Uniaxial Tension Research Articles

Insight into the effect of vibration parameters on deformation mechanism during scratching of nanograin iron alloy by molecular dynamics

Molecular dynamics simulations were employed to study the deformation behavior and microstructure evolution of nanocrystalline iron alloy during vibration-assisted scratching. The mechanical properties of the plastic deformation layer after scratching were tested by uniaxial tension. The results show that dislocation multiplication and twinning occur sequentially during loading, while dislocation rebound and detwinning occur during unloading. High stress induces dislocation multiplication. High strain rate facilitates the formation of deformation twins. Under the inhibitory effect of deformation twins on dislocation activity and the elastic recovery of the surface, dislocation density decreases with increasing frequency but initially increases and decreases with increasing amplitude. The plastic deformation layer at 10 GHz frequency and 1 nm amplitude exhibits optimal yield strength due to dislocation and nanotwin strengthening.

Mechanical Response and Microstructural Evolution of AZ31B Alloy Sheet in Uni-Axial Tension at Middle-Low Strain Rates and Temperatures

Mechanical Response and Microstructural Evolution of AZ31B Alloy Sheet in Uni-Axial Tension at Middle-Low Strain Rates and Temperatures

Mechanical properties and structural evolution of sodium borosilicate glasses during uniaxial tension: Molecular dynamics simulation and experiments

The mechanical properties and structural evolution of sodium borosilicate glasses under the uniaxial tensile process were investigated through molecular dynamics simulation. The simulated properties of sodium borosilicate glasses were in good agreement with the experimental values. [BO3] and Na+ compensated [BO4] groups were generated in the glass network in low boron content, while [BO3] appeared with increasing boron oxide. The structure descriptor, Fnet synthesized the structure and energy information of the glass network which was positively correlated with Young's modulus. The strength has been diminished due to the decreased degree of polymerization of the glass network and the migration of Na+ cations. Simultaneously, the elastic deformation of sodium borosilicate glass arose from the motion of Na+ cations and alterations in the Si-O-Si bond angle. Moreover, the plastic deformation of sodium borosilicate glasses was attributed to the transition from [BO4] to [BO3] and the higher mobility of [BO3] than [BO4] and [SiO4].

Biomechanical analysis of cadaver rabbit Achilles tendons after full transection and suture: Comparison of U-Tang 4-strand with the cross-locked version of U-Tang 4-strand suture technique

IntroductionTendon injures rank as the second most common hand injuries, and unsatisfactory repair can significantly impact a patient's everyday life. Over the years, various suture techniques have been studied in the pursuit of finding the optimal repair method. The ideal tendon repair should achieve maximum strength, while being easy to perform and minimizing tissue trauma. This study aims to compare the mechanical properties of the cross-locked U-Tang 4-strand suture to its unmodified version, the U-Tang 4-strand suture, to assess which technique offers greater repair strength. MethodsSixteen Achilles tendons from New Zealand White rabbits were randomly assigned to one of two suture technique groups; an original U-Tang 4-strand suture or a cross-locked U-Tang 4-strand suture, both performed using a 4-0 Supramid thread. The specimens were tested in uniaxial tension after a preconditioning phase. Cross-sectional area, load until failure, gap formation, stiffness, elastic modulus, and failure stress were determined. ResultsThe standard U-Tang 4-strand suture withstood a maximum force of 25.48 ± 6.06 N, while the cross-locked version endured 33.90 ± 6.09 N. This indicates that the modified version demonstrated significantly greater strength (p = 0.021). The elastic modulus of the cross-locked U-Tang 4-strand suture (0.02 ± 0.003 MPa) was significantly higher than that of the original version (0.01 ± 0.006 MPa) (p = 0.028). No significant differences were observed regarding the cross-sectional area, load at 2 mm gap formation, stiffness and failure stress. ConclusionEmploying the cross-locked U-Tang 4-strand suture results in a significantly greater maximum force and elastic modulus compared to the original U-Tang 4-strand suture, utilizing the same thread and number of strands and knots. Therefore, the cross-locking version provides an alternative for achieving more stable initial repair strength.

Optimization of functionally graded materials to make stress concentration vanish in a plate with circular hole

This paper is devoted to the minimization of the stress concentration factor in infinite plates with circular hole made of functionally graded materials and subjected to a far-field uniform uniaxial tension. Despite the vast literature on the versatility of these materials, the novelty of the results is that the material distribution is not limited to prefixed laws, as in many works available in the literature. Instead, it is assumed to be an unknown piecewise constant function, thus aiming to derive the material distribution by exploiting, at best, the inhomogeneity concept associated with functionally graded materials. After a brief review of the governing equations, the motivation, the statement and the mathematical formulation of the optimization problem are given under the hypothesis of axisymmetric material distribution. Still, the problem could not be solved analytically, therefore a direct transcription approach by the aid of finite difference method has been followed to convert it into a nonlinear programming problem, whose solution has been obtained numerically by dedicated gradient-based solvers. Numerical optimal solutions are reported in graphical forms, thoroughly discussed and validated by means of the finite element method. The developed numerical approach yields a material inhomogeneity obeying a sigmoid-like function and a uniform hoop stress along the radial direction, thus making the stress concentration factor at the rim of the circular hole vanish.

Neural network based rYld2004 anisotropic hardening model under non-associated flow rule for BCC and FCC metals

This paper extends the reduced Yld2004 (rYld2004) function to present the anisotropic hardening behavior for body-centered cubic and face-centered cubic metals under the proportional loading conditions based on neural network. The parameters of the rYld2004 anisotropic hardening model (AH_rYld2004) are determined by the uniaxial tensile yield stresses along 0°, 15°, 30°, 45°, 60°, 75° and 90° from the rolling direction as well as equibiaxial tension. The evolution of anisotropic parameters are described by the back propagation neural network optimized by ant colony optimization algorithm. The predicted data by AH_rYld2004 and some common anisotropic models are compared with the experimental results to verify the precision of the AH_rYld2004 in characterizing anisotropic hardening. The comparison proves that the AH_rYld2004 precisely characterize the anisotropic evolution with increasing plastic deformation for AA 3003-O and QP980. Simultaneously, the AH_rYld2004 function based on neural network is used to accurately simulate of circular cup deep drawing for AA 3003-O and uniaxial tension for QP980. The results indicate that the AH_rYld2004 model is capable to accurately represent the plastic anisotropic evolution for uniaxial tension along seven loading directions and equibiaxial tension.

A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.

Crystal plasticity modeling of prior austenite orientation effects on deformation behaviors of martensitic steels under different strain paths

The influence of prior austenite grain (PAG) orientation on the deformation behavior of a low-carbon martensitic steel is investigated using crystal plasticity (CP) modeling with hierarchical representative volume elements (RVEs). The Kurdjumov-Sachs (K-S) relationship is refined for accurate PAG reconstruction in martensitic steel. A robust calibration strategy for CP parameters based on nanoindentation tests is developed by integrating analytical calculations with inverse methods. Virtual polycrystalline aggregates are subsequently generated by manipulating initial PAG orientations. The simulations reveal that assigning cube texture to PAGs enhances strain hardening of martensite under plane strain tension. Moreover, the RVEs with brass and copper orientated PAGs exhibit similar deformation behavior, and a more homogeneous strain distribution is realized in the RVE with PAG cube orientation. The influence of PAG orientation on stress and strain fields is correlated with lattice rotation behavior during deformation. Notably, different strain paths elicit distinct lattice rotation trajectories, wherein uniaxial tension and plane strain tension favor grains reorientation toward hard γ-fiber, whilst equi-biaxial tension drives the crystal matrix to concentrate on 〈001〉 and 〈011〉 directions. These findings provide insights into the intricate relationship between microstructural orientation and deformation behavior in martensitic steels, which is crucial for performance optimization.

Strain amplitude dependency of cyclic hardening/softening behavior of 490 N/mm2 class steel

Existing studies on the strain amplitude dependency of cyclic softening behavior in structural steels often involve limited cycles or strain amplitudes below 2.5%, failing to provide a comprehensive understanding of stabilized cyclic behavior. This study performed uniaxial tension–compression cyclic loading tests using SN490B structural steel under three loading patterns: constant, variable, and offset constant strain amplitudes. The cyclic hardening and softening behaviors and stress–strain hysteresis loops were compared. Under variable strain amplitude loading, the specimens were subjected to increasing and decreasing strain amplitudes to investigate the strain amplitude dependency of the cyclic hardening and softening behaviors. Under offset constant strain amplitude loading, mean strains were initially introduced in either the tension or compression strain range, followed by cyclic loading with a constant strain amplitude centered around the mean strains. The test results revealed the following: (1) Under constant strain amplitude cyclic loading, the material exhibited cyclic softening and hardening behaviors at strain amplitudes smaller than and larger than 0.5%, respectively; (2) Under variable strain amplitude cyclic loading, increased and reduced strain amplitudes resulted in cyclic hardening and softening behaviors, respectively. The cyclic hardening/softening behavior strongly depended on the strain amplitude. Applying a significant number of cycles after strain amplitude reduction resulted in the stress–strain curves closely resembling those under constant strain amplitude conditions; (3) Even under offset constant strain amplitude cyclic loading conditions with nonzero mean strain, the peak stresses and shapes of the hysteresis loops approached those under constant strain amplitude conditions without mean strain.

To justification of concrete strength criterion at biaxial compression

Introduction. Numerous experimental data from Russian and foreign researchers indicate that the classical plasticity hypotheses do not take into account the different resistance to uniaxial tension and compression, the influence of the spherical tensor. At the same time, experiments show that the ultimate resistance depends on the type of stress state, and hydrostatic pressure increases the strength and plasticity of solids. Aim. To establish the dependence of the influence of the second component of stresses during biaxial compression of concrete on the parameters of the complete diagrams of deformation of the material σbR and εbR it is necessary to describe these diagrams, and to construct a closed curve on the plane of the main stresses (concrete strength criterion). Materials and methods. Based on the experimental materials of foreign and domestic researchers, including the experiments of the authors of the article, methods of mechanics of deformed solids, limit curves and a closed curve on the plane of the main stresses in the form of a chain line forming the smallest area strength surface in the form of a catenoid are proposed. Results. The article provides an analysis of the known strength criteria from the point of view of their geometric interpretation in the stress space. It is shown that these studies relate mainly to metals and metal structures, and for the design of reinforced concrete and steel-concrete structures in a complex stress state, it is necessary to develop an appropriate criterion for the strength of concrete. Conclusions. As a result, the proposed limit curves and the surface (material strength criterion) on the plane of main stresses in the form of a catenoid accurately reflect the behavior of concrete under conditions of uniform and uneven flat stress state, and the equation of the surface in the form of a catenoid is a generalization of the equations of limit curves for each of the three types of flat stress state. At the same time, there is no overestimation of strength in the "compression – compression" area in this case.

A comparison of finite strain viscoelastic models based on the multiplicative decomposition

The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when expressed in the same configuration, enabling the definition of a unified general model. The ability of this general model to reproduce the main features of the behavior of rubbers is then explored. First, its responses are compared to those of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, a comparison is made between a classic generalized Maxwell rheological scheme and a Zener one with a non-constant viscosity, exploring the relevance of both options within the general model’s constitutive equations.

A sawtooth constitutive model describing strain hardening and multiple cracking of ECC under uniaxial tension

Abstract By collecting engineered cementitious composite (ECC) uniaxial tensile experimental research data, aiming at the multiple cracking characteristics of the strain hardening stage of the ECC stress–strain curve, a theoretical model describing the constitutive relationship of the ECC uniaxial tensile stress–strain – the multiple cracking sawtooth model – is proposed. Several model parameters were obtained with the fitting analysis of many ECC uniaxial tensile stress–strain curves. The application conditions and influencing factors of the three-order multi-crack “sawtooth” model of polyvinyl alcohol (PVA)-ECC and polyethylene (PE)-ECC and the four-order multi-crack “sawtooth” model of PVA-ECC are studied. The result shows that the higher the fiber reinforcement index, the better the tensile properties of ECC. The fiber reinforcement index is linearly correlated with the initial crack stress and ultimate tensile stress of PVA-ECC and with the ultimate tensile stress and ultimate tensile strain of PE-ECC. The characteristic points of PVA-ECC in the multi-crack cracking stage are as follows: the greater the initial cracking strain, the smaller the ultimate tensile strain, showing an exponential correlation; The greater the initial cracking stress is, the greater the ultimate tensile stress is, and the two are linearly correlated.

Polyconvex neural network models of thermoelasticity

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

Effects of thermal treatments on the fracture behaviour of a silica-filled NBR: A study on the recovery of the Mullins effect and on the stretch-induced cavity formation

This research work is focused on the study of the fracture behaviour of a silica-filled NBR. The Mullins effect and its thermally-induced recovery are initially studied performing tensile tests: comparing the material's response in uniaxial tension and pure shear deformation conditions, a lower recovery is observed in the pure shear configuration. A similar study is then performed considering the fracture behaviour of the material. Tests are performed in quasi-static loading conditions and by applying a fracture mechanics approach. The fracture toughness is evaluated as J-integral at the crack onset and at the unstable fracture initiation; further, the crack propagation is analysed and the resistance curve is obtained. The dependence of the overall fracture behaviour of the material on the applied thermal history is evaluated. Even though the crosslinking degree seems not to be affected by the thermal treatment, the fracture behaviour is modified. A correlation of these results with a change in the material's propensity to form cavities under stretching is proposed.

Combined effects of local residual stresses, internal pores, and microstructures on the mechanical properties of laser-welded Ti-6Al-4V sheets

Laser-welded Ti-6Al-4 V is prone to severe residual stresses, microstructural variation, and structural defects which are known detrimental to the mechanical properties of weld joints. Residual stress removal is typically applied to weld joints for engineering purposes via heat treatment, in order to avoid premature failure and performance degradation. In the present work, we found that proper welding residual stresses in laser-welded Ti-6Al-4 V sheets can maintain better ductility during uniaxial tension, as opposed to the stress-relieved counterparts. A detailed experimental investigation has been performed on the deformation behaviours of Ti-6Al-4 V butt welds, including residual stress distribution characterizations by focused ion beam ring-coring coupled with digital image correlation (FIB-DIC), X-ray computerized tomography (CT) for internal voids, and in-situ DIC analysis of the subregional strain evolutions. It was found that the pores preferentially distributed near the fusion zone (FZ) boundary, where the compressive residual stress was up to -330 MPa. The removal of residual stress resulted in a changed failure initiation site from the base material to the FZ boundary, the former with ductile and the latter with brittle fracture characteristics under tensile deformation. The combined effects of residual stresses, microstructures, and internal pores on the mechanical responses are discussed in detail. This work highlights the importance of inevitable residual stress and pores in laser weld pieces, leading to key insights for post-welding treatment and service performance evaluations.

Molecular Dynamics Simulation Study of Aluminum-Copper Alloys' Anisotropy under Different Loading Conditions and Different Crystal Orientations.

The commonly used aluminum-copper alloys in industry are mainly rolled plates and extruded or drawn bars. The aluminum-copper alloys' anisotropy generated in the manufacturing process is unfavorable for subsequent applications. Its underlying mechanism shall be interpreted from a microscopic perspective. This paper conducted the loading simulation on Al-4%Cu alloy crystals at the microscopic scale with molecular dynamics technology. Uniaxial tension and compression loading were carried out along three orientations: X-<1¯12>, Y-<11¯1>, and Z-<110>. It analyzes the micro-mechanisms that affect the performance changes of aluminum-copper alloys through the combination of stress-strain curves and different organizational analysis approaches. As shown by the results, the elastic modulus and yield strength are the highest under tension along the <11¯1> direction. Such is the case for the reasons below: The close-packed plane of atoms ensures large atomic binding forces. In addition, the Stair-rod dislocation forms a Lomer-Cottrell dislocation lock, which has a strengthening effect on the material. The elastic modulus and yield strength are the smallest under tension along the <110> direction, and the periodic arrangement of HCP atom stacking faults serves as the main deformation mechanism. This is because the atomic arrangement on the <110> plane is relatively loose, which tends to cause atomic misalignment. When compressed in different directions, the plastic deformation mechanism is mainly dominated by dislocations and stacking faults. When compressed along the <110> direction, it has a relatively high dislocation density and the maximum yield strength. That should be attributed to the facts below. As the atomic arrangement of the <110> plane itself was not dense originally, compression loading would cause an increasingly tighter arrangement. In such a case, the stress could only be released through dislocations. This research aims to provide a reference for optimizing the processing technology and preparation methods of aluminum-copper alloy materials.

Multiscale experimental characterization and physical-based constitutive modeling of silicone adhesive

Silicone adhesive has been widely used in assembly glass curtain walls which leads to its mechanical behaviors under heavy investigation. Due to its complexity, the microstructure of silicone adhesive stays unclear. A detailed description of microstructures of silicone adhesive is the basis to obtain an in-depth understanding of its mechanical behavior and the related mechanisms. In this work, series of multiscale experiments, uniaxial tension, uniaxial compression, simple shear and scanning electron microscopy (SEM) observation, were conducted to characterize mechanical behaviors and microstructure features of silicone adhesive. Stress-strain curves obtained through macroscale experiments were presented. Morphology and dispersion of filler clusters in silicone adhesive were analyzed using Gaussian mixed models. A modification of molecular chain spatial distribution was made to non-affine network model to consider anisotropic damage evolution of polymer matrix. A simplified term was further introduced to account for load-bearing capacity of filler clusters based on fractal theory where fractal dimensions of clusters work as a connection between microscale and macroscale. The modified model was further extended to describe Mullins effect combined with network alteration theory. The results of model validation and comparison demonstrated that due to the consideration of polymer chain anisotropic evolution and filler cluster microscopic features, the proposed model can predict the mechanical behavior of silicone adhesive under different loading conditions as well as the stress softening and permanent set of Mullins effect more accurately.

Data-driven integration of synthetic representative volume elements and machine learning for improved microstructure-property linkage and material performance in ceramics

Ceramic materials, characterized by their heat resistance, dielectric properties, and mechanical performance, are often compromised by brittleness due to microstructural inclusions. These inclusions, such as defects, secondary phases, and pores, are critically analyzed for their impact on material strength and fracture properties. In this study, the linkage between microstructure and properties in ceramic materials is explored through a methodological approach that combines experimental observations with physics-based and machine learning models. A data-driven approach has been employed, utilizing synthetic Representative Volume Elements (RVEs) derived from X-ray computed tomography scans of ceramics. The methodology involves an automated finite element (FE) simulation process for progressive failure analysis under uniaxial compression and tension. The analysis is conducted using statistical, data-driven, and machine learning techniques, including principal component analysis and k-means clustering, to assess the microstructural features' impact on material performance. The study focuses on the use of RVEs for accurately capturing essential microstructural characteristics and addresses the challenges in developing synthetic models and the limitations of simulation capabilities. The study's findings reveal that less uniform inclusion distribution and a higher standard deviation in inclusion size correlate to lower mechanical performance. By applying data-driven methods, this research contributes to the optimization of material performance and the establishment of structure-property relationships, with a particular emphasis on the influence of inclusions and defects on the mechanical behavior of ceramic materials.

Effect of strain state on the surface roughening for hydroforming of aluminum alloy tube based on cross-scale numerical modeling

The complex deformation behavior would result in surface roughening such as orange peel defect during the hydroforming process of aluminum alloy tubular parts. In order to control the surface quality of hydroformed tubular parts, the effect of strain state on the surface roughening for 2219 aluminum alloy tube was analyzed based on a cross-scale model. The model combined the crystal plasticity model and macroscopic finite element model. During the uniaxial tension, the surface morphology reveals an equiaxed pattern characteristic of orange peel due to the strain incompatibilities between grains, and the peak and valley are stretched along the tensile direction. The surface roughness under tension-compression plane strain state is the lowest due to the low through-thickness strain. In the biaxial tension region, the change rate of surface roughness gradually increases with the decrease of the second principal strain especially in the late deformation stage, and the surface features evolve from an orange peel pattern to a ridging pattern. The forming limit diagram under different strain states based on surface roughness was established to guide the optimization of hydroforming process. Compared with the one-step hydroforming, the surface roughness of the bulging peak of 2219 aluminum alloy tube using multi-step hydroforming with the axial self-feeding decreases obviously from 16.3 to 10.8 μm due to the significant reduction of the equivalent strain.

Experimental study of rock fracture behavior under direct tension using three-dimensional digital image correlation

Understanding the mechanical characteristics of rocks when subjected to direct tension is crucial for assessing the stability of rock formations. Within the scope of this research, a series of tests was conducted using Tage tuff to assess the deformation behavior and crack extension of rock under direct tension. The axial, lateral, and shear strain fields as well as crack propagation, localized deformation behavior, and failure mode of the rocks were analyzed using three-dimensional digital image correlation method. The results showed that the axial strain fields on the specimen surface were heterogeneous, with different locations and localization occurring in the pre-peak stage, which was similar to the evolution of shear strain, whereas the lateral strain only showed slight changes. The crack extension direction was inferred, indicating that both tensile and shear stress occurred in the tests. Furthermore, different stress–strain responses were observed for the inside and outside of the localized bands. Then, the surface patterns of specimen failure were scanned and analyzed to assess the failure mode and residual strength of the specimen under direct tensile stress. Finally, the results of direct tension, uniaxial compression, and Brazilian split tests for Tage tuff were compared, and the complete stress–strain curve of uniaxial tension (UT) was simulated using a nonlinear-variable-compliance constitutive equation. This study provides a deeper understanding into the damage behavior of rocks under direct tension.