Energy Release Rate In Mode Research Articles

Parametric investigation of bonded composite joints under Mode II using a new methodology based on design of experiments

ABSTRACT In the pursuit of a sustainable future with limited resources and growing environmental concerns, adhesive joining stands out as a pivotal technology for the advancement of lightweight structures. This study aims to investigate the influence of various variables on the critical strain energy release rate in mode II (GIIc) for End-Notched Flexure (ENF) bonded composite joints, employing a new methodology based on Design of Experiments (DoE) approach. Two-dimensional finite element models of the ENF bonded composite joints are developed using commercial software, with all numerical models generated via Python™ scripts linked with AbaqusⓇ. Eleven design parameters related to the specimen geometry and material properties are systematically evaluated to determine the influence of each variable on GIIc. Numerical force–displacement curves are obtained, followed by the application of the Compliance-Based Beam Method (CBBM) to estimate the critical fracture energy in mode II, represented by a numerical envelope. The influence of each parameter is assessed using the main effect (ME) metric. The top five most influential variables affecting GIIc and CBBM are identified as the adhesive’s critical strain energy release rate in mode II (GIIc), effective laminate longitudinal elastic modulus (), adhesive thickness (tA), adherent thickness (h), and pre-crack length (). Furthermore, the study highlights the epistemic uncertainty associated with the geometric variables. Despite the limitations inherent in the computational model, the Plackett-Burman method consistently proves effective in conducting sensitivity analysis of the variables in the ENF test. These findings demonstrate promising prospects for the application of this procedure in the design of composite joint structures.

Experimental characterization of tensile and compressive translaminar fracture toughness coupling multi-physics measurements

The study of the failure modes of carbon fiber reinforced polymers is essential due to their extensive use in industry. Translaminar failure (at the scale of the laminate) has been studied extensively the main goal being to compute the critical strain energy release rate in mode I of the ply GIC_ply but large variations can be observed between papers. This study investigates this failure mode of a carbon/epoxy laminate, using Compact Tension (CT) and Compact Compression (CC) specimens. The stacking sequence used is [45/-45/(0/90)4]s where 45° plies on the outside efficiently prevented the buckling of the specimen to be observed, as well as plasticity of the matrix. Moreover, this layup is rather similar to real-life industrial stacking sequences. Strains fields and axes displacement were obtained using digital image correlation. Infrared images were used to follow the crack propagation during the loading of the specimen and compared to DIC and X-ray tomography crack length measurements. IR measurements studied from a qualitative point of view were thus shown to be an efficient and reliable method. GIC of the laminate GIC_lam was computed with both the ASTM-E399 and compliance methods, and finally GIC_ply was computed using a rule of mixtures. Secondary damage was detected and its effects on the energy dissipated were quantified using strain fields, X-ray and infrared images. This enabled a more accurate rule of mixtures to be redefined. The failure scenarios of all specimens were eventually exhibited. GIC_ply values in tension were found to be higher than in the literature whereas in compression it was found to be lower than in the literature, due to crack propagation being detected earlier by means of IR measurements.

Experimental characterization of the interlayer fracture toughness of FDM components

The present work is aimed at determining the inter-layer fracture toughness behavior of FDM parts. Double-cantilever beam specimens were produced and tested using already-established testing standards to capture the fracture toughness behavior. A new sample configuration was also proposed to overcome some limitations concerning sample preparation, which is also influenced by human factors. The two kinds of samples were compared to determine the suitability of the proposed solution to address the critical energy release rate in mode I crack opening. The fracture zone characteristics were investigated by ex-situ measurements using optical and scanning electron microscopy. Thermal analysis was performed during the deposition process to capture the variation and distribution of the temperature. The results indicated that the insertion of Polyimide and particularly the pause time required may alter the thermal history leading to lower polymer healing of the tested layer. This leads to an underestimation of the mechanical behavior of the tested samples. On the other hand, the proposed sample with nested spacers does not introduce artifacts in the thermal history leading to a more reliable measurement of the Interlayer Fracture Toughness.

Effect of cellulose nanofibers on the fracture toughness mode II of glass fiber/epoxy composite laminates

Cellulose nanofibers (CNFs) were used to improve the fracture toughness of glass fiber reinforced epoxy composites (GFRPs). Different CNF suspensions were prepared and sprayed onto the surface of woven glass fiber laminates. The vacuum resin transfer molding (VaRTM) process was used to manufacture the GFRP composites. End notch flexure tests were conducted to evaluate the effect of CNFs on the critical energy release rate in mode II fracture toughness GIIC. The results revealed that 0.05 wt% was the optimum concentration. The interlaminar fracture toughness GIIC was improved by 28% with the addition of 0.05 wt% of CNFs to GF/epoxy composites. Whereas 0.1 wt% of CNFs resulted in decreasing GIIC due to the uncomplete impregnation of GF with epoxy resin caused by the thicker CNF layer at the interfacial laminates. The toughening mechanisms were investigated using a field-emission electron microscope. Large epoxy deformations and shear hackles were predominant for improving the interlaminar fracture toughness of GFRP composites.

Compliance Methods For Bonded Joints: Part II - Investigation Of The Equivalent Crack Methodology To Obtain The Strain Energy Release Rate For Mode I

ABSTRACT The present work investigates the equivalent crack methodology by considering the Double Cantilever Beam (DCB) test to obtain the strain energy release rate of adhesive joints, using different compliance methods rather than the Compliance Based Beam Model (CBBM). This procedure allows the determination of the crack length based on the compliance of the specimen, which avoids crack growth monitoring during tests. The compliance values predicted by the analytical methods were studied and compared with a computational model, considering different crack lengths. Results showed that the preciseness of the crack length obtained by the equivalent crack method relies on the accuracy of the respective compliance method in predicting the load-displacement curve of a bonded double cantilever beam. The Euler–Bernoulli and Timoshenko beam models are not recommended to obtain an equivalent crack length based on the specimen’s compliance since they overestimate the actual crack length. Best crack length predictions were obtained using compliance methods based on the beam-on-elastic foundation models, including an elastic interface to model the adhesive layer joint. Similar strain energy release rate results were found for different compliance methods when using the equivalent crack methodology.

Compliance Methods For Bonded Joints: Part I - Investigation Of The Standardized Methods To Obtain The Strain Energy Release Rate For Mode I

ABSTRACT The double cantilever beam (DCB) is the most acceptable geometry to obtain the critical strain energy release rate (GIc ) of adhesive joints under Mode I. However, there are still some areas of uncertainty in the standardized compliance methods recommended by the ISO and ASTM standards in terms of accuracy in estimating the compliance of a bonded double cantilever beam and, consequently, GIc . In this work, an investigation of the standardized compliance methods for fracture characterization of bonded joints under Mode I is conducted, employing a finite element model to obtain the compliance of a double cantilever beam, considering different crack lengths. The compliance values determined from the finite element model are compared with those recommended by the standards. It is concluded that the standardized compliance methods are very sensitive to issues derived from crack length measurements. The crack length correction methodology proposed by the corrected beam theory is inadequate, which can lead to a wrong interpretation of the structure’s behavior and the structural integrity assessment. The best approach to obtain the compliance of a double cantilever beam in respect of crack length is to use a compliance calibration method, fitting an expression for the experimental curve.

Influence of the texturing quality consecutive to Abrasive Water Jet machining on the adhesive properties in mode I of 3D woven composite assemblies

The aim of this study is to analyse the suitability of Abrasive Water Jet Machining (AWJM) as a surface preparation technique for adhesive bonding of 3D woven CFRP substrates and to investigate the influence of the texture-induced quality of the adherends on the adhesive properties of the bonded joints. For this, three specimens with varying levels of texturing qualities were produced by AWJM and quantified using classical criteria such as average roughness “Ra and Sa” as well as a new criterion named “crater volume” (Cv). After adhesive bonding, the assemblies with different levels of texturing quality were subjected to Double Cantilever Beam tests to obtain their critical energy release rate in mode I (GIc), which was compared to values of bonded assemblies prepared by sanding as performed in the industrial context. For the analysis of the damage mechanisms, DCB tests were multi-instrumented with different techniques such as X-ray tomography and digital image correlation. The obtained results showed that, the evolution of GIc as a function of the textured surface quality presented a good correlation with Cv compared to the classical parameter Ra or Sa. In addition, assemblies prepared by AWJM present higher values of GIc compared to sanded ones (up to +60%), with a downward parabolic relationship between GIc and Cv. Post-mortem X-Ray tomography analysis has revealed a change in the crack propagation scenario as Cv increases.

Characterization of the Effect of Hollow Glass Beads on the Mechanical Properties of Structural Adhesives.

Adhesives are extensively used in the automotive and aeronautical industries as they enable the creation of durable and light weight joints, with exceptional strength to weight ratios. The constant search for the means of adapting the mechanical performance of adhesives to each application has led to the use of several types of fillers to change their properties. Following a study on the effect of inorganic fillers, i.e., hollow glass beads, in the failure mechanisms of single lap joint’s (SLJ), this work focuses on the response of the strength and fracture properties of structural adhesives to this filler. To this end, their tensile strength and mode I fracture properties were thoroughly analyzed by performing bulk tensile and double-cantilever beam (DCB) tests, at a quasi-static speed. The specimens were manufactured by adding different %v/v of filler to two epoxy-based crash resistant adhesives. Both adhesives have shown a negligible effect on the tensile strength, a decrease in strain at failure and critical energy release rate in mode I, as well as an increase of the Young’s modulus, for higher % in volume of hollow glass beads. These phenomena were further analyzed recurring to scanning electron microscopy, and the concept of rule of mixtures.

Characterization of the interlaminar fracture toughness of unidirectional thermoplastic composites

In this study, the critical energy release rate in mode I (G1c) for thermoplastic composites made of carbon fiber (CF) and glass fiber (GF) with a polyamide 6 (PA6) matrix is investigated. Double cantilever beam (DCB) was used as the specimen for the mode I test, and the ASTM D 5528-13 was chosen as standard. Moreover, different methodological approaches were applied by comparing different data reduction schemes from the ASTM D 5528-13 and further analytic approaches from the literature. In addition to the conducted experiments, a numerical model of the DCB test is developed and the virtual crack closure technique (VCCT) is performed on the numerical model to determine G1c for PA6-CF and PA6-GF. For the interlaminar fracture toughness G1c a value of 2.87 mJ/mm2 was determined for PA6-GF and a value of 2.16 mJ/mm2 for PA6-CF, which indicate that the use of PA6 as matrix in a composite structure leads to good resistance to damage. A comparison of the different methodological approaches showed a good agreement between the analytical approaches from the literature and the ASTM D 5528-13. In contrast, the values generated for G1c by the VCCT method were significantly higher than those of the other methods.

Prediction of the Delamination at the Steel and CFRP Interface of Hybrid Composite Part.

The purpose of this study was to predict the adhesive behavior of steel and carbon-fiber-reinforced plastic (CFRP) hybrid parts based on the cohesive zone model (CZM). In this study, the steel sheet and CFRP were joined by epoxy resin in the CFRP prepreg during the curing process, which could generate delamination at their interface because of the springback of steel or the thermal contraction of the CFRP. First, double cantilever beam (DCB) and end-notched flexure (ENF) tests were performed to obtain various adhesion properties such as the critical energy release rate of mode I, mode II (GI, GII), and critical stress (σmax). A finite element (FE) simulation was performed to predict delamination using CZM, which was also used to describe the interfacial behavior between the steel sheet and the CFRP. Finally, a U-shape drawing test was performed for the steel/CFRP hybrid parts, and these results were compared with analytical results.

Effect of liquid nitrogen freeze–thaw cycle on fracture toughness and energy release rate of saturated sandstone

To enhance the ability of tight sandstone gas extraction, liquid nitrogen (LN2) freeze–thaw cycle method can be employed to improve the physical and mechanical properties of the sandstone. Rock fracture behaviors and mechanical properties after fracturing play an important role to successfully implement reservoir stimulation. Since tight sandstone gas reservoirs are usually characterized by high water content, the influences of LN2 freeze–thaw cycle on the fracture toughness and energy-release rate of the saturated sandstone are studied in this paper. The three-point bending experiment is carried out on the notched semicircular bending sandstone samples subjected to different LN2 freeze–thaw cycle times under three different modes, that is, mode I, mixed mode (I/II), and mode II. The structure damage and facture morphology analyses are performed to explain the differences in fracturing behaviors. The energy release rate of the saturated sandstone subjected to the LN2 freeze–thaw cycle is corrected by the P-wave velocity. The experimental results indicate that the LN2 freeze–thaw cycle can promote the weakening of cementation between mineral particles and produce microcracks inside the saturated sandstone, further resulting in an increase in the roughness of the crack surface after loading failure. For all three modes, the fracture toughness and the energy-release rate gradually decrease with the increase in the LN2 freeze–thaw cycle times. For all the LN2 freeze–thaw cycles, mode I requires the minimum applied energy for the fracture propagation, while mode II requires maximum applied energy. In the three modes, the energy-release rate in mode I is the largest. Compared with mixed mode and mode II, the fracture toughness and fracture energy of mode I are more sensitive to the LN2 freeze–thaw cycle. The fracture energy depends on both the microstructure characteristics inside rocks and the mechanism of the fracture propagation. The results are helpful to better understand the initiation and propagation of cracks during the sandstone gas extraction.

Damage modelling strategies for unidirectional laminates subjected to impact using CZM and orthotropic plasticity law

In the present paper, the crashworthiness of a thick unidirectional carbon fibre reinforced polymer is investigated. This material is manufactured via compression moulding process. A Low-Velocity Impact (LVI) test is implemented on a quasi-isotropic laminate for the experimental evaluation of the energy absorption due to impact, while the internal failure mechanism is detected using Computerized Tomography (CT). Two different Finite Element (FE) models are applied to model the damage onset and propagation: firstly, a shell-based model and, secondly, a solid-based model using Cohesive Zone Method (CZM). In the CZM, the analytical modelling of the cohesive element properties is adopted, and the critical force evaluated experimentally is related to the energy release rate of mode II, and to the equivalent elastic properties of the laminate. The strength and weakness of the proposed approach in mimicking the impact behaviour and the actual failure mechanism, are discussed, and validated versus numerical simulation. The models are in good agreement with the experimental results; in fact, the relative error of the maximum force is about 4 per cent, and it occurs in the shell-based model.

Cohesive Zone Modeling for Predicting Interfacial Delamination in over mold Components

Delamination is one among the significant issues in over molding and electronic packaging. Notably, because of material compatibility and also the weak adhesion-strength of interfaces makes it complex. Typically, delamination takes place at the bimaterial interfaces. In order to predict interface delamination, the cohesive zone technique may be applied as an attainable tool. However, the proper alternative of the cohesive parameters still forms an obstacle for the general usage. The objectives of the work, analytical & numerical modeling of delamination of interfaces between molding compound and metal frames and its subsequent validation using numerical double cantilever beam test and four-point bend tests. In this work, the double cantilever beam and four-point bend tests are used to obtain the strain energy release rate of mode I and mode II values, these values are used as parameters for the cohesive zone method.

Testing method of critical energy release rate for interfacial mode II crack

The energy release rate of an interfacial crack is a basic performance parameter for characterizing interfacial failure, but there is no direct testing method for this. Therefore, a testing method of the critical energy release rate for mode II cracks was proposed in this paper. First, multiple sets of double shear specimens with different precast interfacial crack lengths were prepared, the interface shear experiments were carried out with the improved interface double shear specimens, testing devices and method, and the load–displacement curves of the specimens were obtained. Then, the load–displacement curve of each specimen was normalized, and the corresponding load–displacement curve equation, and the critical displacement or critical load were determined. Finally, the energy release rate of the interfacial mode II crack was calculated based on its definition, and the critical energy release rate was determined. As an example, the results of the double shear tests on fully-bonded fiber reinforced polymer (FRP)-concrete interface showed that the critical energy release rate is 1.10 N/mm. Compared with the experimental results, the simplified theoretical models and the empirical models with the compressive strength of concrete as the main parameter can be acceptable, and the errors are less than 20%, but the errors of the empirical models with the concrete tensile strength as the main parameter are relatively large, which are about 50%.

Loading rate dependency of strain energy release rate in mode I delamination of composite laminates

This work aims at studying the loading rate dependency of mode I delamination growth in CFRPs, using typical fracture toughness analysis through both the R-curve and the crack tip opening rate. The average SERR is a method of data reduction based on energy balance which has been previously introduced to characterize delamination growth under different types of loading conditions in a similar manner. In the present research, the application of this method was extended to further analyze the results of delamination experiments at different loading rates. Mode I delamination tests on double cantilever beam specimens were performed at displacement rates varying from standard quasi-static testing up to 400 mm/s. A clear decrease in the propagation fracture toughness as well as in the average SERR was observed at high loading rates. The reduced fracture resistance at elevated rates was physically explained in correlation with fiber bridging, fiber breakage, and matrix cleavage observed in fracture surfaces via scanning electron microscopy.

Fatigue crack growth of additively manufactured component under constant amplitude load

Additive manufacturing is used to produce complex shapes and can give optimised components under bending and torsion loads. In additive manufacturing, 3D model of the component is created using the commercially available software and then physical part is obtained using the machine which links CAD model data to manufacturing machine. This method is ideal for batch production and Just in time production methods. The main drawback of additively manufactured components is presence of micro cracks which opens up when component is subjected to repeated axial, bending and torsional loads. It is important to estimate the behaviour of the material under these loading conditions. In this paper, delamination phenomenon in additively manufactured parts is investigated. Crack initiation and growth is modelled and simulated to evaluate the rate of crack growth and energy variation at the crack tip for mode 1 and mode 2 is investigated. Stress intensity factors are computed over the crack length. Stress intensity factors for various contours are investigated. Results indicate that for a given crack length stress intensity factors varies from positive to negative for different contours. For mode 1 crack, energy release increases as the length of the crack increases but decreases after 2.5 mm of the crack to balance the newly surface created due to crack opening new surfaces. Ideally energy release rate for mode 2 should be zero but practically some amount of sliding occurs therefore low values is observed for energy release rate in mode 2.

Report on laboratory tests of sandstone and porphyry for rock fracture analysis

The paper presents the results of mechanical tests of three types of rocks from stone mines in Poland. Compression tests of cubic samples, three-point bending tests of beams, bending of beams with notch and testing of tensile strength using the quasi-Brazilian method were performed. Based on the tests, the compressive strength, tensile strength, Young's modulus, and Poisson's ratios were determined. The stress intensity factor and critical strain energy release rate in mode I were determined from the bending test of the notched beams. The determined values were used as parameters of computer models which are used to verify the authors’ method of predicting the crack propagation in the Abaqus FEA system.

Rubbery nanofibrous interleaves enhance fracture toughness and damping of CFRP laminates

Rubbery electrospun nanofibers represent a smart way for hindering delamination and enhancing damping capacity in Carbon Fiber Reinforced Polymer (CFRP) laminates, which are two of the most serious drawbacks hampering their use. Nitrile Butadiene Rubber / Poly(ε-caprolactone) (NBR/PCL) blend nanofibers, with 20‐40-60%wt of not crosslinked NBR, were interleaved in epoxy-based CFRPs to evaluate their effect on the final composite performance. CFRPs with rubbery mats show a significant increase of the energy release rate in Mode I, both at initiation and propagation stages (+480% and +340%, respectively), thanks to NBR/PCL blend ability to promote high matrix toughening of the fragile epoxy resin. In Mode II a maximum improvement of about 30% was achieved. The presence of highly damping NBR component widens the composite energy dissipation window below room temperature, enhancing the CFRP damping. Similar results were obtained with two different epoxy resins, and the effect of the layering sequence was also discussed. NBR percentage in nanofibers and nanofibrous mats amount may strongly affect the CFRP maximum operating temperature. Nanofibers can be positioned, during lamination, in the critical regions where interlaminar stresses are mostly concentrated due to geometric discontinuities providing a flexible approach to localized modification of laminates.

Mode II interfacial fracture characterization of foam core sandwich materials at elevated temperatures: the effects of frictional stresses between the crack edges

In recent years, composite sandwich material has been widely used in civil engineering due to its high strength to weight ratio, high stiffness to weight ratio and anti-corrosion ability. However, the existing research studies indicated that interfacial delamination between skins and core was a common failure mode for this kind of material, which seriously threatens the durability and safety of structures. Furthermore, up to now, there are no research studies investigating the effects of elevated temperature on the interfacial fracture and damage behavior of the sandwich material. To address the above questions, this paper investigated the effects of elevated temperature on mode II interfacial fracture response of foam core sandwich materials by adopting the end-notched flexure method. Test results showed that the loads and the strain energy release rate decreased under the same crack length as the temperature increased. In the meantime, the corresponding analytical model, considering the effect of frictional stresses between the crack edges, has been proposed to predict the interfacial strain energy release rate. The comparison of the analytical and experimental results revealed that the analytical model could accurately predict the strain energy release rate of mode II interfacial fracture of foam core sandwich materials at elevated temperatures.

Enhancement of Fracture Properties of Composite Laminate with Si C Additive

ASTM standards for short beam test, double cantilever beam and end notched specimen test are followed to compare control specimen with different percentage of Si C test data. Present study shows interlaminar shear strength (ILSS) and delamination fracture toughness values of multilayered composite laminate can be enhanced considerably with the use of Si C admixture in epoxy resin system as nonpolar elements compatible with to polar glass fiber. With respect to control specimen one percentage by weight of Si C w.r.t resin can bring up the ILSS value by as much 70% while the DCB test data on the critical energy release rate of mode I increases by 85% and mode II toughness value becomes double for 1% by weight of Si C. The bidirectional cloth provides more resistance for mode-I delamination fracture toughness when compared to UDL reported in literature and hence for higher fracture properties. The study is useful for design of rocket nozzles and input required for the cohesive zone model to assess the residual strength of composite structures with of delamination.