Deadlines
(Insert Date) : Lab Testing to be Completed
(Insert Date) : Draft of Report Due.
(Insert Date) : Formal Report Due.

Summary
This lab will allow you to explore the various concepts of axial tension and compression on multiple specimens. Using an Instron testing machine, we will study the deformation and failure characteristics of a variety of materials under tensile and compressive loading. We will begin by obtaining a force-displacement curve for each material. Combining these curves with caliper measurements of the samples, you will be able to determine the modulus of elasticity (Young’s modulus), yield stress, ultimate tensile stress, ultimate compressive stress and ductility of each material. The figure to the right demonstrates the setup that we will be using for the tension section.

After gathering data and creating comprehensive plots using MatLab you will be charged with writing up a formal lab report. The report should present your findings in good detail and include outside information from veritable sources showing if your findings lie parallel with those of other sources. If there are discrepancies you must make a reasonable assertion as to why this is. The final section of the lab report requires that you closely examine one material of your choosing and explain some of its main uses and reasons for those uses backed up by quantitative and qualitative data.

Introduction to Concepts
The yield stress, ultimate tensile stress (UTS) and elastic (Young’s) modulus of a material can all be determined from the stress-strain curve for a given material, while a material’s ductility can be calculated as the change in cross-sectional area divided by the original cross-sectional area. Note that conventional stress-strain curves plot engineering stress, which is calculated as the applied force divided by the original cross-sectional area (as opposed to the true stress, which is found by dividing the applied load by the instantaneous cross-sectional area).

METALS:
The curve shown to the right is typical of most metals. At small strain values, the relationship between stress and strain is nearly linear, and the slope of the curve in this region is defined as the elastic modulus. Since many metals lack a sharp yield point (i.e. a sudden, observable transition between elastic and plastic deformation), the yield point is empirically defined as the stress that corresponds to 0.2% permanent plastic strain, which can be determined graphically by finding the intersection of the stress-strain curve with a line of slope equal to the elastic modulus passing through the strain axis at 0.2%. The ultimate tensile strength (UTS) is defined as the maximum stress which the material can withstand.

POLYMERS:
The stress-strain curve for a polymer (such as polyethylene or nylon) differs from that of a metal in both shape and magnitude. The most noticeable difference is that polymers typically reach strain values that are orders of magnitude higher than most metals. As such, the yield point and the ultimate tensile strength are both defined as the maximum stress which the material can withstand. The elastic modulus for a polymer is found in exactly the same manner as it is for a metal, although it is important to recognize that some polymers exhibit more nonlinear behavior in the elastic region.

When a specimen is loaded in uniaxial compression, the force acting over the cross-sectional area generates stress within the material. While the failure modes for tension and compression are often drastically different, the way in which the material deforms under relatively small compressive loads is similar to how it deforms in tension, as can be seen in the elastic region in Figure 1. However, beyond the elastic limit, many materials do not have a compressive limit, and will continue to deform up to the limits of the testing machine. Moreover, some materials (concrete and wood, for example) exhibit completely different behavior and have drastically different ultimate strengths under compressive loading.

FAILURE MODES:
When a ductile specimen is loaded in compression, the Poisson effect will result in an expansion of the cross section (similar to necking found in ductile tensile specimens). Failure of such ductile specimens can be difficult to quantify as the specimen slowly flattens out. In contrast, brittle materials may have a specific fracture point at which the material splits. In compression, the maximum stress is always experienced at failure. This is due in part to a packing effect that occurs. Whereas in tension, minute cracks in a specimen may grow as it is stretched, compressive forces will tend to close such cracks as neighboring material shifts to fill any voids. This packing effect delays failure and allows many materials to withstand significantly higher loads in compression. It is important to note that slender specimens (typically defined as a length-to-diameter ratio of more than than 3:1) will often buckle before reaching compressive failure. The graph above is similar to the graphs you will be creating in that it is a blending of tension and compression data.

ANISOTROPIC MATERIALS:
In contrast to isotropic materials, which have uniform properties in all directions, the material properties of anisotropic materials are dependent upon the orientation of the specimen. Some natural materials (e.g. wood) and many of today’s engineered composites (e.g. carbon fiber) are anisotropic. In particular, wood is primarily composed of long slender packets of cellulose (the “grain”), enclosed by void areas. The long, fibrous nature of the grain leads to very pronounced anisotropic behavior. To examine the anisotropic nature of wood, we will be testing two specimens (one which was cut along the grain, and a second which has been cut against the grain). For loading along the grain, some typical failure modes can be seen in Figure 2.

Procedure
As mentioned above the Instron Machine will be used to test material samples in both tension and compression. Before the materials can be tested however, they must be measured as using dial calipers. First measure the diameter of the sample, then measure its gage-length. Record this data as you will need it to complete the lab.

While you can use the Instron cross-head position measurement to get a decent estimate of strain, you will need more precise strain data during elastic deformation to accurately determine the Young’s modulus. For this purpose, you will use an instrument called an extensometer clip gauge.
The extensometer is a sensitive instrument with a limited range - you must remove it once you pass the material’s yield point.

The actual Instron will be used by a trained professional because it is a heavy piece of machinery that can cause serious harm.

Remove the sample from the machine and record the surface characteristics (color, texture, shape) at the fracture point. Make note of these observations for your report. In addition, note the nature of the plastic deformation in each material (i.e. necking, brittle fracture, extensive plastic flow, etc.). Finally, estimate the final cross-sectional area of each fracture surface and place the two halves of the sample together and estimate values for the final gage length.

Analysis
You will need to generate a stress-strain curve for each of your specimens, together with estimates of the yield stress, ultimate tensile strength, ultimate compressive strength, ductility, and elastic (Young’s) modulus. Note that the curves obtained from the Instron testing machines are load versus displacement curves (i.e. - you must convert these to stress and strain). As mentioned above, you must also compare the graphs you create in MatLab with those of a veritable source. Resources such as the Engineering Library and Google Scholar can help with this task.