Fracture Energy Gf Research Articles

Experimental study of type-I crack propagation in rock monitored by fiber Bragg grating

The occurrence of rock mass engineering disasters can be reduced significantly by obtaining the key information in the process of rock internal fracture accumulation and evolution through advanced monitoring means and taking certain preventive measures. Through fiber Bragg grating monitoring tests of the type-I crack propagation in rock, the spectral characteristics of the fiber Bragg grating in the process of rock failure were analyzed, the bandwidth expansion was extracted to characterize the local tensile strain during the crack propagation process, and the damage variable based on the bandwidth expansion was calculated to describe the type-I crack propagation process. The research results showed the following: (1) The fiber Bragg grating generated a non-uniform local tensile strain during type-I crack propagation. The bandwidth expansion of the wave spectrum was positively correlated with the local tensile strain. The change in the characteristics of the wave spectrum could provide the local real strain in the process of crack propagation. (2) During the steady propagation of the type-I crack, the bandwidth increased obviously, while the number of acoustic emission events was relatively small, and most of them were in the process zone. The gentle increase in the bandwidth corresponded to the unstable growth stage of the type-I crack, which could be used as a precursor of rock sample instability. During loading, the maximum tensile strain of the type-I crack was 6 %, while the maximum shear strain reached 1.8 %, primarily attributed to tensile failure. The average value of fracture toughness KIC, based on the equivalent linear elastic fracture mechanics model, was determined to be 1.21 MPa·m1/2, and the average value of fracture energy Gf was calculated as 57.7 N/m. The variation of peak reflectivity in fiber Bragg grating was associated with the closure of pre-existing defects and the propagation of microcracks in rocks, resulting in unstable shear strain at crack extension sites. (3) The damage variable D defined by the bandwidth broadening began to become concentrated and accumulated in the crack steady growth stage, and it increased slowly in the crack intensification and evolution stage. The grating was sensitive to changes when it was pasted to the surface at 90°, but it could easily fracture or become unable to capture spectral signals in time. Based on a comprehensive comparison, the monitoring effect was the best when the grating was pasted at 60° relative to the crack.

Study on the correlation between homogeneity of mastic and aggregate skeleton on cracking resistance of recycled asphalt mixtures

ABSTRACT The heterogeneous distribution of mastics and aggregates affects the durability of recycled asphalt pavements through cracking and failure behaviour. This study used force chain network analysis to quantify the homogeneity index of stress transfer and established correlations between this homogeneity and the cracking resistance of recycled asphalt mixtures. The results showed a good correlation of 0.8288 between the horizontal homogeneity index DH2, based on the area ratio of RAP and virgin aggregates, and fracture energy Gf. Additionally, the stress transfer efficiency index DH had a significant correlation of 0.7975 with Gf. Bending Beam Rheological tests revealed a high correlation of 0.9507 between the low-temperature performance index S/m and Gf, and a moderate correlation of 0.6115 between the homogeneity index Dm of blended mastics and the coefficient of variation of Gf. Thus, this study established a model that correlated the homogeneity of blended mastic and mixtures with the crack resistance of recycled asphalt mixtures, achieving a correlation coefficient of 0.8492 between the predicted and actual results. These findings enhance the understanding of the relationship between mixture homogeneity and mechanical properties, advancing virtual design technologies for recycled asphalt mixture design.

Characterization of the stress-state dependent ductile fracture behavior for Q960 ultra-high-strength structural steel

Ultra-high-strength structural steels are gaining popularity in civil engineering due to their exceptional strength-to-weight ratio. However, their inherent lower ductility compared to normal strength structural steel warrants particular attention and further investigation for safety assessment. In this study, a total of 24 specimens made of Q960 ultra-high-strength steel (UHSS), including 21 tensile specimens with various stress states and 3 three-point bending specimens, were tested to assess its mechanical behavior undergoing large deformation. Subsequently, the impact of stress state on plasticity, damage evolution and fracture initiation was analyzed and characterized. The Bai-Wierzbicki yield surface with a deviatoric associated flow rule was identified to characterize the complex plasticity behavior of Q960 UHSS. With respect to damage evolution, the stress-state dependent fracture energy Gf was proposed in this study to describe the damage softening behavior. The uncoupled Hosford-Coulomb locus with a non-linear weight function was utilized to predict the fracture initiation behavior. Finally, the utilized stress-state dependent constitutive models for Q960 UHSS, with the calibrated parameters and user-defined material subroutine VUMAT, were successfully verified through the three-point bending test with good agreement. Moreover, based on a parametric analysis of radius-to-thickness ratio, the bendability design regarding the minimum radius-to-thickness ratio of Q960 UHSS was proposed.

Experimental study on Corn Straw Fiber (CSF) toughening EPS concrete

The natural Corn Straw Fiber (CSF), it has the advantages of light weight, high strength, good toughness and renewable, can delay the cracking and improve the toughness of cement-based materials. The effects of different mass fractions of CSF and Expanded-Polystyrene (EPS) particles on the compressive strength, flexural strength, splitting tensile strength and their failure modes, load-displacement curves and toughness of EPS concrete were analyzed by full factorial experimental design method. The compressive toughness index (I0, I1) and fracture energy (Gf) were defined to evaluate the effect of CSF on toughening EPS concrete. The results show that the addition of CSF can improve the compressive strength, flexural strength and cracking toughness of EPS concrete to a certain extent. The maximum compressive strength occurred in the E1F3 specimen with a CSF content of 3 % in Group I, which was 1.12 MPa, and the improvement rate was also the highest among the four groups, reaching 69.7 %. The compressive toughness index I1 also reached its maximum in the E1F3 specimen; The maximum flexural strength occurred in the E3F4 specimen with a 4 % CSF content in Group III, which was 0.885Mpa, with the highest improvement rate of 127.38 %. The maximum fracture energy Gf reached 0.827 in the E3F4 specimen. However, another additive, EPS particles, did not significantly improve the physical and mechanical properties of concrete. According to the SEM images and toughening mechanism analysis, it was discovered that tight adhesion between EPS particles and CSF with cement matrix, and the failure mode of CSF was tensile fracture, which could maximize the effect of CSF high tensile toughness. On the basis of mechanical properties and toughening effect, the relationship formulas between variable factors and strength, toughness index were fitted, and the optimal content of EPS and CSF were determined to be 1.3 % and 3 %, respectively.

Investigation into the interface bond between polyurethane concrete and steel plate

PurposePolyurethane concrete (PUC), as a new type of steel bridge deck paving material, the bond-slip pattern at the interface with the steel plate is not yet clear. In this study, the mechanical properties of the PUC and steel plate interface under the coupled action of temperature, normal force and tangential force were explored through shear tests and numerical simulations. An analytical model for bond-slip at the PUC/steel plate interface and a predictive model for the shear strength of the PUC/steel plate interface were developed.Design/methodology/approachThe new shear test device designed in this paper overcomes the defect that the traditional oblique shear test cannot test the interface shear performance under the condition of fixed normal force. The universal testing machine (UTM) test machine was used to adjust the test temperature conditions. Combined with the results of the bond-slip test, the finite element simulation of the interface is completed by using the COHENSIVE unit to analyze the local stress distribution characteristics of the interface. The use of variance-based uncertainty analysis guaranteed the validity of the simulation.FindingsThe shear strength (τf) at the PUC-plate interface was negatively correlated with temperature while it was positively correlated with normal stress. The effect of temperature on the shear properties was more significant than that of normal stress. The slip corresponding to the maximum shear (D1) positively correlates with both temperature and normal stress. The interfacial shear ductility improves with increasing temperature.Originality/valueBased on the PUC bond-slip measured curves, the relationship between bond stress and slip at different stages was analyzed, and the bond-slip analytical model at different stages was established; the model was defined by key parameters such as elastic ultimate shear stress τ0, peak stress τf and interface fracture energy Gf.

Durability of the liquid rubber‐modified CFRP‐steel interface under freeze–thaw cycles

AbstractAn experimental investigation was carried out to evaluate the feasibility of using a liquid rubber‐modified epoxy resin to improve the bonding durability between steel and carbon fiber‐reinforced polymer (CFRP) plates in a freeze–thaw environment. Forty‐eight CFRP‐steel double strap joints were prepared, with a focus on two key factors: the number of freeze–thaw cycles (0, 50, 100, and 200 cycles) and the amount of liquid rubber in the adhesive (0%, 5%, 10%, and 15% by mass). The bond properties encompassing the damage mode, the ultimate capacity, and the bond–slip response of the CFRP‐steel joints were examined, respectively. The study revealed that the ultimate capacity of the joints decreased as the freeze–thaw cycles increased. The ultimate capacity retention rate for unmodified joints, after undergoing 200 freeze–thaw cycles, was approximately 84.9%, while for the modified joints, it ranged from 90.5% to 96.4%. Furthermore, the impact of the freeze–thaw cycles and liquid rubber content on the key bond indicators in terms of the maximum shear stress τmax, initial slip S1, maximum slip Sf, and fracture energy Gf were ascertained, leading to the establishment of the bond–slip degradation relationship of the liquid rubber modified CFRP‐steel interface under freeze–thaw environment.Highlights The effects of the liquid rubber content and freeze–thaw cycles on the mechanical properties of the epoxy resin‐based adhesive were determined. The influences of both the liquid rubber content and freeze–thaw cycles on the CFRP‐steel interface were analyzed. The bond–slip degradation relationships of the liquid rubber‐modified CFRP–steel interface under freeze–thaw cycles were developed.

A new robust equation for shear strength of GFRP-RC deep beams using hybrid experimental and synthetic data based-FE quasi-static analysis procedure

The main objective of this article is to propose a new, more robust, and comprehensive design equation for Glass-Fiber-Reinforced-Polymer (GFRP) reinforced concrete (RC) Deep Beams (DBs). The investigation is based on a numerical model using Quasi-Static Two-Dimensional FE simulation of GFRP-RC DBs. The numerical model is validated by calibrating four parameters (concrete dilatation angle ψ, concrete tensile strength fct, fracture energy Gf, mesh size) against data from ten full-scale experiments on GFRP-RC DBs available in the literature. Additionally, a numerical parametric study based on a full factorial design with 5 factors (and between 2 and 5 modalities) is conducted using the validated quasi-static FE model, which includes 360 large-scale GFRP-RC DBs. The impacts of primary design variables on the concrete contribution Vc to the shear capacity of GFRP-RC DBs are assessed. The effects of various geometrical and mechanical variables, such as cross-sectional dimensions (width b × height H), concrete compressive strength grade (fc), GFRP properties (modulus Ef, and strength ffu), GFRP reinforcement ratio (ρf), and shear span to depth ratios (a/df), are examined to understand the shear behavior of GFRP-RC DBs.The numerical simulations demonstrate that the proposed FE model accurately captures the behavior of GFRP-RC DBs. Building upon these findings, a new shear design equation is proposed for DBs, and its accuracy and robustness are compared with five established international design codes (ACI-440.1R-15, ISIS-Canada, CAN/CSA-S806-12, JSCE-1997, and BS-8110). The existing design codes significantly underestimate the concrete contribution to shear capacity, leading to uneconomical designs. In contrast, the new design equation provides a fair prediction of Vc, with a standard error of 7.734 % and 20.84 % compared to the FE and experimental datasets, respectively. This represents a substantial improvement over the existing design guides.

Size-scale effects and modelling issues of fibre-reinforced concrete beams

This paper compares numerical and analytical predictions for the shear capacity of fibre-reinforced concrete beams based on experimental literature tests. The authors compared the outcomes of a FE model using the DamageTC3d constitutive model, a literature formulation, and the current proposal of the Eurocode 2 draft for fibre-reinforced structures. The paper evaluates the sensitivity of the beam response to the fracture energy Gf, modified after the Model Code 2010 formulation. The investigation reveals a dependence of the estimated fracture energy on the beam size. Furthermore, the comparison between the numerical estimates and the analytical predictions using the MC2010 and the current EC2 draft proves that the error is substantially independent of the model selection but is strongly affected by the specific case study. This fact confirms the absence of weaknesses in the numerical modelling and highlights the aleatoric uncertainties of the experimental data.

Reinforced L-Shaped Frame Made of Textile-Reinforced Concrete

Textile-reinforced concrete is becoming more and more popular. The material enables the realization of very thin structures and shells, often with organic shapes. However, a problem with this reinforcement occurs when the structure is bent (contains a corner), and the flexural stiffness around this bent area is required. This article presents the design, solution, and load-bearing capacity of an L-shaped rigid frame made of textile-reinforced concrete. Basic material parameters of concrete matrix and carbon textile reinforcement were supplemented by a four-point bending test to calibrate fracture energy Gf, critical compressive displacement Wd, solver type, and other parameters of a numerical model created by Atena Engineering in specialized non-linear structural analysis software for reinforced concrete structures. The calibrated numerical model was used to evaluate different variants of carbon textile reinforcement of the L-shaped frame. The carbon textile reinforcement was homogenized using epoxy resin to ensure the interaction of all fibers, and its surface was modified with fine-grained silica sand to increase the cohesion with the concrete matrix. Specimens were produced based on the most effective variant of the L-shaped frame reinforcement to be experimentally tested. Thanks to the original shaping and anchoring of the reinforcement in the corner area, the frame with composite textile reinforcement is rigid and can transmit the bending stresses in both positive and negative directions. The results of the mechanical loading test on small experimental specimens correspond well to the results of numerical modeling using Atena Engineering software.

Interfacial Bond-Slip Model for CFRP Plate Externally Bonded to Corroded Steel Plate

The purpose of this study is to establish the interfacial bond-slip model for CFRP plate externally bonded to corroded steel plate. The present bond-slip models for CFRP materials bonded to uncorroded steel plate were first reviewed. Thirty-four double-lap joints were tested to investigate the effect of corrosion duration and adhesive thickness on the bond behavior between CFRP plates and corroded steel plates, and the bond-slip curves for the bonding interface with different adhesive thickness and corrosion duration were obtained combined with the CFRP plate strain distribution data. A new bond-slip model for CFRP plate externally bonded to corroded steel plate was proposed, and the expression of the characteristic parameters, which included the maximum bond resistance τf, the relative slip at the peak bond stress s1, the fitting parameter α, and the interfacial fracture energy Gf, were also developed based on the careful regression analysis of the present data. The influence of the corrosion duration and construction adhesive thickness on the bond-slip relationship were accounted together and expressed as a new parameter; that is, the effective adhesive thickness teff. The comparison between the predicted values and experimental results indicated that the proposed bond-slip model can be applied to reproduce the structural response of the CFRP plate-corroded steel plate double-lap joint with reasonable accuracy. The outcome of this study can provide meaningful references and essential data for the reliable application of CFRP strengthening systems in the performance improvement of corroded steel structures.

Fracture behavior of basalt fiber‐reinforced concrete subjected to high temperatures

AbstractThe three‐point bending test was conducted and the digital image correlation (DIC) technique was used to observe the full‐field displacement and strain of the notched beam. The initial cracking load and the crack mouth opening displacement were determined based on the deformation field near the tip and mouth of the notch. The initial cracking toughness Kini and the unstable fracture toughness Kun calculated according to the double‐K fracture model, the fracture energy GF and the ductility index Du determined with a modified method, and the equivalent fracture toughness K at four different deformation stages, were analyzed under different temperatures and basalt fiber contents. The results showed that Kini exhibited a monotonic decrease trend with the increasing temperature, indicating that the notched beam was prone to initial cracking after high temperatures. However, Kini rose slowly with the increase of the fiber content, suggesting that the basalt fiber had little influence on Kini. At the temperatures below 400°C, the Kun, GF, Du, and K at each deformation stage increased with the rise of temperature. At the temperatures above 400°C, the Kun, GF, Du, and K at each deformation stage apparently decreased with the increase of temperature. Under the current test conditions, the basalt fiber content of 0.4% by volume had the greatest improvement on the fracture performances of concrete after high temperatures.

Effects of recycled aggregate combinations and recycled powder contents on fracture behavior of fully recycled aggregate concrete

This paper studied the fracture behavior of fully recycled aggregate concrete (FRAC), which was prepared with 100% recycled coarse and fine aggregates (RCA and RFA) and partial recycled powder (RP). Three-point bending tests on center-notched beams were conducted to evaluate the effects of aggregate combinations and RP contents on the meso-scale fracture mechanism and macro-scale fracture parameters of FRAC. It was found that the FRAC mostly presented transgranular or intergranular failure with RCA or RFA, respectively. The RCA substitution had little effect on the critical crack opening displacements, but the RFA and RP substitution increased and decreased them, respectively. Only the incorporation of RFA led to a reduction of the initial cracking toughness of FRAC. The employment of RAs, especially RCA, reduced the fracture energy Gf and unstable fracture toughness KIcun, while the use of RP had a limited impact. The results of the characteristic length showed that RAs made the fracture behavior of concrete more brittle while RP played an opposite role. Both Gf and KIcun reduced with the decrease of tensile strength. The former was remarkable in FRAC due to the variation of aggregate combination whereas the latter was more likely associated with the aggregate size.

Evolution on fracture properties of concrete during steam curing

This paper investigated the fracture properties of concrete after steam curing ranging from 4 to 48 h at a typical constant temperature of 60 °C. The evolution pattern of fracture properties for concrete during steam curing was revealed, and the equivalent maturity was adopted to estimate the development of fracture parameters. The results indicated similar to the mechanical parameters, the initial fracture toughness KIcini exhibited an increase-decrease tendency as increasing steam curing hold (SCH) time. However, the unstable fracture toughness KIcun and fracture energy GF were found to increase monotonously with SCH time, leveling off approximately between 16 h and 48 h. The equivalent maturity approach was proved to be available to evaluate the fracture parameters of steam-cured concrete with a relative error of less than 10%. In addition, the crack extension resistance during whole fracture process was also analyzed, and it was found the SCH time should be kept within 16 h at 60 °C for the development rate of fracture properties. The test results can provide a basis for the control of cracks of concrete in steam curing process.

Critical Comparison of Phase-Field, Peridynamics, and Crack Band Model M7 in Light of Gap Test and Classical Fracture Tests

Abstract The recently conceived gap test and its simulation revealed that the fracture energy Gf (or Kc, Jcr) of concrete, plastic-hardening metals, composites, and probably most materials can change by ±100%, depending on the crack-parallel stresses σxx, σzz, and their history. Therefore, one must consider not only a finite length but also a finite width of the fracture process zone, along with its tensorial damage behavior. The data from this test, along with ten other classical tests important for fracture problems (nine on concrete, one on sandstone), are optimally fitted to evaluate the performance of the state-of-art phase-field, peridynamic, and crack band models. Thanks to its realistic boundary and crack-face conditions as well as its tensorial nature, the crack band model, combined with the microplane damage constitutive law in its latest version M7, is found to fit all data well. On the contrary, the phase-field models perform poorly. Peridynamic models (both bond based and state based) perform even worse. The recent correction in the bond-associated deformation gradient helps to improve the predictions in some experiments, but not all. This confirms the previous strictly theoretical critique (JAM 2016), which showed that peridynamics of all kinds suffers from several conceptual faults: (1) It implies a lattice microstructure; (2) its particle–skipping interactions are a fiction; (4) it ignores shear-resisted particle rotations (which are what lends the lattice discrete particle model (LDPM) its superior performance); (3) its representation of the boundaries, especially the crack and fracture process zone faces, is physically unrealistic; and (5) it cannot reproduce the transitional size effect—a quintessential characteristic of quasibrittleness. The misleading practice of “verifying” a model with only one or two simple tests matchable by many different models, or showcasing an ad hoc improvement for one type of test while ignoring misfits of others, is pointed out. In closing, the ubiquity of crack-parallel stresses in practical problems of concrete, shale, fiber composites, plastic-hardening metals, and materials on submicrometer scale is emphasized.

Tension stiffening model for the finite element analysis of composite floor systems exposed to fire

PurposeA methodology for producing an elevated-temperature tension stiffening model is presented.Design/methodology/approachThe energy-based stress–strain model of plain concrete developed by Bažant and Oh (1983) was extended to the elevated-temperature domain by developing an analytical formulation for the temperature-dependence of the fracture energy Gf. Then, an elevated-temperature tension stiffening model was developed based on the modification of the proposed elevated-temperature tension softening model.FindingsThe proposed tension stiffening model can be used to predict the response of composite floor slabs exposed to fire with great accuracy, provided that the global parameters TS and Kres are adequately calibrated against global structural response data.Originality/valueIn a finite element analysis of reinforced concrete, a tension stiffening model is required as input for concrete to account for actions such as bond slip and tension stiffening. However, an elevated-temperature tension stiffening model does not exist in the research literature. An approach for developing an elevated-temperature tension stiffening model is presented.

A predictive solution for fracture modeling of alkali-activated slag and fly ash blended sea sand concrete after exposure to elevated temperature

Because of the heterogeneous and discontinuous properties in concrete, realistic fracture parameters were hardly obtained rationally based on traditional methods. The material heterogeneity and discontinuity may be more significant under the attack of high temperature. Therefore, the intention of this paper is to propose a predictive solution for fracture modeling of AASC (alkali-activated ground granulated blast furnace slag (GGBFS) and fly ash (FA) blended sea sand concrete) after exposure to elevated temperature. First, fracture test was performed on AASC after exposure to four high temperatures plus one room temperature. The fracture process and failure mechanism were analyzed and clarified at both macro- and micro-scales. Subsequently, an analytical model was presented to determine the fracture parameters of AASC by incorporating the material heterogeneity and discontinuity. The realistic tensile strength ft, fracture toughness KIC and fracture energy GF were then explicitly linked to the maximum fracture load Fmax by virtue of boundary effect model. Results show that the load-displacement curve becomes gentler and the failure mode is changed from trans-granular fracture to inter-granular fracture as the temperature increases. Once the Fmax is obtained from the test, the realistic ft, KIC and GF from each specimen can be predicted conveniently. The scatters in the predicted parameters would be clarified assisted by statistical analysis. As the temperature increases, the ft is reduced and the reduction becomes larger. But the GF shows insignificant variation until the temperature attains 400 °C, and apparently decreases as the temperature is further enhanced. Moreover, the predicted fracture parameters of AASC with higher GGBFS/FA mass ratio are larger than those of the other AASC below 400 °C. However, the former has higher strength loss than the latter. The crack resistance of AASC after exposure to high temperature can be well clarified based on the proposed predictive model.

A predictive model to determine tensile strength and fracture toughness of 3D printed fiber reinforced concrete loaded in different directions

Concrete 3D printing is getting increased attention in civil engineering. Fibers are generally added to reinforce printed concrete. Crack resistance of 3D printed fiber reinforced concrete in different directions need to be evaluated in a rational manner due to its anisotropic behavior. Therefore, fracture test was performed on printed and mold-cast concrete first in this paper, and failure mechanism were then examined. An analytical model was subsequently proposed based on the analysis of test results to predict the realistic tensile strength ft, fracture toughness KIC and fracture energy GF in different loading directions by incorporating material heterogeneity and discontinuity. The physical meaning of microstructure characteristic parameter reflecting the material heterogeneity was clarified according to the degree of fiber toughness. Closed-form solutions of ft, KIC and GF were obtained related to the maximum fracture load Fmax. The influence of loading direction on the predicted fracture parameters was analyzed and discussed. Results show that the ft, KIC and GF from specimens loaded perpendicularly to the printing direction were significantly larger than those parallel to the printing direction. Besides, the formers were also higher than the parameters from mold-cast specimens due to the fiber preferential alignment along the printing direction in printed concrete.

M&S Highlight: Hillerborg (1985), The theoretical basis of a method to determine the fracture energy GF of concrete

M&S Highlight: Hillerborg (1985), The theoretical basis of a method to determine the fracture energy GF of concrete

Evaluation of fracture behavior of high-strength hydraulic concrete damaged by freeze-thaw cycle test

Hydraulic concrete structures in cold regions are vulnerable to freeze–thaw (FT) damage, which will affect the fracture performance of concrete structures. Hence, the fracture characteristics of high-strength hydraulic concrete subjected to different FT damage (0, 100, 200, 300, 400 FT cycles) are studied by experimental analysis and discrete element method (DEM) simulation. The results show that the FT damage has a significant weakening effect on the fracture characteristics of concrete beams. The elastic modulus E, critical crack length ac, fracture toughness KIc, fracture energy GF and critical crack tip opening displacement CTODc of concrete beams all show a linearly decreasing trend with the increase of the number of FT cycles. In addition, digital image correlation (DIC) and acoustic emission (AE) techniques are used to reveal the evolution law of internal cracks of FT damaged concrete beams under three-point flexural loads. On the basis of experimental research, the influence indexes of FT damage are introduced into DEM parameters, and a fracture model considering real aggregates is established, which can well predict the fracture behavior of concrete beams subjected to different FT cycles.

Fracture properties and potential of asphalt mixtures containing graphene oxide at low and intermediate temperatures

ABSTRACT This work aimed to investigate the fracture resistance of asphalt mixtures containing graphene oxide (GO) using fracture mechanics. Three dense-graded asphalt mixtures with 9.5, 13.2, and 16 mm nominal maximum aggregate size (NMAS) were modified with varying GO contents. Semi-circular bending (SCB) fracture tests were conducted to determine the fracture properties of the asphalt mixtures. Results showed that mode I fracture toughness (KIC) and fracture energy (Gf) at −20 °C, −10 °C, and 0 °C were significantly improved with the addition of GO. Likewise, increasing trends in J-integral were observed with increasing GO content at 0 °C, 10 °C, and 20 °C. The variations of the fracture mechanic parameters suggested that adding GO could help in enhancing the fracture performance at low and intermediate temperatures. The fracture properties showed a high dependency on test temperature. An increase in NMAS resulted in increased fracture strength of the mixtures. Additionally, a two-parameter Weibull distribution model was utilised to further investigate the fracture results. The fracture toughness of the asphalt mixtures was found to comply with the two-parameter Weibull distribution. Response surface methodology (RSM) was used to develop prediction models for the fracture properties. The proposed models exhibited a high degree of correlation.