Mixed-mode Loading Conditions Research Articles

Assessment of Reinforcement Effect of FRP-Strengthened Shield Segment Joint Based on the CZM Model

As the weakest link in the shield segment, the reinforcement and repair technology of shield segment joint has received widespread attention. In this study, an finite element model utilizing a cohesive zone model (CZM) was constructed to simulate the mechanical behavior of the shield segment joint during the whole fracture process. The proposed modeling method of joint allows multiple layers of steel bars to be stacked without interference by applying cohesive elements. Cohesive elements were employed to represent the mechanical response of potential fracture surfaces in concrete, as well as the interfaces between steel–concrete and fiber-reinforced polymer (FRP)–concrete, by utilizing various constitutive models tailored for mixed-mode loading conditions. A group of experiments was chosen to assess the precision of the proposed model by comparing the mechanical response and the fracture patterns. Finally, parameter analyses were conducted to study the reinforcement effect of the FRP bonding length and width on the shield segment joint. The results indicate that external bonding of FRP can effectively enhance the bearing capacity and stiffness of shield segment joints. However, insufficient bonding length or width may significantly reduce the strengthening effect and potentially decrease the ductility of the joint.

Study of fatigue crack propagation on modified CT specimens under variable amplitude loadings using machine learning

This study focuses on predicting fatigue crack paths and fatigue life in modified compact tension specimens, under mixed mode and variable amplitude loading conditions, using Machine Learning techniques. Mixed-mode conditions were induced by using specimens that incorporated holes with different radii and center coordinates. Initially, multiple Finite Element Method (FEM) simulations were conducted to determine the fatigue crack path for different configurations. Subsequently, several configurations were selected for experimental fatigue testing, in which the fatigue crack path was monitored and recorded. The final phase of the study involved Machine Learning (ML) techniques, specifically Artificial Neural Networks (ANN) and k-Nearest Neighbors (kNN), to predict fatigue crack propagation. The models were trained using different numerical and experimental data. Predicted results were then compared with experimentally tested data, and the behavior and accuracy of the models were evaluated. Overall, the implemented models demonstrated the ability to predict fatigue crack path with average deviations (ANN – 1.19 mm; kNN – 1.10 mm) closely resembling results obtained through Finite Element simulations (1.65 mm). The models were also able to predict fatigue life with average errors of 10.1 % (ANN) and 16.7 % (kNN), all achieved with a reduction of computational costs greater than 90 %.

Investigation of the influence of design parameters onto the cracked lap shear specimen

The Cracked Lap Shear (CLS) specimen allows a mixed-mode loading condition to be generated without a special test fixture using a simple tensile test. The mixed-mode ratio generated is nearly constant over a wide range of crack growth and is representative of the loading conditions in many structural applications of bonded joints. However, this specimen is not standardised, leading to very dissimilar specimen designs in the literature. In this study, the primary design parameter is the sample width in terms of its application for adhesive characterisation, with a typical layup having a 0° layer in contact with the bond line. The results of quasi-static and fatigue tests using varying specimen widths between 5 mm and 40 mm emphasise the specimen width’s influence. Moreover, CLS specimens with the same layup but without an adhesive layer between the adherends are investigated to study the effects of width scaling without a toughened adhesive bond. While the static tests show a linear relationship between specimen width and joint strength, it is different in fatigue tests, where the crack growth rate increases with decreasing specimen width, both for specimens with and without adhesive bond between the joining partners.

ATOMISTIC AND CONTINUAL DETERMINATION OF STRESS FIELDS AT A CRACK TIP IN ANISOTROPIC ENVIRONMENT WITH CUBIC SYSTEM

The article presents a comparative analysis of stresses associated with a crack tip in an anisotropic medium with cubic symmetry of elastic properties under mixed mode loading conditions, using two different approaches: atomistic and continuum approaches. The atomistic approach is based on the use of the molecular dynamics method implemented in the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The continuum approach is based on the classical theory of elasticity of anisotropic media, in which the mechanical fields associated with the crack tip are represented using series that generalize the well-known representation of M. Williams to the case of anisotropic media. Using the method of molecular dynamics, a large series of calculations of loading of single-crystal copper and aluminum plates with a face-centered crystal lattice, weakened by a central crack, was carried out using the embedded atom potential (EAM). Molecular dynamics modeling is aimed at determining atomistic stresses and strains near the crack tip. The calculated atomistic stresses were compared with the stress field determined by the continuum theory of elasticity of anisotropic media for crystal lattices with cubic symmetry of elastic properties. A comparative analysis was carried out for the angular dependences of the stress and strain tensor components at different distances from the crack tip for the entire range of mixed strain modes: from perfect normal tension to loadings close to perfect transverse shear. It is established that the fields found on the basis of two fundamentally different approaches (discrete and continuum) are fully consistent with each other. It is demonstrated that the mathematical methods of continuum fracture mechanics can be used to describe stress, strain, and displacement fields at the atomistic level.

Fracture research of adhesive-bonded joints for GFRP laminates under mixed-mode loading condition

Abstract The mixed-mode fracture characterization of adhesively bonded glass fiber-reinforced polymer (GFRP) plate joints is studied based on theoretical and experimental techniques. An improved beam model is used to estimate the compliance and the mixed-mode energy release rate (ERR) for GFRP four-point mixed-mode bending specimens. In this model, the deformation of the upper and lower GFRP plates is mutually independent, and the deformable adhesive is considered to satisfy the displacement compatibility conditions on the bonding interface. The explicit theoretical solutions of the compliance and ERR using the compliance method are reduced. The present theoretical solutions fit well with the finite element solutions by comparison with the rigid joint model. From the critical loads in experiment, the variation in fracture toughness on mixed-mode I/II has been determined by modifying the stiffness of the composite GFRP/GFRP substrate.

Analysis of peel and shear strains in cracked lap shear specimens subjected to fatigue loading using digital image correlation

Adhesive bonding presents many advantages, such as efficient manufacturing and improved structural performance [1]. However, in structures subjected to fatigue, cracks might initiate and propagate in joints, leading to in-service failure [2]. Most adhesively bonded joints are subjected to combination of peel and shear loads, so mixed I+II mode loading conditions are present [3]. In this work, Cracked Lap Shear specimens, which feature mixed I+II mode loading conditions, were tested under fatigue loading. During tests, crack growth was monitored using Visual Testing and Digital Image Correlation. With Digital Image Correlation, opening and sliding displacements in the bondline were extracted from the substrates’ displacement fields and compared against a Finite Element Model, revealing a highly strained process zone ahead of the crack tip. Results highlight the usefulness of DIC in capturing the deformation behaviour of adhesive joints under mixed mode loading conditions.

Integral-based non-local approach to ductile damage and mixed-mode fracture

The present study focuses on the application of an integral-based approach for constructing non-local ductile damage models. The incorporation of non-locality into the damage accumulation rule enhances the modeling framework and yields simulation results that are physically reasonable, avoiding the issue of pathological mesh-dependence. To achieve a precise depiction of damage accumulation and fracture under mixed-mode I/II loading, novel delocalization kernels are proposed. These kernels explicitly consider the heterogeneity of stresses and strains in the fracture process zone; the new kernels are categorized into stress-based and strain-based families. Furthermore, rigorous receiver-based normalization procedures and physically meaningful source-based normalizations are explored for the developed kernels. The outcome of this study is the modeling tool, suitable for end-to-end simulations of damage accumulation and fracture. Using a well-calibrated material model, the practical applicability of the new approach is demonstrated by performing finite element analysis on fracture tests conducted on compact tension–shear specimens. In contrast to the conventional delocalization kernels, the newly introduced families of kernels offer an additional fitting parameter, valuable in accurately describing the structural behavior under mixed-mode loading conditions. In particular, the proposed approach enables control over the shape of the predicted KIc–KIIc diagram.

Simulation of 3D fracture propagation under I-II-III mixed-mode loading

Fracture propagation under mixed-mode loading conditions prevails in many natural geological processes and deep engineering projects, while the corresponding numerical simulation is very challenging in rock mechanics, especially in 3D cases. In most previous studies, the complexity of 3D fracture geometry was over-simplified, and model III loading was often not considered. In this study, we propose to use an efficient stress-based Schöllmann criterion combined with Displacement Discontinuity Method (DDM) to model 3D fracture propagation under arbitrary I ​+ ​II ​+ ​III mixed-mode loading conditions. A novel curve-smoothing algorithm is developed to smoothen the fracture front during propagation, which significantly enhances the model's ability in dealing with complex 3D fracture geometry. In particular, we adopt two different solution schemes, namely staggered and monolithic, to simulate mode I fracture propagation in the case of hydraulic fracturing. The accuracy, efficiency and convergency of the two solution schemes are compared in detail. Our research findings suggest that the degree of coupling between fracture aperture and fluid pressure in hydraulic fracturing lies somewhere between one-way and two-way, which favors the staggered solution scheme. To further test our new model, we provide three additional numerical examples associated with 3D fracture propagation under various mixed-mode loading conditions. Our model shows excellent performance in efficiently locating the new fracture front and reliably capturing the complex 3D fracture geometry. This study provides a generic algorithm to model high-fidelity 3D fracture propagation without simplifying fracture geometry or loading conditions, making it widely applicable to fracture-propagation-related problems.

Simulating delamination growth accounting for fracture directionality using a cohesive element approach

Experiments have shown that the critical energy release rate (ERR) can vary as a function of the delamination in-plane propagation direction, relative to the bounding plies, and out-of-plane direction towards which it tends to grow, often referred to as delamination directionality. Despite the experimental evidence, delamination directionality is typically neglected in simulations. A cohesive element formulation is proposed that can simulate delamination growth while accounting for delamination directionality. The simulated fracture process is defined via piecewise-linear, independent, Mode I, II, and III traction separation laws (TSLs) and a directional mixed-mode fracture criterion. Mixed-mode loading conditions are simulated by scaling the pure mode TSLs based on the fracture criterion and the calculated mode-mixity. The same scaling concept is used in partially damaged material points to ensure that a change in fracture process (e.g. decrease/increase in critical ERR due to a variation in delamination directionality) is captured while preventing spurious delamination growth or healing and minimizing history dependence.

Loading rate effect on mixed-mode I + II fracture of V-notched Brazilian disc rock specimen under impact loads

Dynamic failure processes of rock masses containing numerous discontinuities including pores, cracks and notches have been the major issues in structural safeties of underground buildings subjected to impact loads, such as earthquake, blast and vehicle vibration. At present, most of the studies are focused on the dynamic fracture behaviors of rocks containing crack-like defects, while the studies on rocks containing notch-type defects are very rare, especially under mixed-mode loading conditions. This paper aims to study the effects of loading rate on mixed-mode I + II fracture characteristics of flattened V-notched Brazilian disc rock specimen under impact loads by means of an split Hopkinson pressure bar (SHPB) system combined with a high-speed camera. Dynamic fracture tests were performed on a total of 125 groups of V-notched rock specimens with different notch angles (0°, 30°, 45°, 60°, and 90°) and loading angles (0°, 30°, 45°, 60°, and 90°) at different air pressures (0.16 MPa, 0.18 MPa, 0.20 MPa, 0.22 MPa, and 0.24 MPa). Based on dimensional analysis, a numerical method was proposed to establish the relationship between mixed-mode notch stress intensity factor (NSIF) at the V-notch tip and external axial load. The dynamic notch fracture toughness values of flattened V-notched Brazilian disc rock specimens were calculated from the maximum values of dynamic force in the SHPB tests according to the proposed numerical method. The effects of loading rate, notch angle, and loading angle on the mixed-mode I + II notch fracture toughness value and crack initiation angle were quantitatively analyzed, which were verified using a modified maximum tangential stress (MTS) criterion by considering the loading rate effect. It is found that the loading rate has a significantly positive effect on the notch fracture toughness value, but has a negative effect on the crack initiation angle due to the inertial effect under dynamic impact loads. Generally, pure mode I fracture occurs for the loading angle of 0° or 90°, pure mode II fracture occurs for the loading angle varying from 35° to 45°, and mixed-mode fracture occurs for other loading angles. Good consistencies of the mixed-mode I + II notch fracture toughness values and crack initiation angles of the V-notched rock specimens are observed between the modified MTS criterion prediction and experimental results. This work may improve the understanding of the dynamic fracture behaviors of rock masses containing notch-type defects during tunnel excavation and underground construction process.

Fatigue Crack Growth Studies under Mixed-Mode Loading in AISI 316 Stainless Steel

The objective of this study is to examine the behavior of fatigue crack growth (FCG) in the mixed mode (I/II) of the AISI 316 austenitic stainless steel alloy, considering mode mixity angles of 30°, 45°, and 60°. This particular alloy is widely used in the marine industry and various structural components because of its exceptional properties, such as high corrosion resistance, good formability, weldability, and high-temperature strength. By investigating the crack growth behavior, the study seeks to provide insights into the material’s durability and potential for long-term use in demanding applications. To analyze fatigue crack growth behavior using linear elastic fracture mechanics (LEFM), this study utilizes compact tension shear (CTS) specimens with varying loading angles. The CTS specimens provide an accurate simulation of real-world loading conditions by allowing for the application of various loading configurations, resulting in mixed-mode loading. The ANSYS Mechanical APDL 19.2 software, which includes advanced features such as separating, morphing, and adaptive remeshing technologies (SMART), was utilized in this study to precisely model the path of crack propagation, evaluate the associated fatigue life, and determine stress intensity factors. Through comparison with experimental data, it was confirmed that the loading angle had a significant impact on both the fatigue crack growth paths and the fatigue life cycles. The stress-intensity factor predictions from numerical models were compared to analytical data. Interestingly, it was observed that the maximum shear stress and von Mises stresses occurred when the loading angle was 45 degrees, which is considered a pure shear loading condition. The comparison shows consistent results, indicating that the simulation accurately captures the behavior of the AISI 316 austenitic stainless steel alloy under mixed-mode loading conditions.

A device for studying fluid-induced cracks under mixed-mode loading conditions using x-ray tomography.

We introduce an innovative instrument designed to investigate fluid-induced fractures under mixed loading conditions, including uniaxial tension and shear stress, in gels and similar soft materials. Equipped with sensors for measuring force, torque, and fluid pressure, the device is tailored for compatibility with x-ray tomography scanners, enabling non-invasive 3D analysis of crack geometries. To showcase its capabilities, we conducted a study examining crack-front segmentation in a hydrogel subjected to air pressure and a combination of tension and shear stress.

Experimental Study on Shear-Peeling Debonding Behavior of BFRP Sheet-to-Steel Interfaces.

In order to study the failure mode and debonding behavior of the interface between BFRP (basalt fiber reinforced polymer) sheet and structural steel under mixed-mode loading conditions, eighteen specimens with different initial angles were tested in this study. The specimens were designed with different initial angles to ensure that the interface performed under mixed-mode loading conditions. The relations between the bond strengths, failure modes, and initial angles were investigated. A new evaluation method to predict the interfacial bond strength under shear-peeling loading mode was proposed. The test results show that specimens with a smaller initial angle are more likely to exhibit a shear debonding failure at the interface between the steel plate and adhesive. In contrast, specimens with a larger initial angle are more likely to exhibit peeling of the interface. The ultimate tensile strength of the specimen is higher with a smaller initial angle. The results predicted by the proposed method are in good agreement with the experimental results.

Investigating the effect of raster orientation on fracture behavior of 3D-printed ABS specimens under tension-tear loading

Most of the engineering components are servicing under complex loading conditions or have complex geometries that lead to a multiaxial stress state in the component. Thus, the fracture behavior of parts under mixed-mode loading conditions should be investigated. The Fused Deposition Modeling (FDM) is a subcategory of the Additive Manufacturing (AM) techniques that has some important manufacturing parameters. The raster orientation (or raster angle) is one of fabricating parameters that significantly affect the mechanical behavior of fabricated parts. Therefore, this study aims to investigate the fracture behavior of FDM specimens made of Acrylonitrile Butadiene Styrene (ABS) under mixed-mode I/III loading conditions. To this goal, four different raster configurations of ψR = 0/90°, 15/-75°, 30/-60°, and 45/-45° were selected for FDM fabrication of edge cracked rectangular specimens, and five loading angles of β = 0° (mode I), 40°, 65°, 72°, and 90° (mode III) were used for performing mixed-mode I/III fracture experiments on the pre-cracked specimens. Besides, some tensile experiments were performed on dog-bone specimens fabricated with the mentioned raster configurations. In order to theoretically predict the failure loads in the tested cracked specimens, a theoretical model named Equivalent Material Concept (EMC) was utilized for equating the ductile behavior of FDM-ABS material with a brittle one. The mentioned concept was coupled with J-integral (EMC-J) and Maximum Tangential Stress (EMC-MTS) criteria to predict the failure loads under mixed-mode loading conditions. The results showed that both EMC-J and EMC-MTS criteria could predict the experimental failure loads well. Additionally, Scanning Electron Microscopy (SEM) was performed on the fracture surfaces to analyze the failure mechanisms of the tested specimens. SEM analysis confirmed the presence of three failure features namely air gaps, filament pullouts, and hackle regions that were discussed comprehensively.

Study on two-dimensional mixed-mode fatigue crack growth employing ordinary state-based peridynamics

Mixed-mode fatigue crack propagation analysis is studied using ordinary state-based peridynamics. By introducing the concept of “remaining life”, the fatigue crack nucleation and propagation can be simulated in the PD framework. The PD fatigue modelling and the crack path prediction is carefully investigated. For the comparison purpose, the maximum circumferential stress criterion is introduced. The interaction integral and the peridynamic differential operator is employed to evaluate the fracture mechanics parameters. Two pre-cracked structures under mixed-mode loading conditions are provided with the validations from reference solutions.

Mixed mode (I/III) fracture studies using a new specimen setup

In the present work, mixed mode (I/III) fracture studies have been investigated using a new specimen and an out-of-plane loading fixture that can be used with the conventional uniaxial universal testing machines. The proposed specimen is a single edge cracked circular (SECC) specimen which can be employed on both metallic and non-metallic materials under static and fatigue loads. A large number of three-dimensional finite element analyses have been performed on the proposed specimen setup to demonstrate the efficacy of the proposed setup. Experimental fracture studies have also been performed under mixed mode (I/III) loading conditions. The present experimental results are in very good agreement with the available mixed mode (I/III) fracture criteria. Experimental results indicate that the pure mode III fracture toughness is nearly 1.46 times greater than that of the mode I. This has been found due to an increase in the inelastic region around the crack tip in pure mode III and is in accordance with the published results. Detailed analyses of the fractured surfaces have also been carried out. It has been demonstrated that the fractured surfaces become more rough as the mode III component increases. Preliminary results of mixed mode (I/III) fatigue crack growth studies on Al 7075-T6 using the metallic SECC specimen have also been presented. The results of the present study confirm that the proposed specimen setup can be used to study the mixed mode fracture behavior of linear elastic materials under static and fatigue loading.

The interaction of loading mode and humidity on the properties degradation of an epoxy adhesive subjected to strength, fracture, and fatigue tests

AbstractHygrothermal aging has a significant impact on the performance of adhesives and bonded joints. However, despite extensive investigations into the aging effect of bonded structures, there is still limited knowledge on how aging affects joint performance as a function of the loading type and the load angle. Accordingly, in this study, an epoxy adhesive was tested under different loading types/angles including tensile and shear standard strength tests, mode I and mode II fracture tests, and fatigue and static Arcan tests. All these experiments were performed for both aged and unaged conditions. To understand the influence of loading angle on the failure response of aged bonded joints, Arcan samples were subjected to mixed mode loading conditions as well. A fractography analysis was conducted to provide a better understanding of the failure mechanism of aged samples loaded at different modes. Based on these results, it was found that mode I (tensile loading conditions) is more sensitive to the aging conditions than mode II (shearing) for all loading types (strength, fracture, and fatigue tests). The influence of moisture on fracture toughness was however less relevant than the strength. The results also showed that for the same loading mode and for the same Arcan joints, the fatigue strength is significantly more degraded by the aging conditions than the static strength.

Mixed-mode fracture of compacted tailing soils. I: Fracture toughness

Mine tailings are man-made soils and leftovers from the mineral processing that share the similar geotechnical properties with natural soils. In areas with abundant mineral reserves and developed mining industries, tailings could be utilized as an alternative of natural soils for subgrade materials of pavement and adobes for building and construction constructions. The tailing soils are also the based materials for tailing dams. The compacted tailing soils might thus be subject to combined opening or shearing deformations that were unexplored in the current academic society. In this paper, a test configuration called asymmetric semi-circular bending (ASCB) was adopted to investigate the mixed I/II mode fracture properties of the compacted tailing soils. First, the load–displacement relationships of the SCB specimens for different notch depths and span ratios were presented. The mode I and II fracture toughness components were then calculated by referring to the theoretical solutions derived from classical fracture mechanics. The fracture envelope from mode I and II fracture toughness components were presented. Meanwhile, the mixity parameter was introduced to evaluate the mode mixity of the ASCB specimens. Finally, the crack initiation angles of the SCB specimens were measured through experimental tests and compared to the theoretical results obtained from generalized maximum tangential stress criterion (GMTS). Results show that the mode I fracture toughness component of the compacted tailing soils increased with the span ratio, while the mode II fracture toughness component increased with the decrease of span ratio. The mode mixity and crack initiation angles of the SCB specimens under mixed mode loading conditions increased with the decrease of span ratio.

Investigation on the mixed mode fracture toughness of freshwater ice using the semi-circular bend method

The fracture toughness of ice is of great importance to understand the fracture behaviour of ice impact and blasting. In this study, the mixed mode (I + II) fracture toughness and mode II fracture toughness of granular freshwater ice were first investigated using the semi-circular bend method. A series of fracture tests were carried out to investigate the effects of the grain size (0.8 mm to 4.5 mm) and notch inclination angle (0° to 75°) on the fracture toughness under mixed mode loading conditions. The experimental results indicate that the mode II and mixed mode fracture toughness values slowly decrease in general as the grain size increases. The fracture initiation angles and critical stress intensity factors of the SCB ice specimens were predicted using the generalized maximum tangential stress (GMTS) criteria and conventional maximum tangential Stress (MTS). The GMTS criterion provides a better understanding for mixed mode fracture toughness of ice specimens with various grain sizes, particularly for mode II dominated loading conditions. The grain size of ice directly affects the size of the fracture process zone, which in turn affects the variation law of mixed mode fracture toughness. The strain field and displacement field were initially analysed based on digital image correlation. The results indicate that the variation in the mixed mode crack was complex, eventually exhibiting an asymmetrical distribution of the displacement field.

Adaptive Finite Element Modeling of Linear Elastic Fatigue Crack Growth.

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris' law model. Finally, the performance and capability of the developed program are shown in the application examples.