Two-parameter Fracture Model Research Articles

Effects of adhesive layer thickness on the fracture properties of a concrete-epoxy resin interface

Adhesive layer thickness is a crucial factor that affects the performance of interfaces in cement-based composite structures. However, the influence of adhesive layer thickness on the fracture properties of concrete–epoxy resin remains unclear. In this study, a two-parameter fracture model of a concrete-epoxy resin interface from the perspective of fracture mechanics. Digital image correlation (DIC) technique was used to investigate the evolution of the fracture process zone (FPZ) of nine specimens with adhesive layer thicknesses of 2 mm, 5 mm, and 8 mm, respectively. The interfacial fracture toughness parameters of the concrete-epoxy resin interface were determined based on the four-point bending (FPB) tests. The test results indicated that increasing the adhesive layer thickness changed the failure mode of the interface from approximate-brittle to quasi-brittle. The load-carrying capacity and interfacial stiffness of the concrete-epoxy resin interface decreased by approximately 13.8 % and 61.1 % with an adhesive layer thickness from 2 mm to 8 mm, respectively. The deflection across the specimen increased by approximately 37.2 % with an increase in adhesive layer thickness due to the lower elastic modulus of epoxy resin compare to the concrete. Furthermore, the FPZ for the adhesive layer thickness of 5 mm was the longest; it was approximately 18.7 % longer than that for the test specimen with an adhesive layer thickness of 2 mm. In terms of structural load-bearing capacity and fracture toughness, the concrete-epoxy resin interface exhibited the best working performance when the thickness of the adhesive layer was 5 mm.

Fracture properties of extruded fiber-reinforced mortar with preferentially aligned fibers

The fracture properties of fiber-reinforced mortar were determined in this paper using three-point bend tests on notched beams and employing the two-parameter fracture model (TPFM). A comparison was made between two casting methods: conventional casting and pump-driven extrusion. The hypothesis suggested that the extrusion process would preferentially align fibers parallel to the tensile stresses, thereby enhancing the concrete’s fracture properties. The results corroborated the enhancement of concrete's ductility and post-peak behavior when fibers were added, consistent with previous studies. However, this study revealed a novel insight that preferential fiber alignment achieved through extrusion could further enhance the fracture properties of concrete. Furthermore, digital image correlation was used to obtain the entire displacement field during testing. The crack propagation process and the strain localization were investigated, and the fracture toughness considering crack deflection was calculated using a modified two parameter model (MTPM). The results showed that extrusion-based specimens exhibited more deflected cracks, affirming the hypothesis that fiber alignment via extrusion influenced the crack propagation, thereby enhancing the fracture properties of the composite.

Fracture toughness of matrix cracked FRC and FGC beams using equivalent TPFM

In the present work, the fracture toughness (KIC) of full-depth (FD) fiber-reinforced concrete (FRC) and layered functionally graded concrete (FGC) matrix cracked (MC) beams has been determined by the equivalent relationships of the two-parameter fracture model (ETPFM). Forty-eight MC-FGC and MC-FD FRC beam specimens with span-depth ratios (L/d) equal 4, 5, and 6 were tested under the 3PB configuration. The MC length-depth ratio (ao/d) remained constant equal to one-third. All FRC beams have the same constitutes materials with hooked-end steel fiber volume fraction equals 1%. The FGC beams are composed of three equal layers, i.e., FRC in the bottom layer at the tension side, normal strength concrete (NSC) at the middle layer, and high strength concrete at the upper layer in the compression side. The results showed that the predicted values of KIC obtained from ETPFM are considered logic according to the maximum size of the non-damaged defect concept. The crack mouth opening displacement estimated from ETPFM showed acceptable values close to the present experimental results. The KIC values calculated within the presence of fibers in front of and through the MC for FRC beam specimens having 1% SFs is more than twice the value of NSC.

Brittleness of Concrete under Different Curing Conditions.

In order to shorten construction periods, concrete is often cured using steam and is loaded at an early age. This changes the performance and even the durability of the concrete compared to concrete that has been cured under normal conditions. Thus, the pattern and the mechanism of concrete performance change under different curing conditions, and loading ages are of great significance. The development of brittleness under different curing conditions and loading ages was studied. The evaluation methods that were used to determine concrete brittleness were expounded. Steam, standard, and natural curing conditions were carried out on single-side notched concrete beams as well as on a concrete prism and cubic blocks. The compressive strength and splitting tensile strength of the concrete blocks along with the fracture performance of the concrete beams were tested after 3, 7, 28, and 90 days. The steam curing condition significantly improved the strength of concrete before 28 days had passed, and the standard curing condition improved the strength of concrete after 28 days. Based on the experimental fracture parameters, a two-parameter fracture model was applied to study the development of fracture toughness , critical crack tip opening displacement , and critical strain energy release rate with hydration age under different curing conditions. With respect to long-term performance, the standard curing condition was better at resisting concrete crack propagations than the steam curing condition was. The characteristic length and the material length under the three curing conditions and the long-term development of brittleness in the concrete indicated that steam curing increased the concrete brittleness. Considering the effects of the curing condition and the loading age, a time-dependent concrete fracture toughness model was established, and the predicted value of the model was verified against the measured value. The results indicated that the model was able to accurately predict the fracture toughness with an error rate of less than 16%.

Effect of grading type of aggregate on fracture parameters of concrete

Experimental studies have revealed that fracture parameters of concrete are mainly influenced by four material parameters: compressive strength, maximum aggregate size, water/cement ratio and aggregate type (river or crushed). It has been noted that the fracture parameters of concrete can also be affected by other material parameters such as the type of cement, aggregate/sand ratio, porosity and curing conditions. Aggregates can be dense gap-graded or continuously graded in concrete technology. However, the effect of aggregate gradation (continuously or gap-graded) on the fracture parameters of concrete has not been examined up until now. In this study, the notched and un-notched cubes produced by both gap and continuously graded batches were tested under splitting loading. The results are discussed based on the three most popular fracture approaches, namely the size effect law, the multi-fractal size effect law and the two-parameter fracture model. Although concretes made with an aggregate of either type of grading have similar mechanical properties such as compressive and tensile strength according to the literature, this study emphasises that the mixes with gap-graded aggregates indicate a more ductile behaviour than those with continuously graded aggregates for the same maximum aggregate size.

Two-parameter fracture model for cortical bone

The analysis of the bone fracture behaviour is fundamental for prevention, diagnosis and treatment of traumas. In the present paper, an experimental analysis of the fracture behaviour of a bovine femoral cortical bone is carried out, where specimens are extracted from a diaphysis. Fracture toughness is computed by employing a two-parameter fracture model originally proposed for concrete. In order to take into account the possibility of crack deflection (kinked crack) due to osteons orientation, a modified version of such a model is here discussed. The fracture toughness results are then compared with those reported in the literature, related to a femur of an 18-month-old bovine.

Mode I fracture toughness of fibre-reinforced concrete by means of a modified version of the two-parameter model

The present paper proposes a method to calculate Mode I plane-strain fracture toughness of concrete, by taking into account the possible crack deflection (kinked crack), even in the case of a far-field Mode I loading. As a matter of fact, during fracture extension, cracks may deflect as a result of microstructural inhomogeneities inside the material. Concrete is an inhomogeneous mixture due to aggregates embedded in the cementitious matrix, but additional inhomogeneities may be represented by fibres. Firstly, a two-parameter fracture model based on Mode I analytical expressions of the linear elastic fracture mechanics is employed. Then, in order to take into account the possible crack deflection as a result of the above inhomogeneities, a modified version of such a model is here discussed. Three-point bending tests on both plain concrete specimens and concrete specimens reinforced with micro-synthetic polypropylene fibrillated fibres are experimentally performed, and the modified model is applied.

The fracture response of blended formulations containing limestone powder: Evaluations using two-parameter fracture model and digital image correlation

The fracture response of mortars in which OPC is partially replaced by limestone or a combination of limestone and fly ash/metakaolin (i.e., for total OPC replacement levels of 20% and 35% by volume) is reported. The blended mortars demonstrate fracture parameters (fracture toughness, KICS and critical crack tip opening displacement, CTODc, determined using the two-parameter fracture model, TPFM) that are comparable to or better than those of pure OPC formulations in spite of having slightly lower compressive strengths than the OPC systems. The ternary blends containing limestone and metakaolin at 20% OPC replacement show the best performance: a consequence of the beneficial limestone–alumina synergy that has been previously established. The strain energy release rates also show trends that are in line with the other fracture parameters. The fracture parameters for selected mixtures evaluated through a non-contact digital image correlation technique are found to correspond well to those determined from TPFM. The outcomes highlight that improved ductility can be attained through the judicious use of limestone and synergistic OPC replacement materials.

Fracture behavior of pervious concretes: The effects of pore structure and fibers

The fracture response of pervious concrete specimens proportioned for different porosities, as a function of the pore structure features and fiber volume fraction, is studied. Stereological and morphological methods are used to extract the relevant pore structure features of pervious concretes from planar images. A two-parameter fracture model is used to obtain the mode I stress intensity factor (fracture toughness) and the critical crack tip opening displacement of notched beams under three-point bending. The experimental results show that the fracture toughness is primarily dependent on the porosity of pervious concretes. For a similar porosity, an increase in pore size results in a reduction in fracture toughness. At similar pore sizes, the effect of fibers on the post-peak response is more prominent in mixtures with a higher porosity, as shown by the residual load capacity, stress–crack extension relationships, and resistance curves. These effects are explained using the mean free spacing of pores and pore-to-pore tortuosity in these systems. A sensitivity analysis is employed to quantify the influence of material design parameters on fracture toughness.

Fracture and impact properties of short discrete jute fibre-reinforced cementitious composites

This paper conducted research on fracture and impact properties of short discrete jute fibre reinforced cementitious composites (JFRCC) with various matrix for developing low-cost natural fibre reinforced concretes and mortars for construction. Fracture properties of JFRCC were tested on notched concrete beams at 7, 14 and 28days and the results were interpreted by the two-parameter fracture model (TPFM). Impact resistance of JFRCC were examined on mortar panels with the dimensions of 200×200×20mm3 at 7, 14 and 28days through repeated dropping weight test. Qualitative and quantitative analyses were conducted for crack pattern, impact resistance and energy absorbed by JFRCC mortar panels based on eye observations and measurement from an oscilloscope. In addition, compressive, flexural and splitting tensile strengths of JFRCCs were tested at 7, 14 and 28days conforming to relevant EN standards. It was found that, by combining GGBS with PC as matrix, JFRCC achieved higher compressive strength, tensile strength, fracture toughness, critical strain energy release rate, and critical stress intensity factor than those with combination of PFA and PC as matrix. Impact tests, however, indicated that JFRCC mortar panels with PFA/PC matrix possessed higher impact resistance, absorbed more impact energy and survived more impact blows upon failure than those with GGBS/PC matrix at the ages of 14 and 28days. JFRCC mortar panels did not shatter into pieces and demonstrated a ductile failure while the plain mortar ones behaved very brittle and shattered into pieces. Upon impact failure, fibre pull-out was observed in JFRCC mortar panels with PFA/PC matrix while fibre fracture in those with GGBS/PC matrix. Besides, the impact resistance, in terms of the number of impact blows survived and the total energy absorbed upon failure, of JFRCC mortar panels decreased with age.

Significance of K-dominance zone size and nonsingular stress field in brittle fracture

Stress intensity factor has been used to characterize the fracture toughness of a brittle material. This practice is apparently based on the assumption that the singular stress alone at the crack tip is responsible for fracture and that the nonsingular part of the near tip stress has no effect on fracture. In this study, mode I fracture experiments were conducted on a brittle material (PMMA) with four different specimen configurations. The result indicated that fracture toughness cannot be described by stress intensity alone and that a second parameter representing the influence of the nonsingular stress is needed. A two-parameter fracture model was proposed and validated with the experimental result. This two-parameter model was shown to be able to account for various effects created by specimen configurations, crack sizes, and loading conditions, on the fracture behavior of brittle materials.

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50–50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.

Concrete fracture prediction using bilinear softening

Abstract A finite element-based cohesive zone model was developed using bilinear softening to predict the monotonic load versus crack mouth opening displacement curve of geometrically similar notched concrete specimens. The softening parameters for concrete material are based on concrete fracture tests, total fracture energy (GF), initial fracture energy (Gf), and tensile strength ( f t ′ ) , which are obtained from a three-point bending configuration. The features of the finite element model are that bulk material elements are used for the uncracked regions of the concrete, and an intrinsic-based traction-opening constitutive relationship for the cracked region. Size effect estimations were made based on the material dependent properties (Gf and f t ′ ) and the size dependent property (GF). Experiments using the three-point bending configuration were completed to verify that the model predicts the peak load and softening behavior of concrete for multiple specimen depths. The fracture parameters, based on the size effect method or the two-parameter fracture model, were found to adequately characterize the bilinear softening model.

The influence of notch depth on the fracture mechanics properties of polymer concrete

This research deals with unreinforced and fiber-reinforced Polymer Concrete (PC). Polymer Concrete is usually composed of natural aggregates such as silica sand, binded together with a thermoset resin, such as unsaturated polyester. In this paper it is reported the use of a direct method to calculate two size independent fracture parameters, the critical stress intensity factor, K Ic, and the critical crack tip opening displacement, CTODC, from experimental results of two different size single edge notched beams, 10 and 20 mm, subjected to three point bending under quasi-static loading condition. This method is called the Two Parameter Fracture Model (TPFM). Also the Fracture Energy, G f, of the specimens were measured to verify its size dependency. Epoxy and polyester resin specimens were studied and epoxy resin specimens reinforced specimens with short carbon and glass fibers were considered.

Fracture Analysis of High Strength Concrete Members

A nonlinear model for the fracture analysis of high strength concrete members is developed through the interactive use of experimental data and finite-element analysis. The experimentally obtained tensile softening relationship is incorporated into a nonlinear ABAQUS finite-element program. Finite-element analysis is performed to evaluate flexural strength, process zone size, size effect, and the effect of load line deflection measurements on concrete fracture energy. The finite-element model is simple and shown to be successful in predicting beam test results. Finally, the finite-element model is used to compare the size effect model and the two-parameter fracture model. The fracture energies obtained by these alternatives are compared and discussed.

Strain rate effects on dynamic fracture and strength

An experimental procedure and accompanying theoretical analysis is presented to produce a well-characterized technique for quantifying dynamic fracture properties of quasi-brittle materials. An analytical and experimental investigation of mode I fracture of concrete was conducted under the dynamic loading of a split Hopkinson pressure bar. Fracture specimens in the form of notched-cavity splitting tension cylinders were subjected to stress wave loading that produced strain rates nearing 10/s. Fracture parameters were extracted by the application of the two-parameter fracture model, a nonlinear fracture model for quasi-brittle materials. Finite element analysis verified the experimental configuration and addressed inertial contributions within the dynamic environment. Ultra-high-speed digital photography was synchronized with the fracture process to provide additional validation and insight to the experimental technique. Results show that the effective fracture toughness and specimen strength both increase significantly with loading rate. The numeric and photographic results validate the experimental technique as a new tool in determining rate dependent material properties.

A Systematic Method to Determine Optimal Specimen Geometry for Measuring Concrete Fracture Properties by the Peak-Load Method

Abstract The peak-load method is a simple method for determining the fracture properties KIcS and CTODc of the two-parameter fracture model of concrete. With this method, the fracture properties can be determined from the measured peak loads of several different (or distinct) specimens. Specimens can be made distinct in specimen shape, size, notch length, and loading configuration. To quantitatively identify the degree of specimen distinction, a variable named specimen distinction number is proposed. When test specimens are considerably distinct, random experimental errors have negligible effect, and determination KIcS and CTODc is of high accuracy. Thus test specimens can be optimized to obtain the most accurate values of the fracture properties. A previous experimental program found that change in specimen shape (e.g., a hole drilled at the axis of splitting tension cylinder) can largely expand the specimen distinction. An experimental program reported in this paper shows that changing loading configurations of beams (or prisms) from bending to eccentric compression can also largely enhance the specimen distinction and therefore provide KIcS and CTODc determination of high accuracy.

Splitting tension tests to determine concrete fracture parameters by peak-load method

Abstract An experimental program confirms that the peek-load method can be successfully applied to splitting tension tests to determine fracture parameters KIcS and CTODc of the two-parameter fracture model from the measured peak loads. The peak-load method requires distinct specimens. It is found that a hole drilled at the axis of splitting tension cylinder can largely expand the specimen distinction. Combination of tests on splitting tension cylinders with and without a hole raises the reliability of the KIcS and CTODc values determined by the peak-load method.

Graphical method to determine the parameters of the two-parameter fracture model for concrete

To evaluate the parameters in the two-parameter fracture model, i.e. the critical stress intensity factor and critical crack tip opening displacement for the fracture of plain concrete in Mode 1 for the given test configuration and geometry, considerable computational effort is necessary. A simple graphical method has been proposed using normalized fracture parameters for the three-point bend (3PB) notched specimen and the double-edged notched (DEN) specimen. A similar graphical method is proposed to compute the maximum load carrying capacity of a specimen, using the critical fracture parameters both for 3PB and DEN configurations.

Characterization of the paste-aggregate interfacial transition zone surface roughness and its relationship to the fracture toughness of concrete

Notched concrete beams containing varying amounts of pea gravel aggregate were tested under three-point bend, and their fracture toughness determined. The roughness of the region near the interface between the cement paste and the aggregate was evaluated by digitizing images from a confocal tandem scanning microscope. The average roughness of the paste was found to be related to the fracture parametersKIC (critical stress intensity factor) and Δac (critical crack extension), as determined by the two-parameter fracture model. The roughness in the proximity of the paste-aggregate interface was generally higher than that of the paste far from the aggregate, and it decreased with the distance from the aggregate. This study indicates that aggregate particles increase the toughness of the cement paste portion of concrete, and that this is an important mechanism for toughening concrete.