A line starts near the bottom-left of the graph, deviates, crests, and stops. This line describes how a test piece behaved under tension. The stress-strain curve does not only indicate the failure point; it describes when deformation is recoverable, when it becomes permanent, the magnitude of stress, and the extent of deformation before failure.
The vertical axis indicates stress, the applied force divided by the specimen’s original cross-sectional area. The horizontal axis denotes strain, the extension compared with the initial length. The definition is required; otherwise, specimens with different dimensions cannot be compared. The force and extension are not the same in every case. Before you proceed to analyze the stress-strain curve, read the title, units, scale, and axis labels carefully. Similar-looking graphs, plotted with different scales, can yield very different results.
Have a printed graph or draw one in your observation notebook. Mark and label the start of the test, the elastic behavior range, yield point or region, ultimate tensile strength, and fracture. Write a brief description beside each. This exercise makes the abstract graph more concrete and reminds you of the sequence of events. A common mistake is that the curve becomes nothing but jargon with no link to the actual deformation of the specimen.
The linear-elastic behavior is often close to an initial segment on a typical curve. The elastic behavior implies that the material will return to approximately its initial dimensions if the load is removed from the specimen. The elastic region has a slope; a steeper slope means a higher value for the elastic modulus. A steeper slope does not imply greater strength or toughness. The elastic moduli can vary widely among materials. A stiff ceramic material has a steep slope that is also brittle with relatively low strain at failure. A ductile, polymeric material has a smaller slope and can accommodate a much higher strain.
Some materials will have an onset of plastic deformation or yield point and a yield region. The curve deviates from linearity at these points. The yield strength is typically the engineering stress, at the yield point. Some materials do not yield, but plastic deformation is a distinct feature of the curve. Permanent deformation of a material or part implies that the internal structure has changed. This is true regardless of whether the structure of a material changes in terms of grains, dislocations, polymer chains, or other structural features. The yield strength is often the most important criterion. It means that a part does not permanently deform. A part that yields may also function as a part that has not reached failure. Consider a bracket that has permanently bent. It is not broken but it has failed.
The ultimate tensile strength is the maximum stress shown on a stress-strain graph. In most cases, the stress will increase after the point of yield or the yield point. Eventually, the maximum stress is reached. This peak point is the tensile strength of the material. The curve then declines or continues to fracture. When the strain increases, a part with ductility begins to neck. The cross-section locally starts to reduce. The curve continues as the cross-section is reduced. Fracture occurs at the end of the curve. The strain at fracture indicates the amount of deformation before failure.
The most obvious problem is to attempt to derive each material property from a point on a single curve. The initial slope corresponds with stiffness, the yield region is the onset of permanent deformation, the peak with the ultimate tensile strength, and the area beneath the curve is proportional to energy absorption and toughness. Temperature, testing speed, sample geometry, material history, and environmental conditions also can have an effect on a test result. Do not try to describe or identify the material before you first read the title, units, and axes. Determine the elastic and plastic regions, yield point, ultimate strength, and fracture strain. Then describe the deformation of a specimen from initial loading to complete failure.