**Maximum fiber stress.** Maximum tensile or compressive stress in a homogeneous flexure or torsion test specimen. For a specimen loaded as a simple beam at its midpoint, maximum fiber stress occurs at mid-span and may be calculated by the formula (for rectangular specimens): S=3PL/2bd2 where S is maximum fiber stress; P, load; L, span; b, width of the beam and d, depth of the beam. For a circular cross section member loaded in torsion, maximum fiber stress may be calculated by the following formula: S=Tr/J where T is twisting moment; r, original outer radius and J, polar moment of inertia of original cross section.

**Mean stress. **Algebraic difference between maximum and minimum stress in one cycle of fluctuating loading as in a fatigue test. Tensile stress is considered positive and compressive stress negative.

**Mechanical hysteresis.** Alternate term for elastic hysteresis.

**Microhardness.** Hardness of microscopic areas. Microhardness values differentiate hardness of constituents in a material.

**Minimum bend radius.** Minimum radius to which a sheet or wire can be bent to specified angle without failure.

**Modulus.** Alternate term for modulus of elasticity, often used in connection with rubber.

**Modulus in bending. **Ratio of maximum fiber stress to maximum strain with in elastic limit of stress-strain diagram obtained in flexure test. Alternate term is flexural modulus of elasticity.

**Modulus of elasticity.** Rate of change of strain as a function of stress. The slope of the straight line portion of a stress-strain diagram. Tangent modulus of elasticity is the slope of the stress-strain diagram at any point. Secant modulus of elasticity is stress divided by strain at any given value of stress or strain. It also is called stress strain ratio. Tangent and secant modulus of elasticity are equal up to the proportional limit of a material.

Depending on the type of loading represented by the stress-strain diagram, modulus of elasticity may be reported as compressive modulus of elasticity (or modulus of elasticity in compression), flexural modulus of elasticity (or modulus of elasticity in flexure), shear modulus of elasticity (or modulus of elasticity in shear), tensile modulus of elasticity (or modulus of elasticity in tension) or torsional modulus of elasticity (or modulus of elasticity in torsion). Modulus of elasticity may be determined by dynamic mechanical testing where it can be derived from complex modulus.

Modulus used alone generally refers to tensile modulus of elasticity. Shear modulus is almost always equal to torsional modulus and both are called modulus of rigidity. Moduli of elasticity in tension and compression are approximately equal and are known as Young’s modulus. Modulus of rigidity is related to Young’s modulus by the equation: E = 2G (1 + r) where E is Young’s modulus (psi), G is modulus of rigidity (psi) and r is Poisson’s ratio. Modulus of elasticity also is called elastic modulus and coefficient of elasticity.

**Modulus of rigidity. **Rate of change of strain as a function of stress in a specimen subjected to shear or torsion loading. It is the modulus of elasticity determined in a torsion test. Alternate terms are modulus of elasticity in torsion and modulus of elasticity in shear.

Apparent modulus of rigidity is a measure of the stiffness of plastics measured in a torsion test (ASTM D-1043). It is “apparent” because the specimen may be deflected past its proportional limit and the value calculated may not represent the true modulus of elasticity within the elastic limit of the material.

**Modulus of rupture.** Ultimate strength determined in a flexure or torsion test. In a flexure test, modulus of rupture in bending is the maximum fiber stress at failure. In a torsion test, modulus of rupture in torsion is the maximum shear stress in the extreme fiber of a circular member at failure. Alternate terms are flexural strength and torsional strength.

**Modulus of strain hardening.** Alternate term for rate of strain hardening.

**Monotron hardness.** Measure of indentation hardness. It is the load (kg) required to press a specified ball indentor to a specified depth. Indentors consist of 1 mm diamond (M-2), 1/16 in. tungsten carbide (M-3) and 2.5 mm tungsten carbide (M-4). Standard depth of indentation is 0.045 mm, but for hard materials depth of indentation may be limited is multiplied by 3.

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