Stochastic effects in plasticity in small volumes

Shao, Shuai; Abdolrahim, Niaz; Bahr, David F.; Lin, Guang; Zbib, Hussein M.

doi:10.1016/j.ijplas.2013.09.005

Cited by 36 publications

(12 citation statements)

References 64 publications

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“…The trends observed here for hardness mirror observations reported by Shao et al 54 in dislocation dynamics simulations. In their work, the variability in yield strength of micropillars was found to be strongly dependent upon dislocation density and size of the pillar.…”

Section: Discussionsupporting

confidence: 91%

Variation in the nanoindentation hardness of platinum

Maughan¹,

Zbib

Bahr³

2013

J. Mater. Res.

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Pure platinum was probed with a nanoindenter fitted with a Berkovich tip to various depths. The indent pattern was made on the as-polished specimen prior to heat treating, after heat treating at 500°C for 30 min, and again after further heat treating at 1000°C for 30 min. The variability in the measured hardness decreased as the indentation depth increased from 50 to 300 nm. When the sampled was annealed, the hardness variation was also greater. Increasing hardness variation with decreasing dislocation density and sampling volume indicates that dislocation density plays a critical role in the observed variation, beyond solely instrumentation uncertainty, and supports a defect-based explanation for the stochastic behavior. It appears that the stochastic behavior occurs when multiple dislocations are present in the sampled volume rather than sampling only a single dislocation.

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Section: Discussionsupporting

confidence: 91%

Variation in the nanoindentation hardness of platinum

Maughan¹,

Zbib

Bahr³

2013

J. Mater. Res.

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“…Figure 13 shows the result of compression testing of a miniaturized sample of an Al-30 % Zn alloy, prepared in the form of a micro-pillar from an HPT disk, where the compression was conducted at room temperature using a depth-sensing ultra-microhardness testing facility and the grain size of the material was in the range of *200-400 nm [77,78]. Due to the very limited number of grains that are generally available in micro-pillars prepared from conventional CG materials, they invariably suffer from strain avalanches which arise due to the occurrence of complex and intermittent dislocation slip events [79][80][81][82][83]. By contrast, and as is evident from the protrusion of multiple grains in Fig.…”

Section: Effect Of a Short-term Anneal After Processingmentioning

confidence: 99%

Review: Overcoming the paradox of strength and ductility in ultrafine-grained materials at low temperatures

2015

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Ultrafine-grained (UFG) materials with grain sizes in the submicrometer or nanometer range may be prepared through the application of severe plastic deformation (SPD) to bulk coarse-grained solids. These materials generally exhibit high strength but only very limited ductility in low-temperature testing, thereby giving rise to the so-called paradox of strength and ductility. This paradox is examined and a new quantitative diagram is presented which permits the easy insertion of experimental data. It is shown that relatively simple procedures are available for achieving both high strength and high ductility in UFG materials including processing the material to a very high strain and/or applying a very short-term anneal immediately after the SPD processing. Significant evidence is now available demonstrating the occurrence of grain boundary sliding in these materials at low temperatures, where this is attributed to the presence of non-equilibrium grain boundaries and the occurrence of enhanced diffusion along these boundaries.

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“…We make use of the MDDP simulations of micro-pillars conducted by Shao et al [111], as synthetic data to inform the SGP model parameters while quantifying the uncertainty of the SGP model prediction of the size effect responses. The simulations consist of uniaxial compression of micro-pillars with the aspect ratio of 1×5×1 with the height L (along y axis in Figure 2) ranges from 200 nm to 1000 nm.…”

Section: Mddp Simulations Of Micro-pillarsmentioning

confidence: 99%

A Predictive Discrete-Continuum Multiscale Model of Plasticity With Quantified Uncertainty

Tan

Villa

Shamsaei

et al. 2020

Preprint

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Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distributions of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). The outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.

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Stochastic effects in plasticity in small volumes

Cited by 36 publications

References 64 publications

Variation in the nanoindentation hardness of platinum

Variation in the nanoindentation hardness of platinum

Review: Overcoming the paradox of strength and ductility in ultrafine-grained materials at low temperatures

A Predictive Discrete-Continuum Multiscale Model of Plasticity With Quantified Uncertainty

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