Local Flow Stress Research Articles

Effects of temperature and frequency on cyclic deformation behaviours of Cu single crystals

ABSTRACT Temperature and frequency are significant extrinsic factors that influence the cyclic deformation behaviour of face-centred cubic crystal (fcc) single crystals. For Cu single crystals, an increase in temperature causes the disappearance of the plateau region in the cyclic stress–strain (CSS) curves and a significant decrease in the saturation resolved shear stress at low strain amplitudes. This is attributed to the enlargement of the space between Persistent Slip Band (PSB) ladders, resulting in a lower volume fraction of the rungs in PSBs, leading to a lower saturation shear stress. Conversely, an increase in frequency does not affect the appearance of the plateau behaviour in CSS curves, but it slightly increases the corresponding plateau stress. This is because a higher frequency increases the probability of interaction between edge dislocations, leading to an increase in the local flow stress in the rungs, ultimately resulting in an increment of the saturation stress.

Time-resolved in-situ dislocation density evolution during martensitic transformation by high-energy-XRD experiments: A study of C content and cooling rate effects

Recent studies on the mechanical behavior of martensitic steels show the importance of considering lath martensite as a “polycrystalline aggregate” with a large distribution of the local yield strength. The latter depends on local microstructural features, such as lath sizes, carbon distribution (in solid solution, segregated to defects, in carbides) and density of defects Internal stresses have to be considered as an additional contribution to the yield strength participating to enlarge the distribution of the local flow stresses at the microstructure scale.This study focuses on one of these microstructural features, the dislocation density. Its evolution is followed in situ upon martensitic transformation by High Energy X-Ray Diffraction experiments on a synchrotron beamline. A previously introduced method, based on modified Williamson-Hall (mWH) analysis, is improved in order to take account of the martensite lattice tetragonality when applying the mWH method.The influence of the steel carbon content (0.11, 0.21 and 0.31 wt.% C steels) and of the cooling rate (-10, -50, -100 °C/s and water-quench) on the dislocation density evolution in martensite during the martensitic transformation is established. The effect of the cooling rate on the dislocation density is low between -10 and -100 °C/s, but becomes visible after the water-quench. The higher the C content, the higher the dislocation densities at the end of the transformation. The steels with higher C content also show a wider distribution of the local dislocation density and, therefore, of the local yield strength.

A High-Pressure Shear Testing Approach to Measure Flow Stresses Near a Friction Stir Welding Tool

Abstract A new approach for measuring flow stresses near a spinning friction stir welding (FSW) tool is evaluated on AA 6061-T6 plate. The test consists of plunging a cylindrical tool with a flat face into the plate at different rotational speeds, using a variety of constant vertical loads. A viscosity-based model of the shear layer created under the tool is employed to estimate local flow stresses. The flow stresses measured by this approach exhibited an inverse relationship with temperature and a positive dependence on the pressure imposed by the spinning flat-faced tool. Compared to hot compression and hot torsion results, estimated flow stress levels in high-pressure shear were lower by 20–68 %, for similar temperatures and strain rates, owing to grain refinement induced by continuous dynamic recrystallization. This high-pressure shear approach could be used to characterize material behavior near a rapidly spinning FSW tool, leading to improved process model predictions.

A multi-objective optimization of stent geometries

Stents are scaffolding cardiovascular implants used to restore blood flow in narrowed arteries. However, the presence of the stent alters local blood flow and shear stresses on the surrounding arterial wall, which can cause adverse tissue responses and increase the risk of adverse outcomes. There is a need for optimization of stent designs for hemodynamic performance. We used multi-objective optimization to identify ideal combinations of design variables by assessing potential trade-offs based on common hemodynamic indices associated with clinical risk and mechanical performance of the stents. We studied seven design variables including strut cross-section, strut dimension, strut angle, cell alignment, cell height, connector type and connector arrangement. Optimization objectives were the percentage of vessel area exposed to adversely low time averaged WSS (TAWSS) and adversely high Wall Shear Stress (WSS) assessed using computational fluid dynamics modeling, as well as radial stiffness of the stent using FEA simulation. Two multi-objective optimization algorithms were used and compared to iteratively predict ideal designs. Out of 50 designs, three best designs with respect to each of the three objectives, and two designs in regard to overall performance were identified.

Critical role of Lüders banding in hydrogen embrittlement susceptibility of medium Mn steels

The effect of Lüders banding on hydrogen embrittlement (HE) susceptibility of medium Mn steels was investigated by tuning the degree of yield point elongation (YPE). It was found that the steel with a larger YPE was more susceptible to HE. A larger YPE led to a higher local flow stress and a higher fraction of strain-induced martensite, which in turns resulted in more H-induced cracks in the Lüders banding area and the consequent catastrophic failure. It thus suggests that Lüders banding and the associated localized deformation play a key role in influencing the overall HE susceptibility of medium Mn steels.

Characterisation of dislocation patterning behaviour with a continuum dislocation dynamics model on two parallel slip planes equipped with a deep neural network resolving local microstructures

The self-organisation behaviour of dislocation upon loading is still a mechanistically mysterious phenomenon. The present article aims to present a computationally tractable dislocation dynamics model, which can be used for helping analyse the mechanism behind dislocation pattern formation. With an integrated use of asymptotic analysis and machine learning tools, the discrete dislocation dynamics on two parallel slip planes is self-consistently reformulated at a coarse-grained level. For the present case, asymptotic analysis helps in 1) reformulating the original globally discrete problem by a continuum model underpinned by a database resolving the almost singular short-range elastic interaction of discrete dislocations; 2) identifying the proper input and output quantities for implementing machine learning tools; 3) digging out a hidden but explicit interrelation between mean-field quantities to reduce the dimensionality of the data space. Machine learning tools serve for 1) inferring the inherently implicit interrelationships between continuum quantities; 2) capturing a low-dimensional manifold in the data space corresponding to the local flow stress. The non-monotonically increasing profile of the flow stress - density relationship, as revealed by machine learning, is found to play a key role in the onset of dislocation patterning behaviour seen in the simulation results. A scaling law relating the applied stress to pattern wavelength is also derived, providing a rationale to the widely used empirical similitude relation. The experimentally observed swing in similitude coefficient value is attributed to the randomness in slip plane distributions. In a methodological viewpoint, the treatment of using asymptotic analysis to help design the curriculum for implementing machine learning tools, offers a paradigm for self-consistently upscaling more complicated multiscale systems.

Cutting temperature prediction in negative-rake-angle machining with chamfered insert based on a modified slip-line field model

Chamfered inserts have shown superior edge resistance and prolonged tool life in practical machining process. However, such kind of inserts find limited application in metal cutting due to the inadequate understanding of their sophisticated influences on cutting performance. Researches on material flow mechanism and heat generation issues in the vicinity of the chamfer may contribute to the comprehensive cognition of high-performance cutting with chamfered inserts. In this paper, a novel slip-line field model has been developed for negative-rake-angle machining with chamfered insert. The slip-line field geometry concerning dead metal zone (DMZ) formation is demonstrated utilizing the slip-line approach. Moreover, an iterative methodology is developed to determine local shear flow stresses, interface frictional factors and heat sources intensity. Then, analytical modeling of temperature fields in tool and workpiece is carried out by employing classical orthogonal cutting theory and semi-boundary heat transfer principles. Finally, two main approaches including two-dimensional (2-D) finite-element (FE) simulations and orthogonal cutting trials of AISI 304 stainless steel are adopted for verification. Simulated slip-line field geometry with respect to DMZ and involved angles are extracted to compare against the predictions from the proposed slip-line solution. The simulated and measured temperature fields are compared with the predicted results from the developed thermal model. In addition, a contrastive model from previous literature is also compared with the proposed model. Encouraging agreements have been detected between those comparisons, which indicate the reasonableness and reliability of the given analytical model. The result reveals that the presented model gives much better prediction of temperature distribution upon chamfer insert over the contrastive model, especially at the DMZ-tool interface.

Stiffness based technique to probe cyclic damage accumulation in micro-structurally graded bond coats via micro-beam bending tests

ABSTRACTThis paper highlights a novel technique to delineate the fatigue response of different regions within thin microstructurally graded platinum nickel aluminide bond coats. Notched clamped beam structures fabricated from distinct microstructural zones of these coatings are subjected to programmed cyclic bending using the nano-indentation system. A methodical approach is established herein to quantify the cyclic damage preceding crack pop-in by using the cyclic stiffness of the beam as an indicator to mark failure. Preliminary results from these tests show that there is a characteristic change in the stiffness of the beam before a crack pop-in event occurs and different regions within the coating show different stiffening characteristics. Factors affecting the measured stiffness such as offsets in the loading position and blunting of the notch tip have been estimated using the finite element method. A graded flow stress model has been proposed and implemented in FEM to quantify the local flow stress changes accompanying the measured rise in stiffness. Electron transparent foils lifted off from the notched region of the beam post-testing suggests that the cyclic stiffening of the beams occurs due to dislocation hardening in the plastically deformed region close to the notch tip. Toughening mechanisms active in the crack wake have thus been investigated and correlated to the measured cyclic stiffness.

On the work hardening of titanium: new insights from nanoindentation

Nanoindentation was used to probe the local slip resistance in CP-Ti deformed in compression to different extents. Changes in hardness in the deformed grains and twins were compared with the change in flow stress measured during deformation, with the aim to elucidate the relative contribution of slip and twinning to the work hardening of Ti alloys. The hardness values were calibrated with measurements on binary Ti–Al alloys. The hardness increased only slightly with deformation and cannot explain the observed work hardening. Although twinned regions were found to be harder than the parent grains, this increase was found to be small once the effect of crystal orientation was accounted for. The increase in hardness in the twins was slightly higher for compressive twins than for tensile twins. It is proposed that this modest hardness increase in the twins is more consistent with the presence of twinning stresses than with a change in the local flow stress caused by dislocation interactions. The implications of these findings to the work hardening of CP titanium are discussed.

Hot Deformation Behavior of a 2024 Aluminum Alloy Sheet and its Modeling by Fields-Backofen Model Considering Strain Rate Evolution

The deformation behavior of a 2024 aluminum alloy sheet at elevated temperatures was studied by uniaxial hot tensile tests over the nominal initial strain rate range of 0.001–0.1 s−1 and temperature range of 375–450 °C. In order to analyze the deformation behavior with higher accuracy, a digital image correlation (DIC) system was applied to determine the strain distribution during hot tensile tests. Local stress-strain curves for different local points on the specimens were calculated. The strain rate evolution of each point during the tensile tests was investigated under different deformation conditions. Then, an improved Fields–Backofen (FB) model, taking into account the local strain rate evolution instead of the fixed strain rate, was proposed to describe the constitutive behaviors. It has been found that obvious non-uniform strain distribution occurred when the true strain was larger than 0.3 during hot tensile tests. The strain rate distribution during deformation was also non-uniform. It showed increasing, steady, and decreasing variation tendencies for different points with the increasing of strain, which led to the local flow stress being different at different local points. The flow stresses predicted by the improved FB model showed good agreement with experimental results when the strain rate evolutions of local points during tensile tests were considered. The prediction accuracy was higher than that of traditional FB models.

Evaluation of local strength via microstructural quantification in a pearlitic rail steel deformed by simultaneous compression and torsion

Pearlitic steels are commonly used for railway rails because they combine good strength and wear properties. During service, the passage of trains results in large accumulation of shear strains in the surface layer of the rail, sometimes leading to crack initiation. Knowledge of the material properties versus the shear strain in this layer is therefore important for fatigue life predictions. In this study, fully pearlitic R260 rail steel was deformed using a bi-axial torsion-compression machine to reach different shear strains. Microstructural parameters including interlamellar spacing, thickness of ferrite and cementite lamellae and dislocation density in the ferrite lamellae, as well as hardness were quantitatively characterized at different shear strain levels. Based on the microstructural observations and the quantification of the microstructural parameters, the local flow stresses were estimated based on boundary strengthening and dislocation strengthening models. A good agreement was found between the estimated flow stresses and the flow stresses determined from microhardness measurements.

Evaluation of wear-induced plastic deformation at the trimmed edge of DP980 steel sheets

In order to increase the use of advanced high strength steel (AHSS) for automotive light-weighting, the significant trimming-induced wear damage that AHSS sheets cause to the trim dies should be reduced so as to decrease die maintenance costs and deterioration of the quality of sheared edge. In this research, the wear characteristics in the upper AISI D2 die inserts used for trimming DP980-type AHSS sheets and the wear-induced plastic deformation at the sheared edges of DP980 were studied. Observation of wear profiles at the edge of the upper trim die revealed that material abrasion was the main damage feature. The trimmed edge quality of DP980 deteriorated with the number of strokes, as indicated by an increase in burr width. Plastic strains near the surface of the sheared edge estimated using the displacements of martensite plates, increased from 2.9 at 2.5 μm below the trimmed edge after 40,000th cycles, to 55 after 80,000th cycles. Micro-hardness tests performed to estimate the local flow stresses in the shear affected zone (SAZ) indicated that the flow stress at a distance of 4.5 μm below the trimmed edge increased with the number of trimming cycles to 1.73 GPa in the 80,000th trimmed part.

Local microstructure and flow stress in deformed metals

The microstructure and flow stress of metals are related through many well-known strength-structure relationships based on structural parameters, where grain size and dislocation density are examples. In heterogeneous structures, the local stress and strain are important as they will affect the bulk properties. A microstructural method is presented which allows the local stress in a deformed metal to be estimated based on microstructural parameters determined by an EBSD analysis. These parameters are the average spacing of deformation introduced boundaries and the fraction of high angle boundaries. The method is demonstrated for two heterogeneous structures: (i) a gradient (sub)surface structure in steel deformed by shot peening; (ii) a heterogeneous structure introduced by friction between a tool and a workpiece of aluminum. Flow stress data are calculated based on the microstructural analysis, and validated by hardness measurement and 2D numerical simulations. A good agreement is found over a plastic strain range from ∼1 to 5.

Local flow stresses in interpenetrating-phase composites based on nanoporous gold — In situ diffraction

We report a synchrotron in situ diffraction experiment exploring stress evolution during compression of interpenetrating-phase nanocomposites based on nanoporous gold and polymer. While previous experiments provided indirect indication of local flow conditions based on macroscopic effective flow stress and micromechanics models such as Gibson-Ashby scaling law, the lattice parameter data of our experiment access the flow stress directly. At small structure size we find excellent agreement with previous reports, supporting the match between material and model of those studies. Yet, deviations at larger structure size suggest that coarsening generates defects in metal network structure that are ignored by standard models.

Modeling the strain-hardening effect and plastic deformation of nanocrystalline FCC metals dispersed with the finest grains

A mechanism-based plasticity model focusing on deformation and failure behavior of nanocrystalline (NC) FCC metals dispersed the finest grains (FGs) is proposed. The stress–strain relationship is derived by invoking the impeding effect of the FGs on the movement of grain boundary dislocations along the grain boundaries and the unique role of nanocracks into the constitutive model. A strain-based cumulative distribution function is also included in the present model to account for the contribution of grain boundaries to the local flow stress due to grain refinement during plastic deformation. It is found that the interaction between dislocations and the FGs contributes to the strain-hardening property and the failure behavior is attributed to the nanocrack evolution. Numerical results show that the proposed model can successfully describe the enhanced strength and ductility of the NC metals in previous experimental literatures. It is further noted that the strength and ductility are sensitive to the volume fraction of the FGs and the density of nanocracks. This quantitative continuum plasticity model can be utilized to optimize the mechanical properties of the nanostructured metals by tuning the material structure parameters.

Predicting the flow stress of high pressure die cast magnesium alloys

In the present study, we describe the characterization of three magnesium alloys, AM60, AZ91 and AE44, which were processed by high pressure die casting (HPDC) and gravity casting. Spherical microindentation was used to analyze the influence of microstructural features on the flow stress for both skin (finer grain sizes) and core (larger grain sizes and dendrites) regions of HPDC, as well as different regions of gravity step-cast plate for all three magnesium alloys. It was observed that the local yield stress and flow stress of magnesium alloys depend on grain size. The Hall–Petch slopes determined from indentation testing compared well with the results obtained from uniaxial tensile testing and literature. The Hall–Petch equation was shown to be applicable for predicting the yield strength and the flow stress at several levels of plastic strains.

Making Mg Magnificent

Materials Science When crystalline materials are stressed, defects in the crystal planes become mobile once a critical stress is reached. The stress required for movement of these dislocations along different slip planes can vary considerably, leading to poor ductility. Magnesium is an example of a material with an extreme anisotropy: The critical stress required for deformation along nonbasal planes is 100 times larger than along basal ones. Yu et al. postulated that even though materials are known to be stronger when they are smaller, there are upper bounds to this enhancement, so that the critical anisotropy should decrease. They tested single-crystal Mg samples ranging from 850 to 80 nm in size inside a quantitative electron microscope. At sizes between 200 and 400 nm, significant strengthening of the samples was seen, but the ductility remained poor. Below 100 nm, there was a shift in the deformation behavior. As the local flow stresses approached 2 GPa, there was increasing activation of the nonbasal planes, leading to a large amount of plastic deformation. These size effects could be employed to make better use of other high plastically anisotropic materials. The use of grain boundaries could allow for larger overall samples, because the boundaries will act as stress concentrators and preferred sources for the nucleation and emission of dislocations, which is important during plastic deformation of a sample. Proc. Natl. Acad. Sci. U.S.A. 110 , 13289 (2013).

Computational modelling of hydrogen embrittlement in welded structures

This paper deals with the modelling of the combined hydrogen embrittlement phenomena: hydrogen-enhanced local plasticity (HELP) and hydrogen-induced decohesion (HID) in dissimilar welds through a cohesive zone modelling approach (CZM). Fractured samples of dissimilar weld interfaces in AISI8630/IN625 show that cracks propagate in a region called the “featureless” region located in the Nickel side of the weld. This region is characterized by the presence of a distribution of fine carbides. We model the effect of hydrogen on the material toughness as the result of a synergistic effect of HELP and HID mechanisms where (i) hydrogen enhanced dislocation mobility promotes the development of dislocation structures at the carbides which increases the stress on the particles; while the presence of hydrogen also results in (ii) a reduction in the (a) cohesive strength of the carbide/matrix interface and (b) in the local flow stress of the matrix. The decohesion mechanism at the carbide/matrix interface is modelled through a two-dimensional user-defined cohesive element implemented in a FORTRAN subroutine (UEL) in the commercial finite element code ABAQUS and the effect of the hydrogen on the plasticity properties of the matrix is coded in a UMAT routine. Preliminary analysis on a unit cell representing the matrix/carbide system under plane strain shows that HELP and HID are competitive mechanisms. When the combined mechanism HELP+HID occurs microcracks form at the matrix/carbide interface due to decohesion process followed by localization of plastic flow responsible for the link-up of the microcracks.

Hall–Petch and dislocation strengthening in graded nanostructured steel

The structure and strength of low carbon steel samples have been analyzed after plastic deformation by shot-peening and cold-rolling. The fine scale surface microstructure caused by shot-peening extends to ∼50μm below the surface. The structure is graded and subdivided by dislocation boundaries and high angle boundaries showing a clear resemblance to the lamellar structure, which evolves during conventional rolling of bulk metallic materials from medium to high strain. As the surface is approached, the boundary spacing decreases to ∼50nm at the surface. In parallel, the misorientation angle across boundaries increases to ∼65% of high angle boundaries. The cold-rolled steel shows a low hardening rate at high strain and by assuming additive strength contributions from Hall–Petch and dislocation strengthening, the flow stress has been expressed by the relationship σ-σ0=k2Dav-0.5, where Dav is the average spacing between the low and high angle boundaries which subdivide the microstructure, σ0 is the friction stress and k2 is a number which is expressed in terms of structural parameters which have been determined by electron backscattered diffraction. It is found that calculated k2 values are in accord with an experimental value of 310MPaμm0.5. In the shot-peened steel the increase in Dav with increasing distance from the surface is transformed into a stress profile based on the σ-Dav relationship established for cold-rolled bulk samples. The calculated stress profile is validated by comparison with the experimental profile based on hardness measurements, and good agreement is found. This result points to a wider application of the suggested method to derive the local flow stress in a deformed microstructure based on a measurement of the local boundary spacing and the stress–structure relationship for the bulk material in the deformed state.

A possible explanation for the contradictory results of hydrogen effects on macroscopic deformation

Despite extensive research, there have been many controversies on whether hydrogen hardens or softens iron and steels. Conventional application of hydrogen-enhanced localized plasticity (HELP) theory – including a decrease in the local flow stress in the presence of hydrogen – results in an expansion in the plastic zone ahead of a blunting crack tip rather than the localization of plastic deformation. Therefore, we propose a model to interpret the criterion for the application of local softening concept. According to our physical model, called pinning-softening model, the hydrogen-induced softening merely occurs in the large shear stress regions, e.g. in the vicinity of the crack tip. The remote areas from the stress raisers do not satisfy the critical condition of slip; as such, hydrogen-induced hardening occurs. Our model not only explains the contradictory results of hydrogen effects on the macroscopic deformation, but also gives more insight into the mechanistic understanding of hydrogen embrittlement phenomenon.