Crack Opening Displacement Measurements Research Articles

Prediction of crack opening in steel beam based on strains measured from distributed optical fiber sensor

Optical fiber sensors based on the Brillouin optical time domain analysis (BOTDA) have good accuracy of crack opening displacement (COD) measurements. In this paper, we propose a method for COD quantification based on the area under the Brillouin frequency peaks induced by a crack. The study adopted a three-dimensional (3D) finite element model (FEM) to simulate the strain distribution within a segment of an optical fiber. The simulation results revealed that an increase in COD was associated with an increase in the Brillouin frequency peak area. The peak strain increased by 93 μϵ when the COD increased from 30 μm to 110 μm. The numerical findings were proved experimentally by employing a BOTDA interrogator for distributed sensing of strains. Two cracks in a 15-m-long steel beam were detected with the smallest error of 13%. The COD was predicted from the areas under the crack-introduced strain peaks under varying loads of 97, 196, 294 and 392 N. The effect of different spatial resolutions (10, 20 and 50 cm) and intervals (1, 2.5 and 5 cm) on sensing performance was discussed. Compared to previous research, the 3D FEM not only accurately predicted the changes in distributed optical fibers with cracks but also simplified traditional theoretical analysis. For the first time, a method has been introduced to predict cracks by comparing the area under the Brillouin peaks. This approach not only enhanced linearity but also reduced errors. The proposed method can be easily implemented in engineering practice for multi-point crack sensing in civil infrastructure.

In-situ observation of micro-cracking in a SiC/BN/SiC ceramic matrix composite under tension

Crack spacing and crack opening displacement values are critical for CMC damage and oxidation modeling. A tensile stage used with light and scanning electron microscopy (SEM) was utilized to evaluate micro-cracking under load in SiC/BN/SiC ceramic matrix composites (CMCs). Surface micro-crack spacing and crack composition, a novel measurement introduced in this work, were measured with light microscopy at room temperature. Crack spacing decreased with increasing load, with a majority of cracks being in contact with BN fiber coatings. Crack opening displacement (COD) measurements were taken at room and elevated temperature (600 °C) with scanning electron microscopy. CODS increased nearly linearly with increased load; CODs ranged from 1 to 3 μm at 200–350 MPa at room temperature and at 600 °C ranged from 0.5 to 2 μm at 175–350 MPa. CODs were also related to local microstructure, with CODS being lower near longitudinal fiber tows. Implications on use of the data for CMC oxidation models are discussed.

A new method for the identification of cohesive laws under pure loading modes

In this work, a new and simple methodology is proposed to identify the cohesive law of composite materials submitted to pure mode I and II loading. This methodology combines the experimental measured crack opening displacement and corresponding strain energy release rate with numerical simulation, using finite element method including cohesive zone modelling. The proposed procedure was tested and validated numerically, considering the determination of cohesive laws with different shapes for pure mode I and II loading. This was accomplished using the double cantilever beam (mode I) and end-notched flexure (mode II) tests. It was verified that the proposed methodology points towards the unicity of the identified solution and reproduces well the cohesive laws used as input.

Toughening and Strengthening Response in Ni3Al-Bonded Titanium Carbide Cermets

Abstract Nickel aluminide (Ni3Al) was used as a binder phase to fabricate dense TiC cermets with Ni3Al contents of up to 60 vol. % and TiC grain sizes of ~ 5 to ~ 0.8 μm by either sintering of mixed powders or a melt-infiltration sintering process. These TiC–Ni3Al cermets exhibit high fracture toughness together with exceptional flexure strengths (> 1 GPa), which are retained at temperatures of ~ 1000 °C. While the flexure strength exhibited a modest increase as the Ni3Al content was raised, both the Weibull modulus (up to ~20) and the toughness ~ 18 MPa m $\sqrt m $ exhibited substantial increases. The increased toughness was found to result from a combination of interface debonding and grain cleavage that combined to enhance plastic deformation of the Ni3Al ligaments in the crack wake. Crack opening displacement measurements reveal a blunted crack profile and suggest a bridging zone length in excess of 100 microns.

Monitoring of crack opening displacement of steel structure by PPP-BOTDA-distributed fiber optical sensors: Theory and experiment

Crack opening displacement (COD) is an essential parameter in fracture analysis of steel structures, and a novel methodology was developed for measurement of COD using high-resolution distributed fiber optical sensors. Based on crack-induced strain transfer mechanism, a theoretical model was firstly proposed to explicitly determine COD of steel element by strain singularity considering both the elastic and elastoplastic behavior of the optical fiber coating. The presented theoretical COD equations consider the inclination angle between the sensor axis and crack length as well. An experimental program of a pre-cracked pure bending steel element was then conducted to confirm the feasibility of the proposed monitoring approach. The PPP-BOTDA (Pre-Pump-Pulse Brillouin optical time domain analysis) with 1-cm-level spatial resolution was used in distributed measurement of strain and determination of COD. Estimated CODs were also compared to those measured using traditional electronic digital display micrometer. The results indicate that the inclination effect of the optical fiber is slight on the COD within the inclination angle range of 30°. This proposed approach demonstrates great promise for high accuracy and sensitivity of COD monitoring applications.

Measurement of fracture toughness based on atomic-resolution observations of crack opening behavior

Crack nucleation and propagation in SrTiO3 single crystal were observed at the atomic level by in situ scanning transmission electron microscopy (STEM) loading experiment with a MEMS loading device. It was found that a crack initiated from the bottom of a notch and propagated along the {110} plane. The fracture toughness for the {110} crack was estimated to be KIC=1.4MPam1/2 based on the measured crack opening displacement. In addition, an atomic structure model of the {110} fracture surface was constructed based on the experimental observations, and first-principles calculations showed that its cleavage energy was γ=3.8Jm-2. From the relationship of KIC=(2γE)1/2 (E: Young’s modulus), the fracture toughness is estimated to be =1.4MPam, which agrees well with the experimental value.

Comparison of crack propagation rates in selected structural components made from AISI 304 grades: Three-point bending test

This study focuses on crack propagation rates of AISI 304 stainless-steel specimens made from selected structural components experimentally tested in three-point bending. Components of two productions loaded with constant force with selected stress ratio were submitted to cyclic loading in order to measure crack opening displacement. Experimentally obtained data were evaluated using 3D modelling in finite element modeling software intending to determine fracture mechanical parameters. The tool to describe fatigue behavior was Paris’ law, used to describe crack propagation in intermediate crack growth rate range. Paris–Erdogan equation was evaluated as a fitting of linear part of the graphical plot of crack growth rate with respect to the stress intensity range and material constants were gained from numerical description of the relation. Comparison of fatigue crack behavior in AISI 304 steel components of two productions was studied and evaluated.

Study on fracture behavior of nickel-based single crystal superalloy subjected to high temperature fatigue using digital image correlation

Anisotropic mechanical behavior of nickel-based single crystal superalloy (NBSCS) is studied based on the displacement field near the crack tip during the fatigue crack growth at 980°C. A new distortion calibration technique for bi-prism-based single-lens 3D digital image correlation (BSL3DDIC) is proposed to in-situ and on-line characterize 3D full-field deformation with high precision. Virtual displacement extensometers (VDEs) are arranged from the displacement field for the crack opening displacement (COD) determination. To the best of our knowledge, the effect of VDEs locations on the precision of COD measurement is first theoretically analyzed, and the arrangement of VDEs has been optimized. Noticeably, similar quantitative analyses are conducted to determine crack opening ratio (COR) for crack closure evaluation. Moreover, via fitting full-field displacement data to a theoretical model for anisotropic material, not only mode-Ⅰ effective stress intensity factor (SIF) expressed as KeffI and mode-Ⅱ effective SIF (KeffΠ), but also theoretical SIF (KtheoI), crack opening SIF (KopenI) and crack opening load ratio (COLR) are obtained. Based on these important fatigue parameters, modified Paris’ law is used to describe the high-temperature anisotropic crack growth behavior.

Characterizing environment‐dependent fracture mechanisms of ceramic matrix composites via digital image correlation

AbstractHere, we unveil a methodology for a novel assessment of the fracture mechanics of SiC/SiC ceramic matrix composites enabled by in situ stereoscopic digital image correlation to quantify in‐process flexural strain and crack opening displacement measurements. This technique isolates individual cracks on the composite surface as discontinuities in the spatial displacement field and correlates key fracture characteristics with the flexural strain of composite specimens during coupled four‐point bend / hermeticity testing. Fracture was observed along the specimen length, originating at the tensile underside and propagating around the circumference of the tubular specimens with generally uniform spacing. Multiple specimens were also tested after heat treatments to 1200°C in open air, in vacuum, and in helium for 48 h to evaluate the environmental effects on the fracture mechanisms of SiC/SiC composites, which revealed degradation of flexural properties after treatment in open air resulting in brittle failure. Indentation‐based fracture toughness measurements were performed, which confirmed a 25% reduction in toughness after open air heat treatment relative to the other heat treatments. This assessment indicated that significant oxidation may occur within the composites from these heat treatments and suggested that further protection of the composites may be necessary for high‐temperature applications.

Radiation Tolerant 3D Laser Scanner for Structural Inspections in Nuclear Reactor Vessels and Fuel Storage Pools

Accurate and timely assessment of displacements and/or structural damages in nuclear reactor vessels’ components is a key action in routine inspections for planning maintenance and repairs but also in emergency situations for mitigating consequences of nuclear incidents. Nevertheless, all these components are maintained underwater and reside in high-radiation fields thus imposing harsh operative conditions to inspection devices which must cope with effects such as Cerenkov radiation background, Total Ionizing Radiation (TID), and occlusions in the detectors’ field of view. To date, ultrasonic techniques and video cameras are in use for inspection of components’ integrity and with measurements of volumetric and surface crack opening displacements, respectively. The present work reports the realization of a radiation tolerant laser scanner and the results of tests in a nuclear research reactor vessel for acquisition of 3D models of critical components. The device, qualified for underwater operation and for withstanding up to 1 MGy of TID, is based on a 515 nm laser diode and a fast-scanning electro-optic unit. To evaluate performances in a significant but controlled environment, the device has been deployed in the vessel of a research reactor operated by ENEA in the Casaccia Research Centre in Rome (Italy). A 3D model of the fuel rods assembly through a cooling water column of 7 m has been acquired. The system includes proprietary postprocessing software that automatically recognizes components of interest and provides dimensional analysis. Possible application fields of the system stretch to dimensional analysis also in spent nuclear fuel storage pools.

Study of the biaxial fatigue behaviour and overloads on S355 low carbon steel

This work aimed to study the fatigue behaviour of S355 low carbon steel under uniaxial and biaxial loading conditions and to measure the overload effects under both types of loads. The analysis is performed with a local strain approach and with damage tolerance approach. Local strain based investigation was based on Fatemi-Socie critical plane model. This allows the life reduction caused by growing the crack from a stress raiser to be quantified. The fatigue life reduction caused by applying simultaneously torsional and tension loads was also evaluated with Fatemi-Socie model. In addition, the crack opening displacement (COD) and the effective stress intensity factor (SIF) were evaluated experimentally via full-field technique of digital image correlation (DIC). Both COD and SIF have been useful to understand the transient effects caused by a 40% overload under the two types of load. In addition, COD measurements allowed the offset compliance method for evaluating the opening load to be applied on a cylindrical specimen subjected to tension load. SIF estimation was also useful to quantify the mode mixity (I + II) developed during the experiment under the two types of load.

Estimation of fracture toughness in ZnO ceramics from indentation crack opening displacement measurements

Crack opening displacement (COD) approach on indentation cracks has been successfully utilized in evaluating the fracture toughness of sintered ZnO samples. The study has been conducted on two varieties of sintered samples, made from commercial and ground ZnO powder, with applied loads of 9.8 and 19.6 N in a Vickers hardness tester. Crack opening profiles along the crack length have been measured by scanning electron microscopy (SEM). Fracture toughness in the ground and sintered ZnO sample has been estimated as 2.44 MPa·m0.5 using the crack displacement data for the full length. The slightly lower toughness of 2.10–2.16 MPa·m0.5 measured in the commercial variety of sintered ZnO has been related to the lesser plain strain modulus corresponding to lower density value. The obtained results are within 10% variation of the fracture toughness measured using indentation crack length method for the similar variety of ZnO samples. Irwin’s equation validates the fracture toughness results for the near tip data, within 5 μm from the crack tip.

Effect of hydration and crack orientation on crack-tip strain, crack opening displacement and crack-tip shielding in elephant dentin

ObjectivesTo quantify the extent of crack-tip plasticity, crack opening displacement (COD) and crack bridging for crack growth perpendicular (HAH) and parallel (RAR) to the tubules in elephant dentin under both hydrated and dry conditions to better understand their influence on intrinsic and extrinsic toughening during crack growth. MethodsCompact tension test-pieces were prepared from a tusk of African elephant ivory. Crack-tip strain mapping and COD measurements by digital image correlation (DIC) technique were made under incremental loading and unloading of cracks for hydrated and dry dentin of different orientations. ResultsFor the RAR test-piece the plastic zones were significantly larger in the hydrated condition compared to when dry. By contrast, the plastic strains in the HAH test-piece were negligible in both wet and dry conditions. In the RAR condition the crack front was broken up into overlapping longitudinal ‘fingers’ with crack bridging regions in between, the ligaments extending 400μm behind the crack front in the dry case. This could only be seen in 3D by X-ray CT. Extrinsic shielding reduces the crack-tip stresses by 52% and 40% for hydrated and dry RAR test-pieces respectively. No significant bridging was found in the HAH case. SignificanceFor crack growth parallel to the tubules, collagen plasticity determines the intrinsic toughening, whereas microcracking from the tubules governs extrinsic shielding via ligament bridging, which is maintained further behind the crack in the hydrated case. For cracks grown perpendicular to the tubules, neither toughening mechanisms are significant.

Fatigue crack propagation in [0 1 2] NiTi single crystal alloy

Fatigue crack propagation experiments on nickel titanium single crystal alloy, with [0 1 2] crystallographic orientation, were carried out in this study. Stable microstructure, i.e. stable austenite and stable martensite, with the same chemical composition, were investigated. To this aim, two different values of temperature were analyzed. The digital image correlation (DIC) technique was used to obtain the displacement experienced by the sample during the application of the load. Obtained data were used as input parameters of a numerical procedure, that is able to estimate the effective stress intensity factor the sample actually experiences. The procedure is also able to automatically calculate the effective crack length. Numerical crack opening displacement measurements were also conducted in order to estimate the near crack tip stiffness of the microstructures. Results revealed that the stable austenite exhibits a lower threshold value of the stress intensity factor and a higher crack growth rate. Furthermore, it was demonstrated that, when dealing with martensite, local elastic properties change, as a consequence of the variants reorientation, and this effect has to be taken into account for the fatigue crack growth characterization.

Effect of Thickness on Fatigue Crack Propagation in Injection Molded Short Carbon Fiber Reinforced Plastics

The influence of plate thickness on the fatigue crack propagation behavior was studied by using center-notched specimens which were cut from injection-molded plates of short carbon-fiber reinforced polyphenylene sulfide (PPS) at two fiber angles relative to the molding flow direction (MFD), i. e. θ=0 deg. (MD), 90 deg. (TD). The short carbon-fiber reinforced plastics (SCFRP) plates have three-layer structure where the fiber orientation is parallel to MFD in the shell layer and is nearly perpendicular in the core layer. The fraction of the core layer increases with increase in the plate thickness. In the relation between the crack propagation rate,da/dN, and stress intensity factor,ΔK, da/dNincreases with increase in thickness for MD specimen. Conversely,da/dNdecreases for TD specimen. The crack opening displacement along the crack was measured by using the digital image correlation (DIC) method. The measured crack opening displacement become larger with increase in the plate thickness for MD specimens. Contrary, measured values become smaller with increase in the plate thickness for TD specimen. The crack-tip-opening radius,Δρ, was estimated from the parabolic approximation of the crack opening displacement distribution near the crack tip. The relationships betweenda/dNandΔρfor all specimens tend to merge into a unique relationship.

Measurement of opening displacement and stress intensity factor of two branches of bifurcated notch by Moiré interferometry

Static experiments on dynamic crack branching are carried out, in which Y-shaped notches in plate specimens are regarded as rapidly bifurcating cracks. Moiré interfrometry is applied to measure crack opening displacement, COD, of two branch notches as well as the mother notch of the Y-shaped notch. Stress intensity factor of the branch notches are calculated through the formula for COD of linear elastic fracture mechanics. From the measurement results, it is clarified that how far the singular stress field is developed around the branch crack tip.

Traction-separation relationship for polymer-modified bitumen under Mode I loading: Double cantilever beam experiment with stereo digital image correlation

The traction-separation law under Mode I loading for a polymer modified bitumen commonly used as an adhesive for 3–tab roofing shingles is quantified. Double cantilever experiments are performed at three different loading rates (0.03 mm/min, 0.3 mm/min and 3 mm/min). Load-displacement measurements are synchronized with speckle image acquisition and the data analyzed to determine (a) J-integral, (b) cohesive zone end opening displacement and (c) the crack opening displacement (COD) as a function of crack extension. Imaging is performed using two stereo vision systems equipped for capturing speckle images of the DCB specimen at two different magnifications with fields of view of (a) 14 mm × 12 mm and (b) 170 mm × 140 mm. The stereo vision system used to acquire data at higher magnification is mounted on a translation stage and focused on a region close to the crack tip as the crack propagated. This stereo vision system is used to measure the strain fields near the crack tip and for measurement of crack opening displacement (COD) at 1 mm behind the current crack tip for a range of crack extensions. The second stereo vision system is used to visualize the process zone size and measure the strain fields over larger fields of view ahead of the crack tip. Assessment of the fracture surface for lower loading rates (0.03 mm/min and 0.3 mm/min) revealed a ductile type fracture (rough surface due to void growth in the process zone). For the highest loading rate (3 mm/min), the fracture surface is typical of the type seen during brittle fracture (shiny surface with striations), with intermittent rapid crack propagation events followed by crack arrest along clearly visible arrest fronts.Analysis of the data obtained for the two slower loading rates that exhibited ductile fracture throughout the entire growth process shows that the energy release rate Gcd = 70 J/m2, and the final separation, δcd = 250 µm for the slowest loading rate of 0.03 mm/min and, Gcd = 120 J/m2, and the final separation, δcd = 250 µm for 0.3 mm/min loading rate. For the highest loading rate, which exhibited nominally brittle fracture, the energy release rate Gcb = 10 J/m2, and the final separation δcd = 1.5 µm. The peak cohesive stresses during ductile and brittle fracture are determined to be σd = 0.7 MPa and σb = 9.6 MPa, respectively, for loading rates of 0.3 mm/min and 3 mm/min, respectively. Finally, COD at the onset of crack growth measured at 1.00 mm behind the moving crack tip for the loading rate of 0.3 mm/min, CODd ≈ 0.30 mm, remaining constant for crack lengths, a, in the range 25 mm ≤ a ≤ 165 mm.

Crack opening behavior in ceramic matrix composites

AbstractThe evolution of matrix cracks in a melt‐infiltrated SiC/SiC ceramic matrix composite (CMC) under uniaxial tension was examined using scanning electron microscopy (SEM) combined with digital image correlation (DIC) and manual crack opening displacement (COD) measurements. CMC modeling and life prediction strongly depend a thorough understanding of when matrix cracks occur, the extent of cracking for given conditions (time‐temperature‐environment‐stress), and the interactions of matrix cracks with fibers and interfaces. In this work, strain relaxation due to matrix cracking, the relationship between CODs and applied stress, and damage evolution at stresses below the proportional limit were assessed. Direct experimental observation of strain relaxation adjacent to regions of matrix cracking is presented and discussed. Additionally, crack openings were found to increase linearly with increasing applied stress, and no crack was found to pass fully through the gage cross‐section. This calls into question the modeling assumption of through‐cracks for all loading conditions and fiber architectures, which can obscure oxidation mechanisms that are active in realistic cracking conditions. Finally, the combination of SEM with DIC is demonstrated throughout to be a powerful means for damage identification and quantification in CMCs at stresses well below the proportional limit.

A Comparison of Microscale Techniques for Determining Fracture Toughness of LiMn₂O₄ Particles.

Accurate estimation of fracture behavior of commercial LiMn2O4 particles is of great importance to predict the performance and lifetime of a battery. The present study compares two different microscale techniques to quantify the fracture toughness of LiMn2O4 particles embedded in an epoxy matrix. The first technique uses focused ion beam (FIB) milled micro pillars that are subsequently tested using the nanoindentation technique. The pillar geometry, critical load at pillar failure, and cohesive FEM simulations are then used to compute the fracture toughness. The second technique relies on the use of atomic force microscopy (AFM) to measure the crack opening displacement (COD) and subsequent application of Irwin’s near field theory to measure the mode-I crack tip toughness of the material. Results show pillar splitting method provides a fracture toughness value of ~0.24 MPa.m1/2, while COD measurements give a crack tip toughness of ~0.81 MPa.m1/2. The comparison of fracture toughness values with the estimated value on the reference LiMn2O4 wafer reveals that micro pillar technique provides measurements that are more reliable than the COD method. The difference is associated with ease of experimental setup, calculation simplicity, and little or no influence of external factors as associated with the COD measurements.

片側切欠きばりの4点曲げ試験（4SENB試験）による木材および中密度繊維板の<i>K</i><sub>Ic</sub>値の測定

Mode I critical stress intensity factor KIc obtained by four-point single-edge-notched bending (4SENB) tests of wood and medium-density fiberboard (MDF) was experimentally and numerically analyzed. To determine the critical load for crack propagation, the relationship between the load and loading-line deflection (LLD) and that between the load and crack opening displacement (COD) were measured, and the results obtained were compared with each other. Additionally, a double cantilever beam (DCB) test was conducted and the results were compared with those of 4SENB tests. Similar to the results obtained in several previous studies, the value of KIc was obtained by introducing an additional crack length into appropriate equations as the crack geometry factor used for analyzing the 4SENB test. Additionally, the load-COD relationship was more sensitive in detecting the crack propagation than the load-LLD relationship, so the measurement of COD is recommended for determining the KIc value in the 4SENB test accurately.