Abstract: The compression of granular materials has been traditionally modelled with the limitations of classical elasto-plasticity. The energy was implicitly assumed to dissipate from the frictional interaction of particles. However, the fact that brittle granular materials crush suggests that energy must also be dissipated from the fracturing of the grains, as in fracture mechanics. The concept of breakage as a thermomechanical internal variable was introduced in Part I [Einav, I., 2006. Breakage mechanics—Part I: theory. J. Mech. Phys. Solids 00,000–000] to describe the fracturing mechanisms. The theory allows to treat ideal theoretical materials that undergo dissipation purely from breakage with no other mechanism allowed for the energy consumption. However, as accounted for in elasto-plasticity, dissipation must also occur from the frictional rearrangement of grains. The combination of the two dissipative mechanisms of breakage and plasticity must therefore be investigated, as we do in this paper. Those two mechanisms are generally coupled, in the sense that one inevitably appears when the other develops. Plastic dissipation emerges as a by-product of breakage dissipation because after grains crush, local rearrangement must occur. This scenario may be termed an ‘active breakage mechanism’, and typifies compression deformations. In shear the plastic dissipation is dominant but breakage appears inevitably from grains abrasion. This scenario may be called a ‘passive breakage mechanism’. Based on the coupling assumption, models are developed for granular materials. In particular, we show that in compression isotropic hardening of sands may appear without involving plastic strains, i.e., independent of frictional dissipation. This interpretation of hardening is different from the one used in classical critical state soil mechanics. However, frictional dissipation leads to plastic straining that are necessary for the models to be predictive in unloading.

Abstract: Railway ballast particles undergo significant amount of breakage under repeated train load. Breakage of ballast particles, especially highly angular fresh ones, causes an increase in settlement, contributing to track degradation. The quantitative analysis of the influence of breakage on the stress-strain properties of ballast can be performed either experimentally or numerically. Numerical modeling has the advantage of simulating ballast breakage subject to various types of loading and different boundary conditions for a range of material properties. In this paper, ballast breakage under cyclic loading is simulated using a 2D discrete element method (DEM) utilizing the software PFC2D . A new subroutine is developed and incorporated in the PFC2D analysis to study ballast breakage and to quantify breakage in relation to particle size distribution. The influence of confining pressure on both breakage and permanent deformation is also studied and compared with laboratory observations. The findings of this pap...

Abstract: Publisher Summary This chapter focuses on the process related to the breakage of single particles. Particle breakage in comminution and degradation processes is the result of a number of poorly understood microprocesses. The single-particle fracture process does not terminate after first failure at a flaw because kinetic energy may still be available either from the tools that apply the stresses or from the flying fragments of the particles. This remaining energy must be dissipated during the second stage of the process, which results in secondary fracture of the initial progeny and possibly several further stages of sequential fracture as well. Material characteristics relevant to particle breakage are the fracture strength and the deformation behavior. Fracture strength can be defined in terms of the energy required to cause fracture (or critical tensile stress). A variety of testing methods have been used to measure the breakage characteristics of single particles subject to compression, each of which allowing investigation over a restricted range of deformation rates. These tests can be classified according to the mode of application of stresses and the number of contact points in (1) single impact, (2) double impact, and (3) slow compression.

Abstract: Aggregation and breakage of aggregates of fully destabilized polystyrene latex particles in turbulent flow was studied experimentally in both batch and continuous stirred tanks. Small-angle static light scattering (SASLS) was used to monitor the time evolution of two independent moments of the cluster mass distribution (CMD), namely, the mean radius of gyration and the zero angle scattered light intensity. In addition, information about the structure of the aggregates was obtained in terms of the static light scattering structure factor. It was observed that decreasing the solid volume fraction over more than one order of magnitude resulted in monotonically decreasing steady-state values of both moments of the CMD. Using a combination of batch operation and continuous dilution with particle-free solution in the stirred tank, it was found that the steady-state distributions were fully reversible upon changing the solid volume fraction. These observations indicate that the steady-state CMD in this system is controlled by the dynamic equilibrium between aggregation (with the second-order kinetics in cluster concentration) and breakage (with the first-order kinetics in cluster concentration). In addition, by dilution to very low solid volume fractions, we demonstrate the existence of a critical aggregate size below which breakage is negligible.

Abstract: Biomechanical analyses of intertidal and shallow subtidal seaweeds have elucidated ways in which these organisms avoid breakage in the presence of exceptional hydrodynamic forces imposed by pounding surf. However, comparison of algal material properties to maximum hydrodynamic forces predicts lower rates of breakage and dislodgment than are actually observed. Why the disparity between prediction and reality? Most previous research has measured algal material properties during a single application of force, equivalent to a single wave rushing past an alga. In contrast, intertidal macroalgae may experience more than 8000 waves a day. This repeated loading can cause cracks - introduced, for example, by herbivory or abrasion - to grow and eventually cause breakage, yet fatigue crack growth has not previously been taken into account. Here, we present methods from the engineering field of fracture mechanics that can be used to assess consequences of repeated force imposition for seaweeds. These techniques allow quantification of crack growth in wave-swept macroalgae, a first step towards considering macroalgal breakage in the realistic context of repeated force imposition. These analyses can also be applied to many other soft materials.

Abstract: The process of freeze-thaw not only subjects bioproducts to potentially destabilizing stress, but also imposes challenges to retain container integrity. Shipment and storage of frozen products in glass vials and thawing of the vials prior to use at clinics is a common situation. Vial integrity failure during freeze-thaw results in product loss and safety issues. Formulations of biomolecules often include crystallizable excipients, which can cause glass vial breakage during freeze-thaw operations. In this study, mannitol formulations served as models for mechanistic investigation of root causes for vial breakage. Several parameters and their impacts on vial breakage were investigated, including mannitol concentration (5% and 15%), different freeze-thaw conditions (fast, slow, and staging), fill configurations (varying fill volume/vial size ratio), and vial tray materials (plastic, stainless steel, corrugated cardboard, aluminum, and polyurethane foam). The results in this study were subjected to a statistical proportion test. The data showed that large fill volumes strongly correlated with higher percentage of vial cracks. Furthermore, the 15% mannitol was found to cause more breakage than 5% mannitol, especially with fast temperature gradient. Significantly more thawing vial breakage occurred in the fast compared to slow freeze-thaw with all types of vial trays. The freezing breakage was substantially lower than the thawing breakage using the fast temperature gradient, and the trend was reversed with the slow temperature gradient. An intermediate hold at -30 degrees C prior to further decrease in temperature proved to be a practical approach to minimize mannitol-induced vial breakage. Thermal mechanical analysis (TMA) and strain gage techniques were employed to gain mechanistic insights, and it was found that the primary causes for mannitol-induced vial breakage were partial crystallization during freezing and "secondary" crystallization of non-crystallized fraction during thawing. The strain on the vial's axial direction was significantly higher than the hoop direction, typically resulting in bottom lens of the vial coming off. Without a -30 degrees C hold, rapid volume expansions due to initial crystallization and secondary crystallization of mannitol were observed in TMA profiles, and these expansions were more apparent in 15% mannitol compared to 5% mannitol. With the introduction of a -30 degrees C hold step, abrupt expansions diminished in TMA profiles, suggesting that most of the mannitol crystallization occurred concurrently with ice solidification during the -30 degrees C holding step and, thus, secondary crystallization during thawing was minimal and the sudden expansion event was eliminated. Therefore, vial breakage during both freezing and thawing was reduced.

Abstract: This paper presents the development of new methods for measuring aggregate resistance to polishing, and degradation. These are important properties that influence pavement skid resistance and resistance to distresses under traffic loading. The aggregate imaging system is used to measure aggregate surface texture after different polishing time intervals in the micro-Deval test. Mathematical functions are then used to describe the initial texture, rate of polishing, and final texture. Aggregate abrasion is quantified by the percent difference in surface angularity before and after the micro-Deval test, while aggregate breakage is described by the weight loss in this test. The efficacy of the new methods is demonstrated through the analysis of aggregates from different sources that exhibit a wide range of properties. In addition, the new methods are verified by comparing the measured aggregate properties to the degradation of these aggregates in hot mix asphalt mixtures due to compaction forces.

Abstract: Comminution or size reduction is a commonly used unit operation in a variety of industries including pharmaceuticals. In quantitative analysis of comminution at the process length scale, population balance modeling has been used with an assumption that the breakage rate of particles is first-order and that the population balance model is linear. For certain forms of the specific breakage rate and breakage distribution functions, a similarity solution to the linear population balance exists, and self-similarity plots have been used to show its validity in batch comminution processes. On the other hand, ample experimental batch milling data in the literature indicate the inadequacy of the linear theory. In this study, a theoretical investigation has been conducted within the framework of a recently proposed non-linear theory. The non-linear theory takes into account phenomenologically the non-first-order effects resulting from mechanical multi-particle interactions. Specifically, the cushioning action of small particles on the coarser ones is considered. It is found that self-similarity does not exist in the presence of the non-first-order breakage kinetics. The present study suggests the use of self-similarity plots for an approximate assessment of the impact of non-first-order kinetics on the shape of the cumulative particle size distribution.

Abstract: The effect of drying on the quality of milled rice was investigated. Variables studied were drying temperature, air velocity and air relative humidity. The degree of breakage during milling increased as temperature of drying increased (from 40 to 70°C) and relative humidity decreased. Varying the air velocity between 0.26 and 2.12 m/sec had no effect on breakage. The‘activation energy’ of grain breakage was much higher than of drying.

Abstract: Publisher Summary This chapter highlights the breakage and morphological parameters determined by laboratory tests. Size reduction of solids and minerals by crushers and grinding mills is an important industrial operation involving many aspects of mineral, metallurgical, power and chemical industries. Size reduction by crushers does not create problems because of high energy consumption and capital cost per ton per hour; however, fine grinding by mills consumes a lot of energy and causes high abrasive wear. As mineral particles are reduced to finer product sizes, their surfaces become more important. Surface characteristics and properties affect any of the fine particle processing operations. The particle morphology plays a very important role in many aspects of powder technology and enables one to predict how the minerals may behave when they are ground and to determine how those minerals may respond to processing. Obtaining the breakage and morphological parameters by laboratory studies helps to better understand the breakage behavior and predict the process outputs in desired unit operations to solve complex problems.

Abstract: Hair breakage during combing was evaluated by combing tresses and examining photographs of snags of hair fibers in combs. The resultant hair fiber arrangements suggest that breakage likely involves hair-on-hair interactions, and broken fragment size suggests that breakage occurs primarily at or near the hair-comb interface. Compression forces during combing were also measured, and impact loading of a hair fiber over another hair versus a hair fiber over a comb tooth shows that compression and abrasion are important to breakage during combing and that impact loading of one hair fiber over another during snagging is a probable and important pathway for hair breakage.

Abstract: In an accompanying article we have described parameters that influence vial breakage in freeze-thaw operations when using crystalizable mannitol formulations, and further provided a practical approach to minimize the breakage in manufacturing settings. Using two diagnostic tools-thermal mechanical analysis (TMA) and strain gage, we investigated the mechanism of mannitol vial breakage and concluded that the breakage is related to sudden volume expansions in the frozen plug due to crystallization events. Glass vial breakage has also been observed with a number of frozen protein formulations consisting of only amorphous ingredients. Therefore, in this study, we applied the methodologies and learnings from the prior investigation to further explore the mechanism of vial breakage during freeze-thaw of amorphous protein products. It was found that temperature is a critical factor, as breakage typically occurred when the products were frozen to -70 degrees C, while freezing only to -30 degrees C resulted in negligible breakage. When freezing to -70 degrees C, increased protein concentration and higher fill volume induced more vial breakage, and the breakage occurred mostly during freezing. In contrast to the previous findings for crystallizable formulations, an intermediate staging step at -30 degrees C did not reduce breakage for amorphous protein formulations, and even slightly increased the breakage rate. The TMA profiles revealed substantially higher thermal contraction of frozen protein formulations when freezing below -30 degrees C, as compared to glass. Such thermal contraction of frozen protein formulations caused inward deformation of glass and subsequent rapid movement of glass when the frozen plug separates from the vial. Increasing protein concentration caused more significant inward glass deformation, and therefore a higher level of potential energy was released during the separation between the glass and frozen formulation, causing higher breakage rates. The thermal expansion during thawing generated moderate positive strain on glass and explained the thaw breakage occasionally observed. The mechanism of vial breakage during freeze-thaw of amorphous protein formulations is different compared to crystallizable formulations, and accordingly requires different approaches to reduce vial breakage in manufacturing. Storing and shipping at no lower than -30 degrees C effectively prevents breakage of amorphous protein solutions. If lower temperature such as -70 degrees C is unavoidable, the risk of breakage can be reduced by lowering fill volume.

Abstract: In the present study, the effect of grinding media shape on breakage parameters was investigated. Balls and cylpebs were used as the grinding media. It was observed that the grinding of quartz obeyed first-order breakage kinetics in the case of balls and cylpebs. Higher breakage rates were noted with cylpebs than with balls. Furthermore, it was found that the primary breakage distribution function is dependent on the feed size (i.e., non-normalizable), but independent of the grinding media shape. The effect of grinding time on the product size distribution has also been investigated. Following four and ten minute grindings, cylpebs produced a relatively finer product compared to balls.

Abstract: A breakage model was investigated for thin-layer drying of rough rice. The breakage model developed can predict the percentage of head rice (E/Eo) as an exponential function of the grain moisture. Experimental data of the rice moisture content during drying were fitted with a theoretical model of the drying process to obtain the parameters. Experimental data of percentage head rice and moisture content were fitted to obtain the parameters of breakage model. Both functions were used together to obtain a drying-breakage model. This model allows us to predict the drying time required to achieve a rice moisture content desired and to estimate the head rice yield percentage for this moisture content.