Calculation Of Fracture Energy Research Articles

Fracture Energy Determination of Wedge-opening Double Cantilever Beam Tests

ABSTRACT Adhesive fracture energy is often measured using the double cantilever beam (DCB) test method. However, opening a DCB specimen using a wedge differs the direction of the applied load from that of standard methods. The additional moment due to the longitudinal load alters the load-displacement-crack length relationship, requiring modifications in fracture energy calculation. The energy release rate (ERR) approach and the J-integral approach have been proposed to evaluate the fracture energy in wedge-opening DCB tests. However, these theories have limitations regarding wedge angles. In this study, we extended these theories to accommodate arbitrary wedge angles and performed numerical analyses to evaluate the accuracy of the theories. When the additional moment effect is neglected, the more obtuse the wedge angle and the thinner the adherend, the greater the error in the ERR. The error was over 5% when the wedge angle exceeded 90°. However, using the proposed ERR method, the error was reduced to less than 2% for all the wedge angles. When pin blocks were introduced into the DCB specimen, the additional moment effects increased the error to more than 5% even using the proposed ERR method. In this case, the modified J integral method yielded the lowest error results.

A new approach for fracture process zone evaluation

The study presents a novel method for identifying and monitoring the fracture process zone and its impact on cracking parameters, such as damage rate and fracture energy. Concrete samples subjected to a Wedge Splitting Test were investigated. Digital Image Correlation, a full-field measurement technique, was utilized to measure the experimental displacement fields at various scales. The experimental measurements, optimized through a Newton-Raphson iterative adjustment procedure, revealed the presence of a damaged zone accompanying the cracking process. This analysis also enabled the estimation of the material damage rate and provided a more realistic assessment of cracking parameters by integrating the entire process of damage and macro-cracking into the calculation of fracture energy. The results suggest that the appearance of a fracture process zone correlates with a reduction in the material’s hardness downstream of the crack propagation front.

Mixed mode fracture parameters and fracture characteristics of diorite using cracked straight through Brazilian disc specimen

In this study, the cracked straight through Brazilian disc (CSTBD) specimen was applied to study the I/II mixed mode static fracture of diorite. The fracture load and fracture toughness for different prefabricated crack angles β were determined. The fracture and morphological characteristics were analyzed using digital image correlation (DIC), scanning electron microscope (SEM) and 3D topography scanning techniques. In addition, the key fracture parameters such as fracture energy, crack mouth opening displacement (CMOD) and fracture process zone (FPZ) were characterized, and a fracture energy calculation method considering the primary crack growth was proposed. The results show that the fracture mechanical behavior and fracture trajectories are controlled by the crack angle. At the millimeter measurement scale, the fractal dimensions of fracture surfaces do not vary with crack angle. Further SEM observation shows that intergranular fracture and transgranular fracture are the dominate micro fracture modes of fracture surfaces under mode I and mode II loading, respectively. With the increase of crack angle, the fracture energy first increases and then decreases, while the allowable CMOD decreases monotonically and even appears negative when β ≥ 45°. Based on the displacement gradient method, the calculated width of FPZ for the mode I fracture specimen at peak load is 0.5–1.4 mm and the length is 2.66 mm. Finally, the stress-based and strain-based fracture criteria were modified. It is found that the proposed EEMTSN criterion has the best prediction effect on the mixed mode fracture toughness of diorite.

Effect of interface roughness on fracture energy and fracture process zone of rock‐concrete specimens

AbstractTo investigate the effect of interface roughness on the fracture behaviors of rock‐concrete specimens, the acoustic emission (AE) and digital image correlation (DIC) techniques are used to monitor the fracture process of the granite‐concrete specimens with different interfacial roughnesses under three‐point bending (TPB) load. The initial fracture toughness of rock‐concrete specimens with different interfacial roughnesses is calculated. The characteristic parameters of the AE are also discussed. Based on the fracture mechanics theory, the transient critical response equation and the stress‐crack opening displacement model for the rock‐concrete interface crack opening displacement (COD) based on micro–macro crack interactions are established. The determination of the model parameters is achieved by the DIC technique, and the fracture energies of interfaces with different roughnesses are calculated based on the model with the determined parameters. The validity of the model is verified by comparing the calculation results with those from the existing fracture energy calculation methods.

Investigation of polyurethane toughened epoxy resins for composite cryotank applications. Part II: Theoretical analysis of toughening mechanisms

Based on the phase separation phenomenon, cryogenic mechanical behaviors and toughening effects for polyurethane toughened epoxy (PU/EP) systems demonstrated in our previous work (Part I), as a followed investigation, this study aims to conduct theoretical analysis of temperature-dependent toughening mechanisms. First, 3D finite element unit cells of PU/EP systems with random particle distributions are established to evaluate the maximum stress concentration factor for the theoretical fracture energy calculation. Then, the temperature-dependent fracture energies of PU/EP systems are investigated quantitatively for the first time, and the theoretical results are shown to be in good agreement with the experimental results. From 10 phr to 40 phr, the particle bridging contribution rises from 47.3% to 65.5%, which elucidates that the particle bridging plays a major role in determining the fracture energy at room temperature. As the temperature decreases from RT to −183°C, taking PU10/EP as an example, the untoughened matrix proportion goes up from 30.9% to 65.2%; the particle bridging contribution decreases from 51.8% to 27.8%; the shear banding contribution drops from 17.3% to 7%. This work explores temperature-dependent toughening mechanisms in depth and offers an accurate quantitative evaluation of fracture energies for toughened epoxy matrix for composites cryotank design.

Mode I tensile fracture behavior of adhesively-bonded metal–metal, metal–CFRP, and CFRP–CFRP bi-material combinations analyzed by size effect method

Understanding the adhesive and interfacial fracture is important for developing better adhesive performance in bi-material joints, i.e. adhesive joint between dissimilar materials. However, to characterize the fracturing behavior of various adhesively-bonded materials, it was shown in this work that the Mode I fracture energies estimated from conventional methods (e.g., work-of-fracture, (modified) compliance calibration method, (modified) beam theory, etc.) can be strongly affected by adherend thickness, adhesive bond length, and adherend material type. Consequently, the proper understanding of fracturing in bi-material joints has been hindered since the estimated fracture energies can exhibit unreasonable difference among various material combinations depending on the method of fracture energy calculation. This has led to confusion in the literature due to the unfair comparison of these non-objective results estimated by leveraging conventional methods on the specimens with different geometries or dissimilar adherend materials.This work introduced the size effect method to adhesively-bonded joints and compared the results with conventional methods of calculating the Mode I fracture energies of metal–metal, metal–CFRP, and CFRP–CFRP material combinations via Double Cantilever Beam (DCB) tests. The results showed that the estimated fracture energies obtained using the size effect method were not dependent on the specimen geometries, whereas conventional methods were strongly dependent on specimen geometry for most material combinations. The size effect method allowed objective comparison particularly on the interfacial fracturing between metal/adhesive and CFRP/adhesive combinations. The difference was further explained by and correlated with the damage morphology on the material surface after failure, which was quantified by three-dimensional profilometer.

Investigations on fatigue properties of red sandstone under positive and negative pure bending loads

Brittle materials such as rock and concrete may be subjected to positive and negative cyclic loading effects such as earthquakes and construction disturbances, and bending damage is one of the most likely forms of damage. A four-point bending fixture was designed to conduct fatigue tests with positive and negative stress ratios under pure bending to investigate the influence of cyclic loading on the form and mechanism of damage. The fracture energy calculation equation based on crack mouth opening displacement (CMOD) was derived, and the fracture criterion based on fracture toughness and fracture energy was established, which was in good agreement with the experimental results. Under the pure bending fatigue load, the hysteresis loop of the P-CMOD curve shows a loose-dense-loose law, and the damage curve can be divided into three stages of initial, stable, and accelerated law. Stress level and stress ratio are two main factors affecting fatigue life. The fatigue life of negative stress ratios is greater than that of positive stress ratios because there is a crack closure process in negative stress ratios, which affects the fatigue life. The final damage occurs for positive stress ratio specimens when the fatigue dissipation energy is greater than the static fracture energy. Static CMOD starting and final values were introduced to define the fatigue damage variables, and a damage evolution model was established better to simulate the evolution with positive and negative stress ratios.

Micro Fracture Behavior of Composite Honeycomb Sandwich Structure.

To study the influence of structure size and composite forms on the mechanical properties of the composite double honeycomb sandwich structure, a composite double honeycomb sandwich structure was initially designed. The dynamic response of a composite double-layer honeycomb sandwich structure under high-speed impact was studied through theoretical analysis and numerical simulation. Ls-dyna software was used to simulate the initially designed composite structure. According to the numerical simulation results and the proposed method for calculating the fracture energy of the composite double honeycomb sandwich structure, the effects of different composite forms on the mechanical properties were analyzed. The results show that the proposed fracture energy calculation method can effectively describe the variation trend of the honeycomb structure and the micro-element fracture situation in the valid time. The fracture energy curve has a high sensitivity to cell density and material, and the strength of the top core has a great influence on the overall energy absorption. Compared with the traditional honeycomb protection structure, the energy absorption of the initially designed composite honeycomb sandwich structure was improved effectively.

Fracture energy characterisation of a structured interface by means of a novel J-Integral procedure

In the present investigation, a J-Integral formulation for non-flat crack paths, in the framework of the cohesive zone model, is developed. The formulation allows fracture energy properties in a direction that is not necessarily coplanar with the global crack advance to be analysed. Specifically, the effective fracture energy, [Formula: see text], has been examined based on the horizontal projection of the crack advance, [Formula: see text] (also called effective crack length). The use of [Formula: see text] is convenient in several situations as the case of patterned interfaces in adhesive joints. Finite-element analysis of double cantilever beam specimens including a trapezoidal patterned interface were employed to check the accuracy of this new definition of the contour integral. Post-process of the finite-element model, including those variables involved in the fracture energy calculation, is discussed together with some considerations that distinguish the energy evaluation procedure for flat profiles from structured designs. Finally, [Formula: see text] values obtained using the modified J-Integral formulation are compared with [Formula: see text] values obtained from the load–displacement curve method for comparison purposes.

Wedge Splitting Test on Douglas genotypes using an integrated mixed-mode approach

The objective of this study is to estimate the influence of mixed mode on the global fracture energy. The experimental tests were carried out using three Douglas genotypes. In order to evaluate the fracture parameters the Wedge Splitting Tests were performed. The fracture parameters were estimated from the optical measurements coupled with numerical and analytical approaches. Firstly, the fracture energy was estimated from the work of fracture calculated from the splitting force – Crack Opening Displacement curve. In this case, the Crack Opening Displacement was measured by means of Mark Tracking method. Secondly, the fracture parameters and, consequently the fracture energy was evaluated using an integrated mixed mode approach. In this second case, the experimental measurements were performed by Digital Image Correlation. The fracture energy corresponding to opening and shear modes was calculated by using an adjustment procedure coupled with Stress Intensity Factor calculation and the phase angle. This second approach allowing the calculation of fracture energy without the influence of experimental noises. The results show that the proposed integrated mixed mode approach allows evaluate the part of each mode in the fracture process.

Fracture Simulation of Structural Glass by Element Deletion in Explicit FEM

In finite element simulation of glass cracking for practical engineering problems, the method of element deletion is often used despite its shortcomings. With this technique, an element is removed from the system upon reaching a certain failure criterion. Many different formulations for the failure behaviour of an element are possible, differentiated by the physical correctness of their representation and by their implications on the numerical stability of the calculation. In this paper, three failure models are characterised by use of a unit element model and evaluated for the drop weight impact on a monolithic glass plate. Several issues can be identified: (i) incorrect calculation of fracture energy for large-sized elements; (ii) shock wave propagation upon deletion of an element leading to spurious failure of other elements; (iii) unrealistic crack formation when the failure model does not account for crack directionality. A crack delay failure model for structural glass is proposed to avoid the aforementioned problems. This failure model uses only physical material properties as input and limits the damage rate during fracture.

An In-Situ X-Ray Microtomography Study of Split Cylinder Fracture in Cement-Based Materials

In an effort to quantify microstructure-property relationships, three dimensional imaging experiments were conducted on small cylinder specimens subjected to split cylinder fracture. 3-D images were made using synchrotron-based x-ray microtomography, and the experiments were conducted with an in-situ frame such that a specimen could be examined while under load at varying degrees of damage. The specimens were made of fine-grained portland cement mortar and 0.5 mm glass beads, which served as aggregates. The diameter of the specimens was 5 mm. 3-D image analysis routines were developed or adapted to characterize microstructure and internal damage, which could then be related to bulk splitting strength and fracture energy. For fracture energy calculation, crack surface area could be measured in a way that accounted for roughness, branching, and fragmentation. Results showed that, for the specimens tested, aggregate surface roughness had little effect on strength but significant effect on fracture energy. Split cylinder strength showed correlation with specimen porosity, although there was considerable scatter. Strength did not correlate with maximum flaw size, although flaw location was not evaluated.

Strain Measurements within Fibreboard. Part III: Analyzing the Process Zone at the Crack Tip of Medium Density Fiberboards (MDF) Double Cantilever I-Beam Specimens

This paper is the third part of a study dealing with the mechanical and fracture mechanical characterization of Medium Density Fiberboards (MDF). In the first part, an analysis of internal bond strength testing was performed and in the second part MDF was analyzed by means of the wedge splitting experiment; this part deals with the double cantilever I beam test, which is designed for measuring the fracture energy as well as stress intensity factor in Mode I. For a comparison of isotropic and orthotropic material behavior, finite element modeling was performed. In addition to the calculation of fracture energy the stress intensity factor was analyzed by means of finite elements simulation and calculation. In order to analyze strain deformations and the process zone, electronic speckle pattern interferometry measurements were performed. The results revealed an elongated process zone and lower results for KIC if compared to the wedge splitting experiment. The Gf numbers are higher compared to the wedge splitting results and can be explained by the thicker process zone formed during the crack propagation. The process zone width on its part is influenced by the stiff reinforcements and yields a similar crack surface as with the internal bond test.

Analysis of Fracture in Aluminum Joints Bonded with a Bi-Component Epoxy Adhesive

Abstract Adhesive bonding is a viable alternative to traditional joining systems (e.g., riveting or welding) for a wide class of components belonging to electronic, automotive, and aerospace industries. However, adhesive joints often contain flaws; therefore, the development of such technology requires reliable knowledge of the corresponding fracture properties. In the present paper, the candidate mode I fracture toughness of aluminum/epoxy joints is determined using a double cantilever beam fracture specimen. A proper data reduction scheme for fracture energy calculation has been selected based on the results of a sensitivity analysis. Furthermore, a scanning electron microscope is used in order to explore the locus of failure. Finally, the experimental findings are assessed by means of numerical simulations of crack growth carried out using a cohesive zone model.

Strength of Sawn Lumber and Wood Composite Dowel Connections Loaded Perpendicular to Grain. II: Fracture Mechanics Equations

Splitting failure modes of perpendicular to grain bolted connections have received little attention when compared to splitting modes in parallel to grain connections. Previous research by the authors tested a series of single bolt, double shear perpendicular to grain connections of machine stress rated (MSR) lumber, laminated veneer lumber (LVL), and parallel strand lumber (PSL). Many of the experimental tests resulted in failure by splitting. Two fracture mechanics based models for connections proposed elsewhere were applied. Input parameters for the models were generated by testing matched sections to the connection strength samples. Input properties for the Van der Put model included shear modulus and Mode I fracture energy. Inputs for the Jensen model included shear modulus, modulus of elasticity, Mode I fracture energy, and tension perpendicular to grain strength. Mode I fracture energy of PSL was markedly greater than the energy associated with MSR Lumber and LVL. The Van der Put model overpredicted the experimental connection strength by at least 77%. The Jensen model was found to most accurately predict the connection strength over the entire range of configurations tested. Comparing the Van der Put and Jensen models to the previous work using the national design specification, the Jensen model performed the best in terms of accuracy. The tension perpendicular to grain strength and the method of fracture energy calculation may be important parameters for the capacity of perpendicular to grain loaded wood members.

A theoretical investigation of the fracture energy of heterogeneous brittle materials

It is shown that the fracture surface energy of heterogeneous brittle materials (polycrystals, composites, ceramics, rocks) depends on their microstructural characteristics, namely the fractal properties of the network of microcracks. A quantitative approach for the calculation of fracture energy from microcrack network fractal parameters is suggested. Very high experimental values of fracture energy for heterogeneous brittle materials can be easily explained in the framework of the fractal model.

The interlaminar fracture of organic-matrix, woven reinforcement composites

A study has been made of the interlaminar (transverse) fracture of glass and graphite fabric composites. A double cantilever beam specimen was used and was width-tapered for constant change in compliance with crack length so that the fracture energy calculation is independent of crack length. It was found that the interlaminar fracture energy could be significantly increased either by the addition of elastomeric toughening agents to the epoxy matrix or by using a thermoplastic matrix resin instead of an epoxy. The largest increase in interlaminar fracture energy (approximately eight-fold) was obtained for an epoxy matrix/graphite fabric composite by the addition of elastomeric modifiers.

Fracture testing and toughening of epoxy resins

AbstractThe tapered cantilever cleavage and the single‐edge‐notch tension fracture toughness tests have been shown to give similar results for several cured epoxy resin systems. Methods for the calculation of fracture energy and critical stress intensity factors are described and discussed. These tests have been used to study the influence of rubber modifiers (“Hycar” CTBN and “Blendex” 311) on the toughness of a conventional epoxy resin (“Epikote” 828) reacted with anhydride curing agents. The modifiers used increase fracture energies and stress intensity factors by factors of approximately 5 and 2 respectively.