Uniaxial Data Research Articles

A Novel Method for Estimating Acoustic Emission b Value Using Improved Magnitudes

The acoustic emission (AE) b value plays an important role in studying structural damage evolution and disaster precursors. The b value can be obtained from the least square fit between AE event number and magnitude (the Gutenberg-Richter relationship), where the magnitude is generally calculated through the maximum amplitude of an AE signal. However, the magnitudes obtained from amplitudes of different AE signals may be quite different, due to the influence of coupling state between the sensor and specimen (expressed as the sensor sensitivity coefficient, Sc). Thus, the b values obtained from a single sensor and without magnitude correction may not be reliable. To address this, this study used pencil-lead breaks and far-field theory to obtain Sc values. One Sc value may be as much as double another, demonstrating that signal maximum magnitudes should be corrected before b value estimation. The Sc -corrected median magnitude is then treated as the AE event magnitude and used to estimate the b value. Application to uniaxial compression AE data from a red sandstone indicates that the improved magnitude reduces the instability compared to magnitude based on a single sensor. The b value time series among sensors exhibit large differences, while the improved b values agree well with AE event locations and rock specimen failure mode. This research demonstrates for the first time the necessity of amplitude correction in AE magnitude and b value computation.

An equivalent work-hardening description of an interstitial-free steel sheet based on uniaxial tensile and hydraulic bulge tests

In this work, the plastic behavior of an interstitial-free steel sheet was first evaluated by standard uniaxial tensile and hydraulic bulge tests to reproduce the intermediate and high straining levels commonly observed in sheet metal forming processes. Next, a simple procedure was proposed to obtain an equivalent work-hardening curve, representing the high strain domain instead of the conventional uniaxial tensile data. This procedure involves an anisotropy parameter calculated based on Hill's quadratic criterion using the measured r-values in the rolling and transverse sheet directions. Under the assumption of an isotropic work-hardening, the equivalent curve is defined from the true stress and true thickness plastic-strain results of the hydraulic bulge test. The transformed data were fitted to usual power-law type equations to obtain an adequate work-hardening description for finite element numerical simulation purposes. Based on the goodness-of-fit measures, namely, R-squared, root-mean-square error, and root-mean-square of residual percentage, the combined Swift–Hockett–Sherby equation has proved to be the most suitable choice to describe the plastic behavior of the investigated interstitial-free steel under both intermediate and high strains conditions.

Incorporating fiber recruitment in hyperelastic modeling of vascular tissues by means of kinematic average.

We present a framework for considering the gradual recruitment of collagen fibers in hyperelastic constitutive modeling. An effective stretch, which is a response variable representing the true stretch at the tissue-scale, is introduced. Properties of the effective stretch are discussed in detail. The effective stretch and strain invariants derived from it are used in selected hyperelastic constitutive models to describe the tissue response. This construction is investigated in conjunction with Holzapfel-Gasser-Ogden family strain energy functions. The ensuing models are validated against a large body of uniaxial and bi-axial stress-strain response data from human aortic aneurysm tissues. Both the descriptive and the predictive capabilities are examined. The former is evaluated by the quality of constitutive fitting, and the latter is assessed using finite element simulation. The models significantly improve the quality of fitting, and reproduce the experiment displacement, stress, and strain distributions with high fidelity in the finite element simulation.

Room-temperature plastic behavior and formability of a commercially pure titanium: Mechanical characterization, modeling, and validation

Data on the room temperature behavior of titanium is limited. To assess the anisotropy of the plastic behavior of a commercially pure grade 2 hcp–titanium T40 for different strain paths, in this study both uniaxial tests in various orientations with respect to the rolling direction as well as bulging tests using different die apertures were conducted. Under uniaxial tension, the plastic anisotropy in yielding is moderate, while the anisotropy in plastic strains is very strong. The material also displays tension–compression asymmetry, irrespective of the orientation the flow stress in compression being higher than in tension. The bulging tests data, namely the evolution of the thickness with the fluid pressure complemented with post-test DIC measurements reveal that T40 has unusual deformation and failure characteristics as compared to common materials with cubic crystal structure. Irrespective of the die aperture, instabilities occur suddenly, the reduction in thickness being drastic (snap failure). However, the evolution of strains depends on the die aperture aspect ratio (hemispherical vs. elliptical). The anisotropy of the titanium T40 also leads to a different response depending on the orientation of the material axes with respect to the die axes. To explain these specific characteristics of the behavior of titanium T40 under bulging, two orthotropic criteria were used, one that neglects the tension–compression asymmetry of the material (Hill, 1948) and another that accounts for the combined effects of anisotropy and tension–compression asymmetry (Cazacu et al. (2006) yield criterion). Determination of the parameters involved in both criteria was done using only uniaxial test data. The F.E. results presented show that neglecting the tension–compression asymmetry of T40 leads to less accurate predictions of the fluid pressure and strains at which fracture occurs, and in some cases an incorrect orientation of the zone of localized deformation. Using the Cazacu et al. (2006) criterion, it is possible to accurately predict the sudden occurrence of instabilities, the distribution of plastic strains, and the correct orientation of the zone of localized deformation in both the hemispherical and elliptical bulge tests.

From Uniaxial Testing of Isolated Layers to a Tri-Layered Arterial Wall: A Novel Constitutive Modelling Framework

Mechanical testing and constitutive modelling of isolated arterial layers yields insight into the individual layers’ mechanical properties, but per se fails to recapitulate the in vivo loading state, neglecting layer-specific residual stresses. The aim of this study was to develop a testing/modelling framework that integrates layer-specific uniaxial testing data into a three-layered model of the arterial wall, thereby enabling study of layer-specific mechanics under realistic (patho)physiological conditions. Circumferentially and axially oriented strips of pig thoracic aortas (n = 10) were tested uniaxially. Individual arterial layers were then isolated from the wall, tested, and their mechanical behaviour modelled using a hyperelastic strain energy function. Subsequently, the three layers were computationally assembled into a single flat-walled sample, deformed into a cylindrical vessel, and subjected to physiological tension-inflation. At the in vivo axial stretch of 1.10 ± 0.03, average circumferential wall stress was 75 ± 9 kPa at 100 mmHg, which almost doubled to 138 ± 15 kPa at 160 mmHg. A ~ 200% stiffening of the adventitia over the 60 mmHg pressure increase shifted layer-specific load-bearing from the media (65 ± 10% → 61 ± 14%) to the adventitia (28 ± 9% → 32 ± 14%). Our approach provides valuable insight into the (patho)physiological mechanical roles of individual arterial layers at different loading states, and can be implemented conveniently using simple, inexpensive and widely available uniaxial testing equipment.

Finite Strain Constitutive Modelling of Shape Memory Alloys Considering Partial Phase Transformation with Transformation-Induced Plasticity

This paper presents a unified modelling effort to describe partial phase transformation during cyclic thermo-mechanical loading in Shape Memory Alloys (SMA). To this purpose, a three-dimensional (3D) finite strain constitutive model considering TRansformation-Induced Plasticity (TRIP) is combined with a modified hardening function to enable the accurate and efficient prediction of partial transformations during cyclic thermo-mechanical loading. The capabilities of the proposed model are demonstrated by predicting the behavior of the material under pseudoelastic and actuation operation using finite element analysis. Numerical results of the modified model are presented and compared with the original model without considering the partial transformation feature as well as with uniaxial actuation experimental data. Various aspects of cyclic material behavior under partial transformation are analyzed and discussed for different SMA systems.

Mechanical Behaviour of Large Strain Capacitive Sensor with Barium Titanate Ecoflex Composite Used to Detect Human Motion

In this paper, the effect of strain rate on the output signal of highly stretchable interdigitated capacitive (IDC) strain sensors is studied. IDC sensors fabricated with pristine Ecoflex and a composite based on 40 wt% of 200 nm barium titanate (BTO) dispersed in a silicone elastomer (Ecoflex 00-30TM) were subjected to 1000 stretch and relax cycles to study the effect of dynamic loading conditions on the output signal of the IDC sensor. It was observed that the strain rate has no effect on the output signal of IDC sensor. To study the non-linear elastic behaviour of pristine Ecoflex and composites based on 10, 20, 30, 40 wt% of 200 nm BTO filler dispersed in a silicone elastomer, we conducted uniaxial tensile testing to failure at strain rates of ~5, ~50, and ~500 mm/min. An Ogden second-order model was used to fit the uniaxial tensile test data to understand the non-linearity in the stress-strain responses of BTO-Ecoflex composite at different strain rates. The decrease in Ogden parameters (α1 and α2) indicates the decrease in non-linearity of the stress-strain response of the composite with an increase in filler loading. Scanning electronic microscopy analysis was performed on the cryo-fractured pristine Ecoflex and 10, 20, 30, and 40 wt% of BTO-Ecoflex composites, where it was found that 200 nm BTO is more uniformly distributed in Ecoflex at a higher filler loading levels (40 wt% 200 nm BTO). Therefore, an IDC sensor was fabricated based on a 40 wt% 200 nm BTO-Ecoflex composite and mounted on an elastic elbow sleeve with supporting electronics, and successfully functioned as a reliable and robust flexible sensor, demonstrating an application to measure the bending angle of an elbow at slow and fast movement of the arm. A linear relationship with respect to the elbow bending angle was observed between the IDC sensor output signal under a 50% strain and the deflection of the elbow of hand indicating its potential as a stretchable, flexible, and wearable sensor.

Physical properties and fracture behavior of rocks in uniaxial and triaxial compression: A case-study of Zhdanovskoe deposit, Kola Mining and Metallurgical Company

The paper presents the test data on properties of rocks from Zhdanovskoe deposit located in the Pechenga area of the Murmansk Region. The nature of the elastic energy accumulation in rock specimens and their susceptibility to uncontrollable fracture in the dynamic mode are determined. The uniaxial and triaxial compression test data are used to find mechanical properties and energy characteristics of rock specimens. The tested rocks are assessed as hard and susceptible to dynamic fracture, which is one of the criteria of rockburst hazard.

An improved calibration method of the K&C model for modeling steel-fiber reinforced concrete

The K&C material model, one of the widely used concrete models implemented in LS-DYNA for blast or impact analysis, is modified to improve its numerical accuracy for steel-fiber reinforced concrete (SFRC). Many input parameters are required in this model to describe the material properties of SFRC. To address this, an improved calibration method that can easily predict the stress–strain relationships of SFRC by modifying the three strength surfaces and the damage function η(λ) based on uniaxial and triaxial compression data from previous studies is proposed in this paper. The calibration method is verified by single element tests for unconfined uniaxial and triaxial compressive data. In addition, with the introduction of the dynamic increase factor (DIF), a finite element model is produced to demonstrate the validity and applicability of the proposed method through comparison with the experimental results of SFRC slabs subjected to projectile impact.

Strength and Deformation Characteristics of Fiber Reinforced Longdong Loess and Experimental Study of Modified Duncan -Chang Model

Fiber yarn reinforced loess is prepared through mixing plain loess with a certain proportion of polyester fiber yarn, which is formed by loosening, carding and cutting waste synthetic textile polyester fabric and has rough surface properties and good acid-alkali corrosion resistance. The strength and deformation characteristics of Longdong Loess reinforced by fiber yarn were studied. The test results show that the uniaxial compressive strength of fiber yarn reinforced loess increases with the increase of fiber yarn proportion and fiber yarn length, and decreases with the increase of fiber yarn fineness. Combined with the uniaxial compressive strength data of fiber yarn reinforced loess under the optimal water content and liquid limit water content, an index which can comprehensively reflect the reinforcement performance of fiber yarn reinforced loess is proposed-- Fiber reinforced index. The shear stress-strain relationship of triaxial consolidation drainage of fiber-reinforced loess with different proportion of fiber yarn is strain hardening type. The hypothesis of hyperbolic form is in accordance with Duncan Chang model. By discussing the relationship between the parameters of fiber yarn reinforced loess and plain loess model, the empirical expression of model parameters considering the influence of fiber yarn reinforced loess is obtained. A modified Duncan-Chang E-B model reflecting the influence of different fiber yarn blending ratio was constructed. The rationality of the model is verified by comparing the test curve with the model prediction curve.

Characterization of the dynamic viscoelastic response of the ascending aorta imposed via pulsatile flow

This study characterizes the material properties of a viscoelastic, ex vivo porcine ascending aorta under dynamic-loading conditions via pulsatile flow. The deformation of the opaque vessel wall and the pulsatile flow field inside the vessel were recorded using ultrasound imaging. The internal pressure was extracted from the pulsatile flow results and, when coupled with the vessel-wall expansion, was used to calculate the instantaneous elastic modulus from a novel, time-resolved two-dimensional (i.e. axial and circumferential) stress model. The circumferential instantaneous elasticity obtained from the two-dimensional stress model was found to match the uniaxial tensile test for strains below 50%. The agreement in elasticity between the two stress states reveals that the two-dimensional stress model accurately resolves the circumferential stress of the viscoelastic aorta at physiological strains (8%–30%). At higher strains, results from pulsatile flow generated a more compliant response than the uniaxial measurements. Viscoelastic properties (storage modulus and loss factor) were also calculated using the two-dimensional stress model and compared to those obtained from uniaxial tests. While instantaneous elasticity matched between the cylindrical and uniaxial loading, the viscoelastic behaviour significantly diverged between stress states. The storage modulus obtained from the pulsatile flow data was dependent on mean Reynolds number, while the uniaxial storage modulus results exhibited a strong inverse dependency on the frequency. The loss factor for the pulsatile flow data increased alongside the frequency, while the uniaxial data indicated a constant loss factor over the entire frequency range. The results of the current study show that the two-dimensional stress model can accurately extract the material properties of the ex vivo porcine aorta.

Validation test of a predictor of fatigue failure under biaxial out-of-phase loading conditions

The definition of a new predictor of failure initiation in high-cycle fatigue, previously calibrated for aluminum alloys on the basis of uniaxial experimental data and tested against biaxial in-phase data, was modified to account for biaxial out-of-phase loading. The process of validation, with reference to the results of three biaxial out-of-phase fatigue tests, is described.

A new approach to evaluate material creep properties by C-shape ring specimen with fixed constraints

Small specimen test technique is widely used to evaluate material creep properties for those components operated at the elevated temperatures. However, the existing small specimen test techniques cannot be well applied for small miniature tubular components well, such as steam pipe and gas turbine recuperator in aviation, due to the equivalent gauge length, specimen volume, stress analysis method and conversion relationship. In this paper, combing the advantages of three-point bending specimen with fixed constraints and small ring creep specimen, a new C-shape ring specimen with fixed constraints (CRSFC) was proposed. Based on beam bending model, the conversion relationship between CRSFC and uniaxial creep test data was established by using complementary strain energy and reference stress method. Using finite element method, conversion coefficients and stress evolution process were obtained. Then the feasibility and accuracy of the above conversion relationship were verified by carrying out four sets of CRSFC creep tests of 1.25Cr0.5MoSi at 550 °C. It can be seen that creep parameters obtained by CRSFC agree well with those from uniaxial creep test with the maximum error of 22.6%. Finally, the effects of the straight edge length, indenter radius, eccentric load and indenter-specimen surface friction coefficient on the load-point steady-state displacement rate were investigated by finite element method. The results show that the effect of the straight edge length is negligible. In order to minimize the effects of other parameters, the indenter radius 0.6 mm ≤ r ≤ 1.2 mm, eccentric displacements e ≤ 0.2 mm and friction coefficient f ≤ 0.8 are recommended in CRSFC creep test.

The effect of organic carbon content on soil compression characteristics

We investigated the effect of soil organic carbon (SOC) on the consolidation behaviour of soil from two long term field experiments at Rothamsted; the Broadbalk Wheat Experiment and Hoosfield Spring Barley. These experiments are located on soil with similar particle size distributions, and include treatments with SOC contents ranging from approximately 1–3.5 g/100 g. Soils taken from plots with contrasting SOC contents were compressed and deformed in a triaxial cell and the normal consolidation and critical state lines were determined. We found that the compression index was independent of SOC, but the void ratio at any given effective stress was highly correlated with organic carbon content. By comparison with uniaxial compression data, the apparent influence of SOC on the compression index is likely to be due to its effect on soil hydraulic properties rather than any intrinsic effects of strength. The plastic limit test appears to be a useful and simple test to allow direct comparison of soil physical behaviour and expected soil density.

On the Performance of Isotropic Hyperelastic Constitutive Models for Rubber-Like Materials: A State of the Art Review

Abstract Besides the well-known landmark models for the hyperelastic response of rubberlike materials, many new hyperelastic constitutive models have emerged over the last decade. Despite many reviews on constitutive modeling or elastomers, it is still a challenging endeavor for engineers to decide for a constitutive model for the specific rubber compound and application. In this work, we have reviewed 44 hyperelastic constitutive models for elastomers and assessed their strength and weaknesses under uniaxial, pure shear, and (equi)biaxial deformations. To this end, we first present a novel parameter identification methodology based on various multi-objective optimization strategies for the selection of the best constitutive models from a given set of uniaxial tension, pure shear, and (equi)biaxial tension experiments. We utilize a hybrid multi-objective optimization procedure using a genetic algorithm to generate multiple initial points for gradient-based search algorithm, Fmincon utility in matlab. The novelty of the approach is (i) simultaneous fitting with variable weight factors for uniaxial, equibiaxial, and pure shear data, and (ii) the sorting of the models based on objective normalized quality of fit metric. For the models incapable of simultaneously fitting the three distinct deformation data, the validity range is assessed through a threshold value for the quality of fit measure. Accordingly, 44 hyperelastic models are sorted with respect to their simultaneous fitting performance to the experimental dataset of Treloar and Kawabata. Based on the number of material parameters, and their fitting performance to experimental data, a detailed discussion is carried out.

Mixed-mode crack growth simulation in aviation engine compressor disk

This study focuses on a mixed mode crack growth analysis of an aviation gas turbine engine (GTE) compressor disk based on simulation principles. The operation damages occur via inclined surface cracks in a “dovetail type” disk-and-blade attachment. Based on the sizes and configuration of this attachment, three geometries for simulation models of the GTE compressor disk are proposed. The biaxial loading conditions of the simulation models are determined and numerically verified to reproduce the stress-strain state in critical zones of the compressor disk during operation. To determine the elastic-plastic fracture mechanical parameters, a 3D full-size finite element method (FEM) analysis is conducted for the GTE compressor disk and simulation models, based on operating loading conditions. As a result, the distributions of the new mixed-mode fracture resistance parameters in the form of equivalent elastic and plastic stress intensity factors along the crack front in the disk-and-blade dovetail-type attachment are applied to the experimental uniaxial and biaxial data for crack growth rate interpretation. The possibility of using the proposed simulation principles for an assessment of the structural integrity of GTE rotating disks is discussed.

Full-Field Strain Reconstruction Using Uniaxial Strain Measurements: Application to Damage Detection

This work investigates the inverse problem of reconstructing the continuous displacement field of a structure using a spatially distributed set of discrete uniaxial strain data. The proposed technique is based on the inverse Finite Element Method (iFEM), which has been demonstrated to be suitable for full-field displacement, and subsequently strain, reconstruction in beam and plate structures using discrete or continuous surface strain measurements. The iFEM uses a variationally based approach to displacement reconstruction, where an error functional is discretized using a set of finite elements. The effects of position and orientation of uniaxial strain measurements on the iFEM results are investigated, and the use of certain strain smoothing strategies for improving reconstruction accuracy is discussed. Reconstruction performance using uniaxial strain data is examined numerically using the problem of a thin plate with an internal crack. The results obtained highlight that strain field reconstruction using the proposed strategy can provide useful information regarding the presence, position, and orientation of damage on the plate.

Derivation of a fatigue damage law for an adhesive from in-situ bending tests

The adhesives used for the attachment of electronic components to space boards should withstand harsh vibrations of the space launch, which requires their characterization in fatigue. The present study investigates Ablestik 8-2 epoxy adhesive within this context. Novel adhesive test assemblies were devised, which consist of a rigid ceramic component bonded to a resonant flexible epoxy-fibreglass (E-glass) support. Cantilever and square E-glass supports produced uniaxial and biaxial bending, respectively. The in-situ fatigue tests, conducted on batches of uniaxial/biaxial bending adhesive assemblies, led to distinct data sets of maximum support deflection versus the number of cycles to crack initiation/total failure. The derivation of an intrinsic fatigue damage law of the adhesive relied on the substitution of deflection by the maximum principal strain of each adhesive point while keeping the Basquin’s form. In so doing, the adhesive strain was computed from finite element models of test assemblies built and simulated under Abaqus. The adhesive layer was meshed by cohesive elements created through a Fortran user-element subroutine coupled to Abaqus. The subroutine incorporated an already validated static damage together with the strain-based fatigue damage law sought. The retained Basquin’s fatigue damage law has undergone calibration against uniaxial bending test data and validation by biaxial bending test data.

Effect of ternary additions of Cu and Fe on the hot deformation behavior of NiTi shape memory alloy - A study using processing maps

The addition of ternary alloying elements Cu and Fe on the hot workability of binary NiTi SMA is assessed using the processing maps approach. Uniaxial compression test data obtained in the temperature, T, range 800–1050 °C and strain rate, ε˙, of 10−3 – 10+1 s−1 were utilized to construct power dissipation, instability and strain rate sensitivity maps at true strain, ε = 0.5. These maps and complementary microstructural analyses of the deformed specimens were used to identify various deformation mechanisms operating in different T-ε˙ regimes. Based on the processing maps, three stable domains for processing were identified with Domain-2 occurring at higher T and intermediate ε˙ with power dissipation efficiency of 30–45% being the optimum for thermo-mechanical processing. The addition of Cu in NiTi SMA improves its hot workability through enlarging stable domains for processing whereas Fe addition shrinks it. Microstructural analysis indicates occurrence of dynamic recrystallization (DRX) in NiTi, NiTiFe and dynamic recovery (DRV) in NiTiCu as the dominating deformation mechanism in Domain-2. Sluggish DRX kinetics in NiTiCu SMA in Domain-2 is related to its higher deformation resistance and higher critical stress required for the onset of DRX vis-à-vis NiTi, NiTiFe SMAs. Instability maps corroborated through microstructural analysis showed instability in the form of flow localization.

Ability of Constitutive Models to Characterize the Temperature Dependence of Rubber Hyperelasticity and to Predict the Stress-Strain Behavior of Filled Rubber under Different Defor Mation States.

In this paper, some representative hyperelastic constitutive models of rubber materials were reviewed from the perspectives of molecular chain network statistical mechanics and continuum mechanics. Based on the advantages of existing models, an improved constitutive model was developed, and the stress–strain relationship was derived. Uniaxial tensile tests were performed on two types of filled tire compounds at different temperatures. The physical phenomena related to rubber deformation were analyzed, and the temperature dependence of the mechanical behavior of filled rubber in a larger deformation range (150% strain) was revealed from multiple angles. Based on the experimental data, the ability of several models to describe the stress–strain mechanical response of carbon black filled compound was studied, and the application limitations of some constitutive models were revealed. Combined with the experimental data, the ability of Yeoh model, Ogden model (n = 3), and improved eight-chain model to characterize the temperature dependence was studied, and the laws of temperature dependence of their parameters were revealed. By fitting the uniaxial tensile test data and comparing it with the Yeoh model, the improved eight-chain model was proved to have a better ability to predict the hyperelastic behavior of rubber materials under different deformation states. Finally, the improved eight-chain model was successfully applied to finite element analysis (FEA) and compared with the experimental data. It was found that the improved eight-chain model can accurately describe the stress–strain characteristics of filled rubber.