Uniaxial Tension Research Articles

An anisotropic full-network model with damage surface for the Mullins effect in filled rubbers

The Mullins effect is a highly anisotropic damage phenomenon exhibited by filled rubbers among other soft materials. When filled rubbers are subjected to uniaxial tension, their apparent stiffness drops in the direction of stretching but is essentially unaltered in the transverse directions. However, micromechanical full-network models where Mullins softening is described at the level of individual chains often predict that uniaxial deformations induce transverse softening in addition to softening in the stretching direction. Moreover, these approaches typically require the storage of damage state variables for each chain, which is computationally expensive. Taking an alternative approach, we present a full-network model for the Mullins effect where the damage state is described by a single macroscopic damage tensor from which the damage state in each direction can be calculated. The evolution of damage is specified through damage surfaces and damage flow rules, which depend on the directions of principal stretches. The model is shown to reproduce experimental data for filled rubbers sequentially subjected to uniaxial tension in different directions. The model is also implemented in the finite element software ABAQUS as a user subroutine UMAT to illustrate the suitability of the model to simulate non-homogeneous deformation states.

Mesogen Organizations in Nematic Liquid Crystal Elastomers Under Different Deformation Conditions.

Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and reversible shape-changing behaviors, and so serve as potentially transformative materials for various protective and actuation applications. This study contributes to filling a critical knowledge gap in the field by investigating the microscale mesogen organization of nematic LCEs with diverse macroscopic deformation. A polarized Fourier transform infrared light spectroscopy (FTIR) tester is utilized to examine the mesogen organizations, including both the nematic director and mesogen order parameter. Three types of material deformation are analyzed: uniaxial tension, simple shear, and bi-axial tension, which are all commonly encountered in practical designs of LCEs. By integrating customized loading fixtures into the FTIR tester, mesogen organizations are examined across varying magnitudes of strain levels for each deformation mode. Their relationships with macroscopic stress responses are revealed and compared with predictions from existing theories. Furthermore, this study reveals unique features of mesogen organizations that have not been previously reported, such as simultaneous evolutions of the mesogen order parameter and nematic director in simple shear and bi-axial loading conditions. Overall, the findings presented in this study offer significant new insights for future rational designs, modeling, and applications of LCE materials.

Poisson function and volume ratio of soft anisotropic materials under large deformations

Accurate transverse deformation measurements are required for the estimation of the Poisson function and volume ratio. In this study, pure silicone and soft composite specimens were subjected to uniaxial tension, and the digital image correlation method was used to measure longitudinal and in- and out-of-plane transverse stretches. To minimize the effects of measurement errors on parameter estimation, the measured transverse stretches were defined in terms of the longitudinal stretch using a new formulation based on Poisson's ratios and two stretch-dependent parameters. From this formulation, Poisson functions and volume ratio for soft materials under large deformations were obtained. The results showed that pure silicone can be considered isotropic and nearly incompressible under large deformations, as expected. In contrast, Poisson's ratio of silicone reinforced with extensible fabric can exceed classical bounds, including negative value (auxetic behavior). The incompressibility assumption can be employed for describing the stress-stretch curve of pure silicone, while volume ratios are required for soft composites. Data of human skin, aortic wall, and annulus fibrosus from the literature were selected and analyzed. Except for the aortic wall, which can be considered nearly incompressible, the studied soft tissues must be regarded as compressible. All tissues presented anisotropic behavior.

Cracking Behavior of Environmental Barrier Coatings/CMC System Using Acoustic Emission and Digital Image Correlation

Abstract An investigation into the cracking behavior of advanced environmental barrier coating / woven SiC/SiC ceramic matrix composite (CMC) system under uniaxial tension testing was performed in this study. The effect of substrate (CMC) condition on the coating behavior was also studied. Acoustic emission (AE) and digital image correlation (DIC) were implemented as health monitoring techniques to gain detailed insights into the fracture process of the coating and to identify the origin and location of the fracture events. Fluorescent penetrant inspection was used in-situ in some cases to help identify cracks. Post-test microscopy was performed to correlate the results with DIC and AE. It was evident that for the as-produced woven substrate, the EBC coating cracked prior to substrate cracking; however, for the altered surface substrate, the CMC substrate formed matrix cracks prior to the EBC coating.

An efficient and quantitative approach for fracture toughness measurement of Micron-Thick hard coatings based on crack spacing

Micron-thick hard coatings find widespread applications, with fracture toughness being a crucial property that ensures their usability. However, measuring the fracture toughness of hard coatings is time-consuming and costly due to the susceptibility to cracking and small sample size. Thus, developing a simple, effective and precise measurement method is necessary. This work presents an analytical model that calculates KC from crack spacing induced by uniaxial tension. By measuring the variation of crack spacing, this model determines the fracture toughness from the energy difference during the coating fracture, and residual stress can also be estimated. This simple method overcomes the limitations of uniaxial tension methods, does not require any in-situ observations, and offers low-cost and user-friendly testing. The KC of TiN coatings with 2 μm thickness were tested and found to match the micro-cantilever beam test results from the literature. This model used data from other literature to calculate the toughness of diamond and a-C:H thin coatings, showing its generality. Additionally, our model’s estimation of residual stress in coatings, as reported in the literature, is accurate to within 0.1 ∼ 1 GPa.

Direct application of elasto-visco-plastic self-consistent crystal plasticity model to U-draw bending and springback of dual-phase high strength steel

The incremental elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) was utilized to describe the constitutive behavior of dual-phase 980 (DP980) steel. A simple baseline modeling approach was chosen: the hardening behavior of each constituent phase in the DP980 steel was described by a simple Voce hardening law without explicitly considering the back stress; and it was assumed that using the same single crystal elastic modulus for ferrite and martensite is sufficiently representative. The adequacy of this baseline modeling approach was evaluated by comparing various mechanical experimental data with model predictions in terms of the stress vs. strain curves obtained from uniaxial tension, tension-compression, and loading-unloading-loading (LUL) tests. Additionally, the evolution of experimental lattice strain data reported in literature was used to validate the phase-specific Voce hardening parameters. Despite its minimalistic modeling description, the baseline ΔEVPSC model successfully captured key features: 1) the Bauschinger effect, 2) the decrease in chord modulus, and 3) the non-linearity in the stress vs. strain curves resulting from the LUL test. All three mentioned characteristics are crucial for accurate prediction of springback in sheet metals. The ΔEVPSC model, interfaced with a finite element solver (Abaqus/standard) as the user material subroutine, was employed to simulate the Numisheet93 benchmark problem. The strip of DP980 was first U-drawn followed by springback. The model-predicted springback profile aligned well with the experimental results only when stress relaxation was properly considered, resulting in improved predictive accuracy compared to predictions based on a distortional plasticity model.

Mechanical performance of liquid cold-poured interlayer adhesives in comparison to PVB, EVA, and ionomers

AbstractCurrently, liquid cold-poured adhesives are infrequently used as interlayers of laminated or laminated safety glass in structural glass applications, despite their inherent benefits. The potential advantages of these materials are characterized by easy handling, rapid curing devoid of elevated temperature or pressure requirements, and consequently, a comparatively low energy demand. Despite the prolonged availability of certain products in the market, comprehensive scientific inquiry into their mechanical and thermal material characteristics remains limited. In this paper, two specific liquid cold-poured interlayer adhesives are investigated for their mechanical material properties in an extensive test regime. To be able to classify the characteristic values of the adhesives within a correct framework, the materials currently holding the largest market share, including Polyvinyl Butyral (PVB), Ionomers, and Ethylene Vinyl Acetate (EVA), are also subjected to the experimental program. The temperature dependence of the material behavior is explored through Dynamic Mechanical Thermal Analysis (DMTA) experiments. Furthermore, the time-dependent material behavior at large deformations is scrutinized using various methodologies, such as tensile tests at different strain rates, cyclic tests, creep tests, and relaxation tests, all conducted in uniaxial tension mode. The outcomes of all tests led to promising results for one of the adhesives with advantages over those of PVB and EVA.

Alveolar wall hyperelastic material properties determined using alveolar cluster model with experimental stress-stretch and pressure-volume data

Micro-scale models of lung tissue have been employed by researchers to investigate alveolar mechanics; however, they have been limited by the lack of biofidelic material properties for the alveolar wall. To address this challenge, a finite element model of an alveolar cluster was developed comprising a tetrakaidecahedron array with the nominal characteristics of human alveolar structure. Lung expansion was simulated in the model by prescribing a pressure and monitoring the volume, to produce a pressure-volume (PV) response that could be compared to experimental PV data. The alveolar wall properties in the model were optimized to match experimental PV response of lungs filled with saline, to eliminate surface tension effects and isolate the alveolar wall tissue response. When simulated in uniaxial tension, the model was in agreement with reported experimental properties of uniaxial tension on excised lung tissue. The work presented herein was able to link micro-scale alveolar response to two disparate macroscopic experimental datasets (stress-stretch and PV response of lung) and presents hyperelastic properties of the alveolar wall for use in alveolar scale finite element models and multi-scale models. Future research will incorporate surface tension effects, and investigate alveolar injury mechanisms.

Hyperelastic material models for simulating deformation of silicone ring pessaries

Pessaries are removable gynecological prosthetic devices that provide mechanical support for temporary or long-term symptom relief of pelvic floor disorders, such as pelvic organ prolapse and stress urinary incontinence. To date, limited mechanical tests have been performed on physical pessary designs to characterize their behaviour under load; however, custom pessary manufacturing is expensive and time consuming. As an alternative, finite element (FE) modeling can provide detailed numerical insight into the response of a pessary design under load but to date has seen limited application, with little data available for pessary silicone materials. This study aimed to identify hyperelastic material models for two silicone materials used in custom pessary cocoon moulded manufacturing towards FE analysis of ring with support (RWS) pessaries. It was hypothesized that hyperelastic material models could be identified to capture the force and deformation response of multiple RWS sizes under different boundary conditions and silicone materials (Shore 60A and 40A). To understand the material characteristics of pessary silicone, uniaxial tension and compression tests were performed then the experimental data was fit with Mooney-Rivlin (MR) material models. To ensure the material models characterize the pessary behaviour, data from mechanical tests representing the RWS pessary folding and modified 3-point bending were compared to FE recreations (FEBio) of the same tests with the MR materials applied to the pessaries. The FE model results demonstrated good agreement in the force-displacement response for the fold and 3-point bending models for different pessary sizes and silicone stiffnesses. This work demonstrates the hyperelastic material models’ efficacy and will enable future studies to improve biomechanical analysis of silicone pessary designs.

Crystal plasticity finite element simulations on extruded Mg-10Gd rod with texture gradient

The mechanical properties of an extruded Mg-10Gd sample, specifically designed for vascular stents, are crucial for predicting its behavior under service conditions. Achieving homogeneous stresses in the hoop direction, essential for characterizing vascular stents, poses challenges in experimental testing based on standard specimens featuring a reduced cross section. This study utilizes an elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) with the predominant twinning reorientation (PTR) scheme as a numerical tool, offering an alternative to mechanical testing. For verification, various mechanical experiments, such as uniaxial tension, compression, notched-bar tension, three-point bending, and C-ring compression tests, were conducted. The resulting force vs. displacement curves and textures were then compared with those based on the ΔEVPSC model. The computational model's significance is highlighted by simulation results demonstrating that the differential hardening along with a weak strength differential effect observed in the Mg-10Gd sample is a result of the interplay between micromechanical deformation mechanisms and deformation-induced texture evolution. Furthermore, the study highlights that incorporating the axisymmetric texture from the as-received material incorporating the measured texture gradient significantly improves predictive accuracy on the strength in the hoop direction. Ultimately, the findings suggest that the ΔEVPSC model can effectively predict the mechanical behavior resulting from loading scenarios that are impossible to realize experimentally, emphasizing its valuable contribution as a digital twin.

Prediction of Biaxial Properties of Elastomers and Appropriate Data Processing.

An equibiaxial tension test could be necessary to set up hyperelastic material constants for elastomers exactly. Unfortunately, very often, only uniaxial tension experimental data are available. It is possible to use only uniaxial data to compute hyperelastic constants for a hyperelastic model, but the prediction of behavior in different deformation modes (as is equibiaxial or pure shear) will not work correctly with this model. It is quite obvious that there is some relation between uniaxial and equibiaxial behavior for the elastomers. Thus, we could use uniaxial data to predict equibiaxial behavior. If we were able to predict (at least approximately) equibiaxial data, then we could create a hyperelastic model usable for the general prediction of any deformation mode of elastomer. The method of the appropriate processing of experimental data for such prediction is described in the article and is verified by the comparison with the experiment. The presented results include uniaxial and equibiaxial experimental data, the created average curve of both the deformation modes, and the predicted equibiaxial data. Using Student's t-test, a close coincidence of the real and predicted equibiaxial data was confirmed.

An assumed enhanced strain finite element framework for tensile fracturing processes with dual-mechanism failure in transversely isotropic rocks

We present an assumed enhanced strain finite element framework for the simulation of tensile fracturing processes in transversely isotropic rocks. Fractures along the weak bedding planes and through the anisotropic rock matrix are treated with distinct enrichment, and a recently proposed dual-mechanism tensile failure criterion for transversely isotropic rocks is adopted to determine crack initiation for the two failure modes. The cohesive crack model is adopted to characterize the response of embedded cracks. As for the numerical implementation of the proposed framework, both algorithms for the update of local history variables at Gauss points and of the global finite element system are derived. Four boundary-value problem simulations are carried out with the proposed framework, including uniaxial tension tests of Argillite, pre-notched square loaded in tension, three-point bending tests on Longmaxi shale, and simulations of tensile cracks induced by a strip load around a tunnel in transversely isotropic rocks. Simulation results reveal that the proposed framework can properly capture the tensile strength anisotropy and the anisotropic evolution of tensile cracks in transversely isotropic rocks.

Research of the impact of uniaxial tension on the thermoelectric properties of NbCoX (X=Ge, Sn, Pb) compounds

Half-Heusler materials have been confirmed as excellent thermoelectric materials. To simulate the stress conditions in engineering applications, we adopt uniaxial tensile strain to assess the impact of lattice changes on NbCoX (X=Ge, Sn, Pb) compound's thermoelectric performance. The research reveals that when NbCoX compounds are stretched by 1.5 %, the material almost does not decrease the power factor but significantly reduces thermal conductivity, thereby enhancing the ZT value. At a carrier concentration of 1E22 cm−3 and a temperature of 873 K, the predicted ZT values for p-type NbCoSn compound reach 0.359 and 0.354 after stretching by 1.5 % in the x-y and z directions, respectively. Compared to the previous original values, this improvement is approximately 1.5 times, highlighting the significant role of tensile strain in enhancing thermoelectric performance. This may be attributed to changes in compound lattice symmetry induced by strain, leading to increased defects and interfaces, which complicate phonon transport paths, resulting in a decrease in the average phonon mean free path and consequently lowering thermal conductivity. Additionally, with the increase in atomic number of Ge, Sn, and Pb, their thermoelectric figure of merit also increases continuously, with ZT values remaining higher under stretching than compression. Such research provides a new avenue for designing and optimizing high-performance thermoelectric materials and offers insights into strain engineering for future exploration of thermoelectric materials.

Unravelling the relation between free volume gradient and shear band deflection induced extra plasticity in metallic glasses

Previous experiments have revealed that the controllable introduction of structural gradients in metallic glasses (MGs) can endow the materials with extra plasticity due to the gradient-induced deflection of shear bands. However, the relation between the spatial structural gradient and the initiation of shear band deflection remains unclear. The current study has been focused on investigating the relationship between the improved mechanical properties of MGs and structural gradients specified by the distribution of the intrinsic free volume. Molecular dynamics (MD) simulations are firstly performed on homogeneous MG models containing various initial free volume values, showing that the shear band angle increases with decreasing free volume under uniaxial compression, whereas higher shear band angle is observed under uniaxial tension with increasing free volume. Based on the asymmetric behaviors of MGs under compression and tension, a theoretical model is developed to quantitatively characterize the influence of free volume on the mechanical response of MGs, which incorporates a failure criterion based on free volume generation during external loadings. The model can be further utilized to interpret and predict the fracture strain, shear band angle, maximum stress, and fracture surface morphology of gradient structured MGs in both simulations and experiments. The relationship between free volume gradient and shear band deflection induced extra plasticity established in this study provides valuable guidance for the structural design of MGs with enhanced mechanical properties.

Acoustic emission characteristics of damage evolution of multi-scale fiber reinforced rubberized concrete under uniaxial compression and tension after being subjected to high temperatures

Acoustic emission characteristics of damage evolution of multi-scale fiber reinforced rubberized concrete under uniaxial compression and tension after being subjected to high temperatures

Assessment of location- and orientation- dependent fatigue behaviour for as-deposited LPBF Inconel 718 using miniaturized specimens

The location- and orientation-dependence of tensile properties and low/high cycle fatigue behaviour of additively manufactured IN718 were determined on as-deposited material with the use of miniaturized specimens. Local properties were determined throughout the build height for two orientations by using 39 fatigue samples and 32 tensile test coupons excised from bulk builds. The low cycle fatigue behaviour is described with the use of the Manson-Coffin approach while the high cycle regime was analysed using a Wohler-based assessment. Extensive microstructure characterization included optical microscopy, electron microscopy with EDX and EBSD analyses, fractography and computer tomography in order to rationalize the fatigue anisotropy in certain regimes. Significant anisotropy in the low cycle (i.e. high strain) fatigue regime is attributed to the differences in microstructure, UTS, and ductility in the as-deposited material. The fatigue behaviour in the high cycle (i.e. low strain) regime was worse in Z-oriented samples, partly due to its somewhat lower UTS and detrimental orientation of lack-of-fusion defects that served as fatigue initiation sites. The complete axial fatigue behaviour, which evaluated the whole range from uniaxial tension (i.e. one cycle) through the low cycle to high cycle regime, was attempted with the use of the Stussi model. While the various modelling approaches that used either uniaxial tension or cyclic tension data captured some of the observations, the detrimental effects of process-induced defects and their orientation with respect to the loading direction prevented a complete description of the fatigue behaviour in the high cycle fatigue regime. Nevertheless, the use of miniaturized samples provides a unique capability to examine both the location- and orientation-dependent fatigue behaviour relevant to many engineering structures.

Evaluation of the errors of measuring residual stresses by the hole drilling method

A sample configuration with a specified distribution of residual stresses in depth was developed to elaborate modes for studying residual stresses using mechanical and physical methods. The sample formation technique is based on non-uniform plastic deformation of an aluminum beam of rectangular cross section according to the pure bending scheme. The control of the deformed state during loading was performed on the end surface of the sample by the field of normal deformations obtained using a digital image correlation system. The depth of the plastically deformed layer was 1.3 mm. The theoretical distribution of residual stresses obtained as a result of unloading of a plastically deformed sample was determined from the results of a numerical calculation of a finite element model, with allowance for the physical and mechanical characteristics, elastic-plastic hardening, as well as the deformation curve in true coordinates obtained as a result of uniaxial tension on elementary samples. A study of residual stresses inhomogeneous in depth was carried out by drilling holes in accordance with ASTM E837 on two opposite sides of the sample: the region of tension under loading and the area of compression, respectively. The control of the deformation response resulted from drilling was recorded using three-axis strain gauge rosettes. The results of the actual measurement of the longitudinal component of residual stresses were compared with their theoretical distribution obtained by a numerical method. The root-mean-square error in measuring residual stresses, relative to their theoretical distribution, for an aluminum alloy sample reaches 18.7 MPa. It should be noted that largest measurement errors were recorded at small depths, since they are characterized by small values of deformations comparable to the value of shot noise.

Different impact of recovery annealing and thermal pressure treatments on the microstructure and mechanical properties of rejuvenated Cu64Zr36 metallic glasses: A molecular dynamics study

The interpenetrating connection of icosahedra network (ICOIN) was termed as structural skeleton, which could quantify the strength and ductility of MGs. The impact of different rejuvenation methods on medium-range order (MRO) alterations was rarely studied. This work employed molecular dynamics simulations to examine the difference in MRO evolution of metallic glasses treated by recovery annealing and thermal-pressure treatment during uniaxial tension. All of the specimens obtain enhanced ductility due to improved potential energy. During tension, ICOI of all rejuvenated specimens exhibits an increased destruction rate and a decreased transformation rate. However, there are some converse characteristics in the specimens under different rejuvenation methods. The rejuvenated specimens treated by recovery annealing exhibit increased free volume and decreased ICOIN density. After thermal-pressure treatment, the rejuvenated specimens demonstrated decreased free volume and enhanced ICOIN density. During tension, the enhancement of icosahedral free volume in specimens treated by thermal pressure largely decreased the ICOIN density, thereby increasing the ductility. After tension, the rejuvenated specimens under high pressure have a significant reduction in ICOIN density compared to those under recovery annealing. The significance of this work is to accurately regulate the ICOIN density of rejuvenated specimens.

Constitutive description of distortional hardening in a TWIP steel: Addressing differential hardening under nonlinear strain paths

The present study aims to describe the in-plane differential hardening behaviour of the twinning induced plasticity sheet metal TWIP980 under various stress states, including uniaxial tension, plane strain tension, and pure shear, particularly focusing on non-proportional loading conditions. The true stress–strain curves for each stress states were inversely obtained from their corresponding load–displacement curves and modeled using a differential hardening model that can accommodate all three stress states simultaneously on plastic work (density) contours. For non-proportional loading tests, oversize specimens were initially stretched under uniaxial tension up to a 10% pre-strain along the rolling, diagonal, and transverse directions, respectively. Subsequently, the three stress states were applied to subsize specimens cut from the deformed oversize specimens along the rolling direction. To describe the hardening behaviours during non-proportional loading, a homogeneous anisotropic hardening model was adopted and calibrated using two-step uniaxial tension tests. Subsequently, the differential hardening model was successfully incorporated into the homogeneous anisotropic hardening model to describe both the differential hardening and the strain path change-induced hardening behaviours under the two-step loadings, i.e., uniaxial tension to pure shear and uniaxial tension to plane strain tension. Both experimental and simulation results underscore the necessity to consider differential hardening under non-proportional loading conditions.

Damage evolution and ductile fracture of commercially-pure titanium sheets subjected to simple tension and cyclic bending under tension

This paper describes a study into the evolution of damage in commercial-purity titanium (CP–Ti) sheets subjected to cyclic bending under tension (CBT) and uniaxial tension (simple tension, ST). Sections were taken from sheets that were strained to various levels under both methods and were imaged using X-ray computed tomography (XCT) to reveal insights into the size, density, and distribution of microvoids in the sheets. Digital image correlation (DIC) was also used to observe the surface strain of CBT and ST sheets during testing. These results showed that elongation to failure (ETF) for CBT deformation is about 2.5× higher than for ST, local longitudinal strains in the bulk of the CBT sample are around 1.3× higher than the peak strain in the ST necked region, and 1.7× higher in the localized region of CBT failure. It was found that the volume-density of voids in both sheets followed a similar exponential increase with strain, reaching nearly 45× higher in the CBT than the ST sheets before the onset of failure, mainly due to the higher strain levels achieved. A higher volume density of voids developed in the center of sheets at high levels of strain, for both processes, with the density in the sheet center becoming approximately double that found near the edges. Scanning electron microscopy (SEM) was used to examine the fracture surface of CBT and ST sheets after failure. The observations are presented and discussed highlighting the CBT process as effective to delay ductile fracture of the CP-Ti sheets.