Journal Club Theme of February 2016: Deformation Mechanics of Granular Materials: Local Deformation of Polymer-bonded Sugar at High Strain Rate Loading

Deformation Mechanics of Granular Materials:

Local deformation of Polymer-bonded sugar at high strain rate loading

 Addis Kidane, Suraj Ravindran

Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208

Introduction

Understanding the damage mechanisms in granular materials, such as concrete, polymer bonded explosive (PBX), sands, armor protection materials, etc., under dynamic loading has been a great interest for a long time. The mechanics of granular materials, in general, have been studied in the last four decades for example, [1-9] and many models are proposed.  In the case of soft polymer bonded hard materials such as PBX, due to significant properties mismatch and presence of voids and cracks, the failure mechanism is complex. The computational models are developed over the years to predict the deformation behavior of these materials.

On the other hand, a lack of high temporal and high spatial resolution methods hinder experimental community in understanding the local deformation mechanism of heterogeneous materials at high rate loading. Recently, using X-ray DIC system, Lu et al [10] measured the in-plane deformation of borosilicate glass beads (granular material) subjected to impact loading. Though the  method, is a bit complex, potentially play a great role in understanding the damage mechanisms in heterogeneous materials.  An alternative and a complementary method, an optical based high-speed digital image correlation, has been recently used to measure the local deformation of a copper  at subgrain scale [11]. Recently using high-speed camera along with high-magnification optical system, we are able to measure the local deformation in PBS at a framing rate of up to 1 million/ sec and a spatial resolution of 10 µm/pixel [12].

The question we would like to ask is

What are the major local deformation mechanisms?

In this month’s iMechanica Journal Club, we would like to highlight recent efforts to quantify the local damage mechanisms in PBS. This brief overview, focus only on results from DIC based surface measurement at meso-scale, but we hope it will initiate further discussions in the field including from different approaches and simulations.

PBS is a polymer bonded sugar, a known simulant of PBX. It is made of relatively hard sugar crystal bonded by the soft binder. The grain size of the sugar varies from 300- 500 µm. The specimen preparation and detailed experimental procedure can be obtained elsewhere [12]. The specimens are loaded in Split Hopkinson pressure bar under compression and images are processed using Vic 2D digital image correlation software.

 The experimental result shows that the deformation is highly localized as shown in Fig 1.   Most of the deformation are confined to the polymer binder rich area and where crystals are far apart. More importantly, the deformation formed a clear local band like structure, at a very small axial strain. The observed local damage initiation mechanisms are;

Crystal Rotation

Crystal rotation and sliding have been observed in granular materials under quasi-static and dynamic loading conditions [13, 14]. Figure 2 shows the rotation of each crystal as a function of applied global strain. The magnitude and direction of rotation vary from grain to grain. It is also observed that, in some cases, two or more grains form a group and rotate together up to a certain loading time. For example C2, C4 and C5 form a pair and rotate together up to a strain of 0.8% in an anticlockwise direction. There is no relative rotation between C2, C4 and C5 until this time. On the other hand, some crystals in contact with another rotating crystal are shown to be stationary or rotates in a different direction, which could create sliding and friction between the adjacent crystals. For example C1, which is in contact with C2, rotates in opposite direction but not significantly, which could cause potential sliding friction with C2. In addition, relative rotation between the adjacent crystals can cause delamination at the interface and could be a potential failure mode in PBX.

Shear band formation

 Shear bands formed in this material have been captured as shown in Fig 3. In PBX, at intermediate strain rate, the shear bands can be formed due to two main mechanisms 1) softening due to damage accumulation (micro-cracking), and 2) thermal softening due plastic strain dissipation as heat.  In metals, shear band formation due to thermal softening requires global strain between 10-50%. But in PBX the strain required to form shear-band is one order less than the strain required due to thermal softening. It is clearly observed even at small global strain the localized strain is one order higher, which could cause thermal softening, and the micro cracks could cause the mechanical softening. Therefore, shear band formation can be due to the combined effect; thermal softening due to high strains formed locally in the polymer binder and softening due to damage accumulation in the material. 

Crystal Fracture

Along large interface deformation, crystal fracture is captured in this work. Surprisingly, only a few crystals are fractured, and their location seems arbitrary.  It is difficult to know what makes some crystal fail but others don’t, but a close looking  in the crystals and their neighbor could give insights. For example, a large crystal if it surrounded by another large crystal, is a favorable condition for crystal fracture. In such cases, the number of crystal to crystal contact points will be less and increases the probability of stress concentration. It is distinctly visible from the Fig. 4a that C14 and C13 are crystals have a single point contact, where a sharp corner of C14 hitting C13. Consequently, these conditions cause stress concentration and finally fracturing of C13. An initial crack formed from during materials preparation is also a favorable condition for crystal fracture. Initial crack is apparent in crystals, C4, C6 and C19. From the deformation image, it is clear that the initial crack starts to grow as loading progress and leads to fracture C6 and C19 but not C4.  The large polymer-rich region ahead of crystal C4, might cause a possible force chain mechanism or rigid body rotation. In any way, having a think region of polymer binder between adjacent crystals  will effectively reduce the probability of crystal fracture.

Challenges and opportunities.

·         Capturing hot spot formation in PBX under dynamic loading is  still a great challenge

·         Measuring temperature at high temporal and high spatial resolution could help to confirm what mechanism leads to hot spot formation.

·         With the current method, 10 µm/pixel was achieved and this length scale is great for crystals with the order of 100 µm. To study materials with fine grains, a higher magnification system is required. Due to its low depth of field at high magnification, an optical system may not be adequate to capture nanoscale length deformation at high strain rate loading… any alternative method, or solution could help the society…

Note: additional related studies in the field can be obtained from 19-34. 

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