Mixed Loading Research Articles

Failure Prediction of an Airfoil-Type Crack in Thermoelectric Coupling Materials

Airfoil-type cracks with curved surfaces and sharp tips are frequently encountered in modern engineering applications and the aerospace industry. However, such cracks significantly threaten structures due to stress concentration and further cause damage. This study investigates the theoretical analysis and failure prediction of airfoil-type cracks within thermoelectric coupling materials under the interaction of remote mechanical loads, heat flux and electric current density. By employing complex variable theory, conformal mapping methods, and the analytic continuation theorem, the full-field stress and stress intensity factors of an airfoil-type crack were determined under three different loading conditions. The results indicate that when the airfoil-shaped crack tip is subjected to horizontal compression, vertical tensile mechanical load, and both heat flux and current density parallel to the crack, the crack tip would reach a dangerous state. Additionally, the full-field stress distribution reveals stress concentration around the crack tip, which explains variations in SIFs under different external forces and shape factors. Four critical situations suppressing crack propagation under mixed loading conditions are proposed. Furthermore, using an acrylic plate and bismuth telluride alloy as examples, the critical values of external loading for the mixed-mode fracture are determined based on the strain energy density criterion. These critical values can be used to predict failure initiation, thus reducing the risk of structural failure due to airfoil cracks within thermoelectric coupling materials.

Effective thermodynamic potentials and internal variables: Particulate thermoviscoelastic composites

The problem addressed in this study is the full coupling between three different contributions to the strain in thermoviscoelastic composites, elasticity, viscosity and temperature changes. It shows that even in simple situations, the coupling with temperature may lead to counter-intuitive effects which are not accounted for through the sole overall stress–strain relations. The correspondence principle permits to express the macroscopic strain–stress relation and the macroscopic entropy as a set of ordinary differential equations for two types of effective internal variables, mechanical variables on the one hand and thermal variables on the other hand. Interpreting the macroscopic response as a rheological generalized Maxwell model allows us to compute the macroscopic free energy and the dissipated energy of the composite in terms of these internal variables. Coupled with Hashin–Shtrikman estimates, these thermodynamic functions provide additional information on the statistics of the stress field when the composite is subjected to a mixed loading combining mechanical and thermal effects.

Three-dimensional fracture modes decoupling by means of invariant integrals in wood under mixed mode loading

This paper addresses the determination of the energy release rate in an orthotropic elastic material such as wood with a three-dimensional view of the problem. The mixed mode loading associated with the anisotropy of the material required mode decoupling by isolating the energy release rates in mode I, mode II and in mode III. These energy release rates are calculated using the invariant integral M of Linear Elastic Fracture Mechanics (LEFM). This decoupling has necessitated the introduction of kinetically and statically admissible three-dimensional virtual displacement and stress fields in the vicinity of the crack front. The fracture mode decoupling strategy is presented and implemented through finite element modelling of a Mixed Mode Crack Growth (MMCG) specimen. Different thicknesses are investigated to highlight the 3D effects. The modelling highlighted the effect of Mode II at the edges of free surfaces for mixed loadings including mode III (mode III, mode (II+III) and mode (I+II+III)), while mode III was the predominant at the middle of the specimen. In cases of mixed mode (I+II), the energy release rate GI was highest at the middle of the specimen and lowest at the edges of the free surfaces, regardless of the degree of mixing for a given thickness. The correlation between the results obtained using the proposed approach and the non-dependence of the integration domain, as well as with the usual approaches employed in the literature, is demonstrated.

A quadrilateral inverse plate element for real-time shape-sensing and structural health monitoring of thin plate structures

The inverse finite element method (iFEM) emerged as a powerful tool in shape-sensing and structural health monitoring (SHM) applications with distinct advantages over existing methodologies. In this study, a quadrilateral inverse-plate element is formulated via a sub-parametric approach using bi-linear and non-conforming cubic Hermite basis functions for engineering structures, which can be modeled as thin plates. Numerical validation involves dense and assumed sparse sensor arrangements for in-plane, out-of-plane, and mixed general loading conditions. iFEM analysis reveals efficient monotonic convergence to analytical and high-fidelity finite element reference solutions. After successful numerical validation, defect detection analysis is performed considering minute geometric discontinuities and structural stiffness reduction because of latent subsurface defects under tensile and transverse loading conditions. The inverse formulation successfully resolves the presence of simulated defects under a sparse sensor arrangement. The proposed inverse-plate element is accurate in the full-field reconstruction of shape-sensing profiles and reliable in defect identification and quantification in thin plate structures.

Dyke emplacement under mixed loading conditions: Insights from the Dharwar Craton, India

Dykes are intrusive igneous bodies that play crucial role in the supply and ascent of magma to the Earth’s crust. Magma can intrude along pre-existing anisotropies such as fractures or foliations present within the host rock or it may create its own path by fracturing the host rock. In the latter scenario, when fractures are formed by the pressure exerted by the invading magma, a dyke’s outcrop shape and geometry are diagnostic of the conditions under which it evolved. Here, we report mafic dykes emplaced within the younger granites of Dharwar Craton, peninsular India. Outcrop attributes of these dykes are characteristic of emplacement under conditions of mixed mode loading. We discuss different discrete modes of fracture formation and their possible combinations to understand the generation and eventual emplacement of dykes under mixed mode loading. This leads to the development of a comprehensive sequence of progressive dyke evolution under mixed mode I-III loading and thereby distinguishing incremental orders of dyke horn formation. We further apply this knowledge along with collected field evidence on dyke body geometries to propose an evolutionary model of dyke formation and emplacement within the Chitradurga granite under varying regional stress fields of the Chitradurga Schist Belt, Western Dharwar Craton, India. We infer, that the dykes initiated as extensional fractures within an earlier NE-SW directed compressive stress field and were subsequently sheared sinistrally by the effect of the adjacent Chitradurga Shear Zone on account of a later E-W to ESE-WNW directed compression.

Acoustic emission-based delamination investigation in drilled GFRP under mixed tensile and bending cyclic loading

The drilling process can cause various defects in glass fiber-reinforced polymer (GFRP), such as delamination, which ultimately leads to damage progression, especially under fatigue loading. Therefore, the current study aims to investigate the progression of failure in drilled composites subjected to cyclic bending and tensile loads using acoustic emission (AE), image processing, and mechanical behavior monitoring. The results show tyhat the fatigue diagram consists of three stages associated with resistance of fibers and matrix against delamination propagation, stable delamination progression, and ultimate spread of failure which are accurately identified by AE and mechanical methods. Additionally, the pattern and procedure of all fatigue diagrams under all loading conditions were similar and independent of loading parameters. Results from this study provide a strategy for real-time structural health monitoring (SHM) of delamination propagation in GFRPs under multi-axial fatigue loading.

Atomistic and continuum Ascertainment of The crack tip stress fields in anisotropic elastic cubic media

The article provides a comparative analysis of stresses associated with the crack tip in an anisotropic elastic medium with cubic crystalline symmetry of elastic properties under mixed loading conditions obtained by two fundamentally different approaches: atomistic simulations and continuum fracture mechanics methods. The atomistic modelling approach is premised on the application of the molecular dynamics (MD) method implemented in the open source code program Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The continuum mechanics approach is based on the classical elasticity theory of anisotropic media, in which the mechanical fields associated with the crack tip are represented by the crack tip stress and displacement series expansions generalizing the well-known classical asymptotical presentation of M. Williams to the case of anisotropic media. Using the MD method, a large series of computations of the loading of monocrystalline copper and aluminum plates with a face-centered cubic crystal lattice weakened by a central crack applying the embedded atom potential (EAM) was implemented. MD modeling is aimed at determining the atomic stresses and strains near the crack tip. The computed atomic stresses were compared with the stress field determined by the continuum elasticity theory of anisotropic media for crystal lattices with cubic symmetry of elastic properties. A comparative analysis was carried out for the angular dependencies of the stress and strain tensor components at various selected distances from the crack tip for the entire range of mixed deformation forms starting from pure tensile loading and ending with forms close to pure transverse shear. It is ascertained that the crack tip fields determined on the basis of two fundamentally different approaches, precisely, discrete and continuum, are completely consistent with each other. It is established that mathematical methods of continuum fracture mechanics can be applied to describe stress, strain and displacement fields at the atomic level.

Oxidation model of slabs in an industrial-scale walking-beam reheating furnace with mixed loading

This paper develops a comprehensive numerical model of an industrial-scale walking-beam reheating furnace integrated with an improved oxidation model. The model demonstrates good agreement with experimental data, accurately predicting both temperature distribution and the oxidation process. Utilizing this model, the impact of mixed loading and swirl angles on the oxidation process is investigated. The average porosity of the scale, determined experimentally to be 0.25634, is used as a benchmark for the model. Comparisons of results with and without considering porosity highlight its significant impact on scale thickness distribution. This finding is crucial for the descaling process, allowing for a more accurate determination of descaling pressure and the reduction of production costs. Predicting scale distribution based solely on the temperature at a specific time is challenging due to the lag in scale accumulation. The temperature trend over an extended period is more consistent with the scale distribution. For the reheating furnace studied in this paper, the research results reveal that a swirl angle of 25° emerges as the optimal choice with industrial demands. These results underscore the importance of considering porosity and swirl angle effects on scale distribution and oxidation loss rate, offering valuable guidance for industrial processes.

Acoustic emission analysis for crack initiation in AA7075-T6 alloy under mixed tensile and bending cyclic loading

In most critical components, fatigue occurs under mixed loadings, such as bending and tensile cyclic loading. Furthermore, in the realm of fatigue loading conditions, scant information has been documented regarding the combination of bending and tensile cyclic loading. Therefore, in this paper, Acoustic Emission (AE) as a non-destructive method was used to investigate crack initiation in AA7075-T6 specimens subjected to fatigue conditions involving bending and tensile cyclic loading. The results showed that generated AE signals had the same trend in all tests, and there was a reasonable correlation between AE and mechanical characteristics. By correlating mechanical data and AE data using the sentry function, the failure process, which includes dislocation movement, plastic deformation, work hardening, micro-crack formation, and crack initiation, respectively, was identified. The S-N curve was plotted by using AE monitoring. This curve was depicted as non-destructive and based on the crack initiation cycle. Obtaining the S-N curve through AE monitoring will greatly assist designers in the design of structures under mixed fatigue loading conditions. This will result in a reduced Safety Factor and, consequently, decreased weight and cost for structures while still ensuring that the structure meets the necessary safety requirements.

Spatial variations in effective elastic thickness and loading ratio in the Indo-Burma subduction zone based on the joint inversion of Bouguer coherence and admittance

Our knowledge of the mechanical structure and geodynamic evolution of the Indo-Burma Subduction (IBS) Zone is currently limited. The effective elastic thickness (Te) reflect the thermo-rheological characteristics of the subduction zone that aid in understanding the long-term deformation and geodynamic evolution. In the present study, we employed joint inversion of wavelet admittance and coherence to obtain the spatial variation in Te and the loading structure (F) over IBS based on satellite gravity and topography data. The spatial pattern of Te and F exhibit a remarkable correlation with the tectonic features of IBS. The Indo-Burma ranges (IBR) and the Central Myanmar basins (CMB) in the Burma Terrain (BT) are characterized by high lithospheric strength (Te = 35–40 km). In comparison, low lithospheric strength (Te = 15–20 km) prevails over the Shan Plateau (SP). High F (0.6–0.8) values over the Bay of Bengal and the SP indicate the dominance of the internal loading, while medium F (0.5–0.6) values over the CMB suggest mixed loading, probably related to the combined effect of thick sediments and dense downgoing slabs. Comparative analysis of Te with shear wave velocity and curie point depth indicates that the thermal state is crucial in controlling the lithosphere strength. Further, the absence of modern interplate seismic activity over the strong coupling zones characterized by high Te in BT suggests that the Indo-Burma megathrust is locked.

A three-dimensional phase-field model for studying the orientation-dependent interface evolution in stress-induced martensitic phase transformation

In this study, we address the challenging task of predicting the motion of interfaces in stress-driven martensitic phase transformations within shape memory alloys. The novelty of our approach lies in the introduction of a monolithically solved thermodynamic-based phase-field method, specifically tailored for large strain conditions at the nanoscale for three-dimensional problems. To achieve this, we have developed a custom finite element software seamlessly integrated into the FEniCS open-source framework, providing a sophisticated and efficient tool for the examination of nanostructure evolution. Our investigation delves into five distinct and complex scenarios under diverse loading conditions for two– and three-dimensional problems, each presenting unique challenges: (i) a straightforward uniaxial tension scenario featuring a square domain with a pre-existing martensitic nucleus; (ii) the evolution of interfaces in a square sample incorporating a circular central nanovoid under biaxial tensile stress; (iii) the analysis of a rectangular beam subjected to horizontal and vertical compressive loads; (iv) the assessment of an initially voided rectangular beam experiencing mixed loading conditions; and (v) the three-dimensional simulations of cubic-to-tetragonal phase transformation using various orientation of the habit plane. In contrast to prior studies, our analysis not only explores the standard factors of habit plane reorientation and strain transformation values but also delves into the impact of nanovoids on austenite–martensite interface evolution.

Research on Decoupling Model of Six-Component Force Sensor Based on Artificial Neural Network and Polynomial Regression.

A two-stage decoupling model based on an artificial neural network with polynomial regression is proposed for the six-component force sensor load decoupling problem in the case of multidimensional mixed loading. The six-dimensional load categorization stage model constructed in the first stage combines 63 load category label sets with a deep BP neural network. The six-dimensional load regression stage model was constructed by combining polynomial regression with a BP neural network in the second stage. Meanwhile, the six-component force sensor with a fiber Bragg grating (FBG) sensor as the sensitive element was designed, and the elastomer simulation and calibration experimental dataset was established to realize the validation of the two-stage decoupling model. The results based on the simulation data show that the accuracy of the classification stage is 93.65%. The MAPE for the force channel in the regression stage is 6.29%, and 3.24% for the moment channel. The results based on experimental data show that the accuracy of the classification stage is 87.80%. The MAPE for the force channel in the regression phase is 5.63%, and 4.82% for the moment channel.

Critical loss of primary implant stability in osteosynthesis locking screws under cyclic overloading

Primary implant stability, which refers to the stability of the implant during the initial healing period is a crucial factor in determining the long-term success of the implant and lays the foundation for secondary implant stability achieved through osseointegration. Factors affecting primary stability include implant design, surgical technique, and patient-specific factors like bone quality and morphology. In vivo, the cyclic nature of anatomical loading puts osteosynthesis locking screws under dynamic loads, which can lead to the formation of micro cracks and defects that slowly degrade the mechanical connection between the bone and screw, thus compromising the initial stability and secondary stability of the implant. Monotonic quasi-static loading used for testing the holding capacity of implanted screws is not well suited to capture this behavior since it cannot capture the progressive deterioration of peri‑implant bone at small displacements. In order to address this issue, this study aims to determine a critical point of loss of primary implant stability in osteosynthesis locking screws under cyclic overloading by investigating the evolution of damage, dissipated energy, and permanent deformation. A custom-made test setup was used to test implanted 2.5 mm locking screws under cyclic overloading test. For each loading cycle, maximum forces and displacement were recorded as well as initial and final cycle displacements and used to calculate damage and energy dissipation evolution. The results of this study demonstrate that for axial, shear, and mixed loading significant damage and energy dissipation can be observed at approximately 20 % of the failure force. Additionally, at this load level, permanent deformations on the screw-bone interface were found to be in the range of 50 to 150 mm which promotes osseointegration and secondary implant stability. This research can assist surgeons in making informed preoperative decisions by providing a better understanding of the critical point of loss of primary implant stability, thus improving the long-term success of the implant and overall patient satisfaction.

Dynamic fracture properties and criterion of cyclic freeze-thaw treated granite subjected to mixed-mode loading

Rock masses in high-elevation or cold regions are vulnerable to the combined effects of freeze-thaw (F-T) weathering and dynamic mixed-mode loading, posing a serious threaten to the safety and stability of geotechnical engineering. In this study, a series of dynamic fracture tests were conducted on notched semi-circular bend (NSCB) granite specimens subjected to different mixed-mode loading and F-T cycles using a split Hopkinson pressure bar (SHPB) test system. The effects of F-T treatment and dynamic mixed-mode loading on the fracture properties of granite, including effective fracture toughness, progressive fracture process, and macroscopic morphology of fracture surface, were comprehensively revealed. The experimental results suggest that the dynamic effective fracture toughness of NSCB specimens is dependent on the loading rate, particularly when the mode I loading is dominant. Additionally, the fracture toughness decreases as the number of F-T cycles increases, with an inflection point at 30 F-T cycles. All granite specimens subjected to mixed-mode loading exhibit a curved fracture path, with faster crack propagation speed and more fine cracks in specimens exposed to higher F-T cycles. Macroscopic morphology of fracture surface obtained using three-dimensional (3D) scanning indicates that the fractal dimension of the fracture surface increases with increasing F-T cycles, and the increment is more pronounced for specimens subjected to a higher mode II loading component. Moreover, this study compared the fracture resistance of F-T treated granite subjected to dynamic mixed loading using the maximum tangential stress (MTS) criterion and the generalized maximum tangential stress-based semi-analytical (SA-GMTS) criterion. Compared with the MTS criterion, the SA-GMTS criterion shows a more reasonable consistency with the experimental results, with a root mean square error within ±7%.

Application of a hierarchical quadrature element method to interface crack analysis in bi-material systems

This paper presents an extension of the hierarchical quadrature element method (HQEM) with p-convergence to evaluating fracture mechanical parameters of bi-material interface cracks. The numerical implementation of HQEM in combination with the virtual crack closure method (VCCM) is comprehensively illustrated, and the formulas for calculating the strain energy release rate (SERR) are rederived. The relationship between components of SERR and the complex stress intensity factors (SIFs) is established. In addition, the effectiveness of an auxiliary parameter related to the dual energy release rates in measuring the accuracy of the present method is examined.The feasibility of applying HQEM to the interface crack problems is demonstrated by investigating the benchmark problem of an infinite bi-material plate with a central interface crack. Two loading cases are considered, including pure tensile loading and mixed tensile-shear loading. The influence of the crack tip element size Δa on the convergence characteristics and computational accuracy of fracture parameters is quantitatively investigated to provide guidance for choosing the most reasonable value of Δa. Numerical results show that even with very coarse meshes, together with a virtual crack extension consisting of only one element, HQEM yields highly accurate results for the total SERR and the complex SIFs, making it suitable for complex, large-scale interface crack problems in dissimilar media.

Evolution of the mixed mode FPZ and fracture roughness of Beishan granite after coupled thermo-hydro-mechanical treatment

Deep surrounding rocks contain a network of longitudinally intersecting fissures. Exploration of their fracture process zone (FPZ) size evolution during mixed loading and fracture surface roughness after failure has always been a hot topic, especially for coupled thermo–hydro–mechanical (THM) treatment. This study takes Beishan granite as the research object. The fracture surface roughness and FPZ length were obtained using Grasselli statistical and mixed strain–displacement methods. Finally, an electron microscope was employed to observe the fracture surface after failure at different temperatures and loading angles. Results reveal a notable temperature and load dependence of the fracture surface roughness and FPZ length evolution. In the low-temperature stage (25°C–300°C), the mineral primarily exhibited transgranular fractures and the average fracture surface roughness showed a slightly decrease with increasing temperature. In the high-temperature stage (500℃–650℃), the degree of internal damage to the prepared specimens substantially increased, with intergranular fractures being the dominant fracture mode, and rapid roughness growth occurred. Under the same temperature condition, the roughness value was in the order of mode I > mixed mode > mode II. The FPZ length increased, stabilized, and decreased as the load increased. In the low-temperature stage, the FPZ length reached its maximum value at the maximum load, whereas in the high-temperature stage, the FPZ length was fully developed before the peak load. Under the same loading angle condition, the FPZ lengths corresponding to the three loading modes followed the order of mode I < mixed mode < mode II.

A comprehensive study on structural, optical, electrical, and dielectric properties of PVA-PVP/Ag-TiO2 nanocomposites for dielectric capacitor applications

Nanocomposites made from polymers and nanoparticles (NPs) have a wide range of uses. Herein, the polymer nanocomposite electrolyte films were prepared by blending polyvinyl alcohol (PVA) and polyvinylpyrrolidone (PVP) with hybrid NPs of silver (Ag) and titanium dioxide (TiO2). The structural, optical, electrical, and dielectric properties of the resulting PVA-PVP/Ag-TiO2 nanocomposite electrolytes were analyzed. XRD analysis revealed that the PVA-PVP blend had a semicrystalline structure, and the addition of hybrid NPs reduced the crystallinity ratio. FTIR analysis showed that the intensity decreased as the content ratio of hybrid NPs increased. Optical measurements showed that the nanocomposite electrolyte samples' direct and indirect optical energy gap decreased with the increasing content of hybrid NPs. The electrical conductivity also increased with the hybrid NPs' content, likely due to the higher conductivity of the hybrid NPs compared to the polymer blend matrix's electrical conductivity. The dielectric constant (εr) and dielectric loss (εi) increased with the concentration of hybrid NPs at lower frequencies, indicating the polarization effects of space charges. The capacitance–frequency (C–f) and conductance–frequency (G/ω–f) curves of the prepared polymer nanocomposites exhibited a discernible enhancement correlating with the increased content of Ag-TiO2 nanofillers. The impedance spectroscopy data were analyzed using Nyquist plots, which showed a single semicircular arc whose radius of curvature decreased with increasing the hybrid NPs loading, indicating a decrease in the overall impedance of the nanocomposite electrolytes with the mixed NPs loading. The impedance reduction and dielectric feature increase were attributed to the interfacial polarization between the hybrid NPs and the polymeric matrix. These findings suggest that the PVA-PVP/Ag-TiO2 nanocomposite electrolytes could be used for thin-film dielectric capacitor applications.

A FINITE ELEMENT ANALYSES OF THE EFFECT OF HYDROSTATIC PRESSURE IN A THIN ADHESIVE LAYER ON ITS FRACTURE UNDER MIXED-MODE LOADING

The problem of deformation of a sample, which is a composition of orthotropic bodies bound by an adhesive layer, realizing a mixed loading mode I + II for the layer material in the vicinity of a crack-like defect, is considered. A crack-like defect in a composite was considered both in the form of a mathematical section and a physical section, the thickness of which was considered as a linear parameter. A finite element solution with an elastic description of materials in a state of plane deformation is used. To find critical states, the values of specific elastic energy in the tip of a crack-like defect were analyzed. So, for the mathematical section, the values of energy were associated with stress intensity factors and for the physical section with the energy product in the form of the product of a linear parameter and the average specific free energy on the face of a dead-end finite element of the adhesive layer. Finding the characteristics averaged over the layer thickness was determined within the framework of the Neuber – Novozhilov approach. For a small finite value of the linear parameter the convergence of the energy product to the critical value of the specific elastic energy found for the crack model in the form of a mathematical cut is shown for equivalent loading of the sample with a physical cut and the linear parameter tends to zero. For an adhesive layer of finite thickness an energy fracture criterion is considered which takes into account the loosening of the material due to hydrostatic pressure. The loosening of the material was taken into account by the parameter which was determined from the solution of the problem of normal tension of the adhesive layer by the cantilevers of the two-cantilever beam taking into account the critical values of the specific elastic energy. A comparison is made of the calculated critical external load for the formulation of the problem using a layer of finite thickness and the classical representation of a crack-like defect in the form of a mathematical section and a layer of zero thickness under the appropriate failure criteria.

Mixed reality-based online 3D pallet loading problem to achieve augmented intelligence in e-fulfilment processes

Mixed reality-based online 3D pallet loading problem to achieve augmented intelligence in e-fulfilment processes

NaOH-urea pretreatment enhanced H2 and CH4 yields via optimizing mixed alkali ratio, pretreatment time, and organic loading rate during anaerobic digestion of corn stover

This work studied the impact of NaOH-urea pretreatment on corn stover for H2 and CH4 production through two-stage anaerobic digestion. Results showed that the NaOH-urea pretreatment process improved CH4 production more significantly compared to H2. Optimized by Box-Behnken design (BBD) experiments, the CH4 cumulative yield was increased by 34.2 % at NaOH: urea = 3.2: 26.8, time = 15.7 min, and organic loading rate (OLR) = 23.4 w/v. Microbial community diversity analysis showed that the hydrogen and methane production stages formed communities dominated by Bacteroidales and Methanobacteriales, respectively. In addition, NaOH-urea pretreatment enhanced the metabolite energy recovery efficiency by 28.5–40.9 %. Finally, the return on investment (ROI) of the NaOH-urea pretreatment process reached 26.1 % with significant economic benefits. This research proposed a chemical pretreatment process for anaerobic digestion of corn stover by optimizing the pretreatment conditions of NaOH- urea.