Hello Ruqia Elghareeb,

there is generally an inverse relationship between yield strength and fracture toughness. Materials with high yield strengths tend to have low fracture toughness, while materials with low yield strengths tend to have high fracture toughness. This is because materials that are strong and stiff (i.e., have high yield strengths) are more resistant to deformation but are more brittle and prone to fracture under impact or sudden loads. Materials that are more ductile and have lower yield strengths are more resistant to brittle fracture, but are more prone to deformation under tensile loads.

I highly recommend that you read at least the Wikipedia article on the topic. It may be able to answer some of your initial questions.

https://en.wikipedia.org/wiki/Fracture_toughness

Sincerely,

Pavlo

Hello Ruqia Elghareeb,

The yield strength of a material is a measure of the amount of stress that a material can withstand before it begins to deform permanently, while fracture toughness is a measure of a material's resistance to crack propagation.

In general, materials with high yield strength tend to have lower fracture toughness, and vice versa. This is because as a material's yield strength increases, its ductility (ability to deform without breaking) decreases.

The relationship between the yield strength and fracture toughness is not linear, but the trend is that as the yield strength increases the fracture toughness decreases. This is due to the fact that as the yield strength increases, the material becomes more brittle and less able to absorb energy before cracking.

However, there are also cases where materials can have high yield strength and high fracture toughness, this is due to the fact that these materials have a high strength-to-toughness ratio.

In summary, there is a trade-off relationship between yield strength and fracture toughness, where a material with high yield strength may have lower fracture toughness and vice versa. However, it is not always the case, some materials can have high strength and toughness.