on Ductile Materials The maximum shear stress method of failure prediction

On ductile materials the maximum shear stress method

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on Ductile Materials The maximum shear stress method of failure prediction states that a ductile material begins to yield when the maximum shear stress in a load-carrying component exceeds that in a tensile-test specimen when yielding begins. A Mohr’s circle analysis for the uniaxial tension test, discussed in Section 4–7, shows that the maximum shear stress is one-half of the applied tensile stress. At yield, then, s sy = s y > 2. We use this approach in this book to estimate s sy . Then, for design, use τ max 6 τ d = s sy > N = 0.5 s y > N = s y > 2 N (5–15) The maximum shear stress method of failure prediction has been shown by experimentation to be somewhat con- servative for ductile materials subjected to a combination of normal and shear stresses. It is relatively easy to use and is often chosen by designers. For more precise analysis, the distortion energy method, discussed later, is preferred. 4. Endurance Strength Method for Repeated and Reversed Normal or Shear Stresses on Ductile Material Figure 5–12 shows the special case of repeated and reversed stresses. Note that the magnitudes of the stresses in the posi- tive and negative zones are equal, resulting in a zero mean stress. That is, for normal stresses, σ min = - σ max and σ m = 0 This is the same type of stress shown in Figure 5–2 and is the basis for the determination of the endurance strength of the material, s n . Also, the repeated stress makes the component subject to fatigue failure and stress concentration factors must be considered. Therefore, the design equation for this case is: K t σ max 6 σ d = s = n > N (5–16) Similarly, for reversed and repeated shearing stresses and using the maximum shear stress principle to obtain an esti- mate for the endurance strength in shear, s = sn = 0.5 s = n (estimate for endurance strength in shear) K t τ max 6 τ d = s = sn > N = 0.5 s = n > N (5–17) 5. Goodman Method for Fluctuating Stresses on Ductile Materials Explanation of the Goodman method is required before showing the final design equations used for this very im- portant case. It is perhaps the most-often used analysis for 1. Maximum Normal Stress Method for Uniaxial Static Stress on Brittle Materials The maximum normal stress theory states that a material will fracture when the maximum normal stress (either ten- sion or compression) exceeds the ultimate strength of the material as obtained from a standard tensile or compressive test. Its use is limited, namely for brittle materials under pure uniaxial static tension or compression. When applying this theory, any stress concentration factor at the region of interest should be applied to the computed stress because brittle materials do not yield and therefore cannot redistrib- ute the increased stress. The following equations apply the maximum normal stress theory to design. For tensile stress: K t σ 6 σ d = s ut > N (5–11) For compressive stress: K t σ 6 σ d = s uc > N (5–12) Note that many brittle materials such as gray cast iron have a significantly higher compressive strength than tensile strength. 2. Yield Strength Method for Uniaxial Static Normal
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