Toughness Anisotropy Research Articles

Propagation of multiple hydraulic fractures in different regimes

This study considers the problem of simultaneous propagation of multiple closely spaced hydraulic fractures in homogeneous rocks, under the limited entry condition that ensures uniform flux distribution between the fractures. In particular, the sensitivity of the results to fracture propagation regimes is investigated. There are four primary regimes of hydraulic fracture propagation that are related to interactions between two dissipation mechanisms, related to fluid viscosity and rock toughness, and a fluid storage mechanism (fracturing fluid leak-off), which can occur either inside the fracture or inside the formation. It is shown that the fracture behavior varies dramatically with respect to the fracture propagation regime. In particular, fractures that propagate in the viscosity dominated regime exhibit weak stress shadow interactions, grow predominantly radially, and develop nearly identical fracture geometries. In contrast, fractures that propagate in the toughness regime exhibit strong stress shadow interactions, grow as individual segments avoiding others that are propagating simultaneously, and develop geometrical structures resembling petals in a flower, where the overall geometry is radially uniform, but the individual fractures form non-overlapping segments of the total surface area. Results are presented for the case of Newtonian fluids with and without stress anisotropy, power-law fluids, and consider the case of fracture toughness anisotropy. Finally, the effect of fracture spacing on fracture geometry is investigated for different fracture regimes.

Quality Of Restored Steel Gas Pipes For Re-Application In Construction

The structure and mechanical properties of eight steel gas pipeline single-seam and double-seam pipes that were in operation were studied. It is shown that the degree of corrosion damage to pipe surfaces depends on the chemical composition of the steels. In the studied steels, a significant variation in the hydrogen content between neighboring volumes and the studied pipes was revealed. According to electron-fractographic analysis , there is no significant difference in the degree of embrittlement of the base metal, the weld and the zone of thermal influence. A noticeable effect of hydrogen absorption of steels on the coefficient of anisotropy of the impact toughness has been established, which causes a decrease in the impact toughness on transverse samples to a greater extent than on longitudinal ones. According to the results of mechanical tests for tensile and impact bending, it was found that the restored welded pipes are suitable for use in structures from the first to the fourth groups for the construction, repair and reconstruction of industrial and civil facilities. Naturally, this implies the need for their restoration repair.

Tailoring the residual stress and mechanical properties by electroshocking treatment in cold rolled M50 steel

The residual stress and mechanical anisotropy caused by cold rolling (CR) seriously deteriorate the heat treatment distortion and final service performance of M50 steel. In this work, the effect of electroshocking treatment (EST) on the microstructure, residual stress and mechanical properties of cold rolled M50 steel has been investigated. The microstructure was characterized by X-ray diffraction (XRD), electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The mechanical properties were measured by Vickers hardness, uniaxial tensile and Charpy impact test. The results show that the EST accelerates the movement and annihilation of dislocation and thus promotes the local recrystallization. The dislocation density of treated specimen decreases from 2.37 × 1015 m−2 to 1.96 × 1015 m−2 and the typical deformation texture is obviously weakened after EST treatment. It is also found that the residual stresses in the rolling and transverse direction of the EST specimens decrease by more than 50% with a more homogeneous distribution. In addition, the anisotropy of tensile strength and impact toughness decreases remarkably after EST treatment, which could be ascribed to the local rapid recrystallization and the weakened intensity of deformation texture. Furthermore, due to the release of concentrated stress, the average elongation of EST specimens is increased by 25.5% without loss of tensile strength.

Phase field modeling of hydraulic fracture propagation in transversely isotropic poroelastic media

This paper proposes a phase field model (PFM) for describing hydraulic fracture propagation in transversely isotopic media. The coupling between the fluid flow and displacement fields is established according to the classical Biot poroelasticity theory, while the phase field model characterizes the fracture behavior. The proposed method applies a transversely isotropic constitutive relationship between stress and strain as well as anisotropy in fracture toughness and permeability. We add an additional pressure-related term and an anisotropic fracture toughness tensor in the energy functional, which is then used to obtain the governing equations of strong form via the variational approach. In addition, the phase field is used to construct indicator functions that transit the fluid property from the intact domain to the fully fractured one. Moreover, the proposed PFM is implemented using the finite element method where a staggered scheme is applied to solve the displacement, fluid pressure, and phase field sequentially. Afterward, two examples are used to initially verify the proposed PFM: a transversely isotropic single-edge-notched square plate subjected to tension and an isotropic porous medium subjected to internal fluid pressure. Finally, numerical examples of 2D and 3D transversely isotropic media with one or two interior notches subjected to internal fluid pressure are presented to further prove the capability of the proposed PFM in 2D and 3D problems.

Elucidating the dual role of grain boundaries as dislocation sources and obstacles and its impact on toughness and brittle-to-ductile transition

In this paper, we resolve the role of grain boundaries on toughness and the brittle-to-ductile transition. On the one hand, grain boundaries are obstacles for dislocation glide. On the other hand, the intersection points of grain boundaries with the crack front are assumed to be preferred dislocation nucleation sites. Here, we will show that the single contributions of grain boundaries (obstacles vs. source) on toughness and the brittle-to-ductile transition are contradicting, and we will weight the single contributions by performing carefully designed numerical experiments by means of two-dimensional discrete dislocation dynamics modelling. In our parameter studies, we vary the following parameters: (i) the mean free path for dislocation glide, δ, combined with (ii) the (obstacle) force of the grain boundary, ϕ, and (iii) the dislocation source spacing along the crack front, λ. Our results show that for materials or microstructures for which the mean distance of the intersection points of grain boundaries with the crack front is the relevant measure for λ, a decrease of grain size results in an increase of toughness. The positive impact of grain boundaries outweighs the negative consequences of dislocation blocking. Furthermore, our results explain the evolving anisotropy of toughness in cold-worked metals and give further insight into the question of why the grain-size-dependent fracture toughness passes through a minimum (and the brittle-to-ductile transition temperature passes through a maximum) at an intermediate grain size. Finally, a relation of the grain-size-dependence of fracture toughness in the form of K(dδ, dλ) = KIC + kdδ0.5/dλ is deduced.

Planar hydraulic fracture growth perpendicular to the isotropy plane in a transversely isotropic material

The configuration of a hydraulic fracture (HF) propagating perpendicular to the isotropy plane of a transversely isotropic (TI) material is encountered in most sedimentary basins. We account for both elastic and fracture toughness anisotropy, and investigate fracture growth driven by the injection of a Newtonian fluid at a constant rate from a point source. In addition to the usual dimensionless parameters governing HF growth in isotropy, four dimensionless elastic parameters enter the problem for a TI material: the ratio β of elastic plane-strain modulus in the two orthogonal directions of the material frame, two Thomsen parameters ϵ, δ and the stiffness ratio C13/C11. Moreover, the ratio κ of fracture toughness in the two orthogonal directions as well as the details of the toughness anisotropy also plays a role on the development of the fracture geometry. We quantify HF growth numerically without any a-priori assumptions on the fracture shape. In doing so, we derive the exact expression for the near-tip elastic modulus as a function of propagation direction and extend to TI an implicit level set algorithm coupling a finite discretization with the near-tip solution for a steadily moving HF. A solution for a toughness dominated elliptical HF in a TI material is derived and used to verify our numerical solver. Importantly, the fracture shape is strictly elliptical only for a very peculiar form of toughness anisotropy. The evolution of the HF from the viscosity dominated regime (early time) to the toughness dominated regime (late time) results in an increase of the fracture elongation. The elongation of the fracture in the viscosity dominated regime scales as 0.76β−1/3 and increases as the propagation transition to the toughness dominated regime. We confirm the expressions for the transition time-scales in the two orthogonal directions of the material frame obtained from scaling considerations. The exact form of the toughness anisotropy plays a crucial role on the final fracture elongation in the toughness regime, which scales as β−2 for the case of an isotropic toughness, β−1 for an isotropic fracture energy and as (κ/β)2 for the peculiar case of an ‘elliptical’ fracture anisotropy. Our results also indicate that i) simplified approximations for the near-tip modulus previously derived are only valid for weak anisotropy (β < 1.2) and that ii) the other elastic parameters have a second order effect on HF growth (at most 10 percent).

An explicit algorithm for modeling planar 3D hydraulic fracture growth based on a super-time-stepping method

Hydraulic fracture propagation is a coupled solid-fluid problem involving moving boundaries. The boundary element method is an efficient way to model it in elastic media; however, the computational efficiency is still not promising because in most models the time-consuming implicit approach is used for iteratively solving the stiff equation of the targeted problem. In this paper, we present an explicit super-time-stepping algorithm based on the Runge–Kutta–Legendre method, to simulate a planar 3D hydraulic fracture propagation through the intermediately previous solutions. Each super-time-step covers s stages of single explicit time-step and the results generated can be around s2 times more stable than that using a single explicit time-step. Moreover, an adaptive super-time-step scheme is proposed to capture the marching fracture fronts based on the fracture growth rate. The modeling results are validated against analytical solutions for a penny-shaped hydraulic fracture and experimental results considering stress contrasts. Compared to the implicit iteration approach for the stiff equation, the explicit super-time-stepping algorithm can be up to 30 times faster because of no iteration and super-time-step. Finally, numerical examples are examined for fracture growth in rock formations with stress contrasts and anisotropic toughness, and all the results indicate that the explicit super-time-stepping algorithm can be a promising alternative to the implicit method.

Novel Specimen Design for Measurement of In-Plane Fracture Toughness of Metals

AbstractStandard-compliant measurement of the in-plane fracture toughness of metals is often challenging due to insufficient material in the through-thickness direction to extract a full single edge bending (SEB) or compact tension (CT) fracture specimen. In the present work, we propose a new specimen design methodology to overcome this challenge. A W-shaped SEB specimen (called W-SEB) was developed, and its topology was optimized using finite element simulations. The new specimen design was validated numerically and experimentally on a case study showing excellent agreement with standard ASTM E1820 actual SEB specimen geometry. In view assessing the anisotropy of the fracture toughness (KQ and crack tip opening displacement (CTOD)) of pipeline steels susceptible to hydrogen-induced cracking (HIC), the W-SEB specimen was tested on X65 and X42 pipeline steel samples taken from the field. Experimental results show an increase in the maximum CTOD along the in-plane direction as compared to the transverse direction for both steel grades. Such experimental results could lead to important considerations with respect to accurate fitness for service assessment of HIC-damaged assets.

On the Origin of the Anisotropic Damage of X100 Line Pipe Steel: Part I—In Situ Synchrotron Tomography Experiments

In this study, anisotropic ductility and associated damage mechanisms of a grade X100 line pipe steel previously studied at the macroscopic scale were investigated using in situ synchrotron radiation computed tomography of notched round bars. Line pipe materials have anisotropic mechanical properties, such as tensile strength, ductility and toughness. Specimens were tested for loading along both rolling (L) and transverse (T) directions. The in situ data collected allowed quantifying both specimen deformation (evolution of the cross section) and microscopic damage parameters such as porosity, void shape and void orientation. Nucleation at small particles ($${\hbox {CaS/TiO}}_2$$) aligned along the L direction was observed during plastic deformation. It was shown that only very few anisotropic particle clusters are present in the material. However, these clusters led to substantial early void growth for loading normal to the rolling direction, thereby explaining the toughness anisotropy in this material. Significant void growth was observed at the beginning of load decrease for a relatively limited diameter reduction (about 10%). Coalescence of voids within clusters along L direction (Necklace) clearly explained anisotropic rupture.

Anisotropic influence of fracture toughness on loading rate dependency for granitic rocks

Granite is a significantly anisotropic rock that is affected by the pre-existing microcrack distribution. In rock engineering applications in a variety of fields, it is crucial to understand the influence of the internal microcrack distribution on the mechanical properties of the rock. In this paper, static and dynamic fracture toughness tests were conducted with straight notched disc bend (SNDB) specimens of Youngju granite to investigate the relationship between the microcrack-induced fracture toughness anisotropy and the loading rate dependency. Three groups of specimens were manufactured with three different orthogonal directions, which were determined by the P-wave velocity measurement. In order to conduct the static and dynamic fracture toughness tests, a servo-controlled Material Testing System (MTS) machine and a split Hopkinson pressure bar (SHPB) apparatus were respectively used. In the dynamic test, to achieve the stress equilibrium state in the measurement, a careful pulse shaping technique with a copper and rubber pulse shaper was used. The results of the entire range of tests in this study revealed that the fracture toughness of Youngju granite has a clear loading rate dependency. Further, we found that the preferred orientation of pre-existing microcracks causing strong anisotropy of fracture toughness under static loading rates became significantly weaker in the dynamic loading state. Finally, a possible reason for this relationship between the fracture toughness anisotropy and the loading rate dependency is discussed with different fracturing processes of rock under the static and the dynamic loading states using image analysis for generated cracks.

Quantitative Anisotropic Damage Mechanism in a Forged Aluminum Alloy Studied by Synchrotron Tomography and Finite Element Simulations

A highly anisotropic toughness behavior has been revealed on a forged AA6061 aluminum alloy by toughness tests with CT specimens. The toughness values with specimens loaded on the longitudinal direction are larger than that loaded on the transverse direction due to the anisotropic shape and distribution of coarse precipitates induced by the morphological anisotropy of grains during forging process. Synchrotron radiation computed tomography analysis on as-received material and arrested cracks revealed different fracture modes for the two loading configurations. The damage mechanism has been validated by finite element simulations based on the Gurson–Tvergaard–Needleman micromechanical damage model with different sets of damage parameters for the two loading configurations obtained from quantitative void volume fraction analysis on SRCT data, in situ SEM experiments, and SRCT microstructural analysis.

Apparent Toughness Anisotropy Induced by “Roughness” of In-Situ Stress: A Mechanism That Hinders Vertical Growth of Hydraulic Fractures and Its Simplified Modeling

Summary The height growth of a hydraulic fracture is known to be affected by many factors that are related to the layered structure of sedimentary rocks. Although these factors are often used to qualitatively explain why hydraulic fractures usually have well–bounded height growth, most of them cannot be directly and quantitatively characterized for a given reservoir to enable a priori prediction of fracture–height growth. In this work, we study the role of the “roughness” of in–situ–stress profiles, in particular alternating low and high stress among rock layers, in determining the tendency of a hydraulic fracture to propagate horizontally vs. vertically. We found that a hydraulic fracture propagates horizontally in low–stress layers ahead of neighboring high–stress layers. Under such a configuration, a fracture–mechanics principle dictates that the net pressure required for horizontal growth of high–stress layers within the current fracture height is significantly lower than that required for additional vertical growth across rock layers. Without explicit consideration of the stress–roughness profile, the system behaves as if the rock is tougher against vertical propagation than it is against horizontal fracture propagation. We developed a simple relationship between the apparent differential rock toughness and characteristics of the stress roughness that induce equivalent overall fracture shapes. This relationship enables existing hydraulic–fracture models to represent the effects of rough in–situ stress on fracture growth without directly representing the fine–resolution rough–stress profiles.

Anisotropy of the effective toughness of layered media

This continues the study of the effective toughness of layered materials started in Hossain et al. (2014) and Hsueh et al. (2018), with a focus on anisotropy. We use the phase-field model and the surfing boundary condition to propagate a crack macroscopically at various angles to the layers. We study two idealized situations, the first where the elastic modulus is uniform while the toughness alternates and a second where the toughness is uniform and the elastic modulus alternates. We find that in the first case of toughness heterogeneity the effective toughness displays ‘anomalous isotropy’ in that it is independent of the propagation direction and equal to that of the tougher material except when the crack propagation is parallel to the layers. In the second case of elastic heterogeneity, we find the behavior more anisotropic and consistent with the toughening effects of stress fluctuation and need for crack renucleation at the compliant-to-stiff interface. In both cases, the effective toughness is not convex in the sense of interfacial energy or Wulff shape reflecting the fact that crack propagation follows a critical path. Further, in both cases the crack path is not straight and consistent with a maximal dissipation principle. Finally, the effective toughness depends on the contrast and pinning, rather than on the extent of crack fluctuation.

ANISOTROPIC IMPACT TOUGHNNESS OF CHOPPED CARBON FIBER REINFORCED NYLON FABRICATED BY MATERIAL-EXTRUSION-BASED ADDITIVE MANUFACTURING

3D printed polymer composites are gaining more interest due to weight reduction and high geometrical complexity freedom especially for highly demanding applications such as aerospace and defense. Using the material-extrusion based processes, polymer matrix composite parts with complex geometries can be designed and realized to improve the mechanical properties of pure thermoplastic parts. However, in addition to porosity found at the fracture interfaces, the layered nature additive manufacturing processes may become a limitation for the direct replacement for functional applications. In this study, the results of Charpy impact testing of chopped carbon fiber reinforced nylon fabricated by fused deposition modeling (FDM) are reported. The effects of the build direction and customized density by different infill strategies on the obtained toughness are presented in comparison to the one of nylon without any reinforcement. The toughness results show a severe anisotropy in toughness and high dependence on the infill strategy.

A non-local stress fracture criterion accounting for the anisotropy of the fracture toughness

A comparative assessment between the maximum circumferential stress criterion and the non-local stress criterion applied to mixed mode fracture problems in wood is presented. Various attributes of the two fracture theories, such as the shear stress component acting on the critical plane, the non-singular term of the crack tip stress field and the angular distribution of the fracture toughness, are investigated for their impact on the mixed mode fracture behavior of wood. Predictions of the direction of crack propagation and the fracture locus are validated against experimental data available in the literature, with emphasis on results obtained from single edge-notched wood specimens subjected to on-axis biaxial loading and off-axis tensile and off-axis shear loading.

Effect of Chemical Composition and Structure on Mechanical Properties of High-Strength Welding Steels

Based on the analysis of the Russian-made 4 to 16 mm thick rolled products produced by thermomechanical rolling from high-strength (yield point: 433 to 828 MPa) low-alloyed welding steels obtained as a result of 15 melting runs, the effect of chemical composition and structure on the mechanical properties, such as yield point, impact toughness, and impact toughness anisotropy factor, was studied. It was shown that the yield point of manganese steel (1.62–1.80 wt. % Mn) is mainly caused by microalloying with titanium, and to a lesser degree – with niobium and vanadium. An increase in the yield point of steel in excess of 700 MPa increases its tendency to impact toughness anisotropy. Within the concentration range from 0.001 to 0.08 wt. % Ti, the value of anisotropy factor Ka , which varies from 1.45 to 1.80, does not depend on Ti content, but increases sharply to Ka = 3.19 once the Ti content increases (in excess of 0.08 wt. %). A considerable negative effect of Nb content in steel on impact toughness (KCV– 40), measured on transverse specimens, has been established. A joint negative effect of Ti + Al on KCV– 40 is somewhat less pronounced. The presence of Al in the inclusions of complex composition (Ti-Al-Cr) noticeably reduces (by 4.5 times) the negative effect of Ti on KCV– 40 of highstrength manganese steel.

Strong anisotropy in strength and toughness in defective hexagonal boron nitride

Using a combination of density functional theory calculations and molecular dynamics simulations we show that the strength and toughness of hexagonal boron nitride (hBN) containing isolated vacancy defects are strongly anisotropic, regardless of the size of the defect core. The degree of anisotropy is preserved for a number of defect structures including monovacancy, tetravacancy, tridecavacancy, triheptacontavacancy, or heptatriacontavacancy defects. The chirality-dependent effects are strongly nonlinear and well characterized by close-form mathematical equations indicating pronounced strength and toughness along the zigzag direction compared to the strength and toughness along the armchair direction. Also, the size dependence of the strength and toughness of the defective lattice shows an inverse relationship with the effective diameter of the defect core. An atomistic analysis of the deformation fields reveals that nonuniformity in bond length, bond strain, and force distribution in the nonlinear regime of mechanical deformation surrounding the defect cores forms the physical basis for the observed anisotropy. The anisotropic character of the lattice is governed primarily by the nearest-neighbor covalent interactions (dominated by the first-nearest neighbors). Consequently, as soon as a set of bonds rupture at the defect core, the entire lattice undergoes catastrophic failure underscoring the brittle nature of the fracture state in hBN. Results also suggest that chirality-dependent elastic effects are dominated by the third-order elastic modulus which stiffens the lattice at higher chiral angles, whereas the second- and fourth-order elastic moduli soften the lattice affecting the strength and toughness of the lattice in an intricate manner.

Anisotropy in impact toughness of powder bed fused AISI 304L stainless steel

Anisotropy in impact toughness of powder bed fused AISI 304L stainless steel

Microstructural optimization through heat treatment for enhancing the fracture toughness and fatigue crack growth resistance of selective laser melted Ti[sbnd]6Al[sbnd]4V alloy

The yield strength (σy) of Ti6Al4V alloy, additively manufactured via selective laser melting (SLM) of powder beds, can exceed 1000 MPa while possessing a mode I fracture toughness (KIc) of ∼50 MPam. The possibility of enhancing KIc as well as fatigue crack growth resistance, without a significant penalty on σy, via a judicious heat treatment process that transforms martensitic α’, which is present in the as-SLM microstructure due to rapid cooling of the molten metal, into an α/β phase mixture is examined. It was demonstrated that duplex annealing at temperatures below the β transus temperature of the alloy would lead to such a microstructure while retaining the mesostructure, whose nature depends on the process parameter combinations utilized. Near-doubling of the fracture toughness with only a ∼20% reduction in σy was noted upon heat treatment. While the strength becomes isotropic after heat treatment, significant anisotropy in the fracture toughness of the heat-treated alloy with columnar prior β structure was noted. While the steady state fatigue crack growth (FCG) rates are comparable to corresponding values of the same alloy, but manufactured using conventional means, the threshold for fatigue crack initiation (ΔK0) increases by 34%–56%. The enhancement in ΔK0 was found to be a result of the transition in the near-threshold crack growth, from trans-to inter-granular and caused by the α/β basket weave microstructure, which imparts a high crack path tortuosity. Overall, this study demonstrates that post-processing heat-treatment can improve the damage tolerance of SLM Ti64 by increasing both KIc and ΔK0.

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.