Multiaxial States Research Articles

Planar biaxial testing of CXL strengthening effects

The stiffening effect of corneal crosslinking (CXL) treatment, a therapeutic approach for managing the progression of keratoconus, has been primarily investigated using uniaxial tensile experiments. However, this testing technique has several drawbacks and is unable to measure the mechanical response of cornea under a multiaxial loading state. In this work, we used biaxial mechanical testing method to characterize biomechanical properties of porcine cornea before and after CXL treatment. We also investigated the influence of preconditioning on measured properties and used TEM images to determine microstructural characteristics of the extracellular matrix. The conventional method of CXL treatment was used for crosslinking the porcine cornea. The biaxial experiments were done by an ElectroForce TestBench system at a stretch ratio of 1:1 and a displacement rate of 2 mm/min with and without preconditioning. The experimental measurements showed no significant difference in the mechanical properties of porcine cornea along the nasal temporal (NT) and superior inferior (SI) direction. Furthermore, the CXL therapy significantly enhanced the mechanical properties along both directions without creating anisotropic response. The samples tested with preconditioning showed significantly stiffer response than those tested without preconditioning. The TEM images showed that the CXL therapy did not increase the diameter of collagen fibers but significantly decreased their interfibrillar spacing, consistent with the mechanical property improvement of CXL treated samples.

A data-driven constitutive model for porous elastomers at large strains

A data-driven computational framework is established to implement surrogate constitutive models for porous elastomers undergoing large deformation. Explicit finite element (FE) simulations are conducted to compute the homogenised response of a cubic unit cell of a porous compressible elastomer, subject to a random set of imposed multiaxial strain states. The FE predictions are used to assemble a training dataset for two different surrogate models, based on simple neural networks. The first establishes a non-linear correspondence between six-dimensional strain and stress vectors; the second provides a strain energy potential from which to derive the stress versus strain response. The accuracy of the surrogate models is quantified, and their predictions are compared to those of the Hyperfoam model; it is found that the surrogate models can significantly outperform this well-known phenomenological model.

Research on meso-equivalence simulation method of freeze–thaw concrete under multiaxial loading

In view of the influence of freeze–thaw cycles (FTCs) on the spatial strength of principal stress was not considered, a meso-equivalence simulation method was developed, considering the heterogeneous characteristics of FT concrete, to accurately depict frost damage behavior, which can be used to simulate the spatial strength distribution on principal stress of concrete with FTCs. Additionally, a meso-calculation method was employed to verify the loading boundary conditions and material constitutive models. Subsequently, the effectiveness of the meso-equivalence simulation method was established by its application to the mechanical analysis of FT concrete under multiaxial loads, alongside the formulation of meso-equivalence calculation models for FT-reinforced concrete (RC) beams. The results underscore the efficacy of the meso-calculation and meso-equivalence models in capturing damage mode within concrete, subjected to FTCs under multiaxial loads. Importantly, the strength envelope derived from the calculation model and the corresponding strength criterion for the multiaxial loading limit state of FTC-affected concrete aligns consistently with test findings. Moreover, the validation of the meso-equivalence simulation method is established by comparative analysis of the mechanical behavior of RC beams under FTCs, compared with test results, which not only enhances understanding of FT response but also contributes to the advancement of durability assessment.

Retracted: Breaking Stress Criterion That Changes Everything We Know about Materials Failure

The perennial deficiencies of the failure models in the materials field have profoundly and significantly impacted all associated technical fields that depend on accurate failure predictions. The heart of this study is the presentation of a methodology that identifies a newly derived one-parameter criterion as the only general failure theory for noncompressible, homogeneous, and isotropic materials subjected to multiaxial states of stress and various boundary conditions, providing the solution to this longstanding problem. This theory is the counterpart and companion piece to the theory of elasticity and is in a formalism that is suitable for broad application. Utilizing advanced finite-element analysis, the maximum internal breaking stress corresponding to the maximum applied external force is identified as a unified and universal material failure criterion for determining the structural capacity of any system, regardless of its geometry or architecture. A comparison between the proposed criterion and methodology against design codes reveals that current provisions may underestimate the structural capacity by 2.17 times or overestimate the capacity by 2.096 times. It also shows that existing standards may underestimate the structural capacity by 1.4 times or overestimate the capacity by 2.49 times. The proposed failure criterion and methodology will pave the way for a new era in designing unconventional structural systems composed of unconventional materials.

Robust design procedure for RC plates and shell structures using developed advanced sandwich model

In recent years, a notable increase in the number of complex concrete roofs has been observed. Simultaneously, the design codes lack design approaches for such structures in which the elements are subjected to combined forces (membrane and transverse) and moments (flexure and torsion). The finite element-based design (FEBD) has been provided for these structural elements; however, it is not widely adopted for the design. Hence, there is an urgent need to fill this gap. Therefore, an automatic FEBD procedure is developed in this study based on the equilibrium consideration, named the developed advanced sandwich model (DASM). The element cracking inspection was performed according to the multi-axial compression state of concrete. Subsequently, the DASM was developed to account for the effect of transverse shear forces. The proposed design algorithm was developed using a Python script linked with ABAQUS software to perform an automatic design for all elements and to be presented as a practical design tool. Additionally, the damage-based analysis was performed as an assessment tool to demonstrate the efficiency of the proposed design procedure. This study illustrated that using the DASM reduced the steel reinforcement by up to 40% and increased the ductility by 10–15%. Also, it is observed that the ultimate capacity of the considered examples, including the solid plate and flat plate, slightly decreased by 4.1% and 1.8% (less than 5%), respectively, which hardly affects the overall response of the designed structure. Indeed, these results demonstrate the efficiency of the developed procedure. In summary, the results of this study indicate that the proposed design framework (DASM) presents a highly accurate, relatively simple, and robust procedure for designing plate and shell structures with complex geometry, where the design process can be completed on a standard personal computer in a few seconds.

Role of geometric dynamic recrystallization in nanocrystalline alloys

Nanocrystalline and near-nano-grained metals are plagued with an overall lack of ductility and formability. This is in part due to their inability to support the dislocation mechanisms or undergo the same types of transformations that conventional coarse-grained metals access inorder to increase their workability. Therefore, despite their advanced properties such as high strength, the manufacturing of such fine-grained metals, which exposes them to multi-axial states of stress in operations such as rolling, drawing, extrusion, forging, and bending, has not been possible. In this work, we address this limitation and highlight an important aspect of geometric dynamic recrystallization (GDRX) in nanocrystalline materials as a way to improve manufacturability. In particular, using two different alloy compositions and two different processing techniques, this study points to the fact that if nanocrystalline or near nano metals can be truly stabilized, they can repeatedly undergo the same types of processes that conventional coarse-grained metals endure, increasing both their formability and hence manufacturability. The results reveal that due to a large number of initial high-angle grain boundaries and large applied compressive strains, GDRX is activated in the absence of any discontinuous dynamic recrystallization (DDRX) or continuous dynamic recrystallization (CDRX). This is a unique aspect of stabilized nanocrystalline materials, as traditionally fine-grained metals are not microstructurally stable enough to accommodate such an event.

Experimental behaviour of aeronautical notched carbon fibre reinforced thermoplastic panels under combined tension-shear-pressure loadings

The demonstration of compliance of aeronautical structures with certification requirements is generally based on the building block approach, considering tests from the coupon level up to full-scale level. Coupon-scale tests are numerous and generally focused on uniaxial loading to target elementary failure modes, whereas structures are submitted to complex and combined loadings, leading to costly test campaigns on thousands of coupons. This paper considers intermediate-scale tests to study structural issues at element level. Thin flat samples (558 × 536 mm2) made of carbon fibre reinforced thermoplastic with a large, sharp central notch of 100 mm are considered. The VERTEX test rig is used to apply complex and combined loadings in tension, shear and internal pressure. Metrics are defined and computed to describe the multiaxial loading state and the failure scenario of the samples. Pressure addition clearly precipitates the first failure for shear tests but not for tension tests. With or without pressure, shear tests tend to show failure for lower equivalent fluxes than tension tests.

Creep, fatigue, and creep-fatigue crack growth behaviours of P92 steel at 600 °C

High-temperature components in power generation plant are exposed to creep, fatigue, and creep-fatigue environment during service. The components are usually under multiaxial state of stress condition. Understanding how the material behaves under these loading and environment is essential in order to sustain and keep the plant safe. The present paper aims to investigate the creep rupture and crack growth behaviours of P92 steel at 600 °C. For creep rupture test, notched bars with two different notch radii were prepared and tested under creep condition between 250 and 3500 hours at 600 °C, while the C-shaped specimen was prepared for fatigue and creep-fatigue crack growth tests. The material tested under creep condition showed notch strengthening effect where the life of notched bar specimen increased compared to smooth specimens when the net stress against creep time data was plotted. The effect was more significant as the notch radius decreased. It was also observed that the rupture life of all specimens was von-Mises stress controlled. Based on the fatigue test, it was found that the frequency in a range of 0.1 Hz–10 Hz was insignificantly affecting the crack growth rate. Under creep-fatigue, however, the material showed frequency-dependent behaviour. Observation on the fracture surface revealed that the ductile dimple associated with plasticity was dominant for all creep specimens. In addition, frequency independent specimen was associated with the transgranular fracture, thus flat appearance was evident, while fracture surface of frequency dependent specimen was roughly associated with intergranular fracture.

Advances in Cruciform Biaxial Testing of Fibre-Reinforced Polymers.

The heterogeneity and anisotropy of fibre-reinforced polymer matrix composites results in a highly complex mechanical response and failure under multiaxial loading states. Among the different biaxial testing techniques, tests with cruciform specimens have been a preferred option, although nowadays, they continue to raise a lack of consensus. It is therefore necessary to review the state of the art of this testing methodology applied to fibre-reinforced polymers. In this context, aspects such as the specific constituents, the geometric design of the specimen or the application of different tensile/compressive load ratios must be analysed in detail before being able to establish a suitable testing procedure. In addition, the most significant results obtained in terms of the analytical, numerical and experimental analyses of the biaxial tests with cruciform specimens are collected. Finally, significant modifications proposed in literature are detailed, which can lead to variants or adaptations of the tests with cruciform specimens, increasing their scope.

A complemented multiaxial creep constitutive model for materials with different properties in tension and compression

A complemented multiaxial creep constitutive model is proposed in this paper. The model is able to describe the different creep behaviors in tension and compression under a complex multiaxial stress state. To improve the convergence and adaptability for large-scale structures in engineering, a complemented constitutive model is established by complementing the shear part of the creep constitutive matrixes in principal space through a limitation process. The finite element method and forward Euler method are used to establish the numerical calculation framework. Efficient solution procedures are also proposed and implemented. Room temperature creep experiments of titanium alloy Ti–6Al–3Nb–2Zr–1Mo are performed. It is found that titanium alloy has different creep properties in tension and compression. The numerical results show that the proposed creep constitutive model and numerical calculation framework are in good agreement with the experimental results. The response of each specific creep strain component under a complex stress multiaxial state can be accurately calculated, and the different properties of the creep response in tension and compression in different directions are reflected.

Couple analysis of DIC and FEM to quantify strain fields and crack-flank displacements in structural materials under cyclic mixed-mode I/II fracture

Mixed mode cyclic fracture under multiaxial stress-strain state is critical for the generation of appropriate damage tolerance methodologies. To this end the elaborated approach is dedicated to full range of mixed mode loading for elastic-plastic plane problem. In this study, the digital image correlation (DIC) experimental results are represented as contours as well as radial strain distributions in the local system of coordinate centered at the current crack tip position along curvilinear crack path. As a complement to the DIC measurement, finite element (FE) modelling of the displacement and strain fields around the crack tip in the compact tension shear (CTS) specimen was performed in order to reproduce experimental mixed mode loading conditions. In this study, for comparison aim we used the conventional mechanism-based strain gradient (CMSG) and classical Hutchinson–Rice–Rosengren (HRR) plasticity theories to evaluate the coupled effect of the material plastic properties and the mode mixity on the crack tip behaviour. The new material model is implemented in a commercial finite element software package ANSYS 2021R1 using a user subroutine. The intention with this work was to complement the DIC measurements as well as acquire more detailed information about the local strain ahead of the crack tip and the crack opening. From a sensitivity analysis it has been established that the DIC value depends significantly from the location along the crack direction of the pair of points selected before and behind the crack tip. As a result of the FE calculations of strain distributions, the effects of both the fracture mode and the material properties are determined.

Nonlinear response under several multiaxial loading states in fibre reinforced polymer laminates

The present work includes a summary of the doctoral thesis entitled "Complexity of the structural response of fibre reinforced polymer matrix composites". This PhD thesis focused on analyzing the nonlinear mechanical response of a set of stacking sequences, with main interest in angle-ply laminates, to detail the stress-strain behaviour under a range of loading states: uniaxial tension/compression, loading-unloading-reloading tensile tests, three-point bending and plane stress states. The aim is to delve into the mechanisms of coupling and damage and their influence on the mechanical behaviour, in some cases highly nonlinear, aiming to achieve that the material withstands large strains with the consequent delay of the final failure and the increase in energy absorption capacity. Thanks to the characterization through standard testing, it is possible to calibrate material models based on progressive damage, providing two different numerical approaches which are tested against the different experimentally generated states of plane stress. In addition, it is worth mentioning the biaxial tests on cruciform specimens under different loading ratios, which provide experimental data closer to the actual response of composite structures in service. These tests, due to their greater complexity and lack of standardization, are analyzed in detail by applying numerical simulations and analytical models that ensure the validity of the results, highlighting the possible instabilities generated in the presence of compressive loads.

Examination of stress correction method of the quasi-static true stress - true strain curve considering triaxial stress state after necking initiation (2nd report)

We have proposed Analytical Iterative Uniaxial Stress Correction Method that corrects the average stress in this multiaxial state to the stress value in the uniaxial stress state by using iterative numerical simulations, and for some iron-based metals and aluminum alloys, the true stress - true strain curve in the entire strain range is obtained. In this paper, the validity of this stress correction method was verified using the design optimization / probability / statistical analysis tool LS-OPT.

Investigating the effect of printing speed and mode mixity on the fracture behavior of FDM-ABS specimens

The majority of engineering components are subjected to a multiaxial state of stress. This multiaxiality can be induced by a complex loading or complex geometry of the part. Therefore, investigating the mixed-mode fracture behavior would be an essential task to have an assessment of the fracture resistance in the mechanical components. Additive Manufacturing (AM) as one of the latest fabrication techniques has shown great benefits for design and fabrication of complex components. Among AM techniques, Fused Deposition Modelling (FDM) is one of the favorite processes that is currently used not only for prototyping but also for fabrication of complex structural components. Therefore, this research aims to evaluate mixed mode I/II fracture behavior of the FDM Acrylonitrile Butadiene Styrene (ABS) specimens with special focus on the effects of printing speed and mode mixity on fracture resistance. Four different printing speeds of 30, 50, 70, and 90 mm/s were used for fabricating the test specimens. Aside from these speeds, four different crack angles of 0, 15, 30, and 40° were used to investigate mixed-mode fracture behavior using Semi-Circular Bending (SCB) specimens. The fracture loads of the tested specimens were then predicted by employing the Equivalent Material Concept (EMC) method combined with the J-integral approach and the accuracy of the predictions were studied for various cases. Ultimately, Scanning Electron Microscopy (SEM) was used to investigate the failure mechanisms in fractured SCB specimens and link the fracture features to the fracture resistance of the FDM specimens.

Path‐dependent multiaxial fatigue prediction of welded joints using structural strain method

AbstractThe maximum shear strain's rotational conditions are investigated under multiaxial loading. The additional hardening is closely related to the relative value, rotational range, and gradual or severe rotation way of the maximum shear strain change. A novel path‐dependent loading factor is introduced to account for the nonproportional additional hardening effect. Subsequently, a computational formula of the structural strain method is established for the multiaxial loading state. The structural stress/strain terms and the proposed path‐dependent factor are introduced into the existing energy‐based fatigue parameter based on the critical plane model. The proposed fatigue prediction method provides prediction results showing that more than 68% and 87% of the data are within the scatter bands of 3 and 5, respectively, for the selected tube–flange/tube welded joints under multiaxial loading paths.

The effect of strain biaxiality on the fracture of zirconium alloy fuel cladding

• Experimental device for tubular specimen under biaxial load. • Biaxiality effect on the fracture behavior of zirconium alloy cladding. • Fracture mechnisims of zirconium alloy cladding. During a Reactivity Initiated Accident (RIA), nuclear fuel cladding experiences a multiaxial loading state in which the Pellet-Cladding Mechanical Interaction (PCMI) produces a strain biaxiality ratio (ε zz /ε θθ ) of between 0 and 1. This study examines the effect of the strain biaxiality ratio on the fracture of Zircaloy-4 fuel cladding. A new mechanical test has been developed in order to apply several levels of strain biaxiality. Digital Image Correlation (DIC) is used to measure the strain field, to identify the onset of cladding failure, and to obtain the corresponding critical loading state. Results show that the strain biaxiality has a significant effect on the hoop strain at failure, and the smallest fracture strain is obtained for nearly plane strain conditions. A model is proposed for the accumulation of damage due to plastic deformation, based on the Lode parameter of the plastic strain rate tensor. The model is used to predict the failure hoop strain as a function of the strain biaxiality ratio (ε zz /ε θθ ), and good agreement is found between the experimentally measured and predicted failure strains.

PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys

The PRISMS-Fatigue open-source framework for simulation-based analysis of microstructural influences on fatigue resistance for polycrystalline metals and alloys is presented here. The framework uses the crystal plasticity finite element method as its microstructure analysis tool and provides a highly efficient, scalable, flexible, and easy-to-use ICME community platform. The PRISMS-Fatigue framework is linked to different open-source software to instantiate microstructures, compute the material response, and assess fatigue indicator parameters. The performance of PRISMS-Fatigue is benchmarked against a similar framework implemented using ABAQUS. Results indicate that the multilevel parallelism scheme of PRISMS-Fatigue is more efficient and scalable than ABAQUS for large-scale fatigue simulations. The performance and flexibility of this framework is demonstrated with various examples that assess the driving force for fatigue crack formation of microstructures with different crystallographic textures, grain morphologies, and grain numbers, and under different multiaxial strain states, strain magnitudes, and boundary conditions.

Description of plane strain deformation of FCC crystals by a gradient theory of crystal plasticity

A higher-order gradient crystal plasticity theory applicable to three-dimensional problems is reduced to a plane strain version to be used for the analysis of the deformation of face-centered cubic (FCC) crystals at a particular orientation that the out-of-plane plastic deformation cancels out. Plane strain conditions have been frequently quoted in the literature on theoretical crack problems and experimental studies on FCC crystals since effective information on the fundamental deformation behavior of such materials under multiaxial states of stress and strain is obtained. The present plane strain theory is formulated with planar pseudo slip systems that are contractions of the crystallographic slip systems 111110 of FCC crystals. The resultant theory is purely two-dimensional, but it involves the nature of FCC crystal deformation, i.e., effects of latent hardening, cross slip, and backstresses (equivalently, internal stresses with the opposite sign) associated with the distribution of the edge and screw components of the geometrically necessary dislocations.

Fatigue analysis of airfoil under different working conditions

Within the flight mission envelope, the wing receives different aerodynamic loads in each mission stage, which results in bending and torsion alternating stress, which is prone to deformation or fatigue damage, threatening flight safety. Therefore, it is necessary to predict the fatigue life of the wing structure and maintain it in time to avoid accidents. Fluent software is used to analyze the aerodynamic load state of the wing when the lift-to-drag ratio is the largest under the three conditions of the climb, level flight, and landing, as the loading load of the wing, analyze the stress and strain of the dangerous points at each stage based on the finite element analysis platform, and determine Multiaxial fatigue state. The Brown-Miller multiaxial fatigue analysis method based on the critical surface was adopted, and the fatigue life analysis was carried out using the Fe-safe software and the Abaqus software. The results show that the minimum lifespan first appears at the root of the wing. In the Fe-safe analysis, the design life of the given wing structure is 40000 cycles, and the minimum life of the wing structure is calculated to be 58420 cycles, longer than the design life, and the life safety factor is 1.078, basically in line with the actual situation.

Low-cycle fatigue assessment of offshore mooring chains under service loading

The integrity of mooring chains is essential to the safety of a range of offshore platforms. However, mooring line failures are occurring earlier than their design lives, with a high number of these failures occurring due to fatigue. Early in the fatigue life of the component fatigue initiation processes occur, where the fatigue hotspot is sensitive to the mean load and there is plastic strain accumulation from the multiaxial stress-strain responses of the material, leading to cyclic plastic damage accumulation. The traditional SN approach suggested by mooring standards does not consider these effects, and it is proposed that this lack of consideration under low-cycle fatigue conditions is the reason for the current non-conservative fatigue assessments of mooring chains. This paper aims to develop a fatigue approach based on a critical plane multiaxial fatigue criterion for mooring chains that can consider the damage-induced by the cyclic plasticity and the mean load effect, to investigate the importance of incorporating low-cycle fatigue into the mooring chain life prediction. To develop the critical plane approach, the multiaxial stress-strain states are extracted for the critical plane at the fatigue hotspot from a finite element model of a mooring chain. This is then correlated with a fatigue life prediction provided by conventional fatigue design data. It uses a simulation of an FPSO as a case study to demonstrate the importance of low cycle fatigue, which shows that the mean load effect is significant in reducing the fatigue life for mooring chain applications, while the effect of fatigue damage-induced cyclic plasticity is limited. The fatigue damage accumulation predicted by the critical plane approach is significantly higher than that of the traditional SN approach and should be accounted for in mooring line design.