Tension and compression

Tension and Compression Arrangements. Vessel weighing configurations can be divided into tension and compression systems. 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

F is zero at the equilibrium point r = ro) however, if the atoms are pulled apart by distance (r - Tq) a resisting force appears. For small (r - Tq) the resisting force is proportional to (r - rg) for all materials, in both tension and compression. 

The apparent difference between the curves for tension and compression is due solely to the geometry of testing. If, instead of plotting load, we plot load divided by the actual area of the specimen, A, at any particular elongation or compression, the two curves become much more like one another. In other words, we simply plot true stress (see Chapter 3) as our vertical co-ordinate (Fig. 8.7). This method of plotting allows for the thinning of the material when pulled in tension, or the fattening of the material when compressed. 

But the two curves still do not exactly match, as Fig. 8.7 shows. The reason is a displacement of (for example) u = l f2 in tension and compression gives different strains) it represents a drawing out of the tensile specimen from 1q to 1.5 1q, but a squashing down of the compressive specimen from /q to 0.5/q. The material of the compressive specimen has thus undergone much more plastic deformation than the material in the tensile specimen, and can hardly be expected to be in the same state, or to show the same resistance to plastic deformation. The two conditions can be compared properly by taking small strain increments... 

The second failure mode to consider is fatigue. The drum will revolve about once every second, and each part of the shaft surface will go alternately into tension and compression. The maximum fatigue stress range (of 2 x 56 = 112 MPa) is, however, only a quarter of the fatigue limit for structural steel (Fig. 28.5) and the shaft should therefore last indefinitely. But what about the welds There are in fact a number of reasons for expecting them to have fatigue properties that are poorer than those of the parent steel (see Table 28.1). 

The data presented in Figure 19.7 were obtained on a Sonntag-Universal machine which flexes a beam in tension and compression. Whereas the acetal resin was subjected to stresses at 1800 cycles per minute at 75°F and at 100% RH, the nylons were cycled at only 1200 cycles per minute and had a moisture content of 2.5%. The polyethylene sample was also flexed at 1200 cycles per minute. Whilst the moisture content has not been found to be a significant factor it has been observed that the geometry of the test piece and, in particular, the presence of notches has a profound effect on the fatigue endurance limit. 

Complete stress-strain curve for tension and compression... 

Generally there is a stiffening effect in compression compared to tension. As a first approximation one could assume that tension and compression behaviour are the same. Thomas has shown that typically for PVC, the compression modulus is about 10% greater than the tensile modulus. However, one needs to be careful when comparing the experimental data because normally no account is taken of the changes in cross-sectional area during testing. In tension, the area will decrease so that the true stress will increase whereas in compression the opposite effect will occur. 

For a lamina stressed in its own plane, there are three fundamental strengths if the lamina has equal strengths in tension and compression ... 

If the material has different properties in tension and compression as do most composite materials, then the following strengths are required ... 

The foregoing example is but one of the difficulties encountered in analysis of orthotropic materials with different properties in tension and compression. The example is included to illustrate how basic information in principal material coordinates can be transformed to other useful coordinate directions, depending on the stress field under consideration. Such transformations are simply indications that the basic information. 

For each of the failure criteria, we will generate biaxial stresses by off-axis loading of a unidirectionally reinforced lamina. That is, the uniaxial off-axis stress at 0 to the fibers is transformed into biaxial stresses in the principal material coordinates as shown in Figure 2-35. From the stress-transformation equations in Figure 2-35, a uniaxial loading obviously cannot produce a state of mixed tension and compression in principal material coordinates. Thus, some other loading state must be applied to test any failure criterion against a condition of mixed tension and compression. 

Most comparisons of a failure criterion with failure data will be for the glass-epoxy data shown in Figure 2-36 as a function of off-axis angle 0 for both tension and compression loading [2-21]. The tension data are denoted by solid circles, and the compression data by solid squares. The tension data were obtained by use of dog-bone-shaped specimens, whereas the compression data were obtained by use of specimens with uniform rectangular cross sections. The shear strength for this glass-epoxy is 8 ksi (55 MPa) instead of the 6 ksi (41 MPa) in Table 2-3. 

To account for different strengths in tension and compression, Hoffman added linear terms to Hill s equation (the basis for the Tsai-Hill criterion) [2-23] ... 

Note for materials with equal strengths in tension and compression that P is 45° and the center of the ellipsoid is at the origin. 

A single failure criterion is used in all quadrants of o,-02 space instead of the segments in separate quadrants for the Tsai-Hill failure criterion because of different strengths in tension and compression. 

The terms that are linear in the stresses are useful in representing different strengths in tension and compression. The terms that are quadratic in the stresses are the more or less usual terms to represent an ellipsoid in stress space. However, the independent parameter F,2 is new and quite unlike the dependent coefficient 2H = 1/X in the Tsai-Hill failure criterion on the term involving interaction between normal stresses in the 1- and 2-directions. 

Robert M. Jones, Buckling of Stiffened Multilayered Circular Cylindrical Shells with Different Orthotropic Moduli in Tension and Compression, AtAA Journal, May 1971, pp. 917-923. 

Charles W. Bert, Models for Fibrous Composites with Different Properties in Tension and Compression, Journal of Engineering Materials and Technology, October 1977, pp. 344-349. 

The curves for 3M XP251S fiberglass-epoxy are shown in Figures C-1 through C-5 [C-1]. Curves are given for both tensile and compressive behavior of the direct stresses. Note that the behavior in the fiber direction is essentially linear in both tension and compression. Transverse to the fiber direction, the behavior is nearly linear in tension, but very nonlinear in compression. The shear stress-strain curve is highly nonlinear. The Poisson s ratios (not shown) are essentially constant with values v.,2 =. 25 and V21 =. 09. 

Just obtaining these cylinders does not setde the design. The manufacturer must verify that no cylinder interferences exist and that the rod loading in tension and compression is satisfactory. This design detail is handled by the manufacturer. The final design agreement should be by the manufacturer, as he should be responsible for the final quoted performance of the unit. 

For those not familiar with this type information recognize that the viscoelastic behavior of plastics shows that their deformations are dependent on such factors as the time under load and temperature conditions. Therefore, when structural (load bearing) plastic products are to be designed, it must be remembered that the standard equations that have been historically available for designing steel springs, beams, plates, cylinders, etc. have all been derived under the assumptions that (1) the strains are small, (2) the modulus is constant, (3) the strains are independent of the loading rate or history and are immediately reversible, (4) the material is isotropic, and (5) the material behaves in the same way in tension and compression. 

The stress-strain behavior of plastics in flexure generally follows from the behavior observed in tension and compression for either unreinforced or reinforced plastics. The flexural modulus of elasticity is nominally the average between the tension and compression moduli. The flexural yield point is generally that which is observed in tension, but this is not easily discerned, because the strain gradient in the flexural RP sample essentially eliminates any abrupt change in the flexural stress-strain relationship when the extreme fibers start to yield. 

The moduli of elasticity, G for shear and E for tension, are ratios of stress to strain as measured within the proportional limits of the material. Thus the modulus is really a measure of the rigidity for shear of a material or its stiffness in tension and compression. For shear or torsion, the modulus analogous to that for tension is called the shear modulus or the modulus of rigidity, or sometimes the transverse modulus. 

In simple beam-bending theory a number of assumptions must be made, namely that (1) the beam is initially straight, unstressed, and symmetrical (2) its proportional limit is not exceeded (3) Young s modulus for the material is the same in both tension and compression and (4) all deflections are small so that planar cross-sections remain planar before and after bending. The maximum stress... 

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