Crack Mouth Opening Displacement Research Articles

Calibration and validation of extended back-face strain compliance for a wide range of crack lengths in SENB-4P specimens

Compliance equations based on back-face strain or crack mouth opening displacement, and potential drop techniques are widely used to calculate fatigue crack growth rate. Standard ASTM E647 for fatigue crack growth rate testing does not include compliance based equations for single edge notched four-point bending (SENB-4P) specimens. Equations developed based on finite element (FE) analysis have been reported in literature; however, they are limited to the long crack propagation regime (i.e., relative crack length ratios a/W > 0.15). No compliance relations for crack growth in the physically short crack regime were found in literature. This work reports on a complementary numerical-experimental study towards the development of compliance equations with an extended application range in terms of relative crack length. FE simulations have been used to calibrate a back-face strain compliance equation for calculation of relative crack length in the range 0.05 ≤ a/W ≤ 0.5 for SENB-4P specimens. Four point bending fatigue tests were performed on SENB specimens extracted from 50 mm thick welded steel plates. Direct current potential drop (DCPD) for crack monitoring was used as benchmark and validation of the crack lengths determined from a back-face strain gage.

DIC analysis of nano concrete using functionalized and dispersed carbon nanotubes

Digital Image Correlation (DIC) method is considered as a powerful tool to capture material behavior for improved precision. This paper deals with effect of dispersion and functionalization of multiwall carbon nanotubes (MWCNTs) on fracture mechanics properties such as fracture energy and stress intensity factor. Fracture mechanics properties were found out using DIC technique and also by experimentally using a clip gauge and linear variable differential transformers (LVDT). The experiment was conducted under crack mouth opening displacement (CMOD) controlled manner and rate of loading was set as 0.0005 mm/s. MWCNTs were taken in a proportion of 0.1%, 0.2%, 0.3%, 0.4% and 0.5% by weight of cement and Nano silica and Nano alumina were considered as 3% and 2% by weight of cement respectively. The compressive strength is increased by 45.28% and tensile strength and flexural strength increased by108.26% and 53.249% respectively. It was seen that displacements measured by DIC and by experimentally were in the same line and also Load vs CMOD graphs plotted with both the methods are having similar behavior. Size effect was considered for preparation of all the specimens and by the results it can be seen that all specimens follow Bazant’s Size effect law.

Effect of short-term exposure to moderate temperatures on the residual strength of cracked fibre reinforced concretes

This work studies the effect of short-term exposure to the temperatures of -15°C, 5°C, 40°C and 60°C on the flexural performance of Fibre Reinforced Concretes (FRCs) with steel and synthetic fibres in cracked conditions. The results will be compared with the performance in cracked conditions at 20°C (submerged and air environments). The content of the fibres was chosen to guarantee similar residual strength in all the mixes. The beams were pre-cracked following EN 14651 at ambient temperature after 28 days, up to a crack mouth opening displacement (CMOD) of 0.5 mm. Afterwards, these beams were exposed for 3 days to moderate temperatures, and they were re-loaded up to failure maintaining the target temperature during the test. The residual strength at CMODs of 1.5, 2.5 and 3.5 mm was analysed. Concrete mixes were also characterised by compressive strength, air content, fresh density, and workability. The results show that residual strengths of cracked FRC are more sensitive to sub-zero temperatures than to warm temperatures, similar to the behaviour of uncracked specimens. Synthetic and steel FRCs presented enough flexural response after short-term exposure to moderate temperatures under cracked conditions.

Fracture behavior of concrete containing MSWI vitrified bottom ash

The incorporation of waste materials into concrete allows responding to some of the most significant issues of our society: waste management and climate change. Experimental studies carried out in last decades have shown that municipal solid waste incineration (MSWI) ash, and particularly bottom ash, which constitutes the major solid by-product of incineration process, can be adopted to produce building materials. However, several issues are related to the safety and the environmental impact of MSWI ash utilization for concrete production, mainly linked with the leaching of heavy metals and toxic organic components. To solve these problems, several treatments for MSWI ash can be adopted and, among them, in this work the attention was focused on vitrification technology, which enables to convert the ash in a glassy inert solid material. The aim of the present paper is to study the feasibility of developing a “green concrete” that incorporates vitrified MSWI bottom ash as partial cement replacement, so reducing the cement content and consequently the carbon dioxide emissions as well as the raw materials consumption related to its production. The vitrified MSWI bottom ash, ground at micrometer size, was inserted into the admixtures by considering two percentages of cement substitution (10% and 20% by weight of cement). The flexural behavior of concrete containing vitrified MSWI ash was investigated through three-point bending tests under crack mouth opening displacement control. The crack path evolution was further explored by adopting the Digital Image Correlation technique. By analyzing the obtained results, it can be concluded that the use into concrete of vitrified MSWI bottom ash as cement replacement up to a percentage of 20% by weight of cement, allows reaching comparable flexural resistances with respect to the reference concrete. So, the proposed approach can represent a viable solution for the development of environmental-friendly concretes able to reduce the environmental impact of the concrete industry, which is mostly related to cement production, as known.

Additively manufactured tensile ring-shaped specimens for pipeline material fracture examination - influence of geometry

In order to define a procedure for integrity assessment of pipelines and determining the fracture mechanics parameters, a new type of specimen with a sharp notch, Pipe Ring Notched Tension (PRNT) specimen, is tested. The aim of the study is to determine the influence of the specimen geometry (cylindrical shape, as well as number and length of stress concentrators) on parameters such as force, Crack Mouth Opening Displacement CMOD, Crack Tip Opening Displacement CTOD and J integral. The specimens were fabricated by an additive production method - selective laser sintering (SLS). EOS Formiga P100 machine is used, and the material is polyamide PA12. In addition to Pipe Ring Notched Tension specimens, Single Edge Notched Tension (SENT) specimens with identical cross section were also considered. All specimens were tested on a universal tensile testing machine. A tool specially designed to apply contact pressure to the inner walls in the tension direction was used, simulating the internal pressure. For determining the field of displacement and strain on the surface of the tested samples that occur during the loading, Aramis GOM 2M optical measurement system was used. Aramis is applied for determination of geometry fracture mechanics parameters: CMOD and CTOD (based on δ5 concept). In addition to the examination of fracture properties of additively manufactured PA12, the main topic of this work is the development of the non-standard testing procedure, which will be subsequently applied to the specimens cut from metallic or non-metallic pipes. As an important part of this procedure, the calculation of fracture parameters will be conducted based on the results presented here.

Numerical modelling of mode-I cracking in asphalt concrete

This paper presents a numerical model to simulate mode-I fracture in asphalt concrete. The phase field method is used to simulate diffuse damage in asphalt concrete. In addition to the displacement degrees of freedom, a scalar damage degree of freedom is added at each node of a finite element. Evolution of the damage variable is governed by a crack potential which regularizes a sharp crack over a finite volume. The phase field method does not suffer from mesh dependency problem like the continuum damage models and therefore preferred for damage analysis. A single edge notch beam is analysed to show the performance of the model. The damage pattern as well as load versus crack mouth opening displacement graph is compared with the experimental data. The numerical results show good agreement with the experimental observations.

Influence of Graphite Powder on the Mechanical and Acoustic Emission Characteristics of Concrete

In this paper, uniaxial compressive strength (UCS) test and three-point bending (TPB) test, together with an acoustic emission (AE) system, were performed to investigate the mechanical properties and AE characteristic changes of concrete with different graphite powder (GP) content. The results show that: (1) Poor adhesion and low interlocking of graphite with cement stone increase the initial defects of concrete, reducing its elastic modulus and the cyclo-hoop effect, and thus weakening the compressive strength. (2) For concrete with a low graphite content, the second sharp rise in ringing counts or energy released during the compressive process can be regarded as a failure alarm. However, as GP content increases, the second sharp rise fades away, while the first sharp rise becomes more visible. At high GP content, the first sharp rise is better for predicting failure. (3) The initial defects caused by GP significantly lower the initial fracture toughness, but its bridging effect greatly increases the critical crack mouth opening displacement and thus significantly enhances the unstable fracture toughness of concrete, by up to 9.9% at 9% GP content. (4) In contrast to compressive process, the sharp increase in AE signals preceding failure during the fracture process cannot be used to predict failure because it occurs too close to the ultimate load. However, as GP can significantly increase the AE signals and damage value in the stable period, such failure precursor information can provide a safety warning for damage development.

Investigation of fatigue crack propagation behavior in steel fiber-reinforced ultra-high-performance concrete (UHPC) under cyclic flexural loading

Fatigue crack propagation behavior in ultra-high-performance concrete (UHPC) containing different volume fractions of steel fibers is investigated under cyclic flexural loading at various stress levels. Evolutions of the crack mouth opening displacement, crack tip strain, and crack propagation length are characterized during continuous loading cycles via digital image correlation. Test data are fit to smooth, continuous logarithmic functions to discern relationships between evolving crack length and the number of loading cycles. The crack propagation rates of different UHPC specimens are then determined from the first derivative of these logarithmic functions. A critical crack length of approximately 20 mm is found in UHPC containing a fiber volume fraction (Vf) of 0.5%, while that of other specimens (Vf = 1.0%, 1.5%, and 2.0%) is found to approach 60 mm under the stress levels of 0.80, 0.75, 0.70 and 0.65. Strain diagrams obtained via DIC reveal no obvious changes for the crack growth along the y-direction in UHPC specimens containing fiber volume fractions of 0.5% and 1.0%, while a tendency for strain concentrations oriented at 45° characterizes crack development in specimens containing 1.5% and 2.0% volume fractions of fiber. Crack propagation rates during the stable stage of crack propagation decrease upon reducing applied stress level and with increased content of steel fiber reinforcement, providing predominant means to enhance fatigue life.

Comparative analysis of the effects of aggregates and fibres on the fracture performance of lightweight aggregate concrete based on types I and II fracture test methods

This study aims to evaluate different influencing factors, such as the types of coarse aggregates with different elastic moduli, different mixing methods for aggregates and fibres (steel fibre, basalt fibre and polypropylene fibre) and two fracture test methods, on the fracture performance of concrete. LC30 all-lightweight shale ceramsite (SC) concrete was regarded as the benchmark. SC was replaced with limestone gravel at a volume ratio of 30% and changed into gravel lightweight concrete. Forty-two three-point bending notched beams and 42 single-side double-notched beams were firstly fabricated, then type I tensile test and type II shear test were conducted. The load (P, kN)–deflection (δ, mm) curves and load (P, kN)–crack mouth opening displacement (CMOD, mm) curves were obtained via type I test, and P–δ curves were obtained via type II test. The effects of aggregates and fibres on type I and II failure modes were analysed, and the influence on the initial fracture toughness, unstability fracture toughness and fracture energy was evaluated. The linear relationships between fracture energy and unstability fracture toughness were determined by type I test, and the relations amongst the initial and unstability fracture toughness and shear force were identified by type II test. Comparative analysis shows that the influence of high-modulus aggregates and fibres on the fracture performance is considerable. The peak load of type II test is an order of magnitude larger than that of type I test, and the peak displacement is also much larger. The failure characteristics of type II test have the composite features of type I and II fracture tests. Some kind of ratios exist between the initial and unstability fracture toughness of types II and I. However, the extent of type I impact on type II is difficult to quantify.

Nonlinear ABAQUS Simulations for Notched Concrete Beams.

The numerical simulation of concrete fracture is difficult because of the brittle, inelastic-nonlinear nature of concrete. In this study, notched plain and reinforced concrete beams were investigated numerically to study their flexural response using different crack simulation techniques in ABAQUS. The flexural response was expressed by hardening and softening regime, flexural capacity, failure ductility, damage initiation and propagation, fracture energy, crack path, and crack mouth opening displacement. The employed techniques were the contour integral technique (CIT), the extended finite element method (XFEM), and the virtual crack closure technique (VCCT). A parametric study regarding the initial notch-to-depth ratio (ao/D), the shear span-to-depth ratio (S.S/D), and external post-tensioning (EPT) were investigated. It was found that both XFEM and VCCT produced better results, but XFEM had better flexural simulation. Contrarily, the CIT models failed to express the softening behavior and to capture the crack path. Furthermore, the flexural capacity was increased after reducing the (ao/D) and after decreasing the S.S/D. Additionally, using EPT increased the flexural capacity, showed the ductile flexural response, and reduced the flexural softening. Moreover, using reinforcement led to more ductile behavior, controlled damage propagation, and a dramatic increase in the flexural capacity. Furthermore, CIT showed reliable results for reinforced concrete beams, unlike plain concrete beams.

On the fracture toughness testing for single-edge notched bend specimen of orthotropic materials

Majority of the fracture toughness tests on orthotropic materials reported in the literature are based on the testing methods developed for isotropic materials since there is no available testing standards specifically dealing with orthotropic materials. In this study, a systematic two-dimensional finite element analyses (2D FEA) of orthotropic single-edge notched bend (SENB) specimens are performed to evaluate the stress intensity factor (SIF) and crack mouth opening displacement (CMOD), which are two key parameters used in the fracture toughness tests. The analysis matrix covers a wide range of material orthotropy. Highly accurate regression solutions for SIF, CMOD compliance and its inverse function were developed as functions of orthotropy parameters. Applications of the proposed equations on experimental data are presented and further discussed. The research outcome is expected beneficial to the standardization of the fracture toughness testing on orthotropic composite materials such as wood, bone and unidirectional fiber-reinforced polymer composites.

The outlook for regulatory support for adoption of efficient concretes

The analysis of data obtained under studying scientific, technical and normative literature in the area of applying efficient concretes, in particular, fiber-reinforced concrete, in the world and national tunnel construction is presented herein. The European regulatory documents, standard metrologically certified methods and procedures for analyzing and testing, laboratory test equipment and measuring instruments are indicated. Steel fiber concrete studies was explored at the Scientific and Educational Center for Innovative Technologies of the Architectural and Construction Institute of the Ufa State Petroleum Technical University. Prism bending tests were made with different fiber content. In addition to laboratory tests, other tests were made in accordance with the Russian standards, where the prisms are tested without a notch. The correlation between the slope of the load-to-displacement curve of the crack mouth (CMOD - Crack Mouth Opening Displacement) and the length of the crack was used in the course of the study. The fiber content enabling to get an average residual bending strength of at least 1.5 MPa at 0.5 CMOD (equivalent to 0.47 mm center deviation) and an average residual bending strength of at least 1 MPa at 3.5 mm CMOD (equivalent to 3.02 mm of center deviation) is found. Statistical distributions of the Grubbs tests are analyzed by methods of statistical modeling. The regulatory framework for fiber concrete is not currently well developed in the Russian Federation, thereby reducing greatly the application of new generation concretes meeting the current knowledge. The application of fiber concrete in tunnel construction will prove to be economically justified and the areas of applying effective materials are to be developed in future with the wide participation of scientific, design, production, construction and other specialized organizations, as well as educational and training centers.

Fracture parameters of fly ash geopolymer mortars with carbon black and graphite filler

In this study, the effect of carbon black and graphite filler on the crack initiation and fracture parameters of fly ash geopolymer mortar is investigated. The carbon black was added in the amount of 0.5 and 1.0% and graphite powder in the amount of 5 and 10% relative to the fly ash mass. The reference mixture without any filler was also prepared. The fracture characteristics were determined based on the results of the three-point bending test of prismatic specimens provided with an initial central edge notch. The fracture experiments were conducted at the age of 48 days. The vertical force (F), the displacement measured in the middle of the span length (d), and the crack mouth opening displacement (CMOD) were continuously recorded during the test. The records of fracture tests were subsequently evaluated using the effective crack model, work-of-fracture method, and double-K fracture model. The addition of both fine fillers led to a decrease in monitored mechanical fracture parameters in comparison with reference mortar.

Effects of BFRP Bar Diameter and Cover Thickness on Fracture Behavior of BFRP Bar–Reinforced Ecological High-Ductility Cementitious Composites

Abstract To obtain the design parameters of bridge deck link slabs made of ecological high-ductility cementitious composite (Eco-HDCC) material reinforced with a basalt fiber-reinforced plastic (BFRP) by applying fracture mechanics concepts, the reinforcing effects of a BFRP bar on the fracture properties of BFRP bar–reinforced Eco-HDCC specimens were studied. First, cracking load, crack mouth opening displacement (CMOD), and deflection of specimens were monitored, and BFRP bar diameter and cover thickness were considered. The results indicate that both the diameter and cover thickness of BFRP bar have an obvious influence on the crack kinking angle. In addition, as the diameter of BFRP bar increases, the peak load, peak CMOD, peak deflection, and fracture energy of Eco-HDCC specimens increase, and these peak values of Eco-HDCC specimens after reloading also show the same trend. In addition, the peak load, peak CMOD, peak deflection, and fracture energy are larger if the Eco-HDCC specimen has a smaller cover thickness. However, the Eco-HDCC specimen with a BFRP bar cover thickness of 25 mm has a higher peak load after reloading than the specimen with a cover thickness of 15 mm when the bar diameters are 10 and 12 mm, respectively. In conclusion, BFRP bar diameters from 10 to 14 mm and a cover thickness of 25 mm are recommended when designing bridge deck link slabs.

Full-scale experimental investigation of the fracture behaviours of welding joints of APL X80 wide plate based on DIC technology

With the advances in material research and pipe manufacturing, the construction of oil and gas pipelines is developing continuously, and the evaluation of welding joints with defects has become the focus of pipeline safety research. In this study, two full-scale wide plate tensile tests were performed on Ø1422 mm × 25.7 mm X80 specimens with original and repaired welding joints. By comparing and analysing the experimental load–displacement responses, as well as the synchronous monitoring results of strain gauge and digital image correlation (DIC) system, the variation trend of the crack mouth opening displacement (CMOD) with distal strain, and the strain capacity of welding joints under different critical CMOD conditions were obtained. This way, the difference in bearing capacity between the original and the repaired welding joints was further determined. Under the same load condition, the driving force of the defect crack expansion at the repaired welding joint was smaller. When the critical CMOD was 0.5 mm and 1.0 mm, the strain capacity of the repaired welding joint was increased by 0.12% and 0.35%, respectively. Therefore, the repair operations of the welding joint effectively strengthen its deformation capacity. This research can provide a valuable data basis for the subsequent verification of numerical analysis models, and can also be referenced for the safety evaluation of pipelines with crack defects.

FRACTURE PROPERTIE ANALYSIS OF RECYCLED AGGREGATE CONCRETE BASED ON DIGITAL IMAGE CORRELATION TECHNIQUE

Three point bending fracture tests of recycled aggregate concrete beams with different recycled coarse aggregate replacement ratio (0%, 30%, 50%, 70%, 100%) have been carried out, with results analyzed by digital image correlation (DIC) method and the traditional electrometric method. The double-K fracture parameters, crack-mouth-opening displacement (CMOD), crack-tip-opening displacement (CTOD), crack extension length ( \begin{document}$\Delta a$\end{document} ) and fracture growth path were obtained, and the validity of DIC method was verified. The results show that when the replacement rate is 100%, the crack initiation fracture toughness and unstable fracture toughness of recycled aggregate concrete decrease by 15.81% and 15.39%, respectively. With the increase of the replacement rate of recycled aggregate, the slopes of the descending sections of P-CMOD, P-CTOD and P- \begin{document}$\Delta a$\end{document} curves increase. DIC method can effectively capture the fracture propagation process. The CMOD values measured by DIC method and clip type extenometer are in good agreement. The variation trends of DIC measured value and formula-calculated value of CTOD are relatively consistent. Based on the test results, the estimated values, \begin{document}$\Delta a$\end{document} , of specimens with different replacement rates of recycled aggregate under different loads can be obtained by fitting the curve between \begin{document}$P$\end{document} / \begin{document}${P_{\max }}$\end{document} and \begin{document}$\Delta a$\end{document} / \begin{document}$\Delta {a_{\text{c}}}$\end{document} .

Advanced Evaluation of the Freeze-Thaw Damage of Concrete Based on the Fracture Tests.

This paper presents the results of an experimental program aimed at the assessment of the freeze–thaw (F–T) resistance of concrete based on the evaluation of fracture tests accompanied by acoustic emission measurements. Two concretes of similar mechanical characteristics were manufactured for the experiment. The main difference between the C1 and C2 concrete was in the total number of air voids and in the A300 parameter, where both parameters were higher for C1 by about 35% and 52%, respectively. The evaluation of the fracture characteristics was performed on the basis of experimentally recorded load–deflection and load–crack mouth opening displacement diagrams using two different approaches: linear fracture mechanics completed with the effective crack model and the double-K model. The results show that both approaches gave similar results, especially if the nonlinear behavior before the peak load was considered. According to the results, it can be stated that continuous AE measurement is beneficial for the assessment of the extent of concrete deterioration, and it suitably supplements the fracture test evaluation. A comparison of the results of fracture tests with the resonance method and splitting tensile strength test shows that all testing methods led to the same conclusion, i.e., the C1 concrete was more F–T-resistant than C2. However, the fracture test evaluation provided more detailed information about the internal structure deterioration due to the F–T exposure.

Laboratory Performance and Field Case Study of Asphalt Mixture with Sasobit Treated Aramid Fiber as Modifier

The use of fiber in asphalt mixtures can improve the mixture’s tensile strength and increase its cracking resistance, but the clumping of fiber in the mixture can weaken the improvement effect. The aim of this research is to assess the properties of Sasobit treated aramid fiber modified asphalt mixture and to validate the field case study. The rutting and stripping resistance of the fiber-modified mixture was identified with the Hamburg wheel tracking device. The low-temperature cracking characteristics of the asphalt mixture were quantified with the disk-shaped compact tension test. Moreover, the dynamic modulus test was adopted to reflect the response of the mixture to different loads and frequencies. The creep slope and stripping slope decreased by 67%, and the number of passes to stripping point and fail point increased by more than 250% after fiber modification. The fracture energy, peak load, and maximum crack mouth opening displacement (CMOD) of the mixture increased more than 10% after fiber modification. The dynamic modulus, rutting parameter, and fatigue parameter of the mixture were improved after fiber modification. The fiber in the mixture improved the stiffness of the mixture at high temperatures. The tensile strength improvement at low temperatures promoted the cracking resistance of the mixture. The cracking number in the fiber modified asphalt pavement was less than that in the control asphalt pavement. Thus, fiber modification could significantly restrict the propagation of cracking in the asphalt mixture. The implementation of fiber in the project can provide experience for future fiber application in asphalt pavement.

A simplified estimation method for tensile softening curve of quasi-brittle materials

Based on cohesive zone model (CZM), a simplified method for estimating the tensile softening curve of quasi-brittle materials is proposed. First, assume that the virtual crack opening displacement is linearly distributed. According to Castigliano's theorem, a cohesive displacement proportional function is proposed, which can obtain Crack Tip Opening Displacement (CTOD) directly from Crack Mouth Opening Displacement (CMOD). This simplifies the governing equations of CZM and the tensile softening curve can be obtained quickly. Finally, the effectiveness of the method is verified by experiment and finite element. Highlights A simplified method for estimating the tensile softening curve of quasi-brittle materials is proposed. The proposed simplified method does not require sophisticated mathematical techniques or finite element modeling. The effectiveness of this method is verified by previous experimental results and finite element simulations. It is reasonable to assume that the crack opening displacement in the fracture process zone conforms to the linear distribution. The cohesive displacement proportional function is proposed. CTOD can be directly obtained from CMOD using the function.

Growth Ring Orientation Effects in Transverse Softwood Fracture.

In this study, the fracture mechanics of eastern spruce were characterized in relation to end-grain orientation. Compact tension-type specimens with small pre-formed cracks were prepared such that grain angle varied relative to the load axis. Specimens were loaded under crack mouth opening displacement (CMOD) control as to maintain stable crack growth. Specimen fracture was characterized using both R-curve and bulk fracture energy approaches. The results showed that under a RT grain orientation, as well as grain deviations up to about 40, cracks will follow a path of least resistance in an earlywood region. As the grain angle exceeds 40, the crack will initially move macroscopically in the direction of maximum strain energy release rate, which extends in the direction of the pre-crack, but locally meanders through earlywood and latewood regions before settling once again in an earlywood region. At 45, however, the macroscopic crack takes a turn and follows a straight radial path. The results further show that RT fracture is macroscopically stable, while TR fracture is unstable. None of the end-grain fracture orientations showed rising R-curve behavior, suggesting that there is not a traditional fracture process zone in this orientation.