Toughness Anisotropy Research Articles

Effect of hot deformation and crystallographic texture on toughness anisotropy and fracture behavior of Nb+V microalloyed API X70 steel

The Charpy impact toughness (CVN) properties of a Nb + V microalloyed X70 steel of YS∼ 540 MPa was studied at various angles with respect to the rolling direction. The microstructure of the steel was characterised using light optical microscope, scanning electron microscope (SEM) and the transformation textures were evaluated from the orientation distribution function (ODF) measured from the electron back-scattered diffraction (EBSD) experiments. The skeleton lines, showing intensity distribution, f(g), of the fcc-to-bcc transformation texture, namely the α-fiber (<110> ∥ RD), the γ-fiber (<111> ∥ ND) and ε-fiber (<110> ∥ TD) are considered to explain the observed behavior in mechanical properties. The major components like, {112}<110>, {113}<110>, {332}<113>, {111}<112> and {111}<110>, their relative intensity distribution, are found to act in a complex manner towards controlling the mechanical behavior during impact and tensile testing. It has been observed that, the type and extent of delamination normally observed in broken Charpy specimens, which is commonly believed to be more dependent on the banding of 2nd phases in the microstructure, is found to be controlled by crystallographic texture, mostly clustering of {100} grains in the primary and secondary cleavage planes.

Effect of delta ferrites on the anisotropy of impact toughness in martensitic heat-resistant steel

To avoid brittle failure of the final-stage turbine blades, it is necessary to understand the anisotropy mechanism in martensitic heat-resistant steel 10Cr12Ni3Mo2VN. This study focused on the effect of delta ferrites on the anisotropy of impact toughness by investigating the relationship between the microstructures and the anisotropy of impact toughness. It was mainly interested in the effect of banded delta ferrites on the transverse impact toughness of experimental steel after quenching and tempering. It was found that banded delta ferrites cause banded brittle cracks and induce tempered martensite matrix to fracture in quasi-cleavage mode, which leads to the embrittlement in transverse specimens and the anisotropy of impact toughness. The embrittlement caused by banded delta ferrites is unrelated to other precipitates such as M23C6-type carbides or MX-type precipitates. In addition, by removing the banded delta ferrites, it can eliminate the anisotropy of impact toughness in the experimental steel. It was also found that conventional heat treatment could not improve the isotropy of impact toughness since it has little influence on the content of banded delta ferrites. As suggested, the use of upsetting-stretching forging strategy promises a great of improvement of isotropy of impact toughness as it can remarkably reduce the amount of banded delta ferrites.

Effect of rock anisotropy on wellbore stresses and hydraulic fracture propagation

Using a newly developed 2D numerical model based on the displacement discontinuity method (DDM) and the fictitious stress method (FSM), hydraulic fracture propagation near and away from a horizontal wellbore in anisotropic mudstones is studied. In addition to elastic anisotropy, the effect of fracture toughness anisotropy on hydraulic fracture propagation is included and fluid flow in fractures is fully coupled with rock deformation. Simulations show wellbore failure pressure, fracture trajectory, and near wellbore fracture apertures are significantly affected by elastic and fracture toughness anisotropy. A simple plane strain analytical solution might indicate that near wellbore fracture opening is enhanced in vertically transversely isotropic (VTI) rock. However, near wellbore fracture turning in a rock with high fracture toughness anisotropy results in severe constriction of fracture apertures. This effect becomes more severe with increase in fracture toughness anisotropy and perforation misalignment angle. Simulations of multiple hydraulic fractures from horizontal wellbores suggest that fracture lengths and apertures are affected by their orientation with respect to the directions of elastic symmetry. The spatial extent of the induced normal stresses perpendicular to the fracture surface increases when the fracture is aligned with the direction of least Young's modulus. The larger spatial extent of induced stresses in anisotropic rock leads to early termination of the fractures emanating from the inner perforation clusters, resulting in fracture networks with dominant outer fractures. In the presence of fracture toughness anisotropy, the fractures deviate towards the plane of least fracture toughness under low differential stress conditions.

Strength and toughness anisotropy in hexagonal boron nitride: An atomistic picture

Strength and toughness are two crucial mechanical properties of a solid that determine its ability to function reliably without undergoing failure in extreme conditions. While hexagonal boron nitride (hBN) is known to be elastically isotropic in the linear regime of mechanical deformation, its directional response to extreme mechanical loading remains less understood. Here, using a combination of density functional theory calculations and molecular dynamics simulations, we show that strength and crack nucleation toughness of pristine hBN are strongly anisotropic and chirality dependent. They vary nonlinearly with the chirality of the lattice under symmetry breaking deformation, and the anisotropic behavior is retained over a large temperature range with a decreasing trend at higher temperatures. An atomistic analysis reveals that bond deformation and associated distortion of electron density are nonuniform in the nonlinear regime of mechanical deformation, irrespective of the loading direction. This nonuniformity forms the physical basis for the observed anisotropy under static conditions, whereas reduction in nonuniformity and thermal softening reduce anisotropy at higher temperatures. The chirality-dependent anisotropic effects are well predicted by inverse cubic polynomials.

Experimental study of the dynamic fracture toughness of anisotropic black shale using notched semi-circular bend specimens

This paper investigates the dynamic fracture toughness anisotropy of black shale (BS). Notched semi-circular bend (NSCB) BS specimens are prepared with different loading angles (the angle between the stratification plane and the loading direction). NSCB specimens are dynamically loaded using a modified split Hopkinson pressure bar (SHPB) system. Formulae for calculating mode-I fracture toughness of transversely isotropic material are obtained by finite element method (FEM) in combination with the J-integral method. Dynamic fracture toughness of the NSCB sample is calculated using stress waves recorded in SHPB tests and the obtained formulae. The results show that the fracture toughness of specimens for all loading angles exhibits obvious loading rate dependence, with the fracture toughness increasing with the loading rate. Similar to the static case, the specimens with higher loading angle have larger fracture toughness values as compared with ones with lower loading angles under similar loading rates. We proposed two envelope lines to enclose the fracture toughness of specimens under different loading rate. The difference between two envelope lines decreases with the increase of the loading rate. The anisotropy of black shale diminishes under extreme high loading rate. Anisotropy index, defined as the ratio of the maximum to the minimum of fracture toughness, is equal to 1.75 under static loading and 1.52 under smaller dynamic loading. These conclusions may have significant implications to the design of hydraulic fracturing in shales, e.g., fracture fluids pumping could be considered as static loading and perforation can be considered as dynamic loading. The anisotropy of shales should be considered in both these cases.

Anisotropy of fracture toughness in nanostructured ceramics controlled by grain boundary design

The fracture toughness of nanostructured materials depends on anisotropic physical properties of individual microstructural features, their texture and/or topology. In this work, intentionally sculptured grain boundaries of low cohesive energy were used to form “weak” and “tough” crack propagation directions within a nanocrystalline TiN film, allowing to correlate the directional arrangement of grains and anisotropy of fracture toughness. By using a selective micromechanical testing approach, two different cracking directions were probed in a scanning electron microscope by loading microcantilever beam specimens prepared parallel and perpendicular to the stacked direction of the alternately tilted columnar grains. The fracture toughness along the sculptured grain boundaries was ~30% higher due to effective multiple crack deflection at the kink planes, which was not observed along weak cleavage planes in the stacked direction. The results indicate the fundamental importance of microstructural design in the synthesis of tough nanostructured ceramics, whose anisotropic mechanical properties can be controlled effectively by incorporating dedicated microstructural features of well-defined topology, orientation and density.

On the link between fracture toughness, tensile strength, and fracture process zone in anisotropic rocks

This paper presents experimental results on the anisotropy of the fracture toughness, Brazilian tensile strength, and the fracture process zone (FPZ) in granodiorite samples. The fracture toughness is measured using semi-circular bending tests, while Brazilian disk tests were conducted to measure the tensile strength indirectly. Digital image correlation (DIC) was employed to obtain full-field surface deformation associated with the fracture propagation and identify the FPZ. An averaging scheme is proposed to determine the length and width of the FPZ from the strain field. The DIC results confirm a semi-elliptical FPZ developing ahead of the crack tip, with an average length-to-width ratio of approximately two. The results also indicate that the theoretical models such as Irwin and strip-yield with uniform traction, which are based on plastic deformation near the crack tip, underestimate the extent of the inelastic zone, while the strip-yield model with a linear cohesion stress distribution overestimate the length of the process zone. The anisotropy ratio of the FPZ length obtained from the models, however, agrees very well with the ratio obtained from the DIC measurements. This evidence supports the basis of the theoretical models that predict the FPZ length to be proportional to the square of fracture toughness over tensile strength.

Impact of the anisotropy of fracture toughness on the propagation of planar 3D hydraulic fracture

Sedimentary rocks often exhibit a transverse isotropy due to fine scale layering. We investigate the effect of the anisotropy of fracture toughness on the propagation of a planar 3D hydraulic fracture perpendicular to the isotropy plane: a configuration commonly encountered in sedimentary basins. We extend a fully implicit level set scheme for the simulation of hydraulic fracture growth to the case of anisotropic fracture toughness. We derive an analytical solution for the propagation of an elliptical hydraulic fracture in the toughness dominated regime—a shape which results from a particular form of toughness anisotropy. The developed numerical solver closely matches this solution as well as classical benchmarks for hydraulic fracture growth with isotropic toughness. We then quantify numerically the transition between the viscosity dominated propagation regime at early time—where the fracture grows radially—to the toughness dominated regime at large time where the fracture reaches an elliptical shape in the case of an elliptical anisotropy. The time scale at which the fracture starts to deviate from the radial shape and gets more elongated in the direction of lower toughness is in accordance with the viscosity to toughness transition time-scale for a radial fracture defined with the largest value of fracture toughness. Similarly, the toughness dominated regime is fully reached along the whole fracture front when the time gets significantly larger than the same transition time-scale defined with the lowest value of toughness. Using different toughness anisotropy functions, we also illustrate how the details of the complete variation of fracture toughness with propagation direction governs the final hydraulic fracture shape at large time. Our results highlight toughness anisotropy as a possible hydraulic fracture height containment mechanism as well as the need for its careful characterization beyond measurements in the sole material axes (divider and arrester) directions.

Toughness of Scots pine ‐ polymethyl methacrylate composite

A series of 1,600 samples of the sapwood of Scots pine (Pinus sylvestris), part of them in natural state, but majority subjected to polymerization with various level of impregnation with methyl methacrylate, were tested for toughness on Charpy's impact machine. The goal of the experiment was to investigate how polymerization improves toughness and, additionally, how exposure to low temperatures and to the action of seawater influences this property of the material tested. It was found that within impregnation levels and temperatures tested variability of toughness due to these two factors is almost linear and in practical considerations may be predicted based on an empirical formula. It was also found that exposure to the action of seawater weakens the material. To verify anisotropy of toughness in the plane perpendicular to the grain all samples were consistently cut out such that one pair of opposite lateral faces were tangent to the growth rings. Half of the whole set of samples was fractured with an impact directed perpendicular to the growth rings and the other half with an impact directed in the tangential direction. The results show that although in general toughness is slightly higher in the direction perpendicular to the growth rings than in the tangent direction, the difference may be neglected in practical considerations. POLYM. COMPOS., 40:811–822, 2019. © 2018 Society of Plastics Engineers

Effect of microstructure and crystallographic texture on mechanical anisotropy of Ti-Nb microalloyed hot rolled 800 MPa HSLA steel

The impact toughness of a Ti+Nb HSLA steel plate, conventionally hot rolled in the austenitic region, were measured at four different directions at 0 °C, −20 °C and −40 °C respectively. The microstructure was characterised using light optical microscope, scanning electron microscope (SEM) followed by evaluation of hot rolled texture using X-ray diffraction (XRD) and orientation distribution function (ODF) obtained from electron back-scattered diffraction (EBSD). The anisotropy in the yield strength (YS) and Charpy impact toughness (CVN) were examined in the light of orientation distribution function (ODF) obtained from EBSD. The skeleton lines, showing intensity distribution, f(g), of the fcc-to-bcc transformation texture, namely the α-fiber (⟨110⟩∥ RD), the γ-fiber (⟨111⟩∥ ND) and ε-fiber (⟨110⟩∥ TD) are considered to explain the observed anisotropy along with microstructural features. The major components like, {112}⟨110⟩, {113}⟨110⟩, {332}⟨113⟩, {111}⟨112⟩ and {111}⟨110⟩, their relative intensity distribution, are found to cause the observed anisotropy in yield strength and impact toughness. A stronger presence of {113}⟨110⟩ component of the α-fiber over relatively weaker {332}⟨113⟩ component of the ε-fiber further augments the observed toughness anisotropy. In absence of any microstructural banding, strong the presence of {113}⟨110⟩ and {112}⟨110⟩ can also cause delamination in ductile fracture mode.

Anisotropy of Fracture Toughness of Stabilized Zirconia Investigated by Nano-Identation Method

Anisotropy of Fracture Toughness of Stabilized Zirconia Investigated by Nano-Identation Method

A novel chevron notched short rod bend method for measuring the mode I fracture toughness of rocks

A novel chevron notched short rod bend (CNSRB) method is developed for measuring the mode I fracture toughness (KIc) of rocks. Similar to the conventional short rod (SR) method suggested by the International Society for Rock Mechanics (ISRM), the proposed CNSRB method can also measure the fracture toughness along axial directions of rock cores. Moreover, the CNSRB has obvious advantages compared with the SR method, such as simpler installing and testing procedure, lower requirement on testing machine, higher failure load and lower required amount of intact rock core. To assess the reliability of the CNSRB method, KIc results of CNSRB specimens and ISRM-suggested chevron bend (CB) specimens are both experimentally and theoretically compared. Laboratory tests on two rock types indicate that the CNSRB method can produce KIc values comparable to those measured using the CB method. Moreover, theoretical predictions based on an extended maximum tangential strain (EMTSN) criterion show that, KIc of the CNSRB specimen is closer to that of the CB specimen than that of the SR specimen, which inherently yields higher fracture toughness results than other ISRM-suggested specimens. Therefore, the CNSRB method can be reliably used to measure the mode I fracture toughness of rocks. Most importantly, accompanied with other test methods (e.g., CB), the proposed CNSRB method contributes to forming a complete set of methods for investigating fracture toughness anisotropy from a single rock core.

On the influence of microstructure on the fracture behaviour of hot extruded ferritic ODS steels

• High interfacial particle-matrix strength and small size of sub-micron particles predominantly enhances fracture toughness . • Crack blunting due to elongated coarse grains contributes predominantly towards improving fracture toughness. • Crystallographic texture and sub-micron particle alignment do not play a major role in fracture toughness anisotropy. • Higher flow stress is not the predominant reason for higher fracture toughness.

Anisotropic toughness and strength in graphene and its atomistic origin

This paper presents the implication of crystallographic orientation on toughness and ideal strength in graphene under lattice symmetry-preserving and symmetry-breaking deformations. In symmetry-preserving deformation, both toughness and strength are isotropic, regardless of the chirality of the lattice; whereas, in symmetry-breaking deformation they are strongly anisotropic, even in the presence of vacancy defects. The maximum and minimum of toughness or strength occur for loading along the zigzag direction and the armchair direction, respectively. The anisotropic behavior is governed by a complex interplay among bond-stretching deformation, bond-bending deformation, and the chirality of the lattice. Nevertheless, the condition for crack-nucleation is dictated by the maximum bond-force required for bond rupture, and it is independent of the chiral angle of the lattice or loading direction. At the onset of crack-nucleation a localized nucleation zone is formed, wherein the bonds rupture locally satisfying the maximum bond-force criterion. The nucleation zone acts as the physical origin in triggering the fracture nucleation process, but its presence is undetectable from the macroscopic stress–strain data.

Role of crystallographic texture, delamination and constraint on anisotropy in fracture toughness of API X70 line pipe steels

Fracture toughness studies of line-pipe steels are extremely crucial as line-pipes are exposed to extreme conditions in application. The effects of crystallographic texture and constraint on fracture toughness of API X70 line pipe steel were investigated in this study. The J-integral method was considered to quantify the fracture toughness across orientations and thicknesses of the investigated steel. The difference in the crack initiation toughness clearly demonstrated the presence of strong anisotropy. Further the counteracting effects of thickness and delamination on constraint were found to govern fracture mechanism as well as the fracture toughness of the specimens. The anisotropy in toughness was investigated with macro-texture measurements of the specimens. The major crystallographic textures and their influences on fracture toughness were analyzed. Amongst the observed texture components, strong intensities of {113}<110>component of α-fiber was identified as the major reason for anisotropy in fracture toughness. The distribution of volume fractions of {112}<110> component also showed a strong correlation with the fracture toughness across orientations.

Influence of Anisotropic Microcracking Due to Swelling on the Fracture Toughness of a Clay-Bearing Sandstone

Flaking is a well-known pattern on rich clay stone. As swelling of clay minerals may induce crack propagation under fatigue, a fracture mechanics approach is proposed to investigate its impact on such decay pattern. A clay-bearing sandstone from the Thuringen region is studied because of the scaling effect observed at its surface when exposed to environmental conditions. Semi-circular bending specimens adapted to stone heritage studies are prepared and three configurations are tested, in order to measure toughness with respect to the bedding of this sandstone. Deformations are measured during relative humidity variations. They are measured anisotropic due to position and orientation of the clay phases within the stone. The influence of such natural dimensional variations on Young modulus and fracture toughness is studied. It appears that the induced damage is oriented and is the consequence of opening of the initial microcracks in the direction perpendicular to the maximum swelling. This damage induces an evolution of the fracture properties and behaviour. Toughness decreases as relative humidity increases depending on the orientation of the microcracking. Moreover, the toughness anisotropy of this sandstone appears during humidification. After several cycles of swelling, the microcracking induces an increase in toughness when notch is perpendicular to them. This may explain some stone deterioration patterns, as flakes subparallel to the stone surface.

Strength and ductility of heavily deformed pearlitic microstructures

The fracture toughness and deformation behavior of heavily deformed pearlitic steels have been investigated. A strong anisotropy of the fracture toughness and the plastic deformation behavior with respect to the lamellar orientation is observed. The consequences of this anisotropy both for processing and application, as well as for the limits in strengthening, are discussed.

Theoretical and numerical prediction of crack path in the material with anisotropic fracture toughness

The crack path in the anisotropic medium is studied theoretically and numerically in this paper, with focusing on the effects of the anisotropic fracture toughness. A weak plane model is adopted to characterize the anisotropic fracture toughness and the maximum energy release rate criterion (MERR) is chosen to predict the crack path. We prove that the crack deflecting direction in a weak plane material, theoretically, only relates to the weak plane direction, the weakness of the plane, and the ratio of stress intensity factors before crack extending. Two critical weakness ratios are found: one is for that the weak plane captures all cracks for any loading state; the other is for that the weak plane traps the crack once it is deflected to the plane. To further numerically study the complex crack path in an anisotropic medium, the extended finite element method (XFEM) embedded MERR criterion and weak plane model is developed, in which a mesh independent piecewise linear crack formulation is proposed to capture the curved crack path. By modeling the three point bending loading test, the influences of the weak plane angles and the weaknesses on crack path deflection are studied, and periodically oscillatory crack path behaviors are found as observed in experiments. Further more, the crack extending through multiple layers of weak plane material and isotropic material is numerically studied, which shows that the crack diffracts at the material interface, and the crack path in the anisotropic toughness material is rougher than in the isotropic material. The presented work in this paper will be helpful to understand and control the crack path in the rocks as well as other anisotropic materials.

Experimental investigation on the effect of wetting-drying cycles on mixed mode fracture toughness of sandstone

To investigate the fracture toughness including pure mode I, combined mode I + II, and pure mode II, the CCBD (centrally cracked Brazilian disk) fracture experiments with acoustic emission (AE) detecting are conducted on the shale specimens with distinct bedded inclination angles (0°, 30°, 60°, and 90°), and this research first introduces the detailed derivations on the three dominating fracture criteria. The investigated results demonstrate that the fracture resistances for the tested CCBD shale are insensitive to the bedded direction and the anisotropy of the fracture toughness is regarded as relatively weak, which is reflected in the smoother and more regular rupturing paths. The improved criteria (GMTS, GMTSN, and GMTSEDF) can provide a reasonable agreement with the measured data by considering the variable damaged radius of microcracking zone. The proposed k-means clustering method succeeds in identifying the specific fracture modes for the tested CCBD bedded shale in conjunction with the KDE (kernel density estimation) method, whereas the conventional AE parameter (RA and AF) method fails to analyze the fracture mechanisms.

Evaluation of Anisotropy of Fracture Toughness in Brittle Rock, Migmatized Gneiss

Most rocks in nature are affected by a certain degree of anisotropy. They contain cracks mostly with certain distributions. Therefore their mechanical behaviour is dependent on the direction of the strength distribution, which is different in each direction. We can distinguish the directions in which the rock is relatively firm and conversely the directions in which it is weak. The strength anisotropy and the direction of weakening is useful information for engineering applications. Metamorphic foliation with the specific orientation of rock grains also influences the mechanical behaviour, and the mechanical properties, i.e. strength, are changed in different directions of loading. This change of strength is called the strength anisotropy. The main purpose of this research is to analyze the effect of the orientation of metamorphic foliation distinguished within the rock specimens on their strength anisotropy. In the article, the anisotropy of a mechanical property, i.e. the fracture toughness, of migmatized gneiss is discussed. For this purpose, series of semi-circular bend tests were carried out on specimens of migmatized gneiss with a metamorphic foliation. The methodology used in this research is effective for evaluating the strength anisotropy of a brittle rock.