Crack Opening Displacement Values Research Articles

Hybrid fibre reinforced recycled aggregate concrete: dynamic mechanical properties and durability

Research into recycled aggregate concrete (RAC) has been on the rise as there is a need to preserve natural resources and promote sustainable infrastructure practices. In our previous study, a new hybrid-fibre reinforced recycled aggregate concrete (FRRAC) with micro basalt fibre (BF) and recycled macro polypropylene fibre (PF) was developed and its physical and mechanical properties were investigated. As a continuous work, this study investigated the dynamic mechanical properties and durability of the developed FRRAC. Dynamic compressive and splitting tensile strength tests were undertaken using a Ø 100 mm split Hopkinson pressure bar (SHPB) system. The failure processes and failure modes of RAC and FRRAC specimens under different strain rates were recorded using a high-speed camera. For dynamic compressive strength, the stress-strain curves, dynamic increase factor for compressive strength (DIFf’c) and energy absorption capacities of RAC and FRRAC were evaluated and compared in the strain rate range from around 27.9 s-1 to 138.0 s-1. The stress-time histories, crack-opening displacement values and dynamic increase factor for splitting tensile strength (DIFfst) at the strain rates of around 3.03 s-1 to 8.17 s-1 of the two materials were obtained and compared. The test results indicated that RAC specimens were slightly more strain rate sensitive than natural aggregate concrete (NAC) under dynamic compression and splitting tension. On the other hand, FRRAC specimens showed similar strain rate sensitivity as their counterparts with no fibres under dynamic compression but showed lower DIFfst values with increasing strain rate under splitting tension. Empirical formulae for DIFf’c, DIFfst and energy absorption capacities against strain rates were proposed. In addition, the durability performance was assessed by examining the water absorption, volume of permeable voids (VPV), water sorptivity and chloride ion penetration resistance. Durability test results indicated that RAC and FRRAC in this study are suitable for structural applications.

Singular integral method based closed form solution for moving EMPS model in semipermeable two‐equal‐collinear cracked MEE material

AbstractThis paper presents the analytical closed‐form solutions of moving two equal collinear semipermeable cracks in magneto‐electro‐elastic material considering the strip electric‐magnetic polarization saturation (EMPS) model. To simulate the dynamic/moving cracks problem, two equal collinear Yoffe type cracks moving with a constant subsonic velocity along the plane of the cracks is considered. The problem is solved by considering semipermeable crack face conditions and under the in‐plane electro‐magnetic‐mechanical loading. Applying distributed dislocation technique and symmetry of the collinear cracks, the problem is reduced into simultaneous singular integral equations which have been solved in closed form expressions using finite Hilbert approach. The explicit expressions for dynamic distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), and local stress intensity factors (LSIFs) are evaluated for both the cases of the EMPS model (magnetic zone is smaller or greater than electric zone). For evaluation of inner and outer electric and magnetic zone lengths (MZLs), an iterative approach is applied to solve the developed two non‐linear equations. Also, to implement the semipermeable crack‐face conditions, a bisection iterative method has been applied. Based on the developed closed form solutions, numerical studies are presented for standard fracture parameters with respect to crack propagation velocity, electrical loading and inter‐crack space distance. This study shows that electric displacement and magnetic induction defined over the crack‐surface for semipermeable conditions decrease whereas the numerical values of saturated zone lengths, COD, COP, COI, and LSIFs increase with increasing crack propagation velocity. Moreover, for both static and dynamic cracks problems, the significant crack‐interaction effects have been observed on all the studied fracture parameters except the crack‐face conditions.

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.

Fracture Properties of Plastic-Steel Fiber High-Performance Concrete after High-Temperature Exposure

To study the fracture properties of plastic-steel fiber high-performance concrete at high temperatures, the load-mid-span displacement curve and load-opening displacement curve of plastic-steel fiber concrete were obtained through fracture test conducted before and after exposure to high temperature. By calculating the fracture parameters, fracture energy, and characteristic length of concrete, the relationship of fracture parameters, fracture energy, and characteristic length of concrete with temperature was comparatively analyzed against the experimental results obtained for plain concrete. According to the analytical results, the crack initiation load value, maximum load and crack initiation toughness of SFRC are significantly improved after high-temperature exposure, and the plastic-steel fiber reinforced concrete is effective in reducing the critical value of crack opening displacement for concrete. When the test temperature ranges from 200°C to 600°C, the anti-cracking effect of plastic-steel fiber on concrete is more significant relative to plain concrete. Given temperature rise, the plastic-steel fiber reinforced concrete shows decrease in brittleness but increase in toughness, with the level of fracture energy first increasing and then decreasing. Besides, there is only slight difference observed in characteristic length between plastic-steel fiber reinforced concrete and steel fiber reinforced concrete.

Interaction of shear waves with semi-infinite moving crack inside of a orthotropic media

The present work investigates the motion of a semi-infinite moving crack inside a semi-infinite half-space of orthotropic medium subjected to anti-plane shear wave. The crack is located at a finite depth from the surface of semi-infinite orthotropic medium. Our aim is to examine how such anisotropy and geometric parameters can be adjusted to reduce the magnitude of stress intensity factor (SIF) to control the crack propagation near the crack tip region. As mathematical tools, Fourier transformation and inverse Fourier transformation techniques are employed to convert the governing mixed boundary value problem to the well-known Weiner-Hopf equation with suitable boundary conditions. Some physical quantities such as SIF at the crack tip and crack opening displacement (COD) around the crack tip have been derived. Graphical exhibition has been carried out to show the impact of relevant parameters such as crack velocity, layer depth from the surface to crack and orthotropic material properties on SIF and COD. The numerical results show that SIF decay with crack depth from the layer. It is also observed that SIF decreases with an increase in crack velocity and finally tends to zero as crack velocity approches near SH-wave velocity. Also, the value of COD decays as we move along the damage near the crack tip along negative x-axis and finally tends to zero at the crack tip. This behavior of COD is consistent with the physical nature of the semi-infinite crack of the problem. The results are validated for isotropic material with some reported work and are well in agreement. The study of these physical quantities (SIF, COD) ensures the arrest of onset of crack expansion by monitoring geometric parameters and wave velocity to avoid fracture.

EPFM Analyses of a Complex Crack in Dissimilar Metal Welded Pipes

Abstract Accurate estimation of elastic-plastic fracture mechanics (EPFM) parameters for a crack in nuclear pipes was considered as an important factor for leak-before-break design and evaluation. Yet few EPFM studies have been made to predict the crack opening displacement and J-integral of dissimilar metal welded pipes, which consist of two-layered materials (TLMs), due to the difficulty of complicate analysis encompassing both through-wall crack and internal surface crack in radial and circumferential directions. In this study, a series of finite element analyses to determine the typical EPFM parameters were carried out considering idealized complex-cracked pipes with TLMs. The analyses were elaborated through applying three loading conditions of axial tension, bending moment, and internal pressure. Both J-integral and crack opening displacement values were calculated by assuming two kinds of equivalent materials based on weighted average concepts as well as two different materials. The proposed equivalent schemes can be utilized in not only improving the expansion to existing solutions but also in more accurate detailed leak-before-break assessment of complex cracked nuclear piping with TLMs.

Study of Flexural and Crack Propagation Behavior of Layered Fiber-Reinforced Cementitious Mortar Using the Digital Image Correlation (DIC) Technique.

By optimizing the distribution of steel fibers in fiber-reinforced cementitious mortar (FRCM) through the layered structure, the role of fibers can be fully utilized, thus improving the flexural behavior. In this study, the flexural behavior of layered FRCM at different thicknesses (25 mm, 50 mm, 75 mm, 100 mm) of the steel fiber layer was investigated. The evolution of the crack propagation behavior was analyzed using the digital image correlation (DIC) technique. The results showed that the steel fiber layer thickness of 75 mm has the best flexural behavior. Moreover, the crack propagation path is more tortuous. The maximum value of crack opening displacement (COM) increases with the increase in fiber thickness. In addition, increasing the bottom layer thickness can increase the height of the tensile zone, but the interface inhibits the increase of the tensile zone.

Evaluation of crack opening displacement of through-wall circumferential-cracked pipe using direct weight function method

This paper presents a direct weight function-based method to evaluate the crack opening displacement (COD) which is a key parameter in leak-before-break (LBB) assessment and in probabilistic fracture mechanics (PFM) assessment of nuclear piping systems. The focus of this study is a circumferential-cracked pipe with non-linearly through-wall distributed stress loaded on the crack face. Parametric finite element analyses (FEA) were performed to calculate COD associated with different crack face pressure (CFP) loadings. The analyses matrix covers a wide range of pipe size and crack lengths. The crack mouth COD values at three locations: at outside surface, inner surface and mid-thickness were considered. The numerical results were then used to determine the coefficients that construct the direct weight functions. The proposed solution can be used to predict the COD resulted from given weld residual stress (WRS) field with the general prediction error being less than 8%. The research outcome can provide more computational efficiency in both deterministic LBB assessment as well as PFM analyses of pressurized pipes.

Plastic deformation and mixed-mode I/II fracture behavior of un-plasticized polyvinyl chloride

To further understand the mixed-mode I/II fracture behavior of Un-plasticized Polyvinyl Chloride (UPVC), a series of mixed-mode I/II experiments on analogy compact tension specimens have been conducted using an MTS 810 hydraulic test machine. The evolution of the displacement field during stable crack extension was monitored by two-dimensional digital image correlation technique. Results obtained from the mechanical testing demonstrate that the maximum load of mode II is about 100% higher than that of mode I, and the load-carrying capacity is dependent on orientation and load condition. Fractography observations indicate that the fracture surface can be divided into fatigue region with relatively smooth characters and stable crack extension region with randomly distribution of honeycomb-like voids. Furthermore, mode I failure (opening) should be the main failure mechanism of UPVC rather than mode II (shear failure). The results also suggest that the value of crack opening displacement (COD) tends to be nearly constant when the length of crack exceeds the thickness of the sample, which is independent on orientation and load condition. Therefore, COD criterion can be used to describe the overall severity of plastic deformation in the near-tip region of UPVC, and components of COD, which is perpendicular to the crack surface, should be the predominant controlling parameter of crack propagation.

Influence of splitting load on transport properties of ultra-high performance concrete

This paper presents an experimental investigation on the influence of splitting load on transport properties (air permeability and sorptivity) of UHPC incorporating different dosages of steel fibers (0%, 1%, 2% and 3%). ϕ100 mm × 50 mm specimens were subjected to splitting loads with stress levels varying from 50% to 80% of the ultimate splitting tensile strength. The splitting load induced damage was characterized by the crack pattern, crack opening displacement (COD) and penetrable porosity. Gas permeability and water sorptivity tests were carried out to evaluate the transport property of UHPC specimens after exposure to different levels of splitting load. The correlation among splitting tensile stress level, COD and transport property degradation of UHPC was analyzed. The results indicate that gas permeability and sorptivity of UHPC before loading are much better than that of normal concrete. The splitting tensile strength of UHPC is almost doubled by the addition of 1 ∼ 3% steel fibers in volume and the peak lateral deformation is increased by more than 10 times. Both the maximum value of COD (CODmax) under loading and the residual COD (CODres) after unloading of UHPC specimen increase with the more addition of steel fibers when exposed to the same stress level of splitting load. Both gas permeability and sorptivity of UHPC increase with the splitting load induced CODres. The higher dosage of steel fibers plays a positive effect on improving the transport properties of UHPC with the same CODres value. The sorptivity is more sensitive under a low deformation damage and the gas permeability is a better indicator to describe the durability degradation of UHPC under a high level of deformation.

Analysis of Fatigue Crack Paths in Cold Drawn Pearlitic Steel.

In this paper, a fracto-metallographic analysis was performed on the cracked specimens of cold drawn pearlitic steel subjected to fatigue tests. Fatigue cracks are transcollonial and exhibit a preference for fracturing pearlitic lamellae, with non-uniform crack opening displacement values, micro-discontinuities, branchings, bifurcations and frequent local deflections that create microstructural roughness. At the micro-level, the cold drawn pearlitic steel exhibits higher micro-roughness than the hot rolled bar (this is a consequence of the manufacturing process by cold drawing), so that the actual fractured surface in the cold drawn wire is greater than that in the hot rolled bar, due to the fact that the crack deflection events are more frequent and with higher angle in the former (the heavily drawn prestressing steel wire). These findings show the relevant role on the manufacturing process by cold drawing in the fatigue crack propagation in pearlitic steel.

파단전 누설 평가를 위한 Ramberg - Osgood 상수 결정법

In this study, a method for determining Ramberg–Osgood constants for leak-before-break evaluation was investigated. The Ramberg–Osgood constants were calculated for SA312, TP316, and SA-508 Gr.1a in an operating temperature of 316 oC. Incremental plasticity, using stress–strain data obtained from experiment, and deformation plasticity, using the Ramberg-Osgood constants, were considered in a finite element analysis. Using incremental plasticity and deformation plasticity, J-integrals and crack opening displacement values were calculated and compared. By comparing the results of incremental plasticity and deformation plasticity, a suitable method for determining Ramberg–Osgood constants for leak-before-break evaluation was confirmed. † Corresponding Author, kimy0308@korea.ac.kr C 2015 The Korean Society of Mechanical Engineers 배경동 · 류호완 · 김윤재 · 김진원 · 김종성 · 오영진 646

Experimental investigation of mixed-mode-I/II fracture in polymer mortars using digital image correlation method

The purpose of this work is to investigate experimentally the effects of mixed-mode I/II loading on the fracture behavior of polymer mortars. Three point bend beam specimens with offcenter notch were used in plane-strain fracture toughness tests. Two approaches have been simultaneously used to determine the crack opening displacements. The crack mouth opening displacement was measured by means of a clip gauge, while the crack tip opening displacement was estimated through the Digital Image Correlation method. Fracture parameters, such as critical values of crack opening displacement, energy release rate and mixed-mode stress intensity factor were estimated. In addition, the values of crack mouth opening displacement and crack tip opening displacement were used to evaluate the rotational factor. Finally, the effect of sliding mode-II in fracture was not easily observed using clip gage, however this effect was noticed employing Digital Image Correlation method.

Development of Leak-Before-Break Assessment Method for Japan Sodium Cooled Fast Reactor Pipe—Part 1 Crack Opening Displacement Assessment of Thin Wall Pipes Made of Modified 9Cr-1Mo Steel

This was carried out to establish crack opening displacement (COD) evaluation methods used in leak-before-break (LBB) assessment of sodium pipes of the Japan sodium cooled fast reactor (JSFR). For sodium pipes of JSFR, the continuous leak monitoring will be adopted as an alternative to a volumetric test of the weld joints under conditions that satisfy LBB. The sodium pipes are made of ASME Gr.91 (modified 9Cr-1Mo steel). Thickness of the pipes is small, because the internal pressure is very low. Modified 9Cr-1Mo steel has a relatively large yield stress and small work hardening coefficient comparing to the austenitic stainless steels which are currently used in the conventional plants. In order to assess the LBB behavior of the sodium pipes made of modified 9Cr-1Mo steel, the coolant leak rate from a through-wall crack must be estimated properly. Since the leak rate is strongly related to the COD, an appropriate COD assessment method must be established to perform LBB assessment. However, COD assessment method applicable for JSFR sodium pipes—thin wall and small work hardening material—has not been proposed yet. Thus, a COD assessment method applicable to thin walled large diameter pipe made of modified 9Cr-1Mo steel was proposed in this study. In this method, COD was calculated by classifying the components of COD; elastic, local plastic, and fully plastic. In addition, the verification of this method was performed by comparing with the results of a series of four-point bending tests at elevated temperature using thin wall modified 9Cr-1Mo steel pipe containing a circumferential through-wall crack. As a result, COD values calculated by the proposed method were in a good agreement with the experimental results for the uniform pipe without a weld. In the case that the crack was machined in the weld metal or heat affected zone (HAZ), the proposed method predicted relatively larger COD than the experimental results. The causes of such discrepancies were discussed by comparing with the results of finite element analyses. Based on these examinations, the rational leak rate evaluation method in LBB assessment was proposed.

Mechanical properties of AISI 1045 ceramic coated materials by nano indentation and crack opening displacement method

An effective approach was conducted for estimating fracture toughness using the crack opening displacement (COD) method for plasma enhanced chemical vapor deposition (PECVD) coating materials. For this evaluation, an elastoplastic analysis was used to estimate critical COD values for single edge notched bending (SENB) specimens. The relationship between fracture toughness (K IC) and critical COD for SENB specimens was obtained. Microstructure of the interface between Al2O3-TiO2 composite ceramic coatings and AISI 1045 steel substrates was studied by using scanning electron microscope (SEM). Chemical compositions were clarified by energy-dispersive X-ray spectroscopy (EDS). The results show that the interface between of Al2O3-TiO2 and substrate has mechanical combining. The nanohardness of the coatings can reach 1 200 GPa examined by nanoindentation. The K IC was calculated according to this relationship from critical COD. The bending process produces a significant relationship of COD independent of the axial force applied. Fractographic analysis was conducted to determine the crack length. From the physical analysis of nanoindentation curves, the elastic modulus of 1045/Al2O3-TiO2 is 180 GPa for the 50 μm film. The highest value of fracture toughness for 1045/Al2O3-TiO2-250 μm is 348 MPa·ml/2.

Investigation of mechanical and fracture behavior of plane weave glass fiber/polymer composite with inclined through thickness cracks

The aim of this study is to investigate mechanical and fracture behavior of plane weave glass fiber reinforced high density polyethylene (HDPE) thermoplastic composite using a middle tension (MT) specimen with inclined through-thickness cracks under static tension. In this study, crack growth, crack opening displacement (COD), stress intensity factors and fracture toughness are studied. Crack growth and crack opening displacement values are taken as a damage parameter factor for crack geometry calculations. Experimental results are evaluates using both J-integraland stress intensity factormethods.

The role of ultimate elongation in the determination of valid ligament range of essential work of fracture tests

In this study, the feasibility of a previously proposed ultimate elongation-based criterion of essential work of fracture (EWF) method was reconsidered for several materials. Suitable ductility level (DL) ranges for the EWF testing of polymers were discussed, too. It was shown that there is a relationship between the DL terms and the experimentally estimated crack opening displacement values. Based on Coterell’s estimate of the size of the fracture process zone a lower ligament limit of EWF concept was also presented. This lower bound should be considered for thin samples where the original thickness-dependent criteria seemed to be not severe enough.

CTOD- R curve construction from surface displacement measurements

The construction of a fracture resistance δ– R (or J– R) curve requires the appropriate measurement of crack-tip opening displacement ( CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement- CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD- R, is developed by the local measurement of crack opening displacement ( COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.

Utilising CODmax as an Indirect Fatigue Crack Length Measurement Parameter for M(T) Specimens of an Airframe Aluminium Alloy AA6056

Abstract Accuracy of indirect fatigue crack length measurement by potential drop method or by compliance technique may be affected at low load ratio due to fracture surface contact, crack closure or mixed mode fracture. As an alternative, the maximum value of crack opening displacement, CODmax, from a clip gauge was utilized. Middle crack tension M(T) specimens were used to obtain conservative data at a low load ratio (R = 0.1). Thin sheet specimens (B = 3.2 mm) with different widths (100 mm ≤ W ≤ 400 mm) of AA6056-T4 were investigated in the mid-regime (Paris regime), which is of interest for damage tolerance analysis. The use of CODmax is found to provide crack lengths equivalent to those measured optically. Hence, the method is very suitable for indirect crack length measurement. Furthermore, small width specimens provided data equivalent to large width specimens. Insofar, the size effect is found to be absent, and fatigue crack propagation data can be acquired on small width specimens when material availability is limited.

Investigation of the Fracture Behavior of Woven Fiber Glass-reinforced Low-density Polyethylene Composite

The fracture behavior of woven fiber glass-reinforced low-density polyethylene thermoplastic composite having a middle tension specimen with inclined through-thickness cracks under static loading is studied in this article. Through the experiments, the topics crack growth, crack opening displacement (COD), stress intensity factors, and fracture toughness are studied. Crack growth amount and COD values are used as a damage parameter factor for crack geometry calculations. The consequent results of the experiments are inspected with J-integral method and stress intensity factor. Load-elongation and load-crack mouth opening displacement, the strain energy release rate-crack growth amount, stress intensity factor-crack growth amount graphics were drawn as the material properties under consideration.