Sharp Yield Point Research Articles

Grain Boundary Walls Cause the Upper Yield Point in Steel

Abstract Atomic force microscopy studies show that sharp yield points in steels are explained by the existence of hard grain boundary walls, contrary to current accepted theories.

Cell monolayer deformation microscopy reveals mechanical fragility of cell monolayers following EMT

Tissue and cell mechanics are crucial factors in maintaining homeostasis and in development, with aberrant mechanics contributing to many diseases. During the epithelial-to-mesenchymal transition (EMT), a highly conserved cellular program in organismal development and cancer metastasis, cells gain the ability to detach from their original location and autonomously migrate. While a great deal of biochemical and biophysical changes at the single-cell level have been revealed, how the physical properties of multicellular assemblies change during EMT, and how this may affect disease progression, is unknown. Here we introduce cell monolayer deformation microscopy (CMDM), a new methodology to measure the planar mechanical properties of cell monolayers by locally applying strain and measuring their resistance to deformation. We employ this new method to characterize epithelial multicellular mechanics at early and late stages of EMT, finding the epithelial monolayers to be relatively compliant, ductile, and mechanically homogeneous. By comparison, the transformed mesenchymal monolayers, while much stiffer, were also more brittle, mechanically heterogeneous, displayed more viscoelastic creep, and showed sharp yield points at significantly lower strains. Here, CMDM measurements identify specific biophysical functional states of EMT and offer insight into how cell aggregates fragment under mechanical stress. This mechanical fingerprinting of multicellular assemblies using new quantitative metrics may also offer new diagnostic applications in healthcare to characterize multicellular mechanical changes in disease.

ABOUT THE YIELD PLATEAU UNDER SIGN-VARIABLE LOADING

During tension of samples of low-carbon steels and some other plastic materials, the sharp yield point and the yield plateau are fixed on the deformation diagram. In this case, Chernov-Luders bands appear on the surface of the sample in the local section, which then propagate along the tension axis. The physical nature of the sharp yield point is established: the drop in the load after reaching the (upper) yield limit occurs as a result of dislocations being an extraction out of the cloud of the embedded atoms and vacancies (Cottrell's cloud). At the occurrence of the sharp yield point , the plastic strain is limited to a small area. When the sample deformation increases, the plasticity zone (the yield plateau is marked on the diagram at this time) expands, and the stress-strain state in this zone becomes almost homogeneous, if we do not consider its boundary with the elastic region. At the end of the yield plateau, the entire sample experiences a uniform plastic deformation, excluding its ends (galtels). From this point on, the strain diagram shows the of material hardening; presumably, this hardening occurred from the very beginning, but was hidden under the yield plateau. This is evidenced by the resulting strain-induced anisotropy. After unloading the sample, when the plastic strain front (in the form of Chernov-Luders bands) has not yet passed through the entire sample, and the Bauschinger's effect is observed with the subsequent change in the stress sign. The fact that after the occurrence of the sharp yield point , the plastic strain is not localized in a certain volume, similar to what occurs during the neck formation, but spreads along the sample, serves as proof of the material hardening due to plastic deformation immediately after the load falls. Therefore, if the plastically deformable part of the sample did not have a hardening of the material due to the plastic strain growth, it would not be able to spread to the elastic part of the sample. This paper presents the experimental data of the sign-variable torsion of the thin-walled tubular samples of steel 45 in the annealed state. The deformation atdiagram of the occurrence and development of the yield plateau in distinct sections along the length of the test sample is obtained. The material hardening diagram hidden under the yield plateau is reconstructed using the well-known Masing's principle.

Rate-independent elasto-plastic materials—a brief history and some new developments

The aim of this paper is to briefly discuss the history of the development of modern small deformation elasto-plasticity and its gradual evolution from a model for metal working to dealing with a variety of different responses ranging from fatigue to metal forming. In the process, we will also distinguish what we consider as the “essential” features of plasticity from “useful but perhaps inessential features”. We also summarize an approach to plasticity that incorporates only the essential features of plasticity (namely rate independence and hysteresis). The model exhibits a “diffuse yielding behavior” where there is a gradual transition from elastic to inelastic response which is more in keeping with many inelastic materials. The model shows considerable promise in modeling microplasticity and fatigue behavior. The approach is very computationally “friendly,” and it is possible to use a simple forward Euler with small time steps to integrate. We also describe a numerical implementation using a predictor–corrector approach that is very efficient in simulating the response. Classical plasticity with a sharp yield point is recoverable as a special case.

The Model of Dynamic Stress Relaxation of Elastoplastic Materials

The paper proposes the model of relaxation of the loaded elastoplastic material, with the dislocation kinetics of plastic shear. The proposed model includes two independent strain rates, namely the total strain rate describing the external load rate and the rate of the localized plastic response describing the medium ability to generate deformation defects. This model describes both the localized relaxation processes in the elastoplastic medium and the average stress relaxation in the loaded elastoplastic medium. The proposed model is in essence microscopic. All its parameters are obtained in the independent experiments concerning the evolution of the dislocation continuum during the material loading. The model describes well the observed dynamic effects of the material macroscopic response depending on the strain rate, i.e., the upper and lower yield points (sharp yield point and yield plateau), successive strain hardening, and cyclic and sign-variable loads, and the Bauschinger effect.

Effect of Plate Slenderness on Long-Span Duplex Stainless Steel Plate Girder

The behaviour of stainless-steel material is different from that of carbon steel due to the absence of sharp yield point. In long-span stainless steel plate girder, the part of bending moment carried by the web panel causes a reduction in the shear capacity, thereby producing the M-V interaction. Plate girders are made by connecting the flange plate and the web plate. The main objective of this study is to numerically evaluate the effect of web plate slenderness and flange plate slenderness of stainless plate girder under combined bending and shear using commercial finite element software ABAQUS. The existing experimental study related to the M-V interaction of stainless-steel plate girder was used to validate the numerical model. The variation of shear force for different flange thickness to web thickness ratios were also checked to identify the best relation. This numerical study reports a critical flange thickness to web thickness ratio. Both flange plate slenderness and web plate slenderness affect the shear carrying capacity of stainless-steel plate girder under combined bending and shear.

A Study of the Structure and Strain Resistance of Low-Alloy 09Mn2Si Steel After Its Helical Rolling Under Static and Dynamic Loading

The structure and mechanical properties of a 09Mn2Si ductile ferritic-pearlitic steel is studied after helical rolling (HR). It is shown that a fine-grained structure is formed in the surface layer about 1 mm deep after every pass of HR accompanied by a gradual temperature decrease in the range 850–500°С, which indicates the development of severe plastic deformation, while in the underlying layers a pronounced textured lamellar structure is formed, consisting of thin elongated ferritic grains oriented along the axis of the rod (in the HR direction). The maximum strengthening of steel is observed in the layer up to 3 mm thick, the minimum – in the near axial (core) zone. Under static tensile testing it is found out that HR results in an increase in the yield strength and a decrease in the elongation at break. The loading diagrams of HR-steel samples contain a sharp yield point and an approximately twice longer yield plateau compared to the initial steel. The experiments on impact loading demonstrate that HR results in larger, by 10–25% on average, KCV values of steel, while at negative temperatures the difference may be as large as 60%.

Effect of hydrogen on the flow behavior of a TiAl based alloy during plane strain compression at elevated temperature

Effect of hydrogen on the flow behavior of a TiAl based alloy during plane strain compression at temperatures of 1150 and 1200 °C was investigated in this paper. The results showed that hydrogen obviously softened the alloy and had significant effects on the texture evolution. Hydrogen decreased the number of sharp yield points and hindered the occurrence of Portevin-Le Chatelier effect, which decreased plastic instability of the alloy during plane strain compression. Hydrogen enhanced textures related to γ-phase recrystallization and twinning, as well as α2-phase pyramidal texture component. Additionally, weak α2-phase transverse texture component {11–20}<0001> was present in the hydrogenated samples, and the occurrence of such texture was mainly attributed to hydrogen-increased B2 phase.

Effects of cooling rate and strain rate on phase transformation, microstructure and mechanical behaviour of thermomechanically processed pearlitic steel

In the present investigation, thermomechanical controlled processing of a high carbon steel and a Nb microalloyed high carbon steel have been conducted in a Gleeble 3800 simulator. Different microscopic techniques have been utilised for the characterisation of the microstructure and hardness data has been used for the evaluation of mechanical properties. In order to suppress the transformation enthalpy, experiments are performed under varying cooling rate and strain rate. The effect of niobium microalloying leads to the lowering of recalescence and suppresses austenite to pearlite transformation start and finish temperatures at every cooling rate which leads to the refinement of interlamellar spacing and thereby improve hardness and predicted yield strength values. It is evident that a higher strain rate accelerates the kinetics of pearlite transformation and elevates the pearlite start temperature. The increase of strain rate in the range of 1s–1 to 100s–1 followed by a constant cooling rate (free cooling) leads to the refinement of interlamellar spacing as well as improves mechanical properties. The true stress-true strain diagram at a lower strain rate indicates higher strain hardening with sharp yield point, whereas the same at a higher strain rate indicates the sudden occurrence of strain softening. The variation in recalescence due to the alternation of the cooling rate and strain rate has been correlated with the final microstructure and mechanical properties.

Kinetics and morphology of Lüders deformation in specimens with homogeneous structure and with a weld joint

The presented work focus on the investigation of the elastic-plastic transition in materials with a sharp yield point occurring through the formation and propagation of Lüders band. It has been found that the band nucleation and propagation rates in specimens with homogeneous structure are considerably different. The velocities of Lüders band fronts are correlated so that the total velocity of all moving fronts at any point of deformation is a constant value. As the rate of deformation increases, the Lüders band front velocity increases nonlinearly. If the material contains zones with high structural and phase inhomogeneity, Lüders bands nucleate along the boundaries of these zones. The kinetics and morphology of the Lüders band fronts within these zones are considerably different from those observed in other areas of specimen. It has also been found that the Lüders band front stops upon reaching the boundaries of the zones with structural and phase inhomogeneity. In this case, the front acts as a source of both individual and multiple bands.

Simulation of inextensible elasto-plastic beams based on an implicit rate type model

The aim of this paper is to show that it is possible to model the elasto-plastic behavior of an inextensible beam undergoing finite bending by using a novel implicit rate type response relation directly between the bending moment, curvature, and their rates. This is in contrast to conventional approaches that require the integration of elasto-plastic stress–strain relations across the thickness of the beam at each time step. The model proposed here (a) is rate independent and exhibits hysteresis, (b) requires no notion of plastic strain and no integration across the thickness, and (c) does not have a sharp yield point and instead transits smoothly between nominally elastic and inelastic response. The governing equations are solved numerically as a set of first order differential equations with very low order interpolation functions for quasi-static response and are capable of modeling both hardening and softening behavior as well as the formation of plastic hinges, etc. Since there is no yield function, there is no necessity to use a return mapping algorithm that was developed specifically for use in elasto-plasticity with sharp yield functions. This simplifies the numerical algorithm also. The simulations for an elastic perfectly plastic beam are compared with elasto-plastic models in ABAQUSTM, and they show good agreement at a fraction of the computational time. Moreover we have compared simulations of large deformations of an aluminum alloy bar subject to three point bending experiments. The simulations also match the experimental results very well. We demonstrate that it is possible to incorporate frictionless sliding contact (which is needed for the three point bending comparison) in a relatively straightforward manner without the complexity that arises when it is handled in a full three-dimensional (3D) model.

A study of the sharp yield point of a Ti-22Al-25Nb alloy

Ti-22Al-25Nb alloy containing 0.2 wt. % hydrogen exhibits a sharp yield point on the stress-strain curve when it is tested above 960 °C. The main reason for this phenomenon can be attributed to the unidirectional crystal orientation and low level of lattice distortion above 960 °C, so that the dislocations tend to move in parallel directions with greater mobility and the stress can be rapidly released. Furthermore, strips of brittle α2 phase can cause stress concentration at the grain boundaries before plastic deformation occurs. Fracturing occurs at the strips of α2 phase when micro-deformation occurs, so that the accumulated stresses are rapidly released.

Features of Brittle Material Powder Compaction During Pressing

The compaction of (i) titanium, vanadium, and molybdenum carbide powders, (ii) mixtures of these powders with the addition of nickel, chromium, and niobium carbide powders, and (iii) coarse titanium and tungsten carbides as well as diamond powders clad with cobalt under compressive loading with a constant rate on the powder in a die at room temperature is studied. Based on the variation of the relative density of the compacts with current pressure, the variation of stresses in the matrix (forming a porous body) with its strain is determined. This enables to reveal the features of compaction, strain hardening, and fracture of brittle powder particles during pressing. It is established that for the molybdenum carbide powder, consisting of powder particles with pronounced irregular shape, the initial elastic deformation of the matrix abruptly transits into the stage of plastic deformation with almost linear strain hardening. At the final stage of the powder compaction, the particles are fractured. At the initial stage of pressing, an increase in the packing density of the powder particles and in their strain hardening occurs for titanium and vanadium carbide powders, whose particle shape is close to the rounded. With the increase in the density of the porous body, it is observed an almost linear strain hardening of the matrix, which changes into decay with decreasing shear stress, when the powder body approaches its non-porous state. As a result of pressing, the size of the coherent X-ray scattering areas decreased to 62 nm and the dislocation density in the titanium carbide particles grew to 8.3 · 1010 cm–2. With an increasing content of plastic metallic particles in the matrix with the particles of brittle materials, it is the metallic particles that predominantly undergo the plastic strain with strain hardening. This causes a sharp increase in the total strain hardening, reducing the density of the porous body during pressing. It is established an effective compacting of coarse titanium and tungsten carbide powders with cobalt-clad particles 200–600 μm in size. In this case the variation of the stress in the matrix with the strain of the matrix has a sharp yield point associated with high elastic limit, significantly exceeding the yield stress, and the time delay in the transition from a purely elastic deformation of the body to its plastic flow.

Effect of isocyanate chain extender on the structure and properties of the blends of poly(butylene terephthalate) and thermoplastic polyester elastomer

The effect of diisocyanate chain extender (CE) additives on the change of molecular structural characteristics, rheological, and mechanical properties of the blends comprising of poly(butylene terephthalate) (PBT) and thermoplastic polyester elastomer (TPEE) obtained by reactive compounding in the melt and having different phase structure is studied. It is shown that addition of CE in the amount of 0.2 wt% to 1.25 wt% causes an increase in viscosity of polyester melts and solutions owing to the chain extension reactions and intermolecular cross-linking of macro-chains which occur in the melt. CE has a strong effect on the character of deformation curves at straining of both polyesters in primary form and their blends irrespective of the ratio of components in them (phase structure of materials). At the increase of its concentration, values of high and low flow limits increase and the difference in values of these parameters decreases, that is, a sharp yield point is gradually degenerating. At the same time, increase in Charpy impact strength on notched specimens is observed, including the subzero temperatures range (−40°C). Besides, CE has an effect on crystallizability of both individual polyester components and their blends. The general trend (irrespective of the polyester type and phase structure of the blend) is the decrease in crystallization temperature. This fact is explained by limitation of molecular mobility due to an increase in the molecular weight of polyester and intensification of interchain interactions.

Remarks on the Woodthorpe–Pearce “anomalous” behavior in sheet metals

The capability to accommodate the “Woodthorpe–Pearce ‘anomalous’ behavior” has often been used as a criterion to judge the flexibility of yield functions for sheet metals. For metals which exhibit neither sharp yield points nor perfectly plastic behavior, the meaning of this term becomes ambiguous in common usage; instead, we employ it to refer to what Woodthorpe and Pearce [3] observed and failed to predict in their study on aluminum sheets with average r-value <1, namely: in tension tests the balanced biaxial flow curve always lies above the average uniaxial flow curve in a common figure where the horizontal axis denotes the balanced biaxial true-strain and the uniaxial true-strain for the two curves, respectively. In this paper, using the generalized Hershey–Hosford yield function with isotropic strain hardening, we show that the balanced biaxial flow curves in Woodthorpe and Pearce׳s experiments can be predicted from their corresponding average uniaxial flow curves. Moreover, our analysis and other examples suggest that the aforementioned “anomaly” coined by Woodthorpe and Pearce should be quite common.

Relaxation mechanism of plastic deformation and its justification using the example of the sharp yield point phenomenon in whiskers

The generality of the dynamic approach to a wide range of problems of the continuum mechanics, including deformation at the rates determining quasi-static deformation conditions has been demonstrated using the example of deformation of cadmium and copper whiskers. The sharp yield point phenomenon has been analyzed in terms of the theory of dislocations and phenomenological integrated criteria of plasticity. It has been shown that the characteristic relaxation times used in these criteria, regardless of the applied model of plasticity, reflect essential properties of the very deformation process itself.

Plastic Deformation and Elastic Properties of Ti-Nb-Zr-Ta(-Fe-Si) Biomedical Alloys

Beta titanium alloys are promising biomedical material for their excellent biocompatibility and low elastic modulus. Moderate strength of those materials in beta-annealed condition can be increased by precipitation hardening of alpha phase, but this causes significant increase in elastic modulus. In this study, small additions of Fe and Si are used to increase strength of commercial Ti - 35Nb - 7Zr - 5Ta (TNZT) alloy. Alloys with iron content up to 2% and silicon content up to 1% were manufactured. Elastic properties were investigated by pulse-echo method and flow curves were determined from tensile tests. Modulus of elasticity is increases from initial 60 GPa to 80 GPa due to Fe and Si content. Strength and modulus of elasticity were then related to chemical composition. Yield stress is increased from 450 MPa to 700 MPa thanks to small Fe and Si additions. Fe causes solid solution strengthening exhibited by sharp yield point. (Ti,Zr)5Si3 intermetallic particles further increase strength via precipitation hardening. An alloy containing 0.5% Si and 2% Fe showed improved properties for biomedical use.

The advantage of mucus for adhesive locomotion in gastropods

For many gastropods, locomotion is driven by a succession of periodic muscular waves (contractions and relaxations) moving along the foot. The force generated by these waves is coupled to the substratum by a thin layer of pedal mucus. Gastropod pedal mucus has unusual physical properties: the mucus is a viscoelastic solid at small deformation and shows a sharp yield point; then, at greater strains, the mucus is a viscous liquid, although it will recover its solidity if allowed to heal for a certain period. In this paper, to clarify the role of the mucus and the flexible muscular waves in adhesive locomotion, we use a simple mathematical model to verify that directional migration can be realized through the interaction between the periodic muscular waves and the specific physical features of mucus. Our results indicate that the hysteresis property of mucus is essential in controlling kinetic friction for the realization of crawling locomotion. Furthermore, our numerical calculations show that both the hysteresis property of mucus and the contraction ratio of muscle give rise to two styles of locomotion, direct waves and retrograde waves, which until now have been explained by different mechanisms. The biomechanical effectiveness of mucus in adhesive locomotion is also discussed.

Effect of strain rate and dynamic strain ageing on work-hardening for aluminium alloy AA5182-O

Abstract The work-hardening of the solution-strengthened aluminium alloy AA5182-O is studied as a function of strain rate at room temperature. The main aim is to characterize the influence of strain rate and dynamic strain ageing on the work-hardening of the material. Tensile tests with constant nominal strain rates in the range from 10−6 to 1 s−1 were carried out; additionally, strain-rate jump tests were performed. The material exhibits a sharp yield point, a Lüders plateau, and serrated yielding within the actual range of strain rates. This indicates that the steady-state strain rate sensitivity is negative as a result of dynamic strain ageing. The serrations in the stress–strain curves and the work-hardening are markedly reduced with increasing strain rates. In most cases, the jump tests exhibit the standard behaviour, i.e., after a transient period following the jump in strain rate, the stress–strain curve converges to the steady-state stress–strain curve at the new strain rate.

Spatial and Temporal Characteristics of Propagating Deformation Bands in AA5182 Alloy at Room Temperature

The spatial and temporal characteristics of propagating deformation bands in the Al-Mg alloy AA5182 in O temper were studied experimentally at room temperature. Tensile tests were carried out on flat specimens at strain rates in the range from 10−5 to 10−1 s−1. Digital image correlation (DIC) and digital infrared thermography (DIT) were applied to monitor the propagating bands. It was found that the material exhibits a sharp yield point, and Luders bands were seen at all the strain rates. Jerky flow took place all along the Luders plateau. It thus seems that the Portevin–Le Chatelier (PLC) effect starts at incipient yielding and that there is no critical strain. At the end of the Luders plateau, PLC bands immediately started to propagate back and forth along the gage section of the specimen. The work hardening of the material decreased consistently with increasing strain rate, while the flow stress on the Luders plateau was rather unaffected by the strain rate. This indicates that the dynamic strain aging (DSA) mainly affects the strength of the interaction between mobile and forest dislocations. The strain to necking was found to decrease gradually with strain rate for this alloy, which is consistent with the lower work-hardening rate at the higher strain rates.