Ductility
http://en.wikipedia.org/wiki/Ductility
An object is said to be elastic if it has the ability to return to it's normal state after being stretched or squeezed. Flexibility on the other hand is the ability to bend easily without breaking.
The yield stress of tool steel is the amount of stress that a material can withstand without experiencing permanent deformation. The yield stress of a specific type of tool steel can vary depending on the specific composition and manufacturing process of the steel. In general, tool steels have high yield stresses, typically in the range of 1000 to 2000 megapascals (MPa). This allows them to withstand high levels of stress and strain without deforming permanently. For example, the yield stress of high-speed steel (HSS) can be in the range of 1500 to 2000 MPa, while the yield stress of cold-work tool steel can be in the range of 1200 to 1600 MPa. Overall, the yield stress of tool steel is an important property that determines the material's ability to withstand high levels of stress and strain without deforming permanently.
There are tables that give you the Tensile Strength based on a Rockwell Hardness test of a specimen of metal. For example: Rc of 54 is a Steel of TSU = 300,000 psi. Google the internet for Rockwell Hardness Table.
Wherever there is stress there is strain. In the example you noted, if heated bar expands freely without one end constained it changes its strain without stress; that strain is called eigenstrain. If the same bar is held rigidly then the eigenstrain resisted and you get stress and strain. So stress cannot exist without strain; but strain can exist without stress if it is eigenstrain.
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Ductility http://en.wikipedia.org/wiki/Ductility
That property of the substance is its "malleability".
Load-bearing capacity describes a structure's ability to support a load. It is the maximum load or force that a structure can withstand without collapsing or failing.
Ductility is a physical property.
Transparency is a physical property because it describes the ability of a material to transmit light without scattering. It is based on the interaction of light with the material's structure, rather than its chemical composition.
Ductility is a physical property of copper that describes its ability to be deformed or stretched without breaking, allowing it to be drawn into wires or reshaped into various forms. This property makes copper an ideal material for applications where flexibility and malleability are important.
This is a physical property because it describes a characteristic that can be observed without changing the composition of the substance. The ability of white phosphorus to glow in the dark is due to its property of emitting light when exposed to oxygen.
Ductility and malleability are two properties of metals that describe specific tendencies in certain metals. Ductility describes the property of the ability to stretch a metal, without being damaged. Highly ductile materials are useful for stretching into wires. Malleability describes the property of a metals ability to be deformed under compression. Highly malleable materials can be readily rolled or hammered into sheets. While these properties are similar, different materials react differently in these circumstances. Gold or copper for example, are both highly ductile and malleable, whilst lead is only malleable.
Ductility is a property of a material that describes its ability to deform under tensile stress without breaking. It is considered an intensive property because it does not depend on the amount or size of the material present, but rather on the inherent characteristic of the material itself.
Malleability is the property that describes the ability of a material to be hammered, rolled, or pressed into thin sheets without breaking. This property is often found in metals like gold and aluminum.
The ability of a substance to be hammered without breaking is called malleability. Substances that exhibit this property can be hammered or rolled into thin sheets without shattering. This property is common in metals like gold and copper.
extensibility