Load Angle 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.

Uncovering the Fracturing Mechanism of Granite Under Compressive–Shear Loads for Sustainable Hot Dry Rock Geothermal Exploitation

Shear-dominated hazards, such as induced earthquakes, pose an escalating threat to the sustainability and safety of the geothermal exploitation. Variations in fault orientations and compression–shear stress ratios exert a profound influence on the failure processes underlying these disasters. To better understand these effects on the shear failure mechanisms of hot dry rocks, mode-II fracturing tests on granites were conducted at varying loading angles (specifically, 55°, 60°, 65°, and 70°). These tests were accompanied by a comprehensive analysis of the mechanical properties, energy dissipation behavior, acoustic emission (AE) responses, and digital image correlation (DIC)-extracted displacement fields. The tensile–shear properties of stress-induced microcracks were discerned via AE characteristic parameter analysis and DIC displacement decomposition, and the mode-II fracture energy release rate was quantitatively characterized. The results reveal that with increasing compression–shear loading angles, the mechanical properties of granites are weakened, and the elastic strain energy at peak stress gradually decreases, while the slip-related dissipated energy increases. Throughout the fracturing process, the AE count progressively climbs and reaches a peak near catastrophic failure, with an upsurge in low-frequency and high-amplitude AE events. Microcrack distribution concentrates aggregation along the shear plane, reflecting the emergent displacement discontinuities evident in DIC contours. Both the AE characteristic parameter analysis and DIC displacement decomposition demonstrate that shear-sliding constitutes the paramount mechanism, and the fraction of shear-oriented microcracks and the ratio of tangential versus normal displacement escalate with increases in shear stress. This analysis is supported by the heightened propensity for transgranular microcracking events observed through scanning electron microscopy. As the shear-to-compression stress increases, the energy concentration along the shear band intensifies, with the gradient of the fitting line between cumulative AE energy and slip displacement steepening, indicative of a heightened mode-II energy release rate. These results contribute to a deeper understanding of the mode-II fracture mechanism of rocks, thereby providing a foundational basis for early warnings of shear-dominant geomechanical disasters, and improving the safety and sustainability of subsurface rock engineering.

Investigating the influence of geometric configurations and loading modes on mixed mode I/II fracture characteristics of rocks: Part I-Numerical simulation

The influence of geometric configurations and loading modes is a bottleneck that restricts the accurate determination of rock fracture parameters and the precise understanding of fracture mechanisms. Therefore, the phase field method is employed to analyze the influences of specimen geometry and loading modes on the dimensionless stress intensity factors, peak load, fracture toughness, and crack initiation angle during the rock mixed mode I/II fracture process. Three new configurations of specimens are proposed to test rock mixed mode I/II fracture. The research results indicate that as the prefabricated crack inclination angle increases, the peak load of three-point bending type specimen increases, while the peak load of diametric-compression type specimen decreases. Moreover, the influence of geometric configurations on the fracture parameters of three-point bending specimens is greater than that of diametric-compression disk specimens. The research findings of this work can provide basic supporting data for the establishment of mixed mode I/II fracture testing standards.

Effect of Loading Direction on Tensile-Compressive Mechanical Behaviors of Mg-5Zn-2Gd-0.2Zr Alloy with Heterogeneous Grains

The tension-compression yield asymmetry caused by the strengthening of Mg-Zn-Gd-Zr alloy due to extrusion deformation is an important issue that must be addressed in its application. In this study, the effects of loading direction on the tensile and compressive mechanical behaviors of Mg-5Zn-2Gd-0.2Zr alloy were systematically investigated. As the loading angle (the angle between the loading direction and the extrusion direction) increases from 0° to 30°, 45°, 60° and 90°, the tensile yield strength decreases more significantly than the compressive yield strength. Consequently, the tension-compression yield asymmetry is gradually improved. Additionally, the ultimate compressive strength decreases more markedly than the ultimate tensile strength with the increment of the loading angle. In tensile tests conducted at 0°, 30° and 45°, two distinct stages of decreasing strain hardening rates are typically observed. For the 60° and 90° tensile tests, one unusual ascending stage of strain hardening rate is observed. For all compressive tests, three stages of strain hardening are consistently noted; however, the increment in strain hardening rate caused by {10–12} extension twinning decreases with the increasing loading angle. A model combining loading angle and Schmid factor distribution was established. The calculated results indicate that the dominant deformation modes during the yielding process also vary significantly with the loading conditions. This clarification highlights the differences in yield strength variations between tension and compression. Finally, an analysis of the plane trace and crack propagation direction near the fracture surface reveals the fracture mechanisms associated with tensile and compressive tests at different loading directions. This study promotes understanding of the mechanical behaviors of Mg-5Zn-2Gd-0.2Zr alloy under different loading directions, and helps to thoroughly elucidate the anisotropic effects of texture on the mechanical properties of magnesium alloys.

Coal‐wall spalling prevention mechanism using advance‐grooving pressure relief in the large‐mining‐height working face of a shallow coal seam

AbstractIn mining, the roof structure of a working face with a large mining height in a shallow‐buried coal seam is prone to cutting instability in front of the support, which causes support crushing and coal‐wall spalling. This study analyzes 2201 working faces with large mining heights in the Haiwan No. 3 Mine by investigating the mechanical response law of coal walls under the transient excitation of roof structure instability. A mechanical model of coal walls under dynamic and static load coupling is established, revealing the formation mechanism of coal wall spalling and its main influencing factors. Prevention and control technologies of advanced grooving and pressure relief are proposed, and grooving parameters are determined. The results show that: During the mining process of large mining height working face in shallow buried coal seam, the step change of static response of coal wall is induced by the transient instability of roof structure, and the high abutment pressure is formed on the coal wall. At the same time, the strain energy and gravitational potential energy of roof cutting instability are released to form a dynamic load. Under the action of dynamic and static load, the plastic failure dissipation power of the coal wall is greater than the critical power, and the coal wall spalling occurs. The main influencing factors are mining load, mining height, and internal friction angle of the coal wall. The method of advanced grooving pressure relief can change the roof structure and coal force mechanism, by cutting off the connection between the coal wall and immediate roof, reducing the height of the coal wall force, effectively controlling the position of the roof cut off break line, reducing the static load effect of the roof on the coal, and transferring the position of the dynamic load response to the depth of the coal wall. When the grooving height‐depth ratio k is 0.75, the peak value of the abutment pressure moves 5.57 m to the front of the working face, and the pressure relief effect is the best. The above research results provide an effective active protection method for controlling coal wall spalling in fully mechanised working face with large mining height.

Seismic experiment and performance analysis on embedded optimized steel plate-reinforced concrete composite shear wall under multi-dimensional loading

In order to investigate the seismic performance of reinforced concrete shear walls under multi-dimensional loading mode and its effect on performance improvement, an embedded optimized steel plate-reinforced concrete composite shear wall is proposed. Based on the design principle that the shear wall could adequately bear multi-dimensional loading and the embedded steel plate could reach the full stress state, the X-shaped optimized steel plate (for in-plane loading mode) and the triangular optimized steel plate (for out-of-plane loading mode) are determined using different optimization methods. The combination scheme of these two plates is utilized in the oblique loading mode. Quasi-static loading tests are conducted on eight typical shear wall specimens, and performance parameters such as hysteresis curve, skeleton curve, ductility, stiffness degradation, strain evolution, and damage evaluation of the specimens are compared and analyzed. In addition, variable parameter analysis is performed using finite element software to compare the strain distribution state of each steel plate. The results indicate that the embedded optimized steel plate-reinforced concrete composite shear wall structure exhibits higher bearing capacity, greater deformation capacity, and superior energy dissipation capacity under different loading angles compared to the tradition reinforced concrete shear walls. This composite structure can provide greater lateral stiffness, and the optimized steel plate can reach the full stress state at all loading angles, effectively reducing the damage of steel bars and concrete. These findings offer a foundation for the study of seismic performance and performance improvement methods for shear wall structures under multi-dimensional earthquake action.

The Effects of Loading Angles on the Failure of Cross-Ply Notched Bio-Basalt Composites

A cross-ply basalt V-notched butterfly specimens were subjected to pure tension, combined tension-shear, and shear stress-strain state using a modified Arcan test fixture with loading angles from 0° to 90° with 15° increment. Multiaxial stress and strain states were studied using the principal stress and strain ratio, from which the principal angle was determined and used to represent principal states in the gauge section. The quasi-elastic to non-linear transition stresses were determined for each loading angle. In biaxial stress-strain states and pure shear, the deformation and consequently the shear-induced damage start to accumulate significantly. Also, in biaxial stress-strain states between 15°-75°, the shift from tension-shear to pure shear was observed after the transition to the non-linear part of the stress-strain curve. The digital image correlation (DIC) images and microscopic evaluation show that a large extent of damage is the consequence of the shear deformation after the rotation of 0° clamped fibres, while the 90° fibres maintained their original straight form. In off-axis tests, the principal strain axis rotates towards the weakest material axis even at small off-axis angles. This causes a transition from a tension-shear biaxial state in the linear loading part to shear in the non-linear part, leading to irreversible damage beyond the transition point.

Design and analysis of the speed and torque control of IM with DTC based in predictive control and load angle control for electric vehicle applications

Design and analysis of the speed and torque control of IM with DTC based in predictive control and load angle control for electric vehicle applications

An experimental-cohesive zone model approach to predict fatigue life of adhesive joints with varying modes of loading and joint configurations for automotive applications

ABSTRACT Predictive fatigue life models of adhesive joints are necessary to enable the assessment of automotive-bonded structures while reducing costly experimental testing. However, contemporary models have typically been calibrated for specific joint configurations and modes of loading, limiting their applicability to large-scale structures. Additionally, available models are based on simulation of cumulative fatigue cycling, making them computationally prohibitive. In the current study, cross-tension (CT) (load angles of 0°, 45°, and 90°) and single-lap shear joint (SLJ) configurations were bonded using an epoxy adhesive (BetaGuard CI6125R; PPG, France) used in automotive production (one part) and tested under fatigue cyclic loading. A total of nine joint configurations, having symmetrical (same material and thickness) and asymmetrical (dissimilar material or unequal thickness) joints, were tested. Fatigue tests at load levels between 25% and 75% of the static peak load were performed until joint failure or to runout (two million load cycles). The static tests of the joints were simulated to failure using finite element (FE) models with the cohesive zone method (CZM). The maximum strain energy release rates ( G max ) were calculated within the adhesive bond line at static loads corresponding to the peak loads of the fatigue tests. The G max values, computed from single cycle, specimen-specific FE simulations, were correlated with the measured fatigue life ( N f ) of the adhesive joints with varying modes of loading and joint configurations. The fatigue life prediction model, based on G max − N f correlation and following a crack propagation approach, predicted the cycles to failure for 85% of the fatigue tests, and 81% of the independent validation tests. The proposed fatigue life prediction approach provides computational efficiency and large-scale compatibility.

Experimental study on fracture properties of heat-treated granite in I-II mixed mode suffered from water and liquid nitrogen cooling methods

Hot dry rock (HDR) development is significant for solving energy problems and realizing energy conservation and emission reduction. Liquid nitrogen (LN2) fracturing and hydraulic fracturing can form cracks in the HDR and improve the efficiency of geothermal energy mining. Therefore, it is necessary to study the fracture characteristics of high-temperature granite under different cooling methods. In this study, the deterioration of the physical and mechanical properties of granite subjected to high-temperature treatment under water cooling and LN2 cooling was studied. Two I/II mixed modes (tensile orientation mode and shear orientation mode) and a pure II mode fracture characteristics of cracked straight-through Brazilian disc (CSTBD) specimens made of granite were explored. The displacement and strain fields of cracked granite specimens were measured by using a digital image correlation (DIC) method. The results show that when the temperature is 25℃, 200℃, and 400℃, the loading angle and cooling method have a great influence on the fracture mechanical characteristics of the granite. In general, the increase of loading angle and LN2 cooling will lead to the decrease of peak load. For example, at 200℃, β = 15°, the deterioration degree of water-cooled and LN2-cooled specimens is 13.77 % and 16.69 %, respectively. When β = 23°, it increases to 14.62 % and 19.91 %, respectively. At the same time, an interesting phenomenon was found in the study. At 400℃, due to the Leidenfrost effect, the peak load of LN2-cooled specimens was higher than that of water-cooled specimens, and the further increase of temperature weakened the effect. When the temperature is 600℃, the difference between the loading angle and the cooling method is weakened.

Influence of microstructural and loading direction on the ductility and anisotropy of Ni-based superalloys

The influences of phase coarsening and loading direction on the ductility of Ni-based superalloys with phase coarsening are investigated, and the relationship between their microstructural and macroscopic mechanical properties is also explored in detail. It is found that the precipitation phase and the corresponding phase coarsening significantly influence the ductility of alloys. Furthermore, anisotropic features in ductility are observed after phase coarsening. Generally, as the volume fraction of precipitation particles or the degree of phase coarsening increases, the ductility of alloys gradually decreases; and it initially increases and then decreases gradually with the increase of loading angle, presenting an inverted ‘V’ shape. Comparatively, for the alloys with lower volume fraction of precipitation particles and higher degree of phase coarsening, the ductility shows different variation trends with the degree of phase coarsening and loading angle compared with that in materials with other microstructure features, taking the minimum value at the loading angle of 45°. The variations of ductility are closely connected to the characteristics of precipitate shape, size and distribution. The microstructure evolution and the loading direction significantly affect the initiation and movement of dislocations within the material, and result in various macroscopic ductility characteristics in the Ni-based superalloys.

The Behavior of Post-installed Rebar Connectors in Steel Frame Retrofitted Concrete Structures Under Combined Shear and Tension

To investigate the response of post-installed rebar connectors in steel frame retrofitted concrete structures under combined shear and tension, seven shear-and-tensile tests were conducted. The bearing capacity, stiffness, and hysteresis behavior of the connectors were investigated during the tests. Both Monotonic and cyclic load regimes were applied in the loading process. The results show that with the increase of the loading angle, the deformation capacity, the yield force, ultimate tensile force, and tensile stiffness of the specimen decrease, while the maximum shear force and shear stiffness of the specimen increase. The bearing capacity, stiffness, and energy dissipation performance of the specimen under a monotonic load is greater than that under the coupled shear-and-pull load. The bearing capacity, stiffness, hysteresis curve, and failure status of the specimens are not affected by different loading regimes. At the end, the design formula of anchor bolt for this type of connectors from the design code of China, United States, and Japan were compared. Formulas to calculate the shear strength under combined shear and tension is developed.

Crushing performance and energy absorption characteristics of aluminum/CFRP hybrid thin-walled tubes: Experimental and numerical investigations

This paper presents both experimental and numerical studies with the main purpose of exploring the crushing behavior of aluminum/CFRP hybrid thin-walled tubes under compression conditions. In particular, aluminum/CFRP tubes with 8, 10, and 12 layers of composites are considered, and the energy absorption characteristics are examined by quasi-static crushing experiments. An explicit finite element (FE) model is developed to investigate the axial crushing response and damage behavior of aluminum/CFRP tubes. Following validation against the experimental data, the developed FE model is applied to analyze the effects of number of layers and loading angles on the failure mechanism and energy absorption indexes of different tube configurations. The obtained results provide valuable insights into a practical energy absorption solution for aluminum/CFRP tubes subjected to crushing conditions, thereby contributing to the long-term development of the related industry.

Fatigue crack growth rate under mixed-mode loading conditions (I+III) of a carbide-free bainitic steel designed for rail applications

Carbide-free bainitic steel was designed for railway infrastructure application, focusing on high-speed and heavy-loaded freight tracks. Considering the complex state of stresses occurring on the rails running surface, mode III plays a significant role in the initiation and propagation of fatigue cracks of rails during service. Thus, the Fatigue Crack Growth Rate (FCGR) under mixed-mode loading conditions (I+III) was evaluated. It was revealed, that fatigue lifetime increases with loading angle modes. In the area of fatigue fracture, transgranular cracking mechanisms dominated. For the stable fatigue crack growth, a trend was observed related to the decrease in the fraction of intergranular fracture with the increasing loading angle modes (α). Secondary cracks indicated privileged cracking directions related to the crystallographic structure of bainite. The influence of the mechanical stability of retained austenite during mixed-mode FCGR requires further in-depth research. These studies contribute to understanding the factors influencing the reliability of railway tracks in terms of designing new materials and modeling the rate of crack growth to precise assessment of the life cycle of rails.

Experimental Investigation of Full Hole Embedment Behavior of Bamboo Scrimber with Dowel-Type Fasteners

A comprehensive understanding of the embedment behavior is of great importance in the design of contemporary bamboo constructions with connections utilizing dowel-type fasteners. The objective of this research was to assess the embedment behavior of bamboo scrimber using full-hole embedment tests. To investigate the effect of the loading angle and bolt diameter, a series of tests were performed using bolts of varying diameters (16 mm, 18 mm, and 20 mm) and loading angles (0° to 90°, with an increment of 15°). The experimental results demonstrated that the loading angle has a considerable influence on the embedment behavior. As the loading angle was increased, the failure mode underwent a change from a brittle failure mode, which was dominated by shear mechanisms, to a ductile failure mode, which was dominated by fiber crushing. The yield and ultimate embedment strengths showed an M-shaped response to changes in the loading angle, with the lowest values being 0°, 45°, and 90°. The bolt diameter was found to have no impact on the failure mode of the specimen. However, an increase in bolt diameter resulted in a reduction in the embedment strength when the specimen was loaded at 90°.

A Review of the Properties of Different Concrete-Filled Steel Tube Columns

This paper mainly analyzes different types of concrete-filled steel tube columns to compare different parameters such as loading angle, eccentricity, different steel pipe thickness, different strength grades of concrete, different cross-sectional shapes, etc., and elaborates the changes of mechanical properties of the specimens under the influence of different parameters. The formulas of axial compression and flexural bearing capacity of different concrete-filled steel tube columns and the bearing capacity of concrete-filled steel filled steel tubes after fire were proposed, and the interaction of various materials in the components was studied in depth. The proposed studies are summarized.

Energy absorption of braided composite tubes under quasi-static combined shear-compression loading

In this paper, the energy absorption performance of braided composite tubes under combined shear-compression loading is investigated. ABAQUS/Explicit is employed to analyze the energy absorption of braided composite tubes, and quasi-static compression tests are carried out. Braided composite materials absorb energy through the damage accumulation in laminate. Thus, to maximize energy absorption performance, a progressive crushing mode should be induced. While extensive research has been conducted on cases of axial loading, understanding of the energy absorption performance of braided composite tubes under combined shear-compression loading remains limited. Experimental results reveal that under both axial and combined shear-compression loading at 30 degrees, the braided composite tube exhibits a progressive crushing mode. The test results are utilized to validate the finite element model. Through finite element analysis, it is confirmed that the damage accumulation in laminate is maximized due to the induction of a progressive crushing mode. It means that the energy absorption principles of braided composites apply similarly to combined shear-compression loading, allowing for the maintenance of superior energy absorption performance of braided composites under various load angles.

Perturbation approaches to achieving diverse and competitive designs in topology optimisation

Utilising topology optimisation to generate diverse and competitive structures enables designers to create elegant and efficient designs according to their aesthetic intuition and functional needs. This study proposes load and support perturbation approaches based on the bi-directional evolutionary structural optimisation (BESO) method to achieve diverse designs. During the optimisation process, noise is introduced to the sensitivity calculations by randomly perturbing the load angles or material properties near the supports, leading to a variety of local optima. Numerical results demonstrate that the proposed approaches are capable of creating designs with similar stiffness but distinct geometries. In addition, the diversity of the obtained solutions can be controlled by utilising different perturbation functions. This work is of significant practical importance in both architecture and engineering, where multiple design options of high structural performance are in demand.

Research on eccentric-compressive behavior of steel stub columns with localized corrosion

To explore the impact of localized corrosion on the mechanical properties of hollow steel columns under eccentric loads, a specialized localized immersion-accelerated corrosion apparatus was developed. This device facilitated the creation of 17 locally corroded specimens, all subjected to eccentric loading. A systematic examination was conducted on various corrosion parameters including corrosion length, corrosion angle, localized corrosion rate, and corrosion location as well as loading conditions, which encompassed eccentricity and loading angle. Surface corrosion morphology and statistical parameters of the specimens were obtained using a 3D scanner. Subsequently, a nonuniform corrosion model, based on element displacement, was formulated through finite element analysis. Both experimental findings and numerical simulations indicate that localized corrosion does not alter the failure mode of locally corroded circular steel tubes (LCCSTs), which predominantly undergo local buckling in the compressed region. However, it was noted that localized corrosion leads to the elimination of the ascending segment in the load-displacement curve of the LCCSTs, thereby reducing both the ultimate load and ductility. Interestingly, the ultimate load of the LCCSTs was found to be relatively unaffected by variations in corrosion length and location but significantly influenced by factors such as localized corrosion rate, corrosion angle, eccentricity, and loading angle. Furthermore, through a comparative analysis of existing calculation models for the ultimate load of LCCSTs in major specifications, a practical model that accounts for localized corrosion is proposed. This model demonstrates high accuracy and is expected to enhance the understanding and prediction of the ultimate load capacity of LCCSTs in real-world applications.

Damage assessment of fixed U-shaped stiffeners stiffened square plates subjected to close-in explosions

The aim of this study is to suggest an approach for evaluating the damage modes and damage levels of the U-shaped stiffeners stiffened plates exposed to close-in explosions. To achieve this objective, a numerical model was developed in LS-DYNA, and the numerical model was verified by experimental results of the authors. Using this validated model, various U-shaped stiffeners stiffened plates were examined under different blast loads. The study investigated the factors that influence the damage modes of the plates, including the strength and distribution of the blast loads, as well as the geometry of the stiffened plates. The results indicated that the small size stiffened plates exhibited overall damage mode while the large stiffened plate showed localized damage at the same blast load. The blast load distribution on the different size plate led to different damage modes. Additionally, this study found that the slenderness of the stiffened plate had a great influence on the support rotation angle of the tensile tearing threshold. The larger span to thickness ratio can result in larger tensile tearing threshold. Moreover, 400 numerical cases were included and used to classify the damage modes of stiffened steel plates. Based on the damage mechanism of the stiffened steel plate, the damage number (Φ1 and Φ2) which considering the blast loads and material parameters of plate, the maximum incident angle of the blast load(α), and the relative stiffness of the stiffeners and the flat steel plate (κ1 and κ2), and the thickness to span ratio of the stiffened plate (λ) were combined to identify the damage modes of stiffened plates. Furthermore, a flow chart was constructed for determining damage modes based on these considerations. Additionally, a curve surface fitting was performed using Φ1 and λ, the fitting formulas were then used to estimate the deformation characteristics of the stiffened plates with U-shaped stiffeners. The damage levels of the U-shaped stiffeners stiffened plates were then classified as low damage, medium damage, severe damage, and collapse by combining the nominal support rotation angle with the threshold of the global tensile tearing at boundaries. The study result can provide insight into the damage mode identification and damage level classification of stiffened steel plates under explosion. Additionally, this study was a base of damage evaluation of the structure elements (such as steel box girder) include stiffened steel plates under explosions.