Yield Point: Definition, Characteristics, and Factors
The yield point is the point on a material’s stress-strain graph at which it stops deforming elastically and starts deforming plastically. During elastic deformation, the material will return to its original dimensions, but plastic deformation changes its shape permanently.
In many cases, the yield point on a stress-vs-strain curve can be identified as the point where linear deformation stops and the curve dips down again before rising to the ultimate tensile strength point. Some yield points are not obvious to the eye on a stress-strain graph. Therefore, the point is chosen using an industry convention. First, a 0.2% offset is added to all strain values on the linear part of the graph. That shifts the line slightly to the right. The spot where the new line and old curve intersect is the yield point. The temperature and strain rate of the material can affect the yield point in opposing ways. Strain hardening can also influence the yield point of metals. This article will discuss yield point, its key characteristics, applications, and the factors that affect it.
The yield point is a material property that describes the moment when a material stops deforming elastically and instead begins to permanently deform. Elastic behavior will see the material return to its original dimensions after a load is removed. The yield point of a material is usually determined using a tensile testing machine.
The yield point and the elastic limit are different characteristics but occupy very similar points on a stress-strain graph. Prior to its elastic limit, a material will not permanently deform. The yield point of a material is offset from that point by 0.2% in the strain (positive x) direction, meaning that usually, a material will have experienced a small amount of plastic deformation before reaching the yield point.
The stress-strain curve is a graphical representation of the amount of force applied per unit area against the extension of the material during a tensile test. The stress on the y-axis represents the force per cross-sectional area. The strain equates to the change in length divided by the original length. Most of the curve before the yield point is linear; this is the elastic region of deformation. After the yield point, the line will usually dip slightly and then continue upwards. From this point onwards, the material is plastically (permanently) deforming. For more information, see our guide on What is a Stress-Strain Curve?
Figure 1 below is an example of a stress-strain curve:
Image Credit: Shutterstock.com/Anshuman Rath
Sometimes a yield point is not obvious on a graph, so the yield point must be worked out using an equation. To do this, a parallel line must be offset from the linear elastic line. To work out the gradient of the line, calculate Young’s modulus (force/area divided by the change in length/original length). Now, with a known gradient, an offset of 0.002 can be added to the strain value. This will shift the linear line along the positive x-axis. The point at which the new 0.2% offset line and the original stress-strain curve intersect is the material’s yield point.
The yield point for a given material is not always the same in all cases. It can be influenced by three main factors:
- Strain Hardening: The strain-hardening process loads the raw material beyond its yield point so that it plastically deforms. After the load is removed, the elastic strain will recover, but the material will remain slightly deformed. The yield point will henceforth occur at the maximum stress previously applied, increasing the total stress the material can take without further plastic deformation. This technique is limited to use with metals and must be performed prior to the material’s installation or machining into the end product.
- Strain Rate: As the strain rate from a load increases, so does the yield point. This is because faster strain rates impart more elastic deformation.
- Temperature: The higher the temperature of the material, the more energy it has. More energy means its atoms have an easier time breaking the bonds with their neighbors and beginning to flow. On the macroscopic level, this translates into the material becoming softer, so it’s easier to reach the plastic deformation stage.
When a material surpasses its yield point, it will permanently deform. The region after the yield point is referred to as the plastic region or region of plastic deformation. Shortly after that, the material will reach its peak stress and, if the stress is tensile, begin to neck. The point of peak stress is the ultimate strength and necking is the reduction in cross-sectional area at some point along the material. After this point, more applied force will only cause it to neck further until it fractures completely.
The value of the yield point determines when a material behaves elastically and when it behaves plastically. We call those that fail shortly after their yield point brittle materials, whereas materials that fail long after their yield point are ductile materials. A material's resilience is its ability to deform elastically and therefore absorb energy without permanent damage. Materials with a low yield point are not considered resilient while materials such as rubber have a high resilience.
Every material type has its own yield point, and they vary as widely as any other mechanical property. Below are a few example materials and their yield strengths:
- A36 steel - 350 MPa
- Titanium 11 - 940 MPa
- Nylon - 45 MPa
- Diamond - 1600 MPa
- Polypropylene - 12-43 MPa
No, the yield point of a material cannot be predicted based on material properties. While the yield point is lower than the ultimate tensile stress, it is hard to accurately predict where it will fall for any given material from a theoretical basis. However, both compressive and tensile strength testing are well-established practices and aren’t particularly costly compared to other testing methods. Therefore, there’s rarely a need to predict yield strength through anything other than testing.
The yield point of a material is the transition between elastic and plastic deformation behavior. The ultimate tensile strength is the maximum amount of stress a material can experience. The yield point always precedes ultimate tensile strength. In fact, it’s often used as a marker for the maximum safe load. If yield strength is viewed as the part’s load limit, it will never reach its ultimate tensile strength and break through stress alone. For more information, see our guide on What is Tensile Strength?
By the time a material reaches its yield point, it has already experienced some amount of plastic deformation. The yield strength is the stress value associated with the yield point.
To find the yield point, we must first graph the material’s stress-strain curve. Then, we calculate Young’s modulus (which equals the slope of the graph’s linear portion). By offsetting the strain values of that linear slope by 0.002 (0.2%), we create a second parallel line to that linear portion. The point at which the new line intersects the true stress-strain curve is the yield point, and that point’s value on the stress axis (y-axis) is generally considered the material’s yield strength. For more information, see our guide on How to Calculate Yield Strength.
A material's yield point is critical for deciding the part's allowable mechanical load. The yield point can be used to:
- Choose an upper load limit so as to prevent failure.
- Determine a material's resilience.
- Predict the behavior of a material under load.
As the temperature of a material increases, its yield point will decrease. This is because heat adds energy to its internal molecular bonds. The energy makes the material softer and reduces the amount of external load necessary to plastically deform the material.
It is important to know the yield point of a material when designing a structure. Every material will behave differently after the yield point than it does before the yield point. The most notable difference is the permanent deformation of the material. If the yield point of a structure is exceeded, it will no longer have the same dimensions, even when the stress is released. Additionally, a brittle material (one that shows little deformation after the yield point) will fail with little or no warning after its yield point has been reached. Therefore, engineers typically prefer materials that can experience a large amount of strain after the yield point.
A material’s yield point can change, but not purely due to the passage of time. Other factors and influences on the material that parts may encounter during their useful lifetimes can alter the yield point. For example, as time passes, the temperature of the material can increase, which will decrease the yield point. Strain hardening can also occur, where a material exceeds its yield point by small amounts, creating a new higher yield point.
Yes, there are standards for measuring the yield point of materials. ISO 6892 or ASTM E8 are used for measuring the tensile strength and yield point of metals. Meanwhile, ISO 527 or ASTM D638 are used to measure the tensile strength of plastics and composites.
This article presented yield point, explained what it is, and discussed its various characteristics. To learn more about yield point, contact a Xometry representative.
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