Definition of Yield Limit
Yield strength: It is the yield strength of a metallic material when it yields, that is, the tension that resists slight plastic deformation.
For metallic materials without obvious yielding, the stress value that produces 0.2% residual strain is specified as their yield strength, called the conditional yield strength or yield strength.
External forces exceeding this limit will cause permanent failure of the component and cannot be restored. For example, the yield strength of low carbon steel is 207 MPa.
When external forces greater than this limit are applied, the component will undergo permanent deformation. If it is less than this, the component will return to its original shape.
Importance of yield strength in materials science and engineering
The traditional strength design method considers the yield limit as a standard for plastic materials, with allowable stress (σ)=σys/n, where the safety factor n can vary from 1.1 to 2 or more, depending on the situation.
For brittle materials, the tensile strength is considered standard, with allowable stress (σ) = σb/n, and the safety factor n is generally taken as 6.
It should be noted that the traditional strength design method will inevitably lead to a one-sided pursuit of high yield strength for the material, but as the yield strength of the material increases, the fracture strength decreases and the risk of fracture increases .
The yield point not only has direct practical significance, but also serves as an approximate measure of some mechanical behavior and process performance of the material in engineering.
For example, as the yield strength of the material increases, it becomes more sensitive to stress corrosion cracking and hydrogen brittle fracture; as the yield strength decreases, the cold forming performance and welding performance improve, and so on.
Therefore, the yield point is an important and indispensable index in the performance of the material.
Basics of stress and deformation of materials
Concepts of stress and tension
Stress
When an object deforms due to external factors (forces, humidity, temperature changes, etc.), there are internal forces that interact between the different parts of the object. The internal force per unit area is called stress.
Those perpendicular to the cross section are called normal stress or axial stress, and those tangent to the cross section are called shear stress or shear stress.
Variety
Deformation refers to the relative deformation of an object under the action of external forces and non-uniform temperature fields, among other factors.
Relationship between stress and tension
According to Hooke's law, within a certain proportional limit range, stress and strain have a linear proportional relationship.
The corresponding maximum voltage is called the proportional limit.
The relationship between stress and strain, denoted by E, is called the modulus of elasticity or Young's modulus, and different materials have a fixed Young's modulus.
Although stress cannot be measured directly, it can be calculated by measuring the deformation caused by external forces.
Additional Information
Hooke's law is a basic law in the theory of mechanical elasticity, which states that solid materials have a linear relationship between stress and strain (unit strain) when subjected to tension.
Materials that satisfy Hooke's law are called linear elastics or Hooke's materials.
The expression of Hooke's law is F=k·x or ΔF=k·Δx, where k is a constant, the stiffness coefficient (stiffness) of the object.
In the International System of Units, the unit of F is Newton, the unit of x is meter, and is a deformation variable (elastic deformation), and the unit of k is Newton/meter.
The stiffness coefficient is numerically equal to the spring force when the spring is stretched (or shortened) by a unit length.
Types of stress and tension
What are the types of stress?
Normal stress: The stress component perpendicular to the cross section is called normal stress (or axial stress) and is denoted by σ.
Normal stress represents the stretching and compression between adjacent cross sections within the part.
Normal strain: Normal strain at a point is the elongation along the direction of normal force due to the normal stress distributed in the cross section in that direction.
Shear stress: The stress component tangential to the cross section is called shear stress or shear force, denoted by τ. Shear stress represents the sliding action between two parts.
Shear strain: Shear strain at a point is the change in angle between two perpendicular directions due to shear stress distributed in the cross section. It is also known as shear deformation.
What are the types of tension?
There are basically two types of deformation: linear deformation and angular deformation. Linear strain, also known as normal strain, is the ratio of the increase in length (positive when stretched) of a short line segment in a given direction to its original length.
Angular strain, also known as shear strain or shear strain, is the change in angle (positive when decreased) between two perpendicular line segments due to shear stress. It is expressed in radians.
Determining Yield Resistance
Stress-strain curve
The stress-strain curve diagram (σ-ε) is shown in Figure 3.
Instead of the axial load F, the nominal stress σ = F / A0 is considered, and instead of the extension Δl, the engineering deformation ε = Δl / l0 is considered.
The stress-strain curve still has four stages. The meanings of each characteristic point are:
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In the initial stretching (or compression) stage, the stress σ and the strain ε are linearly related up to point a.
At this point, the voltage value corresponding to point a is called proportional limit, represented by σp.
It is the maximum limit where stress and strain are proportional.
When σ≤σp, there is σ =Eε, also known as Hooke's law, which indicates that stress and strain are proportional.
Therefore, E =σ / ε = tanα, where E is known as modulus of elasticity or Young's modulus, with units equal to σ. When the voltage exceeds the proportional limit to reach point b, the σ-ε relationship deviates from a straight line.
If the stress is discharged to zero at this point, the strain will also disappear (once the stress exceeds point b, a part of the strain cannot be eliminated after discharge).
The stress defined at point b is called the elastic limit σe. σe is the ultimate limit value only for the elastic deformation of the material.
Bac stage:
After the stress exceeds the elastic limit, a phenomenon occurs in which the stress increases very little or not at all, and the deformation increases rapidly.
This phenomenon is called yielding. The point where the flow begins corresponds to the yield limit σs, also known as the yield limit.
In the yielding phase, the stress does not change while the deformation continues to increase, the material appears to have lost its ability to resist deformation, resulting in significant plastic deformation (if unloaded at this point, the deformation will not completely disappear, and there will be no residual deformation).
Therefore, σs is an important index to measure the strength of the material.
When a sample of low carbon steel yields with surface polishing, the surface will show streaks at an angle of 45° to the axis due to the relative slippage of the internal crystal lattice, known as slip lines.
Cae stage:
After passing through the yielding stage, if the sample continues to deform, it must be loaded further, the material appears to have strengthened, and the ce stage is the strengthening stage.
The highest point (point e) in the deformation strengthening step corresponds to the ultimate strength σb. Represents the maximum tension that the material can withstand.
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After passing through the point and, that is, after the tension reaches the resistance limit, the specimen undergoes a strong local contraction, known as narrowing.
Then, cracks occur inside the sample, the nominal stress σ decreases and the sample fractures at point f.
Yield strength (σs) and tensile strength (σb) are important indicators of the strength of materials with good plasticity (such as low-carbon steel).
It should be noted that nominal stress is used and the reduction in cross-sectional area that accompanies stretching deformation is not considered.
Tensile strength (σb) is just the nominal maximum stress that the material can withstand, not the actual maximum stress within the material.
If the actual area of the sample at the time of fracture is used to measure, the actual maximum stress is the stress value corresponding to point i on the line segment di in the figure.
In engineering practice, for reasons of simplicity, practicality and safety, tensile strength (σb) is still used to represent the maximum stress that the material can withstand.
However, when simulating the nonlinear mechanical behavior of materials with a computer, the actual stress-strain curve must be used.
Methods for determining yield strength
For metals without significant yield phenomenon, their tensile strength under prescribed non-proportional extension or residual tensile strain can be measured.
For metals with significant yield phenomenon, their yield strength, upper yield strength and lower yield strength can be measured.
There are two methods for measuring upper and lower yield strength: graphic method and pointer method.
Graphical Method
During the experiment, a jaw force displacement graph is drawn using an automatic recording device.
The proportion of the force axis with the tension represented by each millimeter must be less than 10 N/mm 2 and the curve must be drawn at least until the end of the yield stage.
In the curve, the constant force Fe during the flow, the maximum force Feh before the first decrease in force during the flow stage or the minimum force FeL before the initial instantaneous effect are determined.
Yield limit, upper yield limit and lower yield limit can be calculated using the following formulas:
Formula for calculating the yield limit: Re = Fe/So; Fe is the constant force during flow.
Formula for calculating the upper yield limit: Reh = Feh/So; Feh is the maximum force before the first decrease in force during the yield phase.
Formula for calculating the lower yield limit: ReL = FeL/So; FeL is the minimum force before the initial instantaneous effect.
Pointer method
During the experiment, when the pointer of the force meter stops rotating at the constant force or the maximum force before the first return or the minimum force before the initial instantaneous effect, they correspond to the yield strength, upper yield strength and yield strength lower, respectively.
Factors Affecting Yield Limit
The internal factors that affect the yield point are: bonding, microstructure, structure and atomic nature.
A comparison of the yield strength of metals with ceramics and polymers shows that the effect of bonding is fundamental.
In terms of the impact of microstructure, there are four strengthening mechanisms that affect the yield strength of metallic materials, which are:
(1) strengthening solid solutions;
(2) strain hardening;
(3) strengthening precipitation and strengthening dispersion;
(4) grain boundary and subgrain strengthening. Precipitation strengthening and fine-grained strengthening are the most commonly used means of improving the yield strength of industrial alloys.
Of these reinforcement mechanisms, the first three mechanisms increase the strength of the material while reducing plasticity.
Only refinement of grain and subgrain size can increase the strength and plasticity of the material.
The external factors that affect flow resistance are: temperature, strain rate and stress state.
As the temperature decreases and the strain rate increases, the yield strength of the material increases, especially body-centered cubic metals are particularly sensitive to temperature and strain rate, which leads to brittle fracture of steel at low temperature .
The influence of the state of stress is also important. Although the yield point reflects the inherent performance of a material, the value of the yield point is also different depending on the stress state.
The yield strength of a commonly referred material is generally the yield strength under uniaxial tension.
Common materials and their yield limits
| Steel Grade | Mechanical property | Chemical composition | ||||||||
| yield strength | tensile strength | stretching | W | Yes | Mn | s | P | |||
| MPa | kg/ mm2 | MPa | kg/ mm2 | mm | Less than or equal to. | Less than or equal to. | Less than or equal to. | |||
| Q215A Q215B |
215 | 22 | 335-410 | 3442 | 31 | 0.09-0.15 | 0.03 | 0.25-0.55 | 0.050 0.045 |
0.045 |
| Q235A Q235B Q235C Q235D |
235 | 24 | 375-460 | 38-47 | 26 | 0.14-0.22 0.12-0.20 ≤0.18 ≤0.17 |
0:30 | 0.30-0.65 0.30-0.70 0.35-0.80 0.35-0.80 |
0.5 0.45 0.40 0.035 |
0.045 0.045 0.040 0.035 |
| Mn (Q345B) |
345 | 35 | 510-600. | 51.60 | 22 | 0.12-0.200 | 0.20-0.55 | 1.2-1.6 | 0.045 | 0.045 |
Test Methods for Yield Resistance
The yield strength test is an important indicator of the material's strength characteristics and a critical indicator of the material's performance.
It is commonly used to evaluate material surface strength and plastic performance.
Yield resistance testing methods are generally divided into two types: mechanical and non-mechanical.
Mechanical yield strength test:
This method generally involves three-point bending, tensile testing machine method and compression method. The sample is placed between two supports and a constant force is applied using a mechanical device to determine the yield point.
Non-mechanical yield strength test:
This method usually involves tensile, compression and torsion methods. The sample is mounted on the test instrument and a constant force is applied using a lever or computer control to determine the yield point.
To improve the accuracy and precision of yield strength tests, it is generally necessary to perform multiple tests under the required conditions and obtain the average value.
In all experiments, sample treatment must be standardized and complete, and the sample must be held constant under the applied force. The ultimate yield strength obtained is the maximum strength at which the material can bend under the applied load.
Conclusion
Through studying this article, we learned what yield strength is, the basic principles of stress and strain, methods for determining yield strength, factors that affect yield strength, and applications of yield strength.
We hope this information is useful to everyone.
If there are any queries, feel free to let us know in the comments section.
