Stress engineering

For a component subjected to a uniaxial force, the engineering stress, a, in the material is the applied force (tensile or compressive) divided by the original cross-sectional area. The engineering strain, e, in the material is the extension (or reduction in length) divided by the original length. In a perfectly elastic (Hookean) material the stress, a, is directly proportional to be strain, e, and the relationship may be written, for uniaxial stress and strain, as... 

Data analysis routines may change with time, and it is desirable to be able to reanalyze old data with new analysis software. Our tensile test analysis software creates plots of engineering stress as a function of engineering strain, as illustrated in Figure 3. Our flexure test software plots maximum fiber stress as a function of maximum fiber strain, with the option of including Poisson s ratio in the calculations. Both routines generate printed reports which present the test results in tabular form, as illustrated in Figure 4. 

The examples that we have shown here represent only a small fraction of all the variations possible, There is no such thing as a typical force versus elongation curve for polymers. Samples can break at extensions of only a fraction of a percent up to several thousand percent, with engineering stresses at break ranging from only slightly above zero up to more than 10 GPa,... 

It Is well known that mechanical properties of polymeric materials are greatly deteriorated by UV exposure (2-j)). The nature of this deterioration was determined using non-strained samples which were photooxidized at 37°C. Engineering stress-strain curves as a function of UV exposure are shown in Figure 1. The numbers next to each curve represent days of UV exposure. In terms of degradation, the points of interest are ... 

Figure 1. Engineering stress-strain curves as a function of time of UV exposure (numbers next to each curve represent days of exposure at 37°C)...

Engineering stress (right ordinate) and oxidation (left ordinate) as a function of strain for a given UV exposure (5 days at 37°C)... 

The engineering stress a defined as the force per unit undeformed area follows from Equation (15) as... 

The most convenient measure of the stress exhibited by an elongated elastomeric network is the nominal or engineering stress f = f/A, where f is the equilibrium value of the force and A is the cross-sectional area of the undeformed sample. 

Stress-Strain Data. Figure 1 shows the tensile data obtained on the LHT-240 elastomer at 30°C and at seven crosshead speeds from 0.02 to 20 inches per minute. The nominal or engineering stress a is plotted against... 

Figure 4 shows stress-strain curves measured at an extension rate of 94% per minute on the TIPA elastomer at 30°, —30°, and —40°C. With a decrease in temperature from 30° to -40°C, the ultimate elongation increases from 170% to 600%. The modulus Ecr(l), evaluated from a one-minute stress-strain isochrone, obtained from plots like shown in Figure 1, increases from 1.29 MPa at 30°C to only 1.95 MPa at —40°C. This small increase in the modulus and the large increase in the engineering stress and elongation at fracture results from viscoelastic processes. 

If the cross-sectional area is that of the original undeformed specimen, this is the engineering stress. If the area is continuously monitored or known... 

Engineering resins, 20 56 Engineering strain, 13 473, 482 Engineering stress, 13 473 Engineering surfaces, 15 204 Engineering system of dimensions,... 

The integral U((7m) represents the area under the engineering stress-strain master curve up to the maximum stress (7. The static stress is a function of the energy density function U([Pg.18]

Figure 7.3a-c Effect of LTB on the engineering stress in potato samples, (a) Engineering stress in blanched potato samples, (b) Engineering stress in blanched-and-cooked potato samples, (c) Engineering stress in blanched-frozen-and-cooked potato samples. 

Figure 7.15a-d Engineering stress and PME activity response surfaces and contour plots as functions of blanching temperature and time, (a) Engineering stress response surface, (b) Engineering stress contour plot, (c) PME activity response surface, (d) PME activity contour plot. 

Figure 5.25 Comparison of engineering stress-engineering strain and true stress-true strain plots. Reprinted, by permission, from J. F. Shackelford, Introduction to Materials Science for Engineers, 5th ed., p. 192. Copyright 2000 by Prentice HaU, Inc.

Persons 1, 3 Determine the engineering stress. Use this value and the engineering strain to estimate the elastic modulus. 

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

Note that here af are referred to unit area of the undeformed body. Such stresses are called engineering stresses. Eq. (2) is equivalent to a ret of relations ... 

It should be noted that the stresses usually used are engineering stresses calculated from the ratio of force and original cross section area whereas true stress is the ratio of the force and the actual cross sectional area at that deformation. Clearly, the relationship between stress and strain depends on the definition of stress used and taking the case of tensile strain, for example, the true stress is equal to the engineering stress multiplied by the extension ratio. 

At any point during the test, calculate engineering stress (oeng) and engineering strain (eeng) from the force/deformation data set or plot ... 

For large deformations (e.g., d > 25% Peleg, 1985), convert engineering stress and strain to true stress (CJh) and Henky strain (eh) as follows ... 

Determine sample strength by measuring the stress at failure (of). To do this, determine the force at failure via a force/deformation plot (see Figure H2.1.1) and convert force to either engineering stress or true stress. Also use deformation at failure (d) to calculate the strain at failure (ef). 

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