Opening Displacement Measurements Research Articles

Automatic and time-resolved determination of fracture characteristics from in situ experiments

The characterization of materials in ever smaller dimensions is crucial for the growing demand for miniaturized devices. Hence, in situ fracture experiments are frequently performed at the micron to sub-micron scale. To evaluate fracture process of these experiments, knowledge of the crack length or the crack tip opening displacement is required. Acquired in situ frames provide a direct measurement of the crack length, crack tip opening displacement and -angle. An algorithm was developed to extract these parameters from the in situ frame sequences automatically. To verify the performance of the algorithm, fracture characteristics were measured manually for several frames of the available in situ experiments. The fracture behavior of these samples ranged from brittle over semi-brittle to ductile. The comparison between algorithmic results and manual measurements demonstrated the applicability of the algorithm to different fracture behaviors. Additionally, the fracture characteristics determined by the algorithm are in accordance with the fracture toughness data reported in literature. The crack tip opening displacement measurement gives thorough insight into the plastic deformation during fracture. The automatic extraction of the fracture characteristics allows a more detailed analysis of small-scale fracture processes and enables a reproducible, continuous evaluation of the fracture characteristics of all frames.

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.

Fracture mechanics behavior of coarse-grained MgO–C at room and high temperature

The fracture mechanical properties of coarse-grained MgO–C were investigated in four-point bending tests at single-edge V-notched beams (SEVNB) at room and high temperature. For measurement of the crack mouth opening displacement (CMOD) an optical system was used. Room temperature tests were accompanied with microstructural observations of the crack path with the use of digital image correlation to investigate the mechanisms of crack propagation and to determine the crack length. MgO–C showed stable crack propagation at room temperature as well as up to 1500 °C. Increased fracture toughness KIc and work of fracture were observed in the temperature range from 700 °C to 1200 °C. This behavior was correlated with crack closure, quasi-plastic deformation as well as the activation of visco-plastic creep mechanisms above 1200 °C. Additionally, the results were discussed in terms of Hasselman's thermal shock parameters.

Fracture mechanical behavior of fine-grained carbon-bonded alumina at room and high temperature

The fracture mechanical properties of fine-grained carbon-bonded alumina (Al2O3–C) were investigated in four-point bending tests at single edged V-notched beams (SEVNB) at room and high temperature. Graphite served as a reference material. For measurement of the crack mouth opening displacement (CMOD) an optical system was used. The fracture behavior of Al2O3–C changed from brittle at room temperature to a crack resistance behavior at 1400 °C due to visco-plastic phenomena. The fracture toughness KIc was determined as 0.69 ± 0.07 MPa m1/2 at room temperature and 0.55 ± 0.21 MPa m1/2 at 1400 °C. At room temperature, the work of fracture γwof was determined as 26.3 ± 6.3 J/m2, and Hasselman's thermal shock parameters Rst and R'''' were 8.6 K m1/2 and 0.9 mm, respectively. Although a quantitative analysis of the work of fracture at 1400 °C was hindered by heat shimmer within the chamber, the results indicated significant increases of this parameter as well as Hasselman's thermal shock parameters up to 1400 °C.

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.

Novel Characterizations of Effective SIFs and Fatigue Crack Propagation Rate of Welded Rail Steel Using DIC

The fatigue crack growth-rate test of rail head, waist, and bottom material for U71Mn welded rail was carried out. Digital image correlation (DIC) was used to capture the full-field displacement. The crack-tip position was accurately obtained based on the full-field displacement data, and an accurate crack-tip opening displacement (CTOD) measurement point was found. The CTOD values of the welded rail head under overloaded and unloaded condition were extracted, and the area size of elastic CTOD and plastic CTOD was obtained. According to COD data under different experimental conditions, the corresponding crack opening force was extracted, the crack opening function introduced based on the Elber model, and a calculation method of effective stress-intensity factors (SIFs) considering the plasticity-induced crack closure proposed. The results in this paper provide some references for accurately assessing the fatigue life of welded rail.

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.

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.

Fracture energy evaluation of refractories in wedge splitting tests from notch opening displacements

The work of fracture of refractories is commonly calculated from crack mouth opening displacements (CMODs) in wedge splitting tests (WSTs). This paper proposes a methodology for estimating the fracture energy from notch opening displacement (NOD) measurements, which is useful for setups where CMOD is not accessible. NODs and CMODs are calculated for both faces of two WSTs experiments on a castable refractory via digital image correlation (DIC) and finite element simulations. A quadratic function fits well the non-linear CMOD vs. NOD behavior in the crack initiation regime, while an affine trend describes the propagation regime. Although the nonlinearity associated with crack initiation is more complex, the crack propagation energy can easily be estimated from NOD data when CMODs cannot be measured.

Measurement-based evaluation of interfacial polymer layer inserted in sound deadening laminated sheet

Mixed mode bending (MMB) test associated with measurement of crack tip opening displacement (CTOD) is a practical method to experimentally evaluate mixed-mode cohesive zone model (CZM) properties of polymer layers in various mixed-mode ratios. However, it has an obvious limitation that does not allow for plastic bending of adherends during the tests, making it difficult to evaluate the polymer layer inserted in the sound deadening laminated sheet (SDLS) comprising thin metal sheets which are vulnerable to the plastic bending. This paper provides an experimental technique to suppress the plastic bending of the thin metal sheets during the MMB test. Supporting tools were designed, and bonded to the both outer surfaces of the SDLS. Until delamination occurred, the evolution of fracture toughness (G) was evaluated, and the CTOD was measured in the stereo image using a digital image correlation system. Finally, the mixed-mode CZM properties was successfully established based on the differentiation of the relation between the evolution of G and CTOD.

Study on Iraqi Bauxite Ceramic Reinforced Aluminum Metal Matrix Composite Synthesized by Stir Casting

For the past decades researchers are showing immense interest to investigate the natural advantage of preparation of composites from minerals such as bauxite particles, and proved their effectiveness as cost effective reinforcing agents in fabrication of high performance composites. This study, is a new attempt in using the Iraqi natural bauxite powder with different proportions (2, 4 and 6 wt%) in preparation of aluminum metal matrix composites (AMMCs) using stir casting and Mg additives. In experimental work, the bauxite stones were crashed and milled, then the powder was fired at 1400 ○C. The powders were characterized using particle size, XRD and XRF analysis. The AMMCs casts were machined, polished, preheated, and their properties were characterized using hardness measurements, microstructural observations, and calculation of their Young's modulus, Poisson’s ratio and fracture toughness. Also, their fracture toughness were evaluated by means of crack mouth opening displacement (CMOD) measurements from extensometer recordings. The results proved the successful production of AMMCs with improved fracture toughness, hardness and elastic modulus properties using Mg and Iraqi fired bauxite added at 2 and 4 wt% by stir casting. Moreover, results from CMOD measurements showed the effect of addition bauxite particles at 2 and 4 wt% in increasing maximum at failure and CMOD at critical load of the matrix materials to about 25 and 44% , and 32 and 47%, respectively. Also, at these ratios, the calculated fracture toughness of the matrix materials by means of KIC, and young modulus showed improvement at about “22 and 69%”, and “8 and 12%”, respectively. Addition of bauxite at 6% could not give the required improvement in the fracture toughness despite its effects in recording the highest improvements in hardness (57%) and elastic modulus (22%) due to the brittle behavior of AMMCs at this ratio.

Determination of Crack-Tip Opening Displacement in T-Type Wedge Opening Loaded Specimen

The protective layer at the crack tip of an alloy component can be damaged, and the resistance to crack propagation can be reduced by the combined effects of stress and a corrosive environment. Therefore, the measurement of crack-tip opening displacement (CTOD) can be applied to characterize the crack propagation rate (da/dt) during stress corrosion cracking (SCC) experiments. In the present work, CTOD of a T-type wedge opening loaded (T-WOL) specimen with a built-in loading bolt was initially determined using three-dimensional elastic-plastic finite element analysis (FEA). The influence of stress concentration from side groove on CTOD was clearly evaluated, i.e., the fluctuation of CTOD occurred near the groove-tip plane. However, CTOD became stable on >90% of thickness of T-WOL specimen. Therefore, CTOD at mid-thickness plane of T-WOL specimen could be applied for SCC experiment.

A general framework for determining fracture parameters of concrete based on fracture extreme theory

A general theoretical framework for determining the fracture parameters of concrete was presented based on fracture extreme theory (FET). The method for determining tensile strength ft and initial fracture toughness KIini was established using nil-stress intensity factor (nil-SIF) criterion and initial fracture toughness criterion, respectively. Using the nil-SIF criterion, the ft was determined by the proposed method and verified by experimental values. In addition, the values of KIini calculated using the initial fracture toughness criterion were compared with those using an existing analytical method. The influence of the cohesive stress distribution on KIini was analyzed. With FET, only the experimental peak load of one specimen was needed, and the measurement of the critical crack mouth opening displacement was not required for the calculation.

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.

Digital Image Correlation (DIC) Technique for Fatigue Crack Growth Analysis Using ∆CTOD Criteria

The present paper deals with an experimental determination of fatigue crack growth rate (FCGR) of microalloyed steel (38MnVS6) to study the crack propagation in forged automobile crankshafts. The criterion based on crack tip opening displacement range (∆CTOD) is used to investigate the fatigue crack growth rate. In the current work use of 2D-digital image correlation (DIC) technique for the measurement of crack tip opening displacement (CTOD) and crack length (a) is proposed. Digital Image Correlation (DIC) is a full field displacement and strain measurement technique. It is easier to measure the crack tip opening displacement (CTOD) and crack length (a) with this technique than other. Fatigue crack growth curve based on crack tip opening displacement (CTOD) criteria is presented using DIC.

Fracture toughness evaluation of UFG tungsten foil

The fracture behaviour of pure, ultrafine grained 100 μm tungsten foil was investigated as a function of testing direction and temperature in the range from −196 °C to 800 °C. To study the influence of the anisotropic microstructure on the fracture process, the single-edge-notched specimens were extracted in three different crack orientations relative to the rolling direction. This thorough investigation shows the positive impact of deformation induced grain refinement through extraordinary values of fracture toughness and a reduction of the ductile-to-brittle transition temperature to about room temperature. Furthermore, it was demonstrated that the grain shape anisotropy and a strong rotated cubic texture are decisive factors for anisotropic fracture properties. Fracture surface investigations reveal distinctive behaviour with an increase in temperature. The pronounced transition in failure mode was observed going from brittle, transcrystalline fracture at −196 °C towards pronounced delamination at intermediate temperatures and to ductile failure at highest temperatures. The measurement of the crack tip opening displacement for specimen fracturing in a completely ductile manner enables the determination of more accurate fracture toughness in the elastic plastic regime.

Simplified equations for determining double‐K fracture parameters of concrete for 3‐point bending test

AbstractThe paper presents simplified polynomial equations for determining the double‐K fracture parameters of concrete for 3‐point bending beams with variable strengths and material properties of concrete. The derived equations avoid complexities involved in computations of fracture parameters using existing analytical methods. The input data required for systematic computation in the study for deriving the nondimensional fracture parameters are obtained using a fictitious crack model. It is inferred that for a relative size of initial crack length, critical load and corresponding crack opening displacement maintain a linear relationship in their nondimensional forms. The value of critical mouth opening displacement can also be determined for known value of peak load using the derived nondimensional equation, thus avoiding the measurement of the crack mouth opening displacement in the experiment. Further, the derived polynomial equations predict the double‐K fracture parameters of concrete with negligible error as compared to those obtained based on experimental results.

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.

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.

Comparison of methods to determine CTOD for SENB specimens in different strain hardening steels

AbstractMethods for determining crack tip opening displacement (CTOD) given in national and international standards are compared for steels with a range of strain hardening characteristics.Crack tip opening displacement measurements were made from single‐edge notched bend notches using a silicone rubber casting method. The finite element model produced good agreements with predictions of these CTOD measurements. The versatility of the finite element model enabled CTOD from the original crack tip and the 45° intercept method to be compared. The 45° CTOD generally underestimates the original crack tip CTOD, and is less useful for conditions with stable crack extension.Apart from the high strain hardening material, CTOD calculated using BS 7448‐1, WES 1108 (JWES), and ASTM E1820 was slightly lower than the values determined from silicone measurements and modelling, which is conservative. ASTM E1820 gave the largest underestimation of CTOD, whilst BS 7448‐1 may be unsuitable for higher strain hardening steels, where the standard predicts higher CTOD than measured from the replica. JWES gives the most consistent estimation of CTOD for steels with a wide range of strain hardening values.