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The objectives are: (1) to demonstrate tensile testing of materials and the application of the concepts of stress and strain; and (2) to yield a mathematical relationship between stress and strain for many artificial rubbers and plastics. The experiment, supplies, and procedure are presented.
The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both predictive error on the dataset and the complexity of the description. The discovery of the governing physics of a system can therefore be viewed as a mathematical optimization problem. We outline here a method to optimize the description of arbitrarily complex physical systems by minimizing the entropy of the description of the system. The Recursive Domain Partitioning (RDP) procedure finds the optimum partitioning of each physical domain into subdomains, and the optimum predictive function within each subdomain. Penalty functions are introduced to limit the complexity of the predictive function within each domain. Examples are shown in 1D and 2D. In 1D, the technique effectively discovers the elastic and plastic regions within a stress-strain curve generated by simulations of amorphous carbon material, while in 2D the technique discovers the free-flow region and the inertially-obstructed flow region in the simulation of fluid flow across a plate.
In this paper, a simplified numerical approach for finite element dynamic analysis of an inelastic solid structure subjected to solid object impact is presented. The approach approximates the impacting solid as the selected multiple nodes, for which mass of the impactor is distributed. The node-to-segment contact formulation with the penalty constraint technique incorporated is employed to impose contact conditions between the nodes and the surface of the receiver structure. The node-to-segment algorithm is integrated into Newton–Raphson time integration scheme and the Lagrange multiplier technique is applied to enforce the identical displacements for the selected nodes throughout the analysis process. The approach is verified using two-dimensional plane strain models considering elastic-perfectly-plastic material behavior. The results obtained using the proposed approach are in a good agreement with those simulated using a commercial finite element code, ABAQUS dynamic/implicit, in terms of displacements and stress distribution fields. The proposed approach is shown to be computationally superior to general finite element method-based contact/impact analysis without significantly sacrificing the accuracy.
Abstract The response of a polycrystalline material to a mechanical load depends not only on the response of each individual grain, but also on the interaction with its neighbors. These interactions lead to local, intragranular stress concentrations that often dictate the initiation of plastic deformation and consequently the macroscopic stress–strain behavior. However, very few experimental studies have quantified intragranular stresses across bulk, three-dimensional volumes. In this work, a synchrotron X-ray diffraction technique called point-focused high-energy diffraction microscopy (pf-HEDM) is used to characterize intragranular deformation across a bulk, plastically deformed, polycrystalline titanium specimen. The results reveal the heterogenous stress distributions within individual grains and across grain boundaries, a stress concentration between a low and high Schmid factor grain pair, and a stress gradient near an extension twinning boundary. This work demonstrates the potential for the future use of pf-HEDM for understanding the local deformation associated with networks of grains and informing mesoscale models. Graphical abstract
Particularly in plastically anisotropic crystals, such as hexagonal close packed (HCP) materials, plastic deformation is realized by slip acting in the small volumes within individual crystals. Here we extend a full field fast Fourier transform (FFT)-based elasto-viscoplastic formulation to simulate the development of a single slip band on either prismatic or basal planes spanning a crystal. Calculations of the strain and stress fields induced locally within the band and parent crystal, and ahead of the band/grain boundary junction in the neighboring crystal are analyzed as the slip band intensifies under increasing applied strain. We report a substantial influence of the crystallographic orientation of the nearest neighboring grain on the rate of slip band localization. Performing the analysis on two materials, CP-Ti and Mg, indicates that the strength of the material affects the rate of localization, with stronger materials tending to localize more easily. A slip band tip stress-based criterion is proposed for identifying the nearest neighbor orientations in which slip band transmission is possible and the likely slip system for which it occurs. This indicator is validated against experimental studies on commercially pure Ti, an Mg–Y alloy, and Ti–6Al–4V. Finally, we show that for low GB misorientations, the slip band is likely to transmit into another slip band of the same type in the neighbor grain, while for high GB misorientations, it is likely to transmit into one of a different type or to not transmit at all.
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The monotonic plastic flow behavior of several single crystal nickel-base, superalloys has been shown to vary significantly with crystallographic orientation. In the present study, the cyclic plastic flow response of one such alloy, PWA 1480, was examined at 650 deg C in air. Single crystal specimens aligned near several crystallographic directions were tested in fully reversed, total-strain-controlled low cycle fatigue tests at a frequency of 0.1 Hz. The cyclic stress-strain response and general cyclic hardening behavior was analyzed as a function of crystallographic orientation and inelastic strain range.
In this study, a complex constitutive relation is identified using inverse modeling with the nominal mechanical response as sole experimental input. The methodology is illustrated for a semicrystalline thermoplastic in the presence of strain localization at finite deformations. The experimental database includes cylindrical tensile bars, compression pins and round notched bars loaded at strain rates spanning up to five decades and temperatures below and above T g . The data is organized into a calibration set and a validation set. The response of tensile specimens is determined using finite element analyses and a two-phase constitutive relation for semicrystalline polymers that accounts for temperature- and rate-sensitive plastic flow, pressure-sensitivity, small-strain softening and large-strain orientational hardening of the amorphous phase, along with the evolution of crystallinity. The large number of constitutive parameters is identified using an optimization tool coupled with the finite element solver and the calibration set from experiments. The methodology is shown to be successful in predicting the response of round notched bars and replicating the effects of temperature and strain rate on the severity of necking in tensile bars. The proposed model identification strategy is both simple and effective in comparison with other elaborate methods that attempt to access intrinsic behavior directly from high-fidelity experimental measurements.
Fatigue crack growth rate changes caused by single overloads and an overload followed by an underload have been studied in the high-strength aluminum alloy 7091. Crack-tip plasticity parameters were measured at each step in the loading sequence using the stereoimaging technique. Effective stress-intensity factor was measured with high resolution immediately at the crack tip both before an overload and during the subsequent growth rate retardation period. Crack-tip opening displacement and strain were altered in the same way as growth rate following the overload/underload events, and similitude with respect to crack-tip plasticity was preserved during the growth retardation period. Effective stress-intensity factor was found to correlate well with crack growth rate. Strains within the plastic zone were converted to stress at each step in load change. These stresses were then summed to determine the zone of residual stress caused by the overload. The region of compressive residual stress ahead of the crack tip was found to increase with overload severity but was limited to yield stress in magnitude. An underload shrank the spatial extent of the residual stresses caused by the overload.
On the basis of mechanical tests and metallographic studies, strainrange partitioned lives were predicted by introducing stress-strain materials parameters into the Universal Slopes Equation. This was the result of correlating fatigue damage mechanisms and deformation mechanisms operating at elevated temperatures on the basis of observed mechanical and microstructural behavior. Correlation between high temperature fatigue and stress strain properties for nickel base superalloys and stainless steel substantiated the method. Parameters which must be evaluated for PP- and CC- life are the maximum stress achievable under entirely plastic and creep conditions respectively and corresponding inelastic strains, and the elastic modulus. For plasticity/creep interaction conditions (PC and CP) two more pairs of stress strain parameters must be ascertained.
On the basis of mechanical tests and metallographic studies, strainrange partitioned lives were predicted by introducing stress-strain materials parameters into the Universal Slopes Equation. This was the result of correlating fatigue damage mechanisms and deformation mechanisms operating at elevated temperatures on the basis of observed mechanical and microstructural behavior. Correlation between high temperature fatigue and stress strain properties for nickel base superalloys and stainless steel substantiated the method. Parameters which must be evaluated for PP- and CC- life are the maximum stress achievable under entirely plastic and creep conditions respectively and corresponding inelastic strains, and the two more pairs of stress strain parameters must be ascertained.
An Al2O3 (alumina)-fiber composite with high strain to failure was fabricated with a thermal plastic PEEK (poly-ether-ether-ketone). The Al2O3-PEEK composite shows a marked improvement over thermally setting composite in that it absorbs 150 percent more elastic-strain energy at 76 K than at room temperature. This increase in fracture toughness at low temperatures can provide improved fatigue performance for thermal isolation straps at low temperature. Other mechanical property results suggest improvements for applications where graphite-epoxy materials are presently being used at low temperatures and where light weight is not a critical issue.
Stress-strain curves of polycrystalline metals and composites using single crystal elastoplastic model
High strain-rate (up to 6600 s –1 ) and quasi-static compression tests are conducted on a powder-sintered porous titanium with different pore sizes (mean: 30 μm and 120 μm). In situ X-ray imaging is implemented to characterize the pores-scale deformation dynamics. The yield strength as a function of strain rate exhibits two stages of rate sensitivity, and the transition occurs at 1600 s –1 . X-ray images show that pore compaction and strain localizations occur preferentially at pores oriented perpendicular to the loading direction under quasi-static loading, but become more random under high strain-rate loading as a result of higher driving force and plastic deformation nucleation rate. Here, the more homogeneous nucleation of plastic deformation contributes to the increased rate sensitivity beyond 1600 s –1 . At the same strain rate, the yield strength of porous Ti as well as strain field homogeneity decreases significantly with increasing pore size. The small pore spacing in fine-pored Ti reduces the degree of stress concentrations around pores. Therefore, the higher stress concentrations in coarse-pored Ti lead to an earlier yield of matrix around pores and thus a lower bulk yield strength.
In the framework of density functional theory (DFT), we investigate the structural deformation, and mechanical behavior of the Janus CrSSe, which has out-of-plane structural asymmetry, with conventional transition metal dichalcogenides (TMDs) CrS 2 and CrSe 2 . The Janus CrSSe could be a potential candidate for machinable optoelectronic and piezoelectric applications. Here, we predict that these compounds are chemically, mechanically, and dynamically stable with the covalent bond between the TM(Cr) and chalcogen(X=S, Se) atoms. Due to the influence of tensile strain, the Cr–X bond length of each monolayers increases and the thickness decreases. Interestingly, the in-plane stiffness, shear and layer moduli, Poisson’s ratio, ultimate bi/uni-axial stress of Janus CrSSe are in between the values of CrS 2 and CrSe 2 monolayers. Similar to TMDs, the orientation-dependent in-plane stiffness and Poisson’s ratio demonstrates the isotropic behavior in Janus CrSSe. Furthermore, it can sustain a larger value of uni/bi-axial tensile strain with the critical strain equivalent to CrX 2 monolayers. By applying higher-order strain, we have also found average elastic–plastic behavior as expected. These findings demonstrate that the Janus CrSSe monolayer is a mechanically stable and ductile compound that maintains the hybrid behavior.
Here we present a crystal plasticity model tailored for high-pressure, high-strain-rate conditions that uses a multiscale treatment of dislocation-based slip kinetics. We use this model to analyze the pronounced plasticity-induced lattice rotations observed in shock-compressed polycrystalline tantalum via in situ x-ray diffraction. By making direct comparisons between experimentally measured and simulated texture evolution, we can explain how the details of the underlying slip kinetics control the degree of lattice rotation that ensues. Specifically, we show that only the highly nonlinear kinetics caused by dislocation nucleation can explain the magnitude of the rotation observed under shock compression. We demonstrate a good fit between our crystal plasticity model and x-ray diffraction data and exploit the data to quantify the dislocation nucleation rates that are otherwise poorly constrained by experiment in the dynamic compression regime.
A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.
The nonlinear stress strain behavior of 90 degree/0 degree sub 2s, SiC/Ti-15-3 composite laminate was numerically investigated with a finite element, unit cell approach. Tensile stress-strain curves from room temperature experiments depicted three distinct regions of deformation, and these regions were predicted by finite element analysis. The first region of behavior, which was linear elastic, occurred at low applied stresses. As applied stresses increased, fiber/matrix debonding in the 90 degree plies caused a break in the stress-strain curve and initiated a second linear region. In this second region, matrix plasticity in the 90 degree plies developed. The third region, which was typified by nonlinear, stress-strain behavior occr red at high stresses. In this region, the onset of matrix plasticity in the 0 degree plies stiffened the laminate in the direction transverse to the applied load. Metallographic sections confirmed the existence of matrix plasticity in specific areas of the structure. Finite element analysis also predicted these locations of matrix slip.