Stiffness

It is defined as the ability of a material to resist deformation under stress. The resistance of a material to elastic deformation or deflection is called stiffness or rigidity.

Stiffness relates to how a component bends under load while still returning to its original shape once the load is removed. Since the component dimensions are unchanged after load is removed, stiffness is associated with elastic deformation.

A material can have high strength and low stiffness. If a metal cracks easily, it has low strength, but if it has low stiffness, it can deflect a high load.  The article  explains that stiffness depends on the modulus of elasticity, also known as Young’s Modulus, which is constant for a given metal. Because Young’s Modulus for steel is three times that of aluminum, an aluminum part under load will deflect three times as much as a similarly loaded steel part. The thickness and shape of the formed part also contributes to its stiffness.

All steel has approximately the same stiffness, but comes in many different strengths depending on the alloying metals used.  Stainless steel comes in more than 100 grades which are created by adding alloys such as chromium, silicon, nickel, carbon, nitrogen, and manganese to impart properties such as heat resistance, strength, flexibility, and ductility. Martensitic or semi-austenitic steels are the strongest due to the addition of elements such as aluminum, copper and niobium.

Steel starts out as flat sheet metal or plates and must be manufactured to precise thickness specifications depending on the application for which it is used. It must also be easily machinable so that it can be formed into its permanent shape without cracking. While strength is an advantage in many applications, adding strengthening alloys may contribute poor machinability, meaning the material is difficult to cut and wears down the tooling. Accurate thickness measurement of process-line steel ensures the finished products have specific mechanical properties, including the appropriate strength and stiffness for their application. An excellent way to accomplish this is by processing the material through a cold rolling mill. Cold rolling is a metal forming process in which a sheet of metal is pressed through a pair of rolls to reduce thickness, increase strength and improve surface finish. 

It is frequently necessary to determine how much a part will deform under load to ensure that excessive deformation does not destroy the usefulness of the part. This can occur at stresses well below the yield strength of the material, especially in very long members or in high-precision devices. Stiffness of a material is a function of its modulus of elasticity, sometimes called Young’s modulus:

This can be stated mathematically as :

Therefore, a material having a steeper slope on its stress–strain curve will be stiffer and will deform less under load than a material having a less steep slope. Figure illustrates this concept by showing the straight-line portions of the stress–strain curves for steel, titanium, aluminum, and magnesium. It can be seen that if two otherwise identical parts were made of steel and aluminum, respectively, the aluminum part would deform about three times as much when subjected to the same load.

The design of typical load-carrying members in machines and structures is such that the stress is below the proportional limit, that is, in the straight-line portion of the stress–strain curve. Here we define Hooke’s law:

Many of the formulas used for stress analysis are based on the assumption that Hooke’s law applies. This concept is also useful for experimental stress analysis techniques in which strain is measured at a point. The corresponding stress at the point can be computed from a variation of Equation:

σ = EԐ

This equation is valid only where strain occurs in only one direction. This is called uniaxial strain, and it applies to members subjected to axial tension or compression and to beams in pure bending. When stresses occur in two directions (biaxial stress), an additional effect of the second stress must be considered.

Flexural Strength and Flexural Modulus

Other stiffness and strength measures often reported, particularly for plastics, are called the flexural strength and flexural modulus. As the name implies, a specimen of the material is loaded as a beam in flexure (bending) with data taken and plotted for load versus deflection. From these data and from knowledge of the geometry of the specimen, stress and strain can be computed. The ratio of stress to strain is a measure of the flexural modulus. American Society for Testing and Materials (ASTM) standard D790* defines the complete method. Note that the values are significantly different from the tensile modulus because the stress pattern in the specimen is a combination of tension and compression. The data are useful for comparing the strength and stiffness of different materials when a load-carrying part is subjected to bending in service. ISO standard 178 describes a similar method for determining flexural properties.

Comparison of Specific Strength and Specific Stiffness for Selected Materials

Differencies Table of  among Young’s Modulus – Ultimate Tensile Strength – Yield Strength

• 1 Pa (N/m²) = 1×10^-6 N/mm² = 1.4504×10^-4 psi
•  1 MPa = 10⁶ Pa (N/m²) = 0.145×10³ psi (lb_f/in²) = 0.145 ksi
• 1 GPa = 10⁹ N/m² = 10⁶ N/cm²  = 10³ N/mm² = 0.145×10⁶ psi (lb_f/in²)
• 1 Mpsi = 10⁶ psi = 10³ ksi
  
• 1 psi (lb/in²) = 0.001 ksi = 144 psf (lb_f/ft²) = 6,894.8 Pa (N/m²) = 6.895×10^-3 N/mm²

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