Showing papers on "Stress–strain curve published in 2008"

The Effect of Strain Rate on the Mechanical Properties of Human Cortical Bone

Abstract: Bone mechanical properties are typically evaluated at relatively low strain rates. However, the strain rate related to traumatic failure is likely to be orders of magnitude higher and this higher strain rate is likely to affect the mechanical properties. Previous work reporting on the effect of strain rate on the mechanical properties of bone predominantly used nonhuman bone. In the work reported here, the effect of strain rate on the tensile and compressive properties of human bone was investigated. Human femoral cortical bone was tested longitudinally at strain rates ranging between 0.14-29.1 s(-1) in compression and 0.08-17 s(-1) in tension. Young's modulus generally increased, across this strain rate range, for both tension and compression. Strength and strain (at maximum load) increased slightly in compression and decreased (for strain rates beyond 1 s(-1)) in tension. Stress and strain at yield decreased (for strain rates beyond 1 s(-1)) for both tension and compression. In general, there seemed to be a relatively simple linear relationship between yield properties and strain rate, but the relationships between postyield properties and strain rate were more complicated and indicated that strain rate has a stronger effect on postyield deformation than on initiation of yielding. The behavior seen in compression is broadly in agreement with past literature, while the behavior observed in tension may be explained by a ductile to brittle transition of bone at moderate to high strain rates.

Ultrahigh stress and strain in hierarchically structured hollow nanoparticles

Abstract: Nanocrystalline materials offer very high strength but are typically limited in their strain to failure, and efforts to improve deformability in these materials are usually found to be at the expense of strength. Using a combination of quantitative in situ compression in a transmission electron microscope and finite-element analysis, we show that the mechanical properties of nanoparticles can be directly measured and interpreted on an individual basis. We find that nanocrystalline CdS synthesized into a spherical shell geometry is capable of withstanding extreme stresses (approaching the ideal shear strength of CdS). This unusual strength enables the spherical shells to exhibit considerable deformation to failure (up to 20% of the sphere’s diameter). By taking into account the structural hierarchy intrinsic to novel nanocrystalline materials such as this, we show it is possible to achieve and characterize the ultrahigh stresses and strains that exist within a single nanoparticle during deformation. Nanocrystalline materials usually exhibit high strength and their deformation caused by stress is limited. Nanocrystalline CdS with spherical and hierarchical shell geometry is shown not only to withstand extreme stresses, but also to deform considerably before failure.

Modeling of white layer formation under thermally dominant conditions in orthogonal machining of hardened AISI 52100 steel

Abstract: This paper presents a finite element model for white layer formation in orthogonal machining of hardened AISI 52100 steel under thermally dominant cutting conditions that promote martensitic phase transformations. The model explicitly accounts for the effects of stress and strain, transformation plasticity and the effect of volume expansion accompanying phase transformation on the transformation temperature. Model predictions of white layer depth are found to be in agreement with experimental values. The paper also analyzes the effect of white layer formation on residual stress evolution in orthogonal cutting of AISI 52100 hardened steel. Model simulations show that white layer formation does have a significant impact on the magnitude of surface residual stress and on the location of the peak compressive residual stress.

Three-Stage Full-Range Stress-Strain Model for Stainless Steels

Abstract: Advanced numerical modeling of cold-formed stainless steel members, from manufacturing to full-range response under applied loading, requires knowledge of the stress-strain relationship of the material over a wide range of tensile and compressive strains. Although a number of stress-strain models have been developed for stainless steels, they are only capable of accurate predictions either over a limited strain range or for the tensile stress-strain behavior only. This paper presents a three-stage stress-strain model for stainless steels, which is capable of accurate predictions over the full ranges of both tensile and compressive strains. The new stress-strain model is defined using the three basic Ramberg-Osgood parameters and is based on a careful interpretation of existing experimental data. The accuracy of the proposed model is demonstrated by comparing its predictions with experimental stress-strain curves. These comparisons also clearly demonstrate the advantage of the proposed model over the only existing full-range stress-strain model.

Material characterization at high strain rate by Hopkinson bar tests and finite element optimization

Abstract: In the present work, dynamic tests have been performed on AISI 1018 CR steel specimens by means of a split Hopkinson pressure bar (SHPB). The standard SHPB arrangement has been modified in order to allow running tensile tests avoiding spurious and misleading effects due to wave dispersion, specimen inertia and mechanical impedance mismatch in the clamping region. However, engineering stress–strain curves obtained from experimental tests are far from representing true material properties because of several phenomena that must be taken into account: the strain rate is not constant during the test, the specimen undergoes remarkable necking, so stress and strain distributions are largely non-uniform, and the temperature increases because of plastic work. Experimental data have been post-processed using a finite element-based optimization procedure where the specimen dynamic deformation is reproduced. Optimal sets of material constants for different constitutive models (Johnson–Cook, Zerilli–Armstrong and others) have been computed by fitting, in a least mean square sense, the numerical and experimental load–displacement curves.

A New Experimental Technique for the Multi-axial Testing of Advanced High Strength Steel Sheets

Abstract: This paper deals with the development of a new experimental technique for the multi-axial testing of flat sheets and its application to advanced high strength steels. In close analogy with the traditional tension-torsion test for bulk materials, the sheet material is subject to combined tension and shear loading. Using a custom-made dual actuator hydraulic testing machine, combinations of normal and tangential loading are applied to the boundaries of a flat sheet metal specimen. The specimen shape is optimized to provide uniform stress and strain fields within its gage section. Finite element simulations are carried out to verify the approximate formulas for the shear and normal stress components at the specimen center. The corresponding strain fields are determined from digital image correlation. Two test series are performed on a TRIP-assisted steel sheet. The experimental results demonstrate that this new experimental technique can be used to investigate the large deformation behavior of advanced high strength steel sheets. The evolution of the yield surface of the TRIP700 steel is determined for both radial and non-proportional loading paths.

Molecular Dynamics Studies of Stress−Strain Behavior of Silica Glass under a Tensile Load

Abstract: Molecular dynamics (MD) simulations were carried out to study the stress−strain diagrams of crystalline and amorphous silica under different nonequilibrium conditions. The responses of a tensile load were recorded in two cases. In one case, the system was not allowed to relax along the transverse direction (null Poisson’s ratio), while in the other case, the deformations were allowed in directions perpendicular to the strained one. The higher strength of crystalline silica as compared to amorphous silica resulted from a different distribution of ring sizes. The results obtained for the inert failure strains and intrinsic strength of the silica glass were in good agreement with the experimental data, and the nonlinear elastic behavior of the glass was reproduced along with the effects of strain rate and temperature variation. Elastic properties extracted from stress−strain diagrams also were compared with the properties calculated by means of static methods and with experimental data.

Micromechanical Modelling of the Complete Stress–Strain Relationship for Crack Weakened Rock Subjected to Compressive Loading

Abstract: A micromechanics-based model, able to quantify the effect of various parameters on the complete stress–strain relationship, is described. The closed-form explicit expression for the complete stress–strain relationship of a rock material containing an echelon cracks arrangement subjected to compressive loading is obtained. The complete stress–strain relationship including the stages of linear elasticity, non-linear hardening and strain softening is established. The results show that the complete stress–strain relationship and the strength of rock with echelon cracks depend on the crack interface friction coefficient, the sliding crack spacing, the perpendicular distance between the two adjacent rows, the fracture toughness of rock material and orientation of the cracks. The present model is used to evaluate the complete stress–strain relationship and strength for crack-weakened rock at the underground cavern complex of the Ertan Hydroelectric Project. The predicted strength is in agreement with that obtained by the Hoek–Brown criterion. The numerical results obtained with the complete stress–strain relationship seem to be in good agreement with the measured values.

Stress-Strain relationship of frost-damaged concrete subjected to fatigue loading

Abstract: This study attempted to develop a model for the stress-strain relationship in compression of frost-damaged concrete subjected to fatigue loading. Concrete specimens were prepared and exposed to freeze-thaw cycles followed by application of static and fatigue loading. The strains induced during the freeze-thaw test were carefully measured as well as during a mechanical loading test. It was found that the static strength and the fatigue life of concrete decreases as increasing irreversible tensile strain was induced by frost action. A stress-strain model for frost-damaged concrete under application of static and fatigue loading based on the degradation of initial stiffness caused by frost damage was presented. The degradation of initial stiffness for damaged concrete was empirically formulated as a function of remaining expansion caused by freeze-thaw cycles. The plastic strain under the application of mechanical static and fatigue loading for frost-damaged concrete is higher than that for original concrete. Therefore, plastic strain for damaged concrete was formulated as not only the function of strain level under mechanical loading, but also the function of irreversible strain caused by frost action. The unloading and reloading stiffness factors were introduced to explain the change of stiffness as increasing the number of loading cycles by considering the effect of the degree of frost damage.

Micromechanical modeling of the viscoplastic behavior of olivine

Abstract: [1] Efforts to couple mantle flow models with rheological theories of mineral deformation typically ignore the effect of texture development on flow evolution. The fact that there are only three easy slip systems for dislocation glide in olivine crystals leads to strong mechanical interactions between the grains as the deformation proceeds, and subsequent development of large viscoplastic anisotropy in polycrystals exhibiting pronounced Lattice Preferred Orientations. Using full-field simulations for creep in dry polycrystalline olivine at high temperature and low pressure, it is shown that very large stress and strain rate intragranular heterogeneities can build up with deformation, which increase dramatically with the strength of the hard slip system (included for the purpose of enabling general deformations). Compared with earlier nonlinear extensions of the Self-Consistent mean-field theory to simulate polycrystal deformation, the “Second-Order” method is the only one capable of accurately describing the effect of intraphase stress heterogeneities on the macroscopic flow stress, as well as on the local stress- and strain rate fluctuations in the material. In particular, this approach correctly predicts that olivine polycrystals can deform with only four independent slip systems. The resistance of the fourth system (or accommodation mechanism), which is likely provided by dislocation climb or grain boundary processes as has been observed experimentally, may essentially determine the flow stress of olivine polycrystals. We further show that the “tangent” model, which had been used extensively in prior geophysical studies of the mantle, departs significantly from the full-field reference solutions.

Polyamide–silica nanocomposites: mechanical, morphological and thermomechanical investigations

Abstract: BACKGROUND: The physical properties of polyamides can be enhanced through incorporation of inorganic micro- and nanofillers such as silica nanoparticles. Transparent sol-gel-derived organic-inorganic nanocomposites were successfully prepared by in situ incorporation of a silica network into poly(trimethylhexamethylene terephthalamide) using diethylamine as catalyst. Thin films containing various proportions of inorganic network obtained by evaporating the solvent were characterized using mechanical, dynamic mechanical thermal and morphological analyses. RESULTS: Tensile measurements indicate that modulus as well as stress at yield and at break point improved while elongation at break and toughness decreased for the hybrid materials. The maximum value of stress at yield point (72 MPa) was observed with 10 wt% silica while the maximum stress at break point increased up to 66 MPa with 20 wt% silica relative to that of pure polyamide (44 MPa). Tensile modulus was found to increase up to 2.59 GPa with 10 wt% silica in the matrix. The glass transition temperature and the storage moduli increased with increasing silica content. The maximum increase in the Tg value (144 °C) was observed with 20 wt% silica. Scanning electron microscopy investigation gave the distribution of silica, with an average particle size ranging from 3 to 24 nm. CONCLUSION: These results demonstrate that nanocomposites with high mechanical strength can be prepared through a sol-gel process. The increase in the Tg values suggests better cohesion between the two phases, and the morphological results describe a uniform dispersion of silica particles in the polymer matrix at the nanoscale. Copyright © 2007 Society of Chemical Industry

Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation

Abstract: Local strain data obtained throughout the entire weld region encompassing both the weld nugget and heat affected zones (HAZs) are processed using two methodologies, uniform stress and virtual fields, to estimate specific heterogeneous material properties throughout the weld zone. Results indicate that (a) the heterogeneous stress–strain behavior obtained by using a relatively simple virtual fields model offers a theoretically sound approach for modeling stress–strain behavior in heterogeneous materials, (b) the local stress–strain results obtained using both a uniform stress assumption and a simplified uniaxial virtual fields model are in good agreement for strains ɛ xx < 0.025, (c) the weld nugget region has a higher hardening coefficient, higher initial yield stress and a higher hardening exponent, consistent with the fact that the steel weld is overmatched and (d) for ɛ xx > 0.025, strain localization occurs in the HAZ region of the specimen, resulting in necking and structural effects that complicate the extraction of local stress strain behavior using either of the relatively simple models.

Stress–Strain Characteristics of Tin-Based Solder Alloys for Drop-Impact Modeling

Abstract: The stress–strain properties of eutectic Sn-Pb and lead-free solders at strain rates between 0.1 s−1 and 300 s−1 are required to support finite-element modeling of the solder joints during board-level mechanical shock and product-level drop-impact testing. However, there is very limited data in this range because this is beyond the limit of conventional mechanical testing and below the limit of the split Hopkinson pressure bar test method. In this paper, a specialized drop-weight test was developed and, together with a conventional mechanical tester, the true stress–strain properties of four solder alloys (63Sn-37Pb, Sn-1.0Ag-0.1Cu, Sn-3.5Ag, and Sn-3.0Ag-0.5Cu) were generated for strain rates in the range from 0.005 s−1 to 300 s−1. The sensitivity of the solders was found to be independent of strain level but to increase with increased strain rate. The Sn-3.5Ag and the Sn-3.0Ag-0.5Cu solders exhibited not only higher flow stress at relatively low strain rate but, compared to Sn-37Pb, both also exhibited higher rate sensitivity that contributes to the weakness of these two lead-free solder joints when subjected to drop impact loading.