. Con- sequently, dynamic effects can be neglected. Researchers 7i11 have conducted an extensive experimental and numerical investigation of dynamic crack propagation in unidirectional continuous e ber (prepreg)-laminated composites. The present study examines con- tinuous e ber (e ber tows) unidirectional composites under LVI con- ditions.