Examination of the 4-ENF test for measuring the mode III R-curve of wood

The four-point bend end-notched flexure (4-ENF) test, which was originally developed for measuring the mode II R-curve, is thought to be applicable for measuring the mode III R-curve. In this study, a 4-ENF fracture test of spruce was conducted for obtaining the mode III R-curve, and the test method was numerically and experimentally analyzed. In the numerical analysis, three-dimensional finite element calculations were conducted to determine the distribution of the strain energy release rate along the delamination front by the virtual crack closure technique (VCCT). In the experimental analysis, the mode III R-curve was examined by the modified beam theory and compliance calibration methods of data reduction, which have been conventionally used for analyzing the mode I or mode II R-curve. In addition to these conventional data reduction methods, the strain at each loading point was measured, as was the loading-line displacement and critical load for crack propagation, and the R-curve was obtained by the combination of loading-line compliance, load-longitudinal strain compliance, and critical load for crack propagation, which is named the “compliance combination method”. The finite element analyses suggested that the pure mode III fracture state existed in the mid-section of the specimen in spite of the existence of a small mode II component at the free edges of the delamination front, and the mode III strain energy release rate component calculated by the VCCT coincided well with those obtained by the data reduction methods examined here. The actual R-curve obtained by the compliance combination method coincided well with those by the modified beam theory and compliance calibration methods when the strain was appropriately measured. From these results, therefore, the 4-ENF fracture test is a promising means for obtaining the mode III R-curve of wood.     

Tapered beam on elastic foundation model for compliance rate change of TDCB specimen

A modified beam theory is developed to predict compliance rate change of tapered double cantilever beam (TDCB) specimens for mode-I fracture of hybrid interface bonds, such as polymer composites bonded to wood. The analytical model treats the uncracked region of the specimen as a tapered beam on generalized elastic foundation (TBEF), and the effect of crack tip deformation is incorporated in the formulation. A closed-form solution is obtained to compute the compliance and compliance vs. crack length rate change. The present TBEF model is verified with finite element analyses and experimental calibration data of compliance for wood-wood and wood-composite bonded interfaces. The compliance rate change can be used with experimental critical fracture loads to determine the respective critical strain energy release rates or fracture toughness of interface bonds. The present analytical model, which accounts for the crack tip deformation, can be efficiently and accurately used for compliance and compliance rate-change predictions of TDCB specimens and reduce the experimental calibration effort that is often necessary in fracture studies. Moreover, the constant compliance rate change obtained for linear-slope TDCB specimens can be applied with confidence in mode-I fracture tests of hybrid material interface bonds.     

Mode I and mode II initiation fracture toughness and resistance curve of medium density fiberboard measured by double cantilever beam and three-point bend end-notched flexure tests

Using specimens of medium density fiberboard, double cantilever beam and three-point bend end-notched flexure tests were conducted to obtain the mode I and mode II initiation fracture toughness and resistance curve for in-plane and through-the-thickness systems. The mode I initiation fracture toughness was smaller than that of mode II for the in-plane crack systems, but this tendency was inverse for the through-the-thickness systems. The fracture toughness increased during the crack propagation because of the significant fiber bridgings induced between the crack surfaces, but the increase of the mode I propagation fracture toughness was moderated after the crack reached a certain length. In contrast, the mode II propagation fracture toughness continuously increased during the crack propagation.     

Prestandardization study on mode I interlaminar fracture toughness test for CFRP in Japan

This paper summarizes results from a series of interlaboratory round robin tests (RRTs) performed in order to establish a JIS standard for mode I interlaminar fracture toughness test using double cantilever beam (DCB) specimens. For the case of unidirectional laminates, brittle and toughened CF/epoxy, and CF/PEEK systems were used. Only a brittle CF/epoxy system was used for woven laminates. The round robin tests were conducted with two main aims: first, to examine the influence of starter films and the precracking condition on the initial mode I fracture toughness values; and second, to establish the definition of initial fracture toughness. Polyimide starter films stuck to the epoxy matrix, and caused unstable crack growth from starter films. Comparison of the tests with and without mode I precracks from starter films indicated that tests with precracks gave lower values of initial fracture toughness. The definition of initial fracture toughness values was discussed, based on the reproducibility. A 5% offset point was recommended as the initial fracture toughness from the RRT results. The influence of loading apparatus, data reduction methods, etc. was also discussed.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

A new mode I fracture test for composites with translaminar reinforcements

A new test method is presented for Mode I delamination fracture toughness testing of laminated composites containing a high density of stitches or translaminar reinforcements. The test set up, which is similar to the standard Double Cantilever Beam test, induces an axial tension in the specimen in addition to the transverse forces responsible for propagation of delamination. The tensile stresses reduce the compressive stresses in the vicinity of the crack tip caused by the large bending moments required for crack propagation. The nonlinear differential equations of equilibrium of the new specimen are solved using an iterative procedure to obtain the strain energy release rate as a function of load and crack length. Experiments were conducted using carbon/epoxy specimens containing 6.2 stitches per square centimeter (40 stitches per square inch). Results include Mode I fracture toughness, crack tip bending moment, transverse deflection and slope as a function of crack length. It is found that the apparent fracture toughness of the specimens tested remains constant as the stitches break and crack propagates, and is about sixty times that of unstitched specimens.     

Equivalent crack based analyses of ENF and ELS tests

Equivalent crack based data reduction schemes have been recently proposed for mode II interlaminar fracture tests. These methods avoid the difficulties in monitoring crack propagation throughout the test, as the experimental compliance data is used to calculate the crack position. However, their accuracy has not been demonstrated. In this paper, application of equivalent crack approaches to End-Notched Flexure and End-Loaded Split tests was studied numerically. A cohesive zone damage model based on developed interface finite elements was used. Equivalent crack methods were found to be very accurate for both specimens, while classical beam theory based data reduction schemes underestimated fracture toughness.     

Numerical analysis of the ENF and ELS tests applied to mode II fracture characterization of cortical bone tissue

The objective of this work is to verify numerically the adequacy of the ENF and the ELS tests to determine the fracture toughness under mode II loading of cortical bovine bone tissue. A data‐reduction scheme based on the specimen compliance and the equivalent crack concept is proposed to overcome the difficulties inherent to crack monitoring during its growth. A cohesive damage model was used to simulate damage initiation and growth, thus assessing the efficacy of the proposed data‐reduction scheme. The influences of the initial crack length, local strength and toughness on the measured fracture energy were analysed, taking into account the specimen length restriction. Some limitations related to spurious influence on the fracture process zone of the central loading in the ENF test, and clamping conditions in the ELS test were identified. However, it was verified that a judicious selection of the geometry allows, in both cases, a rigorous estimation of bone toughness in mode II.     

A new jig for mode II interlaminar fracture testing of composite materials under quasi-static and moderately high rates of loading

While it is still debated whether a pure mode II interlaminar fracture can physically exist in composites, several test methods have been proposed for its characterization. Lack of agreement between the results obtained with different test configurations has been attributed to the use of inconsistent data reduction schemes or inadequate correction factors used to correct for, e.g. the large deformations occurring with some tough modern materials.Aim of this work was to design a new jig that could provide an as pure as possible mode II crack initiation in unidirectional composites materials, that would allow a direct determination of fracture toughness, i.e. requiring almost no assumption for data reduction nor side effects correction and could be amenable to being used under impact as well as quasi-static loading conditions.The geometry of the system was designed in order to obtain great compactness, i.e. reduced masses and contained volume, making it usable with drop-weight testing machines, but at the same time enough stiffness to prevent flexural moments from closing or opening the crack faces, so granting the purity of the wanted mode, mode II, of loading. The compactness of the jig plus specimen system and the rigid confinement to which the composite specimen is subjected also grant that quite small displacements and overall deformations are reached at fracture.A static finite element analysis was conducted to optimize the jig geometry and is discussed here. Preliminary numerical and experimental results obtained with moderately high rate tests are also presented. The method employed for data reduction is based on the experimental calibration of the compliance and it is quite straightforward.     

Improving fracture toughness of dental nanocomposites by interface engineering and micromechanics

The fracture toughness of dental nanocomposites fabricated by various methods of mixing, silanization, and loadings of nanoparticles had been characterized using fatigue-precracked compact-tension specimens. The fracture mechanisms near the crack tip were characterized using atomic force microscopy (AFM), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). The near-tip fracture processes in the nanocomposties were identified to involve several sequences of fracture events, including: (1) particle bridging, (2) debonding at the poles of particle/matrix interface, and (3) crack deflection around the particles. Analytical and finite-element methods were utilized to model the observed sequences of fracture events to identify the source of fracture toughness in the dental nanocomposites. Theoretical results indicated that silanization and nanoparticle loadings improved the fracture toughness of dental nanocomposites by a factor of 2-3 through a combination of enhanced interface toughness by silanization, crack deflection, as well as crack bridging. A further increase in the fracture toughness of the nanocomposites can be achieved by increasing the fracture toughness of the matrix, nanofilled particles, or the interface.     

Change of fracture mode in Charpy toughness transition temperature range

Abstract

A transition layer of width 5 - 10 μm was found on the boundary between ductile and brittle fracture for Charpy V notch specimens in the transition temperature range of a structural steel having a microstructure of polygonal ferrite -pearlite. The fracture mode in the transition layer was shearing with occasional submicrometre dimples. From tensile tests on notched specimens, the cleavage fracture stress and flow stress by ductile decohesion were determined. Based on the experimental data and the assumption that the volume of metal involved in the plastic deformation during fracture was related to the volume of the dimples, it was deduced that the transition layer width represents the size of the plastic zone immediately before cleavage initiation. The crack opening displacement and the crack tip radius for the change of fracture mode were calculated.     

Experimental and Numerical Investigation of Mixed-Mode Interlaminar Fracture of Carbon-Polyester Laminated Woven Composite by Using Arcan Set-up

Composite materials are widely used in marine, aerospace and automobile industries. These materials are often subjected to defects and damages from both in-service and manufacturing process. Delamination is the most important of these defects. This paper reports investigation of mixed-mode fracture toughness in carbon–polyester composite by using numerical and experimental methods. All tests were performed by Arcan set-up. By changing the loading angle, α, from 0° to 90° at 15° intervals, mode-I, mixed-mode and mode-II fracture data were obtained. Correction factors for various conditions were obtained by using ABAQUS software. Effects of the crack length and the loading angle on fracture were also studied. The interaction j-integral method was used to separate the mixed–mode stress intensity factors at the crack tip under different loading conditions. As the result, it can be seen that the shearing mode interlaminar fracture toughness is larger than the opening mode interlaminar fracture toughness. This means that interlaminar cracked specimen is tougher in shear loading condition and weaker in tensile loading condition.     

Fracture mechanism of AZ31 magnesium alloy processed by equal channel angular pressing comparing three point bending test and tensile test

A commercial magnesium alloy, AZ31 in hot-rolled condition, has been processed by equal channel angular pressing (ECAP) to get microstructure modified. Uniaxial tensile tests were conducted along the rolling/extrusion direction for as-received AZ31 alloy and ECAPed AZ31 alloy. Then, three point bending fracture tests were conducted for specimens with a pre-crack perpendicular to the extruded direction. Digital image correlation (DIC) technique was adopted to determine the deformation field around the crack tip. The fracture surfaces of the failed specimens after tensile tests and fracture tests were observed by Scanning Electron Microscope (SEM). To explore the deformation mechanism, the microstructure and texture of different regions on the deformed specimens were examined through electron backscatter diffraction (EBSD). The results show ECAP process improves both the tensile elongation and fracture toughness of AZ31 alloy. Different from the slip dominated deformation mechanism in the tensile test, deformation twinning presents in the deformation zone adjacent to the crack tip in the three point bending fracture tests. The fracture surface is characterized by co-occurrence of dimple and cleavage features.     

Comparison of failure mechanisms between rubber-modified and unmodified epoxy adhesives under mode II loading condition

The effect of rubber modification on fracture toughness of adhesive joints under mode II loading condition was investigated in comparison with that under mode I loading, wherein the two adhesives rubber-modified and unmodified were used. To evaluate the fracture toughness on the basis of R-curve characteristics under mode II loading condition, four-point bend tests had been conducted for the adhesively bonded end-notched flexure (ENF) specimens. Thus obtained R-curves revealed the following trend: its behavior did not appear for the unmodified adhesive, whereas the rubber-modified adhesive exhibited a typical behavior. In the initial stage of crack propagation, G _IIC of the rubber-modified adhesive is lower than that of the unmodified adhesive, but becomes greater in the range of Δa > 25 mm. Nevertheless, the significant improvement of the fracture toughness with the rubber modification under mode I loading condition was not observed under mode II loading. Moreover, FEM analysis was made to elucidate the relation between the above fracture behavior and stress distributions near the crack tip. The results gave the reasonable relationship between evolution of plastic zone and the area with high void-fraction as well as the R-curves behavior. In addition, macroscopic and SEM observations for the fracture surfaces were also conducted.     

Fracture characterization of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending

A combined analytical and experimental approach is presented to characterize both mode-II and mixed mode fracture of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending load, and closed-form solutions of compliance and energy release rate of the mode-II (four-point symmetric end-notched flexure) and mixed (four-point asymmetric end-notched flexure) mode fracture specimens are provided. The transverse shear deformation in each sub-layer of bi-material bonded beams is included by modeling each sub-layer as an individual first order shear deformable beam, and the effect of interface crack tip deformation on the compliance and energy release rate are taken into account by applying the interface deformable bi-layer beam theory (i.e., the flexible joint model). The improved accuracy of the present analytical solutions for both the compliance and energy release rate is illustrated by comparing with the solutions predicted by the conventional rigid joint model and finite element analysis. The fracture of Carbon fiber-reinforced polymer-concrete bonded interface is experimentally evaluated using both the four-point symmetric and asymmetric end-notched flexure specimens, and the corresponding values of critical energy release rates are obtained. Comparisons of the compliance rate-changes and resulting critical energy release rates based on the rigid joint model, the present theoretical model, and numerical finite element analysis demonstrate that the crack tip deformation plays an important role in accurately characterizing the mixed mode fracture toughness of hybrid material bonded interfaces under four-point bending load. The improved solution of energy release rates for the four-point symmetric and asymmetric end-notched flexure specimens by the flexible joint model can be used to effectively characterize hybrid material interface, and the fracture toughness values obtained for the Carbon fiber-reinforced polymer-concrete interface under mode-II and mixed mode loading can be employed to predict the interface fracture load of concrete structures strengthened with composites.     

A fracture mechanics analysis of cutting and machining

The process of cutting and machining is analysed using concepts developed in the fracture analysis of beam specimens. Increasing cutting forces and decreasing tool rake angles lead to a sequence of deformation processes from elastic bending to elastic-plastic bending and finally to shear yielding in the chip. The conditions for each mode of deformation are identified. Fracture toughness is included in the analysis as is, in addition, the notion of root rotation at the crack tip. Under some circumstances this gives rise to the condition of the tool tip touching the crack tip during which energy is transferred directly to the fracture process. The tool-chip interface is characterised by Coulomb friction and by the inclusion of an adhesion toughness to model the effects of hot polymeric chips sticking to the rake face of the tool. The combined effects of bending and shearing leading to chip curling and coiling are also analysed.     

Plastic deformation around the tip of a stopped brittle crack in the Robertson test with a temperature gradient

Robertson tests with imposed temperature gradients were carried out to investigate crack stopping in structural steels. Macroscopic fracture toughness in plane strain and plane stress conditions were evaluated using linear elastic fracture mechanics to study the effect of various testing conditions. Both values were expected to be almost equal. On the other hand, microscopic fracture toughness was then deduced from the concept of maximum plastic deformation ahead of the stopped crack tip. The macroscopic and the microscopic fracture toughness agreed well.

The fracture toughness for arrest is shown to depend on extent of plastic deformation at some distance ahead of the stopped crack tip. In consequence, the shear lip on the fracture surface is likely to play only a secondary role in causing arrest.     

Face/core debond fatigue crack growth characterization using the sandwich mixed mode bending specimen

Face/core fatigue crack growth in foam-cored sandwich composites is examined using the mixed mode bending (MMB) test method. The mixed mode loading at the debond crack tip is controlled by changing the load application point in the MMB test fixture. Sandwich specimens were manufactured using H45 and H100 PVC foam cores and E-glass/polyester face sheets. All specimens were pre-cracked in order to define a sharp crack front. The static debond fracture toughness for each material configuration was measured at different mode-mixity phase angles. Fatigue tests were performed at 80% of the static critical load, at load ratios of R = 0.1 and 0.2. The crack length was determined during fatigue testing using the analytical compliance expression and verified by visual measurements. Fatigue crack growth results revealed higher crack growth rates for mode I dominated loading. For specimens with H45 core, the crack grew just below the face/core interface on the core side for all mode-mixities, whereas for specimens with H100 core, the crack propagated in the core or in the face laminate depending on the mode-mixity at the debond crack tip.     

Micromechanism of improvement in crack initiation and propagation toughness of a Ti–Al–Sn–Zr–Mo alloy by coarsening prior β-grains

Abstract

Instrumented Charpy V impact tests and static and dynamic fracture toughness tests were carried out on Ti–6Al–2Sn–4Zr–6Mo alloys in which the prior β-grain size was varied by heat treatment. The effect of microstructure on the toughness was then examined. With increasing prior β-grain size, the elongation, crack initiation, and particularly propagation toughness increased and the strength decreased slightly. The increase in crack initiation toughness was caused mainly by the increase in Widmanstätten α-lath size or spacing, while the increase in crack propagation toughness was caused by the deflection of the crack propagation path, which was brought about by the decrease in intersubcolony spacing. The intersubcolony spacing decreased with increasing number of ‘diffusion controlled’ Widmanstätten α nucleating sites, which were introduced by the deformation strain.

MST/786     

Fracture behavior and toughening mechanism in Zanchor reinforced composites under mode II loading

The mode II interlaminar fracture behavior and the toughening mechanism of Zanchor reinforced composite laminates were investigated by using the End Notched Flexure (ENF) and Interlaminar Shear (ILS) specimens. The ENF test results demonstrated that the Zanchor process was highly effective to improve the mode II fracture toughness of composite laminates, where the fracture toughness increased almost linearly with the Zanchor density. The R-curves of Zanchor composites were roughly divided into the transition and stable regions, where the width of the transition region became larger as the Zanchor density increased. The macroscopic fracture behavior of the Zanchor composites was still brittle under mode II loading like that of the base composite, where the crack tip process zone was estimated to be rather small regardless of the Zanchor density. The ILS test results demonstrated that the square of the normalized shear strength increased linearly with the Zanchor density and agreed quantitatively with the normalized fracture toughness. The wedge effect was supposed to be the dominant toughening mechanism against the mode II fracture, where the entangled fiber bundles partly sustained the shear stress in the vicinity of the crack tip. The entangled fiber bundles played an important role to form the mode II fracture surface, where the microscopic fracture pattern of the entangled fiber bundles was mainly the breakage of the fiber bundles rather than the pull-out or debonding of the fiber bundles.