Biaxial Stress State Research Articles

Failure behaviors of granitic rocks induced by point/local loads under biaxial compression stress state

Failure behaviors of granitic rocks induced by point/local loads under biaxial compression stress state

Finite Element Simulation of Fiber Reinforced Composites Under Bi-Axial Loading

Advances in testing of composite materials in recent years have mostly resulted in the ability to actively characterize the uniaxial response of composites while investigations of multiaxial load cases are rare due to various challenges. One of these challenges is the lack of a suitable specimen geometry for multiaxial testing without unwanted failure modes. Ideally, such geometry should be developed and assessed virtually by means of simulation before costly and time-consuming manufacturing and testing. Therefore, reliable, and efficient simulation methods are required that incorporate the evolution of damage in FRP composites. This study investigates various geometric features virtually of cruciform specimens to test fiber-reinforced composites subjected to in-plane biaxial tensile loadings. The goal is to achieve uniform failure in the gauge region of the specimen due to biaxial stress states and to reduce any premature failure outside the gauge region. Efficient finite element simulation in the commercial software LS-DYNA is used to identify the optimal geometric features.

Energy absorbing multilayered self-recovering metamaterials with chiral topology

A novel energy absorbing material is proposed for the design of shock absorbers and vibrational dampers. A layered architectured microstructure is put forward consisting of the repetition of plane lattices having hexachiral topology with alternate chirality, each being designed as a periodic assembly of rigid disks connected by elastic ligaments. Because of the chiral topology of the single layer, the rotation of the rigid disks takes place when in-plane stress states are applied so implying a relative rotation between the disks of adjacent lattices with opposite chirality. Pins passing through for each stacking of disks impose them the same in-plane displacement. Moreover, frictional dissipative mechanisms at the interface between adjacent disks according to two different compression modes orthogonal to the layers make the metamaterial suitable for either reusing or self-recovering the initial configuration. In the first case the pre-tensioning of the pins implies the compression of plane frictional interfaces. The frictional sliding compatible with the disk relative rotation implies an overall hysteretic bilinear response with remarkable energy dissipation. The metamaterial may be reused once the pins are relaxed and re-tensioned. In the latter case no pre-tension is applied to the pins and the compressive force between the disks is obtained through saw-tooth shaped interfaces between adjacent disks to get elastically constrained transverse dilation when the relative rotations at the interfaces take place. The overall response turns out to be highly dissipative and self-recovering, i.e. able to return to the initial configuration when removing the applied stresses. As shown in the examples the quasi-static behavior of the proposed metamaterial makes it a candidate as an efficient vibration damper and a shock absorber characterized by i) hysteretic response with remarkable energy dissipation under biaxial stress states; ii) reuse or self-recovering after the energy absorption event; iii) bilateral response, i.e. equal behavior under both tension and compression.

A practical biaxial time-dependent material model of PVDF-coated polyester fabrics for structural applications

The utilization of air-supported fabric structures as formwork to construct concrete shells has attracted increasing attention in recent decades. An example of such an airform is the air-supported structure at Dahaize, which consists of a cylindrical part and a hemispherical part, and is 66 m in diameter and 65 m in height. The precise forming analysis of large-span air-supported structures requires the use of a reasonable material model that considers the biaxial stress condition and the creep behavior of the fabric. In this paper, a practical approach to modeling the biaxial time-dependent material behavior of composite fabrics is proposed based on the uniaxial linear viscoelastic theory and the plane stress orthotropic assumption. The multi-Kelvin physical model is developed to the two-dimensional form for the simulation of biaxial creep compliances. Biaxial tensile and biaxial creep tests are conducted on PVDF-coated polyester fabrics to calibrate the material parameters. The experimental stress conditions were determined according to the pre-estimated actual membrane stress distribution. The established material model is employed for the forming analysis of the Dahaize airform under conditions of varying creep times. The simulation results agree well with the on-site measured data, and this validates the accuracy and efficiency of the proposed material model.

Probability embedded failure prediction of unidirectional composites under biaxial loadings combining machine learning and micromechanical modelling

This study presents a data-driven, probability embedded approach for the failure prediction of IM7/8552 unidirectional carbon fibre reinforced polymer (CFRP) composite materials under biaxial stress states based on micromechanical modelling and artificial neural networks (ANNs). High-fidelity 3D representative volume element (RVE) finite element models were used for the generation of failure points. Fibre failure and the friction between fibres and matrix after fibre/matrix debonding were taken into consideration and implemented as VUMAT subroutines, respectively. Uncertainty quantification was conducted based on a coupled experimental–numerical approach and failure probabilities were inserted into the failure points to generate the database for the training of ANNs. A total of 15 biaxial stress combinations were considered for the generation of datasets. Two strategies were considered for the construction of form-free failure criteria based on the ANNs for regression and classification problems. It is found that for the regression problems, an ANN model with 2 hidden layers and 64 neurons can achieve a mean square error (MSE) of 0.027% and a mean absolute error (MAE) of 0.78%. For the classification problems, an ANN model with 3 hidden layers and 32 neurons, presents an excellent performance in the prediction with a probability of 98.1%. A good agreement was observed between the failure strength of composites under transverse and in-plane shear predicted by these ANNs and failure envelopes theoretically predicted by Tsai–Wu and Hashin failure criteria.

Numerical optimization-based design studies on biaxial tensile tests

Biaxial tensile tests are of great significance for the characterization of materials. For ductile materials, they allow the representation of the yield strength curve separating elastic and plastic material behavior. Contrary demands regarding the specimen design arise, if a biaxial stress state with the equivalent stress equal or close to the yield strength shall be obtained. On one hand, the specimen shall be of constant thickness and stiffness, in order to allow an unconstrained deformation without undesired lateral strains. On the other hand, stress concentrations arising from the load introduction make a thickened border region necessary, in order to avoid a premature failure of the specimen. The present paper addresses this problem by a multi-objective structural optimization using Evolutionary Algorithms. Well-defined parametric models of biaxial tensile test specimens allow to systematically investigate the influence of the thickness distribution and the sizing of the border region. Additionally, the influence of actuators of constant force compared to actuators of constant displacement are quantified. In all cases, the minimization of the stress difference as well as the actuation effort are considered as objectives. The results allow a deep insight to the optimal definition of biaxial tensile test specimens and are summed up in well-defined design proposals.

A fracture model for assessing tensile mode crack growth resistance of rocks

Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering. This investigation developed a brittle fracture model to predict tensile mode (mode I) failure loads of cracked rocks. The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone (FPZ) based on the maximum normal strain (MNSN) ahead of the crack tip, and then use the effective crack to calculate the fracture toughness. We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN. In this way, the FPZ, non-singular terms and the biaxial stress state at the crack tip are simultaneously considered. The principle of the model is explicit and easy to apply. To verify the proposed model, laboratory experiments were performed on a rock material using six groups of specimens. The model predicted the specimen geometry dependence of the measured fracture toughness well. Moreover, the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature. The model was demonstrated superior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.

Virtual element method for mixed-mode cohesive fracture simulation with element split and domain integral

We present a computational framework for mixed-mode cohesive fracture simulation based on the virtual element method (VEM). To represent an arbitrary crack path, the element splitting scheme is developed on a polygonal mesh to capitalize its flexibility in element shape. For the accurate evaluation of a crack-tip stress field and crack propagation direction, the virtual grid-based stress recovery scheme is tailored for VEM in conjunction with the maximum strain energy release rate criterion. The mixed-mode fracture examples are illustrated to validate the accuracy and robustness of the proposed computational scheme. Numerical results demonstrate that the domain integral method with the stress recovery scheme captures an accurate crack path without oscillation under the biaxial tensile stress state. Furthermore, the computed cracks using the element splitting scheme show that smooth and curved patterns on polygonal elements are in good agreement with the experimental results.

Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States

Based on the negative Poisson’s ratio effect of the re-entrant honeycomb, the finite element simulation of its buckling mechanical properties was carried out, and 2 buckling modes other than those of the traditional hexagonal honeycomb structures were obtained. The beam-column theory was applied to analyze the buckling strength and mechanism of the 2 buckling modes, where the equilibrium equations including the beam end bending moments and rotation angles were established. The stability equation was built through application of the buckling critical condition, and then the analytical expression of the buckling strength was obtained. The re-entrant honeycomb specimen was printed with the additive manufacturing technology, and its buckling performance was verified by experiments. The results show that, the buckling modes vary significantly under different biaxial loading conditions; the re-entrant honeycomb would buckle under biaxial tension due to the auxetic effect, being quite different from the traditional honeycomb structure; the typical buckling bifurcation phenomenon emerges in the analysis of the buckling failure surfaces under biaxial stress states. This research provides a significant guide for the study on the failure of re-entrant honeycomb structures due to instability, and the active application of this instability to achieve special mechanical properties.

Multiaxial Strength and Deformations of Concrete, Failure Modes and a New Failure Criterion

The multiaxial strength of concrete, the associated stress-strain relationships, the failure modes and the failure criteria are again and again in the interest of researchers. After a historical review the most important bi- and triaxial experiments loading through brushes are analyzed. Based on the principal strengths and the loading path-concept a new, transparent type of presentation of the ultimate strength surface (USS) is introduced. For concrete classes ≤ C100 simplified relative strength-increase values are proposed. The difficulties of deformation measurements are reviewed. The outlines of future bi- and triaxial tests are discussed. Two failure modes are appointed. Stress failure criterion of biaxial state of stress are presented. Instead of the Modified Mohr-Coulomb failure criterion Extended Rankine-type failure criteria are proposed. Further systematic tests are necessary to detect the rate of participation of the loading equipment.

A review of in-plane biaxial fatigue behavior of metallic materials

Aerospace components, such as aircraft fuselage panels, pressurized container and turbine blades are exposed to in-plane biaxial fatigue loading in service. Assessment of the effect of biaxial stress state is of great importance in structural reliability analysis. In this paper, the current state of understanding and development of the fatigue behavior of metallic materials under in-plane biaxial loading is reviewed. The fatigue properties in cruciform specimens were examined under in-phase and out-of-phase biaxial loading as well as in-phase biaxial loading with overloads. The effect of stress biaxiality on the fatigue behavior, including crack initiation, crack trajectory, crack growth rate and fatigue life, were presented. The fracture morphology analysis was shown to clarify the mechanism of biaxial fatigue damage. Furthermore, several models that have been used to predict the biaxial fatigue behavior were analyzed. The applicability of these models in correlating biaxial experimental data were evaluated.

The role of biaxial stress ratio on the mechanical behavior and deformation mechanisms in HCP α-Ti

The mechanical behavior of hexagonal close-packed (HCP) Ti alloy is closely related to the stress state. Renewing the mechanical behavior and associated mechanisms of HCP α-Ti alloy under biaxial stress states is critical for their manufacturability and serviceability. In this work, biaxial tensile tests with different stress ratios closing to actual service conditions were conducted to investigate the mechanical behavior of commercially pure Ti (CP-Ti). Then, comprehensive microstructural characterizations were performed using electron back-scattering diffraction (EBSD) and transmission electron microscopy (TEM) techniques. The effects of biaxial stress ratio on the evolution of dislocation and deformation twinning throughout plastic deformation were clarified. It was found that the activity of prismatic slip was suppressed while pyramidal slip was promoted, which was attributed to the decrease of external stress component on the prismatic planes and the increase of that on the pyramidal planes with increasing biaxiality. Moreover, the increased stress component in the c-axis direction also encouraged the occurrence of extension twinning at high biaxiality. The decrease of prismatic slip with low critical resolved shear stress (CRSS) and the increase of twinning and pyramidal slip with high CRSS contributed to an increase in deformation resistance and work hardening rate with increasing biaxiality.

Elastoplastic Analysis of Circular Steel Tube of CFT Stub Columns under Axial Compression.

Composite action between the components of the concrete-filled steel tube (CFT) is complex and it is difficult to accurately obtain the experimental relationship between the steel tube and the core concrete of CFT columns. The triaxially stressed core concrete has been studied by hydrostatic test in past research, while little research has been focused on the mechanical behavior of steel tube of CFT columns. It is difficult to obtain the experimental constitutive relationship of the steel tube of CFT columns to reflect the real-time influence of biaxial stress state and local buckling of steel plate on the steel tube. To clarify the mechanical behavior of the steel tube of CFT columns, this paper proposed an elastoplastic analytical method considering biaxial stress state and local buckling of steel tube to obtain the stress-strain curve of the steel tube. This method applied the Hook's law and the plasticity theory to interpret the information conveyed by the measured vertical and hoop strain histories of the steel tube. To verify its effectiveness, 11 circular concrete-filled steel tube stub columns were fabricated and tested under axial compression. Superposition results of the axial load-strain of steel tube and core concrete were compared against the experimental curves. The widely used Sakino-Sun model of the confined concrete was adopted to calculate the axial load-strain curve of the core concrete. Satisfactory agreements between the calculated and experimental results confirmed the rationality of the proposed method in tracing the constitutive relation of the biaxially stressed steel tube even after the occurrence of the local buckling. The obtained stress-strain relationship is critical for establishment of mathematical constitutive model and finite element model of steel tube.

An anisotropic plastic‐damage model for 3D nonlinear simulation of masonry structures

AbstractPredicting the structural response of masonry structures with acceptable accuracy is paramount to safeguard the historical heritage and build new constructions with safety margins adequate to modern standards. However, due to the heterogeneous nature and anisotropic response of masonry, such prediction is still difficult to achieve, where most current masonry representations are based upon homogeneous isotropic material models or even more simplified masonry macro‐elements. In this article, a novel anisotropic constitutive model to be used in detailed 3D continuum FE representations is described. This is based upon the application of the transformed‐tensor method to an isotropic uncoupled plastic‐damage model, which is further enhanced by additional novel features enabling the proper definition of the shear behavior both in terms of yielding surface and damage evolution while increasing local computational robustness. Illustrative examples at different scales are presented, highlighting the characteristics and potential of the developed masonry material model. Focus is placed on the mechanical behavior under uniaxial and biaxial stress states considering pure compression on wallets with varying inclination of the material principal axes and the out‐of‐plane response of wall components. The numerical results confirm the ability of the proposed constitutive model to predict typical masonry anisotropic response characteristics, which cannot be accurately represented by standard isotropic representations commonly used in professional practice and research.

Generation of fine extension twins in rolled magnesium alloy AZ31B at room temperature by simple shear

A textured AZ31B plate was subject to simple shear along 45° to its normal direction at room temperature, and extension twinning under biaxial stress was investigated by statistical analyses of electron backscatter diffraction maps. Extension twinning is the primary deformation mechanism up to a plastic shear strain of 15% (8.66% equivalent plastic strain), and the most frequent twin thickness remains to be 1.5 μm. The simple shear suppresses twin growth, yet brings sustained twin nucleation. The critical resolved shear stress of extension twinning is determined as 25 MPa and remains virtually constant up to a plastic shear strain of 10%. The present study suggests that by using biaxial stress state that promotes multi-twin nucleation, a microstructure with dense and fine twins can be produced at room temperature in a conventional Mg alloy, without jeopardizing the contribution of twinning to plastic straining.

Controlled crack propagation of flexible Film/Substrate assembly by biaxial stress

Crack has long been regarded as a form of material failure. At the same time, it is also an effective processing method to create some patterns on the surface of objects. Currently, most crack-based processing methods are achieved by applying equai-biaxial thermal stress. However, the stress ratio of equi-biaxial stress state is fixed, and its flexibility is very limited. In this paper, a method is developed to control the crack propagation in thin film coated on substrate by using generalized biaxial stress. Under some reasonable assumptions on the shear stresses in the interface layer between the film and its substrate, an analytical stress distribution in film under biaxial stress state is obtained. Then, the strain energy density factor is used to predict the propagation direction of a prefabricated crack. By changing the biaxial stress state undergone by film, the crack propagation direction can be controlled. Some verification experiments are conducted, which are consistent with the theoretical prediction.

Experimental study of dynamic biaxial compressive properties of full grade aggregate concrete after freeze thaw cycles

Most hydraulic concrete structures are in complex stress state, this study attempts to take some test of full grade aggregate concrete under biaxial compression after 0, 25, 50, 75, and 100 cycles of freeze-thaw. Five principle compression stress ratios of 1:0, 1:0.25, 1:0.5, 1:0.75 and 1:1 and four different strain rates of 10−5/s, 10−4/s, 10−3/s and 10−2/s were the main variables. The mass loss of concrete after freeze-thaw cycles has been studied. With the increase of freeze-thaw cycles, the quality loss is little. The failure pattern, ultimate strength, peak strain and stress-strain curve under different freeze-thaw cycles, stress ratios and strain rates were obtained. The dependence of ultimate strength on freeze-thaw cycles and ultimate strength, and the relationship between freeze-thaw cycles, stress ratio and strain rate were analyzed according to the testing data. The unified failure criterion of full grade aggregate concrete after freeze-thaw cycles under dynamic biaxial compressive stress state was established in principal stress space and octahedral stress space, respectively. The comparative analysis of experimental results of different types of concrete(large aggregate concrete, ordinary concrete, lightweight aggregate concrete, wet screened concrete) under biaxial compression after freeze-thaw cycles are made. With the increase of freeze-thaw cycles, the ultimate compressive strength of common concrete, wet screened concrete, lightweight aggregate concrete and large aggregate concrete gradually decreases. The results may serve as an experimental and theoretical reference for the design and maintenance of hydraulic structures.

Multi-Criteria Evaluation of the Failure of CFRP Laminates for Frames in the Automotive Industry.

Methods to predict the fracture of thin carbon fibre-reinforced polymers (CFRPs) under load are of great interest in the automotive industry. The manufacturing of composites involves a high risk of defect occurrence, and the identification of those that lead to failure increases the functional reliability and decreases costs. The performance of CFRPs can be significantly reduced in assembled structures containing stress concentrators. This paper presents a hybrid experimental-numerical method based on the Tsai-Hill criterion for behavior of thin CFRPs at complex loadings that can emphasize the threshold of stress by tracing the σ-τ envelope. Modified butterfly samples were made for shearing, traction, or shearing-with-traction tests in the weakened section by changing the angle of force application α. ANSYS simulations were used to determine the zones of maximum stress concentration. For thin CFRP samples tested with stacking sequences [0]8 and [(45/0)2]s, the main mechanical characteristics have been determined using a Dynamic Mechanical Analyzer (DMA) and ultrasound tests. A modified Arcan device (AD) was used to generate data in a biaxial stress state, leading to the characterization of the material as a whole. The generated failure envelope allows for the prediction of failure for other combinations of normal and shear stress, depending on the thickness of the laminations, the stacking order, the pretension of the fasteners, and the method used to produce the laminations. The experimental data using AD and the application of the Tsai-Hill criterion serve to the increase the safety of CFRP components.

The Gap test – Effects of crack parallel compression on fracture in carbon fiber composites

This paper explores the global Mode I fracture energy of a carbon fiber composite subject to a biaxial stress state at the crack tip, specifically in which one stress component is compressive and parallel to the crack. Based on an experimental technique previously coined as The Gap Test and Bažant’s Type II Size Effect Law, it is found that there is a monotonic decrease in the Mode I fracture energy as the crack parallel compressive stress increases. Compared to the nominal value of fracture energy, where no crack parallel compression is applied, the fracture energy is observed to decrease by up to 37% for a compressive stress equal to 44% of the compressive failure limit of the composite. This weakening effect is attributed to splitting cracks that are induced at the crack tip due to the crack parallel compression, which are identified via crack tip photomicroscopy. This is a novel result that challenges the century old hypothesis of fracture energy being a constant material property and further, shows for the first time that crack parallel compression leads to a composite structure being dangerously weaker than expected.The experimental campaign is also buttressed with a computational campaign that provides a framework capable of capturing the effects of crack parallel compression. Through the use of the crack band model, which correctly characterizes the fracture process zone tensorially, coupled with a fully tensorial damage law, the simulated results provide satisfactory agreement with the experimental data. Conversely, when a reduced tensorial damage law defines the crack band it is shown that the structural strength and fracture energy are dangerously overpredicted. This emphasizes the importance of using a crack band model coupled with a fully tensorial damage law to accurately predict fracture in composites.

(Invited, Digital Presentation) Probing Triaxial Stress States Using Curvature-Based Methodology for Enabling Highly Robust and Reliable Integrated 3D Systems-on-Package in Advanced Microelectronics Industries

With the nascent of the systems-on-package in advanced 3D microelectronics, mechanical stress states in the system get much more complicated than in the past. Stress states are increasingly triaxial (as opposed to mostly biaxial stress states in the planar semiconductor devices), and with that, the roles of shear stresses in causing relatively new and unique mechanical damages and failures in the 3D stacks of chips and devices (memory, logic, sensors, actuators, data storage, etc.) cannot be undermined. The difficult stress management in a Through-Silicon Via (TSV) as the vertical interconnection between chips on stack has been an early indication of what more to come to the emerging, advanced microelectronics industries in the near, immediate future. Not only the mechanical damages that come into the picture, but also the delicate interrelation between the mechanical straining of the silicon and the corresponding electronic mobility affecting the very working of the semiconductor devices. The methods of stress determination used in the semiconductor industries so far (X-ray Diffraction, Raman Spectroscopy, etc.) have mostly worked under the assumptions of biaxial stress states which were mostly true in the planar semiconductor chip design. Such assumptions may no longer hold true for enabling highly robust and reliable integrated 3D Systems-on-Package in today’s and tomorrow’s microelectronics industries. In addition, once the 3D stacks of devices are fully integrated, it becomes next to impossible to manage the highly convoluted stress states originating from many silicon devices with mostly surface-based Raman techniques and low-penetration depth of conventional laboratory XRD. In this study, we propose to use the curvature-based approaches that would allow determination of the complete 3D stress states in every level of the stacking of silicon devices, and thus by following the stress state evolution during the stacking, the individual and overall resultant of the stress states in the highly integrated 3D systems may be analyzed. The approach originated from our previous work – on TSV for semiconductor chips as well as on thin silicon solar cells for the emerging photovoltaics industry – using synchrotron-based X-ray microdiffraction to determine the origin and evolution of the stress states in the devices (during thermal cycling or subsequent manufacturing steps). However, during those investigations, we realized that the diffraction science is not necessarily needed for highly accurate stress state determination, in fact, just the detection of the local curvature of the surface of the monocrystalline silicon in the devices would suffice to provide for equally highly accurate stress state determination. We have demonstrated the efficacy of this approach since in our work in silicon-based photovoltaics (Tippabhotla et al. Progress in Photovoltaics 2017). As long as we have the silicon surface from each level of devices (individually and after the stacking), a laser-based system could detect the change in local curvature in high spatial resolution and hence could provide with highly accurate stress state determination. No synchrotron radiation would be needed.