Simulated Stress-strain Curves Research Articles

Simulation of dynamic recrystallization of NiTi shape memory alloy during hot compression deformation based on cellular automaton

Dynamic recrystallization (DRX) occurs in NiTi alloy during compression deformation at the strain rates of 0.001–1s−1 and at the temperatures of 800–1000°C. Cellular automaton (CA) model is used for understanding physical mechanism of DRX of NiTi alloy so that the microstructural evolution, the dislocation density, the flow stress and the grain size are simulated and predicted. The recrystallized grains firstly nucleate at the grain boundaries of the grains in the initial microstructure, where the dislocation density reaches the critical value. DRX is characterized by repeated nucleation and finite growth of the recrystallized grains. The dislocation density decreases with the increase in the deformation temperature, but increases with the increase in the strain rate. The fluctuation of the simulated stress–strain curve is almost the same as the fluctuation of the dislocation density, which is responsible for the competition between hardening and softening. The recrystallized grain size increases with the increase in the deformation temperature, but decreases with the increase in the strain rate. In the case of a given temperature and a given strain rate, the grain size in the initial microstructures has almost no influence on the grain size in the resultant DRX microstructures.

Progressive damage analysis and strength prediction of 2D plain weave composites

A two-step, multi-scale progressive damage analysis is implemented to study the damage and failure behaviors of 2D plain weave composites under various uniaxial and biaxial loadings. In the progressive damage mode (PDM), a formal-unified 3D Hashin-type criterion is formed to facilitate analysis work and engineering application, with shear nonlinearity considered in the stiffness matrix of yarn. The periodic boundary conditions are developed for the off-axis loading simulations. The simulated stress–strain curves under on-axis uniaxial tension and compression show good agreements with experimental results. The influences of different 3D Hashin-type criteria are subsequently discussed. Moreover, the strength decrease at different off-axis angles and the failure envelopes under on-axis and 45° off-axis biaxial loadings are obtained, with the discussion of different failure characteristics under each loading condition.

Nonlinear elastic deformation of magnesium and cobalt by Preisach-Mayergoyz model

A classic hysteretic model, Preisach-Mayergoyz model (P-M model), was used to calculate the nonlinear elastic deformation of magnesium (Mg) and cobalt (Co). Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems: wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals' hysteresis. This model was applied on Mg at room temperature and Co at 300°C. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.

Hardness analysis of cubic metal mononitrides from first principles

Density functional theory calculations are performed to evaluate the hardness of various cubic metal nitrides: rocksalt TiN, VN, ZrN, NbN, AlN, and SiN; zincblende AlN and BN; and diamond C for comparison. The isotropic elastic stiffness constants ${c}_{ij}$, bulk modulus $K$, shear modulus $G$, Young's modulus $E$, and isotropic Poisson's ratio $\overline{\ensuremath{\nu}}$ are calculated. From simulated uniaxial stress-strain curves, ideal strength values ${\ensuremath{\sigma}}_{\mathrm{max}}$ in the [100], [110], and [111] directions are also evaluated for all systems. In particular, rocksalt AlN is found to possess both high elastic moduli and ideal strength. These quantities are then compared for correlations with existing experimental Vicker's hardness data. The bulk modulus is found to be a poor indicator of hardness, while $E$, $G$, $1/\overline{\ensuremath{\nu}}$, and ${\ensuremath{\sigma}}_{\mathrm{max}}$ all exhibit stronger correlations. With a view to circumvent the need to run computationally expensive relaxation steps, different methodologies for approximating uniaxial stress-strain curves are introduced. Utilizing the anisotropic Poisson's ratio to approximate the relaxed transverse lattice parameters at a given axial strain is a good approximation to stress-strain curves, and the ideal strengths obtained in this way exhibit strong correlations to experimental Vicker's hardness values.

Developing the stress–strain curve to failure using mesoscale models parameterized from molecular models

Developing the stress response using the molecular and mesoscale levels is fairly reliable during the initial strain. For instance, modulus is a property that can be established using these techniques and the continuity of scale between the molecular and mesoscale and agreement with experiment suggests that both may be used to establish modulus for parameterizing a macroscale model when measured properties are unavailable. However, the latter part of the stress–strain response that helps to establish ties to crack propagation still needs attention. One problem that was previously found in the mesoscale models was questionable lack of void formation in crosslinked systems due to superficially clean adhesive separation in the simulations. One way to overcome this lack of voiding was to determine how to develop bond breakage criterion that would allow surfaces to develop. This paper discusses development and application of bond breakage on a mesoscale level (which uses a bead-bond breakage criterion so does not explicitly define which bond is broken), and the impact on the simulated stress–strain curves using mesoscale models.

Stress-Strain Behavior and Statistical Continuous Damage Model of Cement Mortar under High Strain Rates

AbstractThe effects of strain rate on the dynamic stress-strain behavior of cement mortar were investigated in split Hopkinson pressure bar (SHPB) tests; the resulting strain rates ranged from 20 to 280 s−1. A total of 39 specimens were subjected to static and dynamic axial compressive loadings. The results showed that cement mortar is a typical strain-rate dependent material. Both dynamic compressive strength and critical strain increased with strain-rate increases. However, there seemed to be no strain-rate effects on the initial elastic modulus of cement mortar. Based on the stress-strain curves of different strain rates, as well as the random statistical distribution hypothesis for strength, a dynamic damage constitutive model of cement model under compression was used. The relationships of the primary parameters for strain rate are also presented in this paper. The simulated stress-strain curves matched the experimental results well. The results showed that the strength of cement mortar obeyed a Wei...

Fabrication and characterization of carbon fiber reinforced clay/epoxy composite

In this study, dynamic mechanical analysis (DMA), thermogravimetric analysis (TGA), and flexural tests were performed on unfilled, 1, 2, 3, and 4 wt% clay filled SC-15 epoxy to identify the effect of clay weight fraction on thermal and mechanical properties of the epoxy matrix. The flexural results indicate that 2.0 wt% clay filled epoxy showed the highest improvement in flexural strength. DMA studies also revealed that 2.0 wt% system exhibit the highest storage modulus and Tg as compared to neat and other weight fraction. However, TGA results show that thermal stability of composite is insensitive to the clay content. Based on these results, the nanophased epoxy with 2 wt% clay was then utilized in a vacuum assisted resin transfer molding set up with carbon fabric to fabricate laminated composites. The effectiveness of clay addition on thermal and mechanical properties of composites has been evaluated by TGA, DMA, tensile, flexural, and fatigue test. 5 °C increase in glass transition temperature was found in nanocomposite, and the tensile and flexural strengths improved by 5.7 and 13.5 %, respectively as compared to the neat composite. The fatigue strength was also improved significantly. Based on the experimental result, a linear damage model combined with the Weibull distribution function has been established to describe static failure processing of neat and nanophased carbon/epoxy. The simulated stress–strain curves from the model are in good agreement with the test data. Simulated results show that damage processing of neat and nanophased carbon/epoxy described by bimodal Weibull distribution function.

Importance of twinning in static and dynamic compression of a Ti–6Al–4V titanium alloy with an equiaxed microstructure

Abstract Whereas deformation twinning is known to be an important deformation mechanism for hexagonal materials like magnesium and pure titanium, so far almost no literature exists on the twinning behaviour of the Ti–6Al–4V alloy. In this work it was shown that the activation of twinning as a deformation mechanism could have a pronounced effect on the mechanical behaviour of the Ti–6Al–4V alloy. This effect is even more pronounced under dynamic loading conditions. Transmission electron microscopy showed that only the { 1 0 1 ¯ 2 } 〈 1 ¯ 0 1 1 〉 tensile twin system was activated under certain loading conditions. Light-optical microscopy and electron backscatter diffraction data were afterwards used to experimentally determine the twin fractions. The importance of twinning for the texture evolution was also studied. It was shown that even small twin fractions can lead to distinct texture features, especially due to the discrete reorientation of the c-axes. The experimental results were compared to simulated results that were obtained with a viscoplastic self-consistent crystal plasticity code, after experimental validation that twinning can be reliably modelled as a unidirectional slip system. Although good agreement was obtained for the experimental and simulated stress–strain curves, the simulated results concerning twinning correlated well only on a qualitative basis as the simulated twin fractions were systematically higher than the experimental fractions. This seems to strengthen the hypothesis made by other research groups that complete grains might reorient by twinning.

Micromechanical modeling for behavior of silty sand with influence of fine content

Silty sand is a soil mixture with coarse grains and fine grains. Experimental observations have shown that small amount of fines may reduce the undrained shear strength significantly. The purpose of this paper is to propose a micromechanical model for the stress–strain behavior of silty sand influenced by fines under drained and undrained conditions. The micromechanical stress–strain model accounts for the influence of fines on the density state of the soil mixture, thus consequently affect the critical state friction angle and the amount of sliding between particles. The present model is examined by simulating typical drained and undrained tests in conventional triaxial conditions. The simulated stress–strain curves are compared with the measured results on samples made of Ottawa sand and Foundry sand with various amounts of fines. The predictive ability of the present model for simulating the behavior of silty sand is discussed.

Insights into the potential functionality of single-chain force-induced conformational transitions in polymer networks: Implications for polysaccharide signaling in the plant cell wall

The behavior of biopolymer networks comprised of clickable polysaccharide chains that can undergo force-induced conformational transitions was investigated during straining using a simulation technique. The simulation was carried out both using an affine deformation field and alternatively using Lees-Edwards boundary conditions as an example of a nonaffine case. In the affine situation the simulated stress-strain curves were found to be consistent with results obtained by evaluating the molecular force-extension curve at a single average extension and calculating the bulk modulus as an average over all possible orientations with respect to the deformation. While in all cases examined the macroscopic mechanical responses of networks of randomly oriented chains, consisting either of simple extensible wormlike chains or their clickable analogs, were found to be indistinguishable, the simulation additionally allowed the number of chains containing sugar rings in different conformational states to be monitored, and this was found to change significantly during straining. This supports the hypothesis that in networks of randomly oriented clickable polysaccharide chains, such conformational transitions could have biological significance as stress switches in signaling processes but that they are unlikely to affect the bulk rheological properties of tissue.

Dynamic behavior of unidirectional fiber-reinforced composites: experiments and modeling

A statistical constitutive model, which takes into account the effect of strain rate, was presented to describe the stress— strain relationship of unidirectional fiber-reinforced composites (UFRC). To verify its reliability, tensile tests on two kinds of UFRC: a glass fiber-reinforced polyster and a unidirectional SiC/Al composite wire, were carried out at different strain rates, and the stress—strain curves were obtained. The testing results show that the strength and ductility of the two composites all increase with increasing strain rate. Simulated stress—strain curves, derived from the constitutive model, fit the tested results well, which indicates that the model is valid and reliable.

A Statistical Constitutive Model for the Strength of Brittle Fiber at Different Strain Rates

A statistical constitutive model, which takes account the effect of strain rate, was presented to describe the stress-strain relationship of brittle fiber bundles. To verify its reliability, tensile tests on two kinds of brittle fibers: glass fiber and SiC fiber, were carried out at different strain rates, and the stress-strain curves were obtained. It was found that the modulus E, the strength and the fracture strain of these fiber bundles all increase with increasing strain rate. The simulated stress-strain curves, derived from the constitutive model, fit the tested results well, which indicates that the model is valid and reliable.

Numerical Analysis on the Compressive Behaviors of Aluminum Foam Material Using Computed Tomography Imaging

In the present study, we used computed tomography (CT) images of aluminum foam material obtained by an industrial volume CT system for a numerical analysis of the compressive behavior of the material. A three-dimensional model of aluminum foam was developed by stacking the CT images. The simulated and experimental compressive behaviors were compared. In particular, the simulated compressive behaviors were compared with those of experiments using various strain rates in order to verify the accuracy of the three-dimensional model. The results showed that the simulated compressive stress-strain curve displayed a similar tendency to that of the experiment, but had a higher compressive strength. The results also showed that the simulated compressive deformation pattern displayed a similar tendency to those of the experiments for all strain rates, and the deformation was significantly affected by the simulation of pore shape and size.

A New Analytical Model for the Flow Stress of Twin-roll Casting Magnesium Sheet at Elevated Temperatures

To evaluate the flow stress of the twin-roll casting magnesium sheet in high temperature forming processes, a new analytical model was proposed by analyzing stress-strain curves measured under various temperatures and strain rates. The model can be parameterized to reflect the volume fraction of semi-sold grain and sold grains undergoing twinning. By applying the new model, the result showed that the simulated stress-strain curves fit the experiment data very well. Such curve fitting can be employed for any magnesium sheet when the deformation conditions are known. Microstructure evolution indicated that it affected the stress-strain curves directly. The mechanisms of dynamic recrystallization (DRX) depended on the operating deformation mechanisms, which changed with temperatures. And the volume fraction and grain size of DRX changed with the Zener-Hollomon parameter and temperatures.

Numerical Study on the Mechanical Behavior of Aluminum Foam Material Using CT Image

In this study, finite element analysis was made to predict the tensile and compressive behaviors of aluminum foam material. The predicted tensile and compressive behaviors were compared with those determined from the tensile and compressive tests. X-ray imaging technique was used to determine internal structure of aluminum foam material. That is, X-ray computed tomography (CT) was used to model the porosities of the material. Three-dimensional finite element modeling was made by stacking two-dimensional tomography of aluminum foam material determined from CT images. The stackings of CT images were processed by three-dimensional modeling program. The results showed that the tensile stress-strain curve predicted from the finite element analysis was similar to that determined by the experiment. The simulated compressive stress-strain curve also showed similar tendency with that of experiment up to about 0.4 strain but exhibited a different behavior from the experimental one after 0.4 strain. The discrepancy of compressive stress-strain curves in a high strain range was associated with the contact of aluminum foam walls broken by the large deformation.

Simulation of magnesium alloy AZ31 sheet during cylindrical cup drawing with rate independent crystal plasticity finite element method

Abstract A rate independent crystal plasticity model is developed to analyze the plastic deformation of hexagonal close packed (HCP) materials by incorporating the crystallography of deformation twinning in plasticity model. The “successive integration method” is used to identify active slip/twinning systems and determine plastic strain. This model is implemented in the commercial finite element code ABAQUS/Explicit to simulate the deformation process of the magnesium alloy sheet. For the determination of model parameters, simulated stress–strain curves for uniaxial tension are adjusted to the measured curves. Then the stamping process of a cylindrical cup is simulated with the developed model, and the effect of initial crystal orientation on final cup earing is discussed.

Comment on “Deformation mechanisms of face-centered-cubic metal nanowires with twin boundaries” [Appl. Phys. Lett. 90, 151909 (2007)

The article by Cao et al. provides some insight into the role of twin boundaries in the deformation mechanisms of Cu nanowires. There are, however, several statements in this letter that could cause considerable confusion for the understanding of mechanical behavior in twinned metal nanowires, if not clarified. Our comment is related to conclusion 2 in the letter of Cao et al.: “ 2 The smaller the TBS i.e., twin boundary size , the higher the twinned nanowire yield stress. The redistribution of interior stress owing to the presence of TBs is responsible for the strengthening of the twinned nanowires.” Such conclusion is drawn on the basis of the stress-strain curves presented in Fig. 2 b , in the analysis of which the authors state that “the precipitous drop of the curve implies the yielding.” This analysis is inaccurate for the case of twinned fcc metal nanowires, because plastic yielding should be characterized by the point when the first partial dislocation is emitted. Later in the paper, the authors provide a contradictory conclusion as follows: “ 3 TBs act as barrier for dislocation movements and consequently lead to hardening effects.” According to this, we conclude that the blockage of dislocation movements by the twin boundaries would make the stress continue to increase even after plastic yielding. Therefore, the maximum stress shown in the stress-strain curves presented in Fig. 2 b cannot possibly represent the yielding stress in all twinned nanowires without further examination. To support our comment, we have repeated the atomistic simulations of Cao et al. on a twin-free nanowire and a five-twin nanowire in Cu using the same procedure and parameters wire shape, relaxation steps, applied boundary conditions, strain rate, temperature, etc. as described in their original work. The simulated stress-strain curves are represented in Fig. 1, where the step corresponding to the onset of plasticity and the emission of the very first dislocation is indicated by an arrow. This figure clearly shows that the yield point in the twin-free nanowire takes place at the stress level corresponding to the “precipitous drop” in the stressstrain curve 7.42 GPa . In the five-twin nanowire, however, there is clear evidence that the emission of the very first dislocation occurs at a much smaller stress 6.08 GPa than the maximum stress 8.24 GPa . This observation also suggests that the tensile yield stress should decrease with the addition of twin boundaries. This hypothesis is supported by a past atomistic study, where it was found that the stress required for the nucleation of the dislocations in twinned gold nanowires was 18%–22% less than that of perfect wires with corresponding diameter. Furthermore, the authors have provided no evidence showing that the presence of twin boundaries would alter the distribution of interior stress. While repeating the atomistic simulations of the Letter of Cao et al., we found that the vicinity of twin boundaries does show a more compressive stress than the twin-free lattice after the energy minimization step, but such a difference may be considered negligible during the following elongation process in tension. The yielding mechanism of metal nanowires remains an open debate and, therefore, the conclusion by the authors that “the redistribution of interior stress owing to the presence of TBs is responsible for the strengthening of the twinned nanowires.” is too early to be drawn without further evidence.

Nonlinear constitutive equation for temperature degraded unidirectional carbon fiber reinforced epoxy

In this study, unidirectional carbon fiber reinforced epoxy was made by vacuum-assisted resin transfer molding (VARTM). Accelerated tests have been conducted on resulting composites at different temperature and different time. Flexural tests results show that modulus and strength decreased with increasing of time and temperature. Based on the experimental result, a linear damage model has been combined with the Weibull distribution function to establish a constitutive equation for carbon/epoxy composite. The parameters in this model are the modulus E, the Weibull shape parameter and Weibull scale parameter. The simulated stress–strain curves from the model are in good agreement with the test data. All three parameters were found to be temperature and time dependent.

Effect of polyhedral-oligomeric-sil-sesquioxanes on thermal and mechanical behavior of SC-15 epoxy

In this study, thermal and mechanical properties of nanocomposites containing SC-15 epoxy resin and polyhe- dral-oligomeric-sil-sesquioxanes (POSS) have been studied. Dynamic Mechanical Analysis (DMA) results show that the addition of 5 wt% of POSS yielded a 13% increase in the storage modulus and a 16°C enhancement in Tg. Thermo gravi- metric Analysis (TGA) results show that the thermal stability of epoxy increased with higher POSS content. Tension tests were used to evaluate the mechanical properties of materials. Both modulus and tensile strength are linear functions of POSS content. Scanning Electric Microscopy (SEM) pictures of fracture surfaces show that the roughness of the fracture surfaces of epoxy increased after adding POSS. Based on experiment results, a three-parameter nonlinear constitutive equa- tion was developed to describe the strain-softening stress-strain relationship behavior of materials. The parameters in this model are the elastic modulus, a strain exponent, m, and a compliance factor, β. Their relationships to the POSS weight fraction were obtained from the experiment results. The simulated stress-strain curves from the model agree with the test data. Analysis of the model shows that both the strain exponent, m, which controls the strain softening and hardening effect of the material, and the compliance parameter, β, which controls the flow stress level of the material, increase with higher POSS content.

Three-dimensional dislocation dynamics simulation of the influence of sample size on the stress–strain behavior of fcc single-crystalline pillars

The size-dependent flow stress in uniformly loaded pillars has been modeled using a discrete dislocation dynamics tool. Starting from Frank-Read sources of given length and random orientation, the simulated flow stress at 0.15% plastic strain shows a clear size effect, similar to experimental findings for larger strains. The scattering of the simulated stress–strain curves decreases with increasing sample size, which reflects that plasticity of small scale samples is very sensitive to the underlying dislocation microstructure.