Materials General Properties
Mechanics of materials, also called strength of materials is a subject which deals with the behaviour of objects withstanding stresses and strains.
The study of strength of materials often refers to various methods of calculating stresses in structural members, such as beams, columns and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes may take into account various properties of the materials other than material yield strength and ultimate strength; for example, failure by buckling is dependent on material stiffness and thus Young's Modulus.
In materials science, the strength of a material is its ability to withstand an applied stress without failure. The field of strength of materials deals with loads, deformations and the forces acting on a material. A load applied to a mechanical member will induce internal forces within the member called stresses. The stresses acting on the material cause deformation of the material. Deformation of the material is called strain, while the intensity of the internal forces is called stress. The applied stress may be tensile, compressive, or shear. The strength of any material relies on three different types of analytical method: strength, stiffness and stability, where strength refers to the load carrying capacity, stiffness refers to the deformation or elongation, and stability refers to the ability to maintain its initial configuration. Material yield strength refers to the point on the engineering stress-strain curve (as opposed to true stress-strain curve) beyond which the material experiences deformations that will not be completely reversed upon removal of the loading. The ultimate strength refers to the point on the engineering stress-strain curve corresponding to the stress that produces fracture.
Types of loadings
1. Transverse loading - Forces applied perpendicular to the longitudinal axis of a member. Transverse loading causes the member to bend and deflect from its original position, with internal tensile and compressive strains accompanying the change in curvature of the member. Transverse loading also induces shear forces that cause shear deformation of the material and increase the transverse deflection of the member.
2. Axial loading - The applied forces are collinear with the longitudinal axis of the member. The forces cause the member to either stretch or shorten.
3. Torsional loading - Twisting action caused by a pair of externally applied equal and oppositely directed force couples acting on parallel planes or by a single external couple applied to a member that has one end fixed against rotation.
Stress terms
A material being loaded in a) compression, b) tension, c) shear.
Uniaxial stress is expressed by
where F is the force [N] acting on an area A [m2]. The area can be the undeformed area or the deformed area, depending on whether engineering stress or true stress is of interest.
1. Compressive stress (or compression) is the stress state caused by an applied load that acts to reduce the length of the material (compression member) in the axis of the applied load, in other words stress state caused by squeezing the material. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than their tensile strength. However, structures loaded in compression are subject to additional failure modes dependent on geometry, such as buckling.
2. Tensile stress is the stress state caused by an applied load that tends to elongate the material in the axis of the applied load, in other words the stress caused by pulling the material. The strength of structures of equal cross sectional area loaded in tension is independent of shape of the cross section. Materials loaded in tension are susceptible to stress concentrations such as material defects or abrupt changes in geometry. However, materials exhibiting ductile behaviour (most metals for example) can tolerate some defects while brittle materials (such as ceramics) can fail well below their ultimate material strength.
3. Shear stress is the stress state caused by a pair of the built energy by opposing forces acting along parallel lines of action through the material, in other words the stress caused by faces of the material sliding relative to one another. An example is cutting paper with scissors or stresses due to torsional loading.
Strength terms
1. Yield strength is the lowest stress that produces a permanent deformation in a material. In some materials, like aluminium alloys, the point of yielding is difficult to identify, thus it is usually defined as the stress required to cause 0.2% plastic strain. This is called a 0.2% proof stress.
2. Compressive strength is a limit state of compressive stress that leads to failure in the manner of ductile failure (infinite theoretical yield) or brittle failure (rupture as the result of crack propagation, or sliding along a weak plane - see shear strength).
3. Tensile strength or ultimate tensile strength is a limit state of tensile stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of that failure, some hardening in the second stage and breakage after a possible "neck" formation) or brittle failure (sudden breaking in two or more pieces at a low stress state). Tensile strength can be quoted as either true stress or engineering stress.
4. Fatigue strength is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Fatigue strength is quoted as stress amplitude or stress range 
, usually at zero mean stress, along with the number of cycles to failure under that condition of stress.
5. Impact strength is the capability of the material to withstand a suddenly applied load and is expressed in terms of energy. Often measured with the Izod impact strength test or Charpy impact test, both of which measure the impact energy required to fracture a sample. Volume, modulus of elasticity, distribution of forces, and yield strength effect the impact strength of a material. In order for a material or object to have higher impact strength the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and high material yield strength.
Strain (deformation) terms
1. Deformation of the material is the change in geometry created when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc.). Deformation is expressed by the displacement field of the material.
2. Strain or reduced deformation is a mathematical term that expresses the trend of the deformation change among the material field. Strain is the deformation per unit length. In the case of uniaxial loading - displacements of a specimen (for example a bar element) strain is expressed as the quotient of the displacement and the length of the specimen. For 3D displacement fields it is expressed as derivatives of displacement functions in terms of a second order tensor (with 6 independent elements).
3. Deflection is a term to describe the magnitude to which a structural element bends under a load.
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