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This report presents methods determining the hardness and tensile strength of metals by showing the effect and dependence of the hardness numbers on the strain-hardening. Relations between the hardness numbers and the ordinary stress-strain diagrams and tensile strength are given. Procedures for finding the Brinell strength are also presented.
This investigation delves into the degradation mechanisms of high-density polyethylene geomembranes (PE GMXs) under a spectrum of conditions, replicating real-world scenarios within a rigorously controlled laboratory setting. The treatment protocols applied induced a notable increase in the crystallinity of the treated specimens relative to the untreated controls. Small-angle x-ray scattering (SAXS) analysis identified an initial long period (interlamellar distance) of 16.9 nm for the untreated polymer, which expanded by 19.5% at a strain of 16.7 percent. Conversely, the treated PE GMXs exhibited a more gradual elongation of the long period, with an increase of merely 10.6% at a strain of 23.3 percent. At an elevated temperature of 65°C, both samples exhibited pronounced strain hardening, with the treated PE GMXs demonstrating superior stability even at a strain of 150 percent. Wide-angle x-ray scattering (WAXS) experiments corroborated these observations, revealing that the diffraction patterns of the untreated PE remained stable up to a strain of 16.7%, whereas those of the treated PE remained distinct up to a strain of 46.1 percent. Scanning electron microscopy (SEM) images substantiated the formation of a shish–kebab structure in the treated samples. The study concludes that the geopolymer underwent oxidation and material degradation as a result of the chemical and mechanical treatments, transitioning to a more crystalline state and concomitantly losing its initial elasticity.
Here, one-step and multi-step nanoindentation experiments were conducted to investigate the mechanical response of an Al-Mg-Li alloy. Opposite to the strain hardening effect observed in the coarse-grained (CG) alloy, the nanograined (NG) alloy exhibits strain softening. Compared with multi-step nanoindentation experiments, the ultralow dislocation density and the grain boundary (GB) segregation promote a higher stress level during one-step nanoindentation experiments. Residual perfect dislocations induced by a previous loading and unloading during multi-step nanoindentation experiments lower the stress required for further plastic deformation. In addition, the storage of partial dislocations also serves to render plastic flow to commence at lower stresses. This work provides new insights for the fabrication and property optimization of NG alloys.
Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when η 0 k , the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same η 0 k but different length scales, characterized by the wavelength λ varying by a factor of 4.9 from 65 to 130 to 320 µ m . Three such targets with different fixed η 0 k ′ s were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as λ decreased. The different η 0 k targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for 320 − 65 µ m wavelength perturbations, the effective strain rates increased from 8.7 × 10 6 to 3.3 × 10 7 s − 1 , a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates. Published by the American Physical Society 2024
For alloys with the baseline refractory metal level of 3 percent Ta and 10 percent W, decreases in Co level from 10 to 0 percent resulted in increased tensile strength and creep resistance. Substitution of W for Ta resulted in decreased creep life at high stresses but improved life at low stresses. Substitution of Ni for Ta caused large reductions in tensile strength and creep resistance, and corresponding increases in ductility. For these alloys with low Ta plus W totals, strength was independent of Co level. The increases in tensile strength with increases in refractory metal content were related to the increases in gamma volume fraction and solid solution hardening. Increases in strength as Co level decreased were considered to be the result of coherency strain hardening from the increased lattice mismatch. Dislocation shear through the gamma-gamma interface is considered to be the rate limiting step in the deformation process.
A uniaxial, uncoupled constitutive model to predict the response of thermal and rate dependent elastic-plastic material behavior is presented. The model is based on an incremental classicial plasticity theory extended to account for thermal, creep, and transient temperature conditions. Revisions to he combined hardening rule of the theory allow for better representation of cyclic phenomenon including the high rate of strain hardening upon cyclic reyield and cyclic saturation. An alternative approach is taken to model the rate dependent inelastic deformation which utilizes hysteresis loops and stress relaxation test data at various temperatures. The model is evaluated and compared to experiments which involve various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy-X.
A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.
Deformation mechanisms in sputter-deposited crystalline Al/amorphous Si nanocomposites with nanolaminate or nanofibrous morphology are characterized by nanoindentation, micropillar compression testing and transmission electron microscopy (TEM). The nanofibrous composite having crystalline Al nanofibers with ~40–50 nm in length and 15–20 nm in diameter embedded in amorphous Si exhibits strain hardening to a maximum flow stress of 2.9 GPa and no shear band (SB) formation in compression up to plastic strain exceeding 24%. On the other hand, nanolaminate composite that is composed of 80 nm crystalline Al layers and 20 nm amorphous Si layers exhibits catastrophic SBs starting at plastic strains in the range of 5–10%. Cross-sectional TEM of the deformed samples reveals a high density of stacking faults and twin boundaries in Al nanofibers and no microshear bands in the nanofibrous composite, suggesting plastic deformation in amorphous Si phase and crystalline Al nanofibers. Further, molecular dynamics simulations revealed that the plastic deformation in amorphous Si phase in the cosputtered films could be favored by the decrease in flow strength of amorphous Si with increasing Al solute concentration trapped in Si.
The effects of stress ratio, prestress cycling and plate thickness on the fatigue crack propagation rate are studied on 2024-T351 aluminum alloy. Fatigue crack propagation rate increases with the plate thickness and the stress ratio. Prestress cycling below the static yield strength has no noticeable effect on the fatigue crack propagation rate. However, prestress cycling above the static yield strength causes the material to strain harden and increases the fatigue crack propagation rate. Crack tip deformation is used to study the fatigue crack propagation. The crack tip strains and the crack opening displacements were measured from moire fringe patterns. The moire fringe patterns were obtained by a double exposure technique, using a very high density master grille (13,400 lines per inch).
Engineered cementitious composites (ECC) is a durable cementitious material with high tensile ductility and strain-hardening characteristics. Although considered as a cost-effective fiber for ECC, polypropylene (PP) fiber is reportedly difficult to disperse in mortar matrix due to its high aspect ratio and hydrophobicity. In this study, the matrix viscosity of a low-carbon ECC based on limestone calcined clay cement was tailored as a variable to improve PP fiber dispersion under a pre-determined mixing protocol. The effect of matrix viscosity on the composite fresh and hardened properties was investigated experimentally. Results suggested an optimal range of matrix viscosity (10.3–11.5 Pa . s) favors the composite tensile strength and strain capacity at 28 days. At the optimal state with a 0.1 % viscosity modifying admixture (VMA)-to-binder mass ratio, PP-ECC achieved 7.0 % tensile strain capacity and 3.5 MPa ultimate tensile strength. When matrix viscosity falls outside the desired range, both ultimate tensile strength and strain capacity were diminished. By tailoring the VMA dosage, the matrix viscosity can be adjusted for desired fiber dispersion, workability, and mechanical properties. Finally, the findings of this study provide a technical reference for the practical design and application of PP-ECC.
Twenty three high temperature low-cycle fatigue tests were conducted on single crystals of the nickel-based superalloy Mar-M 200. Tests were conducted at 760 and 870 C. SEM fractography and transmission electron microscopy were used to determine mechanisms responsible for the observed orientation dependent fatigue behavior. It has been concluded that the plastic characteristics of the alloy lead to orientation-dependent strain hardening and fatigue lives at 760 C. At 870 C, the elastic characteristics of the alloy dominated the behavior, even though the plastic strain ranges were about the same as they were at 760 C. This led to orientation-dependent fatigue lives, but the trends were not the same as they were at 760 C.
A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.
Several key capabilities have been identified by the aerospace community as lacking in the material/models for composite materials currently available within commercial transient dynamic finite element codes such as LS-DYNA. Some of the specific desired features that have been identified include the incorporation of both plasticity and damage within the material model, the capability of using the material model to analyze the response of both three-dimensional solid elements and two dimensional shell elements, and the ability to simulate the response of composites composed with a variety of composite architectures, including laminates, weaves and braids. In addition, a need has been expressed to have a material model that utilizes tabulated experimentally based input to define the evolution of plasticity and damage as opposed to utilizing discrete input parameters (such as modulus and strength) and analytical functions based on curve fitting. To begin to address these needs, an orthotropic macroscopic plasticity based model suitable for implementation within LS-DYNA has been developed. Specifically, the Tsai-Wu composite failure model has been generalized and extended to a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The coefficients in the yield function are determined based on tabulated stress-strain curves in the various normal and shear directions, along with selected off-axis curves. Incorporating rate dependence into the yield function is achieved by using a series of tabluated input curves, each at a different constant strain rate. The non-associative flow-rule is used to compute the evolution of the effective plastic strain. Systematic procedures have been developed to determine the values of the various coefficients in the yield function and the flow rule based on the tabulated input data. An algorithm based on the radial return method has been developed to facilitate the numerical implementation of the material model. The presented paper will present in detail the development of the orthotropic plasticity model and the procedures used to obtain the required material parameters. Methods in which a combination of actual testing and selective numerical testing can be combined to yield the appropriate input data for the model will be described. A specific laminated polymer matrix composite will be examined to demonstrate the application of the model.
The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.
The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.
In polymer-filled granular composites, damage may develop in mechanical loading prior to material failure. Damage mechanisms such as microcracking or plastic deformation in the binder phase can substantially alter the material’s mesostructure. For energetic materials, such as solid propellants and plastic bonded explosives, these mesostructural changes can have far reaching effects including degraded mechanical properties, potentially increased sensitivity to further insults, and changes in expected performance. Unfortunately, predicting damage is nontrivial due to the complex nature of these composites and the entangled interactions between inelastic mechanisms. In this work, we assess the current literature of experimental knowledge, focusing on the pressure-dependent shear response, and propose a simple simulation framework of bonded particles to study four limiting-case material formulations at both meso- and macro-scales. Further, to construct the four cases, we systematically vary the relative interfacial strength between the polymer binder and granular filler phase and also vary the polymer’s glass transition temperature relative to operating temperature which determines how much the binder can plastically deform. These simulations identify key trends in global mechanical response, such as the emergence of strain hardening or softening regimes with increasing pressure which qualitatively resemble experimental results. By quantifying the activation of different inelastic mechanisms, such as bonds breaking and plastically straining, we identify when each mechanism becomes relevant and provide insight into potential origins for changes in mechanical responses. The locations of broken bonds are also used to define larger, mesoscopic cracks to test various metrics of damage. We primarily focus on triaxial compression, but also test the opposite case of triaxial extension to highlight the impact of Lode angle on mechanical behavior.
Application of the endochronic theory of viscoplasticity to creep, creep recovery, and stress relaxation at the small strain and short time range produced the following results: (1) The governing constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation were derived by imposing appropriate constraints on the general constitutive equation of the endochronic theory. (2) A set of material constants was found which correlate strain-hardening, creep, creep recovery, and stress relaxation. (3) The theory predicts with reasonable accuracy the creep and creep recovery behaviors at short time. (4) The initial strain history prior to the creep stage affects the subsequent creep significantly. (5) A critical stress was established for creep recovery. A computer program, written for the misalignment problem is reported.
The present study experimentally characterizes the effects of elevated temperature on the uniaxial tensile behavior of ingot metallurgy 2618 Al alloy and the rapidly solidified FVS 0812 P/M alloy by means of two constitutive formulations: the Ramberg/Osgood equation and the Bodner-Partom (1975) incremental formulation for uniaxial tensile loading. The elastoplastic strain-hardening behavior of the ingot metallurgy alloy is equally well represented by either formulation. Both alloys deform similarly under decreasing load after only 1-5 percent uniform tensile strain, a response which is not described by either constitutive relation.