Stability is well understood, the ability to maintain or restore the original balance form under force. For example, the thin rod under pressure suddenly bends, the load-bearing thin-walled member folds, or the column of a building collapses. Today I will mainly talk about the understanding of stiffness and strength.
1. Strength
Definition: The ability of a component or part to resist damage (fracture) or significant deformation under external force.
Extract keywords, break, and deform significantly.
For example, Sun Yue used the ipad as a weight scale, and when he stood up, the ipad screen was cracked, which was insufficient strength. For example, in Wuhan every summer when watching the sea, many large branches are broken by the wind, which is not strong enough.
Strength is a parameter that reflects the failure of a material such as fracture. Strength generally includes tensile strength, compressive strength, etc., which is the amount of material damage when the stress reaches, and the strength unit is generally MPa.
Brittle fracture: Sudden fracture that occurs without significant plastic deformation. Such as the fracture of cast iron specimens along the cross-section during stretching and the fracture of round section cast iron specimens along the oblique section during torsion.
Shaping yield: The material produces significant plastic deformation and the component loses its ability to work. For example, a low-carbon steel sample will undergo significant plastic deformation when stretched or twisted.
1. Maximum tensile stress theory:
As long as the maximum tensile stress σ1 at a point in the component reaches the ultimate stress σb under the unidirectional stress state, the material will undergo brittle fracture. Therefore, the condition for brittle fracture failure of the component in the complex stress state at the dangerous point is: σ1=σb.
Therefore, the strength condition established according to the first strength theory is: σ1≤[σ].
2. Maximum tensile strain theory:
As long as the maximum tensile strain ε1 reaches the limit value εu in the unidirectional stress state, the material will undergo brittle fracture failure. ε1=σu;
From the generalized Hooke’s law: ε1=[σ1-u(σ2+σ3)]/E, so σ1-u(σ2+σ3)=σb.
The strength condition established according to the second strength theory is: σ1-u(σ2+σ3)≤[σ].
3. Maximum shear stress theory:
As long as the maximum shear stress τmax reaches the ultimate shear stress τ0 in the unidirectional stress state, the material will yield failure. τmax=τ0.
According to the stress formula on the oblique section of axial tension, τ0=σs/2 (σs—the normal stress on the cross section) is obtained by the formula: τmax=(σ1-σ3)/2. So the failure condition is rewritten as σ1-σ3=σs.
The strength condition according to the third strength theory is: σ1-σ3≤[σ].
4. Shape change specific energy theory:
As long as the shape change ratio at a point in the component can reach the limit value under the unidirectional stress state, the material will yield failure.
Therefore, the strength conditions according to the fourth strength theory are:
sqrt(σ1^2+σ2^2+σ3^2-σ1σ2-σ2σ3-σ3σ1)<[σ].
2. Stiffness
Definition: refers to the ability of a component or part to resist elastic deformation or displacement under external force, that is, elastic deformation or the only thing that should not exceed the scope allowed by the project.
Stiffness is a parameter that reflects the relationship between structural deformation and force, that is, how much deformation is generated by how much force the structure is subjected to. Simply put, it is a spring. The stiffness of the spring is divided by the tensile force and the extension. The unit of stiffness is generally N/m.
Stiffness type:
When the applied load is a constant load, it is called static stiffness; when it is an alternating load, it is called dynamic stiffness. The static stiffness mainly includes structural stiffness and contact stiffness. Structural stiffness refers to the stiffness of the component itself, mainly including bending stiffness and torsional stiffness.
1. Bending stiffness: calculated as follows:
Where P-static load (N); δ-elastic deformation in the load direction (μm).
2. The torsional stiffness is calculated as follows:
In the formula, M——acting torque (N·m); L——distance from the torque acting position to the fixed end (m); θ——torsion angle (°)