Have you ever tried to break spaghetti and had pieces fly left and right? The good news is you are not alone.
Figure 1. Spaghetti breaking in more than 2 pieces.
Famed physicist Richard Feynman ’39 once spent a good portion of an evening breaking pasta and looking for a theoretical explanation for why the sticks refused to snap in two. This experiment, famously known as Feynman’s Kitchen Experiment, remained unsolved until a group of French physicists figured it out in 2005. According to their theory, when a stick is bent evenly from both ends, it will break near the center, where it is most curved. The initial break triggers a snap-back effect and a vibration that further fractures the stick. Finally, Feynman’s mystery was solved. However, the question still remained: can a rod of spaghetti be snapped into just two pieces?
Figure 2. Famed Physicist Richard Feynman.
Yes. But there's a twist. According to a new MIT study, researchers found that by simultaneously bending and twisting the rod of spaghetti, the rod can be coerced to break in two. This, combined with stress and strain studies, can be key in understanding one of the most important material properties for additive manufacturing: tensile strength.
The Science Breakdown
Let’s breakdown the dynamics of thin rods as increased uniform curvature is applied. The rod breaks in half at an initial time. Since the rod was bent with uniform curvature, the location of the initial breaking point deflects on either half of the rod, creating new breaking events at a later time and at new points. Breakage appears to be extremely sensitive to the initial curvature. Rods that are closer to their limit curvature tend to break sooner after release, or closer to the end of the release. When a bent rod reaches its limit curvature and breaks at a first point, a burst of flexural waves is sent through the newly formed fragments, which further increase the curvature. The limit curvature is therefore exceeded again at later time, allowing a cascading failure mechanism to take place. The cascade is limited by dissipation (propagation of transverse cracks, damping of flexural waves i.e. by viscoelastic effects in the material). This is the snap-back effect.
The Twist Fix
The team studied the relationship between the length of noodles, twisting angle and the action of forces on the rod-shaped pasta. The team found that a 10 inch noodle must be twisted to about 270 degrees prior to bending, if it is to snap in half. The team also discovered that an effect called twist-back is at play here. When twist-back occurs, the stick will essentially unwind to its original straightened configuration, releasing energy from the rod, and preventing additional fractures.
This work has potential applications outside of the kitchen. It could kick start future research pertaining to other rod-shaped materials prone to fracture, such as nanotubes or even cellular microtubules.
Behind the Breaking Forces
Long, thin supports are ubiquitous in natural and engineered load bearing structures, like the steel struts of a skyscraper. A single rod will buckle and give way under pressure or strain, if too much force is applied along its axis, which can lead to the failure of the structure. The buckling of a slender rod is one of the simplest and most general instabilities of a solid, observable with almost any material. The buckling wavelength can be related to the impact velocity. The scaling law for the buckling wavelength depends on two properties of the rod: the speed of sound, speed at which compression pulse travels through rod, and the diameter.
The velocity of the sound wave is affected by two material properties of matter: elastic properties and density.
Velocity is equal to the square root of elastic properties over material density. The speed of sound is also different for different types of solids, liquids, and gases because the elastic properties are different for different materials. Elastic properties relate to the tendency of a material to maintain its shape and not deform when a force is applied to it. A material such as steel will experience a smaller deformation than rubber when a force is applied to the materials. Steel is a rigid material while rubber deforms easily and is a more flexible material. At the particle level, a rigid material is characterized by atoms and/or molecules with strong forces of attraction for each other. Particles that return to their resting position quickly are ready to move again more quickly, and thus they can vibrate at higher speeds. While the density of a medium also affects the speed of sound, the elastic properties have a greater influence on the wave speed.
Understanding Tubular Properties
The results of fracture of spaghetti can predict theoretical results of other tubular materials which can further enhance the study of fracture cascades and quenched fracture. Although bending-induced fracture of elongated rod-like objects has been intensely studied, the effects of twist and quench dynamics have yet to be explored systematically. There can be intersecting scaling relations for quenched fracture. These theoretical results are expected to apply to torsional and kinetic fracture processes for a wide range of materials.
Understanding fracture and quench dynamics is key in understanding the strength of the material. Having some knowledge on the fracture of tubular materials can help with the understanding of tensile forces. Tensile strength is a key material property used to measure the breaking point of a material after applied force. It is also used to understand the fracture point of 3d printable material. The tensile strength of the material dictates the durability of the final 3d printed product.