Fracture Size Effect Research Articles

Anisotropic Fracture Evolution and Size Effect of the Fracture Process Zone in Laminated Shales Derived from Digital Image Correlation

Anisotropic Fracture Evolution and Size Effect of the Fracture Process Zone in Laminated Shales Derived from Digital Image Correlation

Experimental and Numerical Investigation of Fracture Energy and Size Effect in Carbon Powder Reinforced PLA Parts Manufactured by Fused Deposition Modeling

Experimental and Numerical Investigation of Fracture Energy and Size Effect in Carbon Powder Reinforced PLA Parts Manufactured by Fused Deposition Modeling

Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture

A large structural size effect on brittle fracture energy was observed in studies of impact fracture of steels by Stanton, Batson and Docherty, nearly 100 years ago. The size effect was seen in macroscopically brittle fractures of geometrically similar specimens tested over a large size range. These historical findings have great significance in designing large-scale steel structures such as ships and bridges. However, there has been no physical principle or theory yet to explain the size effects observed by Stanton, Batson and Docherty. In the present work, a new approach based on net-section mechanics is used to explain the size effect. It is shown that the change in net-section strain energy predicts well the size effect on fracture energy , under the constant condition of cleavage crack initiation stress at the notch root. The spectacular decrease in specific fracture energy with increased specimen size is explained by noting the three-dimensional nature of stored strain energy and the two-dimensional nature of fracture energy dissipated in the crack layer. By scaling both energies to a reference cubic specimen volume and equating, an expression that describes the inverse size dependence of specific fracture energy has been formulated. The mechanics of the size effect is illustrated by assessing the theory with extensive experimental data. Further, scaling laws for fracture energy have been developed. This work honours the pioneering studies of Stanton, Batson and Docherty, which have been instrumental for the development of the present theory and analysis.

Mechanical and fracture characteristics in center cracked circular discs of coal specimens with different sizes: An experimental investigation

The propagation of cracks on a small scale can result in dynamic disasters, such as rock bursts induced by large-scale fractures in coal seams. To gain insights into the mechanism of fracture-induced disasters in deep coal seams, this study investigates the micro-process and size effect of crack propagation in coal specimens featuring different sizes of center-crack circular discs (CCCD). We conducted Brazilian splitting tests on coal samples with varying dimensions and employed acoustic emission (AE) and digital image correlation (DIC) techniques to quantitatively describe the crack propagation process. Additionally, coal specimens of different diameters were compared for the size effect characteristics of different fracture parameters during the tensile failure process. The results show that as the specimen size increases, quasi-brittle failure characteristics become pronounced, tensile strength gradually decreases and stabilizes, while fracture toughness and fracture process zone length gradually increase and tend to stabilize. The macroscopic cracks in the coal specimens generally extend from the centre of the specimen to both ends along the precracks. Large energy events are mainly concentrated at the lower end of the precracks. As coal specimen size increases, the number of AE events decreases, while the proportion of large energy events gradually increases, and the critical crack opening quantity exhibits a linear increase with specimen size. By conducting the fracture size effect experiment on coal specimens, we extend the relevant mechanical parameters from laboratory-scale tests to field engineering scales. This provides fundamental parameters for the analysis of large-scale fracture process of in-situ coal based on fracture mechanics.

Size-effects in tensile fracture of rejuvenated and annealed metallic glass

Hundreds of Pt-based metallic glass samples with diameters ranging from sub-100 nm to 100 µm are subjected to cryogenic rejuvenation and annealing above glass transition temperature before tensile loading at room temperature. Shear-localized failure with no ductility is observed in large samples whereas the smaller diameter specimens show ductile necking irrespective of the structural state of metallic glass. With decreasing sample diameter, the fracture surface changes from vein pattern to featureless in the shear-localized samples and the ductility increases in the necked samples. Despite similar size-dependent trends, the changes in deformation mode and fracture morphology occur at different diameters in as-cast, rejuvenated, and annealed samples. The critical diameters for transitions from shear localization to necking and from vein pattern to smooth fracture surface shift to larger values in cryogenically rejuvenated samples whereas annealing has the opposite effect. Rejuvenation promotes homogeneous-like flow and suppresses catastrophic tensile failure in nanoscale metallic glasses.

Fracture behavior and size effect of UHPFRC: Experimental and meso-scale numerical investigation

In this research, the fracture characteristics and size effect of ultra-high performance fiber reinforced concrete (UHPFRC) are investigated by notched three-point bending beam test and meso-scale numerical simulation. Four series of geometrically similar UHPFRC notched-beams with different sizes were tested at quasi-static condition. Crack patterns during the fracture process were obtained by digital image correlation and the phenomenon of crack initiation, multiple cracking and crack localization were well captured. The macro-scale fracture properties are analyzed by double-K fracture model (DKFM) from the perspective of composite toughening. Results show that the initial fracture toughness evaluates the toughness of matrix and the increment from initial fracture toughness to unstable fracture toughness evaluates the toughening due to fiber bridging. The initial fracture toughness and unstable fracture toughness have no size effect and can be treated as material inherent. Experimental results also show a slight decreasing tendency of strength with the increasing of specimen size, which can be approximately fitted by size effect law (SEL). Then a meso-scale numerical model was developed by explicit representation of fibers and directly considering bond-slip relationship of fiber–matrix. Simulation results show that the meso-scale numerical model developed in this research can well simulate the fracture of UHPFRC in terms of crack patterns, fracture process zone, mechanical response and size effect. Parametric study was also conducted based on the meso-scale numerical model and the effects of fiber content, fiber orientation and interfacial bond strength on fracture performance and size effect are analyzed.

Numerical study on fracture behavior of alkali activated concrete mixes for different beam sizes

The present study considers the use of AAC mixes, since the raw materials that are being used to produce concrete are non-renewable natural resources, particularly Ordinary Portland Cement (OPC). Also, production of OPC contributes a greater amount of CO2 to the environment. Hence, an attempt has been made to study alternative construction materials keeping in mind sustainable development. The present numerical study compares the fracture behaviour and size effect of Alkali Activated Concrete (AAC) mixes with Ordinary Portland Cement Concrete (OPCC) mixes by numerically modelling the beams of AAC and OPCC using FEA software ABAQUS. Three different mixes of AAC, characterized by the variation of percentage volume of water-quenched slag (WQS) as a substitute for Natural sand (RS) and one OPCC mix, were studied. A three-point bending test was performed in ABAQUS for the beams of three different sizes, which are geometrically similar with constant thickness. Numerical simulation is performed under displacement control. Load versus CMOD graphs are plotted from the output data obtained from the numerical modelling. Fracture parameters such as Fracture energy (GF), Brittleness number (B), Characteristic length (lch), and Stress intensity factor (KIC) are then calculated from the obtained data and compared to understand the influence of fracture properties and size effect on the behaviour of structural elements since limited research works are available from the literature. From the results, it is observed that OPCC mixes show superior strength, high resistance to crack propagation, more toughness, and high fracture energy when compared to AAC mixes. AAC-50 concrete mix has shown better performance compared to the other two AAC mixes, i.e., AAC-0 and AAC-100. The results of this work can certainly be used to predict the non-linear behaviour of concrete and can be adopted in the design of structural elements.

Study on the dynamic fracture properties and size effect of concrete based on DIC technology

The fracture properties of concrete are highly influenced by the size effect and strain rate effect. To explore the size effect on the dynamic fracture properties of concrete, a fracture experiment on the three-point bending beam was carried out in this paper under four strain rates (10−5/s, 10−4/s, 10−3/s and 10−2/s) and three span to height ratios (2, 2.5 and 3). Then, the fracture characteristic parameters and mechanism were analyzed based on the experimental data combined with the digital image correlation (DIC) technology. The results indicate that the fracture properties of concrete have an obvious strain rate effect and size effect. The fracture load, fracture energy and crack initiation toughness all increase with an increasing strain rate, but decrease with an increasing span to height ratio. On the contrary, the unstable fracture toughness shows no obvious size effect or strain rate effect. Based on the DIC technology, the evolution of crack propagation length in different loading stages was calculated. It is shown that, under the strain rate of 10−5/s, 10−4/s, 10−3/s and 10−2/s, the rapid propagation of crack occurs in the period from Pre-70% to Pre-90%, from Peak load to Post-90%, from Post-90% to Post-80%, and from Post-90% to Post-80%, respectively. More specifically, the crack propagates most rapidly under the strain rate of 10−2/s. The rapid propagation period tends to be delayed with the increase of strain rate, and the strain rate effect is gradually weakened with the increase of span to height ratio. By carrying out in-depth research on the dynamic fracture failure mechanism of concrete, this paper provides reference for the future studies on the dynamic fracture properties of concrete.

A design method for determining fracture toughness and tensile strength pertinent to concrete sieving curve

The aggregate particle gradation of concrete, which is generally characterized by a sieving curve, is a critical factor affecting the formation of the core stress skeleton of concrete specimens. In this paper, a fracture size and boundary effect model that can describe the effect of aggregate gradation on crack propagation at the micro-level in concrete is developed. The critical points on the aggregate sieving curve are selected as the characteristic values of aggregate particles. The individualized calculation method of the fictitious crack growth length under peak load is provided, while the corresponding design application method of the simplified value of the fictitious crack growth length is given. The micro-level explains the physical nature of the discontinuous and jumping expansion of concrete cracks caused by the different aggregate particle gradations. The formula of the novelty design method can link the aggregate particle gradation at the micro-level with the macroscopic fracture and strength parameters. Further, a simplified two-point method to determine the concrete fracture and strength parameters simultaneously by using only two different specimens has been proposed. The proposed model and design method are not limited to the type of specimens. The concrete parameters and structural failure prediction analysis can be carried out by using notched, un-notched, geometrically similar, as well as non-geometrically similar specimens.

Fracture Size Effect of Titanium Sheets in Microforming and Its Meso Damage Criterion

Fracture Size Effect of Titanium Sheets in Microforming and Its Meso Damage Criterion

Specimen and aggregate size effect on the dynamic fracture parameters of concrete under high loading rates

This paper presents a comprehensive experimental investigation of the dynamic size effect and fracture characteristics of concrete. The study involves about two hundred concrete specimens with various maximum aggregate sizes subjected to tensile loading ranging over five orders of magnitude. The effect of structural size and aggregate size on the dynamic strength of concrete is explored using the Work of Fracture Method (WFM) and Size Effect Method (SEM). The experimental results indicate a considerable size effect in concrete subjected to dynamic loading, although the size effect on concrete nominal strength is weakened by increasing the loading rate and aggregate size.

Investigation of fracture properties and size effects of mass concrete using wedge splitting tests on large specimens

This work presents experimental results of fracture tests on very large concrete specimens of mass concrete mixture with a maximum aggregate size of 100 mm. Wedge splitting tests were performed on very large concrete specimens and on moderate-size specimens sawn from large concrete blocks to investigate both size and temperature effects. The digital image correlation (DIC) technique allowed to assess the fracture parameters of these specimens, including the critical crack opening displacement and crack growth length at the peak. These parameters were compared to theoretical computed parameters based on linear elastic fracture mechanics or LEFM theory. Cyclic splitting tests were additionally performed on very large and moderate-size concrete specimens. Interpretation of the results of these cyclic tests via DIC enabled to formulate important conclusions regarding the evolution of the fracture process zone length and critical opening displacement during the tests and to validate the hypotheses associated with the recently developed disturbed fracture process zone theory in terms of the size effect on the fracture energy.

Investigating fracture characteristics and ductility of lightweight concrete containing crumb rubber by means of WFM and SEM methods

The use of lightweight and recycled materials such as crumb rubber due to unknown behavior in concrete can change the cracking behavior and fracture parameters. On the other hand, nowadays, using waste materials as a substitute for natural aggregates in concrete is an effective solution to environmental problems. This study investigated the effect of crumb rubber on the main fracture characteristics and ductility of lightweight concrete (LWC). For this purpose, a part of aggregates replaced with crumb rubber in volume of 4 different percentages (5, 10, 15 and 20%). The main experiment in this research was three-point bending tests that were performed on notched beams. Fracture parameters were determined using two different methods, Work of Fracture Method (WFM) and Size Effect Method (SEM). The results show that by increasing the replacement percentage of crumb rubber instead of fine aggregates from 0 to 20%, the total fracture energy (GF) and characteristic length (Lch) in WFM increase by 63% and 99%, respectively. Also, By increasing the crumb rubber replacement up to 20% in LWC, the initial fracture energy (Gf), length of fracture process zone (Cf) and fracture toughness (KIC) in SEM has increased 1.92, 3.4 and 1.14 times, respectively, compared to lightweight concrete without rubber, while the brittleness number (β) decreased in SEM. Furthermore, the results showed that the fracture surface, the size of the plasticity zone of the crack tip decreases with the reduction of the crumb rubber content. Finally, the ratio of fracture energy obtained from WFM. GF, to initial fracture energy obtained from SEM, Gf, for lightweight concrete containing crumb rubber was approximately 2.8. On the other hand, this study can put a step forward in the fracture mechanics field for sustainable LWC mixtures.

Experimental study of the effect of silica fume and coarse aggregate type on the fracture characteristics of high-strength concrete

This research investigated the fracture properties of high-strength concrete (HSC) using different amounts of silica fume (SF) and coarse aggregate (CA) types and a total of 10 mixing designs and 150 beams. Mix design for plain HSC without SF and three mix designs for SF having contents of 5%, 10%, and 15% by weight of cementitious materials were prepared to evaluate the fracture characteristics in two ratios of water to binder (w/b) of 0.24 and 0.35. In addition, three types of crushed CA, including Limestone, Andesite, and Quartzite were examined to study the effect of CA type on the fracture behavior. The laboratory examination was performed using work of fracture method (WFM) and size effect method (SEM). The results showed that by increasing the amount of SF in two w/b ratios, initial fracture energy (Gf), total fracture energy (GF), characteristic length (Lch), and effective length of fracture process zone (Cf) were decreased, but brittleness number (β) was increased. Furthermore, the CA types significantly affected the fracture and mechanical parameters, and Quartzite and Andesite CA enhanced the fracture energy and the characteristic length compared to Limestone CA.

An assessment of the fracture parameters of ultra-high-performance fiber-reinforced geopolymer concrete (UHPFRGC): The application of work of fracture and size effect methods

This research aimed to study the effects of a certain volume of fiber on the fracture characteristics of ultra-high-performance geopolymer concrete (UHPGC) based on the ground granulated blast furnace slag and silica fume. To this end, seven mixtures were selected and three different volume fractions were used in them. Three mixtures were used to study the effect of steel fiber (SF) volume fraction and the other three mixtures were used to assess the effect of replacing 0.25% of the SF volume fraction with polypropylene fiber (PPF). Fracture parameters, including total fracture energy (GF), initial fracture energy (Gf), characteristic length (Lch), the effective size of process zone (Cf), brittleness number (β), fracture toughness (KIC), and critical effective crack-tip-opening displacement (δc) were calculated by the work of fracture (WF) method and size effect (SE) method, and the results were compared. Furthermore, the relationship between the fiber’s volume fraction with GF, Gf, Lch, Cf, and KIC was individually obtained in the form of polynomial functions. For this purpose, 84 notched beams were tested by three-point bending. The results show that increasing SF volume fraction significantly increased the fracture properties of UHPGC and increased fracture energy and ductility. On the other hand, partial replacement of SF with PPF slightly affected fracture characteristics adversely versus the specimens containing only SF. Finally, the GF/Gf ratio, which is an important parameter in fracture mechanics, was calculated. This ratio was increased with increasing fiber fraction so that it reached from 2.84 for UHPGC to 13.64 for UHPFRGC.

Effects of alkaline solution/binder and Na2SiO3/NaOH ratios on fracture properties and ductility of ambient-cured GGBFS based heavyweight geopolymer concrete

In designing and modelling of nuclear facilities and gravity-based structures constructed with the ambient-cured ground granulated blast furnace slag (GGBFS) based heavyweight geopolymer concrete (ACGHWGC) based on fracture mechanics, it is necessary that fracture parameters of this new material be determined at the first stage. In the present study, effects of alkaline solution to binder ratio (Al/Bi) (i.e. 0.65, 0.75 and 0.85) and Na2SiO3 to NaOH solution ratio (SS/SH) (i.e. 0.25, 0.5 and 0.75) on the fracture properties of the ACGHWGC have been investigated. The fracture parameters of the ACGHWGC including total fracture energy (GF), initial fracture energy (Gf), fracture toughness (KIC), characteristic length (Lch), effective size of the process zone (Cf), critical effective crack-tip-opening displacement (δc) and the brittleness number (β) are determined using work of fracture method (WFM) and size effect method (SEM) and the results obtained are compared. The results show that the Al/Bi ratio has more effects than that of the SS/SH ratio on the fracture properties of the ACGHWGC. The results indicate that as the Al/Bi ratio increases from 0.65 to 0.85, the fracture energy as well as the fracture toughness decrease and the ductility increases. Moreover, maximum fracture energy and fracture toughness and the highest brittleness are obtained from the samples with the SS/SH ratio of 0.5. The results indicate that as the compressive strength increases, the fracture energy, the fracture toughness, and the brittleness are enhanced. In all samples, as both the GF in the WFM and the Gf in the SEM increase, the GF/Gf ratio decreases. In addition, minimum ratio of the GF/Gf (equal to 3.1) is obtained from the ACGHWGC with the Al/Bi and the SS/SH ratios of 0.65 and 0.5, respectively.

Effects of alkaline solution to binder ratio on fracture parameters of steel fiber reinforced heavyweight geopolymer concrete

In the current paper, effects of alkaline solution to binder ratio (Al/Bi) (i.e. 0.65, 0.75 and 0.85) on fracture parameters of steel fiber reinforced heavyweight geopolymer concrete (SFRHWGC) with different fiber volume fractions (Vf) (i.e. 0.5%, 1% and 1.5%) are investigated using work of fracture method (WFM) and size effect method (SEM). Moreover, relationship between each of the fracture parameters, the steel fiber volume fraction and the Al/Bi ratio is proposed in the form of a polynomial function. The results show that: (a) with increase in the steel fiber content, the fracture energy, the fracture toughness and the ductility increase significantly. (b) the effects of steel fiber content on the fracture parameters are more significant at higher ratios of the Al/Bi. (c) at Vf = 1.5%, the total fracture energy (GF), the initial fracture energy (Gf) and the fracture toughness (KIC) can be obtained approximately 95, 8 and 3 times that of control samples, respectively. (d) at Vf = 1.5%, the ductility indices such as the characteristic length (Lch) and the effective size of the process zone (Cf) may be obtained approximately 24 and 8 times that of the control samples, respectively. (e) at a given volume fraction of steel fiber, as the Al/Bi ratio increases, the fracture energy and the fracture toughness reduce while the ductility increases. (f) at Vf = 1.5%, the ratios of the values of the fracture parameters such as GF, Gf, KIC, Lch and Cf at Al/Bi = 0.85 to 0.65 are obtained equal to 0.84, 0.82, 0.71, 2.52 and 1.69, respectively. (g) as both the steel fiber content and the Al/Bi ratio increase, the GF/Gf ratio increases. (h) the GF/Gf ratio for the SFRHWGC is found to be equal to 35.21 ± 5.91%.

Effects of NaOH solution concentration and aging on fracture properties and ductility of ambient-cured heavyweight geopolymer concrete

In this paper, effects of NaOH solution concentration (i.e. 2, 4, and 6 M) and aging (i.e. 3, 7, and 28 days) on fracture properties and ductility behaviour of ambient-cured heavyweight geopolymer concrete (ACHWGC) have been investigated. Fracture parameters of the ACHWGC including total fracture energy (GF), initial fracture energy (Gf), fracture toughness (KIC), characteristic length (Lch), effective size of the process zone (Cf), critical effective crack-tip-opening displacement (δc) and the brittleness number (β) were determined using work of fracture method (WFM) and size effect method (SIZEM) and the results obtained were analysed. The results indicate that: (a) maximum fracture energy and the highest brittleness are achieved for samples with 4 M NaOH concentration. (b) as the age increases, fracture energy and brittleness of the samples increase. (c) the mixes gain approximately 82.47% and 86.26% of their 28-day initial and total fracture energies in the first 3 days, respectively. (d) increase in the rate of fracture energy, and decrease in the rate of characteristic length with respect to the mix age for 4 M NaOH concentration are more than those for the 6 M one. (e) as both the total fracture energy (GF) and the initial fracture energy (Gf) increase by the age, the GF/Gf ratio decreases. (f) at the age of 28 days, the GF/Gf ratios for the specimens with 4 M and 6 M NaOH concentrations are equal to 3.16 and 3.32, respectively and (g) as the compressive strength increases, the fracture energy, the fracture toughness, and the brittleness of the ACHWGC are enhanced.

Lattice Discrete Particle Modeling of Size Effect in Slab Scratch Tests

AbstractFor a long time, geomechanicians have used scratch tests to characterize the compressive behavior and hardness of rocks. In recent years, this test has regained popularity in the field of mechanics, especially after a series of publications that highlighted the potential capability of the scratch test to determine the fracture properties of quasi-brittle materials. However, the complex failure mechanisms observed experimentally in scratch tests led to scientific debates and, in particular, raised the question of the size effect. This article intends to provide a better understanding of the problem by using numerical tools and fracture mechanics considerations. To narrow the investigation area, this study focuses on slab scratch tests of quasi-brittle materials and adopts two different numerical methods: (i) the lattice discrete particle model (LDPM) that includes constitutive laws for cohesive fracturing, frictional shearing, and nonlinear compressive behavior, and (ii) the meshless method based on Shepard function and partition of unity (MSPU) implementing linear elastic fracture mechanics (LEFM). The numerical results are further analyzed through Bažant’s size effect law (SEL) with an appropriate mixed-mode fracture criterion. Fracture properties are then calculated and compared to the results of typical notched three-point bending tests. The results show that mixed-mode fracture considerations are of paramount importance in analyzing the fracture process and size effect of scratch tests.

An investigation of fracture properties and size effects of concrete using the ESPI technique

In order to study the size effect in concrete fracture, three-point bending tests are performed on five groups of geometrically similar concrete beams. The electronic speckle pattern interferometry (ESPI) technique is used to measure the full-field deformation of concrete beams. Crack opening displacement data, which is crucial for understanding crack initiation and the evolution mechanism, but which is not readily available through conventional measurement techniques, is obtained. Fracture parameters of five groups of concrete beams, including the critical crack opening displacements (i.e. CMODc and CTODc) and crack growth lengths (i.e. ac and ae) at the peak, fracture toughness (KIc), fracture energy (GF) and nominal strength (σN), are determined. The influences of beam depth on the fracture parameters of concrete are evaluated and discussed. The results show that the CMODc, CTODc, ac, ae, KIc and GF increase with the increase in beam depth, while σN has a decreasing trend that follows the size effect law. Size-independent fracture toughness and fracture energy are estimated and proposed.