Robust scaling of strength and elastic constants and universal cooperativity in disordered colloidal micropillars

Abstract

We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a bidisperse mixture of 3-and 6-μm polystyrene particles. Mechanical annealing of confined pillars enables variation of the packing fraction across the phase space of colloidal glasses. The measured normalized strengths and elastic moduli of the annealed freestanding micropillars span almost three orders of magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between ultimate strengths and elastic constants that is invariant to relative humidity, implying a critical strain of ∼0.01 that is strikingly similar to that observed in metallic glasses (MGs) [Johnson WL, Samwer K (2005) Phys Rev Lett 95:195501] and suggestive of a universal mode of cooperative plastic deformation. We estimate the characteristic strain of the underlying cooperative plastic event by considering the energy necessary to create an Eshelby-like ellipsoidal inclusion in an elastic matrix. We find that the characteristic strain is similar to that found in experiments and simulations of other disordered solids with distinct bonding and particle sizes, suggesting a universal criterion for the elastic to plastic transition in glassy materials with the capacity for finite plastic flow. In an ideal, defect-free system, the relationship between a material's elastic constants and yield strength is indicative of the underlying plastic event that generates macroscopic yielding. For the case of a crystalline solid, Frenkel predicted the ideal yield stress by estimating the energy necessary to cooperatively shear pristine crystallographic planes. The result estimates that the ideal shear strength, τ y;ideal , scales linearly with the shear modulus, μ, as τ y;ideal = μ=2π (1). This simple, yet striking, prediction implies a singular critical shear strain for yielding, irrespective of the material. Experimental strengths of crystalline metals, however, are found to fall orders of magnitude short of Frenkel's ideal strength, suggestive of plasticity generated by mechanisms other than cooperative slip. In real bulk crystals, microstructural defects, such as dislocations, grain boundaries, and surfaces, become plastically active at stresses well below τ y;ideal , implying a transition to a far less cooperative plastic deformation mechanism. Controlling the character and number density of these defects mediates the strength of crystals; for instance, the Hall-Petch relationship for polycrystals (2, 3) states that τ y ∼ d −1=2 , where τ y is the yield strength and d is the grain size (thus controlling the fraction of planar defects), and Taylor strengthening (4) predicts τ y ∼ ρ 1=2 , where ρ is the dislocation density. This ability to tailor material strength is a reflection of the large catalog of plastic events found in crystals and the associated broad range of energies necessary for their operation. In such defected crystals, the highly cooperative shear mechanism that defines the intrinsic ideal str...

Structure-property relationships from universal signatures of plasticity in disordered solids

“…A constant value of the yield strain in shear of 2.7% was empirically shown for a set of metallic glasses on the basis of mechanical tests (39) and was further corroborated by atomistic simulations (40). Experiments on uniaxially loaded colloidal pillars showed a similar yield strain even though the elastic moduli were smaller by as much as five orders of magnitude (41). …”

“…In contrast, it is known that certain classes of disordered materials share a common value of the yield strain (39–41) despite the heterogeneity of atomic or particle positions within the material. A constant value of the yield strain in shear of 2.7% was empirically shown for a set of metallic glasses on the basis of mechanical tests (39) and was further corroborated by atomistic simulations (40).…”

“…Here, we extend the Ashby chart for disordered solids from five orders of magnitude (41) to more than 13 orders of magnitude in elastic modulus. To do this, we have expanded the class of disordered systems to include covalently bonded amorphous solids (amorphous carbon) and several different metallic glasses (see table S1) as well as extremely weakly attracting or purely repulsive systems (colloids, aqueous foams, and granular materials; see tables S2 and S3).…”

Mechanics of colloidal supraparticles under compression

“…In addition, the size of the agglomerate does not play a role in the model. From the experimental side, the nanomechanical behavior of granular materials in bulk or in specifically shaped specimens has received growing attention (45,(49)(50)(51)(52)(53)(54).…”

Friction and Adhesion Govern Yielding of Disordered Nanoparticle Packings: A Multiscale Adhesive Discrete Element Method Study

“…13 Similar phenomena are also observed in many other amorphous materials, including metallic glasses 15−19 and colloidal glasses. 20,21 Despite these advances, the nature of these localized constituent-level rearrangements is still a rapidly developing area, 22 with many unanswered questions.…”