Effective Stress-strain Curves Research Articles

Mandrel diameter effect on ring-pull testing of nuclear fuel cladding

Inconsistencies in ring-pull testing methods for thin-walled tubes make it difficult to compare a material's mechanical properties in the hoop direction presented in past publications. The effect of test setup, specifically mandrel diameter, was investigated for nuclear fuel cladding tubes of the iron-chromium-aluminium (FeCrAl) alloy, C26M (Fe-12Cr-6Al-2Mo). Mandrel diameter for ring-pull testing can change how the ring deforms and friction effects, further convoluting the results from testing. To address the impact of mandrel size in relation to ring diameter, gaugeless ring-pull samples were tested across a range of mandrel diameters and compared to uniaxial tensile tests from the same tube of material. Two groups of samples were tested: an as-received, low ductility sample set and an annealed, high ductility sample set, both cut from the same extruded tube. By pairing systematic variation of mandrel geometry with analysis of local strain gradients using digital image correlation, this study investigates the effect of test fixture geometry on apparent mechanical properties and effective strain fields and provides guidance for comparing previously published data. Certain features in uniaxial stress-strain curves (namely the yield strength, ultimate tensile strength, and uniform elongation) appeared to have analogies in the effective stress-strain curves from ring-pull testing. These corresponding features are compared to expose biases in the analysis of material properties using gaugeless ring-pull and to provide novel guidance on test setup during experimental design.

Effects of pre-tension and fatigue loadings on the evolution of welding residual stresses in welded plates

Welding-induced residual stresses evolve under external loading and fatigue actions. This paper examines the effects of a variety of influencing factors on the residual stress evolution, such as the pre-tension, load ratio, variable amplitude loading, overloading, plate thickness, and crack depth, for which a comprehensive understanding is yet to be nurtured. The experimental and numerical findings demonstrate that the variable amplitude loading and overloading impose significant effects on the evolution of residual stresses during the cyclic loading test. Based on the experimental observations and numerical analysis, this paper presents four evolution forms of residual stresses and reveals their mechanical principles by the effective stress-strain curves in both the undamaged specimens and the fatigue-cracked specimens. The interaction between the positions with different incremental plastic strains changes the magnitude of residual stress and thus dominates the residual stress evolutions.

Grain-Scale Study of SAC305 Oligocrystalline Solder Joints: Anisotropic Elasto-Plastic Constitutive Properties of Single Crystals

Abstract This paper focuses on anisotropic elastic-plastic constitutive modeling of SAC (SnAgCu) solder grains because of their importance in modeling the behavior of oligocrystalline (few-grained) micron-scale solder joints that are increasingly common in heterogeneous integration. Such grain-scale anisotropic modeling approach provides more accurate assessment of the mechanical response of solder interconnects in terms of predicting different failure modes, failure sites, and variability in time-to-failure. Anisotropic plasticity is represented using Hill–Ramberg–Osgood (RO) continuum plasticity model, which utilizes Hill's anisotropic plastic potential along with a RO power-law plastic hardening flow rule. Mechanistically motivated empirical scaling factors are proposed to extrapolate the stress–strain response for different grain sizes/shapes and for different coarseness of microstructures within each grain (generated with different cooling rates). This scaling factor can therefore also capture the effects of microstructural coarsening due to isothermal aging. This goal is achieved by first conducting monotonic tensile and shear tests on monocrystalline and oligocrystalline SAC305 solder joints containing grains of various geometries and also intragranular microscale (dendritic and eutectic) structures of various coarseness. The grain structures are characterized for each tested specimen using electron backscattered diffraction (EBSD). The Hill–RO model constants and the empirical scaling factors are then estimated by matching grain-scale anisotropic elastic-plastic finite element models of each tested specimen to the measured stress–strain behavior, using an inverse-iteration process. Grain shape is seen to influence the sensitivity of the effective stress–strain curves to the applied stress state (i.e., to the orientation of the principal stress directions) relative to (i) the material principal directions and (ii) the geometric principal directions of grains with high aspect ratio. Limitations of the current results and opportunities for future improvements are discussed.

Compression failure of porous ceramics: A computational study about the effect of volume fraction on damage evolution and failure

The work describes a numerical method to study compression failure of porous ceramics in relation to its volume fraction. The microstructure of an alumina-based foam material manufactured by mechanical stirring of a slurry is studied here. A finite element-based compression failure simulation of a real microstructure obtained from micro computed tomography (μCT) scans is conducted. A recently developed microstructure reconstruction algorithm is utilized to generate 3D artificial microstructures statistically equivalent to the real one obtained from μCT. The accuracy of the reconstruction procedure is established by comparing the simulated effective compression stress-strain behaviour of the reconstructed microstructure with that of the real one along with the experimentally measured results. The effect of sample size on the mean and variability of compression strength is studied by computing effective stress-strain curves for varying sizes of the reconstructed microstructures. Further, artificial microstructures of porous ceramics with different volume fractions are reconstructed along with computing effective stress-strain behaviour to establish relationship between ceramic content (volume fraction) and compression strength of this material. The failure modes of the microstructures with different volume fractions are studied by analysing failure site locations and their evolution with loading. The results are compared with the analytical models and the experimental observations available in the literature.

Effect of core-to-shell flowrate ratio on morphology, crystallinity, mechanical properties and wettability of poly(lactic acid) fibers prepared via modified coaxial electrospinning

In this study, modified coaxial electrospinning (CE) was employed to improve electrospinnability and to tailor surface morphology and bead formation of poly(lactic acid) (PLA) fibers by means of core-to-shell flowrate ratio variation. Chloroform/N,N-dimethylformamide (DMF) mixture was used as sheath solution which serves as a protective layer to prevent rapid solidification of PLA droplet causing needle clogging. Five different core-to-shell flowrate ratios yielded beads-on-a-string PLA fibers with distinctive fiber and bead properties. These diverse morphologies were characterized in terms of fiber diameter (Df), fiber percentage (Pf), number of beads per area (nb), bead area (Ab), bead aspect ratio (Lb/Db), ratio of bead-to-fiber diameter (Db/Df) and surface roughness. From thermal analysis, crystallinity of PLA fibers was shown to be significantly dependent on the fiber processing history, where higher degree of molecular chain orientation and longer jet flight time correspond to higher crystallinity values. Core-to-shell flowrate ratio of 1:3 resulted in PLA fibers with the least nb, smallest Db/Df and highest Lb/Db (spindle-like shape), which correspond to the highest tensile properties and minimum hydrophobicity among beads-on-a-string fibers studied, as indicated by effective stress-strain curve and water contact angle measurement. Furthermore, the results suggested that Db/Df was the dominant factor affecting tensile properties more than the effect of crystallinity, while Lb/Db (bead shape) was the key aspect which influenced the wettability of the PLA beads-on-a-string fibers.

Thermal Processing Map and Microstructure Evolution of Inconel 625 Alloy Sheet Based on Plane Strain Compression Deformation.

Plane strain compression tests were used to study the deformation behavior of an Inconel 625 alloy sheet at various temperatures and strain rates. The peak stress was selected to establish the constitutive equation, and the processing maps under different strains were drawn. The results show that the effective stress–strain curve of Inconel 625 has typical dynamic recrystallization (DRX) characteristics. With the increasing deformation temperature and the decreasing strain rate, the softening effect is significantly enhanced. The parameters of the constitutive equation are calculated, and the average error of the constitutive equation is 5.68%. Through the analysis of the processing map, a deformation temperature of 950–960 °C with a strain rate of 0.007–0.05 s−1 were determined as the unstable region, and obvious local plastic-rheological zones were found in the unstable region. The optimum deformation condition was found to be 1020–1060 °C/0.005–0.03 s−1. Through electron backscattered diffraction (EBSD) characterization, it was found that both the increase of temperature and the decrease of strain rate significantly promote the recrystallization process. At a low strain rate, the main recrystallization mechanism is discontinuous dynamic recrystallization (DDRX). It is expected that the above results can provide references for the optimization of the rolling process and microstructure control of an Inconel 625 alloy sheet.

Non-linear analysis models for Composite Plate Shear Walls-Concrete Filled (C-PSW/CF)

Composite Plate Shear Walls-Concrete Filled (C-PSW/CF) are a special seismic-force resisting system consisting of steel plates and concrete infill. Composite walls have been occasionally built in the past decades, but their use for seismic application is fairly new and particularly attractive. As a result, there is a need (by researchers as well as practicing engineers) for nonlinear inelastic hysteretic models that can be used in pushover analyses, cyclic analyses, and seismic response analysis of C-PSW/CF and coupled C-PSW/CF. This paper describes two different approaches for modeling C-PSW/CF walls for these purposes. In a first approach, walls are modelled using a fiber-hinge elements (i.e., distributed plasticity model) using model with constitutive equations that account for both buckling and fracture of the steel. In the second approach, the walls are modelled with fiber-hinge elements having effective stress-strain curves derived from results of 3D finite element analyses.

Effect of a High Mg Solute Content on the Hot Workability of Al-Mg Alloys.

The workability of Al-xMg alloys with a high Mg content (Al-6Mg, Al-8Mg, Al-9Mg) was evaluated by investigating the microstructure and processing map. Hot torsion tests were conducted in the range of 350-500 °C between 0.1 and 1 s-1. Constitutive equations were derived from various effective stress-strain curves, and the thermal activation energies for deformation obtained were 171 kJ/mol at Al-6Mg, 195 kJ/mol at Al-8Mg, and 220 kJ/mol at Al-9Mg. In the case of the processing map, the instability region, which widened with increasing Mg content, was due mainly to the influence of the Mg solute, which activated grain boundary cracking and flow localization.

Finite element analysis of elastic–plastic and fracture behavior in functionally graded materials (FGMs)

The effect of material property variation on ductility and fracture strain in functionally graded materials (FGMs) is investigated using the finite element method (FEM) and the Gurson–Tvergaard–Needleman (GTN) model, which is strain-controlled for void nucleating. The material properties of FGMs in the tensile tests are assumed to be represented by a power-law distribution in the thickness direction. A gradation index (n) assigns the material property distribution. The lower and upper surfaces are pure hard (n = ∞) and pure soft (n = 0) materials, respectively, in the simulations. The ductility and fracture strain changes with varying gradation index. The development of stress triaxiality slows down in FGMs, and the total void volume fraction is reduced. The analysis is performed for five values of n, and the results are discussed numerically. The aim of this study is to help the researchers for better design and fabrication of FGMs. The necking strain in FGMs is calculated and it is found that it increases when the rate of hardening in the effective stress–strain curve increases. Lastly, it can be concluded that gradation index has significant effect on the elastic–plastic and fracture behavior of the functional graded (FG) specimen.

Prediction of the Effective Stress-Strain Curves of Ductile Polymer 1D-Reinforced Composites Filled with Hollow Fibers Using Parameterized Model Based on Bezier Curves

The article presents the results of numerical and experimental studies of stress-strain curves of 1D-reinforced polymer composite materials based on hollow porous fibers and epoxy matrix. The two-scale nature of the composite under research was taken into account. A surrogate easily parameterized model based on Bezier curves was developed and used to approximate the stress-strain curve of ductile material. The calculations were performed using reversible homogenization and finite element methods, which were implemented in computational subsystem of DCS GCD. Representative volume elements of the investigated materials were created using the geometry generating subsystem of DCS GCD. Test samples were made using three-axis milling machine and compression tests were carried out. Computational results of effective stress-strain curves determination were obtained and compared with experiments.

Microstructure topology optimization by targeting prescribed nonlinear stress-strain relationships

In this paper, we proposed a new material design method by microstructure topology optimization. Novelty of the proposed method is to target the whole nonlinear volume-averaged effective stress-strain curve of microstructure representative volume element (RVE) rather than aiming specific values such as strength, stiffness or Poisson ratio. J2 plasticity model with a linear isotropic hardening model was chosen for local residuals. Global residuals are computed within nonlinear finite element framework for the topology optimization. Sensitivities of the objective function augmented with the residuals and adjoint response vectors with respect to design variables are derived with details and their numerical computational procedures were also presented. Microstructure topologies showing two different targeted stress-strain curves under uniaxial and biaxial loadings were obtained by using the method of moving asymptotes (MMA) optimization algorithm. Accuracy of the sensitivity computations was verified and numerical examples demonstrated a potential of the proposed method in applications to multiscale topology optimization.

Dislocation Structure in Hot Deformed Al-Zn-Mg Alloy by X-ray Line Profile Analysis.

The microstructure of extruded Cu-free Al-Zn-Mg alloy is studied. Hot torsion tests are performed on a Cu-free Al-Zn-Mg alloy to investigate the effect of large strain deformation on the dislocation behavior. The dislocation structure is characterized by X-ray diffraction profile analysis, and the effective stress-strain curves are obtained by hot torsion tests. The dislocation density at low deformation temperature is found to be higher than that at high deformation temperature. The dislocation density of the alloy increases gradually up to ε = 1 with increasing strain and does not change significantly during further deformation.

On the accumulation of irreversible plastic strain during compression loading of open-pore metallic foams

The accumulation of plastic strain as an essential element of the compression behavior of metal foams is investigated by analyzing effective stress-strain curves which were recorded during testing. By applying loading/unloading cycles within the low-strain region until reaching the stress plateau, it is studied how reversible elastic deformation is gradually transformed into irreversible plastic deformation and it is shown that both, elastic and plastic strains, contribute to the total strain ε. This behavior is found to be independent on the investigated mesostructural foam morphologies. Furthermore, a method is derived which can be used to determine a proof stress σϕPl=0.5 at which yielding dominates the deformation of a metal foam.

Hot Ductility of Cast High Nitrogen Fe-Cr-Mn-Ni Steel

Hot deformability and fracture of as-cast Fe-Cr-Mn-Ni stainless steel ingots with high nitrogen and high carbon contents were studied. Effective stress-strain curve indicates a decrease of the UTS from 510MPa to 90MPa with increase of temperatures from 600°C to 1200°C. Effective stress-strain curves exhibited typical work hardening until the final stage of fracture from 600°C up to 900°C. The fracture elongation decreased from 600°C with the increase of temperature up 850°C, but started to increase appreciably as the work softening becomes dominant in the stress-strain curves above 950°C, suggesting the increase of ductility above 950°C is associated with dynamic recrystallization. The high temperature deformability was enhanced above 1000°C by homogenization of the as-cast alloy due to the dissolution and redistribution of segregated particles, providing the homogeneous distribution of the nucleation site of dynamic recrystallization. . The presence of fatal crack at 1,250°C and the loss of hot ductility can be attributed to the partial melting in austenite grain boundaries at high temperatures.

Material modeling of pure titanium sheet and its application to bulge test simulation

The hydraulic bulge test is widely used to obtain stress–strain data over large strain ranges. This study identifies plastic characteristics of pure titanium sheet by conducting several tensile tests and a hydraulic bulge test. Distortional hardening behavior of the tested material is examined experimentally by comparing the uniaxial tensile results of three specimens taken from different orientations. In addition, three stages of deformation were observed in biaxial stress–strain data obtained from the bulge test. Therefore, a constitutive model based on a non-associated flow rule is developed to describe the material characteristics. Evolution Hill’s quadratic functions are adapted to reproduce the yield surface and potential surface transients during plastic deformation. Additionally, a modified Voce hardening model is used to represent the effective stress–strain curve over large strain ranges to capture the three-stage hardening phenomenon of titanium sheet. The developed material model is then applied to simulate the bulge test to verify its accuracy. Based on simulation results, it is concluded that the distortional hardening behavior strongly affects the evaluation of apex height in the bulge test.

On the identification of an effective cross section for a cruciform specimen

AbstractBiaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm2 for the considered specimen.

Micromechanics-based modeling of stress–strain and fracture behavior of heat-treated boron steels for hot stamping process

In the automotive industry, hot stamped parts with tailored properties have shown advantageous safety performance. Such components are produced by applying different heat treatment conditions after forming for different zones in order to obtain various combinations of hard and soft microstructures. In this work, pure martensitic, pure bainitic, and three martensitic/bainitic phase microstructures were initially generated from the boron steel grade 22MnB5 by a two-step quenching procedure in which different holding times in the bainitic temperature range were varied. Increased phase fraction of bainite due to longer holding time led to decreased yield and tensile strength; however, elongation and resulting energy absorbability became significantly higher. To describe mechanical properties and failure behavior of hot stamped parts containing multiphase microstructures, influences of microstructure characteristics should be considered on the micro-scale. Using modeling, 2-D representative volume elements (RVE) were generated from observed real microstructures and flow curves of the individual single phases were defined, taking into account a dislocation theory based model and local chemical compositions. Then, effective stress–strain curves of the heat-treated boron steels were calculated by using the isostrain and non-isostrain methods and compared with tensile test results. Regarding fracture behavior, damage curves of fully martensitic and bainitic structures were determined by means of tensile tests of different notched samples and a hybrid digital image correlation (DIC)–finite element (FE) approach. 2-D RVE simulations of a martensite/bainite mixture were carried out under various states of stress, in which the obtained damage curves were individually applied for each phase. The predicted damage curve from RVE simulations for two-phase boron steel fairly agreed with experimental fracture strains. Moreover, correspondingly normalized Lode angle could be calculated, and the 3-D damage locus was also constructed.

Can tailored non-linearity of hierarchical structures inform future material development?

An analytical investigation into the non-linear elastic response of helical lattice structures coupled with an elastic medium is presented. Novel composite templates are then obtained to produce bespoke material characteristics by exploiting tuned hierarchy. System behaviour is approximated as a combination of three non-linear “springs”, representing the helical lattice, and the axial and circumferential components of the elastic medium via an energy based approach. Non-dimensional parameters governing each component’s non-linear load–displacement behaviour are identified, demonstrating tailoring potential. Further tunable parameters that govern the combined system response, involving form factor, geometric and stiffness ratios are identified. In particular, pseudo-ductile responses are observed. The feasible region of pseudo-ductility, as determined by these non-dimensional parameters, is obtained, allowing discussion of viable materials and geometries. Finally, load–displacement behaviour is utilised to obtain indicative effective stress–strain curves, thus showing promise as a model for future material development.

Validation of the Tabulated Johnson-Cook Model for a Dynamic Compression Simulation

MAT224 is a tabulated version of the Johnson-Cook model in LS-DYNA. Compared with the original Johnson-Cook material, MAT224 was developed to simulate the dynamic response of a material by just defining the effective stress as a function of effective plastic strain at different strain rates and temperatures, thus avoiding the tedious parameter fitting procedures in the traditional Johnson-Cook model. However, the stability and precision of solution is strongly dependent on the effective stress versus effective strain curves in MAT224, and unreasonable curve data will lead to warnings or errors in the process of solution. In the current study, a two-dimensional axisymmetric finite element model for the Ti-6Al-4V titanium alloy under dynamic compression was built, and MAT224 was employed. By investigating the effects of the curve numbers, strain ranges, data points, as well as changing tendencies, on the simulation results, the stability and the reliability for MAT224 are systematically studied.

Determination of Stress-Strain Curve of Dual Phase Steel by Nanoindentation Technique

The advanced high strength (AHS) steels, for example, dual phase (DP) steels, transformation induced plasticity (TRIP) steels and complex (CP) steels principally exhibit multiphase microstructure features. Thus, mechanical behavior of the constituent phases significantly affects the resulting overall properties of such AHS steels. Novel material characterization techniques on micro- and nano-scale have become greatly more important. In this work, stress-strain response of the DP steel grade 1000 was determined by using the Nanoindentation testing. The DP steel showed the microstructure containing finely distributed martensite islands of about 50% phase fraction in the ferritic matrix. The nano-hardness measurements were firstly performed on each individual phase of the examined steel. In parallel, finite element (FE) simulations of the corresponding nano-indentation tests were carried out. Flow curves of the single ferritic and martensitic phases were defined according to a dislocation based theory. Afterwards, the load and penetration depth curves resulted from the experiments and simulations were compared. By this manner, the proper stress-strain responses of both phases were identified and verified. Finally, the effective stress-strain curve of the investigated DP steel could be determined by using 2D representative volume element (RVE) model.