Fracture stress is only less than ultimate tensile strength in an engineering stress-strain diagram. This is because the material will experience a maximum stress before it undergoes necking. After necking, stress will decrease again until the material snaps.
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after ultimate tensile strength (UTS)
It is the ultimate strength of a material subjected to tensile loading. In other words, it is the maximum stress developed in a material in a tension test.
The greatest stress that a material can resist before breaking is called the ultimate tensile strength. It is the maximum amount of stress a material can withstand without breaking under tension. Different materials have different ultimate tensile strengths, and it is an important property to consider for designing and engineering structures.
No the moment of resistance is a defining parameter that can be used to calculate the stress in a cross section of a given material that is subject to flexural loading. The ultimate flexural strength is a numerical value of stress at which the material will crack, tear, rip etc. Think about ultimate tensile strength and the value of Young's Modulus. Young's Modulus is not defined at the point of 'necking' and therefore the ultimate tensile strength cannot be computed from Young's Modulus and Hook's Law, but the UTS is an empirically defined value.
Allowable stress would normally refer to design using Allowable Strength Design, also known as working strength design. In this the allowable stress is usually a fraction of the yield strength and can be different for uniform tension and bending. Typically mild steel has a yield strength of about fy=250MPa with allowable stresses in Tension, 0.6fy=150MPa Bending, 0.66fy=165MPa