•Crack initiation load Pi has been predicted using the maximum fracture load Pmax and FPZ length.•Analytical predictions of Pi have been confirmed by experiments reported in literature.•The ...corresponding toughness Ki and Kun at Pi and Pmax are obtained analytically.•The size-independent fracture toughness KIC are compared with Ki and Kun.•Simple approximation of the tensile stress at the notch tip is provided.
The initial cracking load (Pi) of a notched concrete beam, difficult to measure, has been predicted from the maximum fracture load (Pmax) together with the notch-tip fracture process zone (FPZ) at Pmax. A simple analytical model is used to link Pi and Pmax together through the FPZ. The corresponding initiation and unstable fracture toughness, Ki and Kun, have also been determined. The model assumes that the lower limit of Pmax from a group of identical notched concrete beams corresponds to the lower limit of the FPZ length FPZL, so that the lowest limit Pmax = Pi is established for FPZL = 0. Detailed FPZ measurements before and at Pmax using a digital image correlation technique were analysed and used to predict the initial cracking load Pi. Six different specimens with various sizes (W = 40, 60 and 80 mm), initial notches (a0 = 12 to 48 mm) and FPZL (7 to 13 mm) at Pmax showed the average ratio of FPZL/(W – a0) was around 0.25, indicating the Pi/Pmax ratio was around 0.67 based on the analytical model. The crack growth resistance KR-curve between the crack initiation toughness Ki at Pi and the unstable fracture toughness Kun at Pmax was also established approximately by the simple model. Estimated intrinsic fracture toughness KIC was compared with Ki and Kun. The influence of average aggregate size dav on Pi and FPZL at Pmax was also discussed.
The concrete undergoes brittle failure, which is a disadvantage for stability and safety analysis. This drawback was compensated by addition of different types and size of fibers for improving the ...compressive and fracture characteristics. The incorporation of multi‐scale hybrid fibers in concrete showed enhanced performance at multi‐level than that of single type or size of fiber. This study examined the influence of basalt fiber length (12, 25, 37, and 50 mm) and content (0.15% and 0.3%) on compressive and fracture parameters of hybrid fiber reinforced concrete (HyFRC). Systematic experimentations were performed on mechanical properties which include compressive strength (f'c), toughness index (ɳ) and capability coefficient index (ξ), initial fracture toughness (KiniIC), unstable fracture toughness (KunsIC), and fracture energy (GF). The crack resistance process and fiber‐matrix interaction obtained by scanning electron microscopy analysis were also discussed. The proposed analytical models of HyFRC stress–strain equations indicated great suitability for fitting of experimental behavior with R2 ≥ 0.92. The basalt fiber with different length and contents showed a great potential in HyFRC and indicated a substantial degree of enhancement for the compressive and fracture properties, as compared to that of PC and HyFRC without basalt fiber.
Repetitive hot rolling followed by hot pressing or hybrid severe plastic deformation (HSPD) of Mg-4Zn-4Gd was performed at 450 °C to produce ultrafine-grains (UFG) in the alloy. The processed ...specimens are compared with conventional 75% hot rolled, solutionized (ST) and as-cast (AC) specimens to study the mechanical and microstructural evolution. Prior to HSPD process, the pre-processed blocks were solutionized at 400 °C for 24 h to obtain the equiaxed and residual stress free alloy for easy plastic deformation up to the high absolute true strain value of 1.39. The hot rolling (R) and hot pressing (P) methods were combined to deform the material in three different combinations in terms of true strains to achieve the final deformation with true strain 1.39 (75% reduction). The HSPDed specimens were subjected to tensile, hardness and fracture toughness (KQ and JⅠC) tests. The 50R50P specimen has shown better improvement in yield strength (σYS = 268 MPa), tensile strength (σTS = 284 MPa)), and hardness (2.21 GPa) amongst other HSPDed specimen. The improvement in mechanical properties of 50R50P alloy is nearly 9%, 6.5%, and 81%, respectively over the 75% rolled specimen and 154%, 65%, and 176%, respectively against ST specimens. However, the elongation of 50R50P specimen has improved only up to ~ 27% than ST specimen. The highest JⅠC fracture toughness of the processed alloy is ~ 23.25 kJ/m2 when pre-crack is normal to rolling direction (RD) and ~ 18.51 kJ/m2 when pre-crack is parallel to RD analysed in 50R50P and 70R16P specimens, respectively. The strengthening mechanisms operating in the processed alloy is due to solid solution strengthening and deformation slip based failure mechanism in fine grained alloys, which were elucidated with the help of high resolution transmission electron microscopy (HRTEM). The HRTEM results are correlated with X-ray diffraction results of processed alloy. Fracture phenomena for different HSPDed specimens were analysed through FE-SEM to understand the failure characteristics of the alloy under static load.
Effective toughness of heterogeneous media Hossain, M.Z.; Hsueh, C.-J.; Bourdin, B. ...
Journal of the mechanics and physics of solids,
11/2014, Letnik:
71
Journal Article
Recenzirano
We propose a versatile approach to computing the effective toughness of heterogeneous media. This approach focusses on the material property independent of the details of the boundary condition. The ...key idea is what we call a surfing boundary condition, where a steadily propagating crack opening displacement is applied as a boundary condition to a large domain while the crack set is allowed to evolve as it chooses. The approach is verified and used to study examples in brittle fracture. We demonstrate that effective toughness is different from effective or weighted surface area of the crack set. Furthermore, we demonstrate that elastic heterogeneity can have a profound effect on fracture toughness: it can be a significant toughening mechanism and it can lead to toughness asymmetry wherein the toughness depends not only on the direction but also on the sense of propagation. The role of length-scale is also discussed.
Two different types of strength‐toughness relations are investigated in tempered steel (tempered at 25–420 °C). It is found that there is a trade‐off relation between strength‐fracture toughness and ...becomes invariable relation between strength‐impact toughness. The effect of microstructure on the materials toughness is related to the manner of energy consumption, which should be attributed to the notch root radius of the specimen. The coarse carbides and dislocation density inside the martensite lath have distinct effects on the energy for crack initiation (impact toughness) and crack growth (fracture toughness). Additionally, the mechanism of coarse carbides on the tempered martensite embrittlement is elaborated deeply.
Two different types of strength‐toughness relations are investigated in tempered steel: a trade‐off relation between strength‐fracture toughness and approximately invariable relation between strength‐impact toughness. The effect of microstructure on the materials toughness is related to the manner of energy consumption. The coarse carbides and dislocation density inside the martensite lath have distinct effects on the energy for crack initiation (impact toughness) and crack growth (fracture toughness).
To study the fracture toughness of sandstone, this study investigated the influence of temperature on the mixed-mode (I+II) and mode-II fracture toughness of sandstone using semi-circular bend (SCB) ...specimens. The results showed that temperatures above 500°C significantly influenced mixed-mode (I+II) and mode-II fracture behavior. A comparison of experimental results with pure mode-I fracture toughness showed that the impact of temperature variations on the mixed-mode (I+II) and mode-II fracture toughness was similar to the impact of temperature variations on pure mode-I fracture toughness. The mixed-mode (I+II) and mode-II fracture toughness of sandstone increased slowly from 20 to 100°C and decreased slowly from 100 to 500°C. The mixed-mode (I+II) and mode-II fracture toughness of sandstone decreased sharply from 500 to 600°C. The effective stress intensity factor of mixed-mode (I+II) at artificial pre-crack angles of 15°and 30° decreased by 41.02% and 42.55%, respectively. Mode-II fracture toughness decreased by 54.30%. From 500°C to 600°C, the change of the sandstone structure is the main reason for the sharp decrease of the mixed-mode (I+II) and mode-II fracture toughness. The threshold temperature range for this sharp decrease is 500–600°C for the mixed-mode (I+II) and mode-II fracture toughness are identical to pure mode-I fracture toughness.
Understanding the inconsistent rock fracture toughness (
K
Ic
) measurement results from different test specimen geometries helps provide suitable fracture parameters for engineering applications, ...predict rock fracture load, and assess the safety of flawed rock engineering structures. In this study, fracture experiments using full- or half-disc specimens with chevron notches or straight-through notches were conducted. Experimental results show that the notch types and loading methods (Brazilian-type diametric compression and three-point bending) significantly affect the
K
Ic
measurements. It is indicated that only considering the T-stress or fracture process zone (FPZ) alone cannot explain the test results well, while a good agreement is found between the experimental results and the interpretation based on the combined effects of T-stress and FPZ. Moreover, Brazilian-type compression and three-point bending under a short support span can make the full- or half-disc specimens have higher negative T-stress and larger FPZ, thus producing lower
K
Ic
values than three-point bending under a relatively long support span. Compared with
K
Ic
measurements using the straight-through notch specimens, those utilizing the chevron-notched ones are less affected by FPZ and yield higher
K
Ic
results, providing that the loading method is the same. The notch types have little impact on the T-stresses of the specimens. This study sheds light on the combined influence of T-stress and FPZ on rock fracturing.
In this article, the authors tried to establish a direct correlation between crystallographic variants and impact toughness, and provided some novel insights into the mechanism of cooling rate on the ...impact toughness of coarse grained heat affected zone (CGHAZ) of offshore engineering steel by means of electron back-scattering diffraction (EBSD) analysis. The results showed that variant selection becomes stronger with an decrease in the cooling rate, resulting in the decline of high angle grain boundaries (HAGBs) and thus lower the impact toughness. Moreover, the variation in impact toughness is mainly correlated to the crystallographic block size. The larger the block size, the lower the impact toughness. By visualizing the crystallographic features, it has been clarified that the transition from Bain zone grouping to close-packed plane grouping with the increase of cooling rate, while the corresponding microstructure changes from granular bainite to lath bainite. Furthermore, it has been found that ~ 25% (number fraction) reconstructed prior austenite grains in simulated CGHAZ present a twin-related structure (austenitic twin), which can enhance the variant selection and displays a negative effect on the formation of HAGBs.
Isolation toughness is a vital parameter to evaluate the vulnerability of computer networks. In specific network designing stage, it is necessary to find the lower bound of the isolated toughness, ...and strive to build a network that meets the stability requirements with the least cost. Gao et al.1 conjectured that if a graph
G
with
κ
(
G
)
≥
3
m
+
1
2
satisfies
I
(
G
)
>
7
m
+
5
4
m
+
4
or
I
′
(
G
)
>
7
m
+
5
4
m
+
2
, then
G
is a
(
P
≥
3
,
m
)
‐factor deleted graph. It's proved that this conjecture holds. However, it is found that as the connectivity changes, the tight lower bound of isolated toughness for
(
P
≥
3
,
m
)
‐factor deleted graphs will change as well. Therefore, we propose a new perspective to look into this problem and introduce the concepts of isolated toughness
(
P
≥
3
,
m
)
factor deleted surface and isolated toughness variant
(
P
≥
3
,
m
)
factor deleted surface, where the result of the original conjecture is only a cross‐section on surfaces. The main contribution in this paper is to determine the concrete expression of these two surfaces.
