Uniaxial Stress-strain Curves Research Articles

Size Effect and Influence Factors of Asphalt Mixture Based on Particle Discrete Element

To explore the size effect of asphalt mixture, asphalt mastic asphalt mixture was taken as the research object, and the uniaxial compressive strength was used as the evaluation index. The applicability of the three size effect theories of Bazant, Carpinteri, and Weibull were evaluated, and the corresponding size effect law parameters were calculated. The critical dimensions and critical strength of the asphalt mixture were determined, and the effects of coarse aggregate properties, maximum nominal particle size, and loading rate on the size effect of asphalt mixture were analyzed. Results show that the asphalt mixture has an obvious size effect phenomenon, and the uniaxial compressive stress-strain curves of asphalt samples with different sizes have the characteristics of compaction stage, elastic stage, and transition from plastic deformation to failure stage. The uniaxial compressive strength of the asphalt mixture is negatively correlated with the sample size, and as the sample size increases, the strength reduction decreases gradually. With the increase in the elastic modulus of the coarse aggregate, the critical strength value increases continuously, and the critical dimension decreases. As the maximum nominal particle size increases, the critical dimension and critical strength increase gradually. With the increase in the loading rate, the critical strength continues to increase, and the critical dimension gradually decreases. The Bazant and Carpinteri size effect laws are more suitable for the analysis of the size effect of asphalt mixture, while the Weibull size effect law has a large error. When SMA is used as the pavement structural layer, the ratio S of the structural layer thickness to the maximum nominal particle size calculated by the Bazant size effect law is 2.6 to 3.5, and the S range calculated by the Carpinteri size effect law is 2.6 to 4.0.

Applying a combination of laboratory X-Ray diffraction and digital image correlation for recording uniaxial stress-strain curves in thin surface layers

By combining laboratory-based x-ray diffraction stress analysis with optical digital image correlation recorded in-situ during tensile loading, a new methodology has been developed to obtain for surface specific stress-strain curves. This novel methodology has been validated by comparing the reconstructed stress-strain curves from the x-ray diffraction/optical digital image correlation approach with stress-strain curves recorded using standard methods. The validated methodology enables now the recording of standard mechanical test data of altered surface layers, such as shot peened and machined surfaces or from proton-irradiated samples where the irradiated layer is limited to a depth of 10 s of microns.

Influence of Assumed Strain Hardening Relation on Plastic Stress-Strain Response Identification From Conical Indentation

Abstract Instrumented indentation tests provide an attractive means for obtaining data to characterize the plastic response of engineering materials. One difficulty in doing this is that the relation between the measured indentation force versus indentation depth response and the plastic stress-strain response is not unique. Materials with very different uniaxial stress-strain curves can give essentially identical curves of indentation force versus indentation depth. Zhang et al. (2019, “Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach,” ASME J. Appl. Mech., 86, p. 011002) numerically generated “experimental” conical indentation data and showed that using surface profile data and indentation force versus indentation depth data together with a Bayesian-type statistical analysis permitted the uniaxial plastic stress-strain response to be identified even for materials with indistinguishable indentation force versus indentation depth curves. The same form of hardening relation was used in the identification process as was used to generate the “experimental” data. Generally, a variety of power law expressions have been used to characterize the uniaxial plastic stress-strain response of engineering materials, and, of course, the form that gives the best fit for a material is not known a priori. Here, we use the same Bayesian statistics-based analysis but consider four characterizations of the plastic uniaxial stress-strain response and show that the identification of the hardening relation parameters and the associated uniaxial stress-strain response is not very sensitive to the form of the power law strain hardening relation chosen even with data that have significant noise.

A biostable, anti-fouling zwitterionic polyurethane-urea based on PDMS for use in blood-contacting medical devices.

Polydimethylsiloxane (PDMS) is commonly used in medical devices because it is non-toxic and stable against oxidative stress. Relatively high blood platelet adhesion and the need for chemical crosslinking through curing, however, limit its utility. In this research, a biostable PDMS-based polyurethane-urea bearing zwitterion sulfobetaine (PDMS-SB-UU) was synthesized for potential use in the fabrication or coating of blood-contacting devices, such as a conduits, artificial lungs, and microfluidic devices. The chemical structure and physical properties of synthesized PDMS-SB-UU were confirmed by 1H-nuclear magnetic resonance (1H-NMR), X-ray diffraction (XRD), and uniaxial stress-strain curve. In vitro stability of PDMS-SB-UU was confirmed against lipase and 30% H2O2 for 8 weeks, and PDMS-SB-UU demonstrated significantly higher resistance to fibrinogen adsorption and platelet deposition compared to control PDMS. Moreover, PDMS-SB-UU showed a lack of hemolysis and cytotoxicity with whole ovine blood and rat vascular smooth muscle cells (rSMCs), respectively. The PDMS-SB-UU was successfully processed into small-diameter (0.80 ± 0.05 mm) conduits by electrospinning and coated onto PDMS- and polypropylene-based blood-contacting biomaterials due to its unique physicochemical characteristics from its soft- and hard- segments.

Estimation of Texture-dependent Stress－Strain Curve and <i>r</i>-value of Aluminum Alloy Sheet Using Deep Learning

Deformation of an aluminum alloy sheet is affected by its underlying crystallographic texture and has been widely studied by the crystal plasticity finite element method (CPFEM). The numerical material test based on the CPFEM allows us to quantitatively estimate the stress－strain curve and the Lankford value (r-value), which depend on the texture of aluminum alloy sheets. However, in the use of the numerical material test as a means of optimizing the texture to design aluminum alloys, the CPFEM is computationally expensive. We propose a methodology for rapidly estimating the stress －strain curve and r-value of aluminum alloy sheets using deep learning with a neural network. We train the neural network with synthetic texture and stress－strain curves calculated by the numerical material test. To capture the features of synthetic texture from a {111} pole figure image, the neural network incorporates a convolution neural network. Using the trained neural network, we can estimate the uniaxial stress－strain curve and the in-plane anisotropy of the r-value for various textures that contain Cube and S components. The results indicate that the neural network trained with the results of the numerical material test is a promising methodology for rapidly estimating the deformation of aluminum alloy sheets.

Model for the spherical indentation stress-strain relationships of ion-irradiated materials

In this work, a mechanistic model is proposed to characterize the spherical indentation stress-strain (ISS) relationships of ion-irradiated materials. Three fundamental deformation mechanisms are accounted for by the developed model, including the indentation size effect (ISE) ascribed to geometrically necessary dislocations (GNDs), irradiation hardening determined by irradiation-induced defects and strain softening affected by the removal of defects and unirradiated substrate. The contribution of elastic deformation is involved to model the ISE of spherical indentation, ignoring which can result in the overestimation of the indentation stress at a small indentation strain. In addition, the removal of irradiation-induced defects by outspreading plastic deformation and softening effect induced by the unirradiated substrate are simultaneously considered to account for the strain softening phenomenon with irradiation effect, which is well known in conventional tensile tests after the yield point. A good agreement is observed by comparing our model results with the experimental data of unirradiated materials (iridium, nickel, aluminum and copper) and ion-irradiated Fe-12Cr alloy. The proposed model offers a promising way to qualitatively compare the ISS relationships of ion-irradiated materials and uniaxial stress-strain curves of neutron-irradiated materials.

Elasto-Plastic Behaviour of Transversely Isotropic Cellular Materials with Inner Gas Pressure

The fabrication process of cellular materials, such as foaming, usually leads to cells elongated in one direction, but equiaxed in a plane normal to that direction. This study is aimed at understanding the elasto-plastic behaviour of transversely isotropic cellular materials with inner gas pressure. An idealised ellipsoidal-cell face-centred-cubic foam that is filled with gas was generated and modelled to obtain the uniaxial stress–strain relationship, Poisson’s ratio and multiaxial yield surface. The effects of the elongation ratio and gas pressure on the elasto-plastic properties for a relative density of 0.5 were investigated. It was found that an increase in the elongation ratio caused increases in both the elastic modulus and yield stress for uniaxial loading along the cell elongation direction, and led to a tilted multiaxial yield surface in the mean stress and Mises equivalent stress plane. Compared to isotropic spheroidal-cell foams, the size of the yield surface of the ellipsoidal-cell foam is smaller for high-stress triaxiality, but larger for low-stress triaxiality, and the yield surface rotates counter-clockwise with the Lode angle increasing. The gas pressure caused asymmetry of the uniaxial stress–strain curve (e.g., reduced tensile yield stress), and it increased the nominal plastic Poisson’s ratio for compression, but had the opposite effect for tension. Furthermore, the gas pressure shifted the yield surface towards the negative mean stress axis with a distance equal to the gas pressure. The combined effects of the elongation ratio and gas pressure are complicated, particularly for the elasto-plastic properties in the plane in which the cells are equiaxed.

Development of a Practical Uniaxial Cyclic Constitutive Model for Concrete

The uniaxial stress-strain curves of concrete suggested in Chinese Concrete Standard (GB50010-2010) are combined with the modified Yassin hysteretic rule. The integrated cyclic constitutive model for concrete is aimed at the nonlinear analysis of the reinforced concrete (RC) structures under strong earthquake. The model is implemented into general-purpose FEA software ABAQUS through the user material subroutine VUMAT. Then, some typical performances of the proposed model are verified. Furthermore, a seismic damage analysis of a multi-story RC frame structure is conducted using the cyclic model. The results show that the constitutive model is applicable to the nonlinear seismic analysis of RC structures.

Mechanical and fracture properties of recycled aggregate concrete in design codes and empirical models

AbstractIn this paper the relationships between the mechanical and fracture properties of recycled aggregate concretes (RAC) are investigated based on the own research programs results and an extensive number of experimental data from the literature. The primary aim is the extension of design standards empirical models to the case of RAC with particular emphasis on the effect of replacement ratio on mechanical properties, uniaxial stress–strain curve, fracture energy, and stress–strain softening curve's parameters.It was pointed out that relationships dedicated to assess the mechanical properties of natural aggregate concretes (NAC) are not fully adequate to predict the behavior of RAC. It was established that the elastic modulus Ecm, the tensile splitting strength fctm,sp are related to the mean compressive strength fcm as well as to a parameter taking into account the effect of the recycled aggregates replacement ratio. The validity of many analytical expressions of the stress–strain relationship has been also studied and the effect of replacement ratio was taken into account. The comparison between experimental and analytical stress–strain curves shows that, with the proposed modifications, some models satisfactorily describe the behavior up to failure while others either overestimate or underestimate the postpeak branch. Due to the limited number of available data, no well‐defined relation was found between fracture energy, compressive strength, and formulation parameters.

Constitutive modeling of steel fiber-reinforced concrete

Experimental studies within the previous years showed that the behavior of concrete is improved by adding steel fibers. Due to bridging effect, steel fibers in a concrete matrix prevent crack propagation under static loads. This phenomenon increases the load-bearing capacity of steel fiber-reinforced concrete, specifically after the peak load. In contrast to similar studies, in this study the effect of fibers on steel fiber-reinforced concrete is directly described based on uniaxial compressive and tensile stress–strain curves. For this purpose, the effect of fiber on the stress variations is extracted from the difference between steel fiber-reinforced concrete and its corresponding concrete matrix uniaxial stress–strain curves. These differential stress curves were extracted from 103 experimental specimens, collected from the literature. Then, some equations were developed for them with appropriate accuracy, using genetic programming technique. These equations were only based on primary specifications of fibers and concrete matrix. In the next stage, an elastoplastic damage constitutive model initially developed for plain concrete was modified, using the developed steel fiber-reinforced concrete modeling equations. The proposed model was implemented in a finite element analysis software and successfully simulated the steel fiber-reinforced concrete behavior subjected to uniaxial and flexural experiments.

Prediction of material behavior during biaxial stretching of superplastic 5083 aluminum alloy

In order to predict the flow behavior of a superplastic Al-Mg alloy sheet under near biaxial tension mode, finite element simulation was performed using commercial FE software (ABAQUS). To capture the time-dependent plastic behavior of the material, three constitutive models, i.e., the Voce model, a power law, and a newly introduced variable m value viscoplastic (VmV) model, were implemented in FE simulations. The models’ parameters were assessed from the three uniaxial stress-strain curves ranging from 10−3 to 10−1 s−1. To validate the simulation results, Nakazima hemispherical dome testing was performed under isothermal conditions using a constant strain rate of ~ 0.01 s−1 at 450 °C. After the tests, the thickness of the deformed parts was measured and the volume fractions of cavities at different locations were assessed using X-ray micro-tomography, and the impact of the strain path on the rate of cavitation was discussed. Based on the obtained results, when the material behavior was modeled using the VmV model, the accuracy of the prediction was about 2 and 5 times better than the ones from power law and Voce model, respectively. It was also observed that the volume fraction of the cavities exponentially increases with equivalent plastic strain and it depends on the strain path history.

Prediction of mechanical response for 5000-Series aluminum alloy coupling visco-plastic self-consistent approach with finite element method

In the present work, a hybrid micro macro-approach was adopted to investigate the material behavior of the A5XXX-O object of the Benchmark 3 of Numisheet2018. Starting from the provided uniaxial stress-strain curve and in house microstructure measurements, a mean field approach, by using the VPSC7c code, was used to perform numerical experiments in order to derive the anisotropic macroscopic behavior of the aluminum alloy.Then, at the macroscale, a constitutive model was built on coupling a non-quadratic yield surface function with a damage model developed in the framework of the continuum damage mechanics. Finally, by using MSC.Marc2017.1, finite element simulations of uniaxial and Nakajima bulging tests were performed with the purpose of obtaining the Fracture Forming Limit Curve for the aluminum alloy under investigation.

Experimental data reduction for hyperelasticity

WYPiWYG hyperelasticity is a data-driven, model-free computational procedure for finite element analysis of soft materials. The procedure does not assume the shape of the stored energy function and does not employ material parameters, predicting accurately any smooth prescribed behavior from a complete set of experimental tests. However, fuzzy experimental data may yield useless highly oscillatory, unstable stored energy functions, and classical curvature smoothing gives frequently unsatisfactory results. Aside, the possibility of having experimental data from different specimens for the same test was not considered in previous procedures. In this work we present a novel technique based on spline regression and smoothing penalization using stability conditions. In general, this procedure reduces noisy experimental data or data from multiple specimens for ulterior determination of the stored energy. The procedure only needs the solution of a linear system of equations. Instead of classical curvature-based smoothing, we employ a novel stability-based smoothing, determining for each branch of the uniaxial stress-strain curve the most restrictive stability condition during uniaxial and equibiaxial tests. The resulting stored energy functions are smooth and stable. The procedure has little sensitivity to the number of spline segments or to the choice of the penalization parameter, which are computed automatically.

Comparative study of two elasto-plastic work-hardening spatial models for concrete

A concept of elasto-plastic, work-hardening constitutive models for the multiaxial behaviour of concrete under short-term loading and the comparison with test results is presented in this paper. Two failure surfaces are utilized: the criterion of Podgórski and the three-parameter surface of Willam and Warnke. Both triaxial failure criteria have been calibrated in terms of different multiaxial strength tests. A non-associated flow rule has been used. The plastic potential function has been assumed in the form of the Drucker-Prager cone with variation of the angle of the cone side surface. In order to cover the plastic hardening behaviour, the equivalent uniaxial stress-strain curve has been adopted. An incremental stress-strain relationship has been formulated. The results of the numerical analysis performed by a direct integration of the constitutive relationships for the biaxial stress regime have been compared with the test data.

Constitutive model for full-range cyclic behavior of high strength steels without yield plateau

In order to characterize static and cyclic behavior of high strength structural steels, coupons made of two typical kinds of such steels in China, i.e. Q550 and Q690 steels with nominal yield strength of 550 MPa and 690 MPa respectively, were designed and tested under monotonic tension and a variety of cyclic loading protocols. Uniaxial stress-strain curves from the test show that for both steels no obvious yield plateau was observed, and short-range isotropic softening occurred right after initial yielding, while the subsequent strain hardening was contributed by both kinematic hardening and long-range isotropic hardening. Based on these phenomena, a constitutive model was developed specifically for those high strength steels and implemented in numerical analysis through user-defined subroutines. Calibration method for material parameters in this constitutive model was also established that mainly depends on tension coupon test result. After that, simulation was conducted by using the developed model with its stress-strain curves compared with those from cyclic loading test. Good agreement was obtained. Therefore, the constitutive model and its calibration method can be used for further seismic or dynamic nonlinear analysis of high strength steel structures and will help to develop reasonable and reliable ductile design method of those structures.

On the estimation of ultimate tensile stress from small punch testing

Finite element simulations of the small punch test are performed in order to critically evaluate and improve empirical correlations for the estimation of the ultimate tensile stress from force-deflection and force-displacement curves. For this purpose, generic elastic-plastic material properties are used. A systematic variation of the ultimate tensile stress and total uniform elongation is performed to investigate the effects of these parameters of the uniaxial stress-strain curve on the characteristics of small punch test curves. It is shown, that the maximum force Fm of the small punch test curve is not the appropriate parameter for the estimation of the ultimate tensile stress. Instead, the force Fi at a punch displacement of 1.29 times the specimen thickness (or alternatively at bottom deflection of 1.1 times the specimen thickness) should be used. This force is associated with the onset of plastic instability. A correlation between the force Fi and the ultimate tensile strength is proposed and validated by more than 100 small punch tests of nine different steel heats.

A new method to evaluate the brittleness for brittle rock using crack initiation stress level from uniaxial stress–strain curves

Brittleness has been a prevalent descriptor in rock mass engineering and formation fracturing stimulation. Here a new definition of mechanical brittleness index as crack initiation stress level (σ ci/σ c) is proposed and verified with diorite, granite, marble, sandstone, and shale samples using uniaxial compressive strength (UCS) test. Regression analysis reveals obvious correlation between σ ci/σ c and four brittleness definitions based on UCS and Brazilian tensile strength (BTS) (B19 = σ c/σ t, B20 = (σ c − σ t)/(σ c + σ t), B21 = (σ c × σ t)/2, B22 = (B21)1/2). For diorite, granite, marble, and sandstone, significant relationships exist between B19, B20, and B23; however, for anisotropic shale, obvious relationships were found between B21, B22, and B23. It is suggested that σ ci/σ c can well reflect the heterogeneity and anisotropy of rock and the correlation between B19, B20, B21, B22, and σ ci/σ c depends on the rock structural fabric. In addition, rock with high brittleness generally has a lower σ ci/σ c value and fracture easily occurs during sample deformation. It is not the case that formation with higher brittleness is considered as good fracturing candidates. Fracture pattern was obtained for shale samples from X-ray CT scanning, and the results reveal that fracture density is the maximum for sample with the lowest σ ci/σ c value. The most striking finding is that there exists a good correlation between the stimulated fracture density and σci/σc, and it implies that a good formation for hydraulic fracturing is not of high brittleness. The proposed brittleness index would be helpful to evaluate the formation fracability and screen hydraulic fracturing candidates.

Effect of yield criteria on the formability prediction of dual-phase steel sheets

The yield criterion is the basis of the material model that can describe the plastic behavior of the material under any possible stress states. The influence of diverse yield criteria on the formability prediction was explored via analyzing the hardening behavior and the forming limit of DP590 and DP780 sheets in this paper. The potential of the yield criterion to describe the hardening behavior of sheet metal was evaluated by comparing the equivalent stress-strain curves from the cruciform biaxial tensile tests with the uniaxial stress-strain curve. To characterize the hardening behaviors of dual-phase steel sheets under large strain condition, the hydraulic bulge tests were employed to obtain the equivalent stress-strain data based on different yield criteria. Accordingly, the material models including diverse yield criteria and hardening laws were used to calculate the theoretical forming limit curves (FLCs) based on the M-K model. Through comparing the predicted FLCs and the experimental ones from Nakazima tests, it was found that the theoretical FLCs based on the M-K model largely depend on the accurate yield criterion and hardening law. In addition, the numerical simulations of two stretch tests were carried out to verify the validity of the material models and the theoretical FLCs. The results indicated that the accurate yield criterion is of great significance to the description of hardening behavior and the prediction of FLCs.

Finite-element analyses of light timber-framed walls with and without openings

The static responses of timber-framed shear walls with and without openings of variable dimensions and locations were numerically investigated using the finite-element (FE) method. The lateral load resistance capacities and general load–displacement behaviours of the timber-framed shear walls were investigated. In the FE study, the frame elements were modelled as beams, plates were modelled as shells and nails were modelled as spring elements. The plastic behaviour of the materials was modelled using experimental stress–strain relationships of the materials. For timber frames and oriented strand board (OSB) panels, uniaxial stress–strain curves were experimentally obtained under tensile and compressive loading. From the experimental materials models it was found that spruce exhibited non-linear behaviour under both tensile and compressive stress. In contrast, the OSB sheathing layer used in the analyses exhibited non-linear behaviour under compressive stress and linear behaviour under tensile stress. The numerical results were verified using experimental load–deflection relationships obtained from a previous study. Good agreement was found between the analytical and experimental results. To further examine the applicability of the experimentally verified numerical model, four different timber-framed shear walls were simulated with FE models.

Spherical nanoindentation of proton irradiated 304 stainless steel: A comparison of small scale mechanical test techniques for measuring irradiation hardening

Experimentally quantifying the mechanical effects of radiation damage in reactor materials is necessary for the development and qualification of new materials for improved performance and safety. This can be achieved in a high-throughput fashion through a combination of ion beam irradiation and small scale mechanical testing in contrast to the high cost and laborious nature of bulk testing of reactor irradiated samples. The current work focuses on using spherical nanoindentation stress-strain curves on unirradiated and proton irradiated (10 dpa at 360 °C) 304 stainless steel to quantify the mechanical effects of radiation damage. Spherical nanoindentation stress-strain measurements show a radiation-induced increase in indentation yield strength from 1.36 GPa to 2.72 GPa and a radiation-induced increase in indentation work hardening rate of 10 GPa–30 GPa. These measurements are critically compared against Berkovich nanohardness, micropillar compression, and micro-tension measurements on the same material and similar grain orientations. The ratio of irradiated to unirradiated yield strength increases by a similar factor of 2 when measured via spherical nanoindentation or Berkovich nanohardness testing. A comparison of spherical indentation stress-strain curves to uniaxial (micropillar and micro-tension) stress-strain curves was achieved using a simple scaling relationship which shows good agreement for the unirradiated condition and poor agreement in post-yield behavior for the irradiated condition. The disagreement between spherical nanoindentation and uniaxial stress-strain curves is likely due to the plastic instability that occurs during uniaxial tests but is absent during spherical nanoindentation tests.