Multiaxial Loading Conditions Research Articles

Predicting the mechanical response of the vaginal wall in ball burst tests based on histology.

A histologically motivated (HM) coefficient that establishes a link between tissue's microstructure and material model through histological data is used in the prediction of the mechanical properties of vaginal tissue that is subjected to multiaxial loading conditions. Therefore, the material parameters were based on an HM coefficient obtained from tensile testing and histological data of comparable tissues. Uniaxial tensile test data and histological data were collected from three groups of sheep at different time points in their life cycle, including virgins, pregnant, and parous ewes. From this data, a correlation between material parameters and histological data was obtained. Spherical indentation (ball burst [BB]) tests were then performed in specimens with similar tissue structure. The histological data of these samples were used in conjunction with the correlations already established for the uniaxial samples data, to define the material parameters of the BB samples. Mechanical properties of the BB specimens were predicted through basic histology and using finite element modeling (FEM) simulations, without direct mechanical measurements. The predicted force and displacement values of the FEM simulation displayed a good correlation with the experimental (BB) testing results. No fitting of the BB results was performed. In this way, the use of uniaxial tests coupled with useful histological information offers a promising approach to predicting macroscopic material behavior under multiaxial loading conditions in biomechanics.

An upscaling approach for micromechanics based fatigue: from RVEs to specimens and component life prediction

A novel approach has been developed to estimate fatigue life at the specimen/component level from the simulation of relatively small Representative Volume Elements (RVE) of the polycrystalline microstructure. This technique estimates the statistical distribution of fatigue lives under general multiaxial loading conditions accounting for both microstructure and specimen size. The model relies on computational homogeneization where the crystal behavior follows a crystal plasticity model and simulations are performed using a FFT based solver. The simulation of the cyclic response of a set of different RVEs provides the statistical distribution of Fatigue Indicator Parameters for that RVE size, which can be accurately represented by an extreme value distribution as the Gumbel distribution. This distribution is upscaled to the actual size of the specimen or component of interest using a weakest link approach and is finally transformed into a distribution of fatigue lives using a simple fatigue-life expression fitted with experiments. The framework proposed estimates fatigue lives of specimens with millions of grains from the results obtained with RVEs containing only hundreds of grains and is able to reproduce the specimen size effect on fatigue life. The approach is first numerically validated and then used to predict the statistical distribution of fatigue life of a polycrystalline Ni-based superalloy showing very accurate results.

Numerical modelling of the ratchetting effect under uniaxial and multiaxial loading conditions

Numerical modelling of the ratchetting effect under uniaxial and multiaxial loading conditions

Evaluation of different strain-based damage criteria for predicting the fatigue life of friction stir spot-welded joints under multi-axial loading conditions

In this article, fatigue life of dissimilar friction stir spot welds in Cross-Tension and Lap-Shear specimens is predicted using a number of fatigue damage criteria. The results revealed a relatively good correlation between predicted fatigue crack initiation lives and experimental data. Also, it has been shown that in the whole range of applied load levels, the least discrepancy between predicted fatigue lives and experimental data is related to the Smith–Watson–Topper criterion. Finally, an excellent agreement was found in predicting the location of the crack tips using the Fatemi–Socie criterion in both types of specimens.

A spectral fatigue method incorporating non-proportional multiaxial loading

A frequency domain method incorporating multiaxial non-proportional loading conditions is presented in this paper. The non-proportionality is modelled by implementing a multiaxial cycle counting procedure of path dependent maximum range\\moment of load path proposed recently by Mei and Dong (2016) in frequency domain through a formulation of an effective equivalent structural stress (EESS) transfer function. Additionally, the formulation through transfer functions and the treatment of phase differences between normal and shear stresses represents a unique approach to multiaxial fatigue analysis in frequency domain. The numerous test studies performed on a representative structural detail in marine structure showed rather promising results. Reasonable multiaxial fatigue damage estimations have been obtained through the developed method by comparing the fatigue damages computed with time domain methods.

A simplified continuum damage mechanics based modeling strategy for cumulative fatigue damage assessment of metallic bolted joints

Fatigue damage and consequent failure account for the majority of the failure in metallic bolted joints of aerospace and mechanical engineering applications. In this paper, we present a cumulative fatigue damage evaluation approach for metallic bolted joints based on a combined continuum damage mechanics (CDM) theory and the critical plane approach. The analysis approach is applicable to both proportional and non-proportional multiaxial loading conditions. A cycle jumping based algorithm with a fixed damage evolution rate is adopted for efficient numerical approximation. To further increase the computational efficiency, a simplified modeling strategy is developed to avoid the expensive calculation of the full loading-unloading cyclic stress history. The proposed approach is established based on the assumption that a linear relation can be established between the minimum and maximum stress tensors in high-cycle fatigue analysis and is thus only dependent on the maximum stress states. A set of examples including a notched specimen and a metallic bolted joint with pre-tension are simulated to demonstrate the simplified approach.

Numerical evaluation of surface welding residual stress behavior under multiaxial mechanical loading and experimental validations

Welding residual stresses have been always seen as a threat to the integrity of structures and components during service loadings. However residual stresses could partially or even totally relax under thermal or mechanical external loads if the sum of residual stresses and load stresses exceeds the material yield strength. If the stable portion of residual stresses after relaxation is still significant, care must be taken that residual stresses, similar to mean stresses, could shift the applied stress range. Accordingly, for a reliable structural integrity assessment an accurate insight into the stable residual stress field is essential.A three-dimensional FE model was implemented in software ABAQUS in order to study the relaxation and redistribution of welding residual stresses in a bead on tube weld under multiaxial mechanical loading. The predefined field of residual stress was initially calculated through a welding simulation in software SYSWELD. To verify the numerical simulations, a couple of tubular samples made of steel S355J2H were TIG welded and then mechanically loaded at different applied load levels. The surface residual stresses were measured by means of x-ray diffraction (XRD) in the as-welded condition and also after applying the mechanical loads for further comparisons. Pure torsion and multiaxial tension-torsion loading conditions in the form of quasi-static loading-unloading were investigated experimentally. The predicted welding residual stress relaxation conforms well the measurement results. The accordance between the numerical and experimental relaxation results confirmed the validity of the FE model. The validated model was then used to evaluate numerically the behavior of residual stresses under cyclic torsion loading with regard to the influence of the used material model. Based on the results, for such a material, the major relaxation occurs during the first cycle due to the monotonic yielding but further relaxation may take place in the upcoming cycles due to the accumulation of plastic strains.

Energy dissipation in functionally two-dimensional phase transforming cellular materials

Phase Transforming Cellular Materials (PXCMs) are periodic cellular materials whose unit cells exhibit multiple stable or meta-stable configurations. Transitions between the various (meta-) stable configurations at the unit cell level enable these materials to exhibit reusable solid state energy dissipation. This energy dissipation arises from the storage and non-equilibrium release of strain energy accompanying the limit point traversals underlying these transitions. The material deformation is fully recoverable, and thus the material can be reused to absorb and dissipate energy multiple times. In this work, we present two designs for functionally two-dimensional PXCMs: the S-type with four axes of reflectional symmetry based on a square motif and, the T-type with six axes of symmetry based on a triangular motif. We employ experiments and simulations to understand the various mechanisms that are triggered under multiaxial loading conditions. Our numerical and experimental results indicate that these materials exhibit similar solid state energy dissipation for loads applied along the various axes of reflectional symmetry of the material. The specific energy dissipation capacity of the T-type is slightly greater and less sensitive to the loading direction than the S-type under the most of loading directions. However, both types of material are shown to be very effective in dissipating energy.

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

AbstractIn engineering practice, it is generally accepted that most of components are subjected to multiaxial stress‐strain state. To analyse this complicated loading state, different types of specimens of 2A12 (2124 in the United States) aluminium alloy were tested under multiaxial loading conditions and a new multiaxial fatigue analysis method for the state of three‐dimensional stress and strain is proposed. Elastic‐plastic finite element method (FEM) and a proposed vector computing method are used to describe the loading state at the critical point of specimen, by which the parameter ΓT is calculated at the new defined subcritical plane to consider the effect of additional cyclic hardening. Meanwhile, the principal equivalent strain is still calculated at the traditional critical plane. The new damage parameter is composed of different process parameters, by which the dynamic path of strain state, including loading environments and material properties, are fully considered in one loading cycle. According to experimental verifications with 2A12 aluminium alloy, the results show that the proposed method shows satisfactory, accurate, and reliable results for multiaxial fatigue life prediction in the state of three‐dimensional stress and strain.

A high-performance multiscale space-time approach to high cycle fatigue simulation based on hybrid CPU/GPU computing

A multiscale space/time computational framework for high cycle fatigue (HCF) life predictions is established by integrating the extended space-time finite element method (XTFEM) with a multiscale progressive damage model. While the robustness of the multiscale space/time method has been previously demonstrated, the associated high computational cost remains a critical barrier for practical applications. In this work, a novel hybrid iterative/direct linear system solver is first proposed with a unique preconditioner. Computational efficiency is further improved by taking advantage of the high-performance computing platform featuring hierarchy of the distributed- and the shared-memory parallelisms using CPUs and GPUs. Robustness of the accelerated framework is demonstrated through benchmark problems. It is shown that the serial version of the hybrid solver is at least 1–2 orders of magnitude faster in computing time and cheaper in memory consumption than the conventional sparse direct or iterative solver, while the parallel version efficiently handles XTFEM stiffness matrix equations with over 100 million unknowns using 64 CPU cores. Optimal speedups are achieved in the parallel implementations of the multiscale progressive damage model using either CPUs or GPUs. HCF simulations on 3D specimens are performed to quantify key effects due to mean stress and multiaxial load conditions.

Development of scanning electron microscope-compatible multiaxial miniature testing system

Knowledge of deformation and failure mechanisms at micro- to nano-length scales is important for the prediction of material behavior as well as the development of new materials with desired properties. In situ multiaxial testing with scanning electron microscopes (SEM) can reveal physical deformation mechanisms under realistic multiaxial loading conditions. Although in situ SEM testing has gained traction in recent years, there is currently no multiaxial in situ SEM testing stage available with axial-torsional loading capabilities which can generally be used in any SEM. In this study, we report the development of a multiaxial miniature testing system (MMTS) with a unique capability for performing axial-torsional testing of a tubular specimen with a 1–2 mm outer diameter, inside most SEMs. The different challenges of developing a multiaxial in situ SEM testing stage, such as small load frame size, appropriate specimen position, high vacuum compatibility of MMTS load frame components, as well as the development of installation accessories, were addressed. A custom SEM stage door was developed for the MMTS load frame. Verification tests have confirmed the successful development of the MMTS for in situ SEM testing. In addition, digital image correlation was used with recorded SEM images during the test to determine the surface strain.

Development of new critical plane model for assessment of fatigue life under multi-axial loading conditions

The present work is aimed at development of new critical plane model based on envelope of strain energy density as fatigue damage parameter. This model eliminates the use of hypotheses for evaluation of resultant shear. The fatigue life has been predicted and compared with test life for a large set of multi-axial test data available on SA 333 Gr. 6, 16MnR, S460N and 7075-T651 Al materials. Predicted fatigue life is in good agreement with test life. The predicted crack initiation orientations are also comparable with the measured angles.The shortcomings of existing models have been brought out.

A Multiaxial Theory of Double Network Hydrogels

The incorporation of a stiff and brittle phase into a soft and flexible polymer network makes double network hydrogels remarkably tougher than the conventional one. It also induces a stress softening in cyclic loading, which is seemingly identical to that of filled rubbers. Therefore, material models proposed for double network hydrogel are mostly based on continuum damage theories of filled elastomers. However, recent experimental studies clearly distinguish double network hydrogels from filled elastomers by the damage cross-effect in multiaxial deformation. In this paper, a micromechanical model for double network hydrogels under multiaxial deformation is proposed on the basis of the analytical network-averaging concept. Accordingly, the directional fracture of the first network results from cumulative damage in all directions. Furthermore, the strong interpenetration of the two networks is taken into account. The proposed analytical model includes very few physically motivated material constants and demonstrates excellent agreement with comprehensive experimental data of double network hydrogels under multiaxial loading conditions.

Identification of the material behavior of adhesive joints under dynamic multiaxial loadings

This paper presents a numerical inverse method dedicated to the characterization of adhesive joints under multiaxial and dynamic loading conditions. The properties under scrutiny are the constitutive behavior of the joint as well as the final fracture surface. The experimental setup consists of a Split Hopkinson Pressure Bar system and local strain measurements performed by Digital Image Correlation (DIC) as well as a novel specific sandwich specimen denoted as DODECA. The direct numerical model is an original Finite Element computation combining 3D and 1D elements for an optimal handling of wave reflection and interfaces. It further provides an optimal compromise between computation time and accuracy. The identification method is based on the Finite Element Model Updating method (FEMU). Material parameters are identified for three different multiaxial loading conditions and presented as yield and fracture surfaces in the space of equivalent von Mises stress vs. hydrostatic stress. As a complement of the analysis, uncertainties and confidence of the identified parameters are estimated with precise qualitative tools.

A CPFEM based study to understand the void growth in high strength dual-phase titanium alloy (Ti-10V-2Fe-3Al)

High strength titanium alloys are generally used in widespread applications ranging over, but not limited to biomedical, aerospace, automotive, marine, oil and gas, and energy. Besides other manufacturing processes, forming is one of the common manufacturing process used to produce components out of these alloys. Forming processes generally involve significant plastic deformation of material under complex multiaxial loading conditions. Titanium alloys undergo considerable plastic deformation before failure while later is governed by the mechanisms of void nucleation, growth and coalescence. A number of titanium alloys used for high strength applications are multiphase alloys having α and β phases. It has been reported in the past that the voids tend to nucleate on the phase boundaries. This study is focused on understanding the growth of the nucleated voids at two selected locations in a dual phase titanium alloy (Ti-10V-2Fe-3Al); globular α phase (hexagonal closed pack, HCP) and at the interface of lamellar α and β phases (α - HCP and β – body centred cubic, BCC). This is one of the very few 3D representative volume element (RVE) study of void growth in single crystal titanium (HCP), carried out using crystal plasticity finite element modelling (CPFEM) at higher triaxialities (ranging 1/3-3) and the first one on the interface of bicrystals with different crystal symmetry. The effects of initial porosity, crystal orientation and the Lode parameter on void growth in single crystal (α-HCP) has been studied and it is found that they affects void growth considerably. An effort has been made to explain the physics behind it. In the second part, growth in a void at the interface of two distinct single crystals (α - HCP and β –BCC) was studied. The effects of Burgers orientation relationship (BOR) variant of the two phases, initial porosity, and phase boundary inclination (PBI) on void growth is investigated. It is found that the PBI has a very strong impact on the void growth. The effect of initial porosity is similar to the void growth in single crystals. Choice of BOR variant affected the void growth in moderate triaxialities.

On the interaction of normal and shear stresses in multiaxial fatigue damage

AbstractOne of the important issues in assessing multiaxial fatigue damage is interactions between different components of stress such as normal and shear stresses. The present study investigated this interaction effect on the fatigue behavior of materials with shear failure mode when subjected to multiaxial loading conditions. A method is introduced to model this interaction based on the idea that two types of influence are caused by the normal stress acting on the critical plane orientation. These two types of influence are affecting roughness induced closure, as well as fluctuating normal stress which affects the growth of small cracks in mode II. Shear‐based critical plane damage models which use normal stress as a secondary input, such as FS damage model, could then use the summation of these terms. In order to investigate the effect of the method, constant amplitude load paths with different levels of interaction between the normal and shear stresses, as well as variable amplitude tests with histories both taken from service loading conditions and generated using random numbers were designed for an experimental program. The proposed method was observed to result in improved fatigue life estimations where significant interactions between normal and shear stresses exist.

Impact of in situ nanomechanics on physical metallurgy

Abstract

Large scale 3-dimensional atomistic simulations of screw dislocations interacting with coherent twin boundaries in Al, Cu and Ni under uniaxial and multiaxial loading conditions

Large scale 3D atomistic simulations are performed to study the interaction between a curved dislocation with a dominant screw character and a Coherent Twin Boundary (CTB). Three FCC metals (Al, Cu and Ni) are addressed using 6 embedded-atom method (EAM) potentials. The reaction mechanisms are studied first under uniaxial stress showing that transmission mechanism and critical transmission stress depend on the material considered and differ from results reported in quasi- 2D simulations. Then, the influence of multiaxial stresses including shear components in the CTB is investigated. It is shown that the influence of the loading conditions, which can be represented in terms of the Escaig stress, is material dependent. In Al and Cu, the critical transmission stress is largely dependent on the Escaig stress while only mildly for Ni. The presence of a shear component in the CTB tends to increase the critical transmission stress for all three materials. The absorption and desorption mechanisms of the screw dislocation are correlated with a potential energy barrier.

Evaluation of a phenomenological elastic‐plastic approach for magnesium alloys under multiaxial loading conditions

AbstractMagnesium alloys are greatly appreciated due to their high strength to weight ratio, stiffness, and low density; however, they can exhibit complex types of cyclic plasticity like twinning, de‐twinning, or Bauschinger effect. Recent studies indicate that these types of cyclic plastic deformations cannot be fully characterized using the typical tools used in cyclic characterization of steels and aluminium alloys; thus, it is required new approaches to fully capture their cyclic deformation and plasticity. This study aims to propose and evaluate a phenomenological cyclic elastic‐plastic approach designed to capture the cyclic deformation of magnesium alloys under multiaxial loading conditions. Series of experimental tests were performed to characterize the cyclic mechanical behaviour of the magnesium alloy AZ31BF considering proportional loadings with different strain amplitude ratios and a nonproportional loading with a 45° phase shift. The experimental results were modulated using polynomial functions in order to implement a cyclic plasticity model for the AZ311BF based on the phenomenological approach proposed. Results show good correlations between experiments and estimates.

A novel approach to model fretting-fatigue in multiaxial and non-proportional loading conditions

This article proposes a new method for determining the behavior and service life of contact areas of parts subjected to fretting-fatigue. The first objective was to be able to predict the service life of contact parts with various curvature radii from fretting-fatigue tests on laboratory test geometries such as cylinder-plane. The second objective was to be able to predict the service life for variable amplitude and multiaxial loading conditions from laboratory tests in constant amplitude loading conditions.