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In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line.
In fracture mechanics, the energy release rate, , is the rate at which energy is transformed as a material undergoes fracture.Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, [1] [2] and is thus expressed in terms of energy per unit area.
Strain energy release rate per unit fracture surface area is calculated by J-integral method which is a contour path integral around the crack tip where the path begins and ends on either crack surfaces. J-toughness value signifies the resistance of the material in terms of amount of stress energy required for a crack to grow.
The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
A C is the area in compression A T is the area in tension y C, y T are the distances from the PNA to their centroids. Plastic section modulus and elastic section modulus can be related by a shape factor k: = = This is an indication of a section's capacity beyond the yield strength of material.
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TTT diagram of isothermal transformations of a hypoeutectoid carbon steel; showing the main components obtained when cooling the steel and its relation with the Fe-C phase diagram of carbon steels. Austenite is slightly undercooled when quenched below Eutectoid temperature. When given more time, stable microconstituents can form: ferrite and ...
The stress intensity factor at the crack tip of a compact tension specimen is [4] = [() / / + / / + /] where is the applied load, is the thickness of the specimen, is the crack length, and is the effective width of the specimen being the distance between the centreline of the holes and the backface of the coupon.