A simplified method for measuring plane strain fracture toughness

doi:10.1016/0013-7944(77)90028-5

Engineering Fracture Mechanics

Volume 9, Issue 2, 1977, Pages 361-364, IN5-IN6, 365-369

https://doi.org/10.1016/0013-7944(77)90028-5 Get rights and content

Abstract

A fracture toughness measuring concept is presented which is based on the use of specimen configurations for which the initial crack growth is stable under controlled force (“soft” machine) conditions. The concept is analyzed, and is demonstrated on a specimen configuration consisting of a short rod with narrow longitudinal slots for crack guides. Tests were conducted on two types of aluminum, PMMA, fused quartz and siltstone rock. It is shown that the fracture toughness test is very simple to perform, gives repeatable results, and is equally applicable to both ductile and brittle materials.

References (19)

H.L. Marcus et al.
A crackline-loaded edge-crack stress corrosion specimen
Engng Fracture Mech.
(1971)
J.P. Gallagher
Experimentally determined stress intensity factors for several contoured double cantilever beam specimens
Engng Fracture Mech.
(1971)
Joseph Glucklich
On crack stability in some fracture tests
Engng Fracture Mech.
(1971)
C. Gurney et al.
Stability of cracking
Engng Fracture Mech.
(1972)
F.A. Johnson et al.
Molecular kinetics and the fracture of PMMA
Engng Fracture Mech.
(1972)
ASTM: E 399-72, Standard method of test for plane—strain fracture toughness of metallic...
H.G. Tattersall et al.
The work of fracture and its measurement in metals, ceramics and other materials
J. Mater. Sci.
(1966)
S. Mostovoy et al.
Use of crack-line load specimens for measuring plane-strain fracture toughness
J. Mater.
(1967)
J.A. Kies et al.

There are more references available in the full text version of this article.

Cited by (244)

Experimental investigation on the effect of grain size of granitic rocks on the fracture roughness and toughness
2024, Geomechanics for Energy and the Environment
The fracture surface characterization, such as the fracture roughness, is essential to flow and heat transport through the fracture in the geothermal, oil, and gas reservoirs stimulation by hydraulic fracturing. This research presents an experimental approach to assess the correlation between the fracture roughness and mode I fracture toughness (K_Ic) of the granitic rock with different grain sizes, which is crucial in geothermal reservoirs. Three types of granite with the same mineralogical compositions but fine, medium, and coarse-grained structures were selected and prepared. Fracture toughness values were measured using a novel specimen called ENDB (Edge Notched Disc Bend), in which a cracked disc shape specimen was loaded in three-point bending. The photogrammetric method was used to estimate the value and distribution of surface roughness after ENDB testing and investigate the relationship between fracture morphology and fracture toughness. Based on the experiments, a clear correlation between the roughness and fracture toughness was observed in the three investigated granite types with different grain sizes. The FPZ around the crack tip, tortuosity, intergranular, and transgranular cracks were examined to study the effect of grain size on fracture toughness and roughness precisely. The results show that by increasing the grain size, K_Ic and surface roughness increased. The results also showed that the roughness parameter for the three types of rocks in the direction of the crack growth path is greater than the direction perpendicular to the crack growth path.
Application of R-curve, ANCOVA, and RSM techniques on fracture toughness enhancement in PET fiber-reinforced concrete
2024, Construction and Building Materials
The present study focuses on evaluating the optimal mix-design parameters of waste PET-fiber reinforced concrete (PFRC), aiming to enhance its fracture toughness. This study is divided into three parts. To begin, an experimental examination is carried out to assess the fracture toughness of PFRC using crack mouth opening displacement (CMOD) and R-curve approaches. Secondly, the ANCOVA decomposition method is used which offers insights into the relative contributions of various parameters in resisting crack propagation. Finally, Response Surface Methodology (RSM) is employed to optimize the critical parameters. In this research, plain concrete samples were compared with PFRC samples to assess the impact of fiber reinforcement on fracture toughness. Waste PET fiber of 0.3%, 0.4%, and 0.5% was incorporated into conventional concrete to evaluate its fresh and mechanical properties. ANCOVA decomposition method was employed on the dataset comprised of both published literature and our research work. The results of the study revealed that PET-fiber reinforcement significantly improved the fracture toughness of the concrete. The R-curve analysis demonstrated a more gradual increase in crack resistance with crack extension for the PET-fiber reinforced samples compared to plain concrete. Concrete with 0.5% PET showed more ductility and more resistance to crack as observed from CMOD and R-curve. The ANCOVA decomposition analysis resulted in fiber aspect ratio, fiber volume fraction, fiber length, and W/B ratio as critical parameters. The resulting critical parameters are optimized using RSM with a primary focus on the enhancement of fracture toughness. The RSM optimization process yielded optimal values of 32.5 for aspect ratio, 1.5% for fiber volume fraction, 25 mm for fiber length, and a W/B ratio of 0.50 to maximize fracture toughness. The optimized result has the potential to enhance PFRC quality and performance, offering a more sustainable and cost-effective alternative to conventional concrete.
Experimental characterization of Mode I fracture toughness of the undisturbed Guadalquivir Blue Marl: Effect of suction
2023, Theoretical and Applied Fracture Mechanics
Fracture Mechanics is an extensively developed discipline for a wide range of materials used in scientific and engineering applications. However, the thorough understanding and characterization of fracture phenomena in many soil and rock-type materials are still under development. This work aims to characterize the suction-dependent fracture response in undisturbed clay soils, which will lead to identifying a ductile–brittle behavior threshold. The undisturbed condition will provide information on the behavior of the soil in its natural state. For this purpose, a new experimental procedure is presented in order to obtain a closed-form relationship between mode I fracture toughness ( $K_{Ic}$ ) and a suction range ( $Ψ$ ) for the Guadalquivir blue marl. In order to achieve this objective, an experimental campaign was carried out using a series of semi-circular specimens subjected to the three-point bending test with different suctions. The corresponding loading–displacement curves from the tests are qualitatively analyzed to identify the fracture response of this material, and the linear regression technique is used to finally obtain the desired relationship. Current results show that an increasing value of suction increases both the maximum load and the stiffness, yielding a more brittle behavior associated with an increase in $K_{Ic}$ . Finally, an alternative expression for the determination $K_{Ic}$ with respect to that proposed by Kuruppu and coauthors (Kuruppu et al., 2013) is presented, which involves the explicit inclusion of the suction variable for the more brittle behavior, limited by the threshold found. This provides a new perspective on how moisture content affects the fracture mechanics of clays.
Tensile mode fracture toughness experiments on andesite rock using disc and semi-disc bend geometries with varying loading spans
2022, Theoretical and Applied Fracture Mechanics
Citation Excerpt :
International Society for Rock Mechanics (ISRM) suggests some methods to assign rock fracture toughness for mode I (KIc). The methods of the short rod [1], chevron bend [2], cracked chevron notched Brazilian disc [3,4] and semi-circular bending [5-7] are some of them. Performing fracture toughness tests with some of these methods can be difficult owing to the sample preparation and the testing procedures.
Purpose of this research is to investigate the effect of loading span on mode I fracture toughness for tests conducted by three-point bend geometries. Mode I fracture toughness tests were conducted on Ankara Golbasi Andesite with straight notched disc bending (SNDB) specimens of thicknesses 50 mm and 60 mm. Loading spans were varied in a wide range between 40 mm and 90 mm corresponding to span/radius ratios of S/R = 0.40 to 0.90. Three-point bend tests were conducted with the semi-circular bending (SCB) core specimen geometry for comparison purposes. Mode I fracture toughness results for tests with 60 mm and 50 mm thick SNDB specimens were about 30% greater than the results of SCB tests. It was found that mode I fracture toughness, K_Ic increases with decreasing the span length for both SNDB and SCB specimens. Mode I fracture toughness values was also increased with increasing the specimen thickness for the SNDB geometry. The differences in K_Ic results of different specimen geometries were explained by a mechanism employing maximum normal strain criterion. It was demonstrated that despite the dependency of critical stress intensity factor to the geometry and loading conditions of the tested specimen, the critical value of maximum tangential strain (ε_θθc) at the onset of fracture is a material constant and its value is nearly the same for all disc and semi-disc geometries tested with varying loading spans.
Shear fracture (Mode II) toughness measurement of anisotropic rock
2021, Theoretical and Applied Fracture Mechanics
Fracture toughness of anisotropic shale is an important parameter in shale-gas exploitation technology. Currently available literature is mainly focused on Mode I fracture toughness (K_IC) of anisotropic rock under tensile loading. Although there are the cracked straight through Brazilian disk and crack ring disk used to determine Mode II fracture toughness (K_IIC) of anisotropic rock under pure shear stress, their fracture trajectories are deviated from the original crack plane and cannot be regarded as the true Mode II fracture. In this paper, shear-box test was firstly adopted to measure K_IIC of anisotropic shale. New physical factors Y_I0 and Y_II0 were proposed to describe effects of both the geometry and the material parameters on stress intensity factors (SIFs) of the original crack plane (K_I0 and K_II0) and to derive the calculation formulae of SIFs on arbitrary (K_Iθ and K_IIθ). Calculated results show that K_IIθ reaches its maximum absolute value at θ = 0–10° where K_Iθ is negative, which promotes occurrence of Mode II fracture. The predicted planes of Mode II fracture agree well with the tested fracture trajectories (amostly along the original crack plane). The K_IIC is increased with increase of β (β = 0–90°). K_IIC is 3–4 times as large as K_IC and can be regarded as the true Mode II fracture toughness of anisotropic shale. The shear-box test is an effective method for measuring K_IIC of anisotropic rock.
Local fracture toughness testing of sandstone based on X-ray tomographic reconstruction
2021, International Journal of Rock Mechanics and Mining Sciences
It is well known that the measured values of the fracture toughness of rocks are influenced by material heterogeneity, dimensions, boundary conditions, and asymmetric mechanical behavior. Consequently, the results obtained by standard testing methods developed primarily for homogenous materials with symmetric mechanical behavior, can significantly differ. The standard methods take global approach. Thus, they suppose that the material tested will follow a specific physical model and that one can consider the selected testing method as a black box in which some simple characteristics are measured and the required values can be evaluated. If the material behavior is too different from the theoretically expected one, this global approach will fail. The authors present a method called Local Fracture Toughness Testing (LFTT) to overcome these obstacles. LFFT is calculated independently of the boundary conditions and the crack length. LFTT is based on a complex methodology using a series of tomographic reconstructions, for which data are recorded during specimen loading. Subsequent extended data processing using digital image correlation serves for calculating the evolution of the displacement/strain fields and for identifying the crack which develops during increased loading. Later on, the crack tip opening displacement and the local fracture toughness K_IC are calculated at arbitrarily selected positions independent of the geometry and boundary conditions. The LFTT methodology was tested on a sandstone specimen, since such material is usually considered to be brittle. In this work, the authors demonstrate that even a stable crack extension can be identified after maximal loading. Using a loading machine developed in-house, the experimental data allowed for the measurement of fracture toughness at five loading levels/crack lengths. In addition, fracture toughness was measured in nine planes crossing the crack tip for each loading level.

View all citing articles on Scopus

View full text

A simplified method for measuring plane strain fracture toughness

Abstract

Engng Fracture Mech.

Engng Fracture Mech.

Engng Fracture Mech.

Engng Fracture Mech.

Engng Fracture Mech.

The work of fracture and its measurement in metals, ceramics and other materials

J. Mater. Sci.

Use of crack-line load specimens for measuring plane-strain fracture toughness

J. Mater.