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How to understand Section shrinkage

Choosing appropriate materials is an essential step in the product development process.

Although there are many material performance parameters, the main consideration is still the mechanical properties of the material, such as strength and hardness. Especially, "strength" is often the most important parameter involved in structural stress analysis and calculation.

Parameters like 'Section shrinkage', which seem insignificant, do not participate in the calculation, so (at least on the surface) this parameter does not seem to contribute much to product design.

In fact, the Section shrinkage is usually used as a reference indicator for designers to choose materials. For example, does the designer require the product to have a certain degree of ductility, and does the designer require that extreme cases of failure belong to brittle failure or plastic failure.

Similar to "Section shrinkage" A, "reduction in cross-sectional area" Z is also an indicator for determining the degree of plasticity of materials.

So the question is, since there are already indicators for judging the plasticity of materials, why do we need to start a new one and create a "cross-sectional shrinkage rate"? For example, if Zhu Di had already intended for Zhu Gaoxu to inherit the throne from the bottom of his heart, why did he choose to make Zhu Gaochi the crown prince? Is there nothing to do or is there another hidden reason?

The Section shrinkage is not perfect

Those familiar with material testing know that "Section shrinkage" refers to the ratio of the difference obtained by subtracting the original gauge length from the gauge length after the sample breaks to the original gauge length, that is:

A=(Lx-L0)/L0 formula 1

From this formula, it can be seen that when people use formula 1 to determine the plasticity of a material, the Section shrinkage only looks at the overall length change, and the shape of the sample when it is pulled apart is not at all concerned - no matter how it is broken, as long as the post fracture gauge length is long enough, then I think the plasticity of the material is good enough.

However, the problem lies precisely here.

From formula 1, we can also see that in addition to the post fracture gauge length Lx, the initial gauge length L0 is the benchmark parameter for calculating the post fracture elongation.

In other words, the Section shrinkage of the material and its plasticity depend on who it is compared to. From the perspective of Section shrinkage, it needs to be compared to the initial gauge length. So, this means that it is important to establish initial gauge length selection specifications.

For example, let my friends feel it.

Cut 1m and 10m steel bars from a 10mm diameter rod and pull them apart separately. Based on experience, both steel bars will experience necking and fracture at some point. Except for the fracture site, the cross-section of the steel bar in other areas will hardly change, as shown in Figure 2: the further away from the necking area, the smaller the degree of cross-sectional change, and it is precisely the size change of this necking area that is the main reason for the elongation of the component.

Figure 2: There is no significant change in diameter away from the necking area

This means that after the 1m long steel rod and the 10m long steel rod are each pulled apart, their elongation is almost the same - that is, (Lx-L0) is the same.

So the difference in Section shrinkage calculated based on formula 1 and their respective original lengths L0 is 10 times! For this reason, the relevant standards stipulate that the sample for calculating the Section shrinkage of materials must be processed according to the specified length - that is, the initial gauge length cannot be changed arbitrarily. For details, please refer to GB/T 228.1.

This also seems to imply that the Section shrinkage of materials is related to the size of the pattern. And this is not appropriate, because the strength, hardness, and even Section shrinkage that we are talking about should be inherent properties of the material and should not be related to size.

The above reasons are also why the Section shrinkage A is often required to indicate the length of the sample, for example, A5 refers to the gauge length of 5 times the diameter.

It can be seen that if the plasticity of materials is evaluated by the Section shrinkage, it is necessary to require that the size of the product is sufficient to process a certain length of pattern. This size limitation directly results in small-sized products being unable to determine whether the material plasticity meets the requirements by detecting the Section shrinkage.

The 'cross-sectional shrinkage rate' compensates for this deficiency.

The "cross-sectional shrinkage rate" is commendable

Figure 3 Determination of cross-sectional shrinkage rate

To calculate the cross-sectional shrinkage rate, the first step is to measure the original cross-sectional area A0 of the sample and the cross-sectional area Ax at the fracture site. After taking the difference between the two, compare A0, that is:

Z=(A0 Ax) A0 Formula 2

From this formula, it can be seen that the cross-sectional shrinkage rate of the material is not directly related to the length of the sample. In other words, no matter how long the style is, as long as the original cross-sectional area and the cross-sectional area at the fracture can be measured, the cross-sectional shrinkage rate can be calculated.

The 1m steel rod and 10m steel rod mentioned above have the same cross-sectional shrinkage rate due to the same changes in the necking area.

This also aligns with our understanding of material properties - the performance parameters of materials should be independent of component dimensions.

In addition, the shrinkage rate of the fracture section determines the change in the area of the fracture section, which makes up for the deficiency of only evaluating the plasticity of the material as a whole and ignoring the local deformation situation after fracture elongation. Engineers can use these two parameters to comprehensively judge the material properties.