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Yield strength refers to the stress at which a material begins to undergo macroscopic plastic deformation. For materials with a distinct yield phenomenon, the yield strength is the stress-value at the yield point ； For materials in which yield does not occur clearly, the stress-strain curve is typically used as a reference, with a certain level of residual deformation defined as the criterion; for example, the stress corresponding to 0.2% residual deformation is taken as the yield strength, denoted by σ0.2 or σys. Yield strength is commonly used as an indicator to evaluate the mechanical properties of solid materials, representing the actual limit of use for such materials. Image Image Image Internal factors affecting yield strength Image Image Image The internal factors that affect yield strength include: 1. The nature of the metal and its crystal structure — The yield strength of pure metal single crystals is determined by the resistance encountered during dislocation movement. These resistances can be divided into lattice resistance and the resistance arising from interactions between dislocations. Among them, the crystalline rigidity is related to the dislocation width and the Burgers vector, which in turn are related to the crystal structure. The resistances generated by interactions between dislocations include those resulting from interactions between parallel dislocations, and those resulting from interactions between moving dislocations and screw dislocations. Expressed in formula form: T=αGb/L, where α is the proportionality constant. Since density ρ is proportional to 1/L2, it follows that T=αGbρ1/2. Thus, as the density increases, the yield strength also increases. 2. Grain size and substructure — The effect of grain size is a reflection of the influence of grain boundaries; reducing the grain size increases the number of obstacles to dislocation movement and shortens the length of dislocation pile-ups within the grains, thereby increasing the yield strength. The relationship between the yield strength of many metals and alloys and grain size follows the Hall-Petch equation σs=σj+kyd-1/2, where σj represents the total resistance to the movement of dislocations in the matrix metal, also known as frictional resistance; this value is determined by the crystal structure and dislocation density ； ky is the pinning constant that measures the extent to which grain boundaries contribute to strengthening, or it represents the stress concentration factor at the ends of slip zones ； d is the average grain size. The role of subgrain boundaries is similar to that of grain boundaries, as they also hinder the movement of dislocations. 3. Solute elements — Incorporating solute atoms into pure metals to form interstitial or substitutional solid solution alloys significantly increases the yield strength; this is known as solid solution strengthening. This is mainly due to the different diameters of the solute atoms and solvent atoms, which results in the formation of a lattice distortion stress field around the solute. This stress field exerts interactions that hinder the movement of dislocations, thereby increasing the yield strength. 4. Phase two — engineering metallic materials, whose microstructure is generally multiphase. The influence of the second relative yield strength is closely related to whether the particle itself can deform during the yield deformation of the metal material. Based on this, second-phase particles can be divided into two categories: incompressible and compressible. According to the dislocation theory, dislocation lines can only bypass the inflexible second-phase particles; to do this, it is necessary to overcome the tensile stress of the bent dislocation. In metal materials with indeformable second-phase particles, the yield strength and flow stress are determined by the spacing between these second-phase particles. For deformable second-phase particles, dislocations can pass through them, causing them to deform together with the matrix, which also helps to increase the yield strength. The strengthening effect of the second phase is also related to factors such as its size, shape, quantity, and distribution, as well as the corresponding hardening properties of the strength and plasticity of the second phase and the matrix, the crystallographic compatibility between the two phases, and the interfacial energy. With the same volume ratio in the second phase, elongated particles significantly affect dislocation motion; therefore, metallic materials with such a microstructure exhibit a higher yield strength than those with spherical particles. In summary, yield strength, which represents the resistance of metals to minor plastic deformation, is a mechanical property that is highly sensitive to composition and microstructure. It is influenced by numerous internal factors, and changes in the alloy’s composition or heat treatment processes can result in significant variations in yield strength. Image Image Image External factors affecting yield strength Image Image Image 1. Temperature – Generally, an increase in temperature leads to a decrease in the yield strength of metal materials. However, depending on the crystal structure of the metal material, the trend of this change varies. For example, the yield strength of BCC metals exhibits a strong temperature effect. 2. Strain rate — During stretching, as the loading speed increases, the strain rate rises as well, and the strength of the metal material increases. This is mainly because every metal has its own propagation speed for plastic deformation; if the loading speed exceeds this plastic propagation speed, it will inevitably lead to an increase in the yield point. This is because the loading speed is too fast, resulting in insufficient rotation of the crystal planes in the direction of the external force; thus, sliding is hindered during the growth and expansion of the specimen, which macroscopically manifests as an increase in the resistance to initial plastic deformation. This is because, with the occurrence of strain hardening, the recovery that would spontaneously eliminate this hardening cannot take place, and strain hardening in turn hinders further deformation. Therefore, to achieve the desired residual deformation, it is necessary to continue applying external force, which is also reflected in an increase in the initial plastic deformation resistance. 3. Stress state — The stress state also plays an important role in influencing the yield strength of metal materials. The greater the shear stress component, the more favorable it is for the plastic deformation of the material, and thus the lower its yield strength. Therefore, the yield strength is lower in torsion than in tension, and it is lower in tension than in bending. The difference in yield strength under the same stress conditions is not due to changes in the material’s properties, but rather to differences in the mechanical behavior of the material under different conditions. The yield strength of materials, as we usually refer to it, generally denotes the yield strength under uniaxial tension.