Serrated Stress Strain Curves Research Articles

Effect of natural defects on the fracture behaviors and failure mechanism of basalt through mesotesting and FDEM modeling

As an important geological medium for engineering construction in Southwest China, basalt typically contains natural defects, such as hidden joints and amygdales, which significantly affect its mechanical properties. In this work, the fracture behaviors of basalt with different defects were studied in terms of its strength, deformation and failure characteristics, and crack evolution laws using a comprehensive mesotesting scheme and finite-discrete element method (FDEM) modeling, revealing the failure mechanism of basalt. The results showed that: (1) Intact specimens exhibiting high strength and smooth stress–strain curves burst instantly when loaded to the peak strength, and the corresponding acoustic emission events are abnormally concentrated, indicating a fragmentation failure mode. (2) The strength of fractured samples decreases significantly, the stress–strain curve is bimodal or multimodal, and the acoustic emission events are very active during the entire failure process, which is closely related to the local damage generated during each significant stress drop, with tension dominant, shear dominant, or tension–shear composite failure modes. (3) For amygdaloidal basalt samples with a serrated stress–strain curve, each small-scale stress drop is accompanied by the initiation, propagation, and coalescence of microcracks, resulting in relatively scattered acoustic emission events, indicating a splitting failure mode. (4) Because of the small particle size, dense arrangement, good uniformity, and high strength at the grain scale, intact basalt exhibits a relatively uniform stress field easily induced under loading, leading to an extremely high strength, fragmentation failure mode, and significant brittleness. However, a heterogeneous stress field near the original defects, such as hidden joints or amygdales, is prominent, and it significantly affects the fracture paths, which is the main reason for the strong randomness of the mechanical properties, evident strength reduction, and significant change in the failure modes. The research results can provide reference for revealing the occurrence mechanism, guiding warning systems, and formulating control methods for high-stress disasters in hard brittle rocks.

Mechanical response of lightweight hollow truss metal oxide lattices

Porous metal oxides are an important class of engineering materials with unique combinations of lightweight, mechanical, photovoltaic, catalytic and thermal properties. The structural stability and load-bearing capabilities of porous metal oxides can be improved if stretch/compression-dominated lattice designs are used instead of bending-dominated foam structures. Here, we introduce a simple, scalable technique that involves the dip-coating of 3D printed polymeric lattices, of simple cubic design, in a metal particle (Fe and Cu) suspension. Subsequent heat treatment in a furnace removed the polymeric core and binder, leaving behind a hollow-truss lattice structure composed of sintered and oxidized metal particles. Examination of its microstructure reveals that the hollow-truss lattices have three levels of hierarchy, namely, the length/ width of the lattice strut (∼1 mm), the thickness of the coating (∼0.1 mm) and the size of the pores/ particles (∼0.01 mm). This hierarchical arrangement of material enabled the hollow-truss metal oxide lattices to achieve ∼1% relative density, which is lower than that achievable with ceramic foams. Under quasi-static compression, the hollow-truss lattices experienced multiple steps of fractures and exhibited highly serrated stress–strain curves. The relative modulus and relative strength of hollow-truss lattices were found to be related to the relative density by a power law relationship, with an exponent of 1.2 and ∼1.3, respectively. A detailed analysis showed that the slight deviation of the mechanical properties from an ideal stretch-dominated design was primarily due to the presence of small amounts of porosity in the metal oxide coating. Nevertheless, the load-bearing efficiency exhibited by the hollow-truss metal oxide lattices was found to be comparable or superior to that of hollow-truss alumina micro- and nano-lattices, as well as ceramic foams.

Mechanical Response of Lightweight Hollow Truss Metal Oxide Lattices

Porous metal oxides are an important class of engineering materials with unique combinations of lightweight, mechanical, photovoltaic, catalytic and thermal properties. The structural stability and load-bearing capabilities of porous metal oxides can be improved if stretch/compression-dominated lattice designs are used instead of bending-dominated foam structures. However, current techniques of fabricating orderly metal oxide lattices, such as selective laser sintering, are too costly or, in the case of alumina nanolattices synthesized through 2-photon polymerization and atomic layer deposition, not amenable to production scaling. Here, we introduce a simple, scalable technique that involves the dip-coating of 3D printed polymeric lattices, of simple cubic design, in a metal particle suspension. In the present study, iron particles and copper particles were separately used to demonstrate the feasibility of the technique. Subsequent heat treatment in a furnace removed the polymeric core and binder, leaving behind a hollow-truss lattice structure composed of sintered and oxidized metal particles. Examination of its microstructure reveals that the hollow-truss lattices have three levels of hierarchy, namely, the length/ width of the lattice strut (~ 1 mm), the thickness of the coating (~ 0.1 mm) and the size of the pores/ particles (~ 0.01 mm). This hierarchical arrangement of material enabled the hollow-truss metal oxide lattices to achieve ~ 1% relative density, which is lower than that achievable with ceramic foams. Under quasi-static compression, the hollow-truss lattices experienced multiple steps of fractures and exhibited highly serrated stress-strain curve. The relative modulus and relative strength of hollow-truss lattices were found to be related to the relative density by a power law relationship, with an exponent of 1.2 and ~1.3 respectively. A detailed analysis showed that the slight deviation of the mechanical properties from an ideal stretch-dominated design was primarily due to the presence of porosity in the metal oxide coating. Nevertheless, the load-bearing efficiency exhibited by the hollow-truss metal oxide lattices was found to be comparable or superior to that of hollow-truss alumina micro- and nano- lattices, as well as ceramic foams.

The effect of thermo-mechanical treatment on the high temperature tensile behavior of an alumina-forming austenitic steel

Two different thermo-mechanical treatments (TMT) were performed on an alumina-forming austenitic (AFA) stainless steel, DAFA 29, which was recently developed at Oak Ridge National Laboratory for application in advanced ultra supercritical power plants. The resulting fine-grained TMT materials showed yield stresses more than double the yield stress of the as-received material at room temperature and more than 50% higher at 600ºC, but lower yield stresses (but greater elongations) at 700ºC and above. Strain rate jump tests performed at both 600ºC and 700ºC showed that the TMT materials have greater strain rate sensitivity and lower activation volumes at both temperatures. The strain rate has a power law relationship with the flow stress with a stress exponent of ~5. The as-received AFA alloy showed serrated stress–strain curves at 600ºC suggesting the occurrence of dynamic strain aging.

Continuum nanomechanics for nanocrystalline and ultrafine grain materials

An extension of the classical continuum mechanics model is provided for the solution of boundary value problems at the nanoscale. The resulting continuum nano-mechanical model is based on the introduction of new terms to account for the interaction of bulk and surface points of the medium, which becomes significant as the specimen size is reduced down to the nanometer level. The model can be used to interpret deformation and diffusion phenomena in nanocrystalline (NC) and ultrafine grain (UFG) polycrystals, where a large number of internal surfaces (e.g. grain/twin boundaries) are present. When small material volumes are considered, random effects of the underlying microstructure become pronounced and their interpretation cannot be addressed with deterministic models alone. In this case, the continuum nanomechanics model may be enhanced with stochastic terms accounting for their competition with their deterministic gradient counterparts. The resulting combined gradient-stochastic model can be used to interpret intermittent plasticity and size-dependent serrated stress-strain curves in micro/nano pillars. These ideas have been applied to address certain benchmark problems and configurations of nanoelasticity, nanodiffusion and nanoplasticity. Non-singular expressions can be derived for stresses and strains in the neighborhood of dislocation lines and crack tips contained in a nanograin. Non-linear concentration depth profiles for diffusion in NCs are obtained in agreement with experiments. Corresponding results are obtained herein for coupled elasto-diffusion processes and related size-dependent phase transformation diagrams. When differential equations are not available, deformation features may be revealed through a statistical analysis of the relevant experimental data. This is done here for the interpretation of statistical features of deformed UFG alloys exhibiting serrated stress-strain curves and fractal shear bands.

The effect of a notch on the Portevin–Le Chatelier phenomena in an Al–3Mg model alloy

The aim of this research was to investigate the influence of a geometrical notch on the Portevin–Le Chatelier effect. This phenomenon manifests itself as the serrated stress–strain curve obtained for certain materials when they undergo plastic deformation during tensile tests. The Portevin–Le Chatelier effect can often be observed in aluminum alloys especially those with an addition of magnesium. The material examined in the present experiments was a model Al–3Mg alloy. Samples were prepared with notches cut in the specimens with different depths and shapes. The results clearly indicate that the notch has a significant influence on the Portevin–Le Chatelier effect. With increasing notch depth, the stress amplitude of the serrations increases together with their frequency and the course of the serrations changes.

Effect of dynamic strain aging on the microstructure and mechanical properties of a reactor pressure vessel steel

Analysis of the dynamic strain aging (DSA) effect was carried out for a reactor pressure vessel (RPV) steel, the A508-class3. The aging process includes the application of various plastic strain values of 1%, 2%, 4%, 6% and 8% with different strain rates at certain tempering temperatures. The microstructure of the specimens was analyzed in detail using optical microscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results indicate that serrated stress–strain curves occurred at the DSA process, and the new hardening phase of M23C6 type carbide is precipitated to pin the mobile dislocations. The hardening effect increases with the increase of the strain value within the uniform plastic strain region, even though the softening effect caused by dynamic recovery is obvious. After analyzing the correlations between aging parameters, hardening, ductile-brittle transition temperature and irradiation effect, it is found that the degeneration of mechanical properties caused by DSA is similar to the irradiation effect.

Transformation-induced plasticity as the origin of serrated flow in an NiTi shape memory alloy

Transformation-induced plasticity was observed in an NiTi shape memory alloy. It was found that the austenite phase of a solutionized 50.5at.%Ni–Ti alloy shows a serrated stress–strain curve in a narrow range of 311–328K, just below the temperature at which the deformation mechanism of the austenite phase changes from that of stress-induced martensitic transformation in the low temperature ranges to slip at high temperatures (329K). Microstructure observation and thermal analysis have concluded the simultaneous occurrence of the two deformation mechanisms in the serrated flow. The interaction between the martensitic transformation and slip was investigated.

Plane strain compression of aluminium alloy sheets

The theory of plane strain compression is applied to rolled aluminium alloy sheet. Two contrasting grades of the alloy are tested: naturally aged AC 120 and half-hard HE 30. While AC 120 displays a smooth stress–strain curve under homogenous straining, HE30 shows a serrated stress–strain curve due to its banded plastic strain behaviour. It is shown that, provided the r-values can be established reliably to characterise each sheet’s orthotropy, a flow curve to large strain (≃2) is provided by the plane strain test. Certain modifications to the original test procedure are made to achieve this. Equivalence in flow curves, as required of orthotropic plasticity theory, is examined from plane strain, bulge forming and tension tests conducted at various orientations to the roll. Despite the contrasting limiting strains between the three tests (tension≃0.1, bulge forming≃0.8) an acceptable correlation has been found between their equivalent flow curves across three decades of strain. The dependence of equivalent plastic strain upon equivalent stress for each material conforms to the Hollomon law. The Ramberg–Osgood law allows for the addition of elastic strain.

Dynamic Strain Aging in Biomedical Co–Cr–Mo-Based Alloys with Nitrogen Doping

The Plastic Deformation Behavior of a Biomedical Co–29Cr–6Mo–0.2N (wt.%) Alloy with a Fully γ (fcc) Matrix Was Studied by Compression Tests from Room Temperature to 1073 K. Serrated Stress–Strain Curves Caused by Dynamic Strain Aging (DSA) Was Clearly Observed at Temperatures of 773–973 K at a Strain Rate of 10−4s−1. Such a Flow Behavior Was Not Observed Significantly in other Conditions. Electron Backscatter Diffraction (EBSD) Analysis Revealed that Deformation Microstructures with DSA Occurrence Exhibited a Large Lattice Distortion over the Grains, while Local Strain Preferentially Increased in the Vicinity of Grain Boundaries in the Specimen Deformed at Room Temperature. Dislocations Were Dissociated into Stacking Faults (SFs) Bounded by Shockley Partial Dislocations both before and after Deformation; the DSA Observed in this Alloy Would Originate from the Interactions between Nitrogen Atoms and the Partial Dislocations/SFs.

Correlated heterogeneous deformation of entangled fiber networks

We study the deformation of a network of entangled non-cross-linked semiflexible fibers subjected to compression. We show that the deformation is intermittent, heterogeneous, and dominated by the occurrence of avalanches. Avalanches imply relative fiber sliding and rearrangement and lead to a serrated stress-strain curve. A large fraction of the fibers in the system contribute to an avalanche, and the amplitudes of the sliding events are correlated spatially. This phenomenon is qualitatively similar in systems with and without friction between fibers and is not due to frictional stick slip.

Mechanical Properties of Bulk Metallic Glasses

AbstractIn the absence of dislocation-mediated crystallographic slip, room-temperature deformation in metallic glasses occurs in thin shear bands initially only ∼10 nm thick. A sharp drop in viscosity (shear softening) occurs in deformed glassy matter and facilitates additional flow in existing shear bands. This further localization of plastic flow leads to shearing-off failure without any significant macroscopic plasticity.However, whereas most bulk metallic glasses fail in this manner, some undergo surprisingly extensive plastic deformation (in some cases, up to 50% or more) in compression or bending. When this occurs, the flow is “jerky,” as indicated by serrated stress–strain curves. Each serration may correspond to the emission of a shear band that then ceases to operate, at least temporarily, despite the predicted shear softening. As elastic energy is converted to heat during shear, temperatures rise sharply at or near shear bands. This heating may lead to the growth of nanocrystals that then block propagation of shear bands and cracks. The understanding of the dependence of mechanical response of metallic glasses on intrinsic (elastic constants, chemistry) and extrinsic factors (shapes, flaws) is the subject of intense current interest.

Localized Deformation due to Portevin–LeChatelier Effect in 18Mn–0.6C TWIP Austenitic Steel

The thermo-mechanical properties of low stacking fault energy austenitic Fe18Mn0.6C steel exhibiting twinning-induced plasticity were investigated during uniaxial tensile deformation using infrared thermography. Over a wide strain range, the plastic deformation was by the movement of very few well-defined localized deformation bands. The formation and propagation of Portevin–LeChatelier (PLC) bands lead to type A and type B serrated stress–strain curves, exhibiting a negative strain rate sensitivity. The PLC band properties were analyzed in detail: strain, strain rate and mobile dislocation density within the bands were determined. The microstructures of the un-deformed and deformed Fe18Mn0.6C TWIP steel were studied by transmission electron microscopy. The possible dynamic strain aging processes causing the localized deformation are reviewed.

Dynamic strain aging and related instabilities: experimental, theoretical and numerical aspects

Abstract Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.

The effect of nitrogen on the cold forging properties of 1020 steel

We have studied the effect of nitrogen on the cold forging properties of a low carbon steel as a function of temperature. Five AISI 1020 steels with nitrogen contents from 12 to 180 ppm were examined by tensile testing from 25 to 371 °C. Yield strength, tensile elongation (ductility), ultimate tensile strength (UTS), strain hardening exponents and strength coefficients were determined. The influence of nitrogen on the mechanical property behavior of this low carbon steel exhibits trends as expected—when nitrogen content increases, the strength of the steel increases and the ductility decreases. Likewise, as the temperature increases, the strength of the steel generally decreases; however, the ductility initially decreases, then exhibits an increasing trend. Additionally, there is an intermediate temperature range for these alloys where anomalous behavior is observed. Serrated stress–strain curves seen in this temperature range are indicative of dynamic strain aging. It is probable that this anomalous mechanical property trend is due to dynamic strain aging.

Flow and fracture characteristics of aluminium alloy AA5083–H116 as function of strain rate, temperature and triaxiality

This paper presents a part of an on-going study of light-weight shelters made of aluminium alloy AA5083–H116. A necessary prerequisite for numerical simulations of impact behaviour of such shelters is a calibrated numerical model. Slightly modified versions of the two Johnson–Cook models describing flow stress and fracture strain are applied. In addition to ordinary quasistatic tests with smooth specimens, these models demand tests at elevated temperatures and strain rates, and different triaxiality ratios. All tests to be presented in this paper are uniaxial tension tests performed in servohydraulic test machines or a Split–Hopkinson bar. The test programme involves approximately 100 specimens, and includes coupons from three different directions of the plate material, thereby taking account for the anisotropy. The AA5083 alloy is susceptible to dynamic strain ageing, and this phenomenon is shown to result in serrated stress–strain curves and negative strain rate sensitivity for a rather wide range of strain rates. In particular, the specimen geometry seems to have a strong influence on the serrated curves. The calibration shows that the Johnson–Cook–type models represent most of the observed material behaviour reasonably well, although the negative strain rate sensitivity is not adequately described.

Plastic deformation of yttria stabilized cubic zirconia single crystals

In a limited temperature range, cubic zirconia stabilized with more than 10 mol% yttria exhibits plastic instabilities, i.e. a serrated stress–strain curve as demonstrated in the upper plot [1]. The transmission electron microscopy image below, taken in a high-voltage electron microscope, shows that this effect is due to the collective motion of many dislocations in narrow slip bands [2]. Martin Bartsch works in a research group at the Max Planck Institute of Microstructure Physics in Halle (Saale), studying dislocation processes during plastic deformation.

Modeling of residual stress-induced stress–strain behavior of unidirectional brittle fiber/brittle matrix composite with weak interface

To describe the residual stress-induced interfacial debonding and stress–strain behavior of unidirectional brittle fiber/brittle matrix composite with weak interface, a simulation method, based on the modified shear lag analysis which can take residual stresses into account and Monte Carlo procedure, was presented, and was applied to a model composite similar to polymer-derived SiC/ceramic glass system. Main results are summarized as follows. (1) It was shown concretely that the broken component-induced debonding is encouraged and discouraged when the corresponding component has tensile and compressive residual stresses, respectively. (2) The feature of the damage- (breakage of fiber, breakage of matrix and interfacial debonding)-accumulation process and its influence on the stress–strain curve could be realized in the computer; the damages are accumulated intermittently, resulting in a serrated stress–strain curve of composites. In such a damage accumulation process, the existence of residual stresses change the order and location of occurrence of damages and therefore the stress–strain curve and strength of the composite. (3) The dependence of the composite strength on the matrix strength in the presence of residual stresses was clarified; the composite strength increases significantly with increasing matrix strength when the fiber and matrix have compressive and tensile residual stresses along the fiber axis, respectively, but only marginally when they have reversed residual stresses.

A modeling study on residual stress-induced interfacial debonding and stress–strain behavior of weakly bonded UD composites

Abstract Residual stress-induced interfacial debonding and its influence on stress–strain behavior of unidirectional fiber-reinforced brittle matrix composites with weak interface were studied using mini-composite model by means of the two-dimensional shear lag analysis combined with a Monte Carlo method. Damages (fracture of fiber, matrix and interface) were accumulated intermittently, resulting in serrated stress–strain curve. In this process, the residual stresses changed the strain, order and location of occurrence of damages, and consequently the shape of stress–strain curve and strength of composite. Under the existence of compressive and tensile axial residual stresses in fiber and matrix, respectively, the fracture of the matrix and the debonding from the fracture-ends of matrix were enhanced, while the fracture of fiber and the debonding from the fracture-ends of fiber were suppressed. The residual stress-induced premature fracture of the matrix, followed by debonding, reduced the strength of composite.

Slip systems in a body-centred-cubic Li—Mg alloy

Abstract Single crystals of a Li–65 at.% Mg alloy were deformed in compression at 4±2, 10, 20 and 77 K, and room temperature. Serrated stress—strain curves were observed for deformation at room temperature and at very low temperatures. Slip systems were determined by optical microscopy. The results are expressed in terms of ψ(χ) curves. Unlike the refractory metals, slip on {211} planes is favoured especially at low temperatures and there is a strong asymmetry in the twinning-antitwinning sense. This behaviour cannot be explained easily by the large elastic anisotropy in these alloys but is most probably connected with the detailed structure of the screw dislocation core.