Complex Stress State Research Articles

Investigation into the effect of impact damage on compression behavior of the omega-stiffened composite panels

Abstract With superior performance and weight-saving potential, composite structures have been increasingly applied in the aerospace industry. The damage process and post-buckling deformation of composite panels under compressive load have been proven to limit the application of composite structures. For the purpose of utilizing the full potentiality of thin-walled composite structures, an experimental investigation was employed to explore the influence of impact damage on the buckling behavior and the load-carrying capacity of omega-stiffened composite panels. Pristine panels and impact-damaged panels were under compressive load until failure. The results showed that the pristine panels had higher compressive stability and ultimate strength, and the existence of impact damage led to a decline in the buckling load and the carrying capacity, which were up to 16% and 27%, respectively. Additionally, the complex stress state caused by the introduced impact damage influenced the buckling response and the damage patterns of the omega-stiffened panels. The pristine panels exhibited typical compression failure mode, with matrix crack and fiber breakage in the stringer and the skin. However, the collapse of the pre-damaged panels was dominated by the debonding of the skin-stiffener interface and the out-of-plane deformation of the skin.

Study on micromechanical behavior and energy evolution of granular material generated by latent diffusion model under rotation of principal stresses

In this study, advanced image processing technology is used to analyze the three-dimensional sand composite image, and the topography features of sand particles are successfully extracted and saved as high-quality image files. These image files were then trained using the latent diffusion model (LDM) to generate a large number of sand particles with real morphology, which were then applied to numerical studies. The effects of particle morphology on the macroscopic mechanical behavior and microscopic energy evolution of sand under complex stress paths were studied in detail, combined with the circular and elliptical particles widely used in current tests. The results show that with the increase of the irregularity of the sample shape, the cycle period and radius of the closed circle formed by the partial strain curve gradually decrease, and the center of the circle gradually shifts. In addition, the volume strain and liquefaction strength of sand samples increase with the increase of particle shape irregularity. It is particularly noteworthy that obvious vortex structures exist in the positions near the center where deformation is severe in the samples of circular and elliptical particles. However, such structures are difficult to be directly observed in sample with irregular particles. This phenomenon reveals the influence of particle morphology on the complexity of the mechanical behavior of sand, providing us with new insights into the understanding of the response mechanism of sand soil under complex stress conditions.

Comparison of the mechanical properties and constitutive models of carbon fiber-reinforced coral concrete cubes and prisms under uniaxial compression

Carbon fiber reinforced coral concrete (CFRCC) plays a crucial role in island construction. In engineering applications, CFRCC is often subjected to complex stress states. Multiaxial stress studies usually use cubes, and in order to maintain research consistency, uniaxial studies also often use cubes. Traditional uniaxial stress studies mainly use prisms. However, the differences in uniaxial compression mechanical properties between these two types of specimens have not been thoroughly studied. To fill this gap, this study conducted uniaxial compression tests on cubes and compared the results with previous tests on prisms.The results showed that the failure patterns of the two types of specimens were different. The main cracks of the cubes were vertically distributed, while the main cracks of the prisms mostly unfolded diagonally. The addition of carbon fibers (CFs) reduced the number of large cracks and increased the number of microcracks. The stress-strain curves, peak stress, peak strain, and initial elastic modulus of the two types of specimens show similar variations with CFs, and CFs significantly improve the mechanical properties of coral concrete. The constitutive models based on prisms cannot accurately describe the mechanical behavior of cubes, therefore, we proposed revised constitutive models. The revised constitutive models can accurately describe the mechanical behavior of cubes. This study laid the foundation for subsequent research on multiaxial stress.

An Enhanced Progressive Damage Model for Laminated Fiber-Reinforced Composites Using the 3D Hashin Failure Criterion: A Multi-Level Analysis and Validation.

This paper presents a progressive damage model (PDM) based on the 3D Hashin failure criterion within the ABAQUS/ExplicitTM 2021 framework via a VUMAT subroutine, enhancing the characterization of the mechanical performance and damage evolution in the elastic and softening stages of composite materials via the accurate calculation of damage variables and accommodation of non-monotonic loading conditions. In the subsequent multi-level verification, it is found that the model accurately simulates the primary failure modes at the element level and diminishes the influence of element size, ensuring a reliable behavior representation under non-monotonic loading. At the laminate level, it also accurately forecasts the elastic behavior and damage evolution in open-hole lamina and laminates, demonstrating the final crack band at ultimate failure. This paper also emphasizes the importance of correct characteristic length selection and how to minimize mesh size impact by selecting appropriate values. Compared to ABAQUS's built-in 2D model, the 3D VUMAT subroutine shows superior accuracy and effectiveness, proving its value in characterizing the mechanical behavior and damage mechanisms of fiber-reinforced polymer (FRP) materials. The enhanced 3D PDM accurately characterizes the softening processes in composite materials under simple or complex stress states during monotonic or non-monotonic loading, effectively minimizes the mesh dependency, and reasonably captures failure crack bands, making it suitable for future simulations and resolutions of numerical issues in composite material models under complex, three-dimensional stress states.

Fatigue notch strengthening effect of nickel-based single crystal superalloys under different stress ratios

Nickel-based single crystal superalloys (Ni-SXs) are widely used in turbine blades of aircraft engines. With the increasing demand for higher temperature-bearing capacity, the introduction of film cooling holes, impingement holes, and trailing edge slots for cooling induces stress concentration, which compromises the structural integrity of the blades, generates complex multiaxial stress states, and adversely affects their operational performance. In this study, Ni-SXs, DD6, was utilized to investigate the influence of stress ratios on fatigue performance under complex stress states. Low cycle fatigue (LCF) tests were carried out at different stress ratios with stress concentration coefficient Kt = 1.0, 2.0 and 3.0. The results indicate that the notched specimens exhibit a significant fatigue notch strengthening effect under high stress ratios. The fracture surface and microstructure also indicate that under high stress ratios loading, the notches exhibit significant creep failure characteristics. This means that the main cause of fatigue notch strengthening is similar to creep notch strengthening effect. A macroscopic anisotropic constitutive model coupled with damage was developed and applied to finite element analysis of notched specimens. The results demonstrate that as the stress ratio rises, the stress relaxation effect at the notch becomes more pronounced, yet the level of damage diminishes. Additionally, a stress-equivalent model based on Bridgman stress was proposed, which effectively unifies the lifetime trends of notched and smooth specimens, predicting lifetimes within a threefold error band.

Development of the Views of Yu.N. Rabotnov on Strength Criteria of Composites

Besides the well-known fundamental works of Yu.N. Rabotnov in the field of hereditary elasticity and creep theory, one of the aspects of his scientific activity was the mechanics of composite materials and, in particular, a new class of strength criteria for structurally anisotropic composites proposed by him. The main feature of Yuri Rabotnov’s approach was not an attempt to construct a uniform smooth limiting surface in the stress-space, but taking into account real fracture mechanisms, which, as a rule, are directional in nature. Now such approaches become crucial in calculation algorithms modeling the fracture process with taking into account the degradation of elastic and strength properties, but in the period of the first Yu.N. Rabotnov’s papers they were pioneering and caused certain discussions. Development and application of some of Rabotnov’s proposed types of strength criteria for fiber-reinforced composites in tension, compression and complex stress state are discussed in this anniversary paper.

A dual-channel convolutional neural network with attention mechanism DC_EcaNet-6 for creep life prediction of notched components

Machine learning models offer novel possibilities for creep life prediction of materials and components at elevated temperatures. Present studies primarily focus on material-level creep life prediction, with limited reports on component-level analysis due to the complex stress states around structural discontinuities. Based on this, a dual-channel convolutional neural network with attention mechanism, DC_EcaNet-6, is proposed for creep life prediction of notched components, where the images of Mises stress and stress tri-axiality are employed as the input. The prediction results by the DC_EcaNet-6 model are compared with that by some deep learning models and the simplified method. Creep reliability assessment of notched components using the DC_EcaNet-6 model is conducted. The results indicate that the proposed model provides a more superior creep life prediction accuracy of notched components than other models mentioned. This model provides a potential tool for creep life prediction and reliability assessment of notched components.

Study on plastic yield surfaces of pyramidal lattice materials with circular and rectangular cross-sections

The yield surfaces and the evolution of yield surfaces of a bending-dominated pyramidal lattice material under complex stress states considering the coupling effect of axial force and bending moment of a strut are studied theoretically. The two-dimensional primary yield surfaces, secondary yield surfaces, and complete yield surfaces of pyramidal lattice materials of two kinds of cross-section struts are obtained, and the analytical expressions of yield surfaces are established. The effects of the inclination angle and diameter-to-length ratio of the struts on the yield surfaces of pyramidal lattice materials with circular cross-sections are discussed. The results provide a basis for analyzing homogenized plastic properties of complex lattice material structures.

Research on the stiffness characteristics and contact status of matched angular contact ball bearings considering the effect of varying spatial position of rolling ball

In engineering practice, bearings used as support components are usually installed in pairs in various rotating machines. The mechanical and contact characteristics of bearings play a crucial role in determining the operational accuracy, safety performance and stability of equipment. Numerous studies focused on single bearings have been reported form diffident aspects for enhancing service performance. However, the literature reports on the matched bearings are scarce due to the mutual coupling of rolling elements and the extremely complex stress conditions. Especially the stiffness fluctuation and internal contact status affected by the ball position are difficult to be observed and tested experimentally because of the complex and compact structure, which significantly impacts the safe and reliable operation of rotating machines. To overcome the above shortcomings, this paper investigates the effect of ball position on the stiffness characteristics and contact status of matched angular contact ball bearings based on the coordinate matrix transformation approach and Jones’ statics model. Then, the stiffness results of published literature are used as a benchmark to validate the accuracy of solution method of this paper. Finally, 7206B bearings with different installing forms are used as a numerical example to reveal the effect of ball position on the stiffness characteristics and contact status of matched angular contact ball bearings under different working conditions. The study provides a scientific guidance to investigate the mechanical characteristics and contact mechanism of multi-bearing system.

Calculation method and evolution rule of the strain energy density of sandstone under true triaxial compression

Deep rock masses are typically in complex stress states, and research on the evolution of their strain energy density is of highly important for understanding their failure characteristics. In this work, a true triaxial stress‒balanced unloading test is designed to analyze the ud and ue evolution of sandstone under true triaxial compression conditions. The study results indicate that as σ1 increases, the elastic strain decreases in the σ2 and σ3 directions, whereas the residual strain progressively increases, and the magnitude of decrease in elastic strain exceeds the magnitude of increase in residual strain. Throughout the loading process of σ1, ue progressively decreases in the σ2 and σ3 directions, whereas ud gradually increases, and the magnitude of decrease in ue surpasses the magnitude of increase in ud. The ud and ue of sandstone under different stress levels were calculated via true triaxial stress‒balanced unloading tests, and the evolution of ud and ue in the three principal stress directions and the overall strain energy density of sandstone followed a linear energy storage law. On the basis of this law and the true triaxial stress‒balanced unloading test, a new method for calculating the true triaxial ud and ue was proposed. A study on the σ1 unloading stress path revealed that the σ1 unloading stress path significantly affects the storage and dissipation of the strain energy density in the three principal stress directions of sandstone. On the basis of the research results, the criteria for determining rockbursts were discussed.

Wear of Wave Energy Converters Mooring Lines Belts

Abstract Using a belt as a replacement for a rope on a rotary power take-offs (PTOs) system has become more common for wave energy converters, improving cyclic bend over sheave performance with a smaller bending thickness for belts. However, the service life predictions of PTOs are a major concern in design, because belt performance under harsh underwater environments is largely less studied. In this work, the effect of fleet and twist angles on wear life is being investigated both experimentally and numerically. Two three-dimensional equivalent static finite element models are constructed to evaluate the complex stress state of polyurethane-steel belts around steel drums. The first is to capture the response of the experimental investigation performed on the wear life, and the second to predict the wear life of an existing functional PTO. The results show a significant effect for fleet and twist angles on stress concentrations and estimated service life.

Nonlinear mechanical behaviour and visco-hyperelastic constitutive description of isotropic-genesis, polydomain liquid crystal elastomers at high strain rates

The mechanical behaviour of isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) at various strain rates is systematically investigated via experiments, theoretical analysis, and numerical modelling. Experiments encompassing SEM (scanning electron microscope), DSC (differential scanning calorimetry), TGA (thermogravimetric analyser), quasi-static and dynamic (SHPB – split Hopkinson pressure bar) mechanical tests, as well as drop-weight impact tests, are undertaken to identify the nonlinear, large-strain, rate-dependent relationship between compressive stress and deformation of the I-PLCEs studied. Subsequently, a three-dimensional compressible visco-hyperelastic constitutive model for the material is established based on the summation of Cauchy stress components. The as-used model yields good agreement with experimental data, particularly an excellent description of the mechanical responses at high strain rates of 103∼104 s−1. The fully-calibrated constitutive model is implemented in the commercial finite element code ABAQUS via a virtual user-defined material (VUMAT) subroutine. The inhomogeneous deformation processes of the I-PLCEs, corresponding to impact by a hemispherically-tipped drop weight, which induces complex stress states, are also well described. Finally, when evaluated by two dimensionless physical parameters, the I-PLCEs demonstrate a more pronounced strain rate sensitivity in terms of dynamic strength and impact toughness compared to other commonly used materials, highlighting their superior performance in dynamic loading scenarios. The present study is helpful for the design and development of impact-resistant LCE-based materials and structures.

Triaxial compressive behaviour of ultra-high performance geopolymer concrete (UHPGC) and its applications in contact explosion and projectile impact analysis

Ultra-high performance geopolymer concrete (UHPGC) is increasingly recognised as a promising construction material in protective engineering owing to its exceptional material strength and eco-friendly characteristics. However, there is currently limited research data on the behaviour of UHPGC under complex stress states, and the applicability of some common concrete dynamic constitutive models to UHPGC requires calibration and evaluation. This paper presents an experimental study on the triaxial compression (TXC) behaviour of UHPGC under varying confining pressures with a range of 0–40 MPa. The stress-strain curves under various confinement levels and failure patterns of UHPGC are discussed. The results indicate that the peak axial stress and toughness of UHPGC increase with higher confining pressure levels, but it still exhibits noticeable softening behaviour. Under uniaxial compression, UHPGC typically fails with inclined shear and axial tensile cracks, while under TXC, particularly at confining pressures above 20 MPa, the failure mode transitions to shear failure with prominent oblique shear cracks. Additionally, existing failure criteria are calibrated to match the strength envelop of UHPGC, with the Power-law failure criterion providing the closest fitting results. Subsequently, utilising both current and pre-existing TXC data, three commonly used concrete constitutive models, including HJC, K&C and CSC, are calibrated with respect to the dominant strength parameters for UHPGC in the finite element (FE) hydrocode ANSYS/LS-DYNA. Further, numerical simulations are conducted to evaluate the effectiveness of such three calibrated concrete models in replicating the response of UHPGC panels exposed to the contact explosion or projectile impact. The simulation results demonstrate that the K&C and CSC models effectively replicate the localised damage of UHPGC panels under contact explosions, while the HJC model more accurately simulates the depth of penetration (DOP) for thick UHPGC panels under projectile impact.

Correction method and verification of radial inertia and friction effects under a unified deformation framework in SHPB experiments on soft materials

During the split Hopkinson pressure bar (SHPB) experiments, significant measurement errors can arise due to severe radial inertia and friction effects. Previous studies have developed various correction methods for these two effects. However, these methods have problems such as over-reliance on the volume invariance assumption of the specimen and inconsistent assumptions on the deformation patterns of the two effects, which limit their universality and effectiveness. Therefore, this paper integrates the radial inertia effect and friction effect in a unified deformation framework through reasonable assumptions, and proposes a method to correct the specimen from a complex stress state to a uniaxial stress state. SHPB numerical simulation experiments demonstrate that this method effectively eliminates the combined effects of radial inertia and friction on measurement results for both elastic and viscoelastic materials, including the size effect associated with these two factors. Additionally, the paper presents a scheme to determine the friction coefficient using the size effect of the specimens when the friction coefficient between the specimen and the bar is unknown. Finally, the method was applied to correct the stresses measured in SHPB experiments on silicone rubber of different diameters. It successfully eliminated discrepancies in the stress-strain relationships between specimens of various sizes and determined a friction coefficient that fell within a reasonable range.

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.

Hybrid finite element modeling of subsurface-originated spalling in flexible bearings with hoop stresses

The flexible bearing in a harmonic reducer undergoes structural deformation after being mounted on the cam, causing the bearing to operate under a complex stress state. A hybrid finite element model is developed to investigate crack initiation and propagation in flexible bearings with hoop stress under rolling contact fatigue loading. The model is coupled with continuum damage mechanics, and the damage evolution equation takes the maximum shear stress amplitude as the damage-causing stress since the hoop stress inevitably affects the fatigue life. The model is verified by comparison with the fatigue life of the inner ring without hoop stress. The crack initiation and spalling formation mechanisms in the inner ring assembled with the cam are analyzed in detail. Moreover, the effects of contact load and equivalent interference on the inner ring’s spalling morphology and fatigue life are studied.

Dislocation extension in coarse–grained Al reinforced by SiC nanowires under complex stress condition

Stacking faults (SFs) could be generated in aluminum (Al) via full dislocations extension under extreme stress. However, the extension behavior of the dislocations related to the stress conditions have not been studied comprehensively. In this study, SFs were generated solely under extreme stress condition in coarse–grained Al nanocomposites, where high content of Silicon Carbide nanowires (SiCnw) was introduced as reinforcement. Dislocation extension behaviors under normal and shear stress were predicted using an atomistic approach comparing with experiment methods. The extension ability of full dislocations was studied in terms of complex stress forced on partial dislocations and the relationship between stress condition and the SF width was established by stress analysis. The generated SFs were further proved to offer superb additional strengthening effect for the composites. This study provides a new idea and theory for designing of SF generation in coarse–grained Al based nanocomposites.

To justification of concrete strength criterion at biaxial compression

Introduction. Numerous experimental data from Russian and foreign researchers indicate that the classical plasticity hypotheses do not take into account the different resistance to uniaxial tension and compression, the influence of the spherical tensor. At the same time, experiments show that the ultimate resistance depends on the type of stress state, and hydrostatic pressure increases the strength and plasticity of solids. Aim. To establish the dependence of the influence of the second component of stresses during biaxial compression of concrete on the parameters of the complete diagrams of deformation of the material σbR and εbR it is necessary to describe these diagrams, and to construct a closed curve on the plane of the main stresses (concrete strength criterion). Materials and methods. Based on the experimental materials of foreign and domestic researchers, including the experiments of the authors of the article, methods of mechanics of deformed solids, limit curves and a closed curve on the plane of the main stresses in the form of a chain line forming the smallest area strength surface in the form of a catenoid are proposed. Results. The article provides an analysis of the known strength criteria from the point of view of their geometric interpretation in the stress space. It is shown that these studies relate mainly to metals and metal structures, and for the design of reinforced concrete and steel-concrete structures in a complex stress state, it is necessary to develop an appropriate criterion for the strength of concrete. Conclusions. As a result, the proposed limit curves and the surface (material strength criterion) on the plane of main stresses in the form of a catenoid accurately reflect the behavior of concrete under conditions of uniform and uneven flat stress state, and the equation of the surface in the form of a catenoid is a generalization of the equations of limit curves for each of the three types of flat stress state. At the same time, there is no overestimation of strength in the "compression – compression" area in this case.

Dynamic Performance Analysis of Precast Segment Column Reinforced with CFRP Subject to Vehicle Collision

With the extensive use of a precast segment column in the field of engineering, impact resistance performance has gradually attracted attention, as many accidents have caused huge economic losses and casualties. This study explored the dynamic response and failure modes of a prefabricated segment column both with and without Carbon Fiber-Reinforced Polymers (CFRPs). Firstly, numerical models of a precast segment column and CFRP-wrapped steel column under impact loads were developed, and the modeling method’s accuracy was fully verified. Then, numerical models of a bridge precast segment column with and without CFRPs under vehicle collision were established, and the differences in the dynamic performances between the precast segment column with and without CFRPs are explored. Finally, the effects of impact velocity, concrete strength, and CFRP thickness on the dynamic performance of a precast segment column are considered. The results indicate that in the case of a vehicle collision, multiple cross-sectional positions form highly complex stress states. At 100 km/h, the differences in bending moment and shear force values between reinforced and unreinforced precast segment columns at the impact section are 7.6% and 7.1%, respectively. At this velocity, the peak impact force also increases by 15.8% as the local stiffness of the precast segment column increases after reinforcement with a CFRP. The bottom segment of the precast segment column with a CFRP is crushed, and the precast segment column experiences shear failure under vehicle collision.

Mechanical properties and constitutive model of artificial frozen sandy soils under true triaxial stress state conditions

Triaxial compression tests were conducted on frozen sandy soils under a constant minimum principal stress (σ3 = 1.6 MPa) and various intermediate principal stresses (σ2 = 1.6, 3.4, 5.2, 7.0, 8.8, 9.8 MPa). The purpose of the research was to investigate the influence of intermediate principal stress on mechanical properties of frozen soil, and to establish a constitutive model to predict the stress-strain relationship of frozen soil under complex stress state. The test results obtained demonstrated that the crack damage stress and failure stress initially increase and then decrease with an increase in the intermediate principal stress. However, the crack initiation stress exhibits an initial increase up to a specific value, after which it stabilizes. From the perspective of crack propagation, the influence mechanism of intermediate principal stress on the strength was discussed. With the variation of stress state, the difference between intermediate principal strain and minimum principal strain gradually increases. The deformation difference was revealed using the stress superposition principle and Poisson's effect. Finally, the constitutive model based on the Weibull distribution and Drucker-Prager strength criterion can accurately represent the stress-strain relationships of frozen sandy soils under true triaxial stress states.