When is something fragile?

Answer

In principle, every material is fragile.

Suppose you take a rod of a certain material. You try to stretch it and measure the elongation of the bar as a function of the pull. You will then obtain a figure as shown in the appendix.

In a first phase, if the tensile force is not too great, the elongation will be proportional to the tensile force. The slope of this line is the coefficient of elasticity of the material. A soft material will give a large deformation at a small force (little inclined line), a hard material will give a small deformation at the same force (strongly inclined curve). If you remove the force, the material will return to its original dimensions. This is the regime of the elastic deformation.

But for every material there comes a moment when the force becomes so great that permanent fractures/cracks occur in the material. One comes is the regime of plastic deformation. If you remove the force now, the material will not return to its original dimensions, but it will be permanently deformed (like a spring that you have pulled out too hard). Before you increase the force even further, there comes a point where the material breaks. This is the ultimate strength of the material.

All materials react more or less in this way, but the size of the areas can differ greatly.

Rubber, for example, has a large elastic area and then breaks almost immediately. Ceramic has a short elastic region before it breaks. A material such as chewing gum has a small elastic area and a large area of ​​plastic deformation.

So you need to reformulate your question from ‘what is fragile’ to ‘what is the breaking point of the material’. If your application has forces greater than the breaking point, the material is fragile for you.