Cyclic Uniaxial Tensile Tests Research Articles

Microstructural mechanism underlying the stress recovery behavior of a Fe–Mn–Si shape memory alloy

Recovery stress governs the prestress strengthening effect of Fe–Mn–Si-based shape memory alloys in civil engineering applications. Although the effects of grain size, texture, and precipitates on recovery stresses have been extensively studied, the generation of recovery stress has not been thoroughly discussed regarding martensite growth behavior, especially considering the interaction of martensite variants. This study investigates the stress recovery and ε martensite growth behavior of a Fe–30Mn–6Si–5Cr (wt.%) alloy subjected to varying levels of deformation. The Fe–30Mn–6Si–5Cr (wt.%) alloy exhibits a yield strength of approximately 450 MPa, with an ultimate elongation of 44 % and a tensile strength of 950 MPa observed in uniaxial incremental cyclic tensile tests. Additionally, the results reveal an initial increase in recovery stress with pre-strain, peaking at 7 %, followed by a subsequent decrease with further deformation. With increasing pre-strain, the primary ε martensites initially grow parallelly, followed by the appearance of secondary martensites with a different orientation, intersecting multiple parallel primary martensites along with the increasing density of dislocations and stacking faults. A microstructural mechanism is proposed to elucidate the stress recovery behavior, encompassing the impact of primary martensites and secondary martensites interaction, and the influence of dislocations and stacking faults. This work offers microstructural scenarios that help to understand the generation of recovery stress and provides guidance for regulating recovery stress in Fe–Mn–Si-based shape memory alloys for civil engineering applications requiring prestress strengthening.

Study on tensile performance of welded seams of PVC coated fabric membrane under uniaxial cyclic load

The mechanical performance degradation of welded seams under cyclic loading may lead to the failure of membrane structures. To investigate the influence of the off-axis angle and the the welded width on mechanical performance, the elastic modulus, ratcheting strain, residual strain and strain energy were studied based on the uniaxial cyclic tensile tests of welded seams. The results show that the elastic modulus of the welded seam specimens shows obvious anisotropy under cyclic loading, and the welded width has the greatest influence on the elastic modulus of the welded seam specimens with 15° and 75° off-axis angles, under which off-axis angle the welded seam specimens have good recoverability. The irreversible plastic strain of the axial welded seam specimens is close to that of the membrane specimen. The plastic development of the specimen is obvious under large off-axis angles (30°, 45°, 60°), and the final residual displacement of the welded seam specimens reach 3%–4%.

A Visco-Hyperelastic Constitutive Model to Characterize the Stress-Softening Behavior of Ethylene Propylene Diene Monomer Rubber.

Uniaxial and biaxial cyclic tensile tests and stress relaxation tests were performed on the ethylene propylene diene monomer (EPDM) material to investigate its stress-softening effect. The experimental results reveal that the EPDM material presents a significant Mullins effect during the cyclic stretching processes. Furthermore, it is found that the deformation of the EPDM material does not return to zero simultaneously with the stress, due to the viscoelasticity of the EPDM material. Therefore, this study combines pseudo-elasticity theory and viscoelastic theory to propose a visco-hyperelastic constitutive model. The proposed model is used to fit and analyze the uniaxial and biaxial cyclic test results of EPDM and a comparison is conducted with the corresponding hyper-elastic constitutive model. The results show that the proposed model is in good agreement with the experimental data and superior to the hyper-elastic constitutive model, especially when it comes to the stress-softening unloading process. This work is conducive to accurately characterizing the stress-softening behavior of rubber-like materials at large deformation and can provide some theoretical guidance for their widespread application in industry.

Static Unified Inelastic Model: pre- and post-yield dislocation-mediated deformation

Modelling dislocation glide over the initial part of a stress–strain curve of metals received little attention up to now. However, dislocation glide is essential to ones understanding of the fundamental relationship between inelastic deformation and the evolution of the dislocation network structure. Therefore, we present a model of dislocation-driven deformation under static loading conditions.We reproduce repeated cyclic uniaxial tensile tests on Interstitial-Free and Low-Alloy steels. The elastic mechanical behaviour is described by isotropic linear elasticity, pre-yield anelastic mechanical behaviour by a dislocation bow-out model with dissipation, and the post-yield evolution of dislocation network structure by a statistical storage model. We hypothesise that when the local anelastic compliance is lower than the global plastic compliance, deformation is mechanically recoverable, and vice versa. This hypothesis is corroborated with the classical Taylor relation. We report the relation between stable and unstable dislocation glide using this prototypical modelling framework.We find four structural variables, that are based on dislocation physics, to describe the stress–strain curve: total dislocation density, average dislocation segment length, dislocation junction formation rate, and average dislocation junction length. Firstly, we quantify the dislocation network evolution during uniaxial monotonic loading, and verify work-hardening by dislocation junction formation and a Taylor-type equation for flow. Finally, we present a semi-empirical relation for the evolution of the dislocation network structure. Which allows us to: refine the physical interpretation of the Taylor relationship, and rationalise experimental observations on apparent modulus degradation by thermomechanical processing. Both these findings circumvent the limitations of current, physics-based hardening models.

Uniaxial tensile response and tensile constitutive model of ultra-high performance concrete containing coarse aggregate (CA-UHPC)

To establish the tensile constitutive model of ultra-high performance concrete containing coarse aggregate (CA-UHPC), monotonic and cyclic uniaxial tensile tests for CA-UHPC with fiber volume fractions of 2.5% and 2.0% were conducted. Test results showed that CA-UHPC exhibits approximately linear stress-strain relation up to the tensile strength, and tensile softening response composed of the smeared- and localized-cracking stages, regardless of the tested fiber contents. Based on the monotonic test data, the tensile stress-crack opening model of CA-UHPC was established, and the model was further simplified into tri-linear relation. Based on the cyclic test results, tensile damage evolution laws according to the strain equivalence principle and the energy equivalence principle were developed, respectively. Finally, the proposed tensile constitutive model and the calibrated tensile damage evolution laws were demonstrated to effectively predict the mechanical response of CA-UHPC members under both monotonic tension and cyclic tension through numerical simulations.

Deformation mechanisms of a NiTi alloy under high cycle fatigue

In this paper, high-cycle fatigue mechanisms of a pseudoelastic NiTi shape memory alloy (SMA) under different mean strains are investigated. The uni-axial cyclic tensile tests with small amplitude of 0.25% are operated at three different states, i.e. austenite/elastic region, austenite and martensite coexisted region and martensite/elastic region with a pre-strain. Mechanical results indicate that the cyclic deformation strain is mainly in the inhomogeneous deformation band when the sample cycling in the B2 + B19′ phase coexist status. Cyclic deformation in the B2 + B19’ phase showed cyclic hardening effect. With increasing of the mean strain, the saturation stress is decreased, and saturation rate is reduced. The mean strain effect on the high-cycle fatigue life of NiTi is attributed to the inhomogeneous transformation of martensite. High resolution electron microscopy (HREM) observations and atomic simulations showed that partial dislocations with the Burgers vectors of 1/2<110> are induced on (001)M twin planes, the interaction of dislocations and edge dislocations in martensite results in cyclic hardening in martensite. While cyclic softening in martensite at the upper plateau of stress–strain (S–S) curve is attributed to the grain reorientation/rotation phenomenon. It suggests that newly generated stress-induced martensite at the interface of martensite and austenite could increase the high-cycle fatigue of NiTi SMA.

Experimental characterisation of masonry unit–mortar interface under uniaxial cyclic tension

An experimental investigation of a non-linear mechanical phenomenon occurring in a masonry unit–mortar interface subjected to uniaxial monotonic and cyclic tensile tests is conducted in this study. Some crucial parameters, such as stiffness degradation, residual displacement, damage energy, and plasticity/friction energy were estimated based on cyclic tensile tests and were investigated to understand the mechanical behaviour of the unit–mortar interface. Several correlations were determined between the elastic stiffness, residual displacement, and damage variable with respect to displacement. In addition, the dissipated energy was determined from the secant stiffness, and a good correlation was observed between the energy calculated with and without considering the residual displacement. Ultrasonic measurements were also performed on these tests to monitor mechanical damage.

Enhanced superelasticity and two-way shape memory properties of bamboo-grained Au7Cu5Al4 microwires

A bamboo-like grain structure was obtained in melt-extraction Au7Cu5Al4 microwires via cyclic heat treatment. The superelasticity and two-way shape memory properties were investigated by performing uniaxial cyclic tensile tests and mechanically constrained thermal cycling, respectively. The superelasticity of bamboo-grained microwires was improved significantly duo to a reduction in the constraints caused by triple junctions. A recoverable strain of ∼3% was achieved over a wide temperature range of 358–423 K for the bamboo-grained microwire, which exhibited excellent cyclic stability under a stress of up to 470 MPa. The two-way shape memory properties were determined by conducting load-biased thermal cycling tests, and a recoverable strain of 1.2% with a maximum work output of 1.2 J cm−3 was achieved under a stress of 100 MPa. The results indicate that the Au–Cu–Al shape memory alloy is a potential candidate for small-sized actuators operating in harsh environments.

Viscoelastic-viscoplastic modeling of epoxy based on transient network theory

The expansion of the application of polymers instead of metals has warranted the evaluation and modeling of their mechanical behaviors under various conditions. In the present study, the strain-rate- and temperature-dependent nonlinear mechanical behavior of a glassy polymer from small to large strain ranges is investigated experimentally and numerically. The effects of strain rate and temperature on the mechanical responses and development of the strain field under monotonic and cyclic uniaxial tensile tests of epoxy are evaluated experimentally. In addition, the stress relaxation test is performed to evaluate the time-dependent mechanical behavior of epoxy. In the previous work (Uchida et al. 2019), the concept of the transient network (TN) theory was applied to demonstrate the nonlinear behavior of the thermosetting glassy polymer. In this model, the time-dependent mechanical behavior of the thermosetting glassy polymer was assumed to be characterized by the debonding and rebonding of intermolecular secondary bonds (SBs). In the present study, the TN model is extended to represent the temperature- and strain rate-dependent mechanical behavior of the thermosetting glassy polymer below the glass transition temperature Tg. The decrease in the deformation resistance of a polymer at a higher temperature is represented by a decrease in the SB density. Furthermore, the fixation parameter is introduced to accurately predict the residual strain in the cyclic tensile test. The mechanical responses in the monotonic and cyclic tensile tests and the stress relaxation test predicted by the extended TN model are consistent with the experimental results. The proposed model is further verified using additional experimental results provided in references. The obtained results demonstrate the nonlinear deformation behaviors of glassy polymers under wide ranges of temperature and strain rate.

Investigations into sample geometry effects on the superelastic and fatigue behavior of Nitinol: Modeling and experiments

The sample geometry by way of its influence on stress distribution is expected to control the superelastic and fatigue behavior of Nitinol. A variety of sample geometries are reported in literature for studying the fatigue behavior of Nitinol and it is unclear which geometry is the most suitable. To establish this, we conducted finite element simulations on the different geometries employing the ANSYS software package. Guided by the simulation predictions, samples bearing two different geometries, g_1 and g_5, were fabricated from Nitinol sheetswhich were apriori heat treated at 300 °C. The heat treated Nitinol was characterized by optical microscopy and differential scanning calorimetry to reveal the grain structure and transformation temperatures. Tensile samples of this material were subjected to cyclic uniaxial tensile tests where the maximum stress was increased gradually from 600 to 800 MPa in steps of 100 MPa every 10 cycles. The residual strain at the end of every 10th cycle was noted and found to be higher for g_1 compared to g_5. X-ray diffraction investigations on the cycled samples indicated a higher residual martensite phase in g_1 compared to g_5. The higher residual martensite is considered to be the cause of the poorer fatigue life of samples bearing geometry g_1 compared to that of g_5. Scanning electron microscope studies validated the fatigue measurements as the g_1 fractographs demonstrated higher void fraction vis-à-vis g_5.

Constitutive modelling of rubbers: Mullins effect, residual strain, time-temperature dependence

Filled rubbers are an important part of engineering materials because they have unique properties such as large deformability, increased stiffness and energy dissipation ability. The complexity of the material model parameter identification and the consideration of essential behaviours such as temperature dependence or residual strain may be a great challenge during the constitutive modelling. In this paper, a hyper-visco-pseudo-elastic constitutive equation is introduced and applied to model the complex behaviour of filled rubbers by considering (i) the Mullins effect, (ii) the temperature effect, and (iii) the effect of residual strains. The time-independent material response is provided by the modified Dorfmann–Ogden pseudo-elastic material model, while the time and temperature dependence is taken into consideration by the Prony series-based linear viscoelastic theory and the time-temperature superposition principle. Furthermore, by assuming homogeneous deformations, numerical stress solutions are presented to perform the material model calibration simple and fast, even when considering uniaxial tension/compression and simple shear simultaneously. The material model can be adapted to handle any hyperelastic model, arbitrary damage and residual strain variable, user-defined time-temperature superposition function, and any number of Maxwell elements (spring-dashpot terms). Here, the model parameters are determined from uniaxial stress relaxation-recovery tests, as well as cyclic uniaxial tensile and cyclic simple shear tests of different strain rates. Finally, the theoretical results are compared with experimental data for an EPDM rubber filled with 50 phr of carbon black.

Experimental Analysis of Plantar Fascia Mechanical Properties in Subjects with Foot Pathologies

Plantar Fascia (PF) is a fibrous tissue that plays a key role in supporting the foot arch; it can be affected by several pathologies that can alter foot biomechanics. The present study aims at investigating the mechanical behavior of PF and evaluating possible correlations between mechanical properties and specific pathologies, namely diabetes and plantar fibromatosis (Ledderhose syndrome). PF samples were obtained from 14 human subjects, including patients with Ledderhose syndrome, patients affected by diabetes and healthy subjects. Mechanical properties of PF tissues were evaluated on three samples from each subject, by cyclic uniaxial tensile tests up to 10% of maximum strain and stress relaxation tests for 300 s, in hydrated conditions at room temperature. In tensile tests, PF exhibits non-linear stress–strain behavior, with a higher elastic modulus (up to 25–30 MPa) in patients affected by Ledderhose syndrome and diabetes with respect to healthy subjects (elastic modulus 10 ÷ 14 MPa). Stress-relaxation tests show that PF of patients affected by Ledderhose syndrome and diabetes develop more intense viscous phenomena. The results presented in this work represent the first experimental data on the tensile mechanical propertied of PF in subjects with foot diseases and can provide an insight on foot biomechanics in pathological conditions.

Analysis of tensile behavior of recycled aggregate concrete using acoustic emission technique

Recycled concrete aggregate (RCA) was processed from reinforced concrete edge beams sourced from a demolished bridge. This material replaced different ratios of coarse aggregate in a benchmark concrete. The tensile behavior of the developed concrete mixes was characterized via monotonic and cyclic uniaxial tensile tests performed on notched cylinders. Such tensile tests allow for the quantification of the fracture energy and softening behavior of the concrete. Moreover, acoustic emission (AE) measurements were conducted in conjunction with the cyclic tests to characterize e.g. micro-crack initiation and development, as well as crack localization. The tensile behavior of the various materials was found to be similar with minimal variation in the results. However, the softening behavior suggests that the RCA materials are slightly more brittle compared to both the mother and benchmark materials. The corresponding AE measurements also indicated similarities between the micro-crack initiation and development for these mixes. It can be constituted that if the concrete used to produce RCA is of high quality and from one source, the resulting RAC will have adequate tensile properties with minimal variation, despite the aggregate replacement ratio.

Cyclic tensile tests on prestressing strands embedded in concrete

The fatigue life of prestressed concrete beams, subjected to cyclic bending, mainly depends on the fatigue behaviour of the embedded prestressing strands. An evaluation of international fatigue test results revealed a reduced fatigue life of embedded strands in prestressed concrete beams compared to single strands in air. The reduced fatigue life can be explained by specific influences and fatigue processes caused by the built-in conditions of strands. Due to the lack of basic understanding, systematic investigations are currently carried out to identify, quantify and describe different influencing parameters and fatigue processes as well as to better understand and determine the fatigue behaviour of strands in pre-tensioned concrete beams. In this article, the experimental investigations regarding the fatigue life of strands embedded in concrete are presented. Within cyclic uniaxial tensile tests on strands in air and strands embedded in concrete, the influence of fretting fatigue processes and friction stresses between the outer wires of strands and the surrounding concrete was determined.

A constitutive model for hysteresis: the continuum damage approach for filled rubber-like materials

In this contribution, a constitutive model is proposed for filled rubber-like materials to describe hysteresis. The model is based on the network decomposition concept. Rubber matrix is decomposed into purely elastic and deformable networks. The Gent model is considered to model the purely elastic network. The deformable network is simulated by using the freely jointed chain concept, a probability density function of the chain length and the network alteration theory. Damage in a network is assumed as a debonding of polymer chains from filler surface, which evolves with respect to the chain length over the set of available chains. In the consecutive loading cycles, a new network rearrangement is accounted for the characterization of the hysteresis behavior. Debonded chains in the damaged network are considered to rebond up to the point of the permanent set. The model contains seven material parameters and was successfully tested on the sequential cyclic uniaxial tensile test data of filled rubbers having different filler concentrations.

Influence of Filler Morphology on Electrical Conductivity Variations of Stretchable Wires Printed with Electrically Conductive Pates

Variation in electrical resistivity of stretchable wires printed with electrically conductive pastes containing silver flakes or silver particles was examined during uniaxial cyclic tensile tests. Viscoelastic deformation of the specimens can contribute to suppress increase in electrical resistivity of the wires during loading. Electrical resistivity of the wires significantly increased during unloading not only during loading. This increase in electrical resistivity during unloading is believed to occur related to Mullins effect. Electrical resistivity significantly increases during unloading when the silver micro-particles are used as fillers dispersed in the wires although increase in resistivity can be suppressed during first loading step. Mechanical behavior of the wires that depend on filler morphology plays an important role in determining electrical resistivity variations during the cyclic tensions.

Influence of Long-Term Storage on Shape Memory Performance and Mechanical Behavior of Pre-stretched Commercial Poly(methyl methacrylate) (PMMA).

In this paper, we experimentally investigate the influence of storage at 40 °C on the shape memory performance and mechanical behavior of a pre-stretched commercial poly(methyl methacrylate) (PMMA). This is to simulate the scenario in many applications. Although this is a very important topic in engineering practice, it has rarely been touched upon so far. The shape memory performance is characterized in terms of the shape fixity ratio (after up to one year of storage) and shape recovery ratio (upon heating to previous programming temperature). Programming in the mode of uniaxial tension is carried out at a temperature within the glass transition range to one of four prescribed programming strains (namely 10%, 20%, 40% and 80%). Also investigated is the residual strain after heating for shape recovery. The characterization of the mechanical behavior of programmed samples after storage for up to three months is via cyclic uniaxial tensile test. It is concluded that from an engineering application point view, for this particular PMMA, programming should be done at higher temperatures (i.e., above its Tg of 110 °C) in order to not only achieve reliable and better shape memory performance, but also minimize the influence of storage on the shape memory performance and mechanical behavior of the programmed material. This finding provides a useful guide for engineering applications of shape memory polymers, in particular based on the multiple-shape memory effect, temperature memory effect, and/or low temperature programming.

Fibrous soft tissues damage evaluation with a coupled thermo-visco-hyperelastic model

We model the thermo-visco-hyperelastic behavior of soft tissues using a thermodynamic framework. For this purpose, we develop a rheological model which can predict the stress–stretch behavior as well as the temperature variation due to visco-hyperelasticity and rate-dependent damage of the matrix and fibers. In a second stage, we carry out a set of cyclic uniaxial tensile tests to provide experimental data and calculate the material constants for the constitutive model utilizing the genetic algorithm. Later, with the purpose of validation, we determine the stress–stretch relation, and determine the temperature change in another series of experiments, and draw comparisons with the model predictions. The results show that the material behavior strongly depends on the temperature, strain rate and also the fiber’s direction. We determine that the temperature change is more significant at high strain rate and initial temperature levels and that it is necessary to use the developed coupled model.

Stress whitening effects in transparent structural silicone adhesives

Stress whitening is a common effect in polymers where an increase in brightness or an increased opacity of the material can be observed under mechanical loading. Investigating the stress whitening effect for the transparent structural silicone adhesive (TSSA), this effect occurs in different forms depending on the applied deformation. The intensity and appearance of whitening in TSSA depends decisively on the type of loading, i.e. under isochoric deformation a spot-wise whitening can be observed, whereas under volumetric loading a very dense, cloud-like whitening becomes visible. In order to clarify why the stress whitening effect occurs at all, experimental investigations are carried out on uniaxial cyclic tensile tests and constrained tensile tests. The special feature of the uniaxial cyclic tensile tests is that they are performed in a miniature tensile testing machine, which is positioned under a light microscope. This makes it possible to observe stress whitening during cyclic deformation at a micro-scale. Furthermore, for the observation of whitening during constrained tensile tests, so-called pancake test are investigated and compared with the results of the uniaxial cyclic tensile tests. Since the whitening effect in the pancake test is in clear contrast to the uniaxial tensile tests, differences of both results are presented. Finally, the causes of both forms of whitening are defined and characterized.

Pseudo-elastic cavitation model—part II: extension to cyclic behavior of transparent silicone adhesives

This study investigates the cyclic structural behaviour of adhesive joints of glass and metal using thin, structural silicone adhesives in heavily constrained applications. Based on cyclic uniaxial tensile tests on dog-bone and pancake test samples, the pseudo-elastic cavitation model from part I of this publication will be extended to describe two phenomenons: stress softening due to Mullins effect, as well as a mechanical hysteresis occurring under hydrostatic loading of rubber-like materials. This mechanical hysteresis under hydrostatic loading is associated with the growth and shrinkage of microscopic voids in the materials structure, and shows distinctive differences to the mechanical hysteresis known from isochoric test samples. In order to transfer the already presented pseudo-elastic cavitation model to describe the cyclic material behaviour, the isochoric part of the cavitation model is extended according to the classical theory of pseudo-elasticity to numerically describe stress softening under isochoric deformations. In addition, the volumetric part is provided with a special material formulation so that it can numerically reproduce the void growth hysteresis under cyclic volumetric tests, e.g. pancake tests. For validation, three-dimensional simulations of both cyclic tensile tests (dog-bone and pancake tests) are carried out.