Multiaxial Loading Research Articles

Characterization of the effect of creep and multiaxial loading situations on fatigue of short fiber reinforced thermoplastics

The present study is concerned with an experimental study into the effect of superimposed creep deformation, varying local fiber orientation distributions, and more complex multiaxial stress states on the fatigue of short fiber reinforced thermoplastics. The cross-interaction of these effects is a relevant feature in all fields of applications of short fiber composites since molding related variations of the local fiber orientation states cannot be avoided for injection molded structures. Long term loading will result in a combined occurrence of fatigue and creep and thus an interaction of the related effects. The study is based on a short glass fiber reinforced polyamide 66 as reference material which is a common material grade in many automotive applications. A basic characterization is performed by means of tensile and DMA experiments. Subsequently, creep and creep fatigue experiments are performed at ambient and elevated temperatures. In order to include the effects of locally varying fiber orientation situations and locally multiaxial loading situations, the coupon experiments are complemented by experiments on breadboard specimens featuring notches, holes, and structural component related external geometries. Superimposed creep deformation might accelerate fatigue failure, however, for notched specimens might also result in an increased fatigue lifetime due to creep-induced stress relief at the notch roots. The results reveal that care has to be taken when transferring the results on idealized coupon specimens to generalized, realistic problems. The results also serve as a development and validation data base for a continuum damage mechanics material model presented in an oncoming contribution.

Integrated testing and modelling of substructures using full-field imaging and data fusion

A new integrated testing and modelling paradigm based on full-field imaging and finite element (FE) analysis that utilises full-field data fusion is proposed for structural evaluation and model validation at substructure level. The approach is developed for the assessment of a composite wind turbine blade (WTB) substructure subjected to multiaxial loading, mimicking in-service conditions, using a new reconfigurable loading rig. A steel mock-up equivalent to the WTB substructure was used to demonstrate the new experimental, numerical, full-field imaging, and data fusion approaches. Digital Image Correlation (DIC) and Thermoelastic Stress Analysis (TSA) were used to obtain the complex load response of the substructure. Strains and displacements derived from DIC were fused with numerical predictions obtained using a FE-based stereo-DIC simulator, which provided unparalleled like-for-like data comparisons. A numerical FEA solution for TSA was also obtained that accounts for heat transfer and allowed an independent means of structural evaluation. The challenges of deploying full-field imaging on the substructure scale are highlighted alongside procedures for mitigating multiple deleterious effects that are concatenated in large structures testing. It is demonstrated that high quality and fidelity experimental data can be obtained and fused with numerical models to provide a comprehensive and quantitative structural assessment at the substructure scale. It is shown that the proposed full-field data fusion efficiently reveals uncertainties in both the models and experiments. The work provides important steps to support virtual testing at higher length scales and their integration into the design, development, and certification programs of next generation, high-performance structures.

Application of the Effective critical plane approach for the fatigue assessment of ductile cast iron under multiaxial and non-proportional loading conditions

The fatigue assessment of structural components, especially made of ductile cast iron subjected to complex loading conditions, heavily relies on analyzing fatigue damage resulting from stress concentrations induced by geometric irregularities like notches and shrinkage pores. Standard methodologies, encompassing the Theory of Critical Distances (TCD), Strain Energy Density (SED), and Critical Plane (CP), have played pivotal roles in predicting fatigue strength for components featuring such irregularities. In this work, the authors explore the applicability of the Effective Critical Plane (ECP) approach on ductile cast iron notched specimens subjected to multiaxial and non-proportional loading conditions. The method focuses on evaluating the critical plane factor, after averaging the stress and strain field within a given control volume or area (i.e. defined by a control radius), centered on the critical node. The study aims to enhance the accuracy of fatigue life prediction for structural components made of ductile cast iron, thereby contributing to the improvement and practical applicability of fatigue assessment under complex loading conditions. The methodology, integrating the Smith-Watson-Topper and Fatemi-Socie CP factor, was applied to several experimental fatigue data obtained from ductile cast iron notched specimens, tested under multiaxial non-proportional loading conditions. After establishing the control radius associated with the investigated material, the method was utilized to perform a fatigue life forecast analysis on a specimen with porous defects.

Correction to “Fatigue Crack Characteristics in Gradient Predeformed Pearlitic Steel under Multiaxial Loading”

Correction to “Fatigue Crack Characteristics in Gradient Predeformed Pearlitic Steel under Multiaxial Loading”

Refined finite element analysis of helical wire ropes under multi-axial dynamic loading

Due to high tensile strength, light weight, and good flexibility, the steel wire ropes with helical structures are widely used as crucial load-bearing components in various industrial sectors such as civil engineering. They are subjected to significant vibrations caused by multi-axial dynamic loading during the service period which may eventually result in premature failures. This paper presents a refined finite element analysis method for helical wire ropes under multi-axial dynamic loading. The proposed method employs multi-directional dynamic excitations extracted from the analysis of the overall engineering systems to consider actual loading conditions. Refined finite element analysis of the entire steel wire rope under multi-axial dynamic loading is carried out for the first time based on the global-local finite element model to obtain detailed mechanical responses. The critical rope segment is represented by solid elements taking into account the helical structure, inter-wire frictional contact, slippage, and material nonlinearity, among others, and non-critical segments are simulated with beam elements in the established global-local model, which can achieve good balance between computational efficiency and accuracy. The refined finite element modeling strategy is validated via three numerical examples with comparisons against the results in the literature. The proposed method is illustrated on the suspender cable used in suspension bridges. Detailed mechanical responses and their influencing factors are examined to acquire new insights into the dynamic mechanical characteristics of typical double-helical wire rope. The present work can provide an efficient tool for the assessment of in-service engineering systems containing helical wire ropes.

Experimental study on tsunami-driven debris damming loads on columns of an elevated coastal structure

This study presents experimental findings on debris damming loads on columns of an elevated coastal structure under tsunami-like wave conditions. A total of 183 cases (140 with and 43 without debris) were tested at a 1:20 scale to understand the impact of various factors on debris-driven damming loads, including wave characteristics, structure configurations, and debris shapes. The debris impact and damming processes were observed and quantified from optical measurements, and corresponding loads were measured on the entire structure using a force balance plate and on an individual column in the front row using a multi-axial load cell. The experimental results indicated the horizontal debris damming load on the entire column structure increased by up to 3.2 times compared to conditions without debris, while the load on the individual column increased by up to 11.0 times. The total damming loads for the whole structure increased, but the load for the individual column decreased at a reduced opening ratio. The smaller debris sizes relative to column spacing showed significantly lower chances of debris damming across different column configurations. Overall, the load on the whole structure showed stronger correlations between debris damming loads and hydro-kinematic variables such as flow depth, velocity, momentum flux, and Froude number compared to the loads on the individual column. Among these variables, momentum flux emerged as the most consistently influential across all categories.

On the kinetic physical and mathematical metal creep theory controlled by thermally activated dislocation sliding

The rationale for the prospects of using the physical and mathematical theory of metal creep in creep computations is carried out by a comparative analysis of the classical phenomenological and physical and mathematical metal creep theories. On the example of the description by both theories specific results of non-stationary creep experiments and analysis of the theories equations it is shown that implementing the physical kinetic equation for the actual structural parameter of the material, namely the scalar density of immobile dislocations, makes the physical and mathematical theory universal for solving non-stationary metal creep problems with multiaxial loading, when change, including abruptly, temperature, forces and loading rates.

A New Multi-Axial Functional Stress Analysis Assessing the Longevity of a Ti-6Al-4V Dental Implant Abutment Screw.

This study investigates the impact of tightening torque (preload) and the friction coefficient on stress generation and fatigue resistance of a Ti-6Al-4V abutment screw with an internal hexagonal connection under dynamic multi-axial masticatory loads in high-cycle fatigue (HCF) conditions. A three-dimensional model of the implant-abutment assembly was simulated using ANSYS Workbench 16.2 computer aided engineering software with chewing forces ranging from 300 N to 1000 N, evaluated over 1.35 × 107 cycles, simulating 15 years of service. Results indicate that the healthy range of normal to maximal mastication forces (300-550 N) preserved the screw's structural integrity, while higher loads (≥800 N) exceeded the Ti-6Al-4V alloy's yield strength, indicating a risk of plastic deformation under extreme conditions. Stress peaked near the end of the occluding phase (206.5 ms), marking a critical temporal point for fatigue accumulation. Optimizing the friction coefficient (0.5 µ) and preload management improved stress distribution, minimized fatigue damage, and ensured joint stability. Masticatory forces up to 550 N were well within the abutment screw's capacity to sustain extended service life and maintain its elastic behavior.

Assessment of multiaxially loaded safety components with uniaxial stress state in fatigue critical sites caused by design

AbstractThe focus of this study, using results obtained with hollow specimens of the alloy Al 2024 T3 (AlCuMg2 T3) with a one‐sided bore, was to determine if, under multiaxial loading, the fatigue strength in a notch with a uniaxial stress state can simply be assessed without the application of any multiaxial strength hypothesis. In the fatigue critical location, the bore edge, only a superimposition of normal stress components, resulting from axial loading or/and torsion, occurs. In the case of out‐of‐phase loading, the resulting local uniaxial stress is even lower than the stress under in‐phase loading and leads to an increase of fatigue life to crack initiation under the non‐proportional loading, which is not observed in the case of multiaxial stressing/straining of the material itself. As the local stress state in the crack initiation site is uniaxial, the application of a multiaxial strength hypothesis, for the failure criterion of crack initiation (l=0.2 mm), is not necessary. Furthermore, the benefit of non‐homogenous stress distributions, which allow locally higher stresses than the levels given by the Woehler‐line for unnotched specimens, was underlined by considering highly‐stressed, material‐volume‐related support factors.

A Review of Fatigue Failure and Life Estimation Models: From Classical Methods to Innovative Approaches

This review paper encompasses a comprehensive exploration of fatigue failure and fatigue life estimation techniques which spans from the classical methods to new and innovative approaches. The paper looks into the limitations and advancements of these techniques and highlights their respective strengths and areas for improvement. Some of the models such as artificial neural networks and genetic algorithms exhibit clear advantages in terms of processing speed, accuracy, and adaptability to diverse materials and loading scenarios. For instance, in estimating fatigue life under multiaxial loading, the stress scale factor model emerges as a viable alternative to the critical plane-based approach, as this technique offers superior efficiency under both constant and variable amplitude loadings. Additionally, optimization algorithms such as artificial neural networks and genetic algorithms show promising potential in efficiently estimating fatigue life due to their rapid computational capabilities. Despite the notable successes achieved by these techniques, none of them can be ascribed as a universal model capable of accurately estimating the fatigue life of all materials across diverse operating conditions as each of the techniques possesses its unique strengths and weaknesses, thus, necessitating the study for a better understanding of their applicability. Hence, this paper serves as a valuable compilation of various fatigue analysis techniques, targeted at paving the way towards the development of a universal model capable of handling different materials and loading conditions.

A finite fracture mechanics approach to estimate the fatigue strength of V-notched bars under multiaxial loading

The current study aims to assess the high cycle fatigue strength of sharply V-notched bars under mixed mode I/III loading by applying the coupled Finite Fracture Mechanics (FFM) approach. FFM provides strength predictions by simultaneously satisfying a stress condition and an energy balance. A novel semi-analytical implementation of the FFM criterion is presented for the first time to account for a multiaxial fatigue loading by assuming that fracture early propagates along the notch bisector plane through a circumferential-shaped crack. To validate the model, fatigue life predictions are then compared with a large variety of experimental data related to several metals, V-notch configurations and different multiaxial loading conditions. Although the adopted hypotheses are simplistic and do not fully encompass all the physical phenomena that occur in the multiaxial fatigue process, the approach reveals to be a reliable tool for obtaining semi-analytical fatigue limit predictions useful for engineering design practice.

Capability of different multiaxial fatigue evaluation approaches on adhesively butt-bonded hollow cylinders under multiaxial loading with variable amplitudes

Currently, there is a lack of reliable approaches for the fatigue assessment of adhesively bonded joints that are subject to multiaxial stresses with variable amplitudes. To improve the current situation, investigations are made on the capability of three multiaxial evaluation approaches based on fatigue tests of adhesively butt-bonded hollow cylinders under multiaxial loading with constant phase shift and variable amplitudes.The investigated approaches are the Gough-Pollard criterion, the Findley criterion and a new method presented here, which is based on a multiaxial counting method and an invariant equivalent stress hypothesis (MCES-Method).While the Gough-Pollard criterion has a low computational effort, it does not reflect the fatigue life extending effect due to a phase shift without using a fitting parameter that is not physically based. The Findley criterion is less suitable for the investigated multiaxial stress states (with and without phase shift), although the fatigue life prediction under these load conditions is at least conservative. The MCES-Method has the highest accuracy of the methods considered. By combining research findings from published papers in the context of adhesively bonded joints, all investigated load scenarios are estimated with high prognosis quality.

Research on probability model and reliability of multiaxial fatigue life based on Huffman model

Various uncertainties are widely presented in engineering problems, such as material properties, loads, geometries, etc. Research has indicated that there is a significant relationship between the dispersion of fatigue life and the material properties. Therefore, it is necessary to study the effect of the parameter distribution of the material on the uncertainty of fatigue life. However, there are very few studies involving the distribution of fatigue performance parameters {σf’, εf’} of materials. In this paper, a probability framework of multiaxial fatigue life prediction based on the uncertainty of material parameters {σf’, εf’} was established, which focuses on quantifying the distribution of material parameters {σf’, εf’} based on the Huffman model. Next, based on the Fatemi-Socie (FS) model and the distribution of strain life parameters {σf’, εf’}, the probability field of Δγeq/2-N curves were obtained, and experimental data were distributed around the predicted average life. In addition, a time-dependent multiaxial fatigue reliability analysis method based on the Palmgren-Miner rule and P-Δγeq/2-N was derived, and the reliability curves were obtained under four multiaxial loading cases.

Cemented sand under hollow cylinder multiaxial loading

Improvement of granular soils’ mechanical properties can be achieved by the addition of bonding agents. In this research, low amount of Portland cement was added to a sand, and its beneficial shear strengthening effects were evaluated under a range of multiaxial stress paths. The influence of the orientation of the principal axes of stress and strain on the stress–strain response and failure of cemented sand has only been scarcely investigated. Therefore, this experimental investigation reports the results of a series of consolidated drained hollow cylinder torsional tests with constant principal stress path direction, ασ, varying from 0° to 90°. Results were compared with the shear behaviour of the uncemented sand tested under similar loading conditions. Results show that the addition of cement to the sand matrix increases the soil strength for all multiaxial stress path directions. The suitability of two multiaxial strength criteria for reproducing the shape of the failure envelope as a function of the orientation of principal stress axis ασ has also been analysed.

Failure criterion and damage evolution of high-strength geopolymer concrete under compression-shear composite loading after high temperatures

Geopolymer concrete (GPC) holds significant potential for building fire safety design due to its green, low-carbon, and high-temperature resistant properties. In practical applications, concrete structures often face multiaxial composite loads. Therefore, investigating the composite stress performance of high-strength geopolymer concrete (HGPC) after exposure to high temperatures is crucial for assessing structural damage and enhancing fire prevention measures. This paper examines the compressive shear performance of HGPC at various temperatures T (20°C, 200°C, 400°C, 600°C) and stress ratios k (0.15, 0.3, 0.45, 0.6). The study analyzes failure patterns, shear load-displacement curves, shear strengths and their components, and peak shear deformation. Failure criteria are proposed to describe the damage patterns of HGPC under compressive shear loading after high temperatures. Additionally, the damage evolution process is evaluated using the energy method. The results show that HGPC damage surfaces penetrate the coarse aggregate at room temperature under compression-shear composite loading but shift to the aggregate-mortar interface at 600°C. Shear stiffness, peak shear strength, and residual strength increase with higher stress ratios but decrease with rising temperatures. Temperature affects peak shear strength by over 95 %, significantly more than the stress ratio. The shear strength decreases more slowly than compressive strength up to 400°C but more rapidly beyond 400°C. The cohesive strength of HGPC decreases with increasing stress ratio under different temperatures, while contact friction strength exceeds 50 % of peak shear strength. Shear dilation strength generally increases, then decreases, peaking at k = 0.45. The failure criterion based on the modified twin shear unified strength theory aligns best with experimental results. Furthermore, an increased stress ratio retarded the development of damage evolution, which was first accelerated and then slowed with rising temperature.

Is suture-based cerclage biomechanically superior to traditional metallic cerclage for fixation of periprosthetic femoral fractures: A matched pair cadaveric study

BackgroundWhile traditional metallic cerclage remains the primary method in clinical application, non-metallic cerclage systems have recently gained popularity due to low risks of soft tissue irritation and bone intrusion. The objective of this study was to assess the performance of a novel non-metallic suture-based cerclage in comparison to traditional metallic cerclage cables for fixation of periprosthetic femoral fractures. MethodsAn extended trochanteric osteotomy was performed on eight pairs of cadaveric femora, followed by reduction using either metallic cerclages (Group I) or the suture-based cerclage (Group II). A modular tapered fluted stem was then implanted in each specimen. The fragment translation during canal preparation and stem implantation was quantified using laser-scanning. Subsequently, each specimen underwent 500 cycles of multiaxial loading, with fragment translation and stem subsidence measured using a motion capture system. FindingsFollowing stem implantation, specimens in Group II exhibited a significantly greater lateral fragment translation (466 μm vs 754 μm, p = 0.017). However, there were no significant differences in anterior and distal translation between groups (p > 0.05). During multiaxial loading, the average stem subsidence in Group I was 0.36 mm (range, 0.04–1.42 mm), compared to 0.41 mm (range, 0.03–1.29) in Group II (p > 0.05). No significant difference was found in fragment translations between the two groups (p > 0.05). InterpretationThe suture-based cerclage system exhibited comparable biomechanical performance in fixation stability to conventional metallic cerclage cables. Yet, it was associated with a larger residual lateral gap between the fragments following stem implantation. Ultimately, the choice of fixation method should account for multiple factors, including patient characteristics, surgeon preference, and bone quality.

Nonlinear behavior simulation of ceramic-matrix composites using constituent-volume homogenization method

The nonlinear behavior of ceramic-matrix composites is affected by interface debonding and fiber pull-out. In this paper, we propose the constituent-volume homogenization method (CVHM) to replace the conventional bundle homogenization method, in order to model the behavior of trans-element debonding in woven structures using finite element method. Based on the CVHM, we establish the elastic relation of the relative motion between the fiber and the matrix, and the elastic constitutive relations for the constituents. Methods have also been developed to calculate the microscopic local stress of bundle under pull-out and multiaxial loads. Based on the above studies, we develop a procedure to analyze the stress-strain relation of braided composites using the CVHM. To validate the proposed method, we estimate the nonlinear behavior of the 2D plain-weave ceramic-matrix composites and compare the results with experimental data. The influence of interface shear strength (ISS) and the fiber ultimate tensile strength (UTS) on the nonlinear behavior is investigated.

Characterization of woven composite material under multiaxial loading regimes using FE-based stereocorrelation

In this paper, woven glass fiber composite samples were subjected to three different cyclic loading histories (i.e., tensile, shear and combined loading at 45° via the Modified Arcan Fixture. During the experiments, the samples were monitored by a stereovision system. Finite Element based stereocorrelation was used to measure the displacement and strain fields. The analysis of the experiments revealed different damage mechanisms. Furthermore, for the 45° experiment, the highest strain levels were reached, whereas for the tensile test, the highest stress levels were achieved.

Stress fracture of bone under physiological multiaxial cyclic loading: Activity-based predictive models

While it is known that excessive accumulation of fatigue damage from daily activities contributes to fracture, a model of bone failure under physiologically relevant multiaxial cyclic loading needs to be developed in order to develop effective management strategies for stress or fatigue fractures. The role of strain-induced damage from repetitive loading is a strong candidate for such a model, as cycles of mechanical loading leading to failure can be measured directly. However, this approach has been limited by the restrictions of uniaxial loading models, which often overestimates the fatigue life of bone and suggests that bone will only break well beyond the realistic limits of exercise. To address this gap and develop a physiologically relevant model, our study leverages the power of four commonly used engineering failure criteria as a model for multiaxial loading using a cohort of human tibiae from cadaveric donors (age range 21–85 years old). Four failure criteria (Von Mises, Tsai-Wu, Findley critical plane, and maximum shear strain) were found to be effective in vitro models of tibial fracture when age groups of donors were combined (r2 > 0.84) and stratified (younger: 21–52-years-old versus older: 57–85-years-old) (r2 > 0.83) (p < 0.001). Each failure criterion displayed distinctly lower fatigue curves for the older age group. The maximum shear strain model was used to determine the efficacy of this approach to predict fatigue fractures in humans using published in vivo data from human volunteers. Consistent with in vivo observations in general population, the model demonstrated failure at 5000 to 200,000 loading cycles depending on activities such as jumping, sprinting, and walking, with a 3-fold reduction of fatigue life in older donors. These findings dramatically improve estimates of fatigue life under repetitive loading and demonstrate how age-related changes in bone significantly increase its propensity for fatigue-induced fractures.

The Role of Polarization in Multiaxial Mechanical Loadings Sensing Using Fiber Bragg Gratings

The Role of Polarization in Multiaxial Mechanical Loadings Sensing Using Fiber Bragg Gratings