In this blog post, we will examine the basic concepts of the “engineering stress-strain curve,” the difference between normal stress-strain and true stress-strain, and the material properties that can be determined from the curve.
Selecting materials for manufacturing products in industrial settings requires engineering knowledge. What would happen if, for example, a support bracket designed to hold an object broke too easily, or if a spring failed to return to its original shape after being stretched due to insufficient restoring force, leaving it permanently deformed? In such cases, we must immediately analyze the cause and find a better material. This can be prevented by selecting materials based on a mechanical understanding of them.
The most fundamental aspect of understanding any material mechanically is determining how much force it can withstand. To verify a material’s durability, after manufacturing the material, we conduct experiments to apply force and determine how much it can withstand, then plot the results on a graph. The most straightforward way to visualize this is through a stress-strain curve.
What are stress and strain? Stress refers to the force applied per unit area when a force is applied to a material, while strain refers to the ratio of “extended length ÷ initial length” when a material deforms under applied force. In a stress-strain curve, the x-axis represents strain and the y-axis represents stress. By plotting this graph, we can determine how a material deforms based on the force applied per unit area. Even for the same material, since it is used for various purposes in different sizes, the stress-strain curve addresses the need to plot different graphs depending on the size of the material specimen used in experiments by representing the degree of deformation based on the force per unit area.
There are two types of stress-strain curves. These are engineering stress-strain and true stress-strain. These curves are used to calculate stress and strain in order to analyze data collected while applying force to a material to induce deformation. However, as the material deforms, the area over which the force is applied (the basis for stress) and the original length (the basis for strain) continuously change. True stress-strain involves continuously calculating these values while accurately measuring the constantly changing cross-sectional area and original length. However, conducting an experiment while continuously determining these changing values is extremely difficult. Therefore, in many cases, the changes are ignored, and stress and strain are calculated based on the initial cross-sectional area and original length; this is referred to as engineering stress-strain.
The following graph shows a typical form of the conventional stress-strain curve. The initial blue linear section represents the region of elastic deformation. Elastic deformation refers to deformation in which the material returns to its original state after the applied force is removed. In this region, deformation occurs as force is applied, but since the bonds between atoms or molecules in the material remain intact, the material returns to its original state when the applied force is removed. The curved section that follows the blue straight line represents the region where plastic deformation occurs. Plastic deformation refers to deformation in which, as force is applied and significant deformation occurs, the existing bonds between atoms are broken and new bonds are formed, so that even if the force is removed, the material does not return to its initial state. If force is applied up to this point, both elastic and plastic deformation occur, and if the force is subsequently removed, the material will return to its original state only to the extent of the elastic deformation.
The graph increases within the curve and then begins to decrease after passing a certain point; this point where the stress is highest is called the ultimate tensile stress. It refers to the point with the highest stress, and once this point is exceeded, the material undergoes an irreversible deformation process and eventually breaks when it reaches the point marked with an “X.” (Imagine stretching a piece of taffy: the middle begins to thin out before it snaps.) In other words, the ultimate tensile stress represents the maximum stress a material can withstand. Furthermore, by drawing a perpendicular line from the point marked with an “X” to the x-axis and integrating the area beneath the curve, we can determine the force the material can withstand before breaking. This is called toughness. In addition, by examining the standard stress-strain curve, you can identify the regions of uniform deformation and non-uniform deformation (the region where deformation occurs throughout the entire material and the region where deformation occurs in specific areas subjected to higher stress due to notches or other defects), and obtain data such as the offset yielding stress, which marks the boundary between elastic and plastic deformation.
If you can understand the stress-strain curve, you can grasp the basic properties of the material at a glance, and accordingly, minimize trial and error to select the right material suited to the product and manufacture it. For example, copper deforms easily even under small forces but does not break easily; therefore, it is used in parts such as wires that require significant deformation but are not affected by strength. In contrast, iron has a lower strain rate than copper and does not break easily, so it is used as the framework for structures that require strong support. When researching how to create a material based on its required properties, utilizing such data is extremely helpful because it allows you to quickly and easily identify which aspects of the material you have created are lacking and need improvement.
