Residual Stresses in Glasses

Abstract

The history dependence of the glasses formed from flow-melted steady states by a sudden cessation of the shear rateγ is studied in colloidal suspensions, by molecular dynamics simulations, and modecoupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function ofγt, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables, but differing static properties.PACS numbers: 64.70. P-83.50.-v Materials are often produced by solidification from the melt, involving nonequilibrium quenches. This imprints a history-dependent microstructure that strongly affects macroscopic material properties. One example is residual stresses [1,2]: if particle configurations cannot fully relax to equilibrium, some of the stresses, arising in the presence of flow in the melt, persist in the solid.Small glass droplets (known as Prince Rupert's drops or Dutch tears since the 17th century) vividly display the effects of residual stresses [3]: they withstand the blow of a hammer onto their main body, but explode when the slightest damage is inflicted upon their tail (releasing the frozen-in stress network). Today, safety glass and "Gorilla glass" covers for smartphones are deliberately pre-stressed during production to strengthen them. A theoretical understanding of residual stresses and their microscopic origins is however still not achieved.We seek to understand generic mechanisms by which residual stresses arise. A convenient starting point is to investigate the stress relaxation σ(t) following the cessation of shear flow of rateγ, from a well-defined nonequilibrium stationary state (NESS). Such "mechanical quenches" are ubiquitous in soft matter, where pre-shear is applied to "rejuvenate" the otherwise ill-defined glassy state [4][5][6][7]. For these systems, the soft-glassy rheology model (SGR) [8] predicts asymptotic power laws that imply the relaxation of stresses to zero [9]. In the following, we will reserve the term residual stress to describe a finite, persistent stress remaining in the (ideal) glass even at arbitrarily large times after the cessation of flow.In addition to macroscopic rheology, we investigate the evolution of the microscopic dynamics as characterized by the waiting-time dependent mean-squared displacements (MSD). The latter reveal the dynamical shrinkage of shear-fluidized regions after cessation, and phenomena akin to, yet different from the intensely studied aging dynamics after thermal quenches [10,11].Experiments on a variety of colloidal suspensions, together with molecular-dynamics (MD) simulations, provide a coherent qualitative picture that can be rationalized by mode-coupling theory of the glass transition (MCT) [12] within the integration-through-transients (ITT) formalis...

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“…Additionally, molecular dynamics simulations and experimental results have been compared to the theoretical predictions, thus demonstrating the complementarity of the three techniques [11]. Figure 5 shows the time evolution of the mean squared displacement function for the nonequilibrium scenario (steady state shear flow) and two equilibrium systems, one glassy and the other a dense liquid.…”

“…[11]. Curves are for three volume fractions discussed in the text, the largest being a glassy state and the other two are liquid states described theoretically by an extension of the mode-coupling formalism [11]. Also shown is the dependence on shear rate, 1 s -1 (blue) and 10 -4 s -1 (red).…”

“…First, the onset of yielding during start-up shear was investigated by subjecting suspensions of PMMA particles (267 nm and 788 nm in size) to rheometry and confocal microscopy measurements combined with Brownian particle dynamics simulations [10]. Then the onset of stress relaxation in a flowing suspension when shear rate is abruptly switched off was analyzed by a highly sophisticated theoretical analysis in conjunction with molecular dynamics simulations, in addition to macroscopic rheological measurements [11]. In complementary ways both studies exemplify the essence of microstructure evolution on the mesoscale.…”

“…Turning to the results where the applied shear on a colloidal suspension in steady-state shear flow is suddenly removed [11], we follow the time response of the ensuing stress relaxation as described by the self-consistent mode coupling theory [15] extended for nonlinear response [16]. Figure 4 shows that the normalized stress level (R is size of colloidal particle) does not respond instantaneously upon the cessation of shearing.…”

“…Conversely, it would follow that external shear is disruptive to maintaining the local cages. [11]. Curves are for three volume fractions discussed in the text, the largest being a glassy state and the other two are liquid states described theoretically by an extension of the mode-coupling formalism [11].…”