Principal Loading Direction Research Articles

A new three-dimensional strength criterion considering the transverse isotropy based on the α-Spatial Mobilized Plane

Natural geotechnical materials are affected by sedimentation and exhibit significant anisotropy. To study the transverse isotropy characteristics of soil, the influence of intermediate principal stress and loading direction must be considered. Currently, research on transverse isotropy primarily focuses on the modified stress space, which is cumbersome to apply in multi-yield surface constitutive models. To describe the three-dimensional mechanical properties of geomaterials in real stress space, the α-Spatial Mobilized Plane strength criterion is introduced. Then, combined with the structure tensor, the transverse isotropic three-dimensional strength criterion can account for the effect of the loading angle. Finally, the three-dimensional strengths of Fukakusa clay, unsaturated SP-SC soils, uncemented Monterey sands, Yamaguchi marble, San Francisco Bay mud, Toyoura sand, and Santa Monica Beach sand are predicted on the π-plane. The results show that the αmn-SMP criterion, in the context of transverse isotropy, can describe the three-dimensional mechanical properties reasonably, and it can provide an accurate strength criterion for geotechnical engineering practice.

Deep‐Learning Analysis of Fracture Networks Leading to System‐Size Failure in Rocks

AbstractFracture networks in rocks and other geomaterials form by seismic and aseismic damage processes that could lead to system‐size failure. Here, we use a multi‐view convolutional neural network model to predict the stress proximity to macroscopic failure of experimentally deformed rock samples using two‐dimensional images. Models are trained on time series of fractures observed in rock samples through dynamic in situ synchrotron X‐ray tomography experiments. The results demonstrate that deep learning models outperform traditional estimates based on fracture density, increasing the accuracy of the predictions. Furthermore, the models provide insights into fundamental characteristics of fracture patterns that may provide precursory information on impending material failure. The trained deep learning models estimate the angle of the fracture plane relative to the principal loading direction, which is a key factor contributing to shear failure. The predicted angle of the fracture plane, in the range of 10°–30° with respect to the direction of maximum compressive stress, is consistent with the established failure criteria used in rock mechanics.

Practical fracture limit function considering data flexibility under plane-stress conditions in Lagrangian formulation

Ductile fracture limits have been extensively studied from the perspectives of material science and mechanics. While these studies have provided scientifically significant insights into ductile fracture limits, the influence of the evolution of anisotropy observed in actual experimental data suggests a need to account for diversity in the experimental data. To address this, it may be possible to further develop the model by investigating more influences from the field of materials science. However, from an engineering perspective, it can be effective to represent the diversity of acquired experimental data as practical functions for use, rather than solely focusing on the material science aspect. This paper presents mathematical formulations representing the strain- and stress-based fracture limit surfaces of ductile materials, to consider diverse data set for the evolution of anisotropy, under plane-stress conditions within the framework of the Lagrangian formulation. The model introduces a strain-based fracture limit surface (FLS), which has an additional anisotropic profile function based on the commonly used two-dimensional strain-based fracture limit curve (FLC). The anisotropic profile function is capable of capturing the evolving anisotropic profile based on the deformation mode and principal loading direction to represent more flexible shapes. With this function, a three-dimensional strain-based FLS, which can present the variation in fracture strains in the space of the deformation mode and principal loading direction, can be constructed. Then, the proposed model transformed this strain-based FLS into a stress-based FLS by converting the presented state vector in the former into the corresponding vector in the latter in the Lagrangian formulation. To achieve this, this study developed a formulation that considers the nonlinear evolution of stress anisotropy independent of the strain anisotropy during stress evolution. The two proposed models were validated by experimental results on a dual-phase steel. These models provide flexible fracture limit functions for ductile materials under varying stress and strain conditions in engineering applications.

System fragility evaluation of a curved highway bridge structure considering multi-direction seismic excitations

This paper presents the impact of varying the input seismic excitation directions on the system fragility of a geometrically complex highway bridge structure. The traditional approach of fragility derivation in the principal loading directions (longitudinal and transverse) results in an under/overestimation of the system fragility. To reduce such errors, the contribution of all major vulnerable components to the system fragility in the critical loading direction must be considered. For this purpose, a series of nonlinear time-history analyses were conducted for a testbed configured geometrically curved highway bridge structure in Japan. Shear strain, ductility, and distortion strain were considered as engineering demand parameters for bearings, concrete pier, and steel piers, respectively. The demand dependency among the components was considered using the correlation coefficient matrix for fragility estimation. Subsequently, fragility functions with respect to the input loading directions were generated for the bridge components and system to quantify their sensitivity to seismic input excitation directions. The results show that the component fragility is significantly influenced by the input excitation direction. A relative comparison of the system fragility for different loading directions indicated that a 150° loading direction yielded a higher fragility demand. The findings suggest that the critical fragility assessment should not always be decided only along the principal loading directions.

Effect of a singular planar heterogeneity on tensile failure

Many rocks contain planar heterogeneities, in the form of open fractures, veins and/or stylolites, but scarce data exist on how strength and fracture pattern formation is affected by the presence of a singular planar heterogeneity in an otherwise uniform matrix. The mechanics of stylolite-bearing and/or fractured limestone is of interest to several engineering applications, from quarries to subsurface gas or geothermal reservoirs. We have performed Brazilian Disc tests on pre-fractured Indiana limestone samples and Treuchtlinger Marmor discs which contain cohesive stylolites, investigating Brazilian test Strength and the resulting fracture pattern. All experiments were filmed, and where possible analyzed with particle image velocimetry. When viewed in 2D, the planar discontinuity was set at different rotation angles compared to the principal loading direction, where perpendicular to the loading direction is defined as 0⁰. The results show that all samples are weaker than their intact counterparts. For the pre-fractured Indiana limestone, there is 10–75% angle-dependent weakening. However, in the samples with a stylolite, strength is weakened by 35–75%, independent of direction. Several new cracks appeared when fracturing a stylolite-sample, where the orientation is heavily influenced by the stylolite orientation. The fracture pattern and associated stress drops are more complex for high angles. In these samples always more than one fracture formed, whereas in pre-fractured samples usually only one new fracture formed. This suggests a potential for more permeability increase when hydrofracturing a stylolite-rich interval. Comparison with Finite Element Models indicates that this difference in fracture pattern is caused by the strength contrast between the anastomosing stylolite zone and the matrix material, leading to stress concentrations effects. This causes (micro-) fracture nucleation to occur locally, promotes fracture coalescence and fracture growth at lower overall sample-load conditions compared to intact samples.

Hazard consistent record selection procedures accounting for horizontal and vertical components of the ground motion: Application to liquid storage tanks

AbstractA methodology is proposed to enable state‐of‐the‐art record selection using ground motion components in all three principal loading directions. Relying on the well‐established Conditional Spectrum approach, its fundamental concepts are extended to ensure hazard consistency when the vertical ground motion component is considered along with the horizontal ones. To this end, different record selection techniques are employed, spanning sets of ground motion records with and without vertical motions, as well as with and without vertical ground motion hazard consistency. To demonstrate the effect that each record set can potentially have on a structure, an unanchored liquid storage tank is adopted as a case study, because of the vertical uplift motion it can exhibit, even under the application of horizontal loading only. A reduced‐order structural model is employed to generate the numerical output via multi‐stripe analysis, thus enabling the evaluation of the pertinent record selection approaches. Focusing on uplift and compressive meridional stress, response ratios and response hazard curves are extracted. It is shown that although the vertical ground motion component only mildly affects uplift, its effect on compressive meridional stress, on average, amplifies the response by a factor of 1.8 for moderate intensities and 2.8 for higher ones. Accounting for hazard consistency in the vertical component appears to be important for the case at hand, as it reveals notable discrepancies in the mean annual frequency of exceedance for the response parameters examined.

A Novel Ex Vivo Bone Culture Model for Regulation of Collagen/Apatite Preferential Orientation by Mechanical Loading.

The anisotropic microstructure of bone, composed of collagen fibers and biological apatite crystallites, is an important determinant of its mechanical properties. Recent studies have revealed that the preferential orientation of collagen/apatite composites is closely related to the direction and magnitude of in vivo principal stress. However, the mechanism of alteration in the collagen/apatite microstructure to adapt to the mechanical environment remains unclear. In this study, we established a novel ex vivo bone culture system using embryonic mouse femurs, which enabled artificial control of the mechanical environment. The mineralized femur length significantly increased following cultivation; uniaxial mechanical loading promoted chondrocyte hypertrophy in the growth plates of embryonic mouse femurs. Compressive mechanical loading using the ex vivo bone culture system induced a higher anisotropic microstructure than that observed in the unloaded femur. Osteocytes in the anisotropic bone microstructure were elongated and aligned along the long axis of the femur, which corresponded to the principal loading direction. The ex vivo uniaxial mechanical loading successfully induced the formation of an oriented collagen/apatite microstructure via osteocyte mechano-sensation in a manner quite similar to the in vivo environment.

Orthotropic elastic–plastic–damage model of beech wood based on split Hopkinson pressure and tensile bar experiments

The hardwood is a natural composite, which finds applications in many fields such as an important building material. Attention was paid to the accurate description of the European beech wood under high strain rates in order to constitute a reliable input for the finite element method. It was done on the basis of split Hopkinson tensile bar tests, taking also into consideration the previously reported pressure bar tests to capture the tensile–compressive failure asymmetry, which was incorporated through the stress triaxiality. Strains measured on the steel bars for specimens oriented in all principal loading directions were used to calibrate the fully orthotropic behaviour of elasticity, plasticity and fracture. The concept of continuum damage mechanics was applied to the damage accumulation in order to simulate the crack propagation within explicit finite elements realistically.

Closing the osteon: Do osteocytes sense strain rate rather than fluid flow?

Osteons are cylindrical structures of bone created by matrix resorbing osteoclasts, followed by osteoblasts that deposit new bone. Osteons align with the principal loading direction and it is thought that the osteoclasts are directed by osteocytes, the mechanosensitive cells that reside inside the bone matrix. These osteocytes are presumably controlled by interstitial fluid flow, induced by the physiological loading of bones. Here I consider the stimulation of osteocytes while the osteon is closed by osteoblasts. In a conceptual finite element model, bone is considered a poro-elastic material and subjected to locomotion-induced loading conditions. It appears that the magnitude of flow is constant along the closing cone, while shear strain rate in the bone matrix diminishes linearly with the deposition of bone. This suggests that shear strain rate, rather than fluid flow, is the physical cue that controls osteocytes and bone deposition in newly formed osteons.

Effects of stress path on brittle failure of sandstone: Difference in crack growth between tri-axial compression and extension conditions

The tri-axial testing of rocks under compression is a widely popular measure for the assessment of strength of geological materials in the laboratory. In this regard, mechanical complexities of true tri-axial testing machines impel researchers to opt for simpler conventional tri-axial testing machines. To account for influential factors that affect quality of experimental data, observations derived from laboratory experiments that enable overcoming some drawbacks are presented herein. In the present study, a series of tri-axial tests on Kimachi sandstone under Conventional Tri-axial Compression (CTC), Conventional Tri-axial Extension (CTE), Reduced Tri-axial Compression (RTC), and Reduced Tri-axial Extension (RTE) conditions were carried out. The results suggested higher compressive strengths for the rock under tri-axial extension tests than the compression tests. This observation proves that the effect of intermediate confining pressure on material behavior is important and if feasible, should not be sacrificed for more economical alternatives. Generally, the loading and unloading experiments for a specific test type rendered the same results and the conventional and reduced paths in both the compression and extension tests did not affect the failure strength of the specimens. The effect of pre-existing cracks orientation with respect to the principal loading directions on crack growth was focused upon and related conclusions were subsequently drawn.

Numerical modeling and experiments of Friction Stir Back Extrusion of seamless tubes

In this work, the Friction Stir Back Extrusion (FSBE) process of seamless Mg AZ31B tubes is investigated using numerical modeling and experiments. A Coupled Eulerian Lagrangian thermomechanical model is developed to simulate the FSBE process. Material flow, strains, strain rates, grain size, and temperature histories during the FSBE process were investigated. FSBE experiments were conducted to validate the model. It is shown that the measured reactive body force in the principal loading direction and the temperature histories at different locations of the die agree well with the modeling results. The numerical results show that a maximum strain rate of 90s−1 was attained at the inner surface of the tube. The maximum temperature in the workpiece reaches 599°C. The optical microscopy and numerical results show that fine grains were formed at the inner surface of the tube with diminishing refinement effects as the outer surface is approached. It is revealed that the material in the central region of the workpiece rotates around the tube centerline in a behavior similar to that seen in the rotation zone in friction stir welding. The material near the outer surface of the workpiece moves upward with slight rotation about the tube centerline.

The mechanistic link between macrozones and dwell fatigue in titanium alloys

This paper addresses the role of macrozone crystallography and morphology in dwell fatigue in titanium alloy Ti-6Al-4V. Until now, the relationship between macrozones and dwell fatigue damage has remained mechanistically uncertain, but this paper establishes a mechanistic link between macrozones and dwell fatigue damage, and explains the preference for dwell facets to be sub-surface. It also outlines the criteria which are important in a potential definition of a macrozone (or microtextured region). High aspect ratio (>~4) macrozones are particularly damaging when their long-axes are orientated near-normal to the principal loading direction, such that their basal planes are oriented to within ~15° to the principal stress direction. These criteria may be useful in guiding the development of a diagnostic experimental measurement tool (based on EBSD or ultrasonics for example) for macrozone detection in components.

Modelling of impact behaviour of European beech subjected to split Hopkinson pressure bar test

The hardwood, as a natural composite, may be subjected to the dynamic loading in many applications, such as the high-speed disintegration or structural collapses. The correct material description is needed for finite element modelling that can take place in the design stages of wood manufacturing processes or building the wooden structures. The split Hopkinson pressure (Kolsky) bar test provides the data for high strain rates. The experiments were carried out on the European beech wood in all the principal loading directions. The tests were repeated computationally in order to obtain the material constants of the complex material model, which covered the anisotropy of elasticity, plasticity as well as fracture behaviour. Moreover, the failure was considered non-symmetric with respect to the tension and compression. This was achieved by incorporating the stress triaxiality dependency into the failure model. The crack initiation and propagation were realized through the element deletion technique within LS-DYNA code. The real behaviour was captured quite well including the pulses in the incident and transmission bars.

Effect of Knots and Related Grain Deviation on the Rolling Shear in Dimension Lumber Used in Cross-Laminated Timber Transverse Core Layers

Abstract Cross-laminated timber (CLT) technology has the potential for utilization of lower grades and underused species of lumber, because the core layers perpendicular to the principal loading direction transfer loads through shear, which is not correlated to the grade of lumber. Currently the product standard specifies the minimum grade requirements for all lumber to be used as CLT laminations. In this study, the effect of the presence of knots in the transverse core layer of CLT billets was examined in matched CLT samples where the heavy presence of knots and the related grain disturbance in the transverse core layer were the only variables compared with knot-free reference. All samples were tested as short beams in three-point bending and all failed in rolling shear in the transverse core layer. The presence of knots had no measurable effect on the shear capacity or stiffness of the tested CLT beam samples.

Effect of stiffness anisotropy on topology optimisation of additively manufactured structures

Additive manufacturing has been receiving attention as it is capable of producing complex geometries previously unmanufacturable, particularly those resulting from topology optimisation. However, additive manufacturing processes like Selective Laser Melting result in materials that have varying ratios of anisotropy. Currently, the majority of topology optimisation algorithms utilise an isotropic assumption. Through a case study, the present study confirms the hypothesis that anisotropy in the stiffness of the material has a significant detrimental effect on the optimisation outcome where (1) increasing ratio of anisotropy; and/or (2) increasing deviation of the building angle away from being parallel or perpendicular to the principal loading direction results in the decrease of volume reduction achievable through topology optimisation. Material with an out-of-plane shear modulus which is very different from the “near isotropic” value also performed poorly. Compared with the 50% weight reduction of an isotropic case, the worst anisotropic case only managed approximately 27% weight saving. However, in the cases where both the building angle is small (<30°) and the degree of anisotropy is low (≤±10%), the impact on resultant volume reduction was small (<10%). This study indicates that, in general, material anisotropy should be considered in topology optimisation for additive manufacturing.

Unified constitutive model with consideration for effects of porosity and its application to polyurethane foam

Abstract Polyurethane foam (PUF) is a popular insulation material and has crucial mechanical characteristics under compression in the principal loading direction, including nonlinear behavior dependent on strain rate and temperature, degradation of elastic modulus, and decrease of void fraction. Additionally, its insulation performance relies on the blowing agents in voids. These material characteristics enable the evaluation of the structural integrity and performance of PUF insulation systems, if the prediction of these characteristics and the relationship between change in void fraction and insulation performance are possible. In this paper, a unified constitutive model was proposed for this purpose. This model was verified with corresponding experimental results, and the validation showed that the material characteristics can be depicted successfully. Moreover, for the sake of applicability, the model was used in the evaluation of the insulation system in an LNG Carrier.

Nonlinear In-Plane Deformation Mechanics of Timber Floor Diaphragms in Unreinforced Masonry Buildings

AbstractAn analytical model was developed to describe the nonlinear in-plane deformations of timber floor diaphragms in historic unreinforced masonry buildings. Diaphragm deformation mechanics are detailed for both principal-loading directions (parallel to joists and perpendicular to joists) and are shown to produce differential equations of identical form. The model is formulated based on the assumption of pinned-end conditions, symmetrical configurations, and a uniformly distributed applied lateral load. The model is validated against full-scale diaphragm experimental data and is shown to predict response in both principal-loading directions with good accuracy. It is recommended that further research be undertaken to establish representative parameter values for the governing nail connection load-slip function.

In-Plane Orthotropic Behavior of Timber Floor Diaphragms in Unreinforced Masonry Buildings

AbstractA full-scale experimental program consisting of testing four as-built diaphragms and four retrofitted diaphragms in both principal loading directions is presented. As-built configurations were typical of those found in historic unreinforced masonry buildings in North America and Australasia, whereas retrofitted diaphragms consisted of plywood panel overlays with stapled sheet metal blocking systems (SMBS). Test results were characterized using bilinear representations to establish recognizable performance parameters such as shear strength, shear stiffness, and ductility capacity, which were then used for comparative analysis. The nonlinear and low stiffness behavior of as-built diaphragms was confirmed in each principal loading direction. The plywood overlay and SMBS dramatically improved as-built diaphragm shear strength and shear stiffness and were shown to perform satisfactorily from a serviceability perspective. The orthotropic nature of as-built diaphragms was proven, with perpendicular-to-jo...

Modeling Interparticle Size Effect on Deformation Behavior of Metal Matrix Composites by a Gradient Enhanced Plasticity Model

Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, besides volume fraction, have a considerable effect on the macroscopic mechanical response of metal matrix microreinforced composites. Classical (local) plasticity models unlike nonlocal gradient enhanced plasticity models cannot capture this size dependency due to the absence of a material length scale. In this paper, one form of higher-order gradient plasticity enhanced model, which is derived based on principle of virtual power and laws of thermodynamic, is employed to investigate the size effect of elliptical inclusions with different aspect ratios based on unit cell simulations. It is shown that by decreasing the particle size or equivalently the interparticle spacing (i.e., the spacing between the centers of inclusions), while keeping the volume fraction constant, the average stress–strain response is stronger and more sensitive to the inclusion’s aspect ratio. However, unexpectedly, decreasing the free-path interparticle spacing (i.e., the spacing between the edges of inclusions perpendicular to the principal loading direction) does not necessarily lead to largest strengthening. This is completely dependent on the plastic strain gradient hardening due to distribution and evolution of geometrically necessary dislocations that depend on the particle size and shape. Gradient-hardening significantly alter the stress and plastic strain distributions near the particle-matrix interface.

Does the normal stress parallel to the sliding plane affect the friction of ice upon ice?

AbstractSliding experiments were performed at −10°C on smooth surfaces of freshwater columnar-grained S2 ice sliding against itself at a velocity of 8 × 10−4 m s−1, with the purpose of examining whether normal stress parallel to the sliding plane affects frictional resistance. This component of the stress tensor was varied (0.20–1.83 MPa) using a loading system operated under biaxial compression, by orienting the sliding plane at two different angles, 26° and 64°, with respect to the principal loading direction. Under these conditions, no evidence was found to indicate that the normal stress in the direction of sliding affects the friction coefficient.