Strength Anisotropy Research Articles

Three-dimensional undrained face stability of circular tunnels in non-homogeneous and anisotropic clays

The advanced 3D finite element limit analysis is employed to examine three-dimensional (3D) face stability of circular tunnels in undrained clays with the impact of strength non-homogeneity and anisotropy. The soil behaviour for all analyses is governed by the anisotropic undrained shear (AUS) strength model, which requires three anisotropic undrained shear strengths that are simply evaluated from conventional laboratory tests. The upper and lower bound solutions of 3D face stability of circular tunnels are accurately analyzed by considering four dimensionless parameters, including the cover-to-depth ratio, the overburden stress factor, the strength gradient ratio, and the anisotropic strength ratio. The significance of four dimensionless parameters on the stability load factor of the 3D face stability of circular tunnels, and the predicted failure mechanisms due to the influence of cover depth ratios, are also illustrated. A nonlinear regression analysis is employed to the computed data, which enables a new design equation of the factor of safety incorporating the conventional stability number. Thus, the new tunnel stability factors are proposed for the first time in the literature. A comprehensive application of the proposed safety factor equation is also presented and compared. The 3D effects of the tunnel face configuration between 3D geometry and 2D plane strain heading on the tunnel stability factors are also discussed. The new proposed design equation of the factor of safety provides an accurate and practical tool in assessing face stability of circular tunnels in non-homogeneous and anisotropic clays.

Simplified criterion to predict the lower bounds of the anisotropic ultimate strengths of 3D printing metals

3D printing metals have an intrinsic building orientation, so they have some anisotropy in their strength due to the failure between the printing layers with direction dependence that was commonly seen in composite materials. Although the Tsai-Hill composite strength criterion predicted the ultimate strengths of some 3D printing metals made with selective laser melting and laser powder bed fusion (SLM/LPBF), the current study showed that the composite strength criterion was not applicable to the ultimate strength predictions of all 3D printing metals. Our suggested quadratic strength criterion without stress interaction provided conservative strength predictions to ensure safe 3D printing metal applications. Moreover, the shear strength plays a critical role in strength predictions and should be measured accurately.

A lightweight Fe–Mn–Al–C austenitic steel with ultra-high strength and ductility fabricated via laser powder bed fusion

Lightweight Fe–Mn–Al–C steels have become a topic of significant interest for the defense and automotive industries. These alloys can maintain high strength and ductility while also reducing weight in structural applications. Conventionally processed Fe–Mn–Al–C austenitic steels with high Al content (∼9 wt%) demonstrate greater than 1.5 GPa strength with 35% elongation. Several recent studies have demonstrated success in fabricating steel parts using laser powder bed fusion (L-PBF) additive manufacturing (AM), which can generate near-net-shape components with complex geometries and is capable of local microstructural control. However, studies on L-PBF processing of Fe–Mn–Al–C alloys have focused on low Al content (<5 wt%) compositional regimes representing alloys that undergo transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP). Here, we present the effects of L-PBF processing on the microstructure and mechanical properties of an Fe–30Mn–9Al–1Si-0.5Mo-0.9C austenitic steel. A process optimization framework is employed to determine an ideal L-PBF processing space that will result in >99% density parts. Implementing this framework resulted in near-fully dense specimens fabricated over a broad range of process parameters. Additionally, two bi-directional scan rotation strategies (90° and 67°) were applied to understand their effects on texture and anisotropy in this material. As-printed specimens displayed considerable work-hardening characteristics with average strengths of up to 1.3 GPa and 36% elongation in the build direction. However, solidification microcracks oriented in the build direction resulted in anisotropy in tensile strength and ductility resulting in average strengths of 1.1 GPa and 20% elongation perpendicular to the build direction. The successful L-PBF fabrication of Fe–30Mn–9Al–1Si-0.5Mo-0.9C presented here is expected to open new avenues for weight reduction in structural applications with a high degree of control over part topology.

Consideration of anisotropic properties of pebble soils in calculations of stability of slopes of soil dams

Introduction. The results of experimental studies of the deformation and strength anisotropy of gravel-pebble soil laid in the body of soil dams are presented. In the course of stabilometric tests, different shear angles for the stone were obtained with different orientations of soil particles in the working chamber — horizontal and vertical. With an increase in the hydrostatic pressure in the working chamber to 0.8 MPa, a decrease in the shear angles of the stone by 8–12 degrees was obtained, depending on the direction of the soil layering.&#x0D; &#x0D; Materials and methods. During the processing of experiments, a function of the ratio of shear angles for a stone with different particle orientations, depending on the direction of the main stress at the shear site, was obtained as&#x0D; ψan = φ(min)/φ(max) = f(σ). Graphs of “hodographs of shear angles” are constructed to determine the calculated values of the strength characteristics of gravel-pebble soil, depending on the angle of inclination of the shear site to the axis of soil layering. The author’s calculation program ОТКОС_Ani (Delphi) has been compiled, taking into account the strength anisotropy of pebble soils for calculating the stability of slopes of soil dams and slopes.&#x0D; &#x0D; Results. For stone and stone-earth dams of different designs and heights, slope calculations were carried out and correction coefficients were obtained to account for strength anisotropy in slope stability calculations in the form of a function kan = Knan / Kn = f(H, γ, m).&#x0D; &#x0D; Conclusions. The functions of the kan change depending on the type, height and density of the gravel-pebble soil laying in the body of the dam are obtained. It is found that the “lowering” coefficient for taking into account the decrease in the strength properties of pebble soil with horizontal layering varies in the range from 1 to 0.9, which should be taken into account when choosing the design of soil dams with prisms of gravel-pebble soils.

Exploring quantum phase transitions by the cross derivative of the ground state energy

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models (Chen et al 2020 Phys. Rev. B 101 165123), is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.

Multivariate adaptive regression splines analysis for 3D slope stability in anisotropic and heterogenous clay

Little research can be found in relation to the stability of anisotropic and heterogenous soils in three dimensions. In this paper, we propose a study on the three-dimensional (3D) undrained slopes in anisotropic and heterogenous clay using advanced upper and lower bounds finite element limit analysis (FELA). The obtained stability solutions are normalized, and presented by a stability number that is a function of three geometrical ratios and two material ratios, i.e. depth ratio, length ratio, slope angle, shear strength gradient ratio and anisotropic strength ratio. Numerical results are compared with experimental data in the literature, and charts are presented to cover a wide range of design parameters. Using the multivariate adaptive regression splines (MARS) analysis, the respective influence and sensitivity of each design parameter on the stability number and the failure mechanism are investigated. An empirical equation is also developed to effectively estimate the stability number.

Microstructural modification and enhanced mechanical properties of wire-arc additive manufactured 6061 aluminum alloy via interlayer friction stir processing

In this study, an innovative hybrid additive manufacturing technology that combines wire arc additive manufacturing (WAAM) and interlayer friction stir processing (FSP) is designed to overcome the hot cracking and other solidification issues observed in WAAM of 6061 aluminum alloy. The grain boundary liquation and porosity defects are effectively eliminated by the interlayer FSP technique, and the coarse Si-rich phases are broken up and redistributed, and the coarse columnar grains are transformed into fine equiaxed grains, resulting in superior mechanical properties to the initial WAAM alloy. Furthermore, the anisotropy in strength of the WAAM sample can be eliminated by the WAAM + interlayer FSP technique. It demonstrates that the WAAM + interlayer FSP technique has great potential for use in the fabrication of aluminum alloys susceptible to hot cracking with high performance.

Apparent anisotropic thermal diffusivity measured in cubic single crystals by transient grating spectroscopy

The effect of elastic anisotropy on thermal diffusivity determination by transient grating spectroscopy (TGS) was studied. In experiments performed on a set of cubic single crystals, it was observed that TGS measurements may indicate anisotropy of thermal diffusivity in otherwise thermally isotropic materials, and that the strength of this apparent anisotropy is correlated with the strength of the elastic anisotropy. To find a source of the observed phenomenon, finite-element simulations of the TGS measurements were carried out. Time-domain TGS signals were generated from the simulations and processed identically to the experimental data. The simulation results revealed that the elastic anisotropy affects the detected time-domain signals. Consequently, the thermal diffusivity coefficients determined from them showed the artificial directional dependence. For the chosen set of cubic crystals, ranging from nearly isotropic to strongly anisotropic in terms of elastic constants, this simulated directional dependence was in full agreement with the one observed in the experiments.

Anisotropic microstructure and mechanical properties of as-forged (Ti, Nb)B/Ti2AlNb composites

In situ boride reinforced Ti2AlNb-based composites are a new type of lightweight material that has excellent high-temperature performance exceeding that of Ti-based composites. Forging is one of the effective methods to improve the microstructure and mechanical properties of Ti2AlNb-based composites. After forging, the mechanical properties of the composites exhibit evident anisotropy, but the anisotropic mechanism remains unclear. In this study, the anisotropic mechanical properties of the as-forged (Ti, Nb)B/Ti2AlNb composite and its formation mechanism were investigated. It was found that the as-forged composite possessed higher yield strength along the radial direction (RD) and better plasticity along the compression direction (CD). The microstructural analysis results demonstrated that the O phase formed [100]O//CD fiber texture, and the (Ti, Nb)B reinforcement exhibited [010](Ti, Nb)B//RD fiber texture in the as-forged composite. The analysis based on In-Grain Misorientation Axes (IGMA) suggested that the {1 1‾ 0}<110> was the main activated slip system of the O phase during the deformation. The difference in both the Schmid factor of {11‾ 0}<110> slip system caused by the [100]O//CD texture and the strengthening efficiency induced by [010](Ti, Nb)B//RD texture led to the anisotropy of yield strength. The anisotropy of prior particle boundaries (PPBs) contributed to the different crack propagation modes of the as-forged composite under different loading directions, resulting in plastic anisotropy.

The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice

Geotechnical models developed during the planning stages of open pit mines are three-dimensional so as to capture the spatial variation in lithological, structural, hydrogeological, and geomechanical conditions. Geological models that describe the lithological and structural (faulting and folding) characteristics of a deposit are always 3D. Likewise, boreholes and piezometers used to develop geomechanical properties and groundwater models are drilled at spatial offsets across the deposit to understand the lateral and vertical characteristics. Yet when geotechnical analysis is completed, often the three-dimensional geological, hydrogeological, and structural models as well as geometrically complex 3D mine designs for optimizing economic mineral recovery and overburden removal are simplified to two-dimensional sections. In this paper we demonstrate that this simplification can lead to the wrong failure mechanism being identified, analysed, and/or a conservative factor of safety being calculated and hence an over-estimation of slope stability. Through case studies we show how three-dimensional analysis methods are more suited to rock slopes, particularly those with anisotropic material strength, when singularities such as geological faults are present, and nonlinear slope geometry. When the same slopes are analysed in two dimensions, the failure mechanism calculated is often fundamentally incorrect. The case studies further reveal that the factor of safety calculated in three dimensions is not always higher than the two-dimensional factor of safety.

Effect of strength anisotropy on strain localization in natural clay

Effect of strength anisotropy on strain localization in natural clay

Topology optimization for additive manufacturing with strength constraints considering anisotropy

Abstract Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.

Effects of interval time and interfacial agents on the mechanical characteristics of ultra-high toughnessnn cementitious composites under 3D-printed technology

Anisotropic mechanical characteristics are crucial to the application of the printed structure. This study is aimed to investigate the effects of interval time and interfacial agents on the anisotropic mechanical strength of ultra-high toughness cementitious composite under 3D-printed technology. The bending capacity of ultra-high toughness cementitious composite under 3D-printed technology was compared with mould-casting ultra-high toughness cementitious composite. The compressive strength, flexural strength and splitting tensile strength were measured to represent mechanical properties in different directions and the microstructure of ultra-high toughness cementitious composite under 3D-printed technology with different interval time and interfacial agents were characterized using nanoindentation, scanning electron microscopy, and X-ray computed tomography. The experimental results indicated that the ultimate bending strength and bending toughness of ultra-high toughness cementitious composite under 3D-printed technology were 13.6% and 3.3% to 13.3% higher than those of mould-casting ultra-high toughness cementitious composite at 28 d, respectively. As the interval time increased, the mechanical properties showed differential development patterns. Specifically, compressive strength and splitting tensile strength had a higher rate of decline in the X direction (parallel to the printing path) than in the Y and Z directions but flexural strength was the opposite. A 3-h interval time reduced the 28-d compressive strength and splitting tensile strength in the X direction by 24.02% and 49.64% but the strength only decreased by 10.57% and 26.59% in the Z-direction. The addition of interfacial agents reduced anisotropy in compressive strength and splitting tensile strength but increased the anisotropy of flexural strength. When the interval time was 3 h, the increase rate of the 28-d flexural strength in the X direction, in which the flexural strength was weakest, was 22%–29% lower than that in the Y and Z directions under the effects of interfacial agents. A microstructure analysis showed that the filling effect and high moisture content of interfacial agents counteracted the negative impact of interval time on the width of the interface between layers and the porosity of ultra-high toughness cementitious composite under 3D-printed technology, which can enhance the interlayer bonding. These results can promote the application of ultra-high toughness cementitious composite under 3D-printed technology in additive manufacturing.

Anisotropic Strength, Deformability, and Failure Behavior of Artificial Columnar Jointed Rock Masses under Triaxial Compression

Columnar jointed rock masses (CJRMs) have a complex network structure and, therefore, present a great challenge to geotechnical engineering design. A series of triaxial compression tests is performed on artificial CJRM specimens subjected to a confining pressure of 5 MPa, considering various pore pressures (pw=0 MPa, 2 MPa, and 4 MPa). In this work, the influence of the joint dip angles and pore pressure on the anisotropic strength, deformation, and failure modes of the CJRM is investigated. The anisotropic characteristic stresses, strength parameters (c and φ) and elastic modulus of the CJRM specimens show a U-shaped pattern with increasing joint dip angles (β), while Poisson’s ratio changes inversely. The elastic modulus has a stronger anisotropy than Poisson’s ratio. Moreover, with increasing pore pressure, the characteristic stresses decrease, while the anisotropy of stresses and deformations increases. Finally, three failure modes of CJRM specimens with different joint dip angles are observed under triaxial compression conditions.

Heterogeneity Versus Anisotropy and the State of Stress in Stable Cratons: Observations From a Deep Borehole in Northeastern Alberta, Canada

AbstractGeophysical logs collected from a deep borehole drilled into the North American Craton in Northeastern Alberta shed valuable light on the state of stress in stable cratons. Observed breakout (BO) azimuths rotate between three depth intervals, ranging from 100° at 1,650–2,000 m to 173° at 2,000–2,210 m, and finally to 145° at the bottom. No apparent fractures that might have disturbed the stress field were found. Two potential causes of these rotating BOs can be either a heterogeneous stress field or elastic and strength anisotropy of the formation. The latter interpretation is favored since observed BO azimuths are strongly controlled by rock metamorphic textures, as validated by their close correlations with dip directions of foliation planes and polarization directions from dipole sonic logs. Monte Carlo realizations further demonstrate that anisotropic metamorphic rocks subjected to a uniform horizontal stress direction could result in the observed azimuth‐rotating BOs. Stress magnitudes inferred from this analysis, which incorporates rock anisotropy and weak foliation failure planes, suggest a normal faulting regime and a maximum horizontal compressive direction consistent with that in the overlying Western Canadian Sedimentary Basin (NE‐SW) and the motion of the North American plate. The inferred stress magnitudes are low and Mohr‐Coulomb analyses demonstrate that the formation is not near the critical condition for slip on weak planes. However, more detailed investigations should be conducted since Monte Carlo calculations indicate that analyses from BO widths, particularly when a conventional Kirsch‐based formula is employed, are highly nonunique, allowing for large variations in potential stress states.

Multiscale structural characterizations of anisotropic natural granite residual soil

While the anisotropy of sedimentary soil—particularly the underlying role of soil structure—is well understood, similar knowledge about granite residual soil formed by weathering is scarce. In particular, the evolution of soil structure during the hollow cylinder torsional shear tests (among the most appropriate for studying soil strength anisotropy) remains largely unknown. This study systematically investigates the multiscale structural properties of granite residual soil using stereo microscopy, scanning electron microscopy, energy-dispersive spectrometry, and computed tomography. Furthermore, the structural evolution during hollow cylinder torsional shear tests is traced. Results indicate the strength anisotropy of residual soil is associated with horizontal fissures which cause low shear strength when the soil is sheared with a principal stress direction of 45°. The cementation via Fe is characterized by a uniform distribution. Different evolutionary patterns are observed for soils within the shear band, inside the necking area, and in other regions. It is not always the case that particles are rearranged with their long axis perpendicular to the major principal stress. This study improves the understanding of natural residual soil structure and provides some insights into its anisotropic behavior.

Wellbore stability analysis of inclined wells in transversely isotropic formations accounting for hydraulic-mechanical coupling

As the main hydrocarbon reservoirs, sedimentary formations are usually anisotropic in elasticity, strength, and permeability. Traditional wellbore stability analysis assumes that the surrounding rocks are isotropic and elastic, whereas some analytical and numerical methods assume that the surrounding rocks are anisotropic in both elasticity and strength. Since the anisotropy of permeability is usually ignored, the wellbore instability mechanism in anisotropic formations may not be identified. Therefore, based on the poroelasticity theory and the assumption of generalized plane strain, this study proposed a pseudo-3D coupled hydraulic-mechanical finite element model by considering the anisotropies of elasticity, strength, and permeability. Taking the L203-x well as an example, the elastic and permeability anisotropies and the wellbore trajectory and stability in any bedding plane directions were analyzed parametrically. Results showed that the model simultaneously considering the strength and elastic anisotropies was in line with the actual hole enlargement rate of the L203-x well. With the increased anisotropy index of the elastic parameters, the anisotropic induced pore pressure is opposite to that of isotropic situation on the 2D cross-sectional plane of the wellbore, and the effective stress increased and was deflected at a certain angle. The effective hoop stress was biased toward the direction of higher stiffness, and the shear failure area that grew smaller gradually decreased. With the increased anisotropy index of permeability, the pore pressure rapidly increased along the direction parallel to the bedding plane, the effective radial stress of shape became rectangular along the bedding direction, the high-stress concentration zone of effective hoop stress changed from four to two, and the shear failure area grew smaller. The relative importance order of the anisotropy influences on the wellbore stability was thus: strength anisotropy > elastic parameter anisotropy > permeability anisotropy. A comparison of the well inclination and bedding plane orientation showed that, when the relative angle between the well axis and bedding normal was small, the influence of the bedding plane declined. In practical drilling engineering, avoiding drilling parallel to bedding planes is conducive to borehole stability.

Strength Characteristics of a Heat-Resistant Metal-Matrix Composite Inconel 625–5%NiTi–TiB2 Alloy Fabricated by Direct Laser Deposition under Shock-Wave Loading

The Hugoniot elastic limit and spall strength were measured for a heat-resistant metal-matrix composite Inconel 625–5%NiTi–TiB2 alloy additive manufactured (AM) by direct laser deposition. The strength characteristics of the alloy were obtained from the analysis of the complete wave profiles recorded with a VISAR laser Doppler velocimeter during shock-wave loading of the samples. The samples were loaded using a PP50 pneumatic gun or ad hoc explosive devices along and across the material deposition direction in order to determine the strength anisotropy of the AM alloy under study. The maximum shock compression pressure was ~7 GPa, and the strain rate under tension before spalling varied in the range of 105–106 s–1. Kinetic dependencies of elastic/plastic transition and critical fracture stresses vs. loading conditions were plotted. It was shown that the Hugoniot elastic limit of the alloy under study decreases as the shock wave travels into the sample, while the spall strength increases as the material’s strain rate increases at the moment of spall fracture. A comparison of the strength characteristics of the Inconel 625–NiTi–TiB2 composite alloy with the original Inconel 625 alloy has shown that an addition of 5% of powder based on NiTi-TiB2 leads to a decrease in its elastic limit and critical fracture stresses upon spalling by more than 10%. The alloy under study demonstrates anisotropy of strength properties relative to the material deposition direction.

Implementation of a constitutive model for anisotropic rocks based on modified Lade failure criterion

The strength anisotropy for inherent anisotropic rocks presents a challenge to simulate considering the influence of intermediate principal stress. Based on the modified Lade failure criterion, a new anisotropic modified Lade criterion combining an empirical equation is established and verified using published experimental datasets of anisotropic rocks. The incremental constitutive model for anisotropic rocks is derived by using finite difference theory. The dynamic link library (DLL) module of the model is obtained by using the VC++ program, and then the model is validated against various laboratory test results. It is concluded that the proposed criterion and derived model can describe the strength anisotropy of inherent anisotropic rocks well.

Analysis of Wellbore Stability considering the Interaction between Fluid and Shale

Reservoir shale has the characteristics of bedding planes, strong anisotropy, and strong imbibition ability under ultralow water saturation, which has an important impact on wellbore stability of horizontal wells. Therefore, the physical and chemical properties of reservoir shale were analyzed, and a mechanics model of wellbore stability was established considering the elasticity and strength anisotropy. The wellbore stability was analyzed considering the anisotropy parameters of formation elasticity and strength and imbibition conditions. The results show that the anisotropy of elasticity and strength under the condition of imbibition are important parameters for evaluating the stability of reservoir shale borehole. Considering the interaction between fluid and reservoir shale, the weakening of the strength of the bedding structure is the reason for wellbore instability of reservoir shale. Bedding planes and microfractures provide rapid imbibition channel, and the imbibition volume increases, which further causes fracture expansion and strength weakening, and then leads to wellbore instability. Multistage effective plugging of bedding, microcracks and macroholes during drilling is the key to maintain the stability of shale wellbore.