Mechanical Behavior of Materials by Hosford, William F. | 9780521846707 | 0521846706

Mechanics of Materials

Mechanical Behavior of Materials

108 SOLVED PROBLEMS

Question: 7.4

Reconsider the tension test in example problem 5.3. Let n = 0.226 and m = 0.012 (typical values for low carbon steel) and let f = 0.98 as in the previous problem. Calculate the strain, εa, in the region with the larger diameter if the bar necks to a 25% reduction of area (εb = ln(4/3) = 0.288.) ...

Verified Answer:

Substituting into Equation (7.12),

\int_{0}...

Question: 7.3

A tensile bar is machined so that the diameter at one location is 1% smaller than that for the rest of the bar. The bar is tested at high temperature, so strain-hardening is negligible, but the strain-rate exponent is 0.25. When the strain in the reduced region is 0.20, what is the strain in the ...

Verified Answer:

f=(\pi D^{2}_{1}/4 )/ (\pi D^{2}_{2}/4 )=(...

Question: 7.1

The strain-rate dependence of a zinc alloy can be represented by Equation (7.1) with m = 0.07. What is the ratio of the flow stress at ε = 0.10 for a strain rate of 10³/s to that at ε = 0.10 for a strain rate of 10^−3/s? Repeat for a low carbon steel with m = 0.01. ...

Verified Answer:

For zinc (m = 0.07),

\sigma_{2}/\si...

Question: 6.7

Draw the three-dimensional Mohr’s circle diagrams for the stresses and plastic strains in a body loaded under plane-strain tension, εy = 0, with σz = 0. Assume the von Mises yield criterion. ...

Verified Answer:

From the flow rules,

\varepsilon _{y}=0= \l...

Question: 15.2

The amplitude of a vibrating member decreases so that the amplitude on the 100th cycle is 13% of the amplitude on the 1st cycle. Determine Λ. ...

Verified Answer:

\Lambda =\ln (e_{n}/e_{n+1} )

. Sin...

Question: 8.1

A tensile stress of σ = 5 kPa is applied parallel to the [432] direction of a cubic crystal. Find the shear stress, τ , on the (111) plane in the [011] direction. ...

Verified Answer:

First find

m= \cos \lambda \cos \phi [/late...

Question: 19.1

Predict the ratio of the Young’s moduli for NaCl and MgO, both of which have the rock salt structure. The radii of the ions Na^+ and Cl^− are 0.097 and 0.181 nm, respectively, and the radii of Mg^+2 and O^−2 are 0.066 and 0.140 nm, respectively. ...

Verified Answer:

Because both have the same structure, α is the sam...

Question: 6.2

Consider an isotropic material loaded so that the principal stresses coincide with the x, y, and z axes. Assuming the von Mises yield criterion applies, make a plot of σy versus σx yield locus with σz = 0. ...

Verified Answer:

Let

\sigma_{x} =\sigma_{1}

, [late...

Question: 6.1

Consider an isotropic material, loaded so that the principal stresses coincide with the x, y, and z axes of the material. Assume that the Tresca yield criterion applies. Make a plot of the combinations of σy versus σx that will cause yielding with σz = 0. ...

Verified Answer:

Divide the

\sigma_{y}

versus [late...

Question: 2.5

Derive expressions for the effective Young’s modulus and Poisson’s ratio for a cubic crystal stressed along the [112] direction. ...

Verified Answer:

Let x = [112]. The axes y and z must be normal to ...