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Investigation of the strain rate and stretch level dependent behavior of elastomeric nanocomposites in complex uniaxial tests under finite strains

The mechanical behavior of elastomeric nanocomposites in experiments with nested stress-strain cycles and cyclic tests with increasing strain amplitude were considered. In our proposed testing procedures, long time stops at each stage of the change in loading direction were of great importance. This revealed two significant features of the behavior of elastomeric nanocomposites that have received little attention. It was shown that material softening (the Mullins effect) should be considered not only in the elastic part of the Cauchy stress tensor, but also in its dissipative part. The second peculiarity was the difference between the characteristic relaxation time at loading and the characteristic relaxation time at unloading observed in the experiments.This paper focuses on the behavior of highly-filled elastomeric materials based on different matrices (styrene-butadiene rubber (SBR) and nitrile-butadiene rubber (NBR)) and with different concentrations of carbon black (CB) or a combination of two fillers (CB and purified multi-walled carbon nanotubes (MWCNTs)).A mathematical model of the viscoelastic behavior of elastomeric nanocomposites under finite strains was proposed. It takes into account the peculiarities of the behavior of highly filled elastomers observed in the experiments. The specificity of the model consists in a new variant of the form of the free energy potential. It was shown that the new model satisfies the thermodynamic inequality, which is a consequence of the first law of thermodynamics and the second law in the form of the Clausius-Duhem inequality. A good agreement between theoretical calculations and experimental data was obtained.

Atomistic investigation on the anisotropic elastic and plastic responses of nanotwinned metals

Introducing nanotwins into materials is one of the important strengthening methods to achieve the synergistic improvement of strength and ductility. The anisotropic mechanical behaviors of nanotwinned materials have been widely studied by experimental and computational methods. The dominant deformation mechanisms about dislocation slippages can be effectively switched among three modes, and controlled by twin spacing and the angle between twin boundaries (TBs) orientation and loading direction. Particularly, most of previous researches mainly focused on the deformation mechanisms during the plastic flow stage and researchers paid little attention on the anisotropic characteristics of TBs at the elastic stage which are also essential to manufacture the high-performance materials. Therefore, this study is aiming to systematically investigate the anisotropic effect of TBs both at the elastic and plastic stages within the single crystalline or polycrystalline systems by molecular dynamics (MD) simulations. It is revealed that, when the loading direction is parallel to twin planes, the introduction of TBs in single crystalline models will significantly affect the characteristics of atomic bond rotation and elongation dominated elastic deformation, which can alter the Poisson’s ratio of materials, generate elastic-softening behavior and inhomogeneous elastic deformation. At the plastic flow stage, the deformation mechanism transforms from trans-twin dislocation slippage into the coexistence of Hard Mode I and threading dislocation slippage (Hard Mode II) when the loading direction changes from parallel to perpendicular direction with respect to TBs. Moreover, the dislocation segments at the conjunction of trans-twin dislocation play a momentous role in enhancing material strength. The results for polycrystalline models are consistent with that of single crystalline ones. These findings are expected to be beneficial for the development of high-performance nanostructured materials for structural and functional applications by strain engineering and defect regulation.

Comparison analysis of moisture-dependent orthotropic elasticity between earlywood and latewood in Chinese fir using digital image correlation

Given its orthotropic and hygroscopic nature, Chinese fir exhibits varying mechanical behaviors in earlywood and latewood due to its naturally inhomogeneous structure when exposed to changes in loading direction and given moisture content (MC) range from 7.9 % to 16.1 %. In this study, we combined micro-tensile testing and the digital image correlation (DIC) technique to derive the moisture -dependent orthotropic elastic constants, i.e., Young’s modulus (E), Poisson’s ratio (ν) and shear modulus (G) for both earlywood and latewood in Chinese fir. The findings revealed that when loading in the parallel direction, the restraining effect caused by latewood on earlywood resulted in a difference compared with loading in series. Interestingly, the loading direction impacted the restraining effect more significantly than MC. Additionally, both Young’s modulus and shear modulus exhibited decreases with increasing MC within above range for both earlywood and latewood. Notably, the Young’s modulus of earlywood showed a higher sensitivity to MC variations compared to latewood. However, Poisson’s ratio did not consistently correlate with MC within above range in all orthotropic directions. A three-dimensional coordinate system visualization of the compliance parameters highlighted the differing sensitivities of earlywood and latewood to moisture. The independent moisture-dependent elastic components of earlywood and latewood derived in this study extended the moisture-dependent mechanical model of wood, offering theoretical guidance for the practical application of Chinese fir and other wood species.

Size effect and underlying microstructural mechanism in cyclic deformation behavior of nickel-based superalloy sheet

The nickel-based GH4169 superalloy is widely used in the aerospace field, which has desirable oxidation resistance and strength in extreme environments. However, the size effect and underlying microstructural mechanism in the cyclic deformation of the GH4169 sheet are still not fully elucidated, which affects the forming accuracy precision of thin-walled components. To this end, the cyclic mechanical properties and microstructural evolution of the GH4169 sheets with different thicknesses and grain sizes were systematically investigated via cyclic shearing tests. The superalloy sheet exhibits obvious early re-yielding, instantaneous softening and permanent softening during the cyclic deformation and these cyclic deformation behaviors are obviously affected by size effect. To rationalize the cyclic mechanical responses and size effect, transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD) tests were conducted. The results indicated that the dislocation slip patterns are principally planar array slip and cross slip in the cyclic shearing deformation. Meanwhile, the annihilation of unstable dislocation and the presence of carbides led to the instantaneous softening. Moreover, the change of loading direction, the reduction of texture strength, the proportion of low-angle grain boundary (LAGB), and geometrically necessary dislocation (GND) density together result in the occurrence of permanent softening. Based on the comparative analysis of the microstructure evolution of superalloy sheets with different size factors, the underlying mechanism of size effect on cyclic deformation was clarified. The findings in the research combine the cyclic mechanical response and microstructure evolution closely in the cyclic deformation of superalloy sheets and deepen the understanding of size effect under complex loading paths.

Influence of changing loading directions on damage in sheet metal forming

The impact of the stress state on damage evolution, fracture behavior, and product performance is well understood for proportional loading. However, many complex sheet forming operations involve non-proportional loading, which affect the material's hardening and fracture characteristics. This study investigates the influence of a loading direction change on damage evolution in a dual phase steel DP800. Specimens are pre-strained by tensile tests and subsequently loaded in either the same or orthogonal direction to the initial pre-strain direction by additional tensile tests and bending tests. Damage quantification by scanning electron microscopy reveals lower damage evolution after an orthogonal change of loading direction in contrast to monotonic loading directions. The load paths, defined as a history of triaxiality and Lode parameter during loading, are identified numerically under consideration of kinematic hardening. Since kinematic hardening leads to higher triaxialities after orthogonal changes, the load path is not the dominant influence on damage. A possible explanation for the experimental results is the void characteristics after tensile load. After the pre-straining in tensile test, voids are oriented orthogonally to the tensile direction and located between hard martensitic phases. The influence of this morphology on subsequent void growth is illustrated by a simulation verifying that an orthogonal change of loading direction results in void shrinkage, while monotonic loading directions lead to further void growth.

Failure Behavior and Surrounding Soil Stress Responses of Suction Anchor in Low-Strength Muddy Clay

Anchorage failure of a suction anchor is more likely to occur in low-strength muddy clay. This paper focuses on the failure behaviors of suction anchors and muddy clay stress responses. The centrifugal model test was used to study the loading processes of suction anchors with various pulling angles. Firstly, the multi-stage developing process of anchoring force was analyzed according to the test results. Numerical modeling was used to validate the test results. The displacement of the suction anchor and muddy clay soil were analyzed using the numerical results. Then, the numerical and testing results were compared to analyze the horizontal soil pressure responses around the suction anchors. It was found that the change in loading direction affected the distribution and development of soil stress. The horizontal soil resistance played a crucial role in improving the bearing capacity. The soil stress variation and anchor displacement revealed that the suction anchors exhibited multi-attitude coupling movement during the inclined pulling. The vertical pulling suction anchor showed shear–slip failure behaviors, while the inclined pulling suction anchors showed compression–shear–slip coupling failure behaviors. The results of this study provide insight into the interaction mechanism between suction anchors and muddy clay, serving as a reference for the design and application of suction anchors.

Deformation effect of melt pool boundaries on the mechanical property anisotropy in the SLM AlSi10Mg

The effect of microstructure characteristic on the anisotropy of mechanical properties has been studied for a selective laser melt (SLM) AlSi10Mg material. The cell structure and fine grains at the melt pool boundaries (MPBs) are gradually eliminated by different heat treatment processes. Althought the cell structure of MPB has been eliminated, it is found that the mechanical properties of the transverse specimen and longitudinal specimen are still different due to the heterogeneity of grain. In the process of plastic deformation, when the tensile direction perpendicular to the MPB, the deformation incompatibility between fine grains and columnar grains lead to the excessive stress concentration and rapid fracture along the zone boundary. The change of loading direction can alleviate strain localization and improve the uniform deformation ability of the sample. The heterostructure of SLM AlSi10Mg is related to the remelting and resolidification of MPBs. The results provide guidance for the design of SLM AlSi10Mg material with better mechanical properties.

Mesoscopic unit cell analysis of ductile failure under plane stress conditions

Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.

A multi-axial bounding surface p-y model with application in analyzing pile responses under multi-directional lateral cycling

Multi-directional cyclic loads, as often experienced by piles supporting offshore wind turbines (OWTs), could reduce global soil-pile stiffness, and jeopardize the serviceability of OWTs. Most of the existing p-y models focus on uni-directional soil-pile interaction, with a few multi-directional models developed at the cost of additional parameters that require unusual tests for multi-directional cycling. This study presents a multi-directional bounding-surface based cyclic model for lateral soil-pile interaction in both sand and clay. It can model multi-directional cyclic hysteresis and shakedown using only six parameters, without requiring extra parameters and tests for multi-directional cycling. This is achieved by introducing several uni-directionally loaded springs around the pile at each depth. The cyclic p-y relation for multi-directional loading is derived from that for uni-directional loading, by solving equations on equality of work required for the two models under a given displacement increment. The proposed model is validated against experimental results on piles under uni- and multi-directional cycling with various load- and displacement-controlled paths. It is found that following change of loading direction, the pile displacement accumulation is not only limited to the new loading direction, but includes transverse cycling towards the direction of least soil stiffness softened by the recent loading directions. The transverse cycling causes an additional reduction in the global soil-pile stiffness, facilitating the accumulation of lateral pile displacement.

Experimental characterization and physical modeling of strain path dependent microstructure evolution: A case study of primary hot working of titanium alloy

Lamellar globularization, a multi-stage and significant microstructure transformation behavior during primary hot working of titanium alloys, directly affects the microstructure and performance of the product. However, the lamellae dynamic globularization represents a significant dependence on the strain path, which is hard to be predicted only by experimental characterization. To deepen the scientific insight into the effect of the strain path on the globularization behavior, systematic non-monotonic loading experiments (including multi-axial compression and forward-reverse torsion) were extensively performed to characterize the structure features. Further, an internal-state-variable microstructure model is developed to track the globularization process. Experimental results show that there is a short-term stage where the formed α/α substructures annihilate due to the restoration of ideal BOR during the early deformation after the loading direction changes, which leads to the reduction in globularized fraction. However, on the other hand, the globularization would be improved due to the adjustment in lamellae orientation and accelerated lamellae rotation caused by the change of loading direction. The microstructure model considering the strain path effect is developed by introducing the description of the strain path and coupling it into the physical model incorporating dislocation density and α/α substructures evolution. The proposed model is suitable for predicting the lamellar globularization under monotonic and non-monotonic loading of titanium alloys with the α-colony structure, which has been validated from the comparative analysis of the simulated and experimental results. Compared with the existing microstructure models, it broadens the scope of application and improves prediction efficiency. This work throws some light on the correlation between the strain path and microstructural development, which can be utilized to optimize the primary hot working of titanium alloy aiming at improving microstructural refinement and heterogeneity of forging pieces.

Failure behaviour of various pre-formed steel sheets with respect to the mechanical grain boundary properties

The forming history influences the mechanical properties and the formability of sheet metals. Numerous models and approaches have been published to implement this influence into FE-tools, based on isotropic damage or failure criterions. In this paper, the influence of a uniaxial pre-forming and a change in loading direction on the material parameters is investigated for two different steel grades in tensile tests. It was found, that a change in loading direction significantly affects the mechanical properties of the material. The force–displacement curves obtained from nanoindentation experiments were utilized to determine the flow curves for single grains as well as grain boundaries of the pre-formed materials. This was done by inverse parameter identification using finite element analysis.

Experiments on forming behaviour of the aluminium alloy AA6016

Investigation of the sheet metal formability is an important issue in the design of components. During metal forming different deformation histories occur which may cause various damage and failure mechanisms on the micro-level affecting the quality of products. Therefore, description of the material characteristics by means of a linear limit change curve is not sufficient because the remaining formability and the fracture processes also depend on deformation history. For this purpose the aluminium alloy AA6016 is systematically investigated in order to obtain their forming capability as well as the damage and fracture behaviour after complex deformation paths. Different uniaxial tests with various initially unloaded and preloaded specimens have been performed to identify the effect of the forming history, the loading direction and the stress state on the formability and the mechanical parameters of the investigated material. The results can be used to propose a critical ratio between the pre-strain and the change in loading direction from which on shear failure occurs instead of necking behaviour leading to the loss of formability.

Experimental investigation of the mechanical behaviors and energy evolution characteristics of red sandstone specimens with holes under uniaxial compression

To explore the mechanical behaviors and energy evolution characteristics of rock materials with hole defects, eight types of red sandstone specimens with different hole numbers and arrangements were subjected to a series of single-cycle loading-unloading uniaxial compression tests. The experimental result revealed that the mechanical behaviors and energy evolution characteristics of the red sandstone specimens are significantly influenced by hole defects. As the number of boreholes increases, the compressive strength of rock specimens decreases. When the angle between drilling hole arrangement and loading direction changes from 0° to 27° and then to 90°, the compressive strength first decreases and then increases, and shear-splitting, splitting, and shear failure modes appear respectively. The experimental results also show that the energy evolution characteristics (linear energy storage and dissipation laws) of the rock specimens with hole defects were basically consistent with that of intact rock specimens, while the energy storage coefficient is different in various cases. There was a good correspondence between the compressive strength and energy storage coefficient. The larger the energy storage coefficient is, the greater the compressive strength. The hole arrangement angle shows a stronger effect on energy storage coefficient and compressive strength than the number of holes. Among all the arrangements, the rock specimens containing three holes with an angle of 27° between borehole arrangement and loading direction have the lowest energy storage coefficient and compression strength. The above research results provide a scientific basis for rock fracturing induced by drilling.

Reliability analysis for TO-247 multilayered power module packaging under mechanical oscillation based on finite element method

This paper presents the simulation and hardware test results for determining the fatigue life of the solder joints of a printed circuit board (PCB) including a DC to AC inverter circuit with six power metal oxide semiconductor field effect transistors (MOSFETs) by using the finite element method (FEM) under different vibration effects. This board is exposed under different angles by a vibration machine. The selected angles were performed on the power module to find the maximum stress points of the power module for different vibration frequencies. The results indicate that the maximum stress is observed at the corners of the solder layer. The stress of the solder joints significantly increases when the input frequency increases, and the failure, voids generation and crack formation and propagation are more observable under this condition. Furthermore, the loading direction changes show that the peeling stress of the solder layer is directly affected by lower angles. The shear stress occurs in lower angles of loading directions, and this situation results in the peeling stress. The simulation investigations are proved by the experimental results in the study. According to the observations, the fatigue effects result in the coalescence and the void growths in lower angles of vibration loadings. The paper also investigates the normal loading condition of the power inverter circuit, and the highest reliability is obtained compared to all other experimental tests.

Prediction of limit strains during non-proportional load paths with a change in loading direction

Many different models have been published to predict failure after non-proportional load paths. Most of those models are phenomenological and heuristical models. They require a profound knowledge about the material. Examples are the enhanced Modified Maximum Force Criterion (eMMFC), the Polar Effective Plastic Strain-model (PEPS) or the Generalized Forming Limit Concept (GFLC). In addition to the load path, the loading direction has a significant influence on the formability of sheet metals. The mentioned models currently neglect this influence. By extending the GFLC-model by the parameter of loading direction, this influence is taken into account. By analyzing an acceptable number of bi-linear experiments, it is possible to calibrate the proposed model for a micro-alloyed steel HC340LA. Therewith an arbitrary load path with a change in loading direction can be evaluated. The results of this contribution show the effectiveness of this approach by different experiments.

Pile response to multi-directional lateral loading using P–y curves approach

The most commonly used procedure for prediction of the behaviour of laterally loaded piles is the P–y curve formulation, which gives a simple but efficient framework to predict the response of the pile. This framework is limited to a single direction of loading, while there are several situations in which a pile is subjected to lateral loads with varying direction, as for example in the case of wind or wave loads. Here an extended framework for P–y curve modelling is presented, in which several springs are considered around the pile perimeter at each depth. The advantage of this framework is that it remains as simple and practical as the original P–y curve method and does not need any further information or parameters. A procedure is proposed for the extension of a given unidirectional model to the corresponding multi-directional one. The effects of multi-directional loading are discussed based on the simulation results. With a change in loading direction, misalignment between load direction and total displacement occurs. In addition, this quite simple model enables deduction of the profile of irreversible soil displacements around the pile at various depths.

Water-based helical laser hole-cutting in nickel super-alloy GH4049 assisted by longitudinal and transverse magnetic fields with/without ultrasonic assistance

A novel helical laser hole-cutting (HLHC) technology based on coupled assistance of water-based ultrasonic vibrations and external longitudinal/transverse magnetic fields is reported for cutting holes in nickel super-alloy GH4049 sheets. Effects of external unidirectional transverse and longitudinal magnetic fields on HLHC performance were correspondingly analyzed and compared with and without water-based ultrasonic assistance. The influence of the loading direction of an external magnetic field and the magnetic field intensity of an external longitudinal/transverse magnetic field on HLHC performance is first reported based on systematic corresponding comparisons with and without water-based ultrasonic assistance. The effects of external longitudinal/transverse magnetic fields and beam expanding ratios on actual laser focal spot sizes were analyzed and discussed. It was demonstrated that the latest reported HLHC technology assisted by water-based ultrasonic vibrations and external longitudinal magnetic fields could generate deeper holes with relatively high cutting efficiency, smaller hole taper, higher hole aspect ratio, smaller hole circularity deviation, better hole wall quality, much better performance for relieving residual stress, thinner recast layer, more uniform refinement of grains, and better performance for improving micro hardness. Generally, a stronger external longitudinal magnetic field coupled by water-based ultrasonic vibrations was more helpful for cutting deeper and higher-quality holes. It was shown that the change of loading direction of an external magnetic field with/without ultrasonic assistance did not greatly alter recast layer formation and micro hardness performance for the workpiece helically cut. Compared to the transverse magnetic assistance, a corresponding longitudinal magnetic field coupled with water-based ultrasonic vibrations was more effective for micro hardness improvement for this reported HLHC technology. When using the same water-based ultrasonic vibration assistance, a stronger longitudinal magnetic field was more effective for relieving residual stress for the workpiece helically cut (a stress reduction percentage of around 96.5% was reported in this work). The average laser focal spot size obviously decreased with laser beam expanding ratio, but the external longitudinal/transverse magnetic assistance did not greatly alter the actual laser focal spot size.

Influence of non-proportional load paths and change in loading direction on the failure mode of sheet metals

Many studies have shown that failure following non-proportional load paths cannot be predicted by a linear Forming Limit Curve (FLC), as the deformation history and a change in loading direction influence the formability and failure mode. In this paper, the different failure modes due to different load paths are investigated, for the first time, by conducting Nakajima tests with pre-formed specimens. The main objective of the investigation is to better understand the influence of pre-forming and change in loading direction on the formability. To predict this behaviour, regardless of the failure mode, the Generalized Forming Limit Concept (GFLC) is extended.

Effect of forging steps on microstructure evolution and mechanical properties of Ti-6Al-4V alloy during multidirectional isothermal forging

In this study, the multidirectional isothermal forging (MDIF) was used to modify the β transformed microstructure into an equiaxed α+β structure in Ti-6Al-4V alloy. After two steps forging, the initial β grains were nearly disappeared. α colonies with different orientations became kinked and globularized due to the change of loading direction. The microhardness of the sample was 323 HV. The yield strength and ultimate tensile strength were 859 MPa and 907 MPa, respectively. After three steps forging, the lamellar α structures were globularized completely, a homogeneous microstructure was formed. The microhardness of the sample increased to 335 HV. The yield strength and ultimate tensile strength increased up to 900 MPa and 921 MPa, respectively. The homogeneity of microstructure and mechanical properties were improved with the isothermal forging steps increasing.

The response of suction caissons to multidirectional lateral cyclic loading in sand over clay

Offshore wind turbines and their foundations experience loading from varying directions, yet understanding of the effect of changes in the direction of applied cyclic loading on foundation response remains limited. This study investigates the behaviour of a suction caisson foundation in sand over clay under various types of multidirectional cyclic loading. The findings are significant: although the caisson rotation (or tilt) is affected by changes in load direction, the caisson rotation is less than that in a unidirectional test with the same cyclic load magnitude and symmetry, meaning that a unidirectional test may serve as a conservative estimate of caisson rotation for multidirectional loading. This contrasts with previous findings for monopiles in sand, where prediction of the accumulated displacement based on unidirectional cyclic loading was substantially un-conservative for multidirectional loading. Changes in unloading stiffness due to changes in load direction are slight, varying by an amount that is no greater than the change measured over the course of a unidirectional test. Foundation stiffness and ultimate capacity following multidirectional cyclic loading are largely unaffected, unlike unidirectional cyclic loading, where consolidation of the clay layer improves both the stiffness and capacity.