# Glass Breaking

We were recently asked to explain how glass breaks, or fractures, to some non-technical people. Glass is an amorphous material, without long range atomic order. This is different than crystalline material or polymers. The following is a summary written by mechanical engineers for the layperson.

One approach that an engineer, typically a mechanical engineer, uses to describe how materials behave under stress is to create a constitutive equation. This is a mathematical model that assumes that a material is a continuous media. The general field of this type of work is known as continuum mechanics. Even the notation in this field is complex, and relies on multi-dimensional matrices that use Einstein’s indicial notationThis type of analysis is usually taught in a Mechanical Engineering department at a university, but may also be in Materials Science, Civil Engineering, or Mathematics departments. This approach largely neglects the atomic nature of material, which is more the domain of Materials Science or Applied Physics departments.

Fracture toughness is a material property that attempts to characterize the ability of material to resist propagation for an existing crack. This value is relatively high for ductile materials, such as metals (~ 20 *MPa*×*m*0.5 for aluminum), and is relatively low for brittle materials, such as glass (< 1 *MPa*×*m*0.5). This generally implies that a material with glass properties would experience brittle fracture prior to the onset of a plastic, permanent, deformation.

Stress is simply force per area. For example, your car tires are inflated to 30 pounds per square inch. The stress in materials is given the same units, but is usually much higher than the load applied to the surface. The same force applied over as small area creates a greater stress or pressure; think of the pressure created by a stiletto heel versus a regular shoe.

Estimates of fracture toughness for materials with such properties in general follow the results of surface energy models based on the amount of energy required to generate a free surface starting from the bulk material. Simply, one assumes that there is a crack of a certain size. Then, one may calculate the energy required to create new surfaces when the crack propagates. Rapid crack propagation that results in failure is known as fracture.

### Finite Element Analysis

Stress modeling would also help with calculating stresses concentrated at a tip of a crack for an estimate of an onset of crack propagation. Due to the fundamental nature of such stress field, both analytical and numerical models may be available for this engineering evaluation. Finite element analysis, FEA, is an example of numerical modeling. Fracture of glass generally occurs in a localized state of tension.

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