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Chapter 6: Problem 54

Cite five factors that lead to scatter in measured material properties.

Short Answer

Expert verified
Answer: The five factors that may contribute to scatter in measured material properties are material inhomogeneity, testing conditions, testing method, material anisotropy, and sample size and statistics.

Step by step solution

01

Factor 1: Material Inhomogeneity

Material inhomogeneity refers to the varying composition, structure, or physical properties of a material at different locations. This can be caused by the manufacturing process, defects, or impurities. Inhomogeneous materials can exhibit scatter in measured properties because the properties will vary depending on where the measurements are taken.
02

Factor 2: Testing Conditions

The conditions under which material properties are measured can also introduce scatter in the results. Factors such as temperature, humidity, and atmosphere can affect the material properties being measured. To minimize this type of scatter, testing should ideally be performed under standardized and controlled conditions.
03

Factor 3: Testing Method

The testing method itself may introduce scatter in measured properties due to the inherent limitations or variability of the method. This includes the sensitivity and accuracy of the testing equipment, human error, or differences in applied force, pressure, or strain. It is essential to understand the limitations of the testing methods and account for any potential sources of error.
04

Factor 4: Material Anisotropy

Anisotropic materials possess different properties when measured along different axes. For example, the mechanical strength of a composite material might be stronger along the direction of the fibers compared to perpendicular to them. When testing anisotropic materials, the measured properties may show scatter if the test samples have different orientations compared to one another.
05

Factor 5: Sample Size and Statistics

Finally, the sample size and statistical methods used in testing may also introduce scatter in measured properties. A larger sample size may provide more accurate data, while smaller sample sizes are more likely to be subjected to higher variability. Additionally, the choice of statistical methodology for analyzing the data can influence the amount of scatter observed. It is crucial to select appropriate sample sizes and statistical methods to minimize scatter in measured material properties.

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Most popular questions from this chapter

A steel bar \(100 \mathrm{~mm}\) (4.0 in.) long and having a square cross section \(20 \mathrm{~mm}(0.8 \mathrm{in} .)\) on an edge is pulled in tension with a load of 89,000 \(\mathrm{N}\left(20,000 \mathrm{lb}_{\mathrm{f}}\right)\) and experiences an elongation of \(0.10 \mathrm{~mm}\left(4.0 \times 10^{-3}\right.\) in.). Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel.

Using the data in Problem \(6.29\) and Equations 6.15, 6.16, and 6.18a, generate a true stress-true strain plot for aluminum. Equation \(6.18\) a becomes invalid past the point at which necking begins; therefore, measured diameters are given in the following table for the last four data points, which should be used in true stress computations. $$ \begin{array}{cccccc} \hline \text {Load} & & \text {Length} & & \text {Diameter} \\ \hline \boldsymbol{N} & \boldsymbol{l b}_{f} & \boldsymbol{m m} & \text { in. } & {\boldsymbol{m m}} & \text { in. } \\ \hline 46,100 & 10,400 & 56.896 & 2.240 & 11.71 & 0.461 \\ 44,800 & 10,100 & 57.658 & 2.270 & 11.26 & 0.443 \\ 42,600 & 9,600 & 58.420 & 2.300 & 10.62 & 0.418 \\ 36,400 & 8,200 & 59.182 & 2.330 & 9.40 & 0.370 \\ \hline \end{array} $$

A cylindrical specimen of aluminum having a diameter of \(19 \mathrm{~mm}\) (0.75 in.) and length of 200 \(\mathrm{mm}(8.0 \mathrm{in}\).) is deformed elastically in tension with a force of \(48,800 \mathrm{~N}\left(11,000 \mathrm{lb}_{\mathrm{f}}\right)\). Using the data in Table 6.1, determine the following: (a) The amount by which this specimen will elongate in the direction of the applied stress. (b) The change in diameter of the specimen, Will the diameter increase or decrease?

A cylindrical rod \(380 \mathrm{~mm}\) (15.0 in.) long, having a diameter of \(10.0 \mathrm{~mm}(0.40\) in.), is to be subjected to a tensile load. If the rod is to experience neither plastic deformation nor an elongation of more than \(0.9 \mathrm{~mm}(0.035\) in.) when the applied load is \(24,500 \mathrm{~N}\left(5500 \mathrm{lb}_{\mathrm{f}}\right)\), which of the four metals or alloys listed in the following table are possible candidates? Justify your choice(s). $$ \begin{array}{lccc} \hline & \begin{array}{c} \text { Modulus } \\ \text { Material } \end{array} & \begin{array}{c} \text { \mathrm{ Yield } } \\ \text { of Elasticity } \\ \text { Strength } \\ \text { (GPa) } \end{array} & \begin{array}{c} \text { Tensile } \\ \text { Strength } \\ \text { (MPa) } \end{array} & \begin{array}{c} \text { (MPa) } \end{array} \\ \hline \text { Aluminum alloy } & 70 & 255 & 420 \\ \text { Brass alloy } & 100 & 345 & 420 \\ \text { Copper } & 110 & 250 & 290 \\ \text { Steel alloy } & 207 & 450 & 550 \\ \hline \end{array} $$

As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic; that is, they are dependent on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a general \([u v w]\) direction, \(E_{u v w}\), is described by the relationship $$ \begin{gathered} \frac{1}{E_{u v w}}=\frac{1}{E_{(100}}-3\left(\frac{1}{E_{(100}}-\frac{1}{E_{(111)}}\right) \\\ \left(\alpha^{2} \beta^{2}+\beta^{2} \gamma^{2}+\gamma^{2} \alpha^{2}\right) \end{gathered} $$ where \(E_{100}\) and \(E_{(111)}\) are the moduli of elasticity in \([100]\) and [111] directions, respectively; \(\alpha, \beta\), and \(\gamma\) are the cosines of the angles between \([u v w]\) and the respective \([100],[010]\), and [001] directions. Verify that the \(E_{\langle 110\rangle}\) values for aluminum, copper, and iron in Table \(3.3\) are correct.
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