Last time, we discussed theories that encompass destruction.
This time, we will consider destruction in more detail, looking at various cases of destruction.
After briefly explaining the general types of destruction, I will provide detailed explanations for each case.
General types of destruction
Destruction can be broadly divided into two types: instant destruction and fatigue destruction.
While creep fracture and brittle fracture are also phenomena that should be discussed here, we will cover them in detail on a separate page.
One-shot destruction, as the name suggests, is a phenomenon where something breaks instantly when a load is applied.That is the matter.
Fatigue failure occurs when a certain load is repeatedly applied and then removed, and the material fails after a certain number of cycles.
This time, let's consider a one-shot destruction (we'll explain fatigue failure in detail later).
One-shot destruction can take the form of the following type, as shown in the diagram below.
Broadly speakingThere are only two types: tensile and shear failure..
Regarding failure due to bending (beam deflection, buckling of long columns), the internal forces can be broken down into three components: tensile force, compressive force, and shear force. Therefore, the failure will ultimately be either tensile or shear failure.
Up to this point, we haven't discussed failure due to compressive force, but in fact, pure compression does not cause material failure. However, compression does cause deformation, so the relationship between compressive stress and strain will be explained on a separate page.
In reality, even if something doesn't break under compression, it mostly breaks due to buckling, which ultimately leads to shear failure.
That concludes our introduction to the main lineup of one-shot destroyers.
This time, let's take a closer look at tensile failure, which is a fundamental concept.
Tensile test (stress-strain diagram)
Tensile failure is simply failure caused by tensile force.It simply means that it breaks due to tensile stress caused by a tensile load.
To review, let's look at the stress-strain diagram.
This refers to a graph where a tensile test specimen, as defined by JIS (Japanese Industrial Standards), is pulled, with strain ε on the horizontal axis and tensile stress on the vertical axis.
I want you to remember,There is an elastic region that follows Hooke's Law, and the limiting point of this region is the yield point (yield stress).It is called.
As distortion increases, the Lüders region becomes jagged.There is.
As the distortion increases further...It enters the plastic region (it does not return to its original shape), reaches the maximum tensile stress (tensile strength, fracture stress), and then fractures.To do.
In the plastic regionA distortion that cannot be corrected and remains unchanged is called a permanent distortion, while a distortion that can be corrected and remains unchanged is called an elastic distortion.This is called [a specific term]. If we increase the strain again, the stress returns to its original value in a straight line (linear function) obtained by multiplying the elastic strain by a coefficient, and from there it follows a stress-strain diagram.
As previously mentioned, the basic principle is to design within the elastic region (below the yield point).
Furthermore, the stress-strain diagram shown is for ductile iron (steel); the shape of the stress-strain diagram will differ depending on the material.
Depending on the materialSome materials do not have a clearly defined elastic region, and in such cases, it was stated that the 0.2% yield point, where 0.2% permanent strain remains, should be considered as the hypothetical yield point of the elastic region during the design process.
This is a complete review.
Next, let's take a closer look at the Lüdus region, the plastic region, and the tensile strength beyond the elastic region.
Deformation of tensile test specimens beyond the Lüders region
Now, let's go back to the tensile test specimen from the graph and see what's happening to the object.
Lüders Domain
The Lyudus region is a curious area where the strain increases on the graph, but the tensile stress does not increase.
Let's consider what's actually happening.
The strain is increasing, so the test specimen is deforming.
A closer look at the extended portion of the component reveals the following diagram.
What's interesting here is that even within the same cross-section, the amount of elongation is not uniform but varies from place to place.
The reason is that the deformation due to elastic deformation and deformation due to dislocations (plastic deformation) become mixed together.
Elastic deformation is small because the amount of deformation is proportional to the strain (linear deformation with respect to strain), while deformation due to dislocations is large because the atoms slide along the connections between them (stepwise deformation with respect to strain).
As a result, the stress-strain relationship becomes unstable and jagged because elastic deformation and dislocation-induced deformation are mixed. If the stress increases and dislocations occur uniformly throughout the material, the stress-strain relationship returns to a linear one (the complete plastic region).
Let's take a closer look at the types of stresses that actually occur within the material in the Lyudus region.
Let's consider this using a plane with two points (a', b') that have different amounts of elongation, as shown in the diagram below.
Let's consider plane a'b' as plane A and examine the force relationships. Plane A' is inclined at an angle θ with respect to plane A, and we can assume that their areas are the same.
In cross-section a'b', there is a stress σ perpendicular to the plane and a shear force τ along the plane. Let A be the cross-sectional area of the original cross-section ab, and let σ0 = P/A be the generated stress.
Considering the balance between these forces and the external force, the tensile load P, the following equation holds true.
The direction perpendicular to plane a'b' is $ Pcosθ=σ\frac{A}{cosθ}$.
In the direction parallel to plane a'b', $ Psinθ=τ\frac{A}{cosθ} $
If we rearrange each of the equations
$σ=\frac{P}{A}cos^2θ=σ0cos^2θ $
$ τ=\frac{P}{A}sinθcosθ=\frac{σ0}{2}sin2θ $ Using the double-angle theorem: 2sinθcosθ＝sin2θ
The shear force is greatest and the surface slides when the angle of the surface is 45 degrees (2θ = 90 degrees, sin(90°) = 1).The stress σ perpendicular to the plane is $cos^2θ$ and decreases exponentially as the angle increases, so it can be ignored.
like thisThe slip of the surface appears as countless lines in the cross-section. This phenomenon is called a Lüders line because it was discovered by Mr. Lüders.Actually, it can sometimes be seen if you look closely at the fracture surface. It becomes more visible when a special solution is applied.
For materials with excellent ductility, the line will be at a 45-degree angle, but for brittle materials, the line will be at a much shallower angle.
Returning to the stress-strain diagram, in this region where slippage is occurring, the deformation increases even if the stress remains constant, because the strain is causing the slope to slide. In other words, it does not follow Hooke's Law.
Incidentally, tax-resistant materials slide laterally with low shear forces, so the Lüders region is short.
Once all surfaces of the cross-section have finished sliding laterally, the material enters a plastic region where both stress and strain increase.
This is an interesting physical phenomenon that occurs in the Lüders domain.
plastic region
In the plastic region, although the relationship is not simply proportional, stress increases as strain increases. In other words, deformation increases stress.
このIn the plastic region, deformation not only increases in length, but the cross-sectional area of the specimen also decreases (it is compressed).
If you look closely at the constricted part of the test specimen, you'll see that it stretches and narrows in width due to the strain. Remember that Poisson's ratio was used to illustrate this relationship.
If we let A be the cross-sectional area of the original specimen and A' be the cross-sectional area after deformation and fracture, then the following equation holds true.
$ Cross-sectional shrinkage rate, reduction ratio ψ (psi) = \frac{A - A'}{A} × 100 $
Represented byThis is called the cross-sectional shrinkage rate or reduction ratio. The unit is %.
On the other hand, if we let the original length be l and the length when deformed and broken be λmax, the following equation holds true for elongation.
$ Growth rate ψ (lowercase psi) = \frac{λmax}{l} × 100 $
NextThe growth rate and the listed price are expressed as percentages.
The numbers here are used to determine the toughness (ductility) and brittleness (brittleness) of the material.
However, since Poisson's ratio can give a general idea of the material, the specifications of materials often only list Poisson's ratio.
For example, the Poisson's ratio of highly elastic rubber is approximately 0.45 to 0.50, copper, a representative highly elastic metal, is 0.34, ductile steel used in forging is 0.35, and brittle cast iron is about 0.025.
Poisson's ratio is also extremely important, so if you've forgotten, check this out.
Tensile strength, fracture stress range
In the final fracture region, the material rapidly constricts, reducing stress before breaking.
Depending on the material, even if the strain increases towards the end, the generated stress may not decrease, and the generated stress may reach the material's limit, causing it to break.
The important thing here is to carefully observe the fracture surface after it has broken.
As briefly mentioned in the section on Lüders lines, some materials exhibit slippage at inclines of, for example, 10° and 20°, depending on the material's toughness.
like thatThe fracture surface of the material looks like the following picture. The material on the left is less tough and more brittle, so it slides at a shallower angle.
This isThis shows the mechanism of a single-shot fracture due to tensile load and the appearance of the fracture surface.
To give a familiar example, glass is hard and brittle, so it will have a fracture surface like the one on the far left. I think many people have actually seen this, but although the fracture surface is pointed, the surface itself should be very clean and smooth.
Next, I think many people have experience bending and breaking wire or binder clips. You might not see it often, but the fracture surface has circular, mountain-like marks around the perimeter of the cross-section, as shown in the middle of the diagram, or a fracture surface that is flat in the middle and jagged on the outer edge.
Fracture surfaces like the one on the far right might not be something you see often in everyday life. They're especially common in steel used in applications where strength is crucial, and since they're used in places where they wouldn't normally break under normal use of machinery, perhaps only people involved in development have ever seen them.
このThe cross-sectional shape is very important because when an object breaks during testing, examining the fracture surface allows us to determine what material it is, what load it was subjected to, and why it broke.
If you can't do thisWhen a component fails during testing, it becomes impossible to determine which part broke, which part within that component was the starting point of the failure, and what the mode of failure was.
ThereforeThe relationship between stress and strain that occurs, and the appearance of the fracture surface, are very important.
This data must be used to select the appropriate materials. Detailed information about the materials (heat treatment, crystal structure, specifications) will be explained in the section on metallic materials.
This concludes the explanation of tensile failure (single-shot failure).
Summary
This lesson was mostly a review of stress-strain diagrams. That just goes to show how important they are.
Summary
- There are two types of destruction: instant destruction and fatigue destruction.
- Single-shot failure can be caused by tensile force, shear force, or bending force. Bending is a combination of tensile and shear forces.
- Compression forces do not cause fracture, but deformation occurs.
In the Lüders region of the stress-strain diagram, slippage occurs on the stretched slope of the material.
The toughness of a material can be determined by the reduction ratio and elongation ratio of the cross-section when it breaks.
The shape of the fracture surface differs depending on the material's properties.
It is desirable to be able to determine that it is a tensile fracture and to understand the material properties from the shape of the fracture surface.
Becomes
The stress-strain diagram is the key tool for considering a single-shot destructive event.I think I understand that much better now.
Among these, the ability I would especially like you to acquire isI hope that by examining the fracture surface, it will be possible to estimate the type and material of the fracture to some extent.
Without understanding this, it becomes impossible to understand the mechanism of product destruction, and it becomes completely unclear whether the appropriate approach is to treat it like copper.
In some cases, there are methods such as changing materials or increasing wall thickness, even if it means increasing costs, but if the mechanism and cause of failure are not accurately understood, these countermeasures will be meaningless and the same mistakes will be repeated.
The author broke most of the parts while developing the engine for a race car.
We also conducted durability tests once a week, sometimes twice a week, and for about a year and a half, we experienced failures every time. Thanks to that, we developed the skills to find the broken parts, identify the point of failure, and determine the type of failure.
nowSince young people often have fewer opportunities to interact with destructive processes because they pass simulations before taking tests, I hope that when they do encounter such rare opportunities, they will give it their all and acquire these skills and work processes.
Next time, I'd like to explain deformation of an object due to compression, fracture due to shear force, and torsional fracture.
To those who found this article helpful in understanding design:
While there is basically no textbook covering this content, and it is my own original work, I will introduce the textbook that I have been using since I was a student.
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